From b18114f6d06b2049866db028c3e84a92d239cd89 Mon Sep 17 00:00:00 2001 From: Colin Grambow Date: Fri, 12 Apr 2019 17:38:44 -0400 Subject: [PATCH 001/149] Add training module --- reacdiff/train/__init__.py | 0 reacdiff/train/run_training.py | 77 ++++++++++++++++++++++++++++++++++ reacdiff/train/train.py | 59 ++++++++++++++++++++++++++ 3 files changed, 136 insertions(+) create mode 100644 reacdiff/train/__init__.py create mode 100644 reacdiff/train/run_training.py create mode 100644 reacdiff/train/train.py diff --git a/reacdiff/train/__init__.py b/reacdiff/train/__init__.py new file mode 100644 index 0000000..e69de29 diff --git a/reacdiff/train/run_training.py b/reacdiff/train/run_training.py new file mode 100644 index 0000000..44827dc --- /dev/null +++ b/reacdiff/train/run_training.py @@ -0,0 +1,77 @@ +import os + +import reacdiff.data.data as datamod +import reacdiff.models.crnn as models +import reacdiff.train.train as train + + +def run_training(args): + # Load data + print('Loading data') + data = datamod.Dataset( + datamod.load_data(args.data_path), + datamod.load_data(args.targets_path, targets=True), + None if args.data_path2 is None else datamod.load_data(args.data_path2) + ) + + # Split data + print(f'Splitting data with seed {args.seed}') + train_data, val_data, test_data = datamod.split_data(data, splits=args.splits, seed=args.seed) + + if args.test_data_path is not None and args.test_targets_path is not None: + test_data = datamod.Dataset( + datamod.load_data(args.test_data_path), + datamod.load_data(args.test_targets_path), + None if args.test_data_path2 is None else datamod.load_data(args.test_data_path2) + ) + + os.makedirs(args.save_dir, exist_ok=True) + + if args.save_test_data: + test_data.save(os.path.join(args.save_dir, 'test')) + + print(f'Train size = {len(train_data):,} | val size = {len(val_data):,} | test size = {len(test_data):,}') + + # Build model + crnn = models.CRNN( + time_steps=train_data.data.shape[1], + input_shape=train_data.data.shape[2:], + output_dim=train_data.targets.shape[1], + observables=train_data.get_num_observables(), + rnn_layers=args.rnn_layers, + rnn_units=args.rnn_units, + use_gpu=not args.cpu + ) + crnn.build( + feat_maps=args.feat_maps, + first_conv_size=args.first_conv_size, + first_conv_stride=args.first_conv_stride, + first_pool_size=args.first_pool_size, + first_pool_stride=args.first_pool_stride, + growth_rate=args.growth_rate, + blocks=args.blocks, + dropout=args.dropout, + reduction=args.reduction, + bottleneck=not args.no_bottleneck, + flatten_last=args.flatten_last + ) + + model_dir = os.path.join(args.save_dir, 'model') + os.makedirs(model_dir, exist_ok=True) + + # Train model + train.train(crnn, train_data, model_dir, + batch_size=args.batch_size, + epochs=args.epochs, + val_data=val_data, + patience=args.patience, + lr_start=args.lr_start, + lr_end=args.lr_end, + max_norm=args.max_norm, + quiet=args.quiet) + + # Evaluate on test set + print('Evaluating test data') + metrics = crnn.model.evaluate(test_data.get_data(), test_data.targets, + batch_size=args.batch_size) + print(*(f'{name}: {metric:.4f}' for name, metric in zip(crnn.model.metrics_names, metrics)), sep='; ') diff --git a/reacdiff/train/train.py b/reacdiff/train/train.py new file mode 100644 index 0000000..aa7c8ff --- /dev/null +++ b/reacdiff/train/train.py @@ -0,0 +1,59 @@ +import os + +import keras + +import reacdiff.utils as utils + + +def train(crnn, data, save_dir, + batch_size=32, + epochs=30, + val_data=None, + patience=5, + lr_start=1e-3, + lr_end=1e-4, + max_norm=2.0, + quiet=False): + """ + :param crnn: CRNN instance. + :param data: Training data. + :param save_dir: directory to save models to. + :param batch_size: int, batch size. + :param epochs: maximum number of epochs. + :param val_data: Validation data. + :param patience: patience. + :param lr_start: float, initial learning rate. + :param lr_end: float, final learning rate. + :param max_norm: float, maximum gradient norm. + :param quiet: bool, print less information + """ + optimizer = keras.optimizers.Adam(lr=lr_start, clipnorm=max_norm) + crnn.model.compile(optimizer=optimizer, loss='mse', metrics=[utils.rmse, utils.mae]) + if not quiet: + crnn.encoder.summary() + crnn.rnn.summary() + crnn.model.summary() + + model_name = 'model.{epoch:03d}.h5' + model_path = os.path.join(save_dir, model_name) + + def lr_schedule(epoch, _): + return lr_start * ((lr_end / lr_start) ** (epoch / epochs)) + + checkpoint = keras.callbacks.ModelCheckpoint(filepath=model_path, + verbose=1, + save_best_only=True) + early_stopping = keras.callbacks.EarlyStopping(patience=patience, + verbose=1, + restore_best_weights=True) + lr_scheduler = keras.callbacks.LearningRateScheduler(lr_schedule, + verbose=1) + callbacks = [checkpoint, early_stopping, lr_scheduler] + + crnn.model.fit(data.get_data(), data.targets, + batch_size=batch_size, + epochs=epochs, + validation_data=(val_data.get_data(), val_data.targets), + shuffle=True, + verbose=2 if quiet else 1, + callbacks=callbacks) From 684f322a8727615e71b96d9b06ff51dfda6b305c Mon Sep 17 00:00:00 2001 From: Colin Grambow Date: Fri, 12 Apr 2019 17:38:56 -0400 Subject: [PATCH 002/149] Add training script --- reacdiff/parsing.py | 80 +++++++++++++++++++++++++++++++++++++++++++++ train.py | 9 +++++ 2 files changed, 89 insertions(+) create mode 100644 reacdiff/parsing.py create mode 100644 train.py diff --git a/reacdiff/parsing.py b/reacdiff/parsing.py new file mode 100644 index 0000000..ca68351 --- /dev/null +++ b/reacdiff/parsing.py @@ -0,0 +1,80 @@ +import argparse +import os + + +def parse_train_args(): + parser = argparse.ArgumentParser( + formatter_class=argparse.ArgumentDefaultsHelpFormatter + ) + + # General arguments + parser.add_argument('--data_path', type=str, required=True, + help='Path to data containing observable states') + parser.add_argument('--targets_path', type=str, required=True, + help='Path to targets') + parser.add_argument('--data_path2', type=str, + help='Path to data containing additional observable states') + parser.add_argument('--save_dir', type=str, default=os.getcwd(), + help='Directory where model checkpoints will be saved') + parser.add_argument('--splits', type=float, nargs=3, default=[0.9, 0.05, 0.05], + help='Split proportions for train/validation/test sets') + parser.add_argument('--save_test_data', action='store_true', + help='Save test data and targets to file') + parser.add_argument('--test_data_path', type=str, + help='Path to separate test data') + parser.add_argument('--test_targets_path', type=str, + help='Path to separate test targets') + parser.add_argument('--test_data_path2', type=str, + help='Path to separate test data for additional observable') + parser.add_argument('--quiet', action='store_true', + help='Do not print model details and batch information during training') + parser.add_argument('--cpu', action='store_true', + help='Run on CPU instead of GPU') + parser.add_argument('--seed', type=int, default=7, + help='Random seed for reproducibility') + + # Training arguments + parser.add_argument('--batch_size', type=int, default=32, + help='Batch size') + parser.add_argument('--epochs', type=int, default=30, + help='Maximum number of epochs to run') + parser.add_argument('--lr_start', type=float, default=1e-3, + help='Initial learning rate') + parser.add_argument('--lr_end', type=float, default=1e-4, + help='Final learning rate') + parser.add_argument('--patience', type=int, default=5, + help='Number of epochs without improvement after which training will be stopped') + parser.add_argument('--max_norm', type=float, default=2.0, + help='Maximum gradient norm before clipping occurs') + + # Encoder arguments + parser.add_argument('--feat_maps', type=int, default=16, + help='Number of feature maps in first convolutional layer') + parser.add_argument('--first_conv_size', type=int, default=7, + help='Filter size in first convolutional layer') + parser.add_argument('--first_conv_stride', type=int, default=2, + help='Strides in first convolutional layer') + parser.add_argument('--first_pool_size', type=int, default=3, + help='Window size in first pool') + parser.add_argument('--first_pool_stride', type=int, default=2, + help='Strides in first pool') + parser.add_argument('--growth_rate', type=int, default=12, + help='Growth rate in dense blocks') + parser.add_argument('--blocks', type=int, nargs='+', default=[3, 4, 5], + help='Numbers of layers in each dense block') + parser.add_argument('--dropout', type=float, default=0.0, + help='Dropout rate after convolutions') + parser.add_argument('--reduction', type=float, default=0.5, + help='Compression rate in transition blocks') + parser.add_argument('--no_bottleneck', action='store_true', + help='Do not use bottleneck convolution in dense blocks') + parser.add_argument('--flatten_last', action='store_true', + help='Flatten instead of global pool before output') + + # RNN arguments + parser.add_argument('--rnn_layers', type=int, default=1, + help='Number of RNN layers') + parser.add_argument('--rnn_units', type=int, default=100, + help='Number of units in RNN') + + return parser.parse_args() diff --git a/train.py b/train.py new file mode 100644 index 0000000..2cf6359 --- /dev/null +++ b/train.py @@ -0,0 +1,9 @@ +#!/usr/bin/env python + +import reacdiff.parsing as parsing +import reacdiff.train.run_training as run_training + + +if __name__ == '__main__': + args = parsing.parse_train_args() + run_training.run_training(args) From 567ce2018fbc1e2eea8ed68c84e0f30245d89385 Mon Sep 17 00:00:00 2001 From: Colin Grambow Date: Mon, 15 Apr 2019 15:04:14 -0400 Subject: [PATCH 003/149] Implement data parsing --- prepare_data.py | 9 +++++++++ reacdiff/data/data.py | 20 +++++++++++++------- reacdiff/data/preprocess.py | 34 ++++++++++++++++++++++++++++++++++ reacdiff/parsing.py | 9 +++++++++ reacdiff/train/run_training.py | 2 +- 5 files changed, 66 insertions(+), 8 deletions(-) create mode 100644 prepare_data.py create mode 100644 reacdiff/data/preprocess.py diff --git a/prepare_data.py b/prepare_data.py new file mode 100644 index 0000000..f9d89fb --- /dev/null +++ b/prepare_data.py @@ -0,0 +1,9 @@ +#!/usr/bin/env python + +import reacdiff.parsing as parsing +import reacdiff.data.preprocess as preprocess + + +if __name__ == '__main__': + args = parsing.parse_dataprep_args() + preprocess.preprocess(args.data_path) diff --git a/reacdiff/data/data.py b/reacdiff/data/data.py index b8bbdbe..925d0d2 100644 --- a/reacdiff/data/data.py +++ b/reacdiff/data/data.py @@ -1,3 +1,4 @@ +import h5py import numpy as np import reacdiff.utils as utils @@ -49,16 +50,21 @@ def __getitem__(self, item): return Dataset(self.data[item], self.targets[item], self.data2[item]) -def load_data(path, targets=False): - if targets: - return np.random.rand(100, 26) - data = np.random.rand(100, 50, 128, 128) - data = np.expand_dims(data, axis=-1) +def load_data(path, max_read=None, key='data'): + """ + :param path: An HDF5 file. + :param max_read: Maximum number of samples to read. + :param key: Data key in HDF5 file. + :return: Numpy array of data + """ + with h5py.File(path, 'r') as f: + data = f[key][:] if max_read is None else f[key][:max_read] return data -def save_data(data, path): - raise NotImplementedError +def save_data(data, path, key='data'): + with h5py.File(path, 'w') as f: + f.create_dataset(key, data=data) def split_data(data, splits=(0.9, 0.05, 0.05), seed=None): diff --git a/reacdiff/data/preprocess.py b/reacdiff/data/preprocess.py new file mode 100644 index 0000000..635d60f --- /dev/null +++ b/reacdiff/data/preprocess.py @@ -0,0 +1,34 @@ +import os + +import h5py +import numpy as np + +import reacdiff.data.data as datamod + + +def preprocess(path): + """ + :param path: An HDF5 file. + """ + f = h5py.File(path, 'r') + targets = f['A1'] + states = f['y'] + + assert len(targets.shape) == 2 + assert len(states.shape) == 5 + assert states.shape[0] == 2 + + targets = targets[:] + states = states[:] + targets = np.swapaxes(targets, 0, 1) + states = np.transpose(states, (0, 4, 1, 2, 3)) + data, data2 = np.expand_dims(states, axis=-1) + + name = os.path.splitext(path)[0] + targets_path = name + '_targets.h5' + data_path = name + '_states.h5' + data_path2 = name + '_states2.h5' + + datamod.save_data(targets, targets_path) + datamod.save_data(data, data_path) + datamod.save_data(data2, data_path2) diff --git a/reacdiff/parsing.py b/reacdiff/parsing.py index ca68351..7e53d47 100644 --- a/reacdiff/parsing.py +++ b/reacdiff/parsing.py @@ -2,6 +2,15 @@ import os +def parse_dataprep_args(): + parser = argparse.ArgumentParser( + formatter_class=argparse.ArgumentDefaultsHelpFormatter + ) + parser.add_argument('--data_path', type=str, required=True, + help='Path to HDF5 data file') + return parser.parse_args() + + def parse_train_args(): parser = argparse.ArgumentParser( formatter_class=argparse.ArgumentDefaultsHelpFormatter diff --git a/reacdiff/train/run_training.py b/reacdiff/train/run_training.py index 44827dc..38864ff 100644 --- a/reacdiff/train/run_training.py +++ b/reacdiff/train/run_training.py @@ -10,7 +10,7 @@ def run_training(args): print('Loading data') data = datamod.Dataset( datamod.load_data(args.data_path), - datamod.load_data(args.targets_path, targets=True), + datamod.load_data(args.targets_path), None if args.data_path2 is None else datamod.load_data(args.data_path2) ) From a27022717f602a0809ef1a17efa4c67fb919bf99 Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Mon, 15 Apr 2019 16:07:13 -0400 Subject: [PATCH 004/149] initial commit of turing pattern generator --- solver/LSA.m | 5 + solver/event_gradient.m | 12 ++ solver/formk.m | 15 +++ solver/gradient_norm.m | 11 ++ solver/k2real.m | 101 +++++++++++++++ solver/odeimex.m | 269 ++++++++++++++++++++++++++++++++++++++++ solver/odeimexez.m | 66 ++++++++++ solver/runningcov.m | 15 +++ solver/turing_nlin_bd.m | 26 ++++ solver/turing_ps.m | 116 +++++++++++++++++ 10 files changed, 636 insertions(+) create mode 100644 solver/LSA.m create mode 100644 solver/event_gradient.m create mode 100644 solver/formk.m create mode 100644 solver/gradient_norm.m create mode 100644 solver/k2real.m create mode 100644 solver/odeimex.m create mode 100644 solver/odeimexez.m create mode 100644 solver/runningcov.m create mode 100644 solver/turing_nlin_bd.m create mode 100644 solver/turing_ps.m diff --git a/solver/LSA.m b/solver/LSA.m new file mode 100644 index 0000000..35108c6 --- /dev/null +++ b/solver/LSA.m @@ -0,0 +1,5 @@ +function y = LSA(A,D) + %whether the input parameters satisfy the pattern forming condition from linear stability analysis (Page 11 of support Kondo paper) + %only support one instance, A is a matrix, D is a vector + y = (trace(A)<0) && (det(A)>0) && (A(1,1)*D(2)+A(2,2)*D(1)>0) && ((A(1,1)*D(2)+A(2,2)*D(1))^2 - 4*D(1)*D(2)*det(A)>0); +end diff --git a/solver/event_gradient.m b/solver/event_gradient.m new file mode 100644 index 0000000..8859f2a --- /dev/null +++ b/solver/event_gradient.m @@ -0,0 +1,12 @@ +function y = event_gradient(t,y,k2,thresh,component) + %when the L2 norm of the gradient field is below thresh, the returned y is true, otherwise false. + %note that y is in Fourier space. + %L2 norm of the gradient field is \int_{|| \nabla y(x) ||^2 dx} = \int_{|| k ||^2 ||y(k)||^2 dk} + %k2 should correspond to each row of y + %component (1 by default) is the index of the species + if nargin < 5 + component = 1; + end + dy = gradient_norm(y,k2,component); + y = (dy1 + sgind = num2cell(ones(1,dim)); + sgind{end} = ':'; + k{dim}(sgind{:}) = [0:Nmid-1,Nmid-N(dim):-1]'/L(dim)*2*pi; + else + k{dim} = [0:Nmid-1,Nmid-N(dim):-1]'/L(dim)*2*pi; + end + k2 = k2 + k{dim}.^2; +end diff --git a/solver/gradient_norm.m b/solver/gradient_norm.m new file mode 100644 index 0000000..5e36cb2 --- /dev/null +++ b/solver/gradient_norm.m @@ -0,0 +1,11 @@ +function dy = gradient_norm(y,k2,component) + %L2 norm of the gradient field. + %note that y is in Fourier space. + %L2 norm of the gradient field is \int_{|| \nabla y(x) ||^2 dx} = \int_{|| k ||^2 ||y(k)||^2 dk} + %k2 should correspond to each row of y + %component (1 by default) is the index of the species + if nargin < 5 + component = 1; + end + n = length(k2); + dy = norm(k2.*y((component-1)*n+(1:n),:)); diff --git a/solver/k2real.m b/solver/k2real.m new file mode 100644 index 0000000..6ee999b --- /dev/null +++ b/solver/k2real.m @@ -0,0 +1,101 @@ +function varargout = k2real(y,N,y00,varargin) + %convert from k space to real space + %y comes in as a column vector, each column represent different snapshots Nt + %N is an array for the system size + %y00 is the k=0 component if missing in y, and must have the size of (1-Nt) + %mode: plot (default): show static snapshots; movie; value: calculate the y value in real space, returned in the same format + %caxis: 'auto' (default): each snapshot has its own automatic caxis; 'max': the caxis that accomondates the maximum and minimum of all the snapshots (only works for mode='plot'); 'first': all snapshots follow the min and max of the first snapshot; 'last': all snapshots follow the min and max of the last snapshot; a scalar, all snapshots follow the min and max of the snapshot numbered by the scalar; otherwise, all snapshots' clim specified by what's given. + Nt = size(y,2); + defaultcolumn = max(factor(Nt)); + defaultrow = Nt/defaultcolumn; + if length(y) == prod(N)-1 + if nargin<3 || isempty(y00) + y00 = zeros(1,Nt); + elseif isscalar(y00) + y00 = y00*ones(1,Nt); + end + y = [y00;y]; + end + ps = inputParser; + addParameter(ps,'mode','plot'); + addParameter(ps,'caxis','auto'); + addParameter(ps,'GridSize',[defaultrow,defaultcolumn]); + ps.KeepUnmatched = true; + parse(ps,varargin{:}); + params = ps.Results; + row = params.GridSize(1); + column = params.GridSize(2); + + if isscalar(params.caxis) + yreal = real(ifftn(reshape(y(:,params.caxis),N))); + yreal = yreal(:); + clim = [min(yreal),max(yreal)]; + else + switch params.caxis + case 'max' + clim = 'auto'; + case 'first' + yreal = real(ifftn(reshape(y(:,1),N))); + yreal = yreal(:); + clim = [min(yreal),max(yreal)]; + case 'last' + yreal = real(ifftn(reshape(y(:,end),N))); + yreal = yreal(:); + clim = [min(yreal),max(yreal)]; + otherwise + clim = params.caxis; + end + end + + switch params.mode + case 'plot' + vis = 1; + case 'movie' + vis = 2; + F(Nt) = struct('cdata',[],'colormap',[]); + case 'value' + vis = 0; + end + for i=1:Nt + yreal = real(ifftn(reshape(y(:,i),N))); + if vis == 1 + h(i) = subplot(row,column,i); + imagesc(yreal); + axis(h(i),'equal','tight'); + colormap(h(i),'gray'); + caxis(h(i),clim); + elseif vis == 2 + h = imagesc(yreal); + axis(gca,'equal','tight'); + colormap(gca,'gray'); + caxis(gca,clim); + F(i) = getframe(gcf); + delete(h); + else + y(:,i) = yreal(:); + end + ax = gca; + ax.XTick=[]; ax.YTick=[]; + end + if isequal(params.caxis,'max') && vis == 1 + for i=1:Nt + climi = h(i).CLim; + if i==1 + clim = climi; + else + clim(1) = min(clim(1),climi(1)); + clim(2) = max(clim(2),climi(2)); + end + end + for i=1:Nt + caxis(h(i),clim); + end + end + if vis == 1 + varargout = {h}; + elseif vis == 2 + varargout = {F}; + else + varargout = {y}; + end +end diff --git a/solver/odeimex.m b/solver/odeimex.m new file mode 100644 index 0000000..19cc12b --- /dev/null +++ b/solver/odeimex.m @@ -0,0 +1,269 @@ +function [tout,yout] = odeimex(fnlin,J,Nt,y0,options,pencil) +%a simplified ode solver adapted from ode15s +%the backward diffusion / NDF is applied for the linear part of the equation, in particular, the propotionality constant is J, note that J is the array the same as y0 (equivalent to diagonal) for now, in the near future, generalize J to a matrix. +%The nonlinear part of the equation is explicit, that is, at each time step, this term is dependent only on the previous time step. +%only ODE (not DAE) is supported right now. +%dy/dt = J*y + fnlin +%Nt is the number of time steps +%the format of yout is different from typical ode, each column corresponds to a time point given in tout, which is a column vector. +%03/25/2019, now J can be a matrix or a column vector whose size is the same as y +%pencil(b,hinvGak) should return (Mt-hinvGak*J)\b +%right now J is constant +if nargin<5 + options = []; +end +maxk = odeget(options,'MaxOrder',5,'fast'); +bdf = strcmp(odeget(options,'BDF','off','fast'),'on'); +htry = abs(odeget(options,'InitialStep',[],'fast')); +hmax = abs(odeget(options,'MaxStep',inf,'fast')); +rtol = odeget(options,'RelTol',1e-3,'fast'); +atol = odeget(options,'AbsTol',1e-6,'fast'); +normcontrol = strcmp(odeget(options,'NormControl','off','fast'),'on'); + +neq = length(y0); + +threshold = atol / rtol; +if normcontrol + normy = norm(y0); +end + +tdir = 1; +t = 0; +y = y0; +tout = zeros(Nt,1); +yout = zeros(neq,Nt); +tout(1) = t; +yout(:,1) = y; +vectorJ = all(size(J)==size(y)); +if vectorJ + yp = fnlin(t,y) + J.*y; +else + yp = fnlin(t,y) + J*y; +end + +% Initialize method parameters. +G = [1; 3/2; 11/6; 25/12; 137/60]; +if bdf + alpha = [0; 0; 0; 0; 0]; +else + alpha = [-37/200; -1/9; -0.0823; -0.0415; 0]; +end +invGa = 1 ./ (G .* (1 - alpha)); +erconst = alpha .* G + (1 ./ (2:6)'); +difU = [ -1, -2, -3, -4, -5; % difU is its own inverse! + 0, 1, 3, 6, 10; + 0, 0, -1, -4, -10; + 0, 0, 0, 1, 5; + 0, 0, 0, 0, -1 ]; +maxK = 1:maxk; +[kJ,kI] = meshgrid(maxK,maxK); +difU = difU(maxK,maxK); + +% Determine initial step size + +% hmin is a small number such that t + hmin is clearly different from t in +% the working precision, but with this definition, it is 0 if t = 0. +hmin = 16*eps*abs(t); + +if isempty(htry) + % Compute an initial step size h using yp = y'(t). + if normcontrol + wt = max(normy,threshold); + rh = 1.25 * (norm(yp) / wt) / sqrt(rtol); % 1.25 = 1 / 0.8 + else + wt = max(abs(y),threshold); + rh = 1.25 * norm(yp ./ wt,inf) / sqrt(rtol); + end + absh = hmax; + if absh * rh > 1 + absh = 1 / rh; + end + absh = max(absh, hmin); +else + absh = min(hmax, max(hmin, htry)); +end +h = tdir * absh; + +% Initialize. +k = 1; % start at order 1 with BDF1 +K = 1; % K = 1:k +klast = k; +abshlast = absh; + +dif = zeros(neq,maxk+2); +dif(:,1) = h * yp; + +hinvGak = h * invGa(k); +nconhk = 0; % steps taken with current h and k + +% THE MAIN LOOP + +at_hmin = false; +for step = 2:Nt + + hmin = 16*eps(t); + absh = min(hmax, max(hmin, absh)); + if absh == hmin + if at_hmin + absh = abshlast; % required by stepsize recovery + end + at_hmin = true; + else + at_hmin = false; + end + h = tdir * absh; + + if (absh ~= abshlast) || (k ~= klast) + difRU = cumprod((kI - 1 - kJ*(absh/abshlast)) ./ kI) * difU; + dif(:,K) = dif(:,K) * difRU(K,K); + + hinvGak = h * invGa(k); + nconhk = 0; + + end + + % LOOP FOR ADVANCING ONE STEP. + nofailed = true; % no failed attempts + fex = fnlin(t,y); % the nonlinear part is fixed in the iteration + while true % Evaluate the formula. + % Compute the constant terms in the equation for ynew. + psi = dif(:,K) * (G(K) * invGa(k)); + % Predict a solution at t+h. + tnew = t + h; + pred = y + sum(dif(:,K),2); + ynew = pred; + + if normcontrol + normynew = norm(ynew); + invwt = 1 / max(max(normy,normynew),threshold); + else + invwt = 1 ./ max(max(abs(y),abs(ynew)),threshold); + end + + if vectorJ + ynew2 = (ynew-psi+hinvGak*fex)./(1-hinvGak*J); + else + ynew2 = pencil(ynew-psi+hinvGak*fex,hinvGak); + end + + difkp1 = ynew2-ynew; + ynew = ynew2; + + % difkp1 is now the backward difference of ynew of order k+1. + if normcontrol + err = (norm(difkp1) * invwt) * erconst(k); + else + err = norm(difkp1 .* invwt,inf) * erconst(k); + end + + if err > rtol % Failed step + if absh <= hmin + warning(message('MATLAB:ode15s:IntegrationTolNotMet', sprintf( '%e', t ), sprintf( '%e', hmin ))); + tout(step:end) = []; + yout(step:end,:) = []; + return; + end + + abshlast = absh; + if nofailed + nofailed = false; + hopt = absh * max(0.1, 0.833*(rtol/err)^(1/(k+1))); % 1/1.2 + if k > 1 + if normcontrol + errkm1 = (norm(dif(:,k) + difkp1) * invwt) * erconst(k-1); + else + errkm1 = norm((dif(:,k) + difkp1) .* invwt,inf) * erconst(k-1); + end + hkm1 = absh * max(0.1, 0.769*(rtol/errkm1)^(1/k)); % 1/1.3 + if hkm1 > hopt + hopt = min(absh,hkm1); % don't allow step size increase + k = k - 1; + K = 1:k; + end + end + absh = max(hmin, hopt); + else + absh = max(hmin, 0.5 * absh); + end + h = tdir * absh; + + difRU = cumprod((kI - 1 - kJ*(absh/abshlast)) ./ kI) * difU; + dif(:,K) = dif(:,K) * difRU(K,K); + + hinvGak = h * invGa(k); + nconhk = 0; + + else % Successful step + break; + + end + end % while true + + dif(:,k+2) = difkp1 - dif(:,k+1); + dif(:,k+1) = difkp1; + for j = k:-1:1 + dif(:,j) = dif(:,j) + dif(:,j+1); + end + + klast = k; + abshlast = absh; + nconhk = min(nconhk+1,maxk+2); + if nconhk >= k + 2 + temp = 1.2*(err/rtol)^(1/(k+1)); + if temp > 0.1 + hopt = absh / temp; + else + hopt = 10*absh; + end + kopt = k; + if k > 1 + if normcontrol + errkm1 = (norm(dif(:,k)) * invwt) * erconst(k-1); + else + errkm1 = norm(dif(:,k) .* invwt,inf) * erconst(k-1); + end + temp = 1.3*(errkm1/rtol)^(1/k); + if temp > 0.1 + hkm1 = absh / temp; + else + hkm1 = 10*absh; + end + if hkm1 > hopt + hopt = hkm1; + kopt = k - 1; + end + end + if k < maxk + if normcontrol + errkp1 = (norm(dif(:,k+2)) * invwt) * erconst(k+1); + else + errkp1 = norm(dif(:,k+2) .* invwt,inf) * erconst(k+1); + end + temp = 1.4*(errkp1/rtol)^(1/(k+2)); + if temp > 0.1 + hkp1 = absh / temp; + else + hkp1 = 10*absh; + end + if hkp1 > hopt + hopt = hkp1; + kopt = k + 1; + end + end + if hopt > absh + absh = hopt; + if k ~= kopt + k = kopt; + K = 1:k; + end + end + end + % Advance the integration one step. + t = tnew; + y = ynew; + if normcontrol + normy = normynew; + end + tout(step) = t; + yout(:,step) = y; +end diff --git a/solver/odeimexez.m b/solver/odeimexez.m new file mode 100644 index 0000000..6002922 --- /dev/null +++ b/solver/odeimexez.m @@ -0,0 +1,66 @@ +function [tout,yout,et] = odeimex(fnlin,J,h,Nt,y0,pencil,outputstep,termination,gpu,transform) +%easy version odeimex: fixed time step, no error control +%h: step size +%outputstep: an array that indicates at which step the solution is outputed (must be sorted). By default, it only returns the last step +%termination: a function handle (t,y) that becomes true when the solver should abort the iteration. The output et is true when it's terminated early. By default, termination is empty +%the output yout is stored on gpu if gpu is true. For now, tout is always stored on cpu. By default, gpu is set to false. +%transform is a function handle that transforms the output y (by default empty) +%04/11/2019, now J can be a matrix or a column vector whose size is the same as y +%pencil(b,hinvGak) should return (Mt-hinvGak*J)\b +%right now J is constant +neq = length(y0); +y = y0; +t = 0:h:(h*Nt); +if nargin < 7 || isempty(outputstep) + outputstep = Nt; +end +if nargin < 8 + termination = []; +end +if nargin < 9 || isempty(gpu) + gpu = false; +end +if nargin < 10 + transform = []; +end +tout = t(outputstep); +if gpu + yout = zeros(neq,length(outputstep),'gpuArray'); +else + yout = zeros(neq,length(outputstep)); +end +outputid = 1; +if outputstep(outputid) == 1 + if isempty(transform) + yout(:,outputid) = y; + else + yout(:,outputid) = transform(y); + end + outputid = outputid + 1; +end +et = false; + +vectorJ = all(size(J)==size(y)); + +for step = 2:Nt + fex = fnlin(t(step-1),y); % the nonlinear part is fixed in the iteration + if vectorJ + y = (y+h*fex)./(1-h*J); + else + y = pencil(y+h*fex,h); + end + if outputstep(outputid) == step + if isempty(transform) + yout(:,outputid) = y; + else + yout(:,outputid) = transform(y); + end + outputid = outputid + 1; + end + if ~isempty(termination) + if termination(t(step),y) + et = true; + break; + end + end +end diff --git a/solver/runningcov.m b/solver/runningcov.m new file mode 100644 index 0000000..6c0770f --- /dev/null +++ b/solver/runningcov.m @@ -0,0 +1,15 @@ +function [sigma,runningdyad,runningsum] = runningcov(x,runningdyad,runningsum) + %x can be a row vector or a matrix whose columns represent instances + %The first output sigma is the accumulative covariance + persistent N + if nargin<3 + runningdyad = x'*x; + runningsum = sum(x,1); + N = size(x,1); + else + runningdyad = runningdyad + x'*x; + runningsum = runningsum + sum(x,1); + N = N+size(x,1); + end + sigma = (runningdyad - runningsum'*runningsum/N)/(N-1); +end diff --git a/solver/turing_nlin_bd.m b/solver/turing_nlin_bd.m new file mode 100644 index 0000000..e959087 --- /dev/null +++ b/solver/turing_nlin_bd.m @@ -0,0 +1,26 @@ +function f = turing_nlin_bd(t,y,A,b,lb,ub,N) + %constant term b + %A matrix for linear reaction terms (nspecies-by-nspecies) + %lb and ub are lower and upper boundary for the reaction rate for each species + %N is the size of the grid + nspecies = length(b); + y = reshape(y,prod(N),nspecies); + for i=1:nspecies + y(:,i) = reshape(real(ifftn(reshape(y(:,i),N))),[],1); + end + if size(b,2)==1 + b = b'; + end + f = y*A' + b; + if size(lb,2)==1 + lb = lb'; + end + if size(ub,2)==1 + ub = ub'; + end + f = min(max(f,lb),ub); + for i=1:nspecies + f(:,i) = reshape(fftn(reshape(f(:,i),N)),[],1); + end + f = f(:); +end diff --git a/solver/turing_ps.m b/solver/turing_ps.m new file mode 100644 index 0000000..223ff8a --- /dev/null +++ b/solver/turing_ps.m @@ -0,0 +1,116 @@ +%parameter search +L = [60,60]/2; +N = [256,256]/2; +n = prod(N); +D = [0.02,0.5]; +b = [0.04,-0.15]; +A1 = [0.08,-0.08;0.1,0]; +A2 = -[0.03,0.08]; +lb = [0,0]; +ub = [0.2,0.5]; +u0 = 5; +v0 = 5; +sigma = [0.01,0.01]; + +rng(1); +u0 = u0 + sigma(1)*randn(N); +v0 = v0 + sigma(2)*randn(N); +yu0 = fftn(u0); +yv0 = fftn(v0); +y0 = [yu0(:); yv0(:)]; + +[k2,k] = formk(N,L); + +JD = -k2(:)*D; +J = JD(:) + reshape(ones(n,1)*A2,[],1); + +rungpu = true; +if rungpu + y0 = gpuArray(y0); + A1 = gpuArray(A1); + b = gpuArray(b); + lb = gpuArray(lb); + ub = gpuArray(ub); + J = gpuArray(J); + k2 = gpuArray(k2); +end + +saveresult = true; +if saveresult + filepath = '/home/hbozhao/Dropbox (MIT)/2.168 Project/Data/turing'; + mat = matfile(filepath,'Writable',true); + mat.A1 = []; + mat.y = []; +end +Nsave = 1000; +saveind = 0; + +Nt = 1100; +dt = 0.6; +outputstep = 200:100:Nt; +nall = 10000; +thresh = n*1e-5; +termination = @(t,y) event_gradient(t,y,k2(:),thresh); +if saveresult + transform = @(y) [reshape(real(ifftn(reshape(y(1:n),N))),[],1);reshape(real(ifftn(reshape(y(n+(1:n)),N))),[],1)]; +else + transform = []; +end +naccept = 0; +ind = 0; +if saveresult + nblock = Nsave; +else + nblock = nall; +end +Anorm = norm(A1+diag(A2),inf); +A1 = reshape(A1,1,[]); +nparams = length(A1); +sigma = 0.05*eye(nparams); +if saveresult + yall = zeros(nblock,N(1),N(2),length(outputstep),2,'gpuArray'); +else + yall = zeros(nblock,n*2,length(outputstep),'gpuArray'); +end +A1all = zeros(nblock,nparams,'gpuArray'); +tic; +while naccept < nall + A1new = A1 + mvnrnd(zeros(1,nparams),sigma); + A1new = reshape(A1new,2,2); + Anew = A1new+diag(A2); + if LSA(Anew,D) && (norm(Anew,inf)<5*Anorm) + fnlin = @(t,y) turing_nlin_bd(t,y,A1new,b,lb,ub,N); + [~,y,et] = odeimexez(fnlin,J,dt,Nt,y0,[],outputstep,termination,rungpu,transform); + if ~et + A1 = reshape(A1new,1,[]); + naccept = naccept + 1; + ind = ind + 1; + if saveresult + yall(ind,:,:,:,:) = permute(reshape(y,N(1),N(2),2,[]),[1,2,4,3]); + else + yall(ind,:,:) = y; + end + A1all(ind,:) = A1; + runtime=toc; + disp(['case ',num2str(naccept),' finished: Elapsed time (min): ',num2str(runtime/60),' ETA (min): ',num2str(runtime/60*(nall-naccept)/naccept)]); + if saveresult && mod(naccept,Nsave)==0 + if naccept == Nsave + mat.A1 = gather(A1all); + mat.y = gather(yall); + else + mat.A1(saveind+(1:Nsave),:) = gather(A1all); + mat.y(saveind+(1:Nsave),:,:,:,:) = gather(yall); + end + yall = zeros(nblock,N(1),N(2),length(outputstep),2,'gpuArray'); + A1all = zeros(nblock,nparams,'gpuArray'); + saveind = saveind+Nsave; + ind = 0; + end + end + end +end + +if ~saveresult + figure; + k2real(yall(1:naccept,1:n).',N);%,[],'GridSize',[9,9]); +end From 05ca016f42817f37714d3df8e91b9baec049c956 Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Wed, 17 Apr 2019 20:10:07 -0400 Subject: [PATCH 005/149] fix bugs and debugging of the solver --- solver/k2real.m | 6 ++++++ solver/odeimexez.m | 2 +- solver/turing_ps.m | 13 ++++++++++--- 3 files changed, 17 insertions(+), 4 deletions(-) diff --git a/solver/k2real.m b/solver/k2real.m index 6ee999b..2bbb41f 100644 --- a/solver/k2real.m +++ b/solver/k2real.m @@ -19,6 +19,7 @@ ps = inputParser; addParameter(ps,'mode','plot'); addParameter(ps,'caxis','auto'); + addParameter(ps,'colorbar','off'); addParameter(ps,'GridSize',[defaultrow,defaultcolumn]); ps.KeepUnmatched = true; parse(ps,varargin{:}); @@ -76,6 +77,11 @@ end ax = gca; ax.XTick=[]; ax.YTick=[]; + if isequal(params.colorbar,'on') + colorbar; + else + colorbar(params.colorbar); + end end if isequal(params.caxis,'max') && vis == 1 for i=1:Nt diff --git a/solver/odeimexez.m b/solver/odeimexez.m index 6002922..376ca04 100644 --- a/solver/odeimexez.m +++ b/solver/odeimexez.m @@ -55,7 +55,7 @@ else yout(:,outputid) = transform(y); end - outputid = outputid + 1; + outputid = min(outputid+1,length(outputstep)); end if ~isempty(termination) if termination(t(step),y) diff --git a/solver/turing_ps.m b/solver/turing_ps.m index 223ff8a..51b79dd 100644 --- a/solver/turing_ps.m +++ b/solver/turing_ps.m @@ -35,7 +35,7 @@ k2 = gpuArray(k2); end -saveresult = true; +saveresult = false; if saveresult filepath = '/home/hbozhao/Dropbox (MIT)/2.168 Project/Data/turing'; mat = matfile(filepath,'Writable',true); @@ -48,7 +48,10 @@ Nt = 1100; dt = 0.6; outputstep = 200:100:Nt; -nall = 10000; +dt = 0.2; +Nt = 5000; +outputstep = [1,100:100:1000] ;%[300,1000,2000:1000:Nt]; +nall = 1; thresh = n*1e-5; termination = @(t,y) event_gradient(t,y,k2(:),thresh); if saveresult @@ -112,5 +115,9 @@ if ~saveresult figure; - k2real(yall(1:naccept,1:n).',N);%,[],'GridSize',[9,9]); + if ndims(yall) == 3 + k2real(reshape(permute(yall(1:naccept,1:n,:),[1,3,2]),[],n).',N,[],'colorbar','on'); + else + k2real(yall(1:naccept,1:n,:).',N);%,[],'GridSize',[9,9]); + end end From 533742970d0173ec5c0c57b5330adc35a67ad980 Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Fri, 26 Apr 2019 01:29:38 -0400 Subject: [PATCH 006/149] move rungpu condition to after defintion of yall --- solver/turing_ps.m | 41 ++++++++++++++++++++++------------------- 1 file changed, 22 insertions(+), 19 deletions(-) diff --git a/solver/turing_ps.m b/solver/turing_ps.m index 51b79dd..e71eb89 100644 --- a/solver/turing_ps.m +++ b/solver/turing_ps.m @@ -24,16 +24,6 @@ JD = -k2(:)*D; J = JD(:) + reshape(ones(n,1)*A2,[],1); -rungpu = true; -if rungpu - y0 = gpuArray(y0); - A1 = gpuArray(A1); - b = gpuArray(b); - lb = gpuArray(lb); - ub = gpuArray(ub); - J = gpuArray(J); - k2 = gpuArray(k2); -end saveresult = false; if saveresult @@ -45,12 +35,12 @@ Nsave = 1000; saveind = 0; -Nt = 1100; -dt = 0.6; -outputstep = 200:100:Nt; -dt = 0.2; -Nt = 5000; -outputstep = [1,100:100:1000] ;%[300,1000,2000:1000:Nt]; +Nt = 1000; +dt = 1; +outputstep = 100:100:Nt; +% dt = 0.2; +% Nt = 5000; +% outputstep = [1,100:200:1000] ;%[300,1000,2000:1000:Nt]; nall = 1; thresh = n*1e-5; termination = @(t,y) event_gradient(t,y,k2(:),thresh); @@ -71,11 +61,24 @@ nparams = length(A1); sigma = 0.05*eye(nparams); if saveresult - yall = zeros(nblock,N(1),N(2),length(outputstep),2,'gpuArray'); + yall = zeros(nblock,N(1),N(2),length(outputstep),2); else - yall = zeros(nblock,n*2,length(outputstep),'gpuArray'); + yall = zeros(nblock,n*2,length(outputstep)); +end +A1all = zeros(nblock,nparams); + +rungpu = false; +if rungpu + y0 = gpuArray(y0); + A1 = gpuArray(A1); + b = gpuArray(b); + lb = gpuArray(lb); + ub = gpuArray(ub); + J = gpuArray(J); + k2 = gpuArray(k2); + A1all = gpuArray(A1all); + yall = gpuArray(yall); end -A1all = zeros(nblock,nparams,'gpuArray'); tic; while naccept < nall A1new = A1 + mvnrnd(zeros(1,nparams),sigma); From 8eb6fcc170b28646eb8da6ae4efe4d3ecc446157 Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Fri, 26 Apr 2019 01:31:22 -0400 Subject: [PATCH 007/149] generate turing result using cpu --- solver/turing_cpu.m | 109 ++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 109 insertions(+) create mode 100644 solver/turing_cpu.m diff --git a/solver/turing_cpu.m b/solver/turing_cpu.m new file mode 100644 index 0000000..593fe40 --- /dev/null +++ b/solver/turing_cpu.m @@ -0,0 +1,109 @@ +%parameter search +L = [60,60]/2; +N = [256,256]/2; +n = prod(N); +D = [0.02,0.5]; +b = [0.04,-0.15]; +A1 = [0.08,-0.08;0.1,0]; +A2 = -[0.03,0.08]; +lb = [0,0]; +ub = [0.2,0.5]; +u0 = 5; +v0 = 5; +sigma = [0.01,0.01]; +A1lb = [-0.5,-1.5;-0.5,-1.5]; +A1ub = [1.5,0.5;1.5,0.5]; + +rng(1); +u0 = u0 + sigma(1)*randn(N); +v0 = v0 + sigma(2)*randn(N); +yu0 = fftn(u0); +yv0 = fftn(v0); +y0 = [yu0(:); yv0(:)]; + +[k2,k] = formk(N,L); + +JD = -k2(:)*D; +J = JD(:) + reshape(ones(n,1)*A2,[],1); + + +saveresult = true; +if saveresult + filepath = '/home/hbozhao/Dropbox (MIT)/2.168 Project/Data/turing_v2'; + mat = matfile(filepath,'Writable',true); + mat.A1 = []; + mat.y = []; +end +Nbatch = 250; +nall = 10000; +Nbatch = 2; +nall = 16; +nbatch = nall/(Nbatch*4); %must be integer + +Nt = 1000; +dt = 1; +outputstep = 100:100:Nt; +thresh = n*1e-5; +termination = @(t,y) event_gradient(t,y,k2(:),thresh); +if saveresult + transform = @(y) [reshape(real(ifftn(reshape(y(1:n),N))),[],1);reshape(real(ifftn(reshape(y(n+(1:n)),N))),[],1)]; +else + transform = []; +end +Anorm = norm(A1+diag(A2),inf); +A1 = reshape(A1,1,[]); +nparams = length(A1); +sigma = 0.05*eye(nparams); + +rungpu = false; + +tic; +for batch = 1:nbatch + ybatchall = zeros(4,Nbatch,N(1),N(2),length(outputstep),2); + A1batchall = zeros(4,Nbatch,nparams); + for process = 1:4 + ind = 0; + ybatch = zeros(Nbatch,N(1),N(2),length(outputstep),2); + A1batch = zeros(Nbatch,nparams); + while ind < Nbatch + A1new = A1lb + (A1ub-A1lb).*rand(2); + Anew = A1new+diag(A2); + if LSA(Anew,D) && (norm(Anew,inf)<5*Anorm) + fnlin = @(t,y) turing_nlin_bd(t,y,A1new,b,lb,ub,N); + [~,y,et] = odeimexez(fnlin,J,dt,Nt,y0,[],outputstep,termination,rungpu,transform); + if ~et + A1 = reshape(A1new,1,[]); + ind = ind + 1; + ybatch(ind,:,:,:,:) = permute(reshape(y,N(1),N(2),2,[]),[1,2,4,3]); + A1batch(ind,:) = A1; + end + end + end + A1batchall(process,:,:) = A1batch; + ybatchall(process,:,:,:,:,:) = ybatch; + end + if saveresult + if batch == 1 + mat.A1 = reshape(A1batchall,[],nparams); + mat.y = reshape(ybatchall,[],N(1),N(2),length(outputstep),2); + else + range = (batch-1)*Nbatch*4+(1:Nbatch*4); + mat.A1(range,:) = reshape(A1batchall,[],nparams); + mat.y(range,:,:,:,:) = reshape(ybatchall,[],N(1),N(2),length(outputstep),2); + end + runtime=toc; + disp(['batch ',num2str(batch),' of size ',num2str(Nbatch*4),' saved: Elapsed time (min): ',num2str(runtime/60),' ETA (min): ',num2str(runtime/60*(nbatch-batch)/batch)]); + end +end + +%plot 9 random realizations +figure; +for i=1:9 + subplot(3,3,i); + imagesc(squeeze(mat.y(randi(nall),:,:,end,1))); + colormap gray; + axis equal; + ax = gca; + ax.XTick=[]; ax.YTick=[]; +end +saveas(gcf,[filepath,'_sample'],'png'); From b79482d56817c617e637376bcac4d593738bcb81 Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Sat, 27 Apr 2019 00:42:51 -0400 Subject: [PATCH 008/149] spinodal decomposition --- solver/spdecomp.m | 30 ++++++++++++++++++++++++++++++ solver/spdecomp_nlin.m | 7 +++++++ 2 files changed, 37 insertions(+) create mode 100644 solver/spdecomp.m create mode 100644 solver/spdecomp_nlin.m diff --git a/solver/spdecomp.m b/solver/spdecomp.m new file mode 100644 index 0000000..e637ea2 --- /dev/null +++ b/solver/spdecomp.m @@ -0,0 +1,30 @@ +L = [80,80]; +N = 2^10*[1,1]; +n = prod(N); +kappa = 1; +omega = 3; +sigma = 0.01; + + +rng(1); +y0 = 0.5 + sigma*randn(N); +y0 = fftn(y0); +y0 = y0(:); +[k2,k] = formk(N,L); +k2 = k2(:); + +J = - kappa*k2.^2; + +Nt = 15000; +dt = 0.01; +fps = 30; +outputstep = floor(linspace(1,Nt,fps*10)); +fnlin = @(t,y) spdecomp_nlin(t,y,N,k2,omega); +transform = @(y) reshape(real(ifftn(reshape(y,N))),[],1); +[tout,yout] = odeimexez(fnlin,J,dt,Nt,y0,[],outputstep,[],false,transform); + +myMovie = VideoWriter([largedatapath,'spdecomp_movie']); +set(myMovie,'FrameRate',fps); +open(myMovie); +writeVideo(myMovie,reshape(yout,N(1),N(2),1,[])); +close(myMovie); diff --git a/solver/spdecomp_nlin.m b/solver/spdecomp_nlin.m new file mode 100644 index 0000000..cd1b95d --- /dev/null +++ b/solver/spdecomp_nlin.m @@ -0,0 +1,7 @@ +function f = spdecomp_nlin(t,y,N,k2,omega) + y = reshape(y,N); + yy = real(ifftn(y)); + mu = log(yy./(1-yy))+omega*(1-2*yy); + f = fftn(mu); + f = -f(:).*k2; +end From c4f083994ccc26c12b6057b5ae2e139296a4541b Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Tue, 30 Apr 2019 20:35:16 -0400 Subject: [PATCH 009/149] add the option to reinitialize for each instance --- solver/turing_cpu.m | 10 +++++++++- 1 file changed, 9 insertions(+), 1 deletion(-) diff --git a/solver/turing_cpu.m b/solver/turing_cpu.m index 593fe40..ea5d8c3 100644 --- a/solver/turing_cpu.m +++ b/solver/turing_cpu.m @@ -20,6 +20,7 @@ yu0 = fftn(u0); yv0 = fftn(v0); y0 = [yu0(:); yv0(:)]; +reinitialize = true; [k2,k] = formk(N,L); @@ -29,7 +30,7 @@ saveresult = true; if saveresult - filepath = '/home/hbozhao/Dropbox (MIT)/2.168 Project/Data/turing_v2'; + filepath = '/home/hbozhao/Dropbox (MIT)/2.168 Project/Data/turing_pca'; mat = matfile(filepath,'Writable',true); mat.A1 = []; mat.y = []; @@ -70,6 +71,13 @@ Anew = A1new+diag(A2); if LSA(Anew,D) && (norm(Anew,inf)<5*Anorm) fnlin = @(t,y) turing_nlin_bd(t,y,A1new,b,lb,ub,N); + if reinitialize + u0 = u0 + sigma(1)*randn(N); + v0 = v0 + sigma(2)*randn(N); + yu0 = fftn(u0); + yv0 = fftn(v0); + y0 = [yu0(:); yv0(:)]; + end [~,y,et] = odeimexez(fnlin,J,dt,Nt,y0,[],outputstep,termination,rungpu,transform); if ~et A1 = reshape(A1new,1,[]); From ce3f39ef5c4e4de521067a638f7d4ba98aa64f55 Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Tue, 30 Apr 2019 20:42:23 -0400 Subject: [PATCH 010/149] fix bugs in turing_cpu reinitialize --- solver/turing_cpu.m | 18 ++++++++---------- 1 file changed, 8 insertions(+), 10 deletions(-) diff --git a/solver/turing_cpu.m b/solver/turing_cpu.m index ea5d8c3..ba9b459 100644 --- a/solver/turing_cpu.m +++ b/solver/turing_cpu.m @@ -15,12 +15,14 @@ A1ub = [1.5,0.5;1.5,0.5]; rng(1); -u0 = u0 + sigma(1)*randn(N); -v0 = v0 + sigma(2)*randn(N); -yu0 = fftn(u0); -yv0 = fftn(v0); -y0 = [yu0(:); yv0(:)]; reinitialize = true; +if ~reinitialize + u0 = u0 + sigma(1)*randn(N); + v0 = v0 + sigma(2)*randn(N); + yu0 = fftn(u0); + yv0 = fftn(v0); + y0 = [yu0(:); yv0(:)]; +end [k2,k] = formk(N,L); @@ -72,11 +74,7 @@ if LSA(Anew,D) && (norm(Anew,inf)<5*Anorm) fnlin = @(t,y) turing_nlin_bd(t,y,A1new,b,lb,ub,N); if reinitialize - u0 = u0 + sigma(1)*randn(N); - v0 = v0 + sigma(2)*randn(N); - yu0 = fftn(u0); - yv0 = fftn(v0); - y0 = [yu0(:); yv0(:)]; + y0 = [reshape(fftn(u0 + sigma(1)*randn(N)),[],1); reshape(fftn(v0 + sigma(2)*randn(N)),[],1)]; end [~,y,et] = odeimexez(fnlin,J,dt,Nt,y0,[],outputstep,termination,rungpu,transform); if ~et From fa4c1d8ed627428ae030bc9a3a74890b84f1e91f Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Tue, 30 Apr 2019 22:44:38 -0400 Subject: [PATCH 011/149] in turing_cpu, better loading of result to plot samples --- solver/turing_cpu.m | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/solver/turing_cpu.m b/solver/turing_cpu.m index ba9b459..060c6a0 100644 --- a/solver/turing_cpu.m +++ b/solver/turing_cpu.m @@ -106,7 +106,7 @@ figure; for i=1:9 subplot(3,3,i); - imagesc(squeeze(mat.y(randi(nall),:,:,end,1))); + imagesc(squeeze(mat.y(randi(nall),1:N(1),1:N(2),length(outputstep),1))); colormap gray; axis equal; ax = gca; From 7e5278f1c81ee0fbd1528a5ba0e5362cc127bda4 Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Tue, 30 Apr 2019 22:44:47 -0400 Subject: [PATCH 012/149] pca analysis of turing pattern --- solver/turing_pca.m | 12 ++++++++++++ 1 file changed, 12 insertions(+) create mode 100644 solver/turing_pca.m diff --git a/solver/turing_pca.m b/solver/turing_pca.m new file mode 100644 index 0000000..54a179d --- /dev/null +++ b/solver/turing_pca.m @@ -0,0 +1,12 @@ +filepath = '/home/hbozhao/Dropbox (MIT)/2.168 Project/Data/turing_pca'; +mat = matfile(filepath); +ysize = size(mat,'y'); +data = reshape(mat.y(1:ysize(1),1:ysize(2),1:ysize(3),ysize(4),1),ysize(1),[]); +[coeff,score,latent,tsquared] = pca(data); +figure; +semilogy(latent); +saveas(gcf,[filepath,'_latent'],'png'); +figure; +plotmatrix(score(:,1:10)); +saveas(gcf,[filepath,'_latent_pdf'],'png'); +save([filepath,'_result'],'coeff','latent'); From 335eee6acb52df7484573a751472643b70e6bc74 Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Sat, 4 May 2019 21:10:50 -0400 Subject: [PATCH 013/149] update odeimexez on the usage of event function --- solver/odeimexez.m | 14 +++++++++++--- 1 file changed, 11 insertions(+), 3 deletions(-) diff --git a/solver/odeimexez.m b/solver/odeimexez.m index 376ca04..1e9ca2b 100644 --- a/solver/odeimexez.m +++ b/solver/odeimexez.m @@ -2,7 +2,9 @@ %easy version odeimex: fixed time step, no error control %h: step size %outputstep: an array that indicates at which step the solution is outputed (must be sorted). By default, it only returns the last step -%termination: a function handle (t,y) that becomes true when the solver should abort the iteration. The output et is true when it's terminated early. By default, termination is empty +%termination: a function handle (t,y,yp) that returns true or a nonzero value when the solver should abort the iteration. The output et is true or the corresponding value when it's terminated early. By default, termination is empty +%when the solver terminates, the last column of yout is the y at the time step of termination, the unfilled yout is removed. Similarly for tout +%y is the value at the latest time point, yp is the estimated time derivative (y-yold)/dt %the output yout is stored on gpu if gpu is true. For now, tout is always stored on cpu. By default, gpu is set to false. %transform is a function handle that transforms the output y (by default empty) %04/11/2019, now J can be a matrix or a column vector whose size is the same as y @@ -43,6 +45,7 @@ vectorJ = all(size(J)==size(y)); for step = 2:Nt + yold = y; fex = fnlin(t(step-1),y); % the nonlinear part is fixed in the iteration if vectorJ y = (y+h*fex)./(1-h*J); @@ -58,8 +61,13 @@ outputid = min(outputid+1,length(outputstep)); end if ~isempty(termination) - if termination(t(step),y) - et = true; + yp = (y-yold)/h; + et = termination(t(step),y,yp); + if et + yout(:,outputid) = y; + yout(:,outputid+1:end) = []; + tout(:,outputid) = h*(step-1); + tout(:,outputid+1:end) = []; break; end end From 2a0bffaa372254ad6d707392e91a998299ea2ca9 Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Sat, 4 May 2019 21:11:24 -0400 Subject: [PATCH 014/149] update turing_ps and turing_cpu after odeimexez update --- solver/turing_cpu.m | 12 ++++++------ solver/turing_ps.m | 2 +- 2 files changed, 7 insertions(+), 7 deletions(-) diff --git a/solver/turing_cpu.m b/solver/turing_cpu.m index 060c6a0..1db7ad4 100644 --- a/solver/turing_cpu.m +++ b/solver/turing_cpu.m @@ -30,7 +30,7 @@ J = JD(:) + reshape(ones(n,1)*A2,[],1); -saveresult = true; +saveresult = false; if saveresult filepath = '/home/hbozhao/Dropbox (MIT)/2.168 Project/Data/turing_pca'; mat = matfile(filepath,'Writable',true); @@ -39,15 +39,15 @@ end Nbatch = 250; nall = 10000; -Nbatch = 2; -nall = 16; +%Nbatch = 2; +%nall = 16; nbatch = nall/(Nbatch*4); %must be integer Nt = 1000; dt = 1; -outputstep = 100:100:Nt; +outputstep = Nt; thresh = n*1e-5; -termination = @(t,y) event_gradient(t,y,k2(:),thresh); +termination = @(t,y,~) event_gradient(t,y,k2(:),thresh); if saveresult transform = @(y) [reshape(real(ifftn(reshape(y(1:n),N))),[],1);reshape(real(ifftn(reshape(y(n+(1:n)),N))),[],1)]; else @@ -64,7 +64,7 @@ for batch = 1:nbatch ybatchall = zeros(4,Nbatch,N(1),N(2),length(outputstep),2); A1batchall = zeros(4,Nbatch,nparams); - for process = 1:4 + parfor process = 1:4 ind = 0; ybatch = zeros(Nbatch,N(1),N(2),length(outputstep),2); A1batch = zeros(Nbatch,nparams); diff --git a/solver/turing_ps.m b/solver/turing_ps.m index e71eb89..772ab4b 100644 --- a/solver/turing_ps.m +++ b/solver/turing_ps.m @@ -43,7 +43,7 @@ % outputstep = [1,100:200:1000] ;%[300,1000,2000:1000:Nt]; nall = 1; thresh = n*1e-5; -termination = @(t,y) event_gradient(t,y,k2(:),thresh); +termination = @(t,y,~) event_gradient(t,y,k2(:),thresh); if saveresult transform = @(y) [reshape(real(ifftn(reshape(y(1:n),N))),[],1);reshape(real(ifftn(reshape(y(n+(1:n)),N))),[],1)]; else From 2dd6e0e3316eb324a0c130e515f25a1ef9451543 Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Sat, 4 May 2019 21:12:01 -0400 Subject: [PATCH 015/149] generate turing patterns that are close to steady state --- solver/event_gradient_ss.m | 23 ++++++++ solver/turing_prototype.m | 37 ++++++++++++ solver/turing_ss.m | 116 +++++++++++++++++++++++++++++++++++++ 3 files changed, 176 insertions(+) create mode 100644 solver/event_gradient_ss.m create mode 100644 solver/turing_prototype.m create mode 100644 solver/turing_ss.m diff --git a/solver/event_gradient_ss.m b/solver/event_gradient_ss.m new file mode 100644 index 0000000..d863793 --- /dev/null +++ b/solver/event_gradient_ss.m @@ -0,0 +1,23 @@ +function flag = event_gradient_ss(t,y,yp,k2,thresh,component) + %y = 1 when the L2 norm of the gradient field is below thresh(1) + %y = 2 when the 2-norm of the time derivative yp is below thresh(2) + %note that y is in Fourier space. + %L2 norm of the gradient field is \int_{|| \nabla y(x) ||^2 dx} = \int_{|| k ||^2 ||y(k)||^2 dk} + %k2 should correspond to each row of y + %component (1 by default) is the index of the species + if nargin < 6 + component = 1; + end + flag = false; + dy = gradient_norm(y,k2,component); + if (dy Date: Sat, 4 May 2019 21:12:48 -0400 Subject: [PATCH 016/149] slight modifcation to spdecomp.m for generating spdecomp patterns --- solver/spdecomp.m | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/solver/spdecomp.m b/solver/spdecomp.m index e637ea2..37f8955 100644 --- a/solver/spdecomp.m +++ b/solver/spdecomp.m @@ -1,4 +1,4 @@ -L = [80,80]; +L = [100,100]; N = 2^10*[1,1]; n = prod(N); kappa = 1; @@ -15,10 +15,10 @@ J = - kappa*k2.^2; -Nt = 15000; +Nt = 20000; dt = 0.01; fps = 30; -outputstep = floor(linspace(1,Nt,fps*10)); +outputstep = floor(linspace(1,Nt,fps*20)); fnlin = @(t,y) spdecomp_nlin(t,y,N,k2,omega); transform = @(y) reshape(real(ifftn(reshape(y,N))),[],1); [tout,yout] = odeimexez(fnlin,J,dt,Nt,y0,[],outputstep,[],false,transform); From 82af5f5d7c2f56992c3e7559796ab2b244fb3319 Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Sat, 4 May 2019 21:15:34 -0400 Subject: [PATCH 017/149] fix bug in odeimexez, apply transform when et aborts the iteration --- solver/odeimexez.m | 6 +++++- 1 file changed, 5 insertions(+), 1 deletion(-) diff --git a/solver/odeimexez.m b/solver/odeimexez.m index 1e9ca2b..2240479 100644 --- a/solver/odeimexez.m +++ b/solver/odeimexez.m @@ -64,7 +64,11 @@ yp = (y-yold)/h; et = termination(t(step),y,yp); if et - yout(:,outputid) = y; + if isempty(transform) + yout(:,outputid) = y; + else + yout(:,outputid) = transform(y); + end yout(:,outputid+1:end) = []; tout(:,outputid) = h*(step-1); tout(:,outputid+1:end) = []; From a102293ac6dd5a86df645c580d718cdab41e27cc Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Sun, 5 May 2019 00:24:28 -0400 Subject: [PATCH 018/149] post processing of turing pattern --- solver/turing_pp.m | 40 ++++++++++++++++++++++++++++++++++++++++ 1 file changed, 40 insertions(+) create mode 100644 solver/turing_pp.m diff --git a/solver/turing_pp.m b/solver/turing_pp.m new file mode 100644 index 0000000..0135a6b --- /dev/null +++ b/solver/turing_pp.m @@ -0,0 +1,40 @@ +%image post-processing +filepath = '~/Dropbox (MIT)/2.168 Project/Data/turing_ss'; +mat = matfile(filepath); +ysize = size(mat,'y'); +threshold = 3.5; %a separation of the bimodal distribution of the entire dataset (component 1) +%see for example: +%figure; histogram(mat.y(1:ysize(1),1:ysize(2),1:ysize(3),ysize(4),1) +feature = zeros(ysize(1),8); +ind = 0; +for i=1:ysize(1) + im = squeeze(mat.y(i,1:ysize(2),1:ysize(3),ysize(4),1)); + if ~any(im(:)>threshold) + continue; + end + bw = (im>threshold); + stats = regionprops(bw,'Area','Perimeter'); + area = [stats(:).Area]; + if ~any(area>10) + continue; + end + perimeter = [stats(:).Perimeter]; + circularity = 4*pi*area./perimeter.^2; + ind = ind + 1; + %number of domains + feature(ind,1) = numel(stats); + %mean of domain area + feature(ind,2) = mean(area); + %std of domain area + feature(ind,3) = std(area); + %mean of domain perimeter + feature(ind,4) = mean(perimeter); + feature(ind,5) = std(perimeter); + %min of domain circularity + feature(ind,6) = min(circularity); + %mean of domain circularity + feature(ind,7) = mean(circularity); + %std of domain circularity + feature(ind,8) = std(circularity); +end +feature(ind+1:end,:) = []; From 8c6f7070c56cf5749d2f5a2334fabbbcb5faf686 Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Tue, 7 May 2019 21:05:32 -0400 Subject: [PATCH 019/149] post processing --- solver/turing_pp.m | 3 +++ solver/turing_pp_video.m | 21 +++++++++++++++++++++ 2 files changed, 24 insertions(+) create mode 100644 solver/turing_pp_video.m diff --git a/solver/turing_pp.m b/solver/turing_pp.m index 0135a6b..ebf476b 100644 --- a/solver/turing_pp.m +++ b/solver/turing_pp.m @@ -6,6 +6,7 @@ %see for example: %figure; histogram(mat.y(1:ysize(1),1:ysize(2),1:ysize(3),ysize(4),1) feature = zeros(ysize(1),8); +index = zeros(ysize(1),1); ind = 0; for i=1:ysize(1) im = squeeze(mat.y(i,1:ysize(2),1:ysize(3),ysize(4),1)); @@ -36,5 +37,7 @@ feature(ind,7) = mean(circularity); %std of domain circularity feature(ind,8) = std(circularity); + index(ind) = i; end feature(ind+1:end,:) = []; +index(ind+1:end) = []; diff --git a/solver/turing_pp_video.m b/solver/turing_pp_video.m new file mode 100644 index 0000000..cdc7fd2 --- /dev/null +++ b/solver/turing_pp_video.m @@ -0,0 +1,21 @@ +function turing_pp_video(index,video_file,data_file,fps) +%run after turing_pp +%index is the frame to be saved in video +%video_file is the filepath of the video +%data_file is the filepath of the data +if nargin<3 + data_file = '~/Dropbox (MIT)/2.168 Project/Data/turing_ss'; +end +if nargin<4 + fps = 30; +end +mat = matfile(data_file); +ysize = size(mat,'y'); + +yout = permute(squeeze(mat.y(index_video,1:ysize(2),1:ysize(3),ysize(4),1)),[2,3,4,1]); + +myMovie = VideoWriter(video_file); +set(myMovie,'FrameRate',fps); +open(myMovie); +writeVideo(myMovie,yout); +close(myMovie); From 6b5e4d69e0bdd01ae2923ecdf074e51e94ef2d09 Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Tue, 7 May 2019 23:55:23 -0400 Subject: [PATCH 020/149] fix bug in post processing video --- solver/turing_pp_video.m | 8 ++++---- 1 file changed, 4 insertions(+), 4 deletions(-) diff --git a/solver/turing_pp_video.m b/solver/turing_pp_video.m index cdc7fd2..598158b 100644 --- a/solver/turing_pp_video.m +++ b/solver/turing_pp_video.m @@ -9,11 +9,11 @@ function turing_pp_video(index,video_file,data_file,fps) if nargin<4 fps = 30; end -mat = matfile(data_file); -ysize = size(mat,'y'); - -yout = permute(squeeze(mat.y(index_video,1:ysize(2),1:ysize(3),ysize(4),1)),[2,3,4,1]); +mat = load(data_file); +y = mat.y; +yout = permute(squeeze(y(index,:,:,end,1)),[2,3,4,1]); +yout = yout/max(yout(:)); myMovie = VideoWriter(video_file); set(myMovie,'FrameRate',fps); open(myMovie); From 96d218adb6ba5db3d2ae1b2456043c422782892f Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Mon, 13 May 2019 01:20:01 -0400 Subject: [PATCH 021/149] plot dispersion curve --- solver/dispersion_curve.m | 16 ++++++++++++++++ 1 file changed, 16 insertions(+) create mode 100644 solver/dispersion_curve.m diff --git a/solver/dispersion_curve.m b/solver/dispersion_curve.m new file mode 100644 index 0000000..7d68aa5 --- /dev/null +++ b/solver/dispersion_curve.m @@ -0,0 +1,16 @@ +A1 = [0.08,-0.08;0.1,0]; +A2 = -[0.03,0.08]; +A = A1+diag(A2); +D = [0.02,0.5]; + +k = linspace(0,2,1000); +a = 1; +b = (-trace(A)+sum(D)*k.^2); +c = (prod(D)*k.^4-(A(1,1)*D(2)+A(2,2)*D(1))*k.^2+det(A)); +lambda = (-b+[1;-1]*sqrt(b.^2-4*a*c))./(2*a); +figure; +plot(k,max(real(lambda)),'LineWidth',2); +axis([0,2,-0.05,0.02]); +xlabel('|k|'); +ylabel('max Re \lambda') +print(gcf,'C:\Users\zhbkl\Dropbox (MIT)\MIT Courses\2.168\2.168 Project\Final\dispersion','-dpng','-r400'); From 56d323a3b6269fbd909409c6bbd9a251ce55a571 Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Fri, 28 Jun 2019 00:39:18 -0400 Subject: [PATCH 022/149] add DDFT scripts --- solver/DDFT.m | 24 ++++++++++++++++++++++++ solver/DDFT_nlin.m | 5 +++++ 2 files changed, 29 insertions(+) create mode 100644 solver/DDFT.m create mode 100644 solver/DDFT_nlin.m diff --git a/solver/DDFT.m b/solver/DDFT.m new file mode 100644 index 0000000..dce32de --- /dev/null +++ b/solver/DDFT.m @@ -0,0 +1,24 @@ +%parameter search +L = [5,5]; +N = [256,256]/2; +n = prod(N); +n0 = 0.07; +sigma = 0.01; + +rng(1); +n0 = n0 + sigma*randn(N); +y0 = fftn(n0); +y0 = y0(:); + +[k2,k] = formk(N,L); +k2 = k2(:); +k0 = 10; +alpha = 2; +C2 = exp(-(sqrt(k2)-k0).^2/(2*alpha^2)); +J = -k2.*(-C2); + +Nt = 10000; +options = odeset('AbsTol',1e-3); +[tout,yout] = odeimex(@(t,y) DDFT_nlin(t,y,k2,N),J,Nt,y0); + +k2real(yout(:,end),N); diff --git a/solver/DDFT_nlin.m b/solver/DDFT_nlin.m new file mode 100644 index 0000000..bb6730b --- /dev/null +++ b/solver/DDFT_nlin.m @@ -0,0 +1,5 @@ +function dy = DDFT_nlin(t,y,k2,N) + y = real(ifftn(reshape(y,N))); + mu = log(1+y); + dy = -k2 .* reshape(fftn(mu,N),[],1); +end From 70046d8d3540be1c3cac11ec1c187dc3b1c6a39e Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Fri, 28 Jun 2019 20:11:41 -0400 Subject: [PATCH 023/149] start adding FSA to odeimex --- solver/odeimex.m | 86 +++++++++++++++++++++++++++++++++++++++++++++--- 1 file changed, 82 insertions(+), 4 deletions(-) diff --git a/solver/odeimex.m b/solver/odeimex.m index 19cc12b..8177d53 100644 --- a/solver/odeimex.m +++ b/solver/odeimex.m @@ -1,4 +1,4 @@ -function [tout,yout] = odeimex(fnlin,J,Nt,y0,options,pencil) +function [tout,yout] = odeimex(fnlin,J,Nt,y0,options,pencil,JexMult,exsensFcn,dJdp) %a simplified ode solver adapted from ode15s %the backward diffusion / NDF is applied for the linear part of the equation, in particular, the propotionality constant is J, note that J is the array the same as y0 (equivalent to diagonal) for now, in the near future, generalize J to a matrix. %The nonlinear part of the equation is explicit, that is, at each time step, this term is dependent only on the previous time step. @@ -9,6 +9,10 @@ %03/25/2019, now J can be a matrix or a column vector whose size is the same as y %pencil(b,hinvGak) should return (Mt-hinvGak*J)\b %right now J is constant +%the mass matrix Mt is also constant +%JexMult is the multiplying function for the jacobian of the explicit term (argument: ys, t, y) +%exsensFcn is the sensitivity of the explicit term +%dJdp is the sensitivity of the multiplying matrix of the implicit term if nargin<5 options = []; end @@ -20,11 +24,24 @@ atol = odeget(options,'AbsTol',1e-6,'fast'); normcontrol = strcmp(odeget(options,'NormControl','off','fast'),'on'); +%Forward sensitivity analysis +FSA = moreodeget(moreoptions,'FSA',false,'fast'); +FSAerror = moreodeget(moreoptions,'FSAerror',false,'fast'); +ys = moreodeget(moreoptions,'ys0',[],'fast'); +ysp = moreodeget(moreoptions,'ysp0',[],'fast'); +if isempty(ys) || isempty(ysp) + FSA = false; +end + neq = length(y0); +ninst = size(ys,2); threshold = atol / rtol; if normcontrol normy = norm(y0); + if FSA + normys = vecnorm(ys); + end end tdir = 1; @@ -50,6 +67,7 @@ end invGa = 1 ./ (G .* (1 - alpha)); erconst = alpha .* G + (1 ./ (2:6)'); +G3(1,1,:) = G; % for FSA difU = [ -1, -2, -3, -4, -5; % difU is its own inverse! 0, 1, 3, 6, 10; 0, 0, -1, -4, -10; @@ -89,9 +107,15 @@ K = 1; % K = 1:k klast = k; abshlast = absh; +abshFSA = absh; %record the absh and k at previous FSA stepping +kFSA = k; dif = zeros(neq,maxk+2); dif(:,1) = h * yp; +if FSA + difs = zeros(neq,ninst,maxk+2); + difs(:,:,1) = h * ysp; +end hinvGak = h * invGa(k); nconhk = 0; % steps taken with current h and k @@ -140,10 +164,11 @@ invwt = 1 ./ max(max(abs(y),abs(ynew)),threshold); end + rhs = Mt*(ynew-psi) + hinvGak*fex; if vectorJ - ynew2 = (ynew-psi+hinvGak*fex)./(1-hinvGak*J); + ynew2 = rhs ./ (Mt - hinvGak*J); else - ynew2 = pencil(ynew-psi+hinvGak*fex,hinvGak); + ynew2 = pencil(rhs,hinvGak); end difkp1 = ynew2-ynew; @@ -156,7 +181,54 @@ err = norm(difkp1 .* invwt,inf) * erconst(k); end - if err > rtol % Failed step + fail = (err > rtol); + + if ~fail && FSA %successful, move on to FSA + if abshFSA ~= absh || kFSA ~= k + difRU = cumprod((kI - 1 - kJ*(absh/abshFSA)) ./ kI) * difU; + difRU4d = permute(difRU(K,K),[3,4,1,2]); + difs(:,:,K) = squeeze(sum(difs(:,:,K) .* difRU4d, 3)); + abshFSA = absh; + kFSA = k; + end + %time step is already known + %the following is fixed since time step is fixed and so is difs + psis = sum(difs(:,:,K) .* G3(1,1,K),3) * invGa(k); + preds = ys + sum(difs(:,:,K),3); + ynews = preds; + if normcontrol + normynews = vecnorm(ynews); + invwts = 1 ./ max(max(normys,normynews),threshold); + else + invwts = 1 ./ max(max(abs(ys),abs(ynews)),threshold); + end + + dfexdy = feval(Jex,t,y); + sensval= feval(exsensFcn,t,y); + fs = dfexdy*ys + (dJdp*ynew + sensval); + rhss = Mt*(ynews-psis) + hinvGak*fs; + if vectorJ + ynews2 = rhss ./ (Mt - hinvGak*J); + else + ynews2 = pencil(rhss,hinvGak); + end + difkp1s = ynews2-ynews; + ynews = ynews2; + + if FSAerror + if normcontrol + errs = (vecnorm(difkp1s) .* invwts) * erconst(k); + else + errs = vecnorm(difkp1s .* invwts,inf) * erconst(k); + end + err = max(err,max(errs)); + if err > rtol + fail = true; + end + end + end + + if fail if absh <= hmin warning(message('MATLAB:ode15s:IntegrationTolNotMet', sprintf( '%e', t ), sprintf( '%e', hmin ))); tout(step:end) = []; @@ -261,8 +333,14 @@ % Advance the integration one step. t = tnew; y = ynew; + if FSA + ys = ynews; + end if normcontrol normy = normynew; + if FSA + normys = normynews; + end end tout(step) = t; yout(:,step) = y; From ad37036b966d955f1ddcf0b25637591656b841ad Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Mon, 1 Jul 2019 01:04:49 -0400 Subject: [PATCH 024/149] add moerodeoptions, fix bugs, add output function in odeimex --- solver/DDFT.m | 12 +- solver/moreodeget.m | 117 +++++++++++++++++++ solver/moreodeset.m | 269 ++++++++++++++++++++++++++++++++++++++++++++ solver/odeimex.m | 243 ++++++++++++++++++++++++++++++++++++--- 4 files changed, 623 insertions(+), 18 deletions(-) create mode 100644 solver/moreodeget.m create mode 100644 solver/moreodeset.m diff --git a/solver/DDFT.m b/solver/DDFT.m index dce32de..74e36ba 100644 --- a/solver/DDFT.m +++ b/solver/DDFT.m @@ -10,6 +10,14 @@ y0 = fftn(n0); y0 = y0(:); +% %use image? +% im = imread('cameraman.tif'); +% im = imresize(im,N); +% C2 = fft(im); +% C2 = C2(:); +% C2(1) = 0; +% C2 = C2/max(abs(C2))/1.5; + [k2,k] = formk(N,L); k2 = k2(:); k0 = 10; @@ -17,8 +25,8 @@ C2 = exp(-(sqrt(k2)-k0).^2/(2*alpha^2)); J = -k2.*(-C2); -Nt = 10000; +tspan = linspace(0,1.1,100); options = odeset('AbsTol',1e-3); -[tout,yout] = odeimex(@(t,y) DDFT_nlin(t,y,k2,N),J,Nt,y0); +[tout,yout] = odeimex(@(t,y) DDFT_nlin(t,y,k2,N),J,tspan,y0); k2real(yout(:,end),N); diff --git a/solver/moreodeget.m b/solver/moreodeget.m new file mode 100644 index 0000000..7579806 --- /dev/null +++ b/solver/moreodeget.m @@ -0,0 +1,117 @@ +function o = moreodeget(options,name,default,flag) + % used for moreoptions in myode15s +%ODEGET Get ODE OPTIONS parameters. +% VAL = ODEGET(OPTIONS,'NAME') extracts the value of the named property +% from integrator options structure OPTIONS, returning an empty matrix if +% the property value is not specified in OPTIONS. It is sufficient to type +% only the leading characters that uniquely identify the property. Case is +% ignored for property names. [] is a valid OPTIONS argument. +% +% VAL = ODEGET(OPTIONS,'NAME',DEFAULT) extracts the named property as +% above, but returns VAL = DEFAULT if the named property is not specified +% in OPTIONS. For example +% +% val = odeget(opts,'RelTol',1e-4); +% +% returns val = 1e-4 if the RelTol property is not specified in opts. +% +% See also ODESET, ODE45, ODE23, ODE113, ODE15S, ODE23S, ODE23T, ODE23TB. + +% Mark W. Reichelt and Lawrence F. Shampine, 3/1/94 +% Copyright 1984-2016 The MathWorks, Inc. + +% undocumented usage for fast access with no error checking +if (nargin == 4) && isequal(char(flag),'fast') + o = getknownfield(options,name,default); + return +end + +if nargin < 2 + error(message('MATLAB:odeget:NotEnoughInputs')); +end +if nargin < 3 + default = []; +end +if isstring(name) && isscalar(name) + name = char(name); +end +if ~isempty(options) && ~isa(options,'struct') + error(message('MATLAB:odeget:Arg1NotODESETstruct')); +end + +if isempty(options) + o = default; + return; +end + +Names = [ + 'blockLU ' + 'blockLUadj ' + 'blockIter ' + 'blockIterLead ' + 'blockIterStaticInd ' + 'blockIterStaticJac ' + 'ErrorControl ' + 'FSA ' + 'FSAerror ' + 'gmresmaxit ' + 'gmresTol ' + 'imex ' + 'interpFcn ' + 'jacMult ' + 'Krylov ' + 'linear ' + 'linearMult ' + 'maxit ' + 'pencil ' + 'restart ' + 'sensFcn ' + 'skipInit ' + 'updateJ ' % backward compatibility + 'youtSel ' + 'ysutSel ' + 'ys0 ' + 'ysp0 ' + ]; + +names = lower(Names); + +lowName = lower(name); +j = strmatch(lowName,names); +if isempty(j) % if no matches + error(message('MATLAB:odeget:InvalidPropName', name)); +elseif length(j) > 1 % if more than one match + % Check for any exact matches (in case any names are subsets of others) + k = strmatch(lowName,names,'exact'); + if length(k) == 1 + j = k; + else + matches = deblank(Names(j(1),:)); + for k = j(2:length(j))' + matches = [matches ', ' deblank(Names(k,:))]; %#ok + end + error(message('MATLAB:odeget:AmbiguousPropName',name,matches)); + end +end + +if any(strcmp(fieldnames(options),deblank(Names(j,:)))) + o = options.(deblank(Names(j,:))); + if isempty(o) + o = default; + end +else + o = default; +end + +% -------------------------------------------------------------------------- +function v = getknownfield(s, f, d) +%GETKNOWNFIELD Get field f from struct s, or else yield default d. + +if isfield(s,f) % s could be empty. + v = s.(f); + if isempty(v) + v = d; + end +else + v = d; +end diff --git a/solver/moreodeset.m b/solver/moreodeset.m new file mode 100644 index 0000000..c441646 --- /dev/null +++ b/solver/moreodeset.m @@ -0,0 +1,269 @@ +function options = moreodeset(varargin) +% used for moreoptions in myode15s +%ODESET Create/alter ODE OPTIONS structure. +% OPTIONS = ODESET('NAME1',VALUE1,'NAME2',VALUE2,...) creates an integrator +% options structure OPTIONS in which the named properties have the +% specified values. Any unspecified properties have default values. It is +% sufficient to type only the leading characters that uniquely identify the +% property. Case is ignored for property names. +% +% OPTIONS = ODESET(OLDOPTS,'NAME1',VALUE1,...) alters an existing options +% structure OLDOPTS. +% +% OPTIONS = ODESET(OLDOPTS,NEWOPTS) combines an existing options structure +% OLDOPTS with a new options structure NEWOPTS. Any new properties +% overwrite corresponding old properties. +% +% ODESET with no input arguments displays all property names and their +% possible values. +% +%ODESET PROPERTIES +% +%RelTol - Relative error tolerance [ positive scalar {1e-3} ] +% This scalar applies to all components of the solution vector, and +% defaults to 1e-3 (0.1% accuracy) in all solvers. The estimated error in +% each integration step satisfies e(i) <= max(RelTol*abs(y(i)),AbsTol(i)). +% +%AbsTol - Absolute error tolerance [ positive scalar or vector {1e-6} ] +% A scalar tolerance applies to all components of the solution vector. +% Elements of a vector of tolerances apply to corresponding components of +% the solution vector. AbsTol defaults to 1e-6 in all solvers. See RelTol. +% +%NormControl - Control error relative to norm of solution [ on | {off} ] +% Set this property 'on' to request that the solvers control the error in +% each integration step with norm(e) <= max(RelTol*norm(y),AbsTol). By +% default the solvers use a more stringent component-wise error control. +% +%Refine - Output refinement factor [ positive integer ] +% This property increases the number of output points by the specified +% factor producing smoother output. Refine defaults to 1 in all solvers +% except ODE45, where it is 4. Refine does not apply if length(TSPAN) > 2 +% or the ODE solver returns the solution as a structure. +% +%OutputFcn - Installable output function [ function_handle ] +% This output function is called by the solver after each time step. When +% a solver is called with no output arguments, OutputFcn defaults to +% @odeplot. Otherwise, OutputFcn defaults to []. +% +%OutputSel - Output selection indices [ vector of integers ] +% This vector of indices specifies which components of the solution vector +% are passed to the OutputFcn. OutputSel defaults to all components. +% +%Stats - Display computational cost statistics [ on | {off} ] +% +%Jacobian - Jacobian function [ function_handle | constant matrix ] +% Set this property to @FJac if FJac(t,y) returns dF/dy, or to +% the constant value of dF/dy. +% For ODE15I solving F(t,y,y') = 0, set this property to @FJac if +% [dFdy, dFdyp] = FJac(t,y,yp), or to a cell array of constant +% values {dF/dy,dF/dyp}. +% +%JPattern - Jacobian sparsity pattern [ sparse matrix ] +% Set this property to a sparse matrix S with S(i,j) = 1 if component i of +% F(t,y) depends on component j of y, and 0 otherwise. +% For ODE15I solving F(t,y,y') = 0, set this property to +% {dFdyPattern,dFdypPattern}, the sparsity patterns of dF/dy and +% dF/dy', respectively. +% +%Vectorized - Vectorized ODE function [ on | {off} ] +% Set this property 'on' if the ODE function F is coded so that +% F(t,[y1 y2 ...]) returns [F(t,y1) F(t,y2) ...]. +% For ODE15I solving F(t,y,y') = 0, set this property to +% {yVect,ypVect}. Setting yVect 'on' indicates that +% F(t,[y1 y2 ...],yp) returns [F(t,y1,yp) F(t,y2,yp) ...]. +% Setting ypVect 'on' indicates that F(t,y,[yp1 yp2 ...]) +% returns [F(t,y,yp1) F(t,y,yp2) ...]. +% +%Events - Locate events [ function_handle ] +% To detect events, set this property to the event function. +% +%Mass - Mass matrix [ constant matrix | function_handle ] +% For problems M*y' = f(t,y) set this property to the value of the constant +% mass matrix. For problems with time- or state-dependent mass matrices, +% set this property to a function that evaluates the mass matrix. +% +%MStateDependence - Dependence of the mass matrix on y [ none | {weak} | strong ] +% Set this property to 'none' for problems M(t)*y' = F(t,y). Both 'weak' and +% 'strong' indicate M(t,y), but 'weak' will result in implicit solvers +% using approximations when solving algebraic equations. +% +%MassSingular - Mass matrix is singular [ yes | no | {maybe} ] +% Set this property to 'no' if the mass matrix is not singular. +% +%MvPattern - dMv/dy sparsity pattern [ sparse matrix ] +% Set this property to a sparse matrix S with S(i,j) = 1 if for any k, the +% (i,k) component of M(t,y) depends on component j of y, and 0 otherwise. +% +%InitialSlope - Consistent initial slope yp0 [ vector ] +% yp0 satisfies M(t0,y0)*yp0 = F(t0,y0). +% +%InitialStep - Suggested initial step size [ positive scalar ] +% The solver will try this first. By default the solvers determine an +% initial step size automatically. +% +%MaxStep - Upper bound on step size [ positive scalar ] +% MaxStep defaults to one-tenth of the tspan interval in all solvers. +% +%NonNegative - Non-negative solution components [ vector of integers ] +% This vector of indices specifies which components of the +% solution vector must be non-negative. NonNegative defaults to []. +% This property is not available in ODE23S, ODE15I. In ODE15S, +% ODE23T, and ODE23TB, the property is not available for problems +% where there is a mass matrix. +% +%BDF - Use Backward Differentiation Formulas in ODE15S [ on | {off} ] +% This property specifies whether the Backward Differentiation Formulas +% (Gear's methods) are to be used in ODE15S instead of the default +% Numerical Differentiation Formulas. +% +%MaxOrder - Maximum order of ODE15S and ODE15I [ 1 | 2 | 3 | 4 | {5} ] +% +% See also ODEGET, ODE45, ODE23, ODE113, ODE15I, ODE15S, ODE23S, ODE23T, ODE23TB, +% FUNCTION_HANDLE. + +% Mark W. Reichelt and Lawrence F. Shampine, 5/6/94 +% Copyright 1984-2016 The MathWorks, Inc. + +% Print out possible values of properties. +if (nargin == 0) && (nargout == 0) + fprintf(' blockLU: [ {false} | true ]\n'); + fprintf(' blockLUadj: [ {false} | true ]\n'); + fprintf(' blockIter: [ {false} | true ]\n'); + fprintf(' blockIterLead: [ {Dynamic} | Static | Jacobi ]\n'); + fprintf(' blockIterStaticInd: [ {[]} | integer array ]\n'); + fprintf(' blockIterStaticJac: [ {[]} | struct ]\n'); + fprintf(' ErrorControl: [ {1:neq} | array ]\n'); + fprintf(' FSA: [ {false} | true ]\n'); + fprintf(' FSAerror: [ {false} | true ]\n'); + fprintf(' gmresmaxit: [ {5} | positive integer ]\n'); + fprintf(' gmresTol: [ {0.005} | positive ]\n'); + fprintf(' imex: [ {false} | true ]\n'); + fprintf(' interpFcn: [ {[]} | function handle ]\n'); + fprintf(' jacMult: [ {[]} | function handle ]\n'); + fprintf(' Krylov: [ {false} | true ]\n'); + fprintf(' linear: [ {false} | true ]\n'); + fprintf(' linearMult: [ {[]} | function handle ]\n'); + fprintf(' maxit: [ {4 ~blockIter, 10 blockIter} | integer ]\n'); + fprintf(' pencil: [ {[]} | function handle ]\n'); + fprintf(' restart: [ {5} | positive integer ]\n'); + fprintf(' sensFcn: [ {[]} | function handle ]\n'); + fprintf(' skipInit: [ {false} | true ]\n'); + fprintf(' updateJ: [ {false} | true ]\n'); + fprintf(' youtSel: [ {[]} | positive integer array ]\n'); + fprintf(' ysoutSel: [ {[]} | positive integer array ]\n'); + fprintf(' ys0: [ {[]} | array ]\n'); + fprintf(' ysp0: [ {[]} | array ]\n'); + fprintf('\n'); + return; +end + +Names = [ + 'blockLU ' + 'blockLUadj ' + 'blockIter ' + 'blockIterLead ' + 'blockIterStaticInd ' + 'blockIterStaticJac ' + 'ErrorControl ' + 'FSA ' + 'FSAerror ' + 'gmresmaxit ' + 'gmresTol ' + 'imex ' + 'interpFcn ' + 'jacMult ' + 'Krylov ' + 'linear ' + 'linearMult ' + 'maxit ' + 'pencil ' + 'restart ' + 'sensFcn ' + 'skipInit ' + 'updateJ ' % backward compatibility + 'youtSel ' + 'ysoutSel ' + 'ys0 ' + 'ysp0 ' + ]; +m = size(Names,1); +names = lower(Names); + +% Combine all leading options structures o1, o2, ... in odeset(o1,o2,...). +options = []; +for j = 1:m + options.(deblank(Names(j,:))) = []; +end +i = 1; +while i <= nargin + arg = varargin{i}; + if ischar(arg) || (isstring(arg) && isscalar(arg)) % arg is an option name + break; + end + if ~isempty(arg) % [] is a valid options argument + if ~isa(arg,'struct') + error(message('MATLAB:odeset:NoPropNameOrStruct', i)); + end + for j = 1:m + if any(strcmp(fieldnames(arg),deblank(Names(j,:)))) + val = arg.(deblank(Names(j,:))); + else + val = []; + end + if ~isempty(val) + options.(deblank(Names(j,:))) = val; + end + end + end + i = i + 1; +end +% Convert string arguments and options. +for ii = 1:nargin + if isstring(varargin{ii}) && isscalar(varargin{ii}) + varargin{ii} = char(varargin{ii}); + end +end + +% A finite state machine to parse name-value pairs. +if rem(nargin-i+1,2) ~= 0 + error(message('MATLAB:odeset:ArgNameValueMismatch')); +end +expectval = 0; % start expecting a name, not a value +while i <= nargin + arg = varargin{i}; + + if ~expectval + if ~ischar(arg) + error(message('MATLAB:odeset:NoPropName', i)); + end + + lowArg = lower(arg); + j = strmatch(lowArg,names); + if isempty(j) % if no matches + error(message('MATLAB:odeset:InvalidPropName', arg)); + elseif length(j) > 1 % if more than one match + % Check for any exact matches (in case any names are subsets of others) + k = strmatch(lowArg,names,'exact'); + if length(k) == 1 + j = k; + else + matches = deblank(Names(j(1),:)); + for k = j(2:length(j))' + matches = [matches ', ' deblank(Names(k,:))]; %#ok + end + error(message('MATLAB:odeset:AmbiguousPropName',arg,matches)); + end + end + expectval = 1; % we expect a value next + + else + options.(deblank(Names(j,:))) = arg; + expectval = 0; + + end + i = i + 1; +end + +if expectval + error(message('MATLAB:odeset:NoValueForProp', arg)); +end diff --git a/solver/odeimex.m b/solver/odeimex.m index 8177d53..ce23249 100644 --- a/solver/odeimex.m +++ b/solver/odeimex.m @@ -1,28 +1,65 @@ -function [tout,yout] = odeimex(fnlin,J,Nt,y0,options,pencil,JexMult,exsensFcn,dJdp) +function varargout = odeimex(fnlin,J,tspan,y0,options,pencil,moreoptions,JexMult,exsensFcn,dJdp) %a simplified ode solver adapted from ode15s -%the backward diffusion / NDF is applied for the linear part of the equation, in particular, the propotionality constant is J, note that J is the array the same as y0 (equivalent to diagonal) for now, in the near future, generalize J to a matrix. +%the backward diffusion / NDF is applied for the linear part of the equation, in particular, the propotionality constant is J, note that J can be an array the same as y0 (equivalent to diagonal), in this case, the mass matrix must be diagonal as well. Alternatively, J can be a matrix, in which case pencil is needed. %The nonlinear part of the equation is explicit, that is, at each time step, this term is dependent only on the previous time step. %only ODE (not DAE) is supported right now. %dy/dt = J*y + fnlin %Nt is the number of time steps %the format of yout is different from typical ode, each column corresponds to a time point given in tout, which is a column vector. -%03/25/2019, now J can be a matrix or a column vector whose size is the same as y %pencil(b,hinvGak) should return (Mt-hinvGak*J)\b %right now J is constant %the mass matrix Mt is also constant %JexMult is the multiplying function for the jacobian of the explicit term (argument: ys, t, y) %exsensFcn is the sensitivity of the explicit term %dJdp is the sensitivity of the multiplying matrix of the implicit term + +solver_name = 'ode15s'; + if nargin<5 options = []; end +if nargin<7 + moreoptions = []; +end +%output +FcnHandlesUsed = true; +haveInterpFcn = false; +output_sol = (FcnHandlesUsed && (nargout==1) && ~haveInterpFcn); % sol = odeXX(...) +output_ty = (~output_sol && (nargout > 0) && ~haveInterpFcn); % [t,y,...] = odeXX(...) +sol = []; kvec = []; dif3d = []; difs4d = []; +if output_sol + sol.solver = solver_name; + sol.extdata.odefun = ode; + sol.extdata.options = options; + sol.extdata.varargin = varargin; +end + maxk = odeget(options,'MaxOrder',5,'fast'); bdf = strcmp(odeget(options,'BDF','off','fast'),'on'); htry = abs(odeget(options,'InitialStep',[],'fast')); hmax = abs(odeget(options,'MaxStep',inf,'fast')); rtol = odeget(options,'RelTol',1e-3,'fast'); atol = odeget(options,'AbsTol',1e-6,'fast'); +Mt = odeget(options,'Mass',[],'fast'); normcontrol = strcmp(odeget(options,'NormControl','off','fast'),'on'); +%copied from odearguments +htspan = abs(tspan(2) - tspan(1)); +tspan = tspan(:); +ntspan = length(tspan); +t0 = tspan(1); +next = 2; % next entry in tspan +tfinal = tspan(end); +tdir = sign(tfinal - t0); +refine = max(1,odeget(options,'Refine',1,'fast')); +if ntspan > 2 + outputAt = 'RequestedPoints'; % output only at tspan points +elseif refine <= 1 + outputAt = 'SolverSteps'; % computed points, no refinement +else + outputAt = 'RefinedSteps'; % computed points, with refinement + S = (1:refine-1) / refine; +end +idxNonNegative = []; %Forward sensitivity analysis FSA = moreodeget(moreoptions,'FSA',false,'fast'); @@ -35,6 +72,9 @@ neq = length(y0); ninst = size(ys,2); +if isempty(Mt) + Mt = speye(neq); +end threshold = atol / rtol; if normcontrol @@ -44,16 +84,13 @@ end end -tdir = 1; -t = 0; +t = t0; y = y0; -tout = zeros(Nt,1); -yout = zeros(neq,Nt); -tout(1) = t; -yout(:,1) = y; + vectorJ = all(size(J)==size(y)); if vectorJ yp = fnlin(t,y) + J.*y; + Mtdiag = full(diag(Mt)); else yp = fnlin(t,y) + J*y; end @@ -120,10 +157,50 @@ hinvGak = h * invGa(k); nconhk = 0; % steps taken with current h and k +% Allocate memory if we're generating output. +nout = 0; +tout = []; yout = []; +ysout = []; +if nargout > 0 + if output_sol + chunk = min(max(100,50*refine), refine+floor((2^11)/neq)); + tout = zeros(1,chunk); + yout = zeros(neq,chunk); + kvec = zeros(1,chunk); + dif3d = zeros(neq,maxk+2,chunk); + if FSA + ysout = zeros(neqsout,ninst,chunk); + difs4d = zeros(neqsout,ninst,maxk+2,chunk); + end + else + if ntspan > 2 % output only at tspan points + tout = zeros(1,ntspan); + yout = zeros(neq,ntspan); + if FSA + ysout = zeros(neqsout,ninst,ntspan); + end + else % alloc in chunks + chunk = min(max(100,50*refine), refine+floor((2^13)/neq)); + tout = zeros(1,chunk); + yout = zeros(neq,chunk); + if FSA + ysout = zeros(neqsout,ninst,chunk); + end + end + end + nout = 1; + tout(nout) = t; + yout(:,nout) = y; + if FSA + ysout(:,:,nout) = ys; + end +end + % THE MAIN LOOP +done = false; at_hmin = false; -for step = 2:Nt +while ~done hmin = 16*eps(t); absh = min(hmax, max(hmin, absh)); @@ -137,6 +214,13 @@ end h = tdir * absh; + % Stretch the step if within 10% of tfinal-t. + if 1.1*absh >= abs(tfinal - t) + h = tfinal - t; + absh = abs(h); + done = true; + end + if (absh ~= abshlast) || (k ~= klast) difRU = cumprod((kI - 1 - kJ*(absh/abshlast)) ./ kI) * difU; dif(:,K) = dif(:,K) * difRU(K,K); @@ -150,10 +234,16 @@ nofailed = true; % no failed attempts fex = fnlin(t,y); % the nonlinear part is fixed in the iteration while true % Evaluate the formula. + % Compute the constant terms in the equation for ynew. psi = dif(:,K) * (G(K) * invGa(k)); + % Predict a solution at t+h. tnew = t + h; + if done + tnew = tfinal; % Hit end point exactly. + end + h = tnew - t; % Purify h. pred = y + sum(dif(:,K),2); ynew = pred; @@ -166,7 +256,7 @@ rhs = Mt*(ynew-psi) + hinvGak*fex; if vectorJ - ynew2 = rhs ./ (Mt - hinvGak*J); + ynew2 = rhs ./ (Mtdiag - hinvGak*J); else ynew2 = pencil(rhs,hinvGak); end @@ -208,7 +298,7 @@ fs = dfexdy*ys + (dJdp*ynew + sensval); rhss = Mt*(ynews-psis) + hinvGak*fs; if vectorJ - ynews2 = rhss ./ (Mt - hinvGak*J); + ynews2 = rhss ./ (Mtdiag - hinvGak*J); else ynews2 = pencil(rhss,hinvGak); end @@ -231,8 +321,10 @@ if fail if absh <= hmin warning(message('MATLAB:ode15s:IntegrationTolNotMet', sprintf( '%e', t ), sprintf( '%e', hmin ))); - tout(step:end) = []; - yout(step:end,:) = []; + solver_output = odefinalize_ez(sol,nout,tout,yout,kvec,dif3d,difs4d,idxNonNegative,ysout); + if nargout > 0 + varargout = solver_output; + end return; end @@ -277,6 +369,95 @@ dif(:,j) = dif(:,j) + dif(:,j+1); end + if output_sol + nout = nout + 1; + if nout > length(tout) + tout = [tout, zeros(1,chunk)]; % requires chunk >= refine + yout = [yout, zeros(neq,chunk)]; + kvec = [kvec, zeros(1,chunk)]; + dif3d = cat(3,dif3d, zeros(neq,maxk+2,chunk)); + if FSA + ysout = cat(3,ysout, zeros(neqsout,ninst,chunk)); + difs4d = cat(4,difs4d, zeros(neqsout,ninst,maxk+2,chunk)); + end + end + tout(nout) = tnew; + yout(:,nout) = ynew; + kvec(nout) = k; + dif3d(:,:,nout) = dif; + if FSA + ysout(:,:,nout) = ynews; + difs4d(:,:,:,nout) = difs; + end + end + + if output_ty || haveOutputFcn + switch outputAt + case 'SolverSteps' % computed points, no refinement + nout_new = 1; + tout_new = tnew; + yout_new = ynew; + if FSA + ysout_new = ynews; + end + case 'RefinedSteps' % computed points, with refinement + tref = t + (tnew-t)*S; + nout_new = refine; + tout_new = [tref, tnew]; + yout_new = [ntrp15s(tref,[],[],tnew,ynew,h,dif,k,idxNonNegative), ynew]; + if FSA + ysout_new = cat(3,ntrp15svec(tref,[],[],tnew,ynews,h,difs,k,idxNonNegative), ynews); + end + case 'RequestedPoints' % output only at tspan points + nout_new = 0; + tout_new = []; + yout_new = []; + ysout_new = []; + while next <= ntspan + if tdir * (tnew - tspan(next)) < 0 + break; + end + nout_new = nout_new + 1; + tout_new = [tout_new, tspan(next)]; + if tspan(next) == tnew + yout_new = [yout_new, ynew]; + if FSA + ysout_new = cat(3, ysout_new, ynews); + end + else + yout_new = [yout_new, ntrp15s(tspan(next),[],[],tnew,ynew,h,dif,k,... + idxNonNegative)]; + if FSA + ysout_new = cat(3, ysout_new, ntrp15svec(tspan(next),[],[],tnew,ynews,h,difs,k,... + idxNonNegative)); + end + end + next = next + 1; + end + end + + if nout_new > 0 + if output_ty + oldnout = nout; + nout = nout + nout_new; + if nout > length(tout) + tout = [tout, zeros(1,chunk)]; % requires chunk >= refine + yout = [yout, zeros(neq,chunk)]; + if FSA + ysout = cat(3, ysout, zeros(neqsout,ninst,chunk)); + end + end + idx = oldnout+1:nout; + tout(idx) = tout_new; + yout(:,idx) = yout_new; + if FSA + ysout(:,:,idx) = ysout_new; + end + end + end + end + + klast = k; abshlast = absh; nconhk = min(nconhk+1,maxk+2); @@ -342,6 +523,36 @@ normys = normynews; end end - tout(step) = t; - yout(:,step) = y; +end + +solver_output = odefinalize_ez(sol,nout,tout,yout,kvec,dif3d,difs4d,idxNonNegative,ysout); +if nargout > 0 + varargout = solver_output; +end +end + + +function solver_output = odefinalize_ez(sol,nout,tout,yout,kvec,dif3d,difs4d,idxNonNegative,ysout) + solver_output = {}; + if (nout > 0) % produce output + if isempty(sol) % output [t,y,...] + solver_output{1} = tout(1:nout).'; + solver_output{2} = yout(:,1:nout); + if ~isempty(ysout) + solver_output{3} = permute(ysout(:,:,1:nout),[3,1,2]); + end + else % output sol + % Add remaining fields + sol.x = tout(1:nout); + sol.y = yout(:,1:nout); + sol.idata.kvec = kvec(1:nout); + maxkvec = max(sol.idata.kvec); + sol.idata.dif3d = dif3d(:,1:maxkvec+2,1:nout); + if ~isempty(difs4d) + sol.idata.difs4d = difs4d(:,:,1:maxkvec+2,1:nout); + end + sol.idata.idxNonNegative = idxNonNegative; + solver_output{1} = sol; + end + end end From 622831ca858ee022cce833120c48032fa5d7d95d Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Mon, 1 Jul 2019 19:58:52 -0400 Subject: [PATCH 025/149] add InterpFcn in odeimex and add ntrp15s --- solver/ntrp15s.m | 64 ++++++++++++++++++++++++++++++++++++++++++++++++ solver/odeimex.m | 22 ++++++++++++++++- 2 files changed, 85 insertions(+), 1 deletion(-) create mode 100644 solver/ntrp15s.m diff --git a/solver/ntrp15s.m b/solver/ntrp15s.m new file mode 100644 index 0000000..3276524 --- /dev/null +++ b/solver/ntrp15s.m @@ -0,0 +1,64 @@ +function [yinterp,ypinterp] = ntrp15s(tinterp,~,~,tnew,ynew,h,dif,k,idxNonNegative) +%NTRP15S Interpolation helper function for ODE15S. +% YINTERP = NTRP15S(TINTERP,T,Y,TNEW,YNEW,H,DIF,K,IDX) uses data computed in +% ODE15S to approximate the solution at time TINTERP. TINTREP may be a +% scalar or a row vector. +% The arguments T and Y do not affect the computations. They are required +% for consistency of syntax with other interpolation functions. Any values +% entered for T and Y are ignored. +% +% [YINTERP,YPINTERP] = NTRP15S(TINTERP,T,Y,TNEW,YNEW,H,DIF,K,IDX) returns +% also the derivative of the polynomial approximating the solution. +% +% IDX has indices of solution components that must be non-negative. Negative +% YINTERP(IDX) are replaced with zeros and the derivative YPINTERP(IDX) is +% set to zero. +% +% See also ODE15S, DEVAL. + +% Mark W. Reichelt and Lawrence F. Shampine, 6-13-94 +% Copyright 1984-2009 The MathWorks, Inc. + +s = (tinterp - tnew)/h; + +ypinterp = []; +if k == 1 + yinterp = ynew(:,ones(size(tinterp))) + dif(:,1) * s; + if nargout > 1 + hdif = (1/h)*dif(:,1); + ypinterp = hdif(:,ones(size(tinterp))); + end +else % cumprod collapses vectors + K = (1:k)'; + kI = K(:,ones(size(tinterp))); + yinterp = ynew(:,ones(size(tinterp))) + ... + dif(:,K) * cumprod((s(ones(k,1),:)+kI-1)./kI); + + if nargout > 1 + ypinterp = dif(:,ones(size(tinterp))); + S = ones(size(tinterp)); + dS = ones(size(tinterp)); + for i=2:k + S = S .* (i-2+s)/i; + dS = dS .* (i-1+s)/i + S; + ypinterp = ypinterp + dif(:,i)*dS; + end + ypinterp = ypinterp/h; + end + +end + +% Non-negative solution +if ~isempty(idxNonNegative) + idx = find(yinterp(idxNonNegative,:)<0); % vectorized + if ~isempty(idx) + w = yinterp(idxNonNegative,:); + w(idx) = 0; + yinterp(idxNonNegative,:) = w; + if nargout > 1 % the derivative + w = ypinterp(idxNonNegative,:); + w(idx) = 0; + ypinterp(idxNonNegative,:) = w; + end + end +end diff --git a/solver/odeimex.m b/solver/odeimex.m index ce23249..87c8d21 100644 --- a/solver/odeimex.m +++ b/solver/odeimex.m @@ -13,7 +13,6 @@ %exsensFcn is the sensitivity of the explicit term %dJdp is the sensitivity of the multiplying matrix of the implicit term -solver_name = 'ode15s'; if nargin<5 options = []; @@ -69,6 +68,10 @@ if isempty(ys) || isempty(ysp) FSA = false; end +interpFcn = moreodeget(moreoptions,'interpFcn',[],'fast'); +haveInterpFcn = ~isempty(interpFcn); +%usage: initialize if flag = 'init', while all the other arguments are empty. At the end of each time step taken by the solver, the input to interpFcn is flag = '',info,tnew,ynew,h,dif,k,idxNonNegative, everything needed to do interpolationm the output of interpFcn is info. Note that info is passed from one time step to another and is the output of myode15s varargout. When successfully finalizing, the flag is 'done', when the solver fails, the flag is 'fail', both with the same inputs as before. +%note that if haveInterpFcn, the output will be the output of interpFcn when flag is done, no t, or y or sol wil be outputted! neq = length(y0); ninst = size(ys,2); @@ -196,6 +199,10 @@ end end +if haveInterpFcn + interp_info = feval(interpFcn,'init',[],[],[],[],[],[],[]); +end + % THE MAIN LOOP done = false; @@ -321,6 +328,11 @@ if fail if absh <= hmin warning(message('MATLAB:ode15s:IntegrationTolNotMet', sprintf( '%e', t ), sprintf( '%e', hmin ))); + if haveInterpFcn + interp_info = feval(interpFcn,'fail',interp_info,tnew,ynew,h,dif,k,idxNonNegative); + varargout = interp_info; + return; + end solver_output = odefinalize_ez(sol,nout,tout,yout,kvec,dif3d,difs4d,idxNonNegative,ysout); if nargout > 0 varargout = solver_output; @@ -457,6 +469,9 @@ end end + if haveInterpFcn + interp_info = feval(interpFcn,'',interp_info,tnew,ynew,h,dif,k,idxNonNegative); + end klast = k; abshlast = absh; @@ -525,6 +540,11 @@ end end +if haveInterpFcn + interp_info = feval(interpFcn,'done',interp_info,tnew,ynew,h,dif,k,idxNonNegative); + varargout = interp_info; + return; +end solver_output = odefinalize_ez(sol,nout,tout,yout,kvec,dif3d,difs4d,idxNonNegative,ysout); if nargout > 0 varargout = solver_output; From b97029407a16a0c3ab6329224344a603f3136174 Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Mon, 1 Jul 2019 19:58:58 -0400 Subject: [PATCH 026/149] test another kernel --- solver/DDFT.m | 17 ++++++++++++++--- 1 file changed, 14 insertions(+), 3 deletions(-) diff --git a/solver/DDFT.m b/solver/DDFT.m index 74e36ba..357c076 100644 --- a/solver/DDFT.m +++ b/solver/DDFT.m @@ -20,13 +20,24 @@ [k2,k] = formk(N,L); k2 = k2(:); +kind1 = k{1}; kind2 = k{2}; +[kind1,kind2] = ndgrid(kind1(:),kind2(:)); +theta = angle(kind1+i*kind2); + +theta = theta(:); + k0 = 10; alpha = 2; C2 = exp(-(sqrt(k2)-k0).^2/(2*alpha^2)); -J = -k2.*(-C2); +C22 = C2; +% C22 = C2 .* (1+cos(theta))/2; +% C22 = C2 .* (exp(-(theta-pi/2).^2/(2*(50/180*pi)^2))+exp(-(theta+pi/2).^2/(2*(50/180*pi)^2)))/2; +J = -k2.*(-C22); -tspan = linspace(0,1.1,100); +tspan = linspace(0,0.14,100); +tspan = [0,1.1]; +% tspan = [0,0.14]; options = odeset('AbsTol',1e-3); [tout,yout] = odeimex(@(t,y) DDFT_nlin(t,y,k2,N),J,tspan,y0); -k2real(yout(:,end),N); +figure; k2real(yout(:,end),N); From c1f2076fe5a6a15e5800f8aec90647c0a3eed4db Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Tue, 2 Jul 2019 19:51:55 -0400 Subject: [PATCH 027/149] create a nucleus from DDFT --- solver/DDFT_nucleus.m | 51 +++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 51 insertions(+) create mode 100644 solver/DDFT_nucleus.m diff --git a/solver/DDFT_nucleus.m b/solver/DDFT_nucleus.m new file mode 100644 index 0000000..66105e7 --- /dev/null +++ b/solver/DDFT_nucleus.m @@ -0,0 +1,51 @@ +%parameter search +L = [5,5]*2; +N = [256,256]; +n = prod(N); +n0 = 0.07; +sigma = 0.01; + +rng(1); +n0 = n0 + sigma*randn(N); +y0 = fftn(n0); +y0 = y0(:); + + +[k2,k] = formk(N,L); +k2 = k2(:); +kind1 = k{1}; kind2 = k{2}; +[kind1,kind2] = ndgrid(kind1(:),kind2(:)); +theta = angle(kind1+i*kind2); + +theta = theta(:); + +k0 = 10; +alpha = 2; +C2 = exp(-(sqrt(k2)-k0).^2/(2*alpha^2)); +J = -k2.*(-C2); + +tspan = linspace(0,1.08,100); +options = odeset('AbsTol',1e-3); +[tout,yout] = odeimex(@(t,y) DDFT_nlin(t,y,k2,N),J,tspan,y0); + +y0 = ifftn(reshape(yout(:,end),N)); + +xx = linspace(0,L(1),N(1)); +yy = linspace(0,L(2),N(2)); +[xx,yy] = meshgrid(xx,yy); + +roi = 1./(1+exp(-(xx-0.64*L(1))/0.1)) .* 1./(1+exp((yy-0.4*L(2))/0.1)); +rho = (sum(y0(:)) - sum(roi(:).*y0(:))) / sum(1-roi(:)); +y0new = roi.*y0 + (1-roi)*rho; +%interpolate +y0new = imresize(y0new,2); +y0new = fftn(y0new); +y0new = y0new(:); +N = [256,256]*2; +figure; k2real(y0new,N); + +save('DDFT_nucleus','y0new'); + +tspan2 = linspace(0,1,100); +options = odeset('AbsTol',1e-3); +[tout2,yout2] = odeimex(@(t,y) DDFT_nlin(t,y,k2,N),J,tspan2,y0new); From 530756e2807665f9a4cbb4a82e35e8e11face709 Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Tue, 2 Jul 2019 19:52:09 -0400 Subject: [PATCH 028/149] start working on Krylov-based DDFT solver --- solver/solver_DDFT.m | 64 ++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 64 insertions(+) create mode 100644 solver/solver_DDFT.m diff --git a/solver/solver_DDFT.m b/solver/solver_DDFT.m new file mode 100644 index 0000000..8f09128 --- /dev/null +++ b/solver/solver_DDFT.m @@ -0,0 +1,64 @@ +function solver_DDFT() +%in order to be consistent with formk, the first dimension is x and the second dimension is y + +%Finite differencing operator in real space +I = speye(n,n); +E = sparse(2:n,1:n-1,1,n,n); +D = E+E'-2*I; +%circulant D, periodic boundary condition +D(1,n) = 1; +D(n,1) = 1; +L = kron(D,I)+kron(I,D); +%Finite differencing operator in Fourier space +Lconv = [zeros(1,3); 1,-2,1; zeros(1,3)]/dx(2)^2 + [zeros(3,1), [1;-2;1], zeros(3,1)]/dx(1)^2; +LK = psf2otf(Lconv,N); + +end + +function dy = RHS(t,y,N,dx,C) + %C should be 2D, same below + y = reshape(y,N); + mu = log(1+y); + mu = mu - ifftn(C .* fftn(y)); + dy = 0; + for i = 1:length(N) + dy = dy + (circshift(mu,1,i)+circshift(mu,-1,i)-2*mu)/dx(i)^2; + end +end + +function dfdy = jacobian(t,y) + %this only computes the nonlinear part, as an input to KrylovDecomp + dfdy = 1./(1-y); + +end + +function Pargs = KrylovDecomp(L,Mt,dMpsidy,dfdy,hinvGak) + %here dfdy comes from Jacobian + %L is the finite-difference Laplacian operator + n = length(L); + J = speye(n) - hinvGak*L.*sparse(1:n,1:n,dfdy); + [L,U] = ilu(J); + Pargs = {L,U}; +end + +function yy = KrylovPrecon(LK,N,C,x,L,U,hinvGak,~,~,~) + %LK is the Fourier transform of the finite difference Laplacian operator + x = reshape(x,N); + yy = ifft( fft(x) ./ (1 + hinvGak*LK.*C) ); + yy = U \ (L \ yy); +end + +function yy = pencil(N,C,xi,t,y,hinvGak,info) + if isempty(info) + yy = 1./(1-y); + else + xi = reshape(xi,N); + dfdy = info; + mu = dfdy .* xi; + mu = mu - ifftn(C .* fftn(y)); + yy = 0; + for i = 1:length(N) + yy = dy + (circshift(mu,1,i)+circshift(mu,-1,i)-2*mu)/dx(i)^2; + end + end +end From 91131e4a1798e1ad7d3bc0130f7a554416948a99 Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Wed, 3 Jul 2019 01:19:58 -0400 Subject: [PATCH 029/149] updaet solver_DDFT, and moreode*, seems to work --- solver/moreodeget.m | 2 ++ solver/moreodeset.m | 4 +++ solver/solver_DDFT.m | 86 +++++++++++++++++++++++++++++++++++--------- 3 files changed, 75 insertions(+), 17 deletions(-) diff --git a/solver/moreodeget.m b/solver/moreodeget.m index 7579806..6ca29cd 100644 --- a/solver/moreodeget.m +++ b/solver/moreodeget.m @@ -60,6 +60,8 @@ 'interpFcn ' 'jacMult ' 'Krylov ' + 'KrylovDecomp ' + 'KrylovPrecon ' 'linear ' 'linearMult ' 'maxit ' diff --git a/solver/moreodeset.m b/solver/moreodeset.m index c441646..6c839f3 100644 --- a/solver/moreodeset.m +++ b/solver/moreodeset.m @@ -141,6 +141,8 @@ fprintf(' interpFcn: [ {[]} | function handle ]\n'); fprintf(' jacMult: [ {[]} | function handle ]\n'); fprintf(' Krylov: [ {false} | true ]\n'); + fprintf(' KrylovDecomp: [ {[]} | function handle ]\n'); + fprintf(' KrylovPrecon: [ {[]} | function handle ]\n'); fprintf(' linear: [ {false} | true ]\n'); fprintf(' linearMult: [ {[]} | function handle ]\n'); fprintf(' maxit: [ {4 ~blockIter, 10 blockIter} | integer ]\n'); @@ -173,6 +175,8 @@ 'interpFcn ' 'jacMult ' 'Krylov ' + 'KrylovDecomp ' + 'KrylovPrecon ' 'linear ' 'linearMult ' 'maxit ' diff --git a/solver/solver_DDFT.m b/solver/solver_DDFT.m index 8f09128..c7622d0 100644 --- a/solver/solver_DDFT.m +++ b/solver/solver_DDFT.m @@ -1,38 +1,76 @@ function solver_DDFT() +addpath('../../CHACR/odesolver') %in order to be consistent with formk, the first dimension is x and the second dimension is y +N = [128,128]*2; +L = [5,5]; +dx = L./N; +n = prod(N); +n0 = 0.1; +sigma = 0.01; +rng(1); +y0 = n0 + sigma*randn(N); +y0 = y0(:); +[k2,k] = formk(N,L); +k0 = 10; +alpha = 2; +C = exp(-(sqrt(k2)-k0).^2/(2*alpha^2))*0.95; +tspan = linspace(0,4,100); +% tspan = [0,2]; +t0 = tspan(1); %Finite differencing operator in real space -I = speye(n,n); -E = sparse(2:n,1:n-1,1,n,n); -D = E+E'-2*I; -%circulant D, periodic boundary condition -D(1,n) = 1; -D(n,1) = 1; -L = kron(D,I)+kron(I,D); +for i = 1:2 + NI = N(3-i); + ND = N(i); + I = speye(NI); + E = sparse(2:ND,1:ND-1,1,ND,ND); + D = E+E'-2*I; + %circulant D, periodic boundary condition + D(1,ND) = 1; + D(ND,1) = 1; + if i==1 + L = kron(I,D)/dx(i)^2; + else + L = L + kron(D,I)/dx(i)^2; + end +end %Finite differencing operator in Fourier space Lconv = [zeros(1,3); 1,-2,1; zeros(1,3)]/dx(2)^2 + [zeros(3,1), [1;-2;1], zeros(3,1)]/dx(1)^2; LK = psf2otf(Lconv,N); +yp0 = RHS(t0,y0,N,dx,C); +options = odeset('InitialSlope',yp0,'Jacobian',@jacobian); +moreoptions = moreodeset('skipInit',true,'Krylov',true, ... +'pencil',@(xi,t,y,hinvGak,info) pencil(N,dx,C,xi,t,y,hinvGak,info), ... +'KrylovDecomp',@(~,~,dfdy,hinvGak) KrylovDecomp(L,dfdy,hinvGak), ... +'KrylovPrecon',@(x,L,U,hinvGak,~,~,~) KrylovPrecon(LK,N,C,x,L,U,hinvGak),... +'jacMult',@(xi,t,y,info) jacobian_mult(N,dx,C,xi,t,y,info),... +'gmrestol',1e-3); + +[t,y] = myode15s(@(t,y) RHS(t,y,N,dx,C),tspan,y0,options,moreoptions); + end function dy = RHS(t,y,N,dx,C) %C should be 2D, same below y = reshape(y,N); - mu = log(1+y); +% mu = log(1+y); + mu = y - y.^2/2 + y.^3/3; mu = mu - ifftn(C .* fftn(y)); dy = 0; for i = 1:length(N) dy = dy + (circshift(mu,1,i)+circshift(mu,-1,i)-2*mu)/dx(i)^2; end + dy = dy(:); end function dfdy = jacobian(t,y) %this only computes the nonlinear part, as an input to KrylovDecomp - dfdy = 1./(1-y); - +% dfdy = 1./(1+y); + dfdy = 1 - y + y.^2; end -function Pargs = KrylovDecomp(L,Mt,dMpsidy,dfdy,hinvGak) +function Pargs = KrylovDecomp(L,dfdy,hinvGak) %here dfdy comes from Jacobian %L is the finite-difference Laplacian operator n = length(L); @@ -41,24 +79,38 @@ function solver_DDFT() Pargs = {L,U}; end -function yy = KrylovPrecon(LK,N,C,x,L,U,hinvGak,~,~,~) +function yy = KrylovPrecon(LK,N,C,x,L,U,hinvGak) %LK is the Fourier transform of the finite difference Laplacian operator x = reshape(x,N); yy = ifft( fft(x) ./ (1 + hinvGak*LK.*C) ); + yy = yy(:); yy = U \ (L \ yy); end -function yy = pencil(N,C,xi,t,y,hinvGak,info) - if isempty(info) - yy = 1./(1-y); +function yy = jacobian_mult(N,dx,C,xi,t,y,info) + if isequal(info,'force') + yy = jacobian_mult(N,dx,C,xi,t,y,[]); + yy = jacobian_mult(N,dx,C,xi,t,y,yy); + elseif isempty(info) +% yy = 1./(1+y); + yy = 1 - y + y.^2; + yy = reshape(yy,N); else xi = reshape(xi,N); dfdy = info; mu = dfdy .* xi; - mu = mu - ifftn(C .* fftn(y)); + mu = mu - ifftn(C .* fftn(xi)); yy = 0; for i = 1:length(N) - yy = dy + (circshift(mu,1,i)+circshift(mu,-1,i)-2*mu)/dx(i)^2; + yy = yy + (circshift(mu,1,i)+circshift(mu,-1,i)-2*mu)/dx(i)^2; end + yy = yy(:); + end +end + +function yy = pencil(N,dx,C,xi,t,y,hinvGak,info) + yy = jacobian_mult(N,dx,C,xi,t,y,info); + if ~isempty(info) + yy = xi - hinvGak*yy; end end From e2ba7a568c77a588ed199a9aeeb9660c11e728d8 Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Wed, 3 Jul 2019 18:33:13 -0400 Subject: [PATCH 030/149] update solver_DDFT --- solver/solver_DDFT.m | 136 +++++++++++++++++++++++++++++++------------ 1 file changed, 99 insertions(+), 37 deletions(-) diff --git a/solver/solver_DDFT.m b/solver/solver_DDFT.m index c7622d0..b83a481 100644 --- a/solver/solver_DDFT.m +++ b/solver/solver_DDFT.m @@ -1,21 +1,51 @@ -function solver_DDFT() +function [t,y,params] = solver_DDFT(tspan,y0,params) addpath('../../CHACR/odesolver') %in order to be consistent with formk, the first dimension is x and the second dimension is y -N = [128,128]*2; -L = [5,5]; -dx = L./N; -n = prod(N); -n0 = 0.1; -sigma = 0.01; -rng(1); -y0 = n0 + sigma*randn(N); -y0 = y0(:); -[k2,k] = formk(N,L); -k0 = 10; -alpha = 2; -C = exp(-(sqrt(k2)-k0).^2/(2*alpha^2))*0.95; -tspan = linspace(0,4,100); -% tspan = [0,2]; +if ~isfield(params,'dx') && isfield(params,'N') && isfield(params,'L') + params.dx = params.L ./ params.N; +elseif ~isfield(params,'N') && isfield(params,'dx') && isfield(params,'L') + params.N = params.L ./ params.dx; +elseif ~isfield(params,'L') && isfield(params,'N') && isfield(params,'dx') + params.L = params.N .* params.dx; +elseif ~all(isfield(params,{'dx','N','L'})) + params.N = [128,128]; + params.L = [5,5]; + params.dx = params.L./params.N; +end +n = prod(params.N); +N = params.N; +L = params.L; +dx = params.dx; +if ~isfield(params,'C') + %default + [k2,k] = formk(N,L); + k0 = 10; + alpha = 2; + params.C = exp(-(sqrt(k2)-k0).^2/(2*alpha^2))*0.95; +end +if ~isfield(params,'mu') + params.mu.func = @(x,coeff) x - x.^2/2 + x.^3/3; %@(x) log(1+x) + params.mu.grad = @(x,coeff) 1 - x + x.^2; + params.mu.params = []; +end +% mu.func = @(x,coeff) log((1+x)./(1-x))/2; +% mu.grad = @(x,coeff) 1./(1-x.^2); +% mu.params = []; +if isempty(y0) || isscalar(y0) + %initialization + if isempty(y0) + n0 = 0.1; + else + n0 = y0; + end + sigma = 0.01; + rng(1); + y0 = n0 + sigma*randn(N); + y0 = y0(:); +end +if isempty(tspan) + tspan = linspace(0,4,100); +end t0 = tspan(1); %Finite differencing operator in real space @@ -38,24 +68,26 @@ function solver_DDFT() Lconv = [zeros(1,3); 1,-2,1; zeros(1,3)]/dx(2)^2 + [zeros(3,1), [1;-2;1], zeros(3,1)]/dx(1)^2; LK = psf2otf(Lconv,N); -yp0 = RHS(t0,y0,N,dx,C); -options = odeset('InitialSlope',yp0,'Jacobian',@jacobian); +yp0 = RHS(t0,y0,params); +options = odeset('InitialSlope',yp0,'Jacobian',@(t,y) jacobian(t,y,params)); moreoptions = moreodeset('skipInit',true,'Krylov',true, ... -'pencil',@(xi,t,y,hinvGak,info) pencil(N,dx,C,xi,t,y,hinvGak,info), ... +'pencil',@(xi,t,y,hinvGak,info) pencil(params,xi,t,y,hinvGak,info), ... 'KrylovDecomp',@(~,~,dfdy,hinvGak) KrylovDecomp(L,dfdy,hinvGak), ... -'KrylovPrecon',@(x,L,U,hinvGak,~,~,~) KrylovPrecon(LK,N,C,x,L,U,hinvGak),... -'jacMult',@(xi,t,y,info) jacobian_mult(N,dx,C,xi,t,y,info),... +'KrylovPrecon',@(x,L,U,hinvGak,~,~,~) KrylovPrecon(LK,params,x,L,U,hinvGak),... +'jacMult',@(xi,t,y,info) jacobian_mult(params,xi,t,y,info),... 'gmrestol',1e-3); -[t,y] = myode15s(@(t,y) RHS(t,y,N,dx,C),tspan,y0,options,moreoptions); +[t,y] = myode15s(@(t,y) RHS(t,y,params),tspan,y0,options,moreoptions); end -function dy = RHS(t,y,N,dx,C) +function dy = RHS(t,y,params) %C should be 2D, same below + N = params.N; + dx = params.dx; + C = params.C; y = reshape(y,N); -% mu = log(1+y); - mu = y - y.^2/2 + y.^3/3; + mu = customizeFunGrad(params,'mu','fun',y); mu = mu - ifftn(C .* fftn(y)); dy = 0; for i = 1:length(N) @@ -64,10 +96,9 @@ function solver_DDFT() dy = dy(:); end -function dfdy = jacobian(t,y) +function dfdy = jacobian(t,y,params) %this only computes the nonlinear part, as an input to KrylovDecomp -% dfdy = 1./(1+y); - dfdy = 1 - y + y.^2; + dfdy = customizeFunGrad(params,'mu','grad',y); end function Pargs = KrylovDecomp(L,dfdy,hinvGak) @@ -79,23 +110,27 @@ function solver_DDFT() Pargs = {L,U}; end -function yy = KrylovPrecon(LK,N,C,x,L,U,hinvGak) +function yy = KrylovPrecon(LK,params,x,L,U,hinvGak) %LK is the Fourier transform of the finite difference Laplacian operator + N = params.N; + C = params.C; x = reshape(x,N); yy = ifft( fft(x) ./ (1 + hinvGak*LK.*C) ); yy = yy(:); yy = U \ (L \ yy); end -function yy = jacobian_mult(N,dx,C,xi,t,y,info) +function yy = jacobian_mult(params,xi,t,y,info) if isequal(info,'force') - yy = jacobian_mult(N,dx,C,xi,t,y,[]); - yy = jacobian_mult(N,dx,C,xi,t,y,yy); + yy = jacobian_mult(params,xi,t,y,[]); + yy = jacobian_mult(params,xi,t,y,yy); elseif isempty(info) -% yy = 1./(1+y); - yy = 1 - y + y.^2; - yy = reshape(yy,N); + yy = customizeFunGrad(params,'mu','grad',y); + yy = reshape(yy,params.N); else + N = params.N; + dx = params.dx; + C = params.C; xi = reshape(xi,N); dfdy = info; mu = dfdy .* xi; @@ -108,9 +143,36 @@ function solver_DDFT() end end -function yy = pencil(N,dx,C,xi,t,y,hinvGak,info) - yy = jacobian_mult(N,dx,C,xi,t,y,info); +function yy = pencil(params,xi,t,y,hinvGak,info) + yy = jacobian_mult(params,xi,t,y,info); if ~isempty(info) yy = xi - hinvGak*yy; end end + +function varargout = customizeFunGrad(customize,name,request,varargin) + %allow func to output both fun and grad eval + %request can be 'fun','grad',or 'fungrad', and the output will be the requested evaluation in the corresponding order. + %evaluate fun and grad from func function at the same time if grad doesn't exist + funstr = customize.(name); + params = funstr.params; + fungrad = (~isfield(funstr,'grad')); + if fungrad + [fun,grad] = funstr.func(varargin{:},params); + else + if isequal(request,'fun') || isequal(request,'fungrad') + fun = funstr.func(varargin{:},params); + end + if isequal(request,'grad') || isequal(request,'fungrad') + grad = funstr.grad(varargin{:},params); + end + end + switch request + case 'fun' + varargout = {fun}; + case 'grad' + varargout = {grad}; + case 'fungrad' + varargout = {fun,grad}; + end +end From bcfb49b62b41945a7c323273a178d1b4230c1576 Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Wed, 3 Jul 2019 18:33:24 -0400 Subject: [PATCH 031/149] roi diffuse shape function --- solver/roi_circle.m | 30 ++++++++++++++++++++++++++++++ solver/roi_rectangle.m | 23 +++++++++++++++++++++++ 2 files changed, 53 insertions(+) create mode 100644 solver/roi_circle.m create mode 100644 solver/roi_rectangle.m diff --git a/solver/roi_circle.m b/solver/roi_circle.m new file mode 100644 index 0000000..c4d95f8 --- /dev/null +++ b/solver/roi_circle.m @@ -0,0 +1,30 @@ +function roi = roi_circle(xx,yy,center,radius,d,operation) + %a diffuse shape function for union and intersection of circles, whose centers (N*2) and radii (N*1 or 1*N) are listed as arrays. + %xx and yy can be 1D array in different directions or matrices of the same size + %d is the diffuse layer thickness, it can be a scalar or two element for x and y directions + %operation takes the roi of each circle as input and operate on it + %if operation is not provided, we take the union (sum) + N = size(center,1); + if isscalar(d) + d = d*ones(1,N); + end + union = (nargin < 6) || isempty(operation); + + for i = 1:N + r = sqrt((xx-center(i,1)).^2 + (yy-center(i,2)).^2); + roi_i = 1./(1 + exp((r - radius(i))/d(i))); + if union + if i == 1 + roi = roi_i; + else + roi = max((roi + roi_i),1); %union operator + end + else + roi_out{i} = roi_i; + end + end + + if ~union + roi = feval(operation,roi_out{:}); + end +end diff --git a/solver/roi_rectangle.m b/solver/roi_rectangle.m new file mode 100644 index 0000000..4767605 --- /dev/null +++ b/solver/roi_rectangle.m @@ -0,0 +1,23 @@ +function roi = roi_rectangle(xx,yy,xrange,yrange,d) + %a diffuse shape function for a rectangle, x > xrange(1), x < xrange(2), y > yrange(1), y < yrange(2) + %use Inf or NaN to indicate no bound + %xx and yy are arrays of the same size + %d is the diffuse layer thickness, it can be a scalar or two element for x and y directions + if isscalar(d) + d = [d,d]; + end + roi = ones(size(xx)); + for i = 1:2 + center = xrange(i); + if isfinite(center) + s = 2*i-3; + roi = roi.*(1./(1+exp(s*(xx-center)/d(1)))); + end + end + for i = 1:2 + center = yrange(i); + if isfinite(center) + s = 2*i-3; + roi = roi.*(1./(1+exp(s*(yy-center)/d(2)))); + end + end From 0366d53c45a4dd138a6bd708b99e459626c2daf9 Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Wed, 3 Jul 2019 18:33:38 -0400 Subject: [PATCH 032/149] DDFT_nucleation study nucleation --- solver/DDFT_nucleation.m | 32 ++++++++++++++++++++++++++++++++ 1 file changed, 32 insertions(+) create mode 100644 solver/DDFT_nucleation.m diff --git a/solver/DDFT_nucleation.m b/solver/DDFT_nucleation.m new file mode 100644 index 0000000..f8b99ff --- /dev/null +++ b/solver/DDFT_nucleation.m @@ -0,0 +1,32 @@ +%parameter search +L = [5,5]; +N = [256,256]; +n = prod(N); + +params.N = N; +params.L = L; + +[t1,y1,params] = solver_DDFT([],[],params); + +xx = linspace(0,L(1),N(1)); +yy = linspace(0,L(2),N(2)); +[xx,yy] = ndgrid(xx,yy); +range = [1.5,3.5]; +thickness = 0.1; +roi = roi_rectangle(xx,yy,range,range,thickness); +center = L/2; +radius = 0.18*L(1); +thickness = 0.01*L(1); +roi = roi_circle(xx,yy,center,radius,thickness); + +%nucleus +y0 = y1(end,:)'; +roi = roi(:); +rho = (sum(y0) - sum(roi.*y0)) / sum(1-roi); +y0 = roi.*y0 + (1-roi)*rho; +figure; imagesc(reshape(y0,N)); + +tspan2 = linspace(0,0.4,100); +[t2,y2] = solver_DDFT(tspan2,y0,params); + +figure; visualize([],[],[],y2(1:10:end,:),'c',false,'ImageSize',N); From 7ea11aa826f0479262e6fcd74b07222ffb6c3b5f Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Sat, 6 Jul 2019 00:53:49 -0400 Subject: [PATCH 033/149] work on solver_DDFT and IP_DDFT --- solver/IP_DDFT.m | 126 ++++++++++++++++++++++++ solver/solver_DDFT.m | 224 +++++++++++++++++++++++++++++++++++++------ 2 files changed, 320 insertions(+), 30 deletions(-) create mode 100644 solver/IP_DDFT.m diff --git a/solver/IP_DDFT.m b/solver/IP_DDFT.m new file mode 100644 index 0000000..5889be5 --- /dev/null +++ b/solver/IP_DDFT.m @@ -0,0 +1,126 @@ +function x_opt = IP_DDFT(tdata,ydata,params) +addpath('../../CHACR/GIP') + +% params.N = [256,256]; +% params.L = [5,5]; +% params.dx = params.L ./ params.N; +kernelSize = [21,21]; +NC = floor((prod(kernelSize)+1)/2); +meta.C.index = 1:NC; +meta.C.exp = false; +Cspace = 'k'; +params.Csens = @(y) Csens(y,Cspace,kernelSize); +x_guess = zeros(1,NC); + +tspan = 100; +loss = @(y,ydata,~) MSE(y,ydata,prod(params.dx)); +lossHess = @(dy,~,~) MSE([],[],prod(params.dx),dy); +options = optimoptions('fminunc','SpecifyObjectiveGradient',true,'Display','iter-detailed'); + +x_opt = fminunc(@(x) IP(tdata,ydata,x,meta,params, ... +@(tdata,y0,FSA,meta,params) forwardSolver(tdata,y0,FSA,meta,params,tspan), ... +@adjointSolver, ... +loss,lossHess, ... +@(name,xparam,params) assign(name,xparam,params,Cspace,kernelSize)), ... +x_guess, options); + +end + +function params = assign(name,xparam,params,Cspace,kernelSize) + switch name + case 'mu' + params.(name).params = xparam; + case 'C' + %xparam for C is cut in half due to symmetry. + %For the purpose of symmetry, we require that the kernel size be odd in both dimensions + %if a kernel size is even, it is not a symmetric convolution + %If the size of the kernel provided is N(1)*N(2), then the size of xparam is n = floor((prod(N)+1)/2) + %xparam correspond to the first n in the kernel in linear index, + %the rest is obtained using symmetry. This applies to both real space and k space + %Both real space and k space representation is centered at the kernel center (not 1,1) + %but it must be converted to be centered at 1,1 in the k-space representation used in DDFT solver + %consider other extensions: + %1. Reduce to representing 1D C(k) if it's axisymmetric + if any(mod(kernelSize,2)==0) + error('kernel size must be odd'); + end + n = length(xparam); + if n ~= floor((prod(kernelSize)+1)/2) + error('kernel size incompatible with C input'); + end + %note that n is odd + C = xparam(:); + %symmetry condition + C = [C; flip(C(1:end-1))]; + C = reshape(C, kernelSize); + switch Cspace + case 'k' + % Circularly shift so that the "center" of the OTF is at the + % (1,1) element of the array. (from psf2otf) + padSize = params.N - kernelSize; + C = padarray(C, padSize, 'post'); + C = circshift(C,-floor(kernelSize/2)); + params.C = C; + case 'real' + params.C = psf2otf(C); + end + end +end + +function [tout,y,dy,params] = forwardSolver(tdata,y0,FSA,meta,params,tspan) + %tspan can either be sol or number of time points + if isequal(tspan,'sol') + sol = true; + else + sol = false; + tdata = linspace(tdata(1),tdata(end),tspan); + end + [tout,y,params,dy] = solver_DDFT(tdata,y0,params,meta,'forward',sol,FSA); +end + +function grad = adjointSolver(tdata,sol,lossgrad,meta,discrete,~,params) + grad = solver_DDFT(tdata,sol,params,meta,'adjoint',lossgrad,discrete); +end + +function dy = Csens(y,Cspace,kernelSize) + %Csens takes up a lot of memory!! Csens is now a function handle for multiplying the sensitivity of C with a vector y. (dy = dC * y) Note that y should in the image format and in real space. + %the returned dy has the dimension of size(y,1)*size(y,2)*number of parameters + %for example, if real space representation is used, use circshift, in sensFcn, + %if k space representation is used, for C(k), the sensitivity of -mu is y(k)exp(ikx)+y(-k)exp(-ikx) + %since y is real, this is equal to 2Re(y(k)exp(ikx)) + %again, note that kernelSize must be odd + n = floor((prod(kernelSize)+1)/2); + kernelCenter = ceil(kernelSize/2); + dy = zeros([size(y),n]); + if isequal(Cspace,'k') + imageSize = size(y); + y = fftn(y); + [p1,p2] = ndgrid(0:(imageSize(1)-1),0:(imageSize(2)-1)); + p1 = p1/imageSize(1); + p2= p2/imageSize(2); + end + for i = 1:n + [ind(1),ind(2)] = ind2sub(kernelSize,i); + ind = ind - kernelCenter; + switch Cspace + case 'k' + if all(ind==0) + dy(:,:,i) = y(1,1); + else + if ind(1)>0 + ind(2) = n+1+ind(2); + else + ind = -ind; + end + %manually implement ifft to be faster see doc for ifftn + dy(:,:,i) = 2*real(y(1+ind(1),1+ind(2)) * exp(2*pi*1i*(p1*ind(1)+p2*ind(2)))/prod(imageSize)); + end + case 'real' + if all(ind==0) + dy(:,:,i) = y; + else + dy(:,:,i) = circshift(y,ind) + circshift(y,-ind); + end + end + end +end diff --git a/solver/solver_DDFT.m b/solver/solver_DDFT.m index b83a481..58da8fa 100644 --- a/solver/solver_DDFT.m +++ b/solver/solver_DDFT.m @@ -1,4 +1,16 @@ -function [t,y,params] = solver_DDFT(tspan,y0,params) +function varargout = solver_DDFT(tspan,y0,params,meta,mode,varargin) +%this provides solution to both forward and backward evaluation +%set mode = 'forward' (default) to perform model evaluation, in this mode, we accept two varargin, varargin{1} is sol, when true (false by default), output sol structure (varargin = {tout,sol,params},, when false, varargin = {tout,y,params}. varargin{2} is FSA, when true (false by default), also computes FSA and varargin{4} = ys. +%set mode = 'adjoint' to perform ASA analysis. varargin{1} = error, varargin{2] = discrete, tspan and y0 must be tdata and sol (solution history). varargout = {grad} +ASA = (nargin > 4) && isequal(mode,'adjoint'); +if ASA + error = varargin{1}; + discrete = varargin{2}; +else + sol = ~isempty(varargin) && varargin{1}; + FSA = length(varargin)>1 && varargin{2}; +end + addpath('../../CHACR/odesolver') %in order to be consistent with formk, the first dimension is x and the second dimension is y if ~isfield(params,'dx') && isfield(params,'N') && isfield(params,'L') @@ -31,22 +43,6 @@ % mu.func = @(x,coeff) log((1+x)./(1-x))/2; % mu.grad = @(x,coeff) 1./(1-x.^2); % mu.params = []; -if isempty(y0) || isscalar(y0) - %initialization - if isempty(y0) - n0 = 0.1; - else - n0 = y0; - end - sigma = 0.01; - rng(1); - y0 = n0 + sigma*randn(N); - y0 = y0(:); -end -if isempty(tspan) - tspan = linspace(0,4,100); -end -t0 = tspan(1); %Finite differencing operator in real space for i = 1:2 @@ -68,16 +64,104 @@ Lconv = [zeros(1,3); 1,-2,1; zeros(1,3)]/dx(2)^2 + [zeros(3,1), [1;-2;1], zeros(3,1)]/dx(1)^2; LK = psf2otf(Lconv,N); -yp0 = RHS(t0,y0,params); -options = odeset('InitialSlope',yp0,'Jacobian',@(t,y) jacobian(t,y,params)); +%the Jacobian and mass matrix of the system is Hermitian, so the treatment of pencil is the same for forward and ASA eval moreoptions = moreodeset('skipInit',true,'Krylov',true, ... -'pencil',@(xi,t,y,hinvGak,info) pencil(params,xi,t,y,hinvGak,info), ... -'KrylovDecomp',@(~,~,dfdy,hinvGak) KrylovDecomp(L,dfdy,hinvGak), ... -'KrylovPrecon',@(x,L,U,hinvGak,~,~,~) KrylovPrecon(LK,params,x,L,U,hinvGak),... -'jacMult',@(xi,t,y,info) jacobian_mult(params,xi,t,y,info),... 'gmrestol',1e-3); -[t,y] = myode15s(@(t,y) RHS(t,y,params),tspan,y0,options,moreoptions); +if ~ASA + if isempty(y0) || isscalar(y0) + %initialization + if isempty(y0) + n0 = 0.1; + else + n0 = y0; + end + sigma = 0.01; + rng(1); + y0 = n0 + sigma*randn(N); + y0 = y0(:); + end + if isempty(tspan) + tspan = linspace(0,4,100); + end + t0 = tspan(1); + yp0 = RHS(t0,y0,params); + options = odeset('InitialSlope',yp0,'Jacobian',@(t,y) jacobian(t,y,params)); + moreoptions = moreodeset(moreoptions, ... + 'jacMult',@(xi,t,y,info) jacobian_mult(params,xi,t,y,info), ... + 'pencil',@(xi,t,y,hinvGak,info) pencil(params,xi,t,y,hinvGak,info), ... + 'KrylovDecomp',@(~,~,dfdy,hinvGak) KrylovDecomp(L,dfdy,hinvGak), ... + 'KrylovPrecon',@(x,L,U,hinvGak,~,~,~) KrylovPrecon(LK,params,x,L,U,hinvGak)); + odeFcn = @(t,y) RHS(t,y,params); + + if FSA + moreoptions = moreodeset(moreoptions, ... + 'FSA', true, ... + 'sensFcn', @(t,y) sensFcn(t,y,meta,params), ... + 'ys0', zeros(length(y0),meta.extdata.numParams), ... + 'ysp0', sensFcn(tspan(1),y0,params,meta)); + end + + if sol + y = myode15s(odeFcn,tspan,y0,options,moreoptions); + tout = y.x; + ys = []; + else + [tout,y,ys] = myode15s(odeFcn,tspan,y0,options,moreoptions); + end + varargout = {tout,y,params,ys}; +else + addpath('../../CHACR/GIP') + tdata = tspan; + sol = y0; + ASAQuadNp = 1; + + options = odeset('Jacobian',@(t,y) jacobian(t,sol,params), ... + 'mass', -speye(prod(params.N)),'MassSingular','yes','MStateDependence','none'); + moreoptions = moreodeset(moreoptions, ... + 'jacMult',@(xi,t,y,info) jacobian_mult(params,xi,t,sol,info), ... + 'pencil',@(xi,t,y,hinvGak,info) pencil(params,xi,t,sol,hinvGak,info,true), ... + 'KrylovDecomp',@(~,~,dfdy,hinvGak) KrylovDecomp(L,dfdy,hinvGak,true), ... + 'KrylovPrecon',@(x,L,U,hinvGak,~,~,~) KrylovPrecon(LK,params,x,L,U,hinvGak,true),... + 'interpFcn',@(flag,info,tnew,ynew,h,dif,k,idxNonNegative) ASA_gradient(flag,info,tnew,ynew,h,dif,k,idxNonNegative,sol,@sensFcn,{params},meta,ASAQuadNp)); + + if ~discrete + tspan = [tdata(end),tdata(1)]; + F0 = error(end,:)'; + [y0,yp0] = ASAinit(F0,discrete,params,tspan(1),sol); + options = odeset(options,'InitialSlope',yp0); + moreoptions.linearMult = @(xi,t,info) ASA_mult(t,xi,sol,info,params,tdata,error); + odeFcn = @(t,y) ASA_eqn(t,y,sol,params,tdata,error); + grad = myode15s(odeFcn,tspan,y0,options,moreoptions); + else + y_final = 0; + yp_final = 0; + moreoptions.linearMult = @(xi,t,info) ASA_mult(t,xi,sol,info,params); + odeFcn = @(t,y) ASA_eqn(t,y,sol,params); + %initialize at each time step + y0_list = zeros(n,length(tdata)-1); + yp0_list = y0_list; + for ind = 2:length(tdata) + t0 = tdata(ind); + F0 = error(end,:)'; + [y0_list(:,ind-1),yp0_list(:,ind-1)] = ASAinit(F0,discrete,params,t0,sol); + end + %serial + grad = zeros(1,meta.extdata.numParams); + for ind = (length(tdata)-1):-1:1 + tspan = [tdata(ind+1),tdata(ind)]; + y0 = y0_list(:,ind)+y_final; + yp0 = yp0_list(:,ind)+yp_final; + options = odeset(options,'InitialSlope',yp0); + [grad_new,y_final,yp_final] = myode15s(odeFcn,tspan,y0,options,moreoptions); + grad = grad + grad_new; + if isnan(y_final) + break; + end + end + end + varargout = {grad}; +end end @@ -97,25 +181,39 @@ end function dfdy = jacobian(t,y,params) + %accommondate its usage through ASA when y is a struct + if isstruct(y) + y = sol_interp(y,t); + end %this only computes the nonlinear part, as an input to KrylovDecomp dfdy = customizeFunGrad(params,'mu','grad',y); end -function Pargs = KrylovDecomp(L,dfdy,hinvGak) +function Pargs = KrylovDecomp(L,dfdy,hinvGak,adjoint) %here dfdy comes from Jacobian %L is the finite-difference Laplacian operator + if nargin>3 && adjoint + msign = -1; + else + msign = 1; + end n = length(L); - J = speye(n) - hinvGak*L.*sparse(1:n,1:n,dfdy); + J = msign*speye(n) - hinvGak*L.*sparse(1:n,1:n,dfdy); [L,U] = ilu(J); Pargs = {L,U}; end -function yy = KrylovPrecon(LK,params,x,L,U,hinvGak) +function yy = KrylovPrecon(LK,params,x,L,U,hinvGak,adjoint) %LK is the Fourier transform of the finite difference Laplacian operator + if nargin>6 && adjoint + msign = -1; + else + msign = 1; + end N = params.N; C = params.C; x = reshape(x,N); - yy = ifft( fft(x) ./ (1 + hinvGak*LK.*C) ); + yy = ifft( fft(x) ./ (msign + hinvGak*LK.*C) ); yy = yy(:); yy = U \ (L \ yy); end @@ -125,6 +223,9 @@ yy = jacobian_mult(params,xi,t,y,[]); yy = jacobian_mult(params,xi,t,y,yy); elseif isempty(info) + if isstruct(y) + y = sol_interp(y,t); + end yy = customizeFunGrad(params,'mu','grad',y); yy = reshape(yy,params.N); else @@ -143,10 +244,73 @@ end end -function yy = pencil(params,xi,t,y,hinvGak,info) +function yy = ASA_mult(t,xi,sol,info,params,varargin) + if isempty(info) + yy = jacobian_mult(params,[],t,sol,[]); + else + yy = jacobian_mult(params,xi,[],[],info); + if ~isempty(varargin) + tdata = varargin{1}; + error = varargin{2}; + [interval,alpha] = interval_counter(tdata,t,length(tdata)-1,2); + source = (error(interval,:)*(1-alpha) + error(interval+1,:)*alpha)'; + yy = yy + source; + end + end +end + +function dy = ASA_eqn(t,y,sol,params,varargin) + %wrapper function for odeFcn (not really needed, mostly just a placeholder, except for daeic) + info = ASA_mult(t,y,sol,[],params); + dy = ASA_mult(t,y,sol,info,params,varargin{:}); +end + +function yy = pencil(params,xi,t,y,hinvGak,info,adjoint) + if nargin>6 && adjoint + msign = -1; + else + msign = 1; + end yy = jacobian_mult(params,xi,t,y,info); if ~isempty(info) - yy = xi - hinvGak*yy; + yy = msign*xi - hinvGak*yy; + end +end + +function dy = sensFcn(t,y,meta,params) + N = params.N; + dx = params.dx; + y = reshape(y,N); + names = fieldnames(meta); + numParams = meta.extdata.numParams; + dy = zeros(numel(y),numParams); + + for i = 1:numel(names) + name = names{i}; + if isequal(name,'extdata') + continue + end + paramsIndex = meta.(name).index; + switch name + case 'mu' + mu = customizeSensEval(params,name,y); + case 'C' + mu = -params.Csens(y); + end + dyi = 0; + for i = 1:length(N) + dyi = dyi + (circshift(mu,1,i)+circshift(mu,-1,i)-2*mu)/dx(i)^2; + end + dy(:,paramsIndex) = reshape(dyi,[],numel(paramsIndex)); + end +end + +function [y0,yp0] = ASAinit(F0,discrete,params,t0,sol) + y0 = zeros(size(F0)); + yp0 = F0; + if discrete + y0 = yp0; + yp0 = jacobian_mult(params,y0,t0,sol,'force'); end end From e12586a9727979a5a32bacf617ba5502309574c8 Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Sat, 6 Jul 2019 00:54:13 -0400 Subject: [PATCH 034/149] add a few lines in DDFT_nucleation for IP test --- solver/DDFT_nucleation.m | 6 ++++++ 1 file changed, 6 insertions(+) diff --git a/solver/DDFT_nucleation.m b/solver/DDFT_nucleation.m index f8b99ff..f3793b4 100644 --- a/solver/DDFT_nucleation.m +++ b/solver/DDFT_nucleation.m @@ -30,3 +30,9 @@ [t2,y2] = solver_DDFT(tspan2,y0,params); figure; visualize([],[],[],y2(1:10:end,:),'c',false,'ImageSize',N); + +ind = 1:5:100; +tdata = t2(ind); +ydata = y2(ind,:); + +x_opt = IP_DDFT(tdata,ydata,params); From 5ec85d7e23d75f3a9ccb52e252cfca9380158715 Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Sun, 7 Jul 2019 00:23:49 -0400 Subject: [PATCH 035/149] fix bugs in IP_DDFT and solver_DDFT --- solver/IP_DDFT.m | 22 +++++++++++++++------- solver/solver_DDFT.m | 2 +- 2 files changed, 16 insertions(+), 8 deletions(-) diff --git a/solver/IP_DDFT.m b/solver/IP_DDFT.m index 5889be5..1a9414c 100644 --- a/solver/IP_DDFT.m +++ b/solver/IP_DDFT.m @@ -1,14 +1,12 @@ -function x_opt = IP_DDFT(tdata,ydata,params) +function x_opt = IP_DDFT(tdata,ydata,params,kernelSize,Cspace) addpath('../../CHACR/GIP') % params.N = [256,256]; % params.L = [5,5]; % params.dx = params.L ./ params.N; -kernelSize = [21,21]; NC = floor((prod(kernelSize)+1)/2); meta.C.index = 1:NC; meta.C.exp = false; -Cspace = 'k'; params.Csens = @(y) Csens(y,Cspace,kernelSize); x_guess = zeros(1,NC); @@ -62,7 +60,7 @@ C = circshift(C,-floor(kernelSize/2)); params.C = C; case 'real' - params.C = psf2otf(C); + params.C = psf2otf(C, params.N); end end end @@ -94,6 +92,7 @@ dy = zeros([size(y),n]); if isequal(Cspace,'k') imageSize = size(y); + numPixel = prod(imageSize); y = fftn(y); [p1,p2] = ndgrid(0:(imageSize(1)-1),0:(imageSize(2)-1)); p1 = p1/imageSize(1); @@ -105,16 +104,25 @@ switch Cspace case 'k' if all(ind==0) - dy(:,:,i) = y(1,1); + dy(:,:,i) = y(1,1)/numPixel; else if ind(1)>0 - ind(2) = n+1+ind(2); + ind(2) = imageSize(2)+ind(2); else ind = -ind; end %manually implement ifft to be faster see doc for ifftn - dy(:,:,i) = 2*real(y(1+ind(1),1+ind(2)) * exp(2*pi*1i*(p1*ind(1)+p2*ind(2)))/prod(imageSize)); + dy(:,:,i) = 2*real(y(1+ind(1),1+ind(2)) * exp(2*pi*1i*(p1*ind(1)+p2*ind(2)))/numPixel); end + % %the following code is another version consistent with the definition of C in assign + % C = zeros(1,n); + % C(i) = 1; + % C = [C,flip(C(1:end-1))]; + % C = reshape(C, kernelSize); + % padSize = imageSize - kernelSize; + % C = padarray(C, padSize, 'post'); + % C = circshift(C,-floor(kernelSize/2)); + % dy(:,:,i) = ifftn(C .* y); case 'real' if all(ind==0) dy(:,:,i) = y; diff --git a/solver/solver_DDFT.m b/solver/solver_DDFT.m index 58da8fa..579a502 100644 --- a/solver/solver_DDFT.m +++ b/solver/solver_DDFT.m @@ -213,7 +213,7 @@ N = params.N; C = params.C; x = reshape(x,N); - yy = ifft( fft(x) ./ (msign + hinvGak*LK.*C) ); + yy = ifftn( fftn(x) ./ (msign + hinvGak*LK.*C) ); yy = yy(:); yy = U \ (L \ yy); end From 4cd60d77e786c28f4544fdcc0cb7e189aa90d009 Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Sun, 7 Jul 2019 00:24:04 -0400 Subject: [PATCH 036/149] decrease gmrestol and increase restart in solver_DDFT --- solver/solver_DDFT.m | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/solver/solver_DDFT.m b/solver/solver_DDFT.m index 579a502..58df1b1 100644 --- a/solver/solver_DDFT.m +++ b/solver/solver_DDFT.m @@ -66,7 +66,7 @@ %the Jacobian and mass matrix of the system is Hermitian, so the treatment of pencil is the same for forward and ASA eval moreoptions = moreodeset('skipInit',true,'Krylov',true, ... -'gmrestol',1e-3); +'gmrestol',1e-4,'restart',10); if ~ASA if isempty(y0) || isscalar(y0) From d2d39f6339882dec95b0b78345e79b43acc6fc60 Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Sun, 7 Jul 2019 00:34:48 -0400 Subject: [PATCH 037/149] update DDFT_nucleation, try using real space representation for C --- solver/DDFT_nucleation.m | 7 +++++-- 1 file changed, 5 insertions(+), 2 deletions(-) diff --git a/solver/DDFT_nucleation.m b/solver/DDFT_nucleation.m index f3793b4..3af4c1d 100644 --- a/solver/DDFT_nucleation.m +++ b/solver/DDFT_nucleation.m @@ -1,4 +1,4 @@ -%parameter search +tic; L = [5,5]; N = [256,256]; n = prod(N); @@ -34,5 +34,8 @@ ind = 1:5:100; tdata = t2(ind); ydata = y2(ind,:); +toc -x_opt = IP_DDFT(tdata,ydata,params); +% x_opt = IP_DDFT(tdata,ydata,params,[21,21],'k'); %this stagnates at iter 17 after 63 func counts + +x_opt = IP_DDFT(tdata,ydata,params,[61,61],'real'); From 859a520605a319a08c1e5f4eb7154ded916a38d4 Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Sun, 7 Jul 2019 01:38:41 -0400 Subject: [PATCH 038/149] use the options of sensFcnMultiplier to directly multiply omega with dF in sensFcn --- solver/IP_DDFT.m | 53 +++++++++++++++++++++++++++++++++++++++++++- solver/solver_DDFT.m | 37 ++++++++++++++++++++++++++++++- 2 files changed, 88 insertions(+), 2 deletions(-) diff --git a/solver/IP_DDFT.m b/solver/IP_DDFT.m index 1a9414c..26ead7d 100644 --- a/solver/IP_DDFT.m +++ b/solver/IP_DDFT.m @@ -7,7 +7,7 @@ NC = floor((prod(kernelSize)+1)/2); meta.C.index = 1:NC; meta.C.exp = false; -params.Csens = @(y) Csens(y,Cspace,kernelSize); +params.Csens = @(y,i) Csens_ASA(y,i,Cspace,kernelSize); x_guess = zeros(1,NC); tspan = 100; @@ -132,3 +132,54 @@ end end end + +function dy = Csens_ASA(y,i,Cspace,kernelSize) + %another version of Csens, output only the sensitivity with respect to the ith parameter + %Csens takes up a lot of memory!! Csens is now a function handle for multiplying the sensitivity of C with a vector y. (dy = dC * y) Note that y should in the image format and in real space. + %the returned dy has the dimension of size(y,1)*size(y,2)*number of parameters + %for example, if real space representation is used, use circshift, in sensFcn, + %if k space representation is used, for C(k), the sensitivity of -mu is y(k)exp(ikx)+y(-k)exp(-ikx) + %since y is real, this is equal to 2Re(y(k)exp(ikx)) + %again, note that kernelSize must be odd + n = floor((prod(kernelSize)+1)/2); + kernelCenter = ceil(kernelSize/2); + if isequal(Cspace,'k') + imageSize = size(y); + numPixel = prod(imageSize); + y = fftn(y); + [p1,p2] = ndgrid(0:(imageSize(1)-1),0:(imageSize(2)-1)); + p1 = p1/imageSize(1); + p2= p2/imageSize(2); + end + [ind(1),ind(2)] = ind2sub(kernelSize,i); + ind = ind - kernelCenter; + switch Cspace + case 'k' + if all(ind==0) + dy = y(1,1)/numPixel; + else + if ind(1)>0 + ind(2) = imageSize(2)+ind(2); + else + ind = -ind; + end + %manually implement ifft to be faster see doc for ifftn + dy = 2*real(y(1+ind(1),1+ind(2)) * exp(2*pi*1i*(p1*ind(1)+p2*ind(2)))/numPixel); + end + % %the following code is another version consistent with the definition of C in assign + % C = zeros(1,n); + % C(i) = 1; + % C = [C,flip(C(1:end-1))]; + % C = reshape(C, kernelSize); + % padSize = imageSize - kernelSize; + % C = padarray(C, padSize, 'post'); + % C = circshift(C,-floor(kernelSize/2)); + % dy = ifftn(C .* y); + case 'real' + if all(ind==0) + dy = y; + else + dy = circshift(y,ind) + circshift(y,-ind); + end + end +end diff --git a/solver/solver_DDFT.m b/solver/solver_DDFT.m index 58df1b1..60f9d1b 100644 --- a/solver/solver_DDFT.m +++ b/solver/solver_DDFT.m @@ -123,7 +123,7 @@ 'pencil',@(xi,t,y,hinvGak,info) pencil(params,xi,t,sol,hinvGak,info,true), ... 'KrylovDecomp',@(~,~,dfdy,hinvGak) KrylovDecomp(L,dfdy,hinvGak,true), ... 'KrylovPrecon',@(x,L,U,hinvGak,~,~,~) KrylovPrecon(LK,params,x,L,U,hinvGak,true),... - 'interpFcn',@(flag,info,tnew,ynew,h,dif,k,idxNonNegative) ASA_gradient(flag,info,tnew,ynew,h,dif,k,idxNonNegative,sol,@sensFcn,{params},meta,ASAQuadNp)); + 'interpFcn',@(flag,info,tnew,ynew,h,dif,k,idxNonNegative) ASA_gradient(flag,info,tnew,ynew,h,dif,k,idxNonNegative,sol,@sensFcn_ASA,{params},meta,ASAQuadNp,true)); if ~discrete tspan = [tdata(end),tdata(1)]; @@ -305,6 +305,41 @@ end end +function dy = sensFcn_ASA(t,y,omega,meta,params) + N = params.N; + dx = params.dx; + y = reshape(y,N); + names = fieldnames(meta); + numParams = meta.extdata.numParams; + dy = zeros(1,numParams); + + for i = 1:numel(names) + name = names{i}; + if isequal(name,'extdata') + continue + end + paramsIndex = meta.(name).index; + switch name + case 'mu' + mu = customizeSensEval(params,name,y); + dyi = 0; + for j = 1:length(N) + dyi = dyi + (circshift(mu,1,j)+circshift(mu,-1,j)-2*mu)/dx(j)^2; + end + dy(paramsIndex) = sum(omega.*dyi(:)); + case 'C' + for p = 1:length(paramsIndex) + mu = -params.Csens(y,p); + dyi = 0; + for j = 1:length(N) + dyi = dyi + (circshift(mu,1,j)+circshift(mu,-1,j)-2*mu)/dx(j)^2; + end + dy(paramsIndex(p)) = sum(omega.*dyi(:)); + end + end + end +end + function [y0,yp0] = ASAinit(F0,discrete,params,t0,sol) y0 = zeros(size(F0)); yp0 = F0; From 533c1778d41bb7e54ac879eaa13d31a284b7915e Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Mon, 8 Jul 2019 02:47:56 -0400 Subject: [PATCH 039/149] fix bugs in solver_DDFT --- solver/solver_DDFT.m | 41 +++++++++++++++++++++++++++-------------- 1 file changed, 27 insertions(+), 14 deletions(-) diff --git a/solver/solver_DDFT.m b/solver/solver_DDFT.m index 60f9d1b..43800aa 100644 --- a/solver/solver_DDFT.m +++ b/solver/solver_DDFT.m @@ -99,7 +99,7 @@ 'FSA', true, ... 'sensFcn', @(t,y) sensFcn(t,y,meta,params), ... 'ys0', zeros(length(y0),meta.extdata.numParams), ... - 'ysp0', sensFcn(tspan(1),y0,params,meta)); + 'ysp0', sensFcn(tspan(1),y0,meta,params)); end if sol @@ -122,8 +122,16 @@ 'jacMult',@(xi,t,y,info) jacobian_mult(params,xi,t,sol,info), ... 'pencil',@(xi,t,y,hinvGak,info) pencil(params,xi,t,sol,hinvGak,info,true), ... 'KrylovDecomp',@(~,~,dfdy,hinvGak) KrylovDecomp(L,dfdy,hinvGak,true), ... - 'KrylovPrecon',@(x,L,U,hinvGak,~,~,~) KrylovPrecon(LK,params,x,L,U,hinvGak,true),... - 'interpFcn',@(flag,info,tnew,ynew,h,dif,k,idxNonNegative) ASA_gradient(flag,info,tnew,ynew,h,dif,k,idxNonNegative,sol,@sensFcn_ASA,{params},meta,ASAQuadNp,true)); + 'KrylovPrecon',@(x,L,U,hinvGak,~,~,~) KrylovPrecon(LK,params,x,L,U,hinvGak,true)); + if isfield(params,'Csensval') + sensFcnMultiplier = false; + sF = @sensFcn; + else + sensFcnMultiplier = true; + sF = @sensFcn_ASA; + end + moreoptions = moreodeset(moreoptions, ... + 'interpFcn',@(flag,info,tnew,ynew,h,dif,k,idxNonNegative) ASA_gradient(flag,info,tnew,ynew,h,dif,k,idxNonNegative,sol,sF,{params},meta,ASAQuadNp,sensFcnMultiplier)); if ~discrete tspan = [tdata(end),tdata(1)]; @@ -232,15 +240,16 @@ N = params.N; dx = params.dx; C = params.C; - xi = reshape(xi,N); - dfdy = info; - mu = dfdy .* xi; - mu = mu - ifftn(C .* fftn(xi)); - yy = 0; - for i = 1:length(N) - yy = yy + (circshift(mu,1,i)+circshift(mu,-1,i)-2*mu)/dx(i)^2; + yy = zeros(size(xi)); + for p = 1:length(size(xi,2)) + xip = reshape(xi(:,p),N); + dfdy = info; + mu = dfdy .* xip; + mu = mu - ifftn(C .* fftn(xip)); + for i = 1:length(N) + yy(:,p) = yy(:,p) + reshape((circshift(mu,1,i)+circshift(mu,-1,i)-2*mu)/dx(i)^2, [], 1); + end end - yy = yy(:); end end @@ -295,11 +304,15 @@ case 'mu' mu = customizeSensEval(params,name,y); case 'C' - mu = -params.Csens(y); + if isfield(params,'Csensval') + mu = - ifft2(params.Csensval .* fftn(y),'symmetric'); + else + mu = -params.Csens(y); + end end dyi = 0; - for i = 1:length(N) - dyi = dyi + (circshift(mu,1,i)+circshift(mu,-1,i)-2*mu)/dx(i)^2; + for j = 1:length(N) + dyi = dyi + (circshift(mu,1,j)+circshift(mu,-1,j)-2*mu)/dx(j)^2; end dy(:,paramsIndex) = reshape(dyi,[],numel(paramsIndex)); end From e0c6e91b5627592c01dde646137e0846a16f526f Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Mon, 8 Jul 2019 02:48:32 -0400 Subject: [PATCH 040/149] add fminunc option, add Cspace=isotropic option, increase weight by 100 in IP_DDFT --- solver/IP_DDFT.m | 83 ++++++++++++++++++++++++++++++++---------------- 1 file changed, 55 insertions(+), 28 deletions(-) diff --git a/solver/IP_DDFT.m b/solver/IP_DDFT.m index 26ead7d..b7aa6d8 100644 --- a/solver/IP_DDFT.m +++ b/solver/IP_DDFT.m @@ -1,19 +1,35 @@ -function x_opt = IP_DDFT(tdata,ydata,params,kernelSize,Cspace) +function x_opt = IP_DDFT(tdata,ydata,params,kernelSize,Cspace,options) addpath('../../CHACR/GIP') % params.N = [256,256]; % params.L = [5,5]; % params.dx = params.L ./ params.N; -NC = floor((prod(kernelSize)+1)/2); +if isequal(Cspace,'isotropic') + [k2,~] = formk(params.N,params.L); + k = sqrt(k2); +% bound = [0, 2*pi*params.N(1)/params.L(1)/2]; %assuming at least 5 points across each pattern + bound = [0,max(k(:))]; + expleg = custom_Legendre(1,bound); + params.Cfunc.func = @(x) expleg.func(k,x); + params.Cfunc.sens = @(x) expleg.sens(k,x); + NC = kernelSize; +else + NC = floor((prod(kernelSize)+1)/2); + params.Csens = @(y,i) Csens_ASA(y,i,Cspace,kernelSize); +end + meta.C.index = 1:NC; meta.C.exp = false; -params.Csens = @(y,i) Csens_ASA(y,i,Cspace,kernelSize); x_guess = zeros(1,NC); tspan = 100; -loss = @(y,ydata,~) MSE(y,ydata,prod(params.dx)); -lossHess = @(dy,~,~) MSE([],[],prod(params.dx),dy); -options = optimoptions('fminunc','SpecifyObjectiveGradient',true,'Display','iter-detailed'); +loss = @(y,ydata,~) MSE(y,ydata,prod(params.dx)*100); +lossHess = @(dy,~,~,~) MSE([],[],prod(params.dx)*100,dy); +if nargin > 5 && ~isempty(options) + options = optimoptions(options,'SpecifyObjectiveGradient',true,'Display','iter-detailed'); +else + options = optimoptions('fminunc','SpecifyObjectiveGradient',true,'Display','iter-detailed'); +end x_opt = fminunc(@(x) IP(tdata,ydata,x,meta,params, ... @(tdata,y0,FSA,meta,params) forwardSolver(tdata,y0,FSA,meta,params,tspan), ... @@ -39,34 +55,45 @@ %but it must be converted to be centered at 1,1 in the k-space representation used in DDFT solver %consider other extensions: %1. Reduce to representing 1D C(k) if it's axisymmetric - if any(mod(kernelSize,2)==0) - error('kernel size must be odd'); - end - n = length(xparam); - if n ~= floor((prod(kernelSize)+1)/2) - error('kernel size incompatible with C input'); - end - %note that n is odd - C = xparam(:); - %symmetry condition - C = [C; flip(C(1:end-1))]; - C = reshape(C, kernelSize); - switch Cspace - case 'k' - % Circularly shift so that the "center" of the OTF is at the - % (1,1) element of the array. (from psf2otf) - padSize = params.N - kernelSize; - C = padarray(C, padSize, 'post'); - C = circshift(C,-floor(kernelSize/2)); - params.C = C; - case 'real' - params.C = psf2otf(C, params.N); + if isequal(Cspace,'isotropic') + %C(k) can be represented by a 1D function + params.C = params.Cfunc.func(xparam); + params.Csensval = params.Cfunc.sens(xparam); + else + if any(mod(kernelSize,2)==0) + error('kernel size must be odd'); + end + n = length(xparam); + if n ~= floor((prod(kernelSize)+1)/2) + error('kernel size incompatible with C input'); + end + %note that n is odd + C = xparam(:); + %symmetry condition + C = [C; flip(C(1:end-1))]; + C = reshape(C, kernelSize); + switch Cspace + case 'k' + % Circularly shift so that the "center" of the OTF is at the + % (1,1) element of the array. (from psf2otf) + padSize = params.N - kernelSize; + C = padarray(C, padSize, 'post'); + C = circshift(C,-floor(kernelSize/2)); + params.C = C; + case 'real' + params.C = psf2otf(C, params.N); + end end end end function [tout,y,dy,params] = forwardSolver(tdata,y0,FSA,meta,params,tspan) %tspan can either be sol or number of time points + if any(params.C(:)>2) + tout = NaN; + y = NaN; + dy = NaN; + end if isequal(tspan,'sol') sol = true; else From b0adbe49dcac958189dd64c6a2bb720d60bdaebd Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Mon, 8 Jul 2019 02:56:01 -0400 Subject: [PATCH 041/149] update DDFT_nucleation scripts --- solver/DDFT_nucleation.m | 10 +++++++++- solver/DDFT_nucleation2.m | 40 +++++++++++++++++++++++++++++++++++++++ 2 files changed, 49 insertions(+), 1 deletion(-) create mode 100644 solver/DDFT_nucleation2.m diff --git a/solver/DDFT_nucleation.m b/solver/DDFT_nucleation.m index 3af4c1d..2849b62 100644 --- a/solver/DDFT_nucleation.m +++ b/solver/DDFT_nucleation.m @@ -38,4 +38,12 @@ % x_opt = IP_DDFT(tdata,ydata,params,[21,21],'k'); %this stagnates at iter 17 after 63 func counts -x_opt = IP_DDFT(tdata,ydata,params,[61,61],'real'); +% x_opt = IP_DDFT(tdata,ydata,params,[61,61],'real'); + +options = optimoptions('fminunc','HessianFcn','objective','Algorithm','trust-region'); +x_opt = IP_DDFT(tdata,ydata,params,10,'isotropic',options); + +% ind = 10:3:61; +% tdata = t1(ind); +% ydata = y1(ind,:); +% x_opt = IP_DDFT(tdata,ydata,params,[21,21],'k'); %this stagnates at iter 1 after 37 func counts diff --git a/solver/DDFT_nucleation2.m b/solver/DDFT_nucleation2.m new file mode 100644 index 0000000..171c27d --- /dev/null +++ b/solver/DDFT_nucleation2.m @@ -0,0 +1,40 @@ +tic; +L = [5,5]; +N = [256,256]; +n = prod(N); + +params.N = N; +params.L = L; + +[t1,y1,params] = solver_DDFT([],[],params); + +xx = linspace(0,L(1),N(1)); +yy = linspace(0,L(2),N(2)); +[xx,yy] = ndgrid(xx,yy); +range = [1.5,3.5]; +thickness = 0.1; +roi = roi_rectangle(xx,yy,range,range,thickness); +center = L/2; +radius = 0.06*L(1); +thickness = 0.01*L(1); +roi = roi_circle(xx,yy,center,radius,thickness); + +%nucleus +y0 = y1(end,:)'; +roi = roi(:); +rho = (sum(y0) - sum(roi.*y0)) / sum(1-roi); +y0 = roi.*y0 + (1-roi)*rho; +figure; imagesc(reshape(y0,N)); + +tspan2 = linspace(0,1.05,100); +% tspan2 = linspace(0,1.5,100); +[t2,y2] = solver_DDFT(tspan2,y0,params); + +figure; visualize([],[],[],y2(1:10:end,:),'c',false,'ImageSize',N); + +ind = 20:2:100; +tdata = t2(ind); +ydata = y2(ind,:); +toc + +x_opt = IP_DDFT(tdata,ydata,params,[21,21],'k'); From f82c82fdc8c134b6aba1ce90f626a6fdbfe212e2 Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Mon, 8 Jul 2019 04:30:28 -0400 Subject: [PATCH 042/149] IP_DDFT_debug, plot val and gradient along the search direction --- solver/IP_DDFT_debug.m | 218 +++++++++++++++++++++++++++++++++++++++++ 1 file changed, 218 insertions(+) create mode 100644 solver/IP_DDFT_debug.m diff --git a/solver/IP_DDFT_debug.m b/solver/IP_DDFT_debug.m new file mode 100644 index 0000000..66f1bcf --- /dev/null +++ b/solver/IP_DDFT_debug.m @@ -0,0 +1,218 @@ +function [val,gradient] = IP_DDFT_debug(x_opt,tdata,ydata,params,kernelSize,Cspace,options) + %calculate val and gradient along the x_opt direction +addpath('../../CHACR/GIP') + +% params.N = [256,256]; +% params.L = [5,5]; +% params.dx = params.L ./ params.N; +if isequal(Cspace,'isotropic') + [k2,~] = formk(params.N,params.L); + k = sqrt(k2); +% bound = [0, 2*pi*params.N(1)/params.L(1)/2]; %assuming at least 5 points across each pattern + bound = [0,max(k(:))]; + expleg = custom_Legendre(1,bound); + params.Cfunc.func = @(x) expleg.func(k,x); + params.Cfunc.sens = @(x) expleg.sens(k,x); + NC = kernelSize; +else + NC = floor((prod(kernelSize)+1)/2); + params.Csens = @(y,i) Csens_ASA(y,i,Cspace,kernelSize); +end + +meta.C.index = 1:NC; +meta.C.exp = false; +x_guess = zeros(1,NC); + +tspan = 100; +loss = @(y,ydata,~) MSE(y,ydata,prod(params.dx)*100); +lossHess = @(dy,~,~,~) MSE([],[],prod(params.dx)*100,dy); +if nargin > 6 && ~isempty(options) + options = optimoptions(options,'SpecifyObjectiveGradient',true,'Display','iter-detailed'); +else + options = optimoptions('fminunc','SpecifyObjectiveGradient',true,'Display','iter-detailed'); +end + +Nalpha = 200; +alpha = linspace(0,1,Nalpha); +val = zeros(1,Nalpha); +gradient = zeros(Nalpha,NC); + +for i = 1:length(alpha) + [val(i),gradient(i,:)] = IP(tdata,ydata,x_opt*alpha(i),meta,params, ... + @(tdata,y0,FSA,meta,params) forwardSolver(tdata,y0,FSA,meta,params,tspan), ... + @adjointSolver, ... + loss,lossHess, ... + @(name,xparam,params) assign(name,xparam,params,Cspace,kernelSize)); +end +end + +function params = assign(name,xparam,params,Cspace,kernelSize) + switch name + case 'mu' + params.(name).params = xparam; + case 'C' + %xparam for C is cut in half due to symmetry. + %For the purpose of symmetry, we require that the kernel size be odd in both dimensions + %if a kernel size is even, it is not a symmetric convolution + %If the size of the kernel provided is N(1)*N(2), then the size of xparam is n = floor((prod(N)+1)/2) + %xparam correspond to the first n in the kernel in linear index, + %the rest is obtained using symmetry. This applies to both real space and k space + %Both real space and k space representation is centered at the kernel center (not 1,1) + %but it must be converted to be centered at 1,1 in the k-space representation used in DDFT solver + %consider other extensions: + %1. Reduce to representing 1D C(k) if it's axisymmetric + if isequal(Cspace,'isotropic') + %C(k) can be represented by a 1D function + params.C = params.Cfunc.func(xparam); + params.Csensval = params.Cfunc.sens(xparam); + else + if any(mod(kernelSize,2)==0) + error('kernel size must be odd'); + end + n = length(xparam); + if n ~= floor((prod(kernelSize)+1)/2) + error('kernel size incompatible with C input'); + end + %note that n is odd + C = xparam(:); + %symmetry condition + C = [C; flip(C(1:end-1))]; + C = reshape(C, kernelSize); + switch Cspace + case 'k' + % Circularly shift so that the "center" of the OTF is at the + % (1,1) element of the array. (from psf2otf) + padSize = params.N - kernelSize; + C = padarray(C, padSize, 'post'); + C = circshift(C,-floor(kernelSize/2)); + params.C = C; + case 'real' + params.C = psf2otf(C, params.N); + end + end + end +end + +function [tout,y,dy,params] = forwardSolver(tdata,y0,FSA,meta,params,tspan) + %tspan can either be sol or number of time points + if any(params.C(:)>2) + tout = NaN; + y = NaN; + dy = NaN; + end + if isequal(tspan,'sol') + sol = true; + else + sol = false; + tdata = linspace(tdata(1),tdata(end),tspan); + end + [tout,y,params,dy] = solver_DDFT(tdata,y0,params,meta,'forward',sol,FSA); +end + +function grad = adjointSolver(tdata,sol,lossgrad,meta,discrete,~,params) + grad = solver_DDFT(tdata,sol,params,meta,'adjoint',lossgrad,discrete); +end + +function dy = Csens(y,Cspace,kernelSize) + %Csens takes up a lot of memory!! Csens is now a function handle for multiplying the sensitivity of C with a vector y. (dy = dC * y) Note that y should in the image format and in real space. + %the returned dy has the dimension of size(y,1)*size(y,2)*number of parameters + %for example, if real space representation is used, use circshift, in sensFcn, + %if k space representation is used, for C(k), the sensitivity of -mu is y(k)exp(ikx)+y(-k)exp(-ikx) + %since y is real, this is equal to 2Re(y(k)exp(ikx)) + %again, note that kernelSize must be odd + n = floor((prod(kernelSize)+1)/2); + kernelCenter = ceil(kernelSize/2); + dy = zeros([size(y),n]); + if isequal(Cspace,'k') + imageSize = size(y); + numPixel = prod(imageSize); + y = fftn(y); + [p1,p2] = ndgrid(0:(imageSize(1)-1),0:(imageSize(2)-1)); + p1 = p1/imageSize(1); + p2= p2/imageSize(2); + end + for i = 1:n + [ind(1),ind(2)] = ind2sub(kernelSize,i); + ind = ind - kernelCenter; + switch Cspace + case 'k' + if all(ind==0) + dy(:,:,i) = y(1,1)/numPixel; + else + if ind(1)>0 + ind(2) = imageSize(2)+ind(2); + else + ind = -ind; + end + %manually implement ifft to be faster see doc for ifftn + dy(:,:,i) = 2*real(y(1+ind(1),1+ind(2)) * exp(2*pi*1i*(p1*ind(1)+p2*ind(2)))/numPixel); + end + % %the following code is another version consistent with the definition of C in assign + % C = zeros(1,n); + % C(i) = 1; + % C = [C,flip(C(1:end-1))]; + % C = reshape(C, kernelSize); + % padSize = imageSize - kernelSize; + % C = padarray(C, padSize, 'post'); + % C = circshift(C,-floor(kernelSize/2)); + % dy(:,:,i) = ifftn(C .* y); + case 'real' + if all(ind==0) + dy(:,:,i) = y; + else + dy(:,:,i) = circshift(y,ind) + circshift(y,-ind); + end + end + end +end + +function dy = Csens_ASA(y,i,Cspace,kernelSize) + %another version of Csens, output only the sensitivity with respect to the ith parameter + %Csens takes up a lot of memory!! Csens is now a function handle for multiplying the sensitivity of C with a vector y. (dy = dC * y) Note that y should in the image format and in real space. + %the returned dy has the dimension of size(y,1)*size(y,2)*number of parameters + %for example, if real space representation is used, use circshift, in sensFcn, + %if k space representation is used, for C(k), the sensitivity of -mu is y(k)exp(ikx)+y(-k)exp(-ikx) + %since y is real, this is equal to 2Re(y(k)exp(ikx)) + %again, note that kernelSize must be odd + n = floor((prod(kernelSize)+1)/2); + kernelCenter = ceil(kernelSize/2); + if isequal(Cspace,'k') + imageSize = size(y); + numPixel = prod(imageSize); + y = fftn(y); + [p1,p2] = ndgrid(0:(imageSize(1)-1),0:(imageSize(2)-1)); + p1 = p1/imageSize(1); + p2= p2/imageSize(2); + end + [ind(1),ind(2)] = ind2sub(kernelSize,i); + ind = ind - kernelCenter; + switch Cspace + case 'k' + if all(ind==0) + dy = y(1,1)/numPixel; + else + if ind(1)>0 + ind(2) = imageSize(2)+ind(2); + else + ind = -ind; + end + %manually implement ifft to be faster see doc for ifftn + dy = 2*real(y(1+ind(1),1+ind(2)) * exp(2*pi*1i*(p1*ind(1)+p2*ind(2)))/numPixel); + end + % %the following code is another version consistent with the definition of C in assign + % C = zeros(1,n); + % C(i) = 1; + % C = [C,flip(C(1:end-1))]; + % C = reshape(C, kernelSize); + % padSize = imageSize - kernelSize; + % C = padarray(C, padSize, 'post'); + % C = circshift(C,-floor(kernelSize/2)); + % dy = ifftn(C .* y); + case 'real' + if all(ind==0) + dy = y; + else + dy = circshift(y,ind) + circshift(y,-ind); + end + end +end From 37a11b7bb91e8cfe2ed7f0d9c9d62f4e0cf7c250 Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Mon, 8 Jul 2019 20:07:49 -0400 Subject: [PATCH 043/149] fix bug in roi_circle --- solver/roi_circle.m | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/solver/roi_circle.m b/solver/roi_circle.m index c4d95f8..d97e97f 100644 --- a/solver/roi_circle.m +++ b/solver/roi_circle.m @@ -17,7 +17,7 @@ if i == 1 roi = roi_i; else - roi = max((roi + roi_i),1); %union operator + roi = min((roi + roi_i),1); %union operator end else roi_out{i} = roi_i; From 09e652054f3d464bae1017700bdee862cd244b05 Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Wed, 10 Jul 2019 04:48:24 -0400 Subject: [PATCH 044/149] add x_guess input in IP_DDFT, continue from previous run in DDFT_nucleation2 --- solver/DDFT_nucleation2.m | 13 +++++++++++-- solver/IP_DDFT.m | 6 ++++-- 2 files changed, 15 insertions(+), 4 deletions(-) diff --git a/solver/DDFT_nucleation2.m b/solver/DDFT_nucleation2.m index 171c27d..07db5f8 100644 --- a/solver/DDFT_nucleation2.m +++ b/solver/DDFT_nucleation2.m @@ -1,3 +1,4 @@ +addpath('../../CHACR/GIP') tic; L = [5,5]; N = [256,256]; @@ -27,7 +28,7 @@ figure; imagesc(reshape(y0,N)); tspan2 = linspace(0,1.05,100); -% tspan2 = linspace(0,1.5,100); +tspan2 = linspace(0,1.5,100); [t2,y2] = solver_DDFT(tspan2,y0,params); figure; visualize([],[],[],y2(1:10:end,:),'c',false,'ImageSize',N); @@ -37,4 +38,12 @@ ydata = y2(ind,:); toc -x_opt = IP_DDFT(tdata,ydata,params,[21,21],'k'); +save_history = true; +resultpath = [largedatapath,'DDFT_nucleation2.mat']; +options = optimoptions('fminunc'); +if save_history + options = optimoptions(options,'OutputFcn', @(x,optimvalues,state) save_opt_history(x,optimvalues,state,resultpath)); +end + +x_opt = IP_DDFT(tdata,ydata,params,[21,21],'k',options,x_opt); +% [val,gradient] = IP_DDFT_debug(x_opt/max(x_opt)*1.2,tdata,ydata,params,[21,21],'k'); diff --git a/solver/IP_DDFT.m b/solver/IP_DDFT.m index b7aa6d8..1fc548d 100644 --- a/solver/IP_DDFT.m +++ b/solver/IP_DDFT.m @@ -1,4 +1,4 @@ -function x_opt = IP_DDFT(tdata,ydata,params,kernelSize,Cspace,options) +function x_opt = IP_DDFT(tdata,ydata,params,kernelSize,Cspace,options,x_guess) addpath('../../CHACR/GIP') % params.N = [256,256]; @@ -20,7 +20,9 @@ meta.C.index = 1:NC; meta.C.exp = false; -x_guess = zeros(1,NC); +if nargin < 7 || isempty(x_guess) + x_guess = zeros(1,NC); +end tspan = 100; loss = @(y,ydata,~) MSE(y,ydata,prod(params.dx)*100); From 7b95fbd98c2df294e2f4d4e838f03667040ab60f Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Wed, 10 Jul 2019 23:36:02 -0400 Subject: [PATCH 045/149] continue DDFT_nucleation2 from the previous run --- solver/DDFT_nucleation2_helper.m | 11 +++++++++++ 1 file changed, 11 insertions(+) create mode 100644 solver/DDFT_nucleation2_helper.m diff --git a/solver/DDFT_nucleation2_helper.m b/solver/DDFT_nucleation2_helper.m new file mode 100644 index 0000000..6bd0238 --- /dev/null +++ b/solver/DDFT_nucleation2_helper.m @@ -0,0 +1,11 @@ +addpath('../../CHACR/GIP'); +save_history = true; +resultpath = [largedatapath,'DDFT_nucleation2.mat']; + +options = optimoptions('fminunc','OutputFcn',@(x,optimvalues,state) save_opt_history(x,optimvalues,state,resultpath)); +x_opt = IP_DDFT(tdata,ydata,params,[21,21],'k',options,x_opt); + + + + + From 30d432524e66daaf852a22f508fd13fec75d0de7 Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Thu, 11 Jul 2019 00:13:00 -0400 Subject: [PATCH 046/149] add the mode of eval (output model solution) and fval and exitflag output in IP_DDFT --- solver/IP_DDFT.m | 34 +++++++++++++++++++++------------- 1 file changed, 21 insertions(+), 13 deletions(-) diff --git a/solver/IP_DDFT.m b/solver/IP_DDFT.m index 1fc548d..d2ad420 100644 --- a/solver/IP_DDFT.m +++ b/solver/IP_DDFT.m @@ -1,4 +1,5 @@ -function x_opt = IP_DDFT(tdata,ydata,params,kernelSize,Cspace,options,x_guess) +function [x_opt,fval,exitflag] = IP_DDFT(tdata,ydata,params,kernelSize,Cspace,options,x_guess,mode) +%set mode = 'eval' to only do the forward solve and return addpath('../../CHACR/GIP') % params.N = [256,256]; @@ -25,21 +26,28 @@ end tspan = 100; -loss = @(y,ydata,~) MSE(y,ydata,prod(params.dx)*100); -lossHess = @(dy,~,~,~) MSE([],[],prod(params.dx)*100,dy); -if nargin > 5 && ~isempty(options) - options = optimoptions(options,'SpecifyObjectiveGradient',true,'Display','iter-detailed'); + +if nargin > 7 && isequal(mode,'eval') + x_opt = IP(tdata,ydata,x_guess,meta,params, ... + @(tdata,y0,FSA,meta,params) forwardSolver(tdata,y0,FSA,meta,params,tspan), ... + [], [], [],... + @(name,xparam,params) assign(name,xparam,params,Cspace,kernelSize),'eval',true); else - options = optimoptions('fminunc','SpecifyObjectiveGradient',true,'Display','iter-detailed'); + loss = @(y,ydata,~) MSE(y,ydata,prod(params.dx)*100); + lossHess = @(dy,~,~,~) MSE([],[],prod(params.dx)*100,dy); + if nargin > 5 && ~isempty(options) + options = optimoptions(options,'SpecifyObjectiveGradient',true,'Display','iter-detailed'); + else + options = optimoptions('fminunc','SpecifyObjectiveGradient',true,'Display','iter-detailed'); + end + [x_opt,fval,exitflag] = fminunc(@(x) IP(tdata,ydata,x,meta,params, ... + @(tdata,y0,FSA,meta,params) forwardSolver(tdata,y0,FSA,meta,params,tspan), ... + @adjointSolver, ... + loss,lossHess, ... + @(name,xparam,params) assign(name,xparam,params,Cspace,kernelSize)), ... + x_guess, options); end -x_opt = fminunc(@(x) IP(tdata,ydata,x,meta,params, ... -@(tdata,y0,FSA,meta,params) forwardSolver(tdata,y0,FSA,meta,params,tspan), ... -@adjointSolver, ... -loss,lossHess, ... -@(name,xparam,params) assign(name,xparam,params,Cspace,kernelSize)), ... -x_guess, options); - end function params = assign(name,xparam,params,Cspace,kernelSize) From c25a6312a78badd5cb3336e69799955079e79fe5 Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Thu, 11 Jul 2019 00:13:22 -0400 Subject: [PATCH 047/149] add history_production, producing figures for DDFT IP (need more work) --- solver/history_production.m | 162 ++++++++++++++++++++++++++++++++++++ 1 file changed, 162 insertions(+) create mode 100644 solver/history_production.m diff --git a/solver/history_production.m b/solver/history_production.m new file mode 100644 index 0000000..f491191 --- /dev/null +++ b/solver/history_production.m @@ -0,0 +1,162 @@ +function history_production(resultpath,ind,modelfunc,arg,meta,tdata,ydata,params,kernelSize,Cspace,varargin) +%Two figures for figure handle +%note that ind is the indices of the optimization steps to be plotted. ind can also be 'end', in order to quickly visualize the final result. +%Use name value pair; +%'label'=true (default) to label the iteration number somewhere according to 'labelPosition'(= 'best' by default) for the first figure and to the left of each row for the second figure +%'labelxpos', coordinate of the x position of the label +%'labelHorizontalAlignment', 'left' (default), 'center','right' +%'ExchangeCurrentFieldColorScale', +%FrameIndex: selectively plot frames of c field by their index. ':' by default, meaning plotting all frames. +%Orientation: horizontal (default) arranges iterations (specified by ind) horizontally and different functions vertically; vertical does the other way +%yyaxisLim: each row corresponds to the ylim of each curve +%use CtruthSubplot as a vector to specify where to put the Ctruth +%If there is more than one functions to plot, modelfunc should be a struct, whose field names match those in the meta. If there is only one function to plot, modelfunc can either be a struct or simply a function handle +%the result file can also contain y, the solution to the PDE at each step, in which case we don't need to recompute +ps = inputParser; +addParameter(ps,'label',true); +addParameter(ps,'labelPosition','top'); +addParameter(ps,'labelxpos',0.1); +addParameter(ps,'labelHorizontalAlignment','left'); +addParameter(ps,'ExchangeCurrentFieldColorScale',[]); +addParameter(ps,'FrameIndex',':'); +addParameter(ps,'Orientation','horizontal'); +addParameter(ps,'yyaxisLim',[]); +addParameter(ps,'timeLabel',true); +addParameter(ps,'FontSize',12); +addParameter(ps,'legend',[]); +addParameter(ps,'scale',[]); +addParameter(ps,'CtruthSubplot',[]); +parse(ps,varargin{:}); +ps = ps.Results; + +varload = load(resultpath); +history = varload.history; +history = [zeros(1,size(history,2)); history]; %hardcoded!!! +if isempty(ind) + ind = 1:size(history,1); +elseif isequal(ind,'end') + ind = size(history,1); +end + + +%plot target and fitted function +names = fieldnames(meta); +numFunc = numel(names); +numIter = length(ind); +if isempty(ps.scale) + ps.scale = false(1,numIter); +end + +frameindex = ps.FrameIndex; +if isequal(frameindex,':') + column = size(ydata,1); + frameindex = 1:column; +else + column = length(frameindex); +end +rowtotal = numIter+1; +columntotal = column; +frameindex_model = frameindex; +frameindex_model(frameindex==1) = []; %remove the initial condition + +% 'color',[0.8500,0.3250,0.0980] +stparg = {0.05,[0.05,0.08],0.05}; +figure; +clim = [min(min(ydata(frameindex,:))),max(max(ydata(frameindex,:)))]; +h = visualize([],[],[],ydata(frameindex,:),'c',false,'ImageSize',params.N,'caxis',clim,'GridSize',[1,NaN],'OuterGridSize',[rowtotal,1],'OuterSubplot',[1,1],'ColumnTotal',columntotal,'StarterInd',0,'subtightplot',stparg); +if ps.timeLabel + for j = 1:length(h) + title(h(j),['t = ',num2str(tdata(frameindex(j)),2)]); + end + axes(h(1)); + text(0.1,1.5,'Data','Units','normalized','HorizontalAlignment',ps.labelHorizontalAlignment); +end +for i = 1:numIter + if isfield(varload,'y') + y = varload.y; + visualize([],[],[],y{ind(i)}(frameindex_model,:),'c',false,'ImageSize',params.N,'caxis',clim,'GridSize',[1,NaN],'OuterGridSize',[rowtotal,1],'OuterSubplot',[i+1,1],'ColumnTotal',columntotal,'StarterInd',i*columntotal+1,'subtightplot',stparg); + else + yhistory = IP_DDFT(tdata,ydata,params,kernelSize,Cspace,[],history(ind(i),:),'eval'); + visualize([],[],[],yhistory(frameindex_model,:),'c',false,'ImageSize',params.N,'caxis',clim,'GridSize',[1,NaN],'OuterGridSize',[rowtotal,1],'OuterSubplot',[i+1,1],'ColumnTotal',columntotal,'StarterInd',i*columntotal+1,'subtightplot',stparg); + end + subtightplot(rowtotal,columntotal,i*columntotal+1,stparg{:}); + for j=1:numFunc + name = names{j}; + if isequal(name,'kappa') + continue; + end + if isequal(name,'C') + C = history(ind(i),:); + C = [C,flip(C(1:end-1))]; + C = reshape(C,kernelSize); + imagesc(C); + caxis([0,1]); + ax = gca; + axis(ax,'image'); + ax.XTick = []; + ax.YTick = []; + ax.Box = 'off'; + else + if j==1 + yyaxis left + elseif j==2 + yyaxis right + end + plot(arg,target{j},'--','LineWidth',2); + ax = gca; + ylimtemp = ax.YLim; + hold on; + if isfield(meta,'kappa') && ps.scale(i) + scale = exp(history(ind(i),meta.kappa.index)) / params.kappa; + if isequal(name,'ChemicalPotential') + scale = 1/scale; + end + else + scale = 1; + end + plot(arg,customfunc(arg,history(ind(i),meta.(name).index))*scale,'LineWidth',2); + if isempty(ps.yyaxisLim) + ax.YLim = ylimtemp; + else + ax.YLim = ps.yyaxisLim(j,:); + end + axis square + end + if ps.label && j==1 + text(0.1,1.2,['Iter. ',num2str(ind(i)-1)],'Units','normalized','HorizontalAlignment',ps.labelHorizontalAlignment); + end + end +end +if isfield(meta,'C') && ~isempty(ps.CtruthSubplot) + axC = subtightplot(rowtotal,columntotal,columntotal*(ps.CtruthSubplot(1)-1)+ps.CtruthSubplot(2),stparg{:}); + CC = params.C; + halfSize = (kernelSize-1)/2; + CC((2+halfSize(1)):(end-halfSize(1)),:)=[]; + CC(:,(2+halfSize(2)):(end-halfSize(2)))=[]; + imagesc(fftshift(CC)); + axis(axC,'image'); + axC.XTick = []; + axC.YTick = []; + axC.Box = 'off'; + title('C_2 (truth)') + colormap(gca,'default') +end +set(findall(gcf,'-property','FontName'),'FontName','Arial'); +set(findall(gcf,'-property','FontWeight'),'FontWeight','normal'); +set(findall(gcf,'-property','FontSize'),'FontSize',ps.FontSize); + +end + +function hOut = TextLocation(textString,varargin) + +l = legend(textString,varargin{:}); +t = annotation('textbox'); +t.String = textString; +t.Position = l.Position; +delete(l); +% t.LineStyle = 'None'; + +if nargout + hOut = t; +end +end From 5e087bf06e30669fdabb4192e322fb9fc8cfbb57 Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Thu, 11 Jul 2019 00:14:15 -0400 Subject: [PATCH 048/149] visualize DDFT_nucleation2, update DDFT_nucleation2_helper to do optim loop --- solver/DDFT_nucleation2.m | 92 +++++++++++++++++++------------- solver/DDFT_nucleation2_helper.m | 12 ++--- 2 files changed, 60 insertions(+), 44 deletions(-) diff --git a/solver/DDFT_nucleation2.m b/solver/DDFT_nucleation2.m index 07db5f8..b25dbf6 100644 --- a/solver/DDFT_nucleation2.m +++ b/solver/DDFT_nucleation2.m @@ -1,4 +1,6 @@ addpath('../../CHACR/GIP') +runoptim = false; + tic; L = [5,5]; N = [256,256]; @@ -7,43 +9,57 @@ params.N = N; params.L = L; -[t1,y1,params] = solver_DDFT([],[],params); - -xx = linspace(0,L(1),N(1)); -yy = linspace(0,L(2),N(2)); -[xx,yy] = ndgrid(xx,yy); -range = [1.5,3.5]; -thickness = 0.1; -roi = roi_rectangle(xx,yy,range,range,thickness); -center = L/2; -radius = 0.06*L(1); -thickness = 0.01*L(1); -roi = roi_circle(xx,yy,center,radius,thickness); - -%nucleus -y0 = y1(end,:)'; -roi = roi(:); -rho = (sum(y0) - sum(roi.*y0)) / sum(1-roi); -y0 = roi.*y0 + (1-roi)*rho; -figure; imagesc(reshape(y0,N)); - -tspan2 = linspace(0,1.05,100); -tspan2 = linspace(0,1.5,100); -[t2,y2] = solver_DDFT(tspan2,y0,params); - -figure; visualize([],[],[],y2(1:10:end,:),'c',false,'ImageSize',N); - -ind = 20:2:100; -tdata = t2(ind); -ydata = y2(ind,:); -toc - -save_history = true; -resultpath = [largedatapath,'DDFT_nucleation2.mat']; -options = optimoptions('fminunc'); -if save_history - options = optimoptions(options,'OutputFcn', @(x,optimvalues,state) save_opt_history(x,optimvalues,state,resultpath)); +if ~exist('tdata','var') + [t1,y1,params] = solver_DDFT([],[],params); + + xx = linspace(0,L(1),N(1)); + yy = linspace(0,L(2),N(2)); + [xx,yy] = ndgrid(xx,yy); + range = [1.5,3.5]; + thickness = 0.1; + roi = roi_rectangle(xx,yy,range,range,thickness); + center = L/2; + radius = 0.06*L(1); + thickness = 0.01*L(1); + roi = roi_circle(xx,yy,center,radius,thickness); + + %nucleus + y0 = y1(end,:)'; + roi = roi(:); + rho = (sum(y0) - sum(roi.*y0)) / sum(1-roi); + y0 = roi.*y0 + (1-roi)*rho; + figure; imagesc(reshape(y0,N)); + + tspan2 = linspace(0,1.05,100); + tspan2 = linspace(0,1.5,100); + [t2,y2] = solver_DDFT(tspan2,y0,params); + + figure; visualize([],[],[],y2(1:10:end,:),'c',false,'ImageSize',N); + + ind = 20:2:100; + tdata = t2(ind); + ydata = y2(ind,:); + toc end -x_opt = IP_DDFT(tdata,ydata,params,[21,21],'k',options,x_opt); -% [val,gradient] = IP_DDFT_debug(x_opt/max(x_opt)*1.2,tdata,ydata,params,[21,21],'k'); +kernelSize = [21,21]; +Cspace = 'k'; + +resultpath = [largedatapath,'DDFT_nucleation2.mat']; +if runoptim + save_history = true; + options = optimoptions('fminunc'); + if save_history + options = optimoptions(options,'OutputFcn', @(x,optimvalues,state) save_opt_history(x,optimvalues,state,resultpath)); + end + + x_opt = IP_DDFT(tdata,ydata,params,kernelSize,Cspace,options,x_opt); + % [val,gradient] = IP_DDFT_debug(x_opt/max(x_opt)*1.2,tdata,ydata,params,[21,21],'k'); +else + meta.C.index = floor((prod(kernelSize)+1)/2); + meta.C.exp = false; + frameindex = [1,6,12,23,41]; + history_production(resultpath,[1,2,11,71,171],[],[],meta,tdata-tdata(1),ydata,params,kernelSize,Cspace,'FrameIndex',frameindex,'CtruthSubplot',[2,length(frameindex)]); + f = gcf; + f.Position = [680 337 522 641]; +end diff --git a/solver/DDFT_nucleation2_helper.m b/solver/DDFT_nucleation2_helper.m index 6bd0238..91eb566 100644 --- a/solver/DDFT_nucleation2_helper.m +++ b/solver/DDFT_nucleation2_helper.m @@ -1,11 +1,11 @@ addpath('../../CHACR/GIP'); save_history = true; resultpath = [largedatapath,'DDFT_nucleation2.mat']; +varload = load(resultpath); +x_opt = varload.history(end,:); -options = optimoptions('fminunc','OutputFcn',@(x,optimvalues,state) save_opt_history(x,optimvalues,state,resultpath)); -x_opt = IP_DDFT(tdata,ydata,params,[21,21],'k',options,x_opt); - - - - +options = optimoptions('fminunc','OutputFcn',@(x,optimvalues,state) save_opt_history(x,optimvalues,state,resultpath,[],true)); +while (exitflag==5) + [x_opt,~,exitflag] = IP_DDFT(tdata,ydata,params,[21,21],'k',options,x_opt); +end From 5af0e2b5a7d6632f6719727607f6ce3a7ae4aff1 Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Sun, 14 Jul 2019 01:42:59 -0400 Subject: [PATCH 049/149] update IP_DDFT, add tspan and eval options --- solver/IP_DDFT.m | 17 ++++++++++++----- solver/history_production.m | 2 +- 2 files changed, 13 insertions(+), 6 deletions(-) diff --git a/solver/IP_DDFT.m b/solver/IP_DDFT.m index d2ad420..0b75c54 100644 --- a/solver/IP_DDFT.m +++ b/solver/IP_DDFT.m @@ -1,5 +1,14 @@ -function [x_opt,fval,exitflag] = IP_DDFT(tdata,ydata,params,kernelSize,Cspace,options,x_guess,mode) -%set mode = 'eval' to only do the forward solve and return +function [x_opt,fval,exitflag] = IP_DDFT(tdata,ydata,params,kernelSize,Cspace,options,x_guess,varargin) +ps = inputParser; +addParameter(ps,'eval',false); +%set eval = true to only do the forward solve and return +addParameter(ps,'tspan',100); +%set tspan to a positive integer or 'sol' to specify the number of time points returned for solution history +ps.CaseSensitive = false; +parse(ps,varargin{:}); +tspan = ps.Results.tspan; +eval = ps.Results.eval; + addpath('../../CHACR/GIP') % params.N = [256,256]; @@ -25,9 +34,7 @@ x_guess = zeros(1,NC); end -tspan = 100; - -if nargin > 7 && isequal(mode,'eval') +if eval x_opt = IP(tdata,ydata,x_guess,meta,params, ... @(tdata,y0,FSA,meta,params) forwardSolver(tdata,y0,FSA,meta,params,tspan), ... [], [], [],... diff --git a/solver/history_production.m b/solver/history_production.m index f491191..e430b19 100644 --- a/solver/history_production.m +++ b/solver/history_production.m @@ -76,7 +76,7 @@ function history_production(resultpath,ind,modelfunc,arg,meta,tdata,ydata,params y = varload.y; visualize([],[],[],y{ind(i)}(frameindex_model,:),'c',false,'ImageSize',params.N,'caxis',clim,'GridSize',[1,NaN],'OuterGridSize',[rowtotal,1],'OuterSubplot',[i+1,1],'ColumnTotal',columntotal,'StarterInd',i*columntotal+1,'subtightplot',stparg); else - yhistory = IP_DDFT(tdata,ydata,params,kernelSize,Cspace,[],history(ind(i),:),'eval'); + yhistory = IP_DDFT(tdata,ydata,params,kernelSize,Cspace,[],history(ind(i),:),'eval',true); visualize([],[],[],yhistory(frameindex_model,:),'c',false,'ImageSize',params.N,'caxis',clim,'GridSize',[1,NaN],'OuterGridSize',[rowtotal,1],'OuterSubplot',[i+1,1],'ColumnTotal',columntotal,'StarterInd',i*columntotal+1,'subtightplot',stparg); end subtightplot(rowtotal,columntotal,i*columntotal+1,stparg{:}); From 317d33bc8ab1f4555ba71dab348c12a9be547aee Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Sun, 14 Jul 2019 01:43:22 -0400 Subject: [PATCH 050/149] add DDFT_nucleation3, a larger alpha, small n0 for nucleation event --- solver/DDFT_nucleation3.m | 65 +++++++++++++++++++++++++++++++++++++++ 1 file changed, 65 insertions(+) create mode 100644 solver/DDFT_nucleation3.m diff --git a/solver/DDFT_nucleation3.m b/solver/DDFT_nucleation3.m new file mode 100644 index 0000000..ab3f4e3 --- /dev/null +++ b/solver/DDFT_nucleation3.m @@ -0,0 +1,65 @@ +addpath('../../CHACR/GIP') +runoptim = true; + +tic; +L = [5,5]; +N = [256,256]; +n = prod(N); + +params.N = N; +params.L = L; + +[k2,k] = formk(N,L); +k0 = 10; +alpha = 5; +params.C = exp(-(sqrt(k2)-k0).^2/(2*alpha^2))*0.95; + +[t1,y1,params] = solver_DDFT([],[],params); + +xx = linspace(0,L(1),N(1)); +yy = linspace(0,L(2),N(2)); +[xx,yy] = ndgrid(xx,yy); +center = L/2; +radius = 0.06*L(1); +thickness = 0.01*L(1); +roi = roi_circle(xx,yy,center,radius,thickness); + +%nucleus +y0 = y1(end,:)'; +roi = roi(:); +y02 = 0.045; +rho = (y02*n - sum(roi.*y0)) / sum(1-roi); +y0 = roi.*y0 + (1-roi)*rho; + +tspan2 = linspace(0,1.5,100); +[t2,y2] = solver_DDFT(tspan2,y0,params); + +ind = 1:100; +tdata = t2(ind); +ydata = y2(ind,:); +toc + +kernelSize = [41,41]; +Cspace = 'k'; + +resultpath = [largedatapath,'DDFT_nucleation3.mat']; +if runoptim + save_history = true; + options = optimoptions('fminunc'); + if save_history + options = optimoptions(options,'OutputFcn', @(x,optimvalues,state) save_opt_history(x,optimvalues,state,resultpath,[],true)); + end + NC = floor((prod(kernelSize)+1)/2); + x_opt = zeros(1,NC); + exitflag = 5; + while (exitflag==5) + [x_opt,~,exitflag] = IP_DDFT(tdata,ydata,params,kernelSize,Cspace,options,x_opt,'tspan','sol'); + end +else + meta.C.index = floor((prod(kernelSize)+1)/2); + meta.C.exp = false; + frameindex = [1,6,12,23,41]; + history_production(resultpath,[1,2,11,71,171],[],[],meta,tdata-tdata(1),ydata,params,kernelSize,Cspace,'FrameIndex',frameindex,'CtruthSubplot',[2,length(frameindex)]); + f = gcf; + f.Position = [680 337 522 641]; +end From 64efb7c743449ec34b68b447b9680480a27aa174 Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Sun, 14 Jul 2019 19:13:21 -0400 Subject: [PATCH 051/149] try alternate between 2 datasets DDFT_nucleation3 --- solver/DDFT_nucleation3.m | 17 ++++++++++------- 1 file changed, 10 insertions(+), 7 deletions(-) diff --git a/solver/DDFT_nucleation3.m b/solver/DDFT_nucleation3.m index ab3f4e3..587418d 100644 --- a/solver/DDFT_nucleation3.m +++ b/solver/DDFT_nucleation3.m @@ -34,9 +34,12 @@ tspan2 = linspace(0,1.5,100); [t2,y2] = solver_DDFT(tspan2,y0,params); -ind = 1:100; -tdata = t2(ind); -ydata = y2(ind,:); +ind = 1:50; +tdata1 = t2(ind); +ydata1 = y2(ind,:); +ind = 50:100; +tdata2 = t2(ind); +ydata2 = y2(ind,:); toc kernelSize = [41,41]; @@ -45,15 +48,15 @@ resultpath = [largedatapath,'DDFT_nucleation3.mat']; if runoptim save_history = true; - options = optimoptions('fminunc'); + options = optimoptions('fminunc','MaxIterations',5); if save_history options = optimoptions(options,'OutputFcn', @(x,optimvalues,state) save_opt_history(x,optimvalues,state,resultpath,[],true)); end NC = floor((prod(kernelSize)+1)/2); x_opt = zeros(1,NC); - exitflag = 5; - while (exitflag==5) - [x_opt,~,exitflag] = IP_DDFT(tdata,ydata,params,kernelSize,Cspace,options,x_opt,'tspan','sol'); + while true + x_opt = IP_DDFT(tdata1,ydata1,params,kernelSize,Cspace,options,x_opt,'tspan',200); + x_opt = IP_DDFT(tdata2,ydata2,params,kernelSize,Cspace,options,x_opt,'tspan',200); end else meta.C.index = floor((prod(kernelSize)+1)/2); From 9555e50ad1b447e1ef7265733828ba5f89a6afc6 Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Mon, 15 Jul 2019 20:14:33 -0400 Subject: [PATCH 052/149] update solver_DDFT to allow empty C and mu in params --- solver/solver_DDFT.m | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/solver/solver_DDFT.m b/solver/solver_DDFT.m index 43800aa..dd73c0e 100644 --- a/solver/solver_DDFT.m +++ b/solver/solver_DDFT.m @@ -28,14 +28,14 @@ N = params.N; L = params.L; dx = params.dx; -if ~isfield(params,'C') +if ~isfield(params,'C') || isempty(params.C) %default [k2,k] = formk(N,L); k0 = 10; alpha = 2; params.C = exp(-(sqrt(k2)-k0).^2/(2*alpha^2))*0.95; end -if ~isfield(params,'mu') +if ~isfield(params,'mu') || isempty(params.mu) params.mu.func = @(x,coeff) x - x.^2/2 + x.^3/3; %@(x) log(1+x) params.mu.grad = @(x,coeff) 1 - x + x.^2; params.mu.params = []; From 8285010efac894e28e56d7d63be7f4ef682fe67f Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Mon, 15 Jul 2019 20:14:58 -0400 Subject: [PATCH 053/149] switch to custom_EvenPoly for Cspace=isotropic in IP_DDFT --- solver/IP_DDFT.m | 8 +++----- 1 file changed, 3 insertions(+), 5 deletions(-) diff --git a/solver/IP_DDFT.m b/solver/IP_DDFT.m index 0b75c54..4846891 100644 --- a/solver/IP_DDFT.m +++ b/solver/IP_DDFT.m @@ -17,11 +17,9 @@ if isequal(Cspace,'isotropic') [k2,~] = formk(params.N,params.L); k = sqrt(k2); -% bound = [0, 2*pi*params.N(1)/params.L(1)/2]; %assuming at least 5 points across each pattern - bound = [0,max(k(:))]; - expleg = custom_Legendre(1,bound); - params.Cfunc.func = @(x) expleg.func(k,x); - params.Cfunc.sens = @(x) expleg.sens(k,x); + evenpoly = custom_EvenPoly; + params.Cfunc.func = @(x) evenpoly.func(k,x); + params.Cfunc.sens = @(x) evenpoly.sens(k,x); NC = kernelSize; else NC = floor((prod(kernelSize)+1)/2); From d47fe29fa872e8c20852e50cfabeeb3db518552b Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Mon, 15 Jul 2019 20:15:19 -0400 Subject: [PATCH 054/149] DDFT_nucleation_PFC, use PFC kernel --- solver/DDFT_nucleation_PFC.m | 38 ++++++++++++++++++++++++++++++++++++ 1 file changed, 38 insertions(+) create mode 100644 solver/DDFT_nucleation_PFC.m diff --git a/solver/DDFT_nucleation_PFC.m b/solver/DDFT_nucleation_PFC.m new file mode 100644 index 0000000..a9061f5 --- /dev/null +++ b/solver/DDFT_nucleation_PFC.m @@ -0,0 +1,38 @@ +addpath('../../CHACR/GIP') +runoptim = false; + +tic; +L = [5,5]; +N = [256,256]; +n = prod(N); + +params.N = N; +params.L = L; + +[k2,k] = formk(N,L); +k0 = 10; +alpha = 5; +params.C = - (1-(k2/k0^2)).^2 + 0.95; + +[t1,y1,params] = solver_DDFT([],[],params); + +% params.C = []; +% [t2,y2,params] = solver_DDFT([],[],params); + +xx = linspace(0,L(1),N(1)); +yy = linspace(0,L(2),N(2)); +[xx,yy] = ndgrid(xx,yy); +center = L/2; +radius = 0.06*L(1); +thickness = 0.01*L(1); +roi = roi_circle(xx,yy,center,radius,thickness); + +%nucleus +y0 = y1(end,:)'; +roi = roi(:); +y02 = 0.045; +rho = (y02*n - sum(roi.*y0)) / sum(1-roi); +y0 = roi.*y0 + (1-roi)*rho; + +tspan2 = linspace(0,1.5,100); +[t2,y2] = solver_DDFT(tspan2,y0,params); From 834adaddd31d909acea5cf6e20a0cafbf982cf77 Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Tue, 16 Jul 2019 02:03:47 -0400 Subject: [PATCH 055/149] update IP_DDFT, parameter prescreening and isotropic Cspace, highest order must be negative --- solver/IP_DDFT.m | 46 ++++++++++++++++++++++++++++++++++------------ 1 file changed, 34 insertions(+), 12 deletions(-) diff --git a/solver/IP_DDFT.m b/solver/IP_DDFT.m index 4846891..d6cee6a 100644 --- a/solver/IP_DDFT.m +++ b/solver/IP_DDFT.m @@ -11,30 +11,30 @@ addpath('../../CHACR/GIP') -% params.N = [256,256]; -% params.L = [5,5]; -% params.dx = params.L ./ params.N; +ybound = [min(ydata(:)),max(ydata(:))]; + if isequal(Cspace,'isotropic') [k2,~] = formk(params.N,params.L); - k = sqrt(k2); - evenpoly = custom_EvenPoly; - params.Cfunc.func = @(x) evenpoly.func(k,x); - params.Cfunc.sens = @(x) evenpoly.sens(k,x); + p = custom_Poly; + params.Cfunc.func = @(x) C_funcwrapper(k2,x,p.func); + params.Cfunc.sens = @(x) C_senswrapper(k2,x,p.sens); NC = kernelSize; + meta.C.exp = false(1,NC); + meta.C.exp(end) = true; else NC = floor((prod(kernelSize)+1)/2); params.Csens = @(y,i) Csens_ASA(y,i,Cspace,kernelSize); + meta.C.exp = false; end meta.C.index = 1:NC; -meta.C.exp = false; if nargin < 7 || isempty(x_guess) x_guess = zeros(1,NC); end if eval x_opt = IP(tdata,ydata,x_guess,meta,params, ... - @(tdata,y0,FSA,meta,params) forwardSolver(tdata,y0,FSA,meta,params,tspan), ... + @(tdata,y0,FSA,meta,params) forwardSolver(tdata,y0,FSA,meta,params,tspan,ybound), ... [], [], [],... @(name,xparam,params) assign(name,xparam,params,Cspace,kernelSize),'eval',true); else @@ -46,7 +46,7 @@ options = optimoptions('fminunc','SpecifyObjectiveGradient',true,'Display','iter-detailed'); end [x_opt,fval,exitflag] = fminunc(@(x) IP(tdata,ydata,x,meta,params, ... - @(tdata,y0,FSA,meta,params) forwardSolver(tdata,y0,FSA,meta,params,tspan), ... + @(tdata,y0,FSA,meta,params) forwardSolver(tdata,y0,FSA,meta,params,tspan,ybound), ... @adjointSolver, ... loss,lossHess, ... @(name,xparam,params) assign(name,xparam,params,Cspace,kernelSize)), ... @@ -102,12 +102,19 @@ end end -function [tout,y,dy,params] = forwardSolver(tdata,y0,FSA,meta,params,tspan) +function [tout,y,dy,params] = forwardSolver(tdata,y0,FSA,meta,params,tspan,ybound) %tspan can either be sol or number of time points - if any(params.C(:)>2) + if ~isfield(params,'mu') || isempty(params.mu) + dmu = 1 - ybound + ybound.^2; + else + dmu = customizeFunGrad(params,'mu','grad',ybound); + end + if any(dmu-max(params.C(:))<0) + %instability even at the max or min y value tout = NaN; y = NaN; dy = NaN; + return end if isequal(tspan,'sol') sol = true; @@ -225,3 +232,18 @@ end end end + +function [y,dy] = C_funcwrapper(x,coeff,polyfunc) + coeff(end) = -coeff(end); + if nargout<2 + y = feval(polyfunc,x,coeff); + else + [y,dy] = feval(polyfunc,x,coeff); + end +end + +function dy = C_senswrapper(x,coeff,polysens) + coeff(end) = - coeff(end); + dy = feval(polysens,x,coeff); + dy(:,:,end) = -dy(:,:,end); +end From e688147aa76ed4c056978a5a441b13bc71d02fd3 Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Tue, 16 Jul 2019 02:06:13 -0400 Subject: [PATCH 056/149] add DDFT_nucleation4 fit DDFT to a 4-th order PFC --- solver/DDFT_nucleation4.m | 55 +++++++++++++++++++++++++++++++++++++++ 1 file changed, 55 insertions(+) create mode 100644 solver/DDFT_nucleation4.m diff --git a/solver/DDFT_nucleation4.m b/solver/DDFT_nucleation4.m new file mode 100644 index 0000000..7de0b08 --- /dev/null +++ b/solver/DDFT_nucleation4.m @@ -0,0 +1,55 @@ +%data from DDFT_nucleation3 +%use PFC to fit +addpath('../../CHACR/GIP') +runoptim = true; + +tic; +L = [5,5]; +N = [256,256]; +n = prod(N); + +params.N = N; +params.L = L; + +[k2,k] = formk(N,L); +k0 = 10; +alpha = 5; +params.C = exp(-(sqrt(k2)-k0).^2/(2*alpha^2))*0.95; + +[t1,y1,params] = solver_DDFT([],[],params); + +xx = linspace(0,L(1),N(1)); +yy = linspace(0,L(2),N(2)); +[xx,yy] = ndgrid(xx,yy); +center = L/2; +radius = 0.06*L(1); +thickness = 0.01*L(1); +roi = roi_circle(xx,yy,center,radius,thickness); + +%nucleus +y0 = y1(end,:)'; +roi = roi(:); +y02 = 0.045; +rho = (y02*n - sum(roi.*y0)) / sum(1-roi); +y0 = roi.*y0 + (1-roi)*rho; + +tspan2 = linspace(0,1.5,100); +[t2,y2] = solver_DDFT(tspan2,y0,params); + +ind = 10:100; +tdata = t2(ind); +ydata = y2(ind,:); +toc + +kernelSize = 3; +Cspace = 'isotropic'; + +resultpath = [largedatapath,'DDFT_nucleation4.mat']; + +options = optimoptions('fminunc','OutputFcn', @(x,optimvalues,state) save_opt_history(x,optimvalues,state,resultpath,[],true)); + +x_opt = [0,0,-10]; +exitflag==5; +while (exitflag==5) + [x_opt,~,exitflag] = IP_DDFT(tdata,ydata,params,kernelSize,Cspace,options,x_opt); +end From 834156ab2924b20f775e1f6dafd1823ec980da23 Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Tue, 16 Jul 2019 18:21:43 -0400 Subject: [PATCH 057/149] fix critical bug in jacobian_mult in solver_DDFT, for loop index wrong, vectorize jacobian_mult over columns of xi, FSA now works for DDFT --- solver/solver_DDFT.m | 15 ++++++--------- 1 file changed, 6 insertions(+), 9 deletions(-) diff --git a/solver/solver_DDFT.m b/solver/solver_DDFT.m index dd73c0e..3b42ac4 100644 --- a/solver/solver_DDFT.m +++ b/solver/solver_DDFT.m @@ -240,16 +240,13 @@ N = params.N; dx = params.dx; C = params.C; - yy = zeros(size(xi)); - for p = 1:length(size(xi,2)) - xip = reshape(xi(:,p),N); - dfdy = info; - mu = dfdy .* xip; - mu = mu - ifftn(C .* fftn(xip)); - for i = 1:length(N) - yy(:,p) = yy(:,p) + reshape((circshift(mu,1,i)+circshift(mu,-1,i)-2*mu)/dx(i)^2, [], 1); - end + xi = reshape(xi,N(1),N(2),[]); + mu = info .* xi - ifft2(C .* fft2(xi), 'symmetric'); + yy = 0; + for i = 1:length(N) + yy = yy + (circshift(mu,1,i)+circshift(mu,-1,i)-2*mu)/dx(i)^2; end + yy = reshape(yy,prod(N),[]); end end From c90e58ffecbfb1f9170d685d4b5347b987e81697 Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Tue, 16 Jul 2019 18:24:34 -0400 Subject: [PATCH 058/149] add FDcoeff to compute 1D finite difference coefficient --- solver/FDcoeff.m | 27 +++++++++++++++++++++++++++ 1 file changed, 27 insertions(+) create mode 100644 solver/FDcoeff.m diff --git a/solver/FDcoeff.m b/solver/FDcoeff.m new file mode 100644 index 0000000..5c9dfc4 --- /dev/null +++ b/solver/FDcoeff.m @@ -0,0 +1,27 @@ +function y = FDcoeff(npts,h,deriv,x) + %coefficients of 1D finite difference + %ntps: number of points, h: distance + %deriv: coefficients of the derivatives. It can be a 1D array, or if 2D, each column is a set of coefficient + %in increasing order 0 through npts-1 + %for example, to get 4th order derivative, deriv = [0;0;0;0;1] + %to get 2nd and 4th, deriv = [0,0;0,0;1,0;0,0;0,1]; + %if x is provided, x is the positions of the points, discarding npts and h information + if nargin < 4 || isempty(x) + n = (npts-1)/2; + x = h*(-n:n); + elseif size(x,2)==1 + x = x'; + npts = size(x,2); + end + if size(deriv,1)==1 + deriv = deriv'; + end + if size(deriv,1) Date: Tue, 16 Jul 2019 18:26:58 -0400 Subject: [PATCH 059/149] rewrite Cspace=isotropic, add Cspace=FD --- solver/IP_DDFT.m | 62 ++++++++++++++++++++++++++++++++---------------- 1 file changed, 42 insertions(+), 20 deletions(-) diff --git a/solver/IP_DDFT.m b/solver/IP_DDFT.m index d6cee6a..745c91a 100644 --- a/solver/IP_DDFT.m +++ b/solver/IP_DDFT.m @@ -14,13 +14,20 @@ ybound = [min(ydata(:)),max(ydata(:))]; if isequal(Cspace,'isotropic') + NC = kernelSize; + meta.C.exp = false(1,NC); + meta.C.exp(end) = true; [k2,~] = formk(params.N,params.L); p = custom_Poly; - params.Cfunc.func = @(x) C_funcwrapper(k2,x,p.func); - params.Cfunc.sens = @(x) C_senswrapper(k2,x,p.sens); + Csensval = feval(p.sens,k2,ones(1,NC)); + %let the basis of the last derivative be negative + Csensval(:,:,end) = -Csensval(:,:,end); + params.Csensval = Csensval; +elseif isequal(Cspace,'FD') NC = kernelSize; meta.C.exp = false(1,NC); meta.C.exp(end) = true; + params = FD2otf(NC,params); else NC = floor((prod(kernelSize)+1)/2); params.Csens = @(y,i) Csens_ASA(y,i,Cspace,kernelSize); @@ -70,11 +77,13 @@ %but it must be converted to be centered at 1,1 in the k-space representation used in DDFT solver %consider other extensions: %1. Reduce to representing 1D C(k) if it's axisymmetric - if isequal(Cspace,'isotropic') - %C(k) can be represented by a 1D function - params.C = params.Cfunc.func(xparam); - params.Csensval = params.Cfunc.sens(xparam); - else + %Cspace = isotropic, C(k) = a1 + a2*k^2 + a3*k^4 + ... + %Cspace = FD, C = a1 - a2*nabla + a3*nabla^2 + ... + switch Cspace + case {'isotropic','FD'} + coeff(1,1,:) = xparam; + params.C = sum(params.Csensval .* coeff,3); + case {'k','real'} if any(mod(kernelSize,2)==0) error('kernel size must be odd'); end @@ -233,17 +242,30 @@ end end -function [y,dy] = C_funcwrapper(x,coeff,polyfunc) - coeff(end) = -coeff(end); - if nargout<2 - y = feval(polyfunc,x,coeff); - else - [y,dy] = feval(polyfunc,x,coeff); - end -end - -function dy = C_senswrapper(x,coeff,polysens) - coeff(end) = - coeff(end); - dy = feval(polysens,x,coeff); - dy(:,:,end) = -dy(:,:,end); +function params = FD2otf(numDeriv,params) + %transform finite difference coefficient to otf + %y(:,:,i) is the otf of the 2(i-1)th derivative + %in total, there are numDeriv derivatives + npts = numDeriv*2-1; + %switch to 0, k^2, k^4, ... rather than 0, nabla^2, nabla^4 + %but, to be consistent with Cspace = 'isotropic' + %let the basis of the last derivative be negative + derivcoeff = ones(numDeriv,1); + derivcoeff(2:2:end) = -1; + derivcoeff(end) = -1; + derivdiag = accumarray([1:2:npts;1:numDeriv]',derivcoeff); + coeffx = FDcoeff(npts,params.dx(1),derivdiag); + coeffy = FDcoeff(npts,params.dx(2),derivdiag); + row = [numDeriv*ones(1,npts),1:npts]; + column = [1:npts,numDeriv*ones(1,npts)]; + C = zeros(params.N(1),params.N(2),numDeriv); + for i = 1:numDeriv + if i==1 + kernel = 1; + else + kernel = accumarray([row',column'],[coeffx(:,i);coeffy(:,i)]); + end + C(:,:,i) = psf2otf(kernel,params.N); + end + params.Csensval = C; end From 8ef80df4e22cf02036059842522d800958ff810b Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Tue, 16 Jul 2019 18:27:28 -0400 Subject: [PATCH 060/149] use parser in solver_DDFT, add option and moreoptions in params, update IP_DDFT --- solver/IP_DDFT.m | 4 ++-- solver/solver_DDFT.m | 27 +++++++++++++++++++++------ 2 files changed, 23 insertions(+), 8 deletions(-) diff --git a/solver/IP_DDFT.m b/solver/IP_DDFT.m index 745c91a..2faaabd 100644 --- a/solver/IP_DDFT.m +++ b/solver/IP_DDFT.m @@ -131,11 +131,11 @@ sol = false; tdata = linspace(tdata(1),tdata(end),tspan); end - [tout,y,params,dy] = solver_DDFT(tdata,y0,params,meta,'forward',sol,FSA); + [tout,y,params,dy] = solver_DDFT(tdata,y0,params,meta,'forward','sol',sol,'FSA',FSA); end function grad = adjointSolver(tdata,sol,lossgrad,meta,discrete,~,params) - grad = solver_DDFT(tdata,sol,params,meta,'adjoint',lossgrad,discrete); + grad = solver_DDFT(tdata,sol,params,meta,'adjoint','error',lossgrad,'discrete',discrete); end function dy = Csens(y,Cspace,kernelSize) diff --git a/solver/solver_DDFT.m b/solver/solver_DDFT.m index 3b42ac4..8ade0d5 100644 --- a/solver/solver_DDFT.m +++ b/solver/solver_DDFT.m @@ -2,13 +2,21 @@ %this provides solution to both forward and backward evaluation %set mode = 'forward' (default) to perform model evaluation, in this mode, we accept two varargin, varargin{1} is sol, when true (false by default), output sol structure (varargin = {tout,sol,params},, when false, varargin = {tout,y,params}. varargin{2} is FSA, when true (false by default), also computes FSA and varargin{4} = ys. %set mode = 'adjoint' to perform ASA analysis. varargin{1} = error, varargin{2] = discrete, tspan and y0 must be tdata and sol (solution history). varargout = {grad} +%params can also contain options and moreoptions ASA = (nargin > 4) && isequal(mode,'adjoint'); +ps = inputParser; +addParameter(ps,'error',[]); +addParameter(ps,'discrete',[]); +addParameter(ps,'sol',false); +addParameter(ps,'FSA',false); +ps.CaseSensitive = false; +parse(ps,varargin{:}); if ASA - error = varargin{1}; - discrete = varargin{2}; + error = ps.Results.error; + discrete = ps.Results.discrete; else - sol = ~isempty(varargin) && varargin{1}; - FSA = length(varargin)>1 && varargin{2}; + sol = ps.Results.sol; + FSA = ps.Results.FSA; end addpath('../../CHACR/odesolver') @@ -67,6 +75,13 @@ %the Jacobian and mass matrix of the system is Hermitian, so the treatment of pencil is the same for forward and ASA eval moreoptions = moreodeset('skipInit',true,'Krylov',true, ... 'gmrestol',1e-4,'restart',10); +if isfield(params,'moreoptions') && ~isempty(params.moreoptions) + moreoptions = moreodeset(moreoptions,params.moreoptions); +end +options = odeset; +if isfield(params,'options') && ~isempty(params.options) + options = moreodeset(options,params.options); +end if ~ASA if isempty(y0) || isscalar(y0) @@ -86,7 +101,7 @@ end t0 = tspan(1); yp0 = RHS(t0,y0,params); - options = odeset('InitialSlope',yp0,'Jacobian',@(t,y) jacobian(t,y,params)); + options = odeset(options,'InitialSlope',yp0,'Jacobian',@(t,y) jacobian(t,y,params)); moreoptions = moreodeset(moreoptions, ... 'jacMult',@(xi,t,y,info) jacobian_mult(params,xi,t,y,info), ... 'pencil',@(xi,t,y,hinvGak,info) pencil(params,xi,t,y,hinvGak,info), ... @@ -116,7 +131,7 @@ sol = y0; ASAQuadNp = 1; - options = odeset('Jacobian',@(t,y) jacobian(t,sol,params), ... + options = odeset(options,'Jacobian',@(t,y) jacobian(t,sol,params), ... 'mass', -speye(prod(params.N)),'MassSingular','yes','MStateDependence','none'); moreoptions = moreodeset(moreoptions, ... 'jacMult',@(xi,t,y,info) jacobian_mult(params,xi,t,sol,info), ... From 0e8d85f5186fe3101f2c45705f1681956439ae5d Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Tue, 16 Jul 2019 18:41:24 -0400 Subject: [PATCH 061/149] DDFT_nucleation6 --- solver/DDFT_nucleation6.m | 57 +++++++++++++++++++++++++++++++++++++++ 1 file changed, 57 insertions(+) create mode 100644 solver/DDFT_nucleation6.m diff --git a/solver/DDFT_nucleation6.m b/solver/DDFT_nucleation6.m new file mode 100644 index 0000000..e4c9bb7 --- /dev/null +++ b/solver/DDFT_nucleation6.m @@ -0,0 +1,57 @@ +%data from DDFT_nucleation3 +%based on DDFT_nucleation4, use 4 derivatives +%use PFC to fit +addpath('../../CHACR/GIP') +runoptim = true; + +tic; +L = [5,5]; +N = [256,256]; +n = prod(N); + +params.N = N; +params.L = L; + +[k2,k] = formk(N,L); +k0 = 10; +alpha = 5; +params.C = exp(-(sqrt(k2)-k0).^2/(2*alpha^2))*0.95; + +[t1,y1,params] = solver_DDFT([],[],params); + +xx = linspace(0,L(1),N(1)); +yy = linspace(0,L(2),N(2)); +[xx,yy] = ndgrid(xx,yy); +center = L/2; +radius = 0.06*L(1); +thickness = 0.01*L(1); +roi = roi_circle(xx,yy,center,radius,thickness); + +%nucleus +y0 = y1(end,:)'; +roi = roi(:); +y02 = 0.045; +rho = (y02*n - sum(roi.*y0)) / sum(1-roi); +y0 = roi.*y0 + (1-roi)*rho; + +tspan2 = linspace(0,1.5,100); +[t2,y2] = solver_DDFT(tspan2,y0,params); + +ind = 10:100; +tdata = t2(ind); +ydata = y2(ind,:); +toc + +kernelSize = 4; +Cspace = 'isotropic'; +params.moreoptions = moreodeset('gmresTol',0.2*1e-5); + +resultpath = [largedatapath,'DDFT_nucleation6.mat']; + +options = optimoptions('fminunc','OutputFcn', @(x,optimvalues,state) save_opt_history(x,optimvalues,state,resultpath,[],true)); +options = optimoptions(options,'HessianFcn','objective','Algorithm','trust-region'); + +varload = load([largedatapath,'DDFT_nucleation4.mat']); +x_guess = varload.history(end,:); +x_guess = [x_guess,-20]; +[x_opt,~,exitflag] = IP_DDFT(tdata,ydata,params,kernelSize,Cspace,options,x_guess); From 2664bcc010c87941f23a4481cc5f8e9999bd89c8 Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Tue, 16 Jul 2019 18:53:10 -0400 Subject: [PATCH 062/149] DDFT_nucleation6 and 7 --- solver/DDFT_nucleation6.m | 3 ++- solver/DDFT_nucleation7.m | 56 +++++++++++++++++++++++++++++++++++++++ 2 files changed, 58 insertions(+), 1 deletion(-) create mode 100644 solver/DDFT_nucleation7.m diff --git a/solver/DDFT_nucleation6.m b/solver/DDFT_nucleation6.m index e4c9bb7..6f08970 100644 --- a/solver/DDFT_nucleation6.m +++ b/solver/DDFT_nucleation6.m @@ -53,5 +53,6 @@ varload = load([largedatapath,'DDFT_nucleation4.mat']); x_guess = varload.history(end,:); -x_guess = [x_guess,-20]; +x_guess(end) = -exp(x_guess(end)); +x_guess = [x_guess,-10]; [x_opt,~,exitflag] = IP_DDFT(tdata,ydata,params,kernelSize,Cspace,options,x_guess); diff --git a/solver/DDFT_nucleation7.m b/solver/DDFT_nucleation7.m new file mode 100644 index 0000000..8c83d86 --- /dev/null +++ b/solver/DDFT_nucleation7.m @@ -0,0 +1,56 @@ +%data from DDFT_nucleation3 +%use PFC to fit +%based on DDFT_nucleation4, where we found the result is insensitive to the 4th order +%use a larger value for initial guess of 4th order coefficient +addpath('../../CHACR/GIP') +runoptim = true; + +tic; +L = [5,5]; +N = [256,256]; +n = prod(N); + +params.N = N; +params.L = L; + +[k2,k] = formk(N,L); +k0 = 10; +alpha = 5; +params.C = exp(-(sqrt(k2)-k0).^2/(2*alpha^2))*0.95; + +[t1,y1,params] = solver_DDFT([],[],params); + +xx = linspace(0,L(1),N(1)); +yy = linspace(0,L(2),N(2)); +[xx,yy] = ndgrid(xx,yy); +center = L/2; +radius = 0.06*L(1); +thickness = 0.01*L(1); +roi = roi_circle(xx,yy,center,radius,thickness); + +%nucleus +y0 = y1(end,:)'; +roi = roi(:); +y02 = 0.045; +rho = (y02*n - sum(roi.*y0)) / sum(1-roi); +y0 = roi.*y0 + (1-roi)*rho; + +tspan2 = linspace(0,1.5,100); +[t2,y2] = solver_DDFT(tspan2,y0,params); + +ind = 10:100; +tdata = t2(ind); +ydata = y2(ind,:); +toc + +kernelSize = 3; +Cspace = 'isotropic'; +params.moreoptions = moreodeset('gmresTol',1e-5); + +resultpath = [largedatapath,'DDFT_nucleation7.mat']; + +options = optimoptions('fminunc','OutputFcn', @(x,optimvalues,state) save_opt_history(x,optimvalues,state,resultpath,[],true)); +options = optimoptions(options,'HessianFcn','objective','Algorithm','trust-region'); + +x_guess = [0,0,-5]; +[x_opt,~,exitflag] = IP_DDFT(tdata,ydata,params,kernelSize,Cspace,options,x_guess); From 67dfd8302b81e866213dcb2088bb7d210075e1de Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Wed, 17 Jul 2019 00:56:04 -0400 Subject: [PATCH 063/149] add Cspace='isotropic_CmE', add optimizing mu params in IP_DDFT --- solver/IP_DDFT.m | 48 +++++++++++++++++++++++++++++++++++++++++++++--- 1 file changed, 45 insertions(+), 3 deletions(-) diff --git a/solver/IP_DDFT.m b/solver/IP_DDFT.m index 2faaabd..25e8501 100644 --- a/solver/IP_DDFT.m +++ b/solver/IP_DDFT.m @@ -4,16 +4,20 @@ %set eval = true to only do the forward solve and return addParameter(ps,'tspan',100); %set tspan to a positive integer or 'sol' to specify the number of time points returned for solution history +addParameter(ps,'bound',[]); %this is more Cspace = isotropic_CmE +addParameter(ps,'Nmu',0,@(x) (mod(x,2)==1)); %number of parameters for mu, must be odd ps.CaseSensitive = false; parse(ps,varargin{:}); tspan = ps.Results.tspan; eval = ps.Results.eval; +Nmu = ps.Results.Nmu; addpath('../../CHACR/GIP') ybound = [min(ydata(:)),max(ydata(:))]; -if isequal(Cspace,'isotropic') +switch Cspace +case 'isotropic' NC = kernelSize; meta.C.exp = false(1,NC); meta.C.exp(end) = true; @@ -23,12 +27,25 @@ %let the basis of the last derivative be negative Csensval(:,:,end) = -Csensval(:,:,end); params.Csensval = Csensval; -elseif isequal(Cspace,'FD') +case 'isotropic_CmE' + %constant minus exponential + NC = kernelSize; + meta.C.exp = false; + [k2,~] = formk(params.N,params.L); + if isempty(ps.Results.bound) + bound = [0,max(k2(:))]; + else + bound = ps.Results.bound; + end + expleg = custom_ExpLegendre(1,bound); + params.Cfunc.func = @(coeff) coeff(1)-expleg.func(k2,coeff(2:end)); + params.Cfunc.sens = @(coeff) CmE_sens(k2,coeff,expleg.sens); +case 'FD' NC = kernelSize; meta.C.exp = false(1,NC); meta.C.exp(end) = true; params = FD2otf(NC,params); -else +otherwise NC = floor((prod(kernelSize)+1)/2); params.Csens = @(y,i) Csens_ASA(y,i,Cspace,kernelSize); meta.C.exp = false; @@ -39,6 +56,23 @@ x_guess = zeros(1,NC); end +if Nmu>0 + meta.mu.index = NC+(1:Nmu); + meta.mu.exp = false(1,Nmu); + meta.mu.exp(end) = true; %the coefficient of the higher odd order term must be positive + params.mu = ChemPotential_Legendre(1,ybound,false,'onlyEnthalpy'); + if length(x_guess)<(NC+Nmu) + mu_guess = zeros(1,Nmu); + mu_guess(1) = 2; + %the following makes mu nonmonotonic if Nmu>1 + % mu_guess = [zeros(1,Nmu-1),1]; + % [~,dmu] = feval(params.mu.func,ybound(2),mu_guess); + % %set the gradient at ybound to be 2 + % mu_guess(end) = log(2/dmu); + x_guess = [x_guess(1:NC), mu_guess]; + end +end + if eval x_opt = IP(tdata,ydata,x_guess,meta,params, ... @(tdata,y0,FSA,meta,params) forwardSolver(tdata,y0,FSA,meta,params,tspan,ybound), ... @@ -83,6 +117,9 @@ case {'isotropic','FD'} coeff(1,1,:) = xparam; params.C = sum(params.Csensval .* coeff,3); + case 'isotropic_CmE' + params.C = params.Cfunc.func(xparam); + params.Csensval = params.Cfunc.sens(xparam); case {'k','real'} if any(mod(kernelSize,2)==0) error('kernel size must be odd'); @@ -269,3 +306,8 @@ end params.Csensval = C; end + +function y = CmE_sens(x,coeff,expleg_sens) + y = -feval(expleg_sens,x,coeff(2:end)); + y = cat(3,ones(size(x)),y); +end From 8656cfad56236fa4fd0e397fbb144492803bbcc6 Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Wed, 17 Jul 2019 00:56:20 -0400 Subject: [PATCH 064/149] update and add DDFT_nucleation(4,9) --- solver/DDFT_nucleation4.m | 11 ++++---- solver/DDFT_nucleation9.m | 54 +++++++++++++++++++++++++++++++++++++++ 2 files changed, 59 insertions(+), 6 deletions(-) create mode 100644 solver/DDFT_nucleation9.m diff --git a/solver/DDFT_nucleation4.m b/solver/DDFT_nucleation4.m index 7de0b08..427c75d 100644 --- a/solver/DDFT_nucleation4.m +++ b/solver/DDFT_nucleation4.m @@ -43,13 +43,12 @@ kernelSize = 3; Cspace = 'isotropic'; +params.moreoptions = moreodeset('gmresTol',1e-5); resultpath = [largedatapath,'DDFT_nucleation4.mat']; -options = optimoptions('fminunc','OutputFcn', @(x,optimvalues,state) save_opt_history(x,optimvalues,state,resultpath,[],true)); +options = optimoptions('fminunc','OutputFcn', @(x,optimvalues,state) save_opt_history(x,optimvalues,state,resultpath)); +options = optimoptions(options,'HessianFcn','objective','Algorithm','trust-region'); -x_opt = [0,0,-10]; -exitflag==5; -while (exitflag==5) - [x_opt,~,exitflag] = IP_DDFT(tdata,ydata,params,kernelSize,Cspace,options,x_opt); -end +x_guess = [0,0,-10]; +[x_opt,~,exitflag] = IP_DDFT(tdata,ydata,params,kernelSize,Cspace,options,x_guess); diff --git a/solver/DDFT_nucleation9.m b/solver/DDFT_nucleation9.m new file mode 100644 index 0000000..814a9e7 --- /dev/null +++ b/solver/DDFT_nucleation9.m @@ -0,0 +1,54 @@ +%data from DDFT_nucleation3 +%use PFC to fit, fit C and mu +addpath('../../CHACR/GIP') +runoptim = true; + +tic; +L = [5,5]; +N = [256,256]; +n = prod(N); + +params.N = N; +params.L = L; + +[k2,k] = formk(N,L); +k0 = 10; +alpha = 5; +params.C = exp(-(sqrt(k2)-k0).^2/(2*alpha^2))*0.95; + +[t1,y1,params] = solver_DDFT([],[],params); + +xx = linspace(0,L(1),N(1)); +yy = linspace(0,L(2),N(2)); +[xx,yy] = ndgrid(xx,yy); +center = L/2; +radius = 0.06*L(1); +thickness = 0.01*L(1); +roi = roi_circle(xx,yy,center,radius,thickness); + +%nucleus +y0 = y1(end,:)'; +roi = roi(:); +y02 = 0.045; +rho = (y02*n - sum(roi.*y0)) / sum(1-roi); +y0 = roi.*y0 + (1-roi)*rho; + +tspan2 = linspace(0,1.5,100); +[t2,y2] = solver_DDFT(tspan2,y0,params); + +ind = 10:100; +tdata = t2(ind); +ydata = y2(ind,:); +toc + +kernelSize = 3; +Cspace = 'isotropic'; +params.moreoptions = moreodeset('gmresTol',1e-5); + +resultpath = [largedatapath,'DDFT_nucleation9.mat']; + +options = optimoptions('fminunc','OutputFcn', @(x,optimvalues,state) save_opt_history(x,optimvalues,state,resultpath)); +options = optimoptions(options,'HessianFcn','objective','Algorithm','trust-region'); + +x_guess = [0,0,-10]; +[x_opt,~,exitflag] = IP_DDFT(tdata,ydata,params,kernelSize,Cspace,options,x_guess,'Nmu',3); From 1f422b844ad682a2cfa680b8c65a9322a309e61c Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Fri, 19 Jul 2019 01:31:02 -0400 Subject: [PATCH 065/149] DDFT_nucleation15, based on 13, with a different initial guess --- solver/DDFT_nucleation15.m | 65 ++++++++++++++++++++++++++++++++++++++ 1 file changed, 65 insertions(+) create mode 100644 solver/DDFT_nucleation15.m diff --git a/solver/DDFT_nucleation15.m b/solver/DDFT_nucleation15.m new file mode 100644 index 0000000..15a10a3 --- /dev/null +++ b/solver/DDFT_nucleation15.m @@ -0,0 +1,65 @@ +%based on DDFT_nucleation11 +%same time range as 13, a different initial guess +addpath('../../CHACR/GIP') +runoptim = true; + +tic; +L = [5,5]; +N = [256,256]; +n = prod(N); + +params.N = N; +params.L = L; + +[k2,k] = formk(N,L); +k0 = 10; +alpha = 5; +params.C = exp(-(sqrt(k2)-k0).^2/(2*alpha^2))*0.95; + +[t1,y1,params] = solver_DDFT([],[],params); + +xx = linspace(0,L(1),N(1)); +yy = linspace(0,L(2),N(2)); +[xx,yy] = ndgrid(xx,yy); +center = L/2; +radius = 0.06*L(1); +thickness = 0.01*L(1); +roi = roi_circle(xx,yy,center,radius,thickness); + +%nucleus +y0 = y1(end,:)'; +roi = roi(:); +y02 = 0.045; +rho = (y02*n - sum(roi.*y0)) / sum(1-roi); +y0 = roi.*y0 + (1-roi)*rho; + +tspan2 = linspace(0,2.5,100); +[t2,y2] = solver_DDFT(tspan2,y0,params); + +ind = 1:100; +tdata = t2(ind); +ydata = y2(ind,:); +toc + + +kernelSize = 2; +Cspace = 'isotropic'; +params.moreoptions = moreodeset('gmresTol',1e-5); + + +resultpath = [largedatapath,'DDFT_nucleation15.mat']; + +options = optimoptions('fminunc','OutputFcn', @(x,optimvalues,state) save_opt_history(x,optimvalues,state,resultpath)); +options = optimoptions(options,'HessianFcn','objective','Algorithm','trust-region','MaxFunctionEvaluations',10000,'MaxIterations',10000); + +x_guess = [0,-12,0.5,0,-3]; + + + + + +[x_opt,~,exitflag,params] = IP_DDFT(tdata,ydata,params,kernelSize,Cspace,options,x_guess,'Nmu',3,'tspan',300); + + + +% ypred = IP_DDFT(tdata,ydata,params,kernelSize,Cspace,[],x_opt,'Nmu',3,'eval',true); From 70a568b799e19cd9e42a1e6b68972923e104a736 Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Fri, 19 Jul 2019 01:40:49 -0400 Subject: [PATCH 066/149] if mu is optimized, the constant term in C is removed in IP_DDFT --- solver/IP_DDFT.m | 20 ++++++++++++++++---- 1 file changed, 16 insertions(+), 4 deletions(-) diff --git a/solver/IP_DDFT.m b/solver/IP_DDFT.m index 25e8501..6b7b77b 100644 --- a/solver/IP_DDFT.m +++ b/solver/IP_DDFT.m @@ -1,4 +1,4 @@ -function [x_opt,fval,exitflag] = IP_DDFT(tdata,ydata,params,kernelSize,Cspace,options,x_guess,varargin) +function [x_opt,fval,exitflag,params] = IP_DDFT(tdata,ydata,params,kernelSize,Cspace,options,x_guess,varargin) ps = inputParser; addParameter(ps,'eval',false); %set eval = true to only do the forward solve and return @@ -23,7 +23,13 @@ meta.C.exp(end) = true; [k2,~] = formk(params.N,params.L); p = custom_Poly; - Csensval = feval(p.sens,k2,ones(1,NC)); + if Nmu>0 + %throw the constant term to mu, note that kernelSize is now the number of non-constant polynomials + Csensval = feval(p.sens,k2,ones(1,NC+1)); + Csensval(:,:,1) = []; + else + Csensval = feval(p.sens,k2,ones(1,NC)); + end %let the basis of the last derivative be negative Csensval(:,:,end) = -Csensval(:,:,end); params.Csensval = Csensval; @@ -38,8 +44,14 @@ bound = ps.Results.bound; end expleg = custom_ExpLegendre(1,bound); - params.Cfunc.func = @(coeff) coeff(1)-expleg.func(k2,coeff(2:end)); - params.Cfunc.sens = @(coeff) CmE_sens(k2,coeff,expleg.sens); + if Nmu>0 + %minus exponential only + params.Cfunc.func = @(coeff) -expleg.func(k2,coeff); + params.Cfunc.sens = @(coeff) -expleg.sens(k2,coeff); + else + params.Cfunc.func = @(coeff) coeff(1)-expleg.func(k2,coeff(2:end)); + params.Cfunc.sens = @(coeff) CmE_sens(k2,coeff,expleg.sens); + end case 'FD' NC = kernelSize; meta.C.exp = false(1,NC); From a565a77bacc75df3e747edb919becfaa9d876641 Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Fri, 19 Jul 2019 02:15:23 -0400 Subject: [PATCH 067/149] add the option to optimize D as well --- solver/IP_DDFT.m | 20 +++++++++++++++++--- solver/solver_DDFT.m | 28 +++++++++++++++++++++++++--- 2 files changed, 42 insertions(+), 6 deletions(-) diff --git a/solver/IP_DDFT.m b/solver/IP_DDFT.m index 6b7b77b..1ff93f0 100644 --- a/solver/IP_DDFT.m +++ b/solver/IP_DDFT.m @@ -6,6 +6,7 @@ %set tspan to a positive integer or 'sol' to specify the number of time points returned for solution history addParameter(ps,'bound',[]); %this is more Cspace = isotropic_CmE addParameter(ps,'Nmu',0,@(x) (mod(x,2)==1)); %number of parameters for mu, must be odd +addParameter(ps,'D',true); %setting this to true turns on optimizing over D ps.CaseSensitive = false; parse(ps,varargin{:}); tspan = ps.Results.tspan; @@ -68,12 +69,13 @@ x_guess = zeros(1,NC); end +numParams = NC; if Nmu>0 - meta.mu.index = NC+(1:Nmu); + meta.mu.index = numParams+(1:Nmu); meta.mu.exp = false(1,Nmu); meta.mu.exp(end) = true; %the coefficient of the higher odd order term must be positive params.mu = ChemPotential_Legendre(1,ybound,false,'onlyEnthalpy'); - if length(x_guess)<(NC+Nmu) + if length(x_guess)<(numParams+Nmu) mu_guess = zeros(1,Nmu); mu_guess(1) = 2; %the following makes mu nonmonotonic if Nmu>1 @@ -81,7 +83,17 @@ % [~,dmu] = feval(params.mu.func,ybound(2),mu_guess); % %set the gradient at ybound to be 2 % mu_guess(end) = log(2/dmu); - x_guess = [x_guess(1:NC), mu_guess]; + x_guess = [x_guess(1:numParams), mu_guess]; + end + numParams = NC+Nmu; +end + +if ps.Results.D + meta.D.index = numParams+1; + meta.D.exp = true; + if length(x_guess)<(numParams+1) + D_guess = -3; + x_guess = [x_guess(1:numParams), D_guess]; end end @@ -112,6 +124,8 @@ switch name case 'mu' params.(name).params = xparam; + case 'D' + params.(name) = xparam; case 'C' %xparam for C is cut in half due to symmetry. %For the purpose of symmetry, we require that the kernel size be odd in both dimensions diff --git a/solver/solver_DDFT.m b/solver/solver_DDFT.m index 8ade0d5..ae8a04b 100644 --- a/solver/solver_DDFT.m +++ b/solver/solver_DDFT.m @@ -36,6 +36,10 @@ N = params.N; L = params.L; dx = params.dx; +if ~isfield(params,'D') || isempty(params.D) + %here D is a constant diffusivity that sets the time scale + params.D = 1; +end if ~isfield(params,'C') || isempty(params.C) %default [k2,k] = formk(N,L); @@ -201,6 +205,7 @@ dy = dy + (circshift(mu,1,i)+circshift(mu,-1,i)-2*mu)/dx(i)^2; end dy = dy(:); + dy = params.D * dy; end function dfdy = jacobian(t,y,params) @@ -210,6 +215,7 @@ end %this only computes the nonlinear part, as an input to KrylovDecomp dfdy = customizeFunGrad(params,'mu','grad',y); + dfdy = params.D * dfdy; end function Pargs = KrylovDecomp(L,dfdy,hinvGak,adjoint) @@ -235,8 +241,9 @@ end N = params.N; C = params.C; + D = params.D; x = reshape(x,N); - yy = ifftn( fftn(x) ./ (msign + hinvGak*LK.*C) ); + yy = ifftn( fftn(x) ./ (msign + hinvGak*D*LK.*C) ); yy = yy(:); yy = U \ (L \ yy); end @@ -262,6 +269,7 @@ yy = yy + (circshift(mu,1,i)+circshift(mu,-1,i)-2*mu)/dx(i)^2; end yy = reshape(yy,prod(N),[]); + yy = params.D * yy; end end @@ -321,12 +329,18 @@ else mu = -params.Csens(y); end + case 'D' + mu = customizeFunGrad(params,'mu','fun',y); + mu = mu - ifftn(params.C .* fftn(y)); end dyi = 0; for j = 1:length(N) dyi = dyi + (circshift(mu,1,j)+circshift(mu,-1,j)-2*mu)/dx(j)^2; end dy(:,paramsIndex) = reshape(dyi,[],numel(paramsIndex)); + if ~isequal(name,'D') + dy(:,paramsIndex) = params.D * dy(:,paramsIndex); + end end end @@ -351,7 +365,7 @@ for j = 1:length(N) dyi = dyi + (circshift(mu,1,j)+circshift(mu,-1,j)-2*mu)/dx(j)^2; end - dy(paramsIndex) = sum(omega.*dyi(:)); + dy(paramsIndex) = params.D * sum(omega.*reshape(dyi,[],numel(paramsIndex))); case 'C' for p = 1:length(paramsIndex) mu = -params.Csens(y,p); @@ -359,8 +373,16 @@ for j = 1:length(N) dyi = dyi + (circshift(mu,1,j)+circshift(mu,-1,j)-2*mu)/dx(j)^2; end - dy(paramsIndex(p)) = sum(omega.*dyi(:)); + dy(paramsIndex(p)) = params.D * sum(omega.*dyi(:)); + end + case 'D' + mu = customizeFunGrad(params,'mu','fun',y); + mu = mu - ifftn(params.C .* fftn(y)); + dyi = 0; + for j = 1:length(N) + dyi = dyi + (circshift(mu,1,j)+circshift(mu,-1,j)-2*mu)/dx(j)^2; end + dy(paramsIndex) = sum(omega.*reshape(dyi,[],numel(paramsIndex))); end end end From 3cdd8c23f421f40493d45edb15c5db801b57325c Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Fri, 19 Jul 2019 02:15:46 -0400 Subject: [PATCH 068/149] add DDFT_nucleation17 and 18 to test optimizing mu, C, and D at the same time with full data --- solver/DDFT_nucleation17.m | 62 ++++++++++++++++++++++++++++++++++++++ solver/DDFT_nucleation18.m | 62 ++++++++++++++++++++++++++++++++++++++ 2 files changed, 124 insertions(+) create mode 100644 solver/DDFT_nucleation17.m create mode 100644 solver/DDFT_nucleation18.m diff --git a/solver/DDFT_nucleation17.m b/solver/DDFT_nucleation17.m new file mode 100644 index 0000000..ea37407 --- /dev/null +++ b/solver/DDFT_nucleation17.m @@ -0,0 +1,62 @@ +%based on DDFT_nucleation11 +%same time range as 15, a different initial guess +%optimize D as well +addpath('../../CHACR/GIP') +runoptim = true; + +tic; +L = [5,5]; +N = [256,256]; +n = prod(N); + +params.N = N; +params.L = L; + +[k2,k] = formk(N,L); +k0 = 10; +alpha = 5; +params.C = exp(-(sqrt(k2)-k0).^2/(2*alpha^2))*0.95; + +[t1,y1,params] = solver_DDFT([],[],params); + +xx = linspace(0,L(1),N(1)); +yy = linspace(0,L(2),N(2)); +[xx,yy] = ndgrid(xx,yy); +center = L/2; +radius = 0.06*L(1); +thickness = 0.01*L(1); +roi = roi_circle(xx,yy,center,radius,thickness); + +%nucleus +y0 = y1(end,:)'; +roi = roi(:); +y02 = 0.045; +rho = (y02*n - sum(roi.*y0)) / sum(1-roi); +y0 = roi.*y0 + (1-roi)*rho; + +tspan2 = linspace(0,2.5,100); +[t2,y2] = solver_DDFT(tspan2,y0,params); + +ind = 1:100; +tdata = t2(ind); +ydata = y2(ind,:); +toc + + +kernelSize = 2; +Cspace = 'isotropic'; +params.moreoptions = moreodeset('gmresTol',1e-5); + + +resultpath = [largedatapath,'DDFT_nucleation17.mat']; + +options = optimoptions('fminunc','OutputFcn', @(x,optimvalues,state) save_opt_history(x,optimvalues,state,resultpath)); +options = optimoptions(options,'HessianFcn','objective','Algorithm','trust-region','MaxFunctionEvaluations',10000,'MaxIterations',10000); + +x_guess = [0,-12,0.5,0,-3,-3]; + +[x_opt,~,exitflag,params] = IP_DDFT(tdata,ydata,params,kernelSize,Cspace,options,x_guess,'Nmu',3,'D',true,'tspan',300); + + + +% ypred = IP_DDFT(tdata,ydata,params,kernelSize,Cspace,[],x_opt,'Nmu',3,'eval',true); diff --git a/solver/DDFT_nucleation18.m b/solver/DDFT_nucleation18.m new file mode 100644 index 0000000..00dbf18 --- /dev/null +++ b/solver/DDFT_nucleation18.m @@ -0,0 +1,62 @@ +%based on DDFT_nucleation11 +%same time range as 15, easy initial guess +%optimize D as well +addpath('../../CHACR/GIP') +runoptim = true; + +tic; +L = [5,5]; +N = [256,256]; +n = prod(N); + +params.N = N; +params.L = L; + +[k2,k] = formk(N,L); +k0 = 10; +alpha = 5; +params.C = exp(-(sqrt(k2)-k0).^2/(2*alpha^2))*0.95; + +[t1,y1,params] = solver_DDFT([],[],params); + +xx = linspace(0,L(1),N(1)); +yy = linspace(0,L(2),N(2)); +[xx,yy] = ndgrid(xx,yy); +center = L/2; +radius = 0.06*L(1); +thickness = 0.01*L(1); +roi = roi_circle(xx,yy,center,radius,thickness); + +%nucleus +y0 = y1(end,:)'; +roi = roi(:); +y02 = 0.045; +rho = (y02*n - sum(roi.*y0)) / sum(1-roi); +y0 = roi.*y0 + (1-roi)*rho; + +tspan2 = linspace(0,2.5,100); +[t2,y2] = solver_DDFT(tspan2,y0,params); + +ind = 1:100; +tdata = t2(ind); +ydata = y2(ind,:); +toc + + +kernelSize = 2; +Cspace = 'isotropic'; +params.moreoptions = moreodeset('gmresTol',1e-5); + + +resultpath = [largedatapath,'DDFT_nucleation18.mat']; + +options = optimoptions('fminunc','OutputFcn', @(x,optimvalues,state) save_opt_history(x,optimvalues,state,resultpath)); +options = optimoptions(options,'HessianFcn','objective','Algorithm','trust-region','MaxFunctionEvaluations',10000,'MaxIterations',10000); + +x_guess = [0,-10,0.5,0,-3,-3]; + +[x_opt,~,exitflag,params] = IP_DDFT(tdata,ydata,params,kernelSize,Cspace,options,x_guess,'Nmu',3,'D',true,'tspan',300); + + + +% ypred = IP_DDFT(tdata,ydata,params,kernelSize,Cspace,[],x_opt,'Nmu',3,'eval',true); From 3cd783e377396cd4417218b61a3770701b8cd147 Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Fri, 19 Jul 2019 15:27:08 -0400 Subject: [PATCH 069/149] DDFT_nucleation19, use 10 frames --- solver/DDFT_nucleation19.m | 61 ++++++++++++++++++++++++++++++++++++++ 1 file changed, 61 insertions(+) create mode 100644 solver/DDFT_nucleation19.m diff --git a/solver/DDFT_nucleation19.m b/solver/DDFT_nucleation19.m new file mode 100644 index 0000000..d34b871 --- /dev/null +++ b/solver/DDFT_nucleation19.m @@ -0,0 +1,61 @@ +%based on DDFT_nucleation13 +%with discrete number of points +addpath('../../CHACR/GIP') +runoptim = true; + +tic; +L = [5,5]; +N = [256,256]; +n = prod(N); + +params.N = N; +params.L = L; + +[k2,k] = formk(N,L); +k0 = 10; +alpha = 5; +params.C = exp(-(sqrt(k2)-k0).^2/(2*alpha^2))*0.95; + +[t1,y1,params] = solver_DDFT([],[],params); + +xx = linspace(0,L(1),N(1)); +yy = linspace(0,L(2),N(2)); +[xx,yy] = ndgrid(xx,yy); +center = L/2; +radius = 0.06*L(1); +thickness = 0.01*L(1); +roi = roi_circle(xx,yy,center,radius,thickness); + +%nucleus +y0 = y1(end,:)'; +roi = roi(:); +y02 = 0.045; +rho = (y02*n - sum(roi.*y0)) / sum(1-roi); +y0 = roi.*y0 + (1-roi)*rho; + +tspan2 = linspace(0,2.5,100); +[t2,y2] = solver_DDFT(tspan2,y0,params); + +ind = 1:10:100; +tdata = t2(ind); +ydata = y2(ind,:); +toc + + +kernelSize = 2; +Cspace = 'isotropic'; +params.moreoptions = moreodeset('gmresTol',1e-5); + + +resultpath = [largedatapath,'DDFT_nucleation19.mat']; + +options = optimoptions('fminunc','OutputFcn', @(x,optimvalues,state) save_opt_history(x,optimvalues,state,resultpath)); +options = optimoptions(options,'HessianFcn','objective','Algorithm','trust-region','MaxFunctionEvaluations',10000,'MaxIterations',10000); + +x_guess = [0,-10,0.5,0,-3]; + + +[x_opt,~,exitflag,params] = IP_DDFT(tdata,ydata,params,kernelSize,Cspace,options,x_guess,'Nmu',3); + + +% ypred = IP_DDFT(tdata,ydata,params,kernelSize,Cspace,[],x_opt,'Nmu',3,'eval',true); From ae2013fbfd1860c9e541fe96eb7638955c5492dc Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Fri, 19 Jul 2019 15:33:19 -0400 Subject: [PATCH 070/149] add the option of discrete IP in IP_DDFT, update 19 --- solver/DDFT_nucleation19.m | 2 +- solver/IP_DDFT.m | 4 +++- 2 files changed, 4 insertions(+), 2 deletions(-) diff --git a/solver/DDFT_nucleation19.m b/solver/DDFT_nucleation19.m index d34b871..7389b16 100644 --- a/solver/DDFT_nucleation19.m +++ b/solver/DDFT_nucleation19.m @@ -55,7 +55,7 @@ x_guess = [0,-10,0.5,0,-3]; -[x_opt,~,exitflag,params] = IP_DDFT(tdata,ydata,params,kernelSize,Cspace,options,x_guess,'Nmu',3); +[x_opt,~,exitflag,params] = IP_DDFT(tdata,ydata,params,kernelSize,Cspace,options,x_guess,'Nmu',3,'discrete',true); % ypred = IP_DDFT(tdata,ydata,params,kernelSize,Cspace,[],x_opt,'Nmu',3,'eval',true); diff --git a/solver/IP_DDFT.m b/solver/IP_DDFT.m index 1ff93f0..edfe5ac 100644 --- a/solver/IP_DDFT.m +++ b/solver/IP_DDFT.m @@ -7,11 +7,13 @@ addParameter(ps,'bound',[]); %this is more Cspace = isotropic_CmE addParameter(ps,'Nmu',0,@(x) (mod(x,2)==1)); %number of parameters for mu, must be odd addParameter(ps,'D',true); %setting this to true turns on optimizing over D +addParameter(ps,'discrete',false); ps.CaseSensitive = false; parse(ps,varargin{:}); tspan = ps.Results.tspan; eval = ps.Results.eval; Nmu = ps.Results.Nmu; +discrete = ps.Results.discrete; addpath('../../CHACR/GIP') @@ -114,7 +116,7 @@ @(tdata,y0,FSA,meta,params) forwardSolver(tdata,y0,FSA,meta,params,tspan,ybound), ... @adjointSolver, ... loss,lossHess, ... - @(name,xparam,params) assign(name,xparam,params,Cspace,kernelSize)), ... + @(name,xparam,params) assign(name,xparam,params,Cspace,kernelSize),'discrete',discrete), ... x_guess, options); end From cbbb9ea6c172149a5078c61ee71f019a8816c7b3 Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Fri, 19 Jul 2019 19:27:37 -0400 Subject: [PATCH 071/149] fix bug in IP_DDFT about the default of D, and set tspan for solver_DDFT equal to tdata when discrete --- solver/IP_DDFT.m | 14 ++++++++++---- 1 file changed, 10 insertions(+), 4 deletions(-) diff --git a/solver/IP_DDFT.m b/solver/IP_DDFT.m index edfe5ac..b37b77d 100644 --- a/solver/IP_DDFT.m +++ b/solver/IP_DDFT.m @@ -3,10 +3,10 @@ addParameter(ps,'eval',false); %set eval = true to only do the forward solve and return addParameter(ps,'tspan',100); -%set tspan to a positive integer or 'sol' to specify the number of time points returned for solution history +%set tspan to a positive integer or 'sol' to specify the number of time points returned for solution history. Inactive and automatically set to 'discrete' if discrete = true addParameter(ps,'bound',[]); %this is more Cspace = isotropic_CmE addParameter(ps,'Nmu',0,@(x) (mod(x,2)==1)); %number of parameters for mu, must be odd -addParameter(ps,'D',true); %setting this to true turns on optimizing over D +addParameter(ps,'D',false); %setting this to true turns on optimizing over D addParameter(ps,'discrete',false); ps.CaseSensitive = false; parse(ps,varargin{:}); @@ -14,6 +14,9 @@ eval = ps.Results.eval; Nmu = ps.Results.Nmu; discrete = ps.Results.discrete; +if discrete + tspan = 'discrete'; +end addpath('../../CHACR/GIP') @@ -190,9 +193,12 @@ dy = NaN; return end - if isequal(tspan,'sol') + switch tspan + case 'sol' sol = true; - else + case 'discrete' + sol = false; + otherwise sol = false; tdata = linspace(tdata(1),tdata(end),tspan); end From af428a5a8b6b0443e836ad059b28d993258aeb0b Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Fri, 19 Jul 2019 20:16:15 -0400 Subject: [PATCH 072/149] add mode in IP_DDFT, prepare for post processing --- solver/IP_DDFT.m | 17 ++++++++++++----- solver/history_production.m | 2 +- 2 files changed, 13 insertions(+), 6 deletions(-) diff --git a/solver/IP_DDFT.m b/solver/IP_DDFT.m index b37b77d..f4e0b89 100644 --- a/solver/IP_DDFT.m +++ b/solver/IP_DDFT.m @@ -1,6 +1,6 @@ -function [x_opt,fval,exitflag,params] = IP_DDFT(tdata,ydata,params,kernelSize,Cspace,options,x_guess,varargin) +function [x_opt,fval,exitflag,pp] = IP_DDFT(tdata,ydata,params,kernelSize,Cspace,options,x_guess,varargin) ps = inputParser; -addParameter(ps,'eval',false); +addParameter(ps,'mode','IP'); %IP, eval, pp (walks through the function without eval or IP) %set eval = true to only do the forward solve and return addParameter(ps,'tspan',100); %set tspan to a positive integer or 'sol' to specify the number of time points returned for solution history. Inactive and automatically set to 'discrete' if discrete = true @@ -11,7 +11,7 @@ ps.CaseSensitive = false; parse(ps,varargin{:}); tspan = ps.Results.tspan; -eval = ps.Results.eval; +mode = ps.Results.mode; Nmu = ps.Results.Nmu; discrete = ps.Results.discrete; if discrete @@ -102,12 +102,15 @@ end end -if eval +switch mode +case 'eval' x_opt = IP(tdata,ydata,x_guess,meta,params, ... @(tdata,y0,FSA,meta,params) forwardSolver(tdata,y0,FSA,meta,params,tspan,ybound), ... [], [], [],... @(name,xparam,params) assign(name,xparam,params,Cspace,kernelSize),'eval',true); -else + fval = []; + exitflag = []; +case 'IP' loss = @(y,ydata,~) MSE(y,ydata,prod(params.dx)*100); lossHess = @(dy,~,~,~) MSE([],[],prod(params.dx)*100,dy); if nargin > 5 && ~isempty(options) @@ -123,6 +126,10 @@ x_guess, options); end +if nargout > 3 + %post processing +end + end function params = assign(name,xparam,params,Cspace,kernelSize) diff --git a/solver/history_production.m b/solver/history_production.m index e430b19..6600a51 100644 --- a/solver/history_production.m +++ b/solver/history_production.m @@ -76,7 +76,7 @@ function history_production(resultpath,ind,modelfunc,arg,meta,tdata,ydata,params y = varload.y; visualize([],[],[],y{ind(i)}(frameindex_model,:),'c',false,'ImageSize',params.N,'caxis',clim,'GridSize',[1,NaN],'OuterGridSize',[rowtotal,1],'OuterSubplot',[i+1,1],'ColumnTotal',columntotal,'StarterInd',i*columntotal+1,'subtightplot',stparg); else - yhistory = IP_DDFT(tdata,ydata,params,kernelSize,Cspace,[],history(ind(i),:),'eval',true); + yhistory = IP_DDFT(tdata,ydata,params,kernelSize,Cspace,[],history(ind(i),:),'mode','eval'); visualize([],[],[],yhistory(frameindex_model,:),'c',false,'ImageSize',params.N,'caxis',clim,'GridSize',[1,NaN],'OuterGridSize',[rowtotal,1],'OuterSubplot',[i+1,1],'ColumnTotal',columntotal,'StarterInd',i*columntotal+1,'subtightplot',stparg); end subtightplot(rowtotal,columntotal,i*columntotal+1,stparg{:}); From 0bdab362e887b43b77fa935169974d73abd3d70f Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Fri, 19 Jul 2019 20:23:37 -0400 Subject: [PATCH 073/149] add DDFT_nucleation files --- solver/DDFT_nucleation11.m | 55 ++++++++++++++++++++++++++++++++ solver/DDFT_nucleation12.m | 55 ++++++++++++++++++++++++++++++++ solver/DDFT_nucleation13.m | 54 +++++++++++++++++++++++++++++++ solver/DDFT_nucleation14.m | 64 +++++++++++++++++++++++++++++++++++++ solver/DDFT_nucleation16.m | 65 ++++++++++++++++++++++++++++++++++++++ solver/DDFT_nucleation17.m | 3 +- solver/DDFT_nucleation18.m | 3 +- solver/DDFT_nucleation19.m | 4 +-- solver/DDFT_nucleation20.m | 58 ++++++++++++++++++++++++++++++++++ 9 files changed, 357 insertions(+), 4 deletions(-) create mode 100644 solver/DDFT_nucleation11.m create mode 100644 solver/DDFT_nucleation12.m create mode 100644 solver/DDFT_nucleation13.m create mode 100644 solver/DDFT_nucleation14.m create mode 100644 solver/DDFT_nucleation16.m create mode 100644 solver/DDFT_nucleation20.m diff --git a/solver/DDFT_nucleation11.m b/solver/DDFT_nucleation11.m new file mode 100644 index 0000000..82c176a --- /dev/null +++ b/solver/DDFT_nucleation11.m @@ -0,0 +1,55 @@ +%data from DDFT_nucleation3 +%use PFC to fit, fit C and mu +addpath('../../CHACR/GIP') +runoptim = true; + +tic; +L = [5,5]; +N = [256,256]; +n = prod(N); + +params.N = N; +params.L = L; + +[k2,k] = formk(N,L); +k0 = 10; +alpha = 5; +params.C = exp(-(sqrt(k2)-k0).^2/(2*alpha^2))*0.95; + +[t1,y1,params] = solver_DDFT([],[],params); + +xx = linspace(0,L(1),N(1)); +yy = linspace(0,L(2),N(2)); +[xx,yy] = ndgrid(xx,yy); +center = L/2; +radius = 0.06*L(1); +thickness = 0.01*L(1); +roi = roi_circle(xx,yy,center,radius,thickness); + +%nucleus +y0 = y1(end,:)'; +roi = roi(:); +y02 = 0.045; +rho = (y02*n - sum(roi.*y0)) / sum(1-roi); +y0 = roi.*y0 + (1-roi)*rho; + +tspan2 = linspace(0,1.5,100); +[t2,y2] = solver_DDFT(tspan2,y0,params); + +ind = 10:100; +tdata = t2(ind); +ydata = y2(ind,:); +toc + +kernelSize = 2; +Cspace = 'isotropic'; +params.moreoptions = moreodeset('gmresTol',1e-5); + +resultpath = [largedatapath,'DDFT_nucleation11.mat']; + +options = optimoptions('fminunc','OutputFcn', @(x,optimvalues,state) save_opt_history(x,optimvalues,state,resultpath)); +options = optimoptions(options,'HessianFcn','objective','Algorithm','trust-region'); + +x_guess = [0,-10,2,0,-3]; +x_guess = [0,-10,0.5,0,-3]; %11 +[x_opt,~,exitflag] = IP_DDFT(tdata,ydata,params,kernelSize,Cspace,options,x_guess,'Nmu',3); diff --git a/solver/DDFT_nucleation12.m b/solver/DDFT_nucleation12.m new file mode 100644 index 0000000..00ddbeb --- /dev/null +++ b/solver/DDFT_nucleation12.m @@ -0,0 +1,55 @@ +%data from DDFT_nucleation3 +%based on DDFT_nucleation11, with a different initial guess (same for C as DDFT_nucleation7) +addpath('../../CHACR/GIP') +addpath('../../CHACR'); +runoptim = true; + +tic; +L = [5,5]; +N = [256,256]; +n = prod(N); + +params.N = N; +params.L = L; + +[k2,k] = formk(N,L); +k0 = 10; +alpha = 5; +params.C = exp(-(sqrt(k2)-k0).^2/(2*alpha^2))*0.95; + +[t1,y1,params] = solver_DDFT([],[],params); + +xx = linspace(0,L(1),N(1)); +yy = linspace(0,L(2),N(2)); +[xx,yy] = ndgrid(xx,yy); +center = L/2; +radius = 0.06*L(1); +thickness = 0.01*L(1); +roi = roi_circle(xx,yy,center,radius,thickness); + +%nucleus +y0 = y1(end,:)'; +roi = roi(:); +y02 = 0.045; +rho = (y02*n - sum(roi.*y0)) / sum(1-roi); +y0 = roi.*y0 + (1-roi)*rho; + +tspan2 = linspace(0,1.5,100); +[t2,y2] = solver_DDFT(tspan2,y0,params); + +ind = 10:100; +tdata = t2(ind); +ydata = y2(ind,:); +toc + +kernelSize = 2; +Cspace = 'isotropic'; +params.moreoptions = moreodeset('gmresTol',1e-5); + +resultpath = [largedatapath,'DDFT_nucleation12.mat']; + +options = optimoptions('fminunc','OutputFcn', @(x,optimvalues,state) save_opt_history(x,optimvalues,state,resultpath)); +options = optimoptions(options,'HessianFcn','objective','Algorithm','trust-region'); + +x_guess = [0,-5,0.5,0,-3]; +[x_opt,~,exitflag] = IP_DDFT(tdata,ydata,params,kernelSize,Cspace,options,x_guess,'Nmu',3); diff --git a/solver/DDFT_nucleation13.m b/solver/DDFT_nucleation13.m new file mode 100644 index 0000000..4c99f8f --- /dev/null +++ b/solver/DDFT_nucleation13.m @@ -0,0 +1,54 @@ +%based on DDFT_nucleation11 +%use a different time range +addpath('../../CHACR/GIP') +runoptim = true; + +tic; +L = [5,5]; +N = [256,256]; +n = prod(N); + +params.N = N; +params.L = L; + +[k2,k] = formk(N,L); +k0 = 10; +alpha = 5; +params.C = exp(-(sqrt(k2)-k0).^2/(2*alpha^2))*0.95; + +[t1,y1,params] = solver_DDFT([],[],params); + +xx = linspace(0,L(1),N(1)); +yy = linspace(0,L(2),N(2)); +[xx,yy] = ndgrid(xx,yy); +center = L/2; +radius = 0.06*L(1); +thickness = 0.01*L(1); +roi = roi_circle(xx,yy,center,radius,thickness); + +%nucleus +y0 = y1(end,:)'; +roi = roi(:); +y02 = 0.045; +rho = (y02*n - sum(roi.*y0)) / sum(1-roi); +y0 = roi.*y0 + (1-roi)*rho; + +tspan2 = linspace(0,2.5,100); +[t2,y2] = solver_DDFT(tspan2,y0,params); + +ind = 1:100; +tdata = t2(ind); +ydata = y2(ind,:); +toc + +kernelSize = 2; +Cspace = 'isotropic'; +params.moreoptions = moreodeset('gmresTol',1e-5); + +resultpath = [largedatapath,'DDFT_nucleation13.mat']; + +options = optimoptions('fminunc','OutputFcn', @(x,optimvalues,state) save_opt_history(x,optimvalues,state,resultpath)); +options = optimoptions(options,'HessianFcn','objective','Algorithm','trust-region'); + +x_guess = [0,-10,0.5,0,-3]; +[x_opt,~,exitflag,params] = IP_DDFT(tdata,ydata,params,kernelSize,Cspace,options,x_guess,'Nmu',3,'tspan',300); diff --git a/solver/DDFT_nucleation14.m b/solver/DDFT_nucleation14.m new file mode 100644 index 0000000..bfd34b3 --- /dev/null +++ b/solver/DDFT_nucleation14.m @@ -0,0 +1,64 @@ +%based on DDFT_nucleation11 +%same time range as 13, use up to 8th order PFC +%fail +addpath('../../CHACR/GIP') +runoptim = true; + +tic; +L = [5,5]; +N = [256,256]; +n = prod(N); + +params.N = N; +params.L = L; + +[k2,k] = formk(N,L); +k0 = 10; +alpha = 5; +params.C = exp(-(sqrt(k2)-k0).^2/(2*alpha^2))*0.95; + +[t1,y1,params] = solver_DDFT([],[],params); + +xx = linspace(0,L(1),N(1)); +yy = linspace(0,L(2),N(2)); +[xx,yy] = ndgrid(xx,yy); +center = L/2; +radius = 0.06*L(1); +thickness = 0.01*L(1); +roi = roi_circle(xx,yy,center,radius,thickness); + +%nucleus +y0 = y1(end,:)'; +roi = roi(:); +y02 = 0.045; +rho = (y02*n - sum(roi.*y0)) / sum(1-roi); +y0 = roi.*y0 + (1-roi)*rho; + +tspan2 = linspace(0,2.5,100); +[t2,y2] = solver_DDFT(tspan2,y0,params); + +ind = 1:100; +tdata = t2(ind); +ydata = y2(ind,:); +toc + +kernelSize = 3; +Cspace = 'isotropic'; +params.moreoptions = moreodeset('gmresTol',1e-5); + +resultpath = [largedatapath,'DDFT_nucleation14.mat']; + +options = optimoptions('fminunc','OutputFcn', @(x,optimvalues,state) save_opt_history(x,optimvalues,state,resultpath)); +options = optimoptions(options,'HessianFcn','objective','Algorithm','trust-region'); + +%x_guess = [0,0,-20,0.5,0,-3] + +varload = load([largedatapath,'DDFT_nucleation11']); +x_opt = varload.history(end,:); +x_opt(2) = -exp(x_opt(2)); +x_guess = [x_opt(1:2),-30,x_opt(3:5)]; +[x_opt,~,exitflag,params] = IP_DDFT(tdata,ydata,params,kernelSize,Cspace,options,x_guess,'Nmu',3,'tspan',300); + +% varload = load([largedatapath,'DDFT_nucleation11']); +% x_opt = varload.history(end,:); +% ypred = IP_DDFT(tdata,ydata,params,kernelSize,Cspace,[],x_opt,'Nmu',3,'eval',true); diff --git a/solver/DDFT_nucleation16.m b/solver/DDFT_nucleation16.m new file mode 100644 index 0000000..11b8b0e --- /dev/null +++ b/solver/DDFT_nucleation16.m @@ -0,0 +1,65 @@ +%based on DDFT_nucleation11 +%same time range as 13, a different initial guess +addpath('../../CHACR/GIP') +runoptim = true; + +tic; +L = [5,5]; +N = [256,256]; +n = prod(N); + +params.N = N; +params.L = L; + +[k2,k] = formk(N,L); +k0 = 10; +alpha = 5; +params.C = exp(-(sqrt(k2)-k0).^2/(2*alpha^2))*0.95; + +[t1,y1,params] = solver_DDFT([],[],params); + +xx = linspace(0,L(1),N(1)); +yy = linspace(0,L(2),N(2)); +[xx,yy] = ndgrid(xx,yy); +center = L/2; +radius = 0.06*L(1); +thickness = 0.01*L(1); +roi = roi_circle(xx,yy,center,radius,thickness); + +%nucleus +y0 = y1(end,:)'; +roi = roi(:); +y02 = 0.045; +rho = (y02*n - sum(roi.*y0)) / sum(1-roi); +y0 = roi.*y0 + (1-roi)*rho; + +tspan2 = linspace(0,2.5,100); +[t2,y2] = solver_DDFT(tspan2,y0,params); + +ind = 1:100; +tdata = t2(ind); +ydata = y2(ind,:); +toc + + +kernelSize = 2; +Cspace = 'isotropic'; +params.moreoptions = moreodeset('gmresTol',1e-5); + + +resultpath = [largedatapath,'DDFT_nucleation15.mat']; + +options = optimoptions('fminunc','OutputFcn', @(x,optimvalues,state) save_opt_history(x,optimvalues,state,resultpath)); +options = optimoptions(options,'HessianFcn','objective','Algorithm','trust-region'); + +x_guess = [0,-12,0.5,0,-3]; + + + + + +[x_opt,~,exitflag,params] = IP_DDFT(tdata,ydata,params,kernelSize,Cspace,options,x_guess,'Nmu',3,'tspan',300); + + + +% ypred = IP_DDFT(tdata,ydata,params,kernelSize,Cspace,[],x_opt,'Nmu',3,'eval',true); diff --git a/solver/DDFT_nucleation17.m b/solver/DDFT_nucleation17.m index ea37407..3dd54b0 100644 --- a/solver/DDFT_nucleation17.m +++ b/solver/DDFT_nucleation17.m @@ -1,6 +1,7 @@ %based on DDFT_nucleation11 %same time range as 15, a different initial guess %optimize D as well +%fail, no need to optimize D together addpath('../../CHACR/GIP') runoptim = true; @@ -53,7 +54,7 @@ options = optimoptions('fminunc','OutputFcn', @(x,optimvalues,state) save_opt_history(x,optimvalues,state,resultpath)); options = optimoptions(options,'HessianFcn','objective','Algorithm','trust-region','MaxFunctionEvaluations',10000,'MaxIterations',10000); -x_guess = [0,-12,0.5,0,-3,-3]; +x_guess = [0,-12,0.5,0,-3,log(0.1)]; [x_opt,~,exitflag,params] = IP_DDFT(tdata,ydata,params,kernelSize,Cspace,options,x_guess,'Nmu',3,'D',true,'tspan',300); diff --git a/solver/DDFT_nucleation18.m b/solver/DDFT_nucleation18.m index 00dbf18..9dc56bf 100644 --- a/solver/DDFT_nucleation18.m +++ b/solver/DDFT_nucleation18.m @@ -1,6 +1,7 @@ %based on DDFT_nucleation11 %same time range as 15, easy initial guess %optimize D as well +%fail, no need to optimize D together addpath('../../CHACR/GIP') runoptim = true; @@ -53,7 +54,7 @@ options = optimoptions('fminunc','OutputFcn', @(x,optimvalues,state) save_opt_history(x,optimvalues,state,resultpath)); options = optimoptions(options,'HessianFcn','objective','Algorithm','trust-region','MaxFunctionEvaluations',10000,'MaxIterations',10000); -x_guess = [0,-10,0.5,0,-3,-3]; +x_guess = [0,-10,0.5,0,-3,log(0.1)]; [x_opt,~,exitflag,params] = IP_DDFT(tdata,ydata,params,kernelSize,Cspace,options,x_guess,'Nmu',3,'D',true,'tspan',300); diff --git a/solver/DDFT_nucleation19.m b/solver/DDFT_nucleation19.m index 7389b16..7ba5209 100644 --- a/solver/DDFT_nucleation19.m +++ b/solver/DDFT_nucleation19.m @@ -36,7 +36,7 @@ tspan2 = linspace(0,2.5,100); [t2,y2] = solver_DDFT(tspan2,y0,params); -ind = 1:10:100; +ind = 1:100; tdata = t2(ind); ydata = y2(ind,:); toc @@ -55,7 +55,7 @@ x_guess = [0,-10,0.5,0,-3]; -[x_opt,~,exitflag,params] = IP_DDFT(tdata,ydata,params,kernelSize,Cspace,options,x_guess,'Nmu',3,'discrete',true); +[x_opt,~,exitflag,params] = IP_DDFT(tdata,ydata,params,kernelSize,Cspace,options,x_guess,'Nmu',3,'discrete',false); % ypred = IP_DDFT(tdata,ydata,params,kernelSize,Cspace,[],x_opt,'Nmu',3,'eval',true); diff --git a/solver/DDFT_nucleation20.m b/solver/DDFT_nucleation20.m new file mode 100644 index 0000000..eb4a2a5 --- /dev/null +++ b/solver/DDFT_nucleation20.m @@ -0,0 +1,58 @@ +%based on DDFT_nucleation13 +%with discrete number of points +addpath('../../CHACR/GIP') +runoptim = true; + +tic; +L = [5,5]; +N = [256,256]; +n = prod(N); + +params.N = N; +params.L = L; + +[k2,k] = formk(N,L); +k0 = 10; +alpha = 5; +params.C = exp(-(sqrt(k2)-k0).^2/(2*alpha^2))*0.95; + +[t1,y1,params] = solver_DDFT([],[],params); + +xx = linspace(0,L(1),N(1)); +yy = linspace(0,L(2),N(2)); +[xx,yy] = ndgrid(xx,yy); +center = L/2; +radius = 0.06*L(1); +thickness = 0.01*L(1); +roi = roi_circle(xx,yy,center,radius,thickness); + +%nucleus +y0 = y1(end,:)'; +roi = roi(:); +y02 = 0.045; +rho = (y02*n - sum(roi.*y0)) / sum(1-roi); +y0 = roi.*y0 + (1-roi)*rho; + +tspan2 = linspace(0,2.5,100); +[t2,y2] = solver_DDFT(tspan2,y0,params); + +ind = 1:5:100; +tdata = t2(ind); +ydata = y2(ind,:); +toc + + +kernelSize = 2; +Cspace = 'isotropic'; +params.moreoptions = moreodeset('gmresTol',1e-5); + + +resultpath = [largedatapath,'DDFT_nucleation20.mat']; + +options = optimoptions('fminunc','OutputFcn', @(x,optimvalues,state) save_opt_history(x,optimvalues,state,resultpath)); +options = optimoptions(options,'HessianFcn','objective','Algorithm','trust-region','MaxFunctionEvaluations',10000,'MaxIterations',10000,'FunctionTolerance',1e-7); + +x_guess = [0,-10,0.5,0,-3]; + + +[x_opt,~,exitflag,params] = IP_DDFT(tdata,ydata,params,kernelSize,Cspace,options,x_guess,'Nmu',3,'discrete',true); From 2a983401c120c99e0ec9ea950b00ea1768ba813c Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Mon, 22 Jul 2019 02:21:32 -0400 Subject: [PATCH 074/149] in IP_DDFT, mode=eval, output modified params and meta for postprocessing --- solver/IP_DDFT.m | 19 ++++++++++++++++++- 1 file changed, 18 insertions(+), 1 deletion(-) diff --git a/solver/IP_DDFT.m b/solver/IP_DDFT.m index f4e0b89..fb56006 100644 --- a/solver/IP_DDFT.m +++ b/solver/IP_DDFT.m @@ -104,7 +104,7 @@ switch mode case 'eval' - x_opt = IP(tdata,ydata,x_guess,meta,params, ... + [x_opt,~,params] = IP(tdata,ydata,x_guess,meta,params, ... @(tdata,y0,FSA,meta,params) forwardSolver(tdata,y0,FSA,meta,params,tspan,ybound), ... [], [], [],... @(name,xparam,params) assign(name,xparam,params,Cspace,kernelSize),'eval',true); @@ -128,6 +128,21 @@ if nargout > 3 %post processing + if isequal(Cspace,'isotropic') + if Nmu>0 + params.Cfunc.func = @(x,coeff) p.func(x.^2,[0,coeff(1:end-1),-coeff(end)]); + else + params.Cfunc.func = @(x,coeff) p.func(x.^2,[coeff(1:end-1),-coeff(end)]); + end + elseif isequal(Cspace,'isotropic_CmE') + if Nmu>0 + params.Cfunc.func = @(x,coeff) -expleg.func(x.^2,coeff); + else + params.Cfunc.func = @(x,coeff) coeff(1)-expleg.func(x.^2,coeff(2:end)); + end + end + pp.params = params; + pp.meta = meta; end end @@ -155,9 +170,11 @@ case {'isotropic','FD'} coeff(1,1,:) = xparam; params.C = sum(params.Csensval .* coeff,3); + params.Cfunc.params = xparam; case 'isotropic_CmE' params.C = params.Cfunc.func(xparam); params.Csensval = params.Cfunc.sens(xparam); + params.Cfunc.params = xparam; case {'k','real'} if any(mod(kernelSize,2)==0) error('kernel size must be odd'); From 699a60bdde649bfbf00a4ba87808c0fa36a12fdc Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Mon, 22 Jul 2019 02:21:48 -0400 Subject: [PATCH 075/149] update history_production after IP_DDFT update --- solver/history_production.m | 73 +++++++++++++++++++++++++------------ 1 file changed, 49 insertions(+), 24 deletions(-) diff --git a/solver/history_production.m b/solver/history_production.m index 6600a51..87a565f 100644 --- a/solver/history_production.m +++ b/solver/history_production.m @@ -1,5 +1,5 @@ -function history_production(resultpath,ind,modelfunc,arg,meta,tdata,ydata,params,kernelSize,Cspace,varargin) -%Two figures for figure handle +function history_production(resultpath,ind,modelfunc,arg,tdata,ydata,params,kernelSize,Cspace,varargin) +%modelfunc and arg should both be struct with fieldnames corresponding to the parameters to be plotted %note that ind is the indices of the optimization steps to be plotted. ind can also be 'end', in order to quickly visualize the final result. %Use name value pair; %'label'=true (default) to label the iteration number somewhere according to 'labelPosition'(= 'best' by default) for the first figure and to the left of each row for the second figure @@ -12,6 +12,7 @@ function history_production(resultpath,ind,modelfunc,arg,meta,tdata,ydata,params %use CtruthSubplot as a vector to specify where to put the Ctruth %If there is more than one functions to plot, modelfunc should be a struct, whose field names match those in the meta. If there is only one function to plot, modelfunc can either be a struct or simply a function handle %the result file can also contain y, the solution to the PDE at each step, in which case we don't need to recompute +%IP_DDFT_arg, varargin for IP_DDFT ps = inputParser; addParameter(ps,'label',true); addParameter(ps,'labelPosition','top'); @@ -21,17 +22,19 @@ function history_production(resultpath,ind,modelfunc,arg,meta,tdata,ydata,params addParameter(ps,'FrameIndex',':'); addParameter(ps,'Orientation','horizontal'); addParameter(ps,'yyaxisLim',[]); +addParameter(ps,'xlim',[]); addParameter(ps,'timeLabel',true); addParameter(ps,'FontSize',12); addParameter(ps,'legend',[]); addParameter(ps,'scale',[]); addParameter(ps,'CtruthSubplot',[]); +addParameter(ps,'IP_DDFT_arg',{}); +addParameter(ps,'k0',1); %used to scale k parse(ps,varargin{:}); ps = ps.Results; varload = load(resultpath); history = varload.history; -history = [zeros(1,size(history,2)); history]; %hardcoded!!! if isempty(ind) ind = 1:size(history,1); elseif isequal(ind,'end') @@ -39,9 +42,6 @@ function history_production(resultpath,ind,modelfunc,arg,meta,tdata,ydata,params end -%plot target and fitted function -names = fieldnames(meta); -numFunc = numel(names); numIter = length(ind); if isempty(ps.scale) ps.scale = false(1,numIter); @@ -76,20 +76,20 @@ function history_production(resultpath,ind,modelfunc,arg,meta,tdata,ydata,params y = varload.y; visualize([],[],[],y{ind(i)}(frameindex_model,:),'c',false,'ImageSize',params.N,'caxis',clim,'GridSize',[1,NaN],'OuterGridSize',[rowtotal,1],'OuterSubplot',[i+1,1],'ColumnTotal',columntotal,'StarterInd',i*columntotal+1,'subtightplot',stparg); else - yhistory = IP_DDFT(tdata,ydata,params,kernelSize,Cspace,[],history(ind(i),:),'mode','eval'); + [yhistory,~,~,pp] = IP_DDFT(tdata,ydata,params,kernelSize,Cspace,[],history(ind(i),:),'mode','eval',ps.IP_DDFT_arg{:}); visualize([],[],[],yhistory(frameindex_model,:),'c',false,'ImageSize',params.N,'caxis',clim,'GridSize',[1,NaN],'OuterGridSize',[rowtotal,1],'OuterSubplot',[i+1,1],'ColumnTotal',columntotal,'StarterInd',i*columntotal+1,'subtightplot',stparg); end + meta = pp.meta; + names = fieldnames(meta); + numFunc = numel(names); subtightplot(rowtotal,columntotal,i*columntotal+1,stparg{:}); for j=1:numFunc name = names{j}; - if isequal(name,'kappa') + if ismember(name,{'D','extdata'}) continue; end - if isequal(name,'C') - C = history(ind(i),:); - C = [C,flip(C(1:end-1))]; - C = reshape(C,kernelSize); - imagesc(C); + if isequal(name,'C') && ismember(Cspace,{'k','real'}) + imagesc(pp.params.C); caxis([0,1]); ax = gca; axis(ax,'image'); @@ -97,37 +97,62 @@ function history_production(resultpath,ind,modelfunc,arg,meta,tdata,ydata,params ax.YTick = []; ax.Box = 'off'; else + if isequal(name,'C') && ismember(Cspace,{'isotropic','isotropic_CmE'}) + customfunc = pp.params.Cfunc.func; + customparams = pp.params.Cfunc.params; + else + customfunc = pp.params.(name).func; + customparams = pp.params.(name).params; + end if j==1 yyaxis left elseif j==2 yyaxis right end - plot(arg,target{j},'--','LineWidth',2); + argj = arg.(name); + if isequal(name,'C') && ismember(Cspace,{'isotropic','isotropic_CmE'}) + xscale = ps.k0; + else + xscale = 1; + end + plot(argj,modelfunc.(name)(argj*xscale),'--','LineWidth',2); ax = gca; ylimtemp = ax.YLim; hold on; - if isfield(meta,'kappa') && ps.scale(i) - scale = exp(history(ind(i),meta.kappa.index)) / params.kappa; - if isequal(name,'ChemicalPotential') - scale = 1/scale; - end - else - scale = 1; - end - plot(arg,customfunc(arg,history(ind(i),meta.(name).index))*scale,'LineWidth',2); + plot(argj,customfunc(argj*xscale,customparams),'LineWidth',2); if isempty(ps.yyaxisLim) ax.YLim = ylimtemp; else ax.YLim = ps.yyaxisLim(j,:); end + if ~isempty(ps.xlim) + ax.XLim = ps.xlim; + end axis square + if i~=numIter + ax.XTick = []; + else + namesflag = ismember({'mu','C'},names); + if namesflag(1) && ~namesflag(2) + xl = '\psi'; + elseif ~namesflag(1) && namesflag(2) + xl = 'k/k_0'; + elseif all(namesflag) + xl = '\psi or k/k_0'; + end + xlabel(xl); + if ~isempty(ps.legend) + legend(ps.legend{:}); + legend('boxoff'); + end + end end if ps.label && j==1 text(0.1,1.2,['Iter. ',num2str(ind(i)-1)],'Units','normalized','HorizontalAlignment',ps.labelHorizontalAlignment); end end end -if isfield(meta,'C') && ~isempty(ps.CtruthSubplot) +if isfield(meta,'C') && ismember(Cspace,{'k','real'}) && ~isempty(ps.CtruthSubplot) axC = subtightplot(rowtotal,columntotal,columntotal*(ps.CtruthSubplot(1)-1)+ps.CtruthSubplot(2),stparg{:}); CC = params.C; halfSize = (kernelSize-1)/2; From 7b8e3a92f865f798d53b7a9018f49c5280ebb2b6 Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Mon, 22 Jul 2019 02:22:05 -0400 Subject: [PATCH 076/149] update DDFT_nucleation13 for visualization --- solver/DDFT_nucleation13.m | 17 ++++++++++++++--- 1 file changed, 14 insertions(+), 3 deletions(-) diff --git a/solver/DDFT_nucleation13.m b/solver/DDFT_nucleation13.m index 4c99f8f..5b2e68a 100644 --- a/solver/DDFT_nucleation13.m +++ b/solver/DDFT_nucleation13.m @@ -1,7 +1,7 @@ %based on DDFT_nucleation11 %use a different time range addpath('../../CHACR/GIP') -runoptim = true; +runoptim = false; tic; L = [5,5]; @@ -50,5 +50,16 @@ options = optimoptions('fminunc','OutputFcn', @(x,optimvalues,state) save_opt_history(x,optimvalues,state,resultpath)); options = optimoptions(options,'HessianFcn','objective','Algorithm','trust-region'); -x_guess = [0,-10,0.5,0,-3]; -[x_opt,~,exitflag,params] = IP_DDFT(tdata,ydata,params,kernelSize,Cspace,options,x_guess,'Nmu',3,'tspan',300); +if runoptim + x_guess = [0,-10,0.5,0,-3]; + [x_opt,~,exitflag,params] = IP_DDFT(tdata,ydata,params,kernelSize,Cspace,options,x_guess,'Nmu',3,'tspan',300); +else + modelfunc.C = @(k) exp(-(k-k0).^2/(2*alpha^2))*0.95; + modelfunc.mu = @(x) x - x.^2/2 + x.^3/3; + arg.C = linspace(0,2,500); + arg.mu = linspace(min(ydata(:)),max(ydata(:)),100); + frameindex = 1:20:100; + history_production(resultpath,[1,21,45,125],modelfunc,arg,tdata-tdata(1),ydata,params,kernelSize,Cspace,'FrameIndex',frameindex,'IP_DDFT_arg',{'Nmu',3},'yyaxisLim',[-1,1;-1,1],'k0',k0,'xlim',[min(ydata(:)),2]); + f = gcf; + f.Position = [680 337 522 641]; +end From b2851ff71fcde0e69a6d67a5774321cd60e0b00b Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Mon, 22 Jul 2019 19:45:32 -0400 Subject: [PATCH 077/149] update history_production to rescale and shift mu and C --- solver/history_production.m | 24 ++++++++++++++++++++---- 1 file changed, 20 insertions(+), 4 deletions(-) diff --git a/solver/history_production.m b/solver/history_production.m index 87a565f..3123f31 100644 --- a/solver/history_production.m +++ b/solver/history_production.m @@ -13,6 +13,7 @@ function history_production(resultpath,ind,modelfunc,arg,tdata,ydata,params,kern %If there is more than one functions to plot, modelfunc should be a struct, whose field names match those in the meta. If there is only one function to plot, modelfunc can either be a struct or simply a function handle %the result file can also contain y, the solution to the PDE at each step, in which case we don't need to recompute %IP_DDFT_arg, varargin for IP_DDFT +addpath('../../CHACR/IP') ps = inputParser; addParameter(ps,'label',true); addParameter(ps,'labelPosition','top'); @@ -30,6 +31,8 @@ function history_production(resultpath,ind,modelfunc,arg,tdata,ydata,params,kern addParameter(ps,'CtruthSubplot',[]); addParameter(ps,'IP_DDFT_arg',{}); addParameter(ps,'k0',1); %used to scale k +addParameter(ps,'dmu_at_0',1); %when meta has both mu and C, rescale so that dmu/dx at 0 has this value +addParameter(ps,'mu_at_0',0); %offset mu so that mu at 0 has this value parse(ps,varargin{:}); ps = ps.Results; @@ -81,15 +84,27 @@ function history_production(resultpath,ind,modelfunc,arg,tdata,ydata,params,kern end meta = pp.meta; names = fieldnames(meta); + namesflag = ismember({'mu','C'},names); numFunc = numel(names); subtightplot(rowtotal,columntotal,i*columntotal+1,stparg{:}); + if all(namesflag) + %calculate current gradient of mu at x=0 + grad0 = customizeFunGrad(pp.params,'mu','grad',0); + %gradient of the first order basis function of mu + [~,grad1] = feval(pp.params.mu.func,0,1); + %set the gradient of mu at x=0 to be 1. The offset is + offset = (ps.dmu_at_0-grad0)/grad1; + pp.params.mu.params(1) = pp.params.mu.params(1) + offset; + else + offset = 0; + end for j=1:numFunc name = names{j}; if ismember(name,{'D','extdata'}) continue; end if isequal(name,'C') && ismember(Cspace,{'k','real'}) - imagesc(pp.params.C); + imagesc(pp.params.C-offset); caxis([0,1]); ax = gca; axis(ax,'image'); @@ -100,9 +115,11 @@ function history_production(resultpath,ind,modelfunc,arg,tdata,ydata,params,kern if isequal(name,'C') && ismember(Cspace,{'isotropic','isotropic_CmE'}) customfunc = pp.params.Cfunc.func; customparams = pp.params.Cfunc.params; - else + yoffset = offset; + elseif isequal(name,'mu') customfunc = pp.params.(name).func; customparams = pp.params.(name).params; + yoffset = - customfunc(0,customparams); end if j==1 yyaxis left @@ -119,7 +136,7 @@ function history_production(resultpath,ind,modelfunc,arg,tdata,ydata,params,kern ax = gca; ylimtemp = ax.YLim; hold on; - plot(argj,customfunc(argj*xscale,customparams),'LineWidth',2); + plot(argj,customfunc(argj*xscale,customparams)+yoffset,'LineWidth',2); if isempty(ps.yyaxisLim) ax.YLim = ylimtemp; else @@ -132,7 +149,6 @@ function history_production(resultpath,ind,modelfunc,arg,tdata,ydata,params,kern if i~=numIter ax.XTick = []; else - namesflag = ismember({'mu','C'},names); if namesflag(1) && ~namesflag(2) xl = '\psi'; elseif ~namesflag(1) && namesflag(2) From 7db47cff52c9b6f990029316b2f1869f69bfd654 Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Tue, 23 Jul 2019 00:28:59 -0400 Subject: [PATCH 078/149] two more files with different initial conditions --- solver/DDFT_nucleation22.m | 59 ++++++++++++++++++++++++++++++++++++++ solver/DDFT_nucleation23.m | 59 ++++++++++++++++++++++++++++++++++++++ 2 files changed, 118 insertions(+) create mode 100644 solver/DDFT_nucleation22.m create mode 100644 solver/DDFT_nucleation23.m diff --git a/solver/DDFT_nucleation22.m b/solver/DDFT_nucleation22.m new file mode 100644 index 0000000..a75c93a --- /dev/null +++ b/solver/DDFT_nucleation22.m @@ -0,0 +1,59 @@ +%based on DDFT_nucleation21 +%different initial condition +%with discrete number of points +addpath('../../CHACR/GIP') +runoptim = true; + +tic; +L = [5,5]; +N = [256,256]; +n = prod(N); + +params.N = N; +params.L = L; + +[k2,k] = formk(N,L); +k0 = 10; +alpha = 5; +params.C = exp(-(sqrt(k2)-k0).^2/(2*alpha^2))*0.95; + +[t1,y1,params] = solver_DDFT([],[],params); + +xx = linspace(0,L(1),N(1)); +yy = linspace(0,L(2),N(2)); +[xx,yy] = ndgrid(xx,yy); +center = L/2; +radius = 0.06*L(1); +thickness = 0.01*L(1); +roi = roi_circle(xx,yy,center,radius,thickness); + +%nucleus +y0 = y1(end,:)'; +roi = roi(:); +y02 = 0.045; +rho = (y02*n - sum(roi.*y0)) / sum(1-roi); +y0 = roi.*y0 + (1-roi)*rho; + +tspan2 = linspace(0,2.5,100); +[t2,y2] = solver_DDFT(tspan2,y0,params); + +ind = 1:20:100; +tdata = t2(ind); +ydata = y2(ind,:); +toc + + +kernelSize = 2; +Cspace = 'isotropic'; +params.moreoptions = moreodeset('gmresTol',1e-5); + + +resultpath = [largedatapath,'DDFT_nucleation22']; + +options = optimoptions('fminunc','OutputFcn', @(x,optimvalues,state) save_opt_history(x,optimvalues,state,resultpath)); +options = optimoptions(options,'HessianFcn','objective','Algorithm','trust-region','MaxFunctionEvaluations',10000,'MaxIterations',10000,'FunctionTolerance',1e-7); + +x_guess = [0,-10,0.5,0,-6]; + + +[x_opt,~,exitflag,params] = IP_DDFT(tdata,ydata,params,kernelSize,Cspace,options,x_guess,'Nmu',3,'discrete',true); diff --git a/solver/DDFT_nucleation23.m b/solver/DDFT_nucleation23.m new file mode 100644 index 0000000..b67a614 --- /dev/null +++ b/solver/DDFT_nucleation23.m @@ -0,0 +1,59 @@ +%based on DDFT_nucleation21 +%different initial condition +%with discrete number of points +addpath('../../CHACR/GIP') +runoptim = true; + +tic; +L = [5,5]; +N = [256,256]; +n = prod(N); + +params.N = N; +params.L = L; + +[k2,k] = formk(N,L); +k0 = 10; +alpha = 5; +params.C = exp(-(sqrt(k2)-k0).^2/(2*alpha^2))*0.95; + +[t1,y1,params] = solver_DDFT([],[],params); + +xx = linspace(0,L(1),N(1)); +yy = linspace(0,L(2),N(2)); +[xx,yy] = ndgrid(xx,yy); +center = L/2; +radius = 0.06*L(1); +thickness = 0.01*L(1); +roi = roi_circle(xx,yy,center,radius,thickness); + +%nucleus +y0 = y1(end,:)'; +roi = roi(:); +y02 = 0.045; +rho = (y02*n - sum(roi.*y0)) / sum(1-roi); +y0 = roi.*y0 + (1-roi)*rho; + +tspan2 = linspace(0,2.5,100); +[t2,y2] = solver_DDFT(tspan2,y0,params); + +ind = 1:20:100; +tdata = t2(ind); +ydata = y2(ind,:); +toc + + +kernelSize = 2; +Cspace = 'isotropic'; +params.moreoptions = moreodeset('gmresTol',1e-5); + + +resultpath = [largedatapath,'DDFT_nucleation23']; + +options = optimoptions('fminunc','OutputFcn', @(x,optimvalues,state) save_opt_history(x,optimvalues,state,resultpath)); +options = optimoptions(options,'HessianFcn','objective','Algorithm','trust-region','MaxFunctionEvaluations',10000,'MaxIterations',10000,'FunctionTolerance',1e-7); + +x_guess = [0,-9,0.5,0,-3]; + + +[x_opt,~,exitflag,params] = IP_DDFT(tdata,ydata,params,kernelSize,Cspace,options,x_guess,'Nmu',3,'discrete',true); From 852a5c8a12007ff0b5540cb34a9c116cca47a253 Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Tue, 23 Jul 2019 00:31:09 -0400 Subject: [PATCH 079/149] add mu_positive option in IP_DDFT, doesn't seem to work at least yet --- solver/IP_DDFT.m | 6 +++++- 1 file changed, 5 insertions(+), 1 deletion(-) diff --git a/solver/IP_DDFT.m b/solver/IP_DDFT.m index fb56006..84be927 100644 --- a/solver/IP_DDFT.m +++ b/solver/IP_DDFT.m @@ -6,6 +6,7 @@ %set tspan to a positive integer or 'sol' to specify the number of time points returned for solution history. Inactive and automatically set to 'discrete' if discrete = true addParameter(ps,'bound',[]); %this is more Cspace = isotropic_CmE addParameter(ps,'Nmu',0,@(x) (mod(x,2)==1)); %number of parameters for mu, must be odd +addParameter(ps,'mu_positive',true); %set the higher order polynomial of mu to be positive (exponentiated) addParameter(ps,'D',false); %setting this to true turns on optimizing over D addParameter(ps,'discrete',false); ps.CaseSensitive = false; @@ -13,6 +14,7 @@ tspan = ps.Results.tspan; mode = ps.Results.mode; Nmu = ps.Results.Nmu; +mu_positive = ps.Results.mu_positive; discrete = ps.Results.discrete; if discrete tspan = 'discrete'; @@ -78,7 +80,9 @@ if Nmu>0 meta.mu.index = numParams+(1:Nmu); meta.mu.exp = false(1,Nmu); - meta.mu.exp(end) = true; %the coefficient of the higher odd order term must be positive + if mu_positive + meta.mu.exp(end) = true; %the coefficient of the higher odd order term must be positive + end params.mu = ChemPotential_Legendre(1,ybound,false,'onlyEnthalpy'); if length(x_guess)<(numParams+Nmu) mu_guess = zeros(1,Nmu); From f7712aab3fc64355379d9c20ad152b84233066d9 Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Thu, 25 Jul 2019 00:34:30 -0400 Subject: [PATCH 080/149] add mode='sens' in IP_DDFT --- solver/IP_DDFT.m | 10 +++++++++- 1 file changed, 9 insertions(+), 1 deletion(-) diff --git a/solver/IP_DDFT.m b/solver/IP_DDFT.m index 84be927..a5d0b03 100644 --- a/solver/IP_DDFT.m +++ b/solver/IP_DDFT.m @@ -1,7 +1,8 @@ function [x_opt,fval,exitflag,pp] = IP_DDFT(tdata,ydata,params,kernelSize,Cspace,options,x_guess,varargin) ps = inputParser; addParameter(ps,'mode','IP'); %IP, eval, pp (walks through the function without eval or IP) -%set eval = true to only do the forward solve and return +%set mode = 'eval' to only do the forward solve and return the solution as x_opt, fval and exitflag will be empty +%set mode = 'sens' to perform sensitivity analysis at x_guess, x_opt, fval, exitflag are hessian, hessian_t (hessian at eqch time step), and dy, respectively addParameter(ps,'tspan',100); %set tspan to a positive integer or 'sol' to specify the number of time points returned for solution history. Inactive and automatically set to 'discrete' if discrete = true addParameter(ps,'bound',[]); %this is more Cspace = isotropic_CmE @@ -128,6 +129,13 @@ loss,lossHess, ... @(name,xparam,params) assign(name,xparam,params,Cspace,kernelSize),'discrete',discrete), ... x_guess, options); +case 'sens' + loss = @(y,ydata,~) MSE(y,ydata,prod(params.dx)); + lossHess = @(dy,~,~,~) MSE([],[],prod(params.dx),dy); + [~,~,~,x_opt,exitflag,fval] = IP(tdata,ydata,x_guess,meta,params, ... + @(tdata,y0,FSA,meta,params) forwardSolver(tdata,y0,FSA,meta,params,tspan,ybound), ... + [],loss,lossHess, ... + @(name,xparam,params) assign(name,xparam,params,Cspace,kernelSize),'discrete',discrete); end if nargout > 3 From fb0fc3f11ded44d7f6c2e1a241ef52c972ffd593 Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Thu, 25 Jul 2019 18:12:16 -0400 Subject: [PATCH 081/149] add Cspace='isotropic_cutoff', add assign_suppress options in IP_DDFT --- solver/IP_DDFT.m | 33 +++++++++++++++++++++++++++++---- 1 file changed, 29 insertions(+), 4 deletions(-) diff --git a/solver/IP_DDFT.m b/solver/IP_DDFT.m index a5d0b03..3cda85c 100644 --- a/solver/IP_DDFT.m +++ b/solver/IP_DDFT.m @@ -10,6 +10,9 @@ addParameter(ps,'mu_positive',true); %set the higher order polynomial of mu to be positive (exponentiated) addParameter(ps,'D',false); %setting this to true turns on optimizing over D addParameter(ps,'discrete',false); +addParameter(ps,'cutoff',[]); %must be provided if Cspace = isotropic_cutoff +addParameter(ps,'assign_suppress',{}); +%when mode='sens', use this to suppress the reassignment of certain parameters, however parameters of interest is still stored in meta. Be careful, this only works for things whose senstivity doesn't depend on the parameters themselves ps.CaseSensitive = false; parse(ps,varargin{:}); tspan = ps.Results.tspan; @@ -17,6 +20,8 @@ Nmu = ps.Results.Nmu; mu_positive = ps.Results.mu_positive; discrete = ps.Results.discrete; +cutoff = ps.Results.cutoff; +suppress = ps.Results.assign_suppress; if discrete tspan = 'discrete'; end @@ -42,6 +47,23 @@ %let the basis of the last derivative be negative Csensval(:,:,end) = -Csensval(:,:,end); params.Csensval = Csensval; +case 'isotropic_cutoff' + %use a cutoff value beyond which C is zero, below that, Legendre polynomials are used + %NB: we use |k| as the argument of Legenre polynomials + NC = kernelSize; + meta.C.exp = false; + [k2,~] = formk(params.N,params.L); + k = sqrt(k2); + p = custom_Legendre(1,[0,cutoff]); + if Nmu>0 + %throw the constant term to mu, note that kernelSize is now the number of non-constant polynomials + Csensval = feval(p.sens,k,ones(1,NC+1)); + Csensval(:,:,1) = []; + else + Csensval = feval(p.sens,k,ones(1,NC)); + end + mask = 1*(k<=cutoff); + params.Csensval = Csensval .* mask; case 'isotropic_CmE' %constant minus exponential NC = kernelSize; @@ -132,10 +154,10 @@ case 'sens' loss = @(y,ydata,~) MSE(y,ydata,prod(params.dx)); lossHess = @(dy,~,~,~) MSE([],[],prod(params.dx),dy); - [~,~,~,x_opt,exitflag,fval] = IP(tdata,ydata,x_guess,meta,params, ... + [~,~,x_opt,exitflag,fval] = IP(tdata,ydata,x_guess,meta,params, ... @(tdata,y0,FSA,meta,params) forwardSolver(tdata,y0,FSA,meta,params,tspan,ybound), ... [],loss,lossHess, ... - @(name,xparam,params) assign(name,xparam,params,Cspace,kernelSize),'discrete',discrete); + @(name,xparam,params) assign(name,xparam,params,Cspace,kernelSize,suppress),'discrete',discrete); end if nargout > 3 @@ -159,7 +181,10 @@ end -function params = assign(name,xparam,params,Cspace,kernelSize) +function params = assign(name,xparam,params,Cspace,kernelSize,suppress) + if nargin>5 && ismember(name,suppress) + return; + end switch name case 'mu' params.(name).params = xparam; @@ -179,7 +204,7 @@ %Cspace = isotropic, C(k) = a1 + a2*k^2 + a3*k^4 + ... %Cspace = FD, C = a1 - a2*nabla + a3*nabla^2 + ... switch Cspace - case {'isotropic','FD'} + case {'isotropic','FD','isotropic_cutoff'} coeff(1,1,:) = xparam; params.C = sum(params.Csensval .* coeff,3); params.Cfunc.params = xparam; From 81eac818f8b95c2e8c5e58679eb3d8b8fcd129dd Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Sat, 27 Jul 2019 15:03:43 -0400 Subject: [PATCH 082/149] in IP_DDFT, remove isotropic_cutoff, add istropic_cos_cutoff and isotropic_poly_cutoff/scale, based on scaled Legendre on [0,1] --- solver/IP_DDFT.m | 50 ++++++++++++++++++++++++++++++++++-------------- 1 file changed, 36 insertions(+), 14 deletions(-) diff --git a/solver/IP_DDFT.m b/solver/IP_DDFT.m index 3cda85c..0e64dab 100644 --- a/solver/IP_DDFT.m +++ b/solver/IP_DDFT.m @@ -6,11 +6,11 @@ addParameter(ps,'tspan',100); %set tspan to a positive integer or 'sol' to specify the number of time points returned for solution history. Inactive and automatically set to 'discrete' if discrete = true addParameter(ps,'bound',[]); %this is more Cspace = isotropic_CmE -addParameter(ps,'Nmu',0,@(x) (mod(x,2)==1)); %number of parameters for mu, must be odd +addParameter(ps,'Nmu',0,@(x) (mod(x,2)==1) || (x==0)); %number of parameters for mu, must be odd addParameter(ps,'mu_positive',true); %set the higher order polynomial of mu to be positive (exponentiated) addParameter(ps,'D',false); %setting this to true turns on optimizing over D addParameter(ps,'discrete',false); -addParameter(ps,'cutoff',[]); %must be provided if Cspace = isotropic_cutoff +addParameter(ps,'cutoff',[]); %must be provided if Cspace = isotropic_*_cutoff/scale (cutoff or scale value) addParameter(ps,'assign_suppress',{}); %when mode='sens', use this to suppress the reassignment of certain parameters, however parameters of interest is still stored in meta. Be careful, this only works for things whose senstivity doesn't depend on the parameters themselves ps.CaseSensitive = false; @@ -47,23 +47,45 @@ %let the basis of the last derivative be negative Csensval(:,:,end) = -Csensval(:,:,end); params.Csensval = Csensval; -case 'isotropic_cutoff' - %use a cutoff value beyond which C is zero, below that, Legendre polynomials are used +case 'isotropic_cos_cutoff' + NC = kernelSize; + meta.C.exp = false; + [k2,~] = formk(params.N,params.L); + k = sqrt(k2)/cutoff; + %use cos((n+1/2)*pi*k/cutoff) + Csensval = ones(size(k,1),size(k,2),NC); + if Nmu > 0 + for i = 1:NC + Csensval(:,:,i) = cos((i-1/2)*pi*k); + end + else + for i = 2:NC + Csensval(:,:,i) = cos((i-3/2)*pi*k); + end + end + mask = 1*(k<=1); + params.Csensval = Csensval .* mask; +case {'isotropic_poly_cutoff','isotropic_poly_scale'} %NB: we use |k| as the argument of Legenre polynomials + %scale k by cutoff, if using poly_cutoff, beyond cutoff, C is set to zero. + %Legendre polynomial on [0,1]. Consider using even polynomials. NC = kernelSize; meta.C.exp = false; [k2,~] = formk(params.N,params.L); - k = sqrt(k2); - p = custom_Legendre(1,[0,cutoff]); + k = sqrt(k2)/cutoff; if Nmu>0 %throw the constant term to mu, note that kernelSize is now the number of non-constant polynomials - Csensval = feval(p.sens,k,ones(1,NC+1)); + Csensval = legendrepoly(k,NC+1,[],1); Csensval(:,:,1) = []; + Csensval = Csensval-1; else - Csensval = feval(p.sens,k,ones(1,NC)); + Csensval = legendrepoly(k,NC,[],1); + Csensval(:,:,2:end) = Csensval(:,:,2:end)-1; end - mask = 1*(k<=cutoff); - params.Csensval = Csensval .* mask; + if isequal(Cspace,'isotropic_poly_cutoff') + Csensval = Csensval .* mask; + end + params.Csensval = Csensval; case 'isotropic_CmE' %constant minus exponential NC = kernelSize; @@ -204,10 +226,6 @@ %Cspace = isotropic, C(k) = a1 + a2*k^2 + a3*k^4 + ... %Cspace = FD, C = a1 - a2*nabla + a3*nabla^2 + ... switch Cspace - case {'isotropic','FD','isotropic_cutoff'} - coeff(1,1,:) = xparam; - params.C = sum(params.Csensval .* coeff,3); - params.Cfunc.params = xparam; case 'isotropic_CmE' params.C = params.Cfunc.func(xparam); params.Csensval = params.Cfunc.sens(xparam); @@ -236,6 +254,10 @@ case 'real' params.C = psf2otf(C, params.N); end + otherwise + coeff(1,1,:) = xparam; + params.C = sum(params.Csensval .* coeff,3); + params.Cfunc.params = xparam; end end end From b103af496e3da214f283ab7a78d3772e5db7a318 Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Sat, 27 Jul 2019 15:04:36 -0400 Subject: [PATCH 083/149] DDFT_nucleation26 and 27, try isotropic_poly_scale --- solver/DDFT_nucleation26.m | 57 ++++++++++++++++++++++++++++++++++++++ solver/DDFT_nucleation27.m | 57 ++++++++++++++++++++++++++++++++++++++ 2 files changed, 114 insertions(+) create mode 100644 solver/DDFT_nucleation26.m create mode 100644 solver/DDFT_nucleation27.m diff --git a/solver/DDFT_nucleation26.m b/solver/DDFT_nucleation26.m new file mode 100644 index 0000000..cce32b8 --- /dev/null +++ b/solver/DDFT_nucleation26.m @@ -0,0 +1,57 @@ +%based on DDFT_nucleation15 +%isotropic_poly_scale +addpath('../../CHACR/GIP') +runoptim = true; + +tic; +L = [5,5]; +N = [256,256]; +n = prod(N); + +params.N = N; +params.L = L; + +[k2,k] = formk(N,L); +k0 = 10; +alpha = 5; +params.C = exp(-(sqrt(k2)-k0).^2/(2*alpha^2))*0.95; + +[t1,y1,params] = solver_DDFT([],[],params); + +xx = linspace(0,L(1),N(1)); +yy = linspace(0,L(2),N(2)); +[xx,yy] = ndgrid(xx,yy); +center = L/2; +radius = 0.06*L(1); +thickness = 0.01*L(1); +roi = roi_circle(xx,yy,center,radius,thickness); + +%nucleus +y0 = y1(end,:)'; +roi = roi(:); +y02 = 0.045; +rho = (y02*n - sum(roi.*y0)) / sum(1-roi); +y0 = roi.*y0 + (1-roi)*rho; + +tspan2 = linspace(0,2.5,100); +[t2,y2] = solver_DDFT(tspan2,y0,params); + +ind = 1:100; +tdata = t2(ind); +ydata = y2(ind,:); +toc + + +kernelSize = 5; +Cspace = 'isotropic_poly_scale'; +params.moreoptions = moreodeset('gmresTol',1e-5); + + +resultpath = [largedatapath,'DDFT_nucleation26.mat']; + +options = optimoptions('fminunc','OutputFcn', @(x,optimvalues,state) save_opt_history(x,optimvalues,state,resultpath)); +options = optimoptions(options,'HessianFcn','objective','Algorithm','trust-region','MaxFunctionEvaluations',10000,'MaxIterations',10000); + +x_guess = [0,0,0,0,0];%,0.5,0,-3]; + +[x_opt,~,exitflag,params] = IP_DDFT(tdata,ydata,params,kernelSize,Cspace,options,x_guess,'Nmu',0,'tspan',300,'cutoff',30); diff --git a/solver/DDFT_nucleation27.m b/solver/DDFT_nucleation27.m new file mode 100644 index 0000000..77ae5f7 --- /dev/null +++ b/solver/DDFT_nucleation27.m @@ -0,0 +1,57 @@ +%based on DDFT_nucleation26 +%kernelSize=7 (up to 6th order) +addpath('../../CHACR/GIP') +runoptim = true; + +tic; +L = [5,5]; +N = [256,256]; +n = prod(N); + +params.N = N; +params.L = L; + +[k2,k] = formk(N,L); +k0 = 10; +alpha = 5; +params.C = exp(-(sqrt(k2)-k0).^2/(2*alpha^2))*0.95; + +[t1,y1,params] = solver_DDFT([],[],params); + +xx = linspace(0,L(1),N(1)); +yy = linspace(0,L(2),N(2)); +[xx,yy] = ndgrid(xx,yy); +center = L/2; +radius = 0.06*L(1); +thickness = 0.01*L(1); +roi = roi_circle(xx,yy,center,radius,thickness); + +%nucleus +y0 = y1(end,:)'; +roi = roi(:); +y02 = 0.045; +rho = (y02*n - sum(roi.*y0)) / sum(1-roi); +y0 = roi.*y0 + (1-roi)*rho; + +tspan2 = linspace(0,2.5,100); +[t2,y2] = solver_DDFT(tspan2,y0,params); + +ind = 1:100; +tdata = t2(ind); +ydata = y2(ind,:); +toc + + +kernelSize = 7; +Cspace = 'isotropic_poly_scale'; +params.moreoptions = moreodeset('gmresTol',1e-5); + + +resultpath = [largedatapath,'DDFT_nucleation27.mat']; + +options = optimoptions('fminunc','OutputFcn', @(x,optimvalues,state) save_opt_history(x,optimvalues,state,resultpath)); +options = optimoptions(options,'HessianFcn','objective','Algorithm','trust-region','MaxFunctionEvaluations',10000,'MaxIterations',10000); + +x_guess = zeros(1,kernelSize); + +[x_opt,~,exitflag,params] = IP_DDFT(tdata,ydata,params,kernelSize,Cspace,options,x_guess,'Nmu',0,'tspan',300,'cutoff',30); From a1bcf798d75ee5f39747a8bf34a20e7f3e72393e Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Sat, 27 Jul 2019 20:52:51 -0400 Subject: [PATCH 084/149] add istropic_even option in IP_DDFT to use even legendrepolynomials only --- solver/IP_DDFT.m | 18 +++++++++++++++--- 1 file changed, 15 insertions(+), 3 deletions(-) diff --git a/solver/IP_DDFT.m b/solver/IP_DDFT.m index 0e64dab..e60d2e8 100644 --- a/solver/IP_DDFT.m +++ b/solver/IP_DDFT.m @@ -11,6 +11,7 @@ addParameter(ps,'D',false); %setting this to true turns on optimizing over D addParameter(ps,'discrete',false); addParameter(ps,'cutoff',[]); %must be provided if Cspace = isotropic_*_cutoff/scale (cutoff or scale value) +addParameter(ps,'isotropic_even',false); %set to true if even polynomials are used (Cspace = isotropic_poly_*) addParameter(ps,'assign_suppress',{}); %when mode='sens', use this to suppress the reassignment of certain parameters, however parameters of interest is still stored in meta. Be careful, this only works for things whose senstivity doesn't depend on the parameters themselves ps.CaseSensitive = false; @@ -20,6 +21,7 @@ Nmu = ps.Results.Nmu; mu_positive = ps.Results.mu_positive; discrete = ps.Results.discrete; +isotropic_even = ps.Results.isotropic_even; cutoff = ps.Results.cutoff; suppress = ps.Results.assign_suppress; if discrete @@ -75,15 +77,25 @@ k = sqrt(k2)/cutoff; if Nmu>0 %throw the constant term to mu, note that kernelSize is now the number of non-constant polynomials - Csensval = legendrepoly(k,NC+1,[],1); + nval = NC+1; + else + nval = NC; + end + if isotropic_even + nval = 2*nval-1; + end + Csensval = legendrepoly(k,nval,[],1); + if isotropic_even + Csensval(:,:,2*(1:floor(nval/2))) = []; + end + if Nmu>0 Csensval(:,:,1) = []; Csensval = Csensval-1; else - Csensval = legendrepoly(k,NC,[],1); Csensval(:,:,2:end) = Csensval(:,:,2:end)-1; end if isequal(Cspace,'isotropic_poly_cutoff') - Csensval = Csensval .* mask; + Csensval = Csensval .* (1*(k<=1)); end params.Csensval = Csensval; case 'isotropic_CmE' From 9b741195dc5464a15924198cdd33a20c3bc06f02 Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Sat, 27 Jul 2019 20:53:43 -0400 Subject: [PATCH 085/149] DDFT_nucleation28, try isotropic_poly_scale with isotropic_even = true --- solver/DDFT_nucleation28.m | 57 ++++++++++++++++++++++++++++++++++++++ 1 file changed, 57 insertions(+) create mode 100644 solver/DDFT_nucleation28.m diff --git a/solver/DDFT_nucleation28.m b/solver/DDFT_nucleation28.m new file mode 100644 index 0000000..40ac647 --- /dev/null +++ b/solver/DDFT_nucleation28.m @@ -0,0 +1,57 @@ +%based on DDFT_nucleation15 +%isotropic_poly_scale with isotropic_even = true +addpath('../../CHACR/GIP') +runoptim = true; + +tic; +L = [5,5]; +N = [256,256]; +n = prod(N); + +params.N = N; +params.L = L; + +[k2,k] = formk(N,L); +k0 = 10; +alpha = 5; +params.C = exp(-(sqrt(k2)-k0).^2/(2*alpha^2))*0.95; + +[t1,y1,params] = solver_DDFT([],[],params); + +xx = linspace(0,L(1),N(1)); +yy = linspace(0,L(2),N(2)); +[xx,yy] = ndgrid(xx,yy); +center = L/2; +radius = 0.06*L(1); +thickness = 0.01*L(1); +roi = roi_circle(xx,yy,center,radius,thickness); + +%nucleus +y0 = y1(end,:)'; +roi = roi(:); +y02 = 0.045; +rho = (y02*n - sum(roi.*y0)) / sum(1-roi); +y0 = roi.*y0 + (1-roi)*rho; + +tspan2 = linspace(0,2.5,100); +[t2,y2] = solver_DDFT(tspan2,y0,params); + +ind = 1:100; +tdata = t2(ind); +ydata = y2(ind,:); +toc + + +kernelSize = 3; +Cspace = 'isotropic_poly_scale'; +params.moreoptions = moreodeset('gmresTol',1e-5); + + +resultpath = [largedatapath,'DDFT_nucleation28.mat']; + +options = optimoptions('fminunc','OutputFcn', @(x,optimvalues,state) save_opt_history(x,optimvalues,state,resultpath)); +options = optimoptions(options,'HessianFcn','objective','Algorithm','trust-region','MaxFunctionEvaluations',10000,'MaxIterations',10000); + +x_guess = zeros(1,kernelSize); + +[x_opt,~,exitflag,params] = IP_DDFT(tdata,ydata,params,kernelSize,Cspace,options,x_guess,'Nmu',0,'tspan',300,'cutoff',2*k0,'isotropic_even',true); From 36f7fe3622e28359db73d0ab854636282483ffca Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Sun, 28 Jul 2019 02:43:14 -0400 Subject: [PATCH 086/149] update IP_DDFT, remove shifting by 1 for isotropic_poly, add 29 to test it --- solver/DDFT_nucleation29.m | 58 ++++++++++++++++++++++++++++++++++++++ solver/IP_DDFT.m | 3 -- 2 files changed, 58 insertions(+), 3 deletions(-) create mode 100644 solver/DDFT_nucleation29.m diff --git a/solver/DDFT_nucleation29.m b/solver/DDFT_nucleation29.m new file mode 100644 index 0000000..f1ceff6 --- /dev/null +++ b/solver/DDFT_nucleation29.m @@ -0,0 +1,58 @@ +%based on DDFT_nucleation15 +%isotropic_poly_scale with isotropic_even = false +%remove constant shift 1 in IP_DDFT, cutoff = 1.5*k9 +addpath('../../CHACR/GIP') +runoptim = true; + +tic; +L = [5,5]; +N = [256,256]; +n = prod(N); + +params.N = N; +params.L = L; + +[k2,k] = formk(N,L); +k0 = 10; +alpha = 5; +params.C = exp(-(sqrt(k2)-k0).^2/(2*alpha^2))*0.95; + +[t1,y1,params] = solver_DDFT([],[],params); + +xx = linspace(0,L(1),N(1)); +yy = linspace(0,L(2),N(2)); +[xx,yy] = ndgrid(xx,yy); +center = L/2; +radius = 0.06*L(1); +thickness = 0.01*L(1); +roi = roi_circle(xx,yy,center,radius,thickness); + +%nucleus +y0 = y1(end,:)'; +roi = roi(:); +y02 = 0.045; +rho = (y02*n - sum(roi.*y0)) / sum(1-roi); +y0 = roi.*y0 + (1-roi)*rho; + +tspan2 = linspace(0,2.5,100); +[t2,y2] = solver_DDFT(tspan2,y0,params); + +ind = 1:100; +tdata = t2(ind); +ydata = y2(ind,:); +toc + + +kernelSize = 5; +Cspace = 'isotropic_poly_scale'; +params.moreoptions = moreodeset('gmresTol',1e-5); + + +resultpath = [largedatapath,'DDFT_nucleation29.mat']; + +options = optimoptions('fminunc','OutputFcn', @(x,optimvalues,state) save_opt_history(x,optimvalues,state,resultpath)); +options = optimoptions(options,'HessianFcn','objective','Algorithm','trust-region','MaxFunctionEvaluations',10000,'MaxIterations',10000); + +x_guess = zeros(1,kernelSize); + +[x_opt,~,exitflag,params] = IP_DDFT(tdata,ydata,params,kernelSize,Cspace,options,x_guess,'Nmu',0,'tspan',300,'cutoff',1.5*k0,'isotropic_even',false); diff --git a/solver/IP_DDFT.m b/solver/IP_DDFT.m index e60d2e8..2783e2e 100644 --- a/solver/IP_DDFT.m +++ b/solver/IP_DDFT.m @@ -90,9 +90,6 @@ end if Nmu>0 Csensval(:,:,1) = []; - Csensval = Csensval-1; - else - Csensval(:,:,2:end) = Csensval(:,:,2:end)-1; end if isequal(Cspace,'isotropic_poly_cutoff') Csensval = Csensval .* (1*(k<=1)); From d70e88870a903fb908064a0556078ad13a6fbb4e Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Sun, 28 Jul 2019 16:47:07 -0400 Subject: [PATCH 087/149] Revert "update IP_DDFT, remove shifting by 1 for isotropic_poly, add 29 to test it" This reverts commit 36f7fe3622e28359db73d0ab854636282483ffca. --- solver/DDFT_nucleation29.m | 58 -------------------------------------- solver/IP_DDFT.m | 3 ++ 2 files changed, 3 insertions(+), 58 deletions(-) delete mode 100644 solver/DDFT_nucleation29.m diff --git a/solver/DDFT_nucleation29.m b/solver/DDFT_nucleation29.m deleted file mode 100644 index f1ceff6..0000000 --- a/solver/DDFT_nucleation29.m +++ /dev/null @@ -1,58 +0,0 @@ -%based on DDFT_nucleation15 -%isotropic_poly_scale with isotropic_even = false -%remove constant shift 1 in IP_DDFT, cutoff = 1.5*k9 -addpath('../../CHACR/GIP') -runoptim = true; - -tic; -L = [5,5]; -N = [256,256]; -n = prod(N); - -params.N = N; -params.L = L; - -[k2,k] = formk(N,L); -k0 = 10; -alpha = 5; -params.C = exp(-(sqrt(k2)-k0).^2/(2*alpha^2))*0.95; - -[t1,y1,params] = solver_DDFT([],[],params); - -xx = linspace(0,L(1),N(1)); -yy = linspace(0,L(2),N(2)); -[xx,yy] = ndgrid(xx,yy); -center = L/2; -radius = 0.06*L(1); -thickness = 0.01*L(1); -roi = roi_circle(xx,yy,center,radius,thickness); - -%nucleus -y0 = y1(end,:)'; -roi = roi(:); -y02 = 0.045; -rho = (y02*n - sum(roi.*y0)) / sum(1-roi); -y0 = roi.*y0 + (1-roi)*rho; - -tspan2 = linspace(0,2.5,100); -[t2,y2] = solver_DDFT(tspan2,y0,params); - -ind = 1:100; -tdata = t2(ind); -ydata = y2(ind,:); -toc - - -kernelSize = 5; -Cspace = 'isotropic_poly_scale'; -params.moreoptions = moreodeset('gmresTol',1e-5); - - -resultpath = [largedatapath,'DDFT_nucleation29.mat']; - -options = optimoptions('fminunc','OutputFcn', @(x,optimvalues,state) save_opt_history(x,optimvalues,state,resultpath)); -options = optimoptions(options,'HessianFcn','objective','Algorithm','trust-region','MaxFunctionEvaluations',10000,'MaxIterations',10000); - -x_guess = zeros(1,kernelSize); - -[x_opt,~,exitflag,params] = IP_DDFT(tdata,ydata,params,kernelSize,Cspace,options,x_guess,'Nmu',0,'tspan',300,'cutoff',1.5*k0,'isotropic_even',false); diff --git a/solver/IP_DDFT.m b/solver/IP_DDFT.m index 2783e2e..e60d2e8 100644 --- a/solver/IP_DDFT.m +++ b/solver/IP_DDFT.m @@ -90,6 +90,9 @@ end if Nmu>0 Csensval(:,:,1) = []; + Csensval = Csensval-1; + else + Csensval(:,:,2:end) = Csensval(:,:,2:end)-1; end if isequal(Cspace,'isotropic_poly_cutoff') Csensval = Csensval .* (1*(k<=1)); From dbefb7618c2418e7269638837cf841288a07fd1e Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Sun, 28 Jul 2019 17:02:20 -0400 Subject: [PATCH 088/149] add isotropic_hermite_scale in IP_DDFT --- solver/IP_DDFT.m | 7 +++++++ 1 file changed, 7 insertions(+) diff --git a/solver/IP_DDFT.m b/solver/IP_DDFT.m index e60d2e8..33cb62d 100644 --- a/solver/IP_DDFT.m +++ b/solver/IP_DDFT.m @@ -98,6 +98,13 @@ Csensval = Csensval .* (1*(k<=1)); end params.Csensval = Csensval; +case 'isotropic_hermite_scale' + %|k| scaled by cutoff + NC = kernelSize; + meta.C.exp = false; + [k2,~] = formk(params.N,params.L); + k = sqrt(k2)/cutoff; + params.Csensval = hermitefunction(k,NC,[],1); case 'isotropic_CmE' %constant minus exponential NC = kernelSize; From 4eb1de1c9c6af0c447d852883b8555eaccd2561d Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Sun, 28 Jul 2019 17:06:18 -0400 Subject: [PATCH 089/149] add DDFT_nucleation29 t try isotropic_hermite_scale --- solver/DDFT_nucleation29.m | 57 ++++++++++++++++++++++++++++++++++++++ 1 file changed, 57 insertions(+) create mode 100644 solver/DDFT_nucleation29.m diff --git a/solver/DDFT_nucleation29.m b/solver/DDFT_nucleation29.m new file mode 100644 index 0000000..b5647ff --- /dev/null +++ b/solver/DDFT_nucleation29.m @@ -0,0 +1,57 @@ +%based on DDFT_nucleation15 +%Cspace = isotropic_hermite_scale +addpath('../../CHACR/GIP') +runoptim = true; + +tic; +L = [5,5]; +N = [256,256]; +n = prod(N); + +params.N = N; +params.L = L; + +[k2,k] = formk(N,L); +k0 = 10; +alpha = 5; +params.C = exp(-(sqrt(k2)-k0).^2/(2*alpha^2))*0.95; + +[t1,y1,params] = solver_DDFT([],[],params); + +xx = linspace(0,L(1),N(1)); +yy = linspace(0,L(2),N(2)); +[xx,yy] = ndgrid(xx,yy); +center = L/2; +radius = 0.06*L(1); +thickness = 0.01*L(1); +roi = roi_circle(xx,yy,center,radius,thickness); + +%nucleus +y0 = y1(end,:)'; +roi = roi(:); +y02 = 0.045; +rho = (y02*n - sum(roi.*y0)) / sum(1-roi); +y0 = roi.*y0 + (1-roi)*rho; + +tspan2 = linspace(0,2.5,100); +[t2,y2] = solver_DDFT(tspan2,y0,params); + +ind = 1:100; +tdata = t2(ind); +ydata = y2(ind,:); +toc + + +kernelSize = 6; +Cspace = 'isotropic_hermite_scale'; +params.moreoptions = moreodeset('gmresTol',1e-5); + + +resultpath = [largedatapath,'DDFT_nucleation29.mat']; + +options = optimoptions('fminunc','OutputFcn', @(x,optimvalues,state) save_opt_history(x,optimvalues,state,resultpath)); +options = optimoptions(options,'HessianFcn','objective','Algorithm','trust-region','MaxFunctionEvaluations',10000,'MaxIterations',10000); + +x_guess = zeros(1,kernelSize); + +[x_opt,~,exitflag,params] = IP_DDFT(tdata,ydata,params,kernelSize,Cspace,options,x_guess,'Nmu',0,'tspan',300,'cutoff',k0); From 54a5892bdea3634d369601fc2c6106978aab9a71 Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Sun, 28 Jul 2019 22:25:39 -0400 Subject: [PATCH 090/149] upload DDFT_nucleation* on HZ-BazantLab --- solver/DDFT_nucleation13.m | 2 +- solver/DDFT_nucleation20.m | 4 +- solver/DDFT_nucleation21.m | 70 ++++++++++++++++++++++++++++++++ solver/DDFT_nucleation22.m | 2 +- solver/DDFT_nucleation24.m | 53 ++++++++++++++++++++++++ solver/DDFT_nucleation25.m | 66 ++++++++++++++++++++++++++++++ solver/DDFT_nucleation2_helper.m | 2 +- 7 files changed, 194 insertions(+), 5 deletions(-) create mode 100644 solver/DDFT_nucleation21.m create mode 100644 solver/DDFT_nucleation24.m create mode 100644 solver/DDFT_nucleation25.m diff --git a/solver/DDFT_nucleation13.m b/solver/DDFT_nucleation13.m index 5b2e68a..7e625a4 100644 --- a/solver/DDFT_nucleation13.m +++ b/solver/DDFT_nucleation13.m @@ -59,7 +59,7 @@ arg.C = linspace(0,2,500); arg.mu = linspace(min(ydata(:)),max(ydata(:)),100); frameindex = 1:20:100; - history_production(resultpath,[1,21,45,125],modelfunc,arg,tdata-tdata(1),ydata,params,kernelSize,Cspace,'FrameIndex',frameindex,'IP_DDFT_arg',{'Nmu',3},'yyaxisLim',[-1,1;-1,1],'k0',k0,'xlim',[min(ydata(:)),2]); + history_production(resultpath,[1,21,45,125],modelfunc,arg,tdata-tdata(1),ydata,params,kernelSize,Cspace,'FrameIndex',frameindex,'IP_DDFT_arg',{'Nmu',3},'yyaxisLim',[-0.5,1.5;-1,1.2],'k0',k0,'xlim',[min(ydata(:)),2]); f = gcf; f.Position = [680 337 522 641]; end diff --git a/solver/DDFT_nucleation20.m b/solver/DDFT_nucleation20.m index eb4a2a5..5ceba00 100644 --- a/solver/DDFT_nucleation20.m +++ b/solver/DDFT_nucleation20.m @@ -36,7 +36,7 @@ tspan2 = linspace(0,2.5,100); [t2,y2] = solver_DDFT(tspan2,y0,params); -ind = 1:5:100; +ind = 1:10:100; tdata = t2(ind); ydata = y2(ind,:); toc @@ -52,7 +52,7 @@ options = optimoptions('fminunc','OutputFcn', @(x,optimvalues,state) save_opt_history(x,optimvalues,state,resultpath)); options = optimoptions(options,'HessianFcn','objective','Algorithm','trust-region','MaxFunctionEvaluations',10000,'MaxIterations',10000,'FunctionTolerance',1e-7); -x_guess = [0,-10,0.5,0,-3]; +x_guess = [0,-11,0.5,0,-3]; [x_opt,~,exitflag,params] = IP_DDFT(tdata,ydata,params,kernelSize,Cspace,options,x_guess,'Nmu',3,'discrete',true); diff --git a/solver/DDFT_nucleation21.m b/solver/DDFT_nucleation21.m new file mode 100644 index 0000000..ba0716d --- /dev/null +++ b/solver/DDFT_nucleation21.m @@ -0,0 +1,70 @@ +%based on DDFT_nucleation13 +%with discrete number of points +addpath('../../CHACR/GIP') +runoptim = false; + +L = [5,5]; +N = [256,256]; +n = prod(N); + +params.N = N; +params.L = L; +params.dx = L./N; + +[k2,k] = formk(N,L); +k0 = 10; +alpha = 5; +params.C = exp(-(sqrt(k2)-k0).^2/(2*alpha^2))*0.95; + +if ~exist('t2','var') + tic; + [t1,y1,params] = solver_DDFT([],[],params); + + xx = linspace(0,L(1),N(1)); + yy = linspace(0,L(2),N(2)); + [xx,yy] = ndgrid(xx,yy); + center = L/2; + radius = 0.06*L(1); + thickness = 0.01*L(1); + roi = roi_circle(xx,yy,center,radius,thickness); + + %nucleus + y0 = y1(end,:)'; + roi = roi(:); + y02 = 0.045; + rho = (y02*n - sum(roi.*y0)) / sum(1-roi); + y0 = roi.*y0 + (1-roi)*rho; + + tspan2 = linspace(0,2.5,100); + [t2,y2] = solver_DDFT(tspan2,y0,params); + toc +end + +ind = 1:20:100; +tdata = t2(ind); +ydata = y2(ind,:); + + +kernelSize = 2; +Cspace = 'isotropic'; +params.moreoptions = moreodeset('gmresTol',1e-5); + + +resultpath = [largedatapath,'DDFT_nucleation21.mat']; + +options = optimoptions('fminunc','OutputFcn', @(x,optimvalues,state) save_opt_history(x,optimvalues,state,resultpath)); +options = optimoptions(options,'HessianFcn','objective','Algorithm','trust-region','MaxFunctionEvaluations',10000,'MaxIterations',10000,'FunctionTolerance',1e-7); + + +if runoptim + x_guess = [0,-11,0.5,0,-3]; + [x_opt,~,exitflag,params] = IP_DDFT(tdata,ydata,params,kernelSize,Cspace,options,x_guess,'Nmu',3,'discrete',true); +else + modelfunc.C = @(k) exp(-(k-k0).^2/(2*alpha^2))*0.95; + modelfunc.mu = @(x) x - x.^2/2 + x.^3/3; + arg.C = linspace(0,2,500); + arg.mu = linspace(min(ydata(:)),max(ydata(:)),100); + history_production(resultpath,[1,41,71,1667],modelfunc,arg,tdata-tdata(1),ydata,params,kernelSize,Cspace,'IP_DDFT_arg',{'Nmu',3},'yyaxisLim',[-0.5,1.5;-1,1.2],'k0',k0,'xlim',[min(ydata(:)),2]); + f = gcf; + f.Position = [680 337 522 641]; +end diff --git a/solver/DDFT_nucleation22.m b/solver/DDFT_nucleation22.m index a75c93a..59fbf60 100644 --- a/solver/DDFT_nucleation22.m +++ b/solver/DDFT_nucleation22.m @@ -53,7 +53,7 @@ options = optimoptions('fminunc','OutputFcn', @(x,optimvalues,state) save_opt_history(x,optimvalues,state,resultpath)); options = optimoptions(options,'HessianFcn','objective','Algorithm','trust-region','MaxFunctionEvaluations',10000,'MaxIterations',10000,'FunctionTolerance',1e-7); -x_guess = [0,-10,0.5,0,-6]; +x_guess = [0,-8,0.5,0,-3]; [x_opt,~,exitflag,params] = IP_DDFT(tdata,ydata,params,kernelSize,Cspace,options,x_guess,'Nmu',3,'discrete',true); diff --git a/solver/DDFT_nucleation24.m b/solver/DDFT_nucleation24.m new file mode 100644 index 0000000..c103a60 --- /dev/null +++ b/solver/DDFT_nucleation24.m @@ -0,0 +1,53 @@ +%based on DDFT_nucleation13 +%use isotropic_cutoff +addpath('../../CHACR/GIP') +runoptim = true; + +L = [5,5]; +N = [256,256]; +n = prod(N); + +params.N = N; +params.L = L; +params.dx = L./N; + +[k2,k] = formk(N,L); +k0 = 10; +alpha = 5; +params.C = exp(-(sqrt(k2)-k0).^2/(2*alpha^2))*0.95; + +if ~exist('t2','var') + tic; + [t1,y1,params] = solver_DDFT([],[],params); + + xx = linspace(0,L(1),N(1)); + yy = linspace(0,L(2),N(2)); + [xx,yy] = ndgrid(xx,yy); + center = L/2; + radius = 0.06*L(1); + thickness = 0.01*L(1); + roi = roi_circle(xx,yy,center,radius,thickness); + + %nucleus + y0 = y1(end,:)'; + roi = roi(:); + y02 = 0.045; + rho = (y02*n - sum(roi.*y0)) / sum(1-roi); + y0 = roi.*y0 + (1-roi)*rho; + + tspan2 = linspace(0,2.5,100); + [t2,y2] = solver_DDFT(tspan2,y0,params); + toc +end + +ind = 1:20:100; +tdata = t2(ind); +ydata = y2(ind,:); + +kernelSize = 50; +Cspace = 'isotropic_cutoff'; +params.moreoptions = moreodeset('gmresTol',1e-5); + +resultpath = [largedatapath,'DDFT_nucleation24.mat']; + +[hessian,hessian_t,dy] = IP_DDFT(tdata,ydata,params,kernelSize,Cspace,[],[],'discrete',true,'cutoff',30,'assign_suppress',{'C'},'mode','sens'); diff --git a/solver/DDFT_nucleation25.m b/solver/DDFT_nucleation25.m new file mode 100644 index 0000000..48d0c3e --- /dev/null +++ b/solver/DDFT_nucleation25.m @@ -0,0 +1,66 @@ +%based on DDFT_nucleation15 +%use a different time range +addpath('../../CHACR/GIP') +runoptim = true; + +tic; +L = [5,5]; +N = [256,256]; +n = prod(N); + +params.N = N; +params.L = L; + +[k2,k] = formk(N,L); +k0 = 10; +alpha = 5; +params.C = exp(-(sqrt(k2)-k0).^2/(2*alpha^2))*0.95; + +[t1,y1,params] = solver_DDFT([],[],params); + +xx = linspace(0,L(1),N(1)); +yy = linspace(0,L(2),N(2)); +[xx,yy] = ndgrid(xx,yy); +center = L/2; +radius = 0.06*L(1); +thickness = 0.01*L(1); +roi = roi_circle(xx,yy,center,radius,thickness); + +%nucleus +y0 = y1(end,:)'; +roi = roi(:); +y02 = 0.045; +rho = (y02*n - sum(roi.*y0)) / sum(1-roi); +y0 = roi.*y0 + (1-roi)*rho; + +tspan2 = linspace(0,2.5,100); +[t2,y2] = solver_DDFT(tspan2,y0,params); + +ind = 1:100; +tdata = t2(ind); +ydata = y2(ind,:); +toc + + +kernelSize = 4; +Cspace = 'isotropic_cutoff'; +params.moreoptions = moreodeset('gmresTol',1e-5); + +resultpath = [largedatapath,'DDFT_nucleation25.mat']; + +options = optimoptions('fminunc','OutputFcn', @(x,optimvalues,state) save_opt_history(x,optimvalues,state,resultpath)); +options = optimoptions(options,'HessianFcn','objective','Algorithm','trust-region'); + +if runoptim + x_guess = [0,0,0,0,0.3,0,-3]; + [x_opt,~,exitflag,params] = IP_DDFT(tdata,ydata,params,kernelSize,Cspace,options,x_guess,'Nmu',3,'tspan',300,'cutoff',30); +else + modelfunc.C = @(k) exp(-(k-k0).^2/(2*alpha^2))*0.95; + modelfunc.mu = @(x) x - x.^2/2 + x.^3/3; + arg.C = linspace(0,2,500); + arg.mu = linspace(min(ydata(:)),max(ydata(:)),100); + frameindex = 1:20:100; + history_production(resultpath,[1,21,45,125],modelfunc,arg,tdata-tdata(1),ydata,params,kernelSize,Cspace,'FrameIndex',frameindex,'IP_DDFT_arg',{'Nmu',3},'yyaxisLim',[-0.5,1.5;-1,1.2],'k0',k0,'xlim',[min(ydata(:)),2]); + f = gcf; + f.Position = [680 337 522 641]; +end diff --git a/solver/DDFT_nucleation2_helper.m b/solver/DDFT_nucleation2_helper.m index 91eb566..b910520 100644 --- a/solver/DDFT_nucleation2_helper.m +++ b/solver/DDFT_nucleation2_helper.m @@ -3,7 +3,7 @@ resultpath = [largedatapath,'DDFT_nucleation2.mat']; varload = load(resultpath); x_opt = varload.history(end,:); - +exitflag = 5; options = optimoptions('fminunc','OutputFcn',@(x,optimvalues,state) save_opt_history(x,optimvalues,state,resultpath,[],true)); while (exitflag==5) From a9322361e4d5521a5dc9d727cf0f80e6f7db00b8 Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Sun, 28 Jul 2019 22:59:10 -0400 Subject: [PATCH 091/149] DDFT_nucleation30/31 to test isotropic_hermite_scale with discrete images and mu --- solver/DDFT_nucleation30.m | 57 ++++++++++++++++++++++++++++++++++++++ solver/DDFT_nucleation31.m | 57 ++++++++++++++++++++++++++++++++++++++ 2 files changed, 114 insertions(+) create mode 100644 solver/DDFT_nucleation30.m create mode 100644 solver/DDFT_nucleation31.m diff --git a/solver/DDFT_nucleation30.m b/solver/DDFT_nucleation30.m new file mode 100644 index 0000000..6f02b84 --- /dev/null +++ b/solver/DDFT_nucleation30.m @@ -0,0 +1,57 @@ +%based on DDFT_nucleation29 +%5 snapshots. kernelSize = 10 +addpath('../../CHACR/GIP') +runoptim = true; + +tic; +L = [5,5]; +N = [256,256]; +n = prod(N); + +params.N = N; +params.L = L; + +[k2,k] = formk(N,L); +k0 = 10; +alpha = 5; +params.C = exp(-(sqrt(k2)-k0).^2/(2*alpha^2))*0.95; + +[t1,y1,params] = solver_DDFT([],[],params); + +xx = linspace(0,L(1),N(1)); +yy = linspace(0,L(2),N(2)); +[xx,yy] = ndgrid(xx,yy); +center = L/2; +radius = 0.06*L(1); +thickness = 0.01*L(1); +roi = roi_circle(xx,yy,center,radius,thickness); + +%nucleus +y0 = y1(end,:)'; +roi = roi(:); +y02 = 0.045; +rho = (y02*n - sum(roi.*y0)) / sum(1-roi); +y0 = roi.*y0 + (1-roi)*rho; + +tspan2 = linspace(0,2.5,100); +[t2,y2] = solver_DDFT(tspan2,y0,params); + +ind = 1:20:100; +tdata = t2(ind); +ydata = y2(ind,:); +toc + + +kernelSize = 10; +Cspace = 'isotropic_hermite_scale'; +params.moreoptions = moreodeset('gmresTol',1e-5); + + +resultpath = [largedatapath,'DDFT_nucleation30.mat']; + +options = optimoptions('fminunc','OutputFcn', @(x,optimvalues,state) save_opt_history(x,optimvalues,state,resultpath)); +options = optimoptions(options,'HessianFcn','objective','Algorithm','trust-region','MaxFunctionEvaluations',10000,'MaxIterations',10000); + +x_guess = zeros(1,kernelSize); + +[x_opt,~,exitflag,params] = IP_DDFT(tdata,ydata,params,kernelSize,Cspace,options,x_guess,'Nmu',0,'discrete',true,'cutoff',k0); diff --git a/solver/DDFT_nucleation31.m b/solver/DDFT_nucleation31.m new file mode 100644 index 0000000..362cc95 --- /dev/null +++ b/solver/DDFT_nucleation31.m @@ -0,0 +1,57 @@ +%based on DDFT_nucleation29 +%5 snapshots. optimize mu +addpath('../../CHACR/GIP') +runoptim = true; + +tic; +L = [5,5]; +N = [256,256]; +n = prod(N); + +params.N = N; +params.L = L; + +[k2,k] = formk(N,L); +k0 = 10; +alpha = 5; +params.C = exp(-(sqrt(k2)-k0).^2/(2*alpha^2))*0.95; + +[t1,y1,params] = solver_DDFT([],[],params); + +xx = linspace(0,L(1),N(1)); +yy = linspace(0,L(2),N(2)); +[xx,yy] = ndgrid(xx,yy); +center = L/2; +radius = 0.06*L(1); +thickness = 0.01*L(1); +roi = roi_circle(xx,yy,center,radius,thickness); + +%nucleus +y0 = y1(end,:)'; +roi = roi(:); +y02 = 0.045; +rho = (y02*n - sum(roi.*y0)) / sum(1-roi); +y0 = roi.*y0 + (1-roi)*rho; + +tspan2 = linspace(0,2.5,100); +[t2,y2] = solver_DDFT(tspan2,y0,params); + +ind = 1:100; +tdata = t2(ind); +ydata = y2(ind,:); +toc + + +kernelSize = 6; +Cspace = 'isotropic_hermite_scale'; +params.moreoptions = moreodeset('gmresTol',1e-5); + + +resultpath = [largedatapath,'DDFT_nucleation31.mat']; + +options = optimoptions('fminunc','OutputFcn', @(x,optimvalues,state) save_opt_history(x,optimvalues,state,resultpath)); +options = optimoptions(options,'HessianFcn','objective','Algorithm','trust-region','MaxFunctionEvaluations',10000,'MaxIterations',10000); + +x_guess = [zeros(1,kernelSize),0.5,0,-3]; + +[x_opt,~,exitflag,params] = IP_DDFT(tdata,ydata,params,kernelSize,Cspace,options,x_guess,'Nmu',3,'discrete',true,'cutoff',k0); From 1db12c00f3e8b1573e24e07d412552251dfd5dc0 Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Mon, 29 Jul 2019 03:06:16 -0400 Subject: [PATCH 092/149] more DDFT_nucleation32/33 on adding mu while isotropic_hermite_scale --- solver/DDFT_nucleation32.m | 57 ++++++++++++++++++++++++++++++++++++++ solver/DDFT_nucleation33.m | 57 ++++++++++++++++++++++++++++++++++++++ 2 files changed, 114 insertions(+) create mode 100644 solver/DDFT_nucleation32.m create mode 100644 solver/DDFT_nucleation33.m diff --git a/solver/DDFT_nucleation32.m b/solver/DDFT_nucleation32.m new file mode 100644 index 0000000..f1b4937 --- /dev/null +++ b/solver/DDFT_nucleation32.m @@ -0,0 +1,57 @@ +%based on DDFT_nucleation29 +%5 snapshots. optimize mu, kernelSize = 10 +addpath('../../CHACR/GIP') +runoptim = true; + +tic; +L = [5,5]; +N = [256,256]; +n = prod(N); + +params.N = N; +params.L = L; + +[k2,k] = formk(N,L); +k0 = 10; +alpha = 5; +params.C = exp(-(sqrt(k2)-k0).^2/(2*alpha^2))*0.95; + +[t1,y1,params] = solver_DDFT([],[],params); + +xx = linspace(0,L(1),N(1)); +yy = linspace(0,L(2),N(2)); +[xx,yy] = ndgrid(xx,yy); +center = L/2; +radius = 0.06*L(1); +thickness = 0.01*L(1); +roi = roi_circle(xx,yy,center,radius,thickness); + +%nucleus +y0 = y1(end,:)'; +roi = roi(:); +y02 = 0.045; +rho = (y02*n - sum(roi.*y0)) / sum(1-roi); +y0 = roi.*y0 + (1-roi)*rho; + +tspan2 = linspace(0,2.5,100); +[t2,y2] = solver_DDFT(tspan2,y0,params); + +ind = 1:20:100; +tdata = t2(ind); +ydata = y2(ind,:); +toc + + +kernelSize = 10; +Cspace = 'isotropic_hermite_scale'; +params.moreoptions = moreodeset('gmresTol',1e-5); + + +resultpath = [largedatapath,'DDFT_nucleation32.mat']; + +options = optimoptions('fminunc','OutputFcn', @(x,optimvalues,state) save_opt_history(x,optimvalues,state,resultpath)); +options = optimoptions(options,'HessianFcn','objective','Algorithm','trust-region','MaxFunctionEvaluations',10000,'MaxIterations',10000); + +x_guess = [zeros(1,kernelSize),0.5,0,-3]; + +[x_opt,~,exitflag,params] = IP_DDFT(tdata,ydata,params,kernelSize,Cspace,options,x_guess,'Nmu',3,'discrete',true,'cutoff',k0); diff --git a/solver/DDFT_nucleation33.m b/solver/DDFT_nucleation33.m new file mode 100644 index 0000000..5360317 --- /dev/null +++ b/solver/DDFT_nucleation33.m @@ -0,0 +1,57 @@ +%based on DDFT_nucleation29 +%5 snapshots. optimize mu, kernelSize = 10, mu_positive = false; +addpath('../../CHACR/GIP') +runoptim = true; + +tic; +L = [5,5]; +N = [256,256]; +n = prod(N); + +params.N = N; +params.L = L; + +[k2,k] = formk(N,L); +k0 = 10; +alpha = 5; +params.C = exp(-(sqrt(k2)-k0).^2/(2*alpha^2))*0.95; + +[t1,y1,params] = solver_DDFT([],[],params); + +xx = linspace(0,L(1),N(1)); +yy = linspace(0,L(2),N(2)); +[xx,yy] = ndgrid(xx,yy); +center = L/2; +radius = 0.06*L(1); +thickness = 0.01*L(1); +roi = roi_circle(xx,yy,center,radius,thickness); + +%nucleus +y0 = y1(end,:)'; +roi = roi(:); +y02 = 0.045; +rho = (y02*n - sum(roi.*y0)) / sum(1-roi); +y0 = roi.*y0 + (1-roi)*rho; + +tspan2 = linspace(0,2.5,100); +[t2,y2] = solver_DDFT(tspan2,y0,params); + +ind = 1:20:100; +tdata = t2(ind); +ydata = y2(ind,:); +toc + + +kernelSize = 10; +Cspace = 'isotropic_hermite_scale'; +params.moreoptions = moreodeset('gmresTol',1e-5); + + +resultpath = [largedatapath,'DDFT_nucleation33.mat']; + +options = optimoptions('fminunc','OutputFcn', @(x,optimvalues,state) save_opt_history(x,optimvalues,state,resultpath)); +options = optimoptions(options,'HessianFcn','objective','Algorithm','trust-region','MaxFunctionEvaluations',10000,'MaxIterations',10000); + +x_guess = [zeros(1,kernelSize),0.5,0,0]; + +[x_opt,~,exitflag,params] = IP_DDFT(tdata,ydata,params,kernelSize,Cspace,options,x_guess,'Nmu',3,'discrete',true,'cutoff',k0,'mu_positive',false); From 912931b2e70783ebc49ac00f4ec44e60a950dd8a Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Wed, 31 Jul 2019 01:20:02 -0400 Subject: [PATCH 093/149] visualization of DDFT_nucleation23 --- solver/DDFT_nucleation23.m | 18 +++++++++++++----- 1 file changed, 13 insertions(+), 5 deletions(-) diff --git a/solver/DDFT_nucleation23.m b/solver/DDFT_nucleation23.m index b67a614..888db4d 100644 --- a/solver/DDFT_nucleation23.m +++ b/solver/DDFT_nucleation23.m @@ -2,7 +2,7 @@ %different initial condition %with discrete number of points addpath('../../CHACR/GIP') -runoptim = true; +runoptim = false; tic; L = [5,5]; @@ -53,7 +53,15 @@ options = optimoptions('fminunc','OutputFcn', @(x,optimvalues,state) save_opt_history(x,optimvalues,state,resultpath)); options = optimoptions(options,'HessianFcn','objective','Algorithm','trust-region','MaxFunctionEvaluations',10000,'MaxIterations',10000,'FunctionTolerance',1e-7); -x_guess = [0,-9,0.5,0,-3]; - - -[x_opt,~,exitflag,params] = IP_DDFT(tdata,ydata,params,kernelSize,Cspace,options,x_guess,'Nmu',3,'discrete',true); +if runoptim + x_guess = [0,-9,0.5,0,-3]; + [x_opt,~,exitflag,params] = IP_DDFT(tdata,ydata,params,kernelSize,Cspace,options,x_guess,'Nmu',3,'discrete',true); +else + modelfunc.C = @(k) exp(-(k-k0).^2/(2*alpha^2))*0.95; + modelfunc.mu = @(x) x - x.^2/2 + x.^3/3; + arg.C = linspace(0,2,500); + arg.mu = linspace(min(ydata(:)),max(ydata(:)),100); + history_production(resultpath,[1,21,38,1797],modelfunc,arg,tdata-tdata(1),ydata,params,kernelSize,Cspace,'IP_DDFT_arg',{'Nmu',3},'yyaxisLim',[-0.5,1.5;-1,1.2],'k0',k0,'xlim',[min(ydata(:)),2]); + f = gcf; + f.Position = [680 337 522 641]; +end From 102e1e942bf20f6848188486fc086934de219918 Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Wed, 31 Jul 2019 01:21:13 -0400 Subject: [PATCH 094/149] add optional cutoff/scaling for Cspace=isotropic in IP_DDFT --- solver/IP_DDFT.m | 5 ++++- 1 file changed, 4 insertions(+), 1 deletion(-) diff --git a/solver/IP_DDFT.m b/solver/IP_DDFT.m index 33cb62d..b1b70c6 100644 --- a/solver/IP_DDFT.m +++ b/solver/IP_DDFT.m @@ -10,7 +10,7 @@ addParameter(ps,'mu_positive',true); %set the higher order polynomial of mu to be positive (exponentiated) addParameter(ps,'D',false); %setting this to true turns on optimizing over D addParameter(ps,'discrete',false); -addParameter(ps,'cutoff',[]); %must be provided if Cspace = isotropic_*_cutoff/scale (cutoff or scale value) +addParameter(ps,'cutoff',[]); %must be provided if Cspace = isotropic_*_cutoff/scale (cutoff or scale value), optional for Cspace = isotropic addParameter(ps,'isotropic_even',false); %set to true if even polynomials are used (Cspace = isotropic_poly_*) addParameter(ps,'assign_suppress',{}); %when mode='sens', use this to suppress the reassignment of certain parameters, however parameters of interest is still stored in meta. Be careful, this only works for things whose senstivity doesn't depend on the parameters themselves @@ -38,6 +38,9 @@ meta.C.exp = false(1,NC); meta.C.exp(end) = true; [k2,~] = formk(params.N,params.L); + if ~isempty(cutoff) + k2 = k2/cutoff^2; + end p = custom_Poly; if Nmu>0 %throw the constant term to mu, note that kernelSize is now the number of non-constant polynomials From cc72c43171f2afcdb699d11e36934f785588adc8 Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Wed, 31 Jul 2019 01:21:41 -0400 Subject: [PATCH 095/149] DDFT_nucleation34 try isotropic with scaling by k0 --- solver/DDFT_nucleation34.m | 66 ++++++++++++++++++++++++++++++++++++++ 1 file changed, 66 insertions(+) create mode 100644 solver/DDFT_nucleation34.m diff --git a/solver/DDFT_nucleation34.m b/solver/DDFT_nucleation34.m new file mode 100644 index 0000000..6a1a58b --- /dev/null +++ b/solver/DDFT_nucleation34.m @@ -0,0 +1,66 @@ +%based on DDFT_nucleation23 +%use scaling cutoff = k0 for Cspace=isotropic +addpath('../../CHACR/GIP') +runoptim = true; + +tic; +L = [5,5]; +N = [256,256]; +n = prod(N); + +params.N = N; +params.L = L; + +[k2,k] = formk(N,L); +k0 = 10; +alpha = 5; +params.C = exp(-(sqrt(k2)-k0).^2/(2*alpha^2))*0.95; + +[t1,y1,params] = solver_DDFT([],[],params); + +xx = linspace(0,L(1),N(1)); +yy = linspace(0,L(2),N(2)); +[xx,yy] = ndgrid(xx,yy); +center = L/2; +radius = 0.06*L(1); +thickness = 0.01*L(1); +roi = roi_circle(xx,yy,center,radius,thickness); + +%nucleus +y0 = y1(end,:)'; +roi = roi(:); +y02 = 0.045; +rho = (y02*n - sum(roi.*y0)) / sum(1-roi); +y0 = roi.*y0 + (1-roi)*rho; + +tspan2 = linspace(0,2.5,100); +[t2,y2] = solver_DDFT(tspan2,y0,params); + +ind = 1:20:100; +tdata = t2(ind); +ydata = y2(ind,:); +toc + + +kernelSize = 2; +Cspace = 'isotropic'; +params.moreoptions = moreodeset('gmresTol',1e-5); + + +resultpath = [largedatapath,'DDFT_nucleation34']; + +options = optimoptions('fminunc','OutputFcn', @(x,optimvalues,state) save_opt_history(x,optimvalues,state,resultpath)); +options = optimoptions(options,'HessianFcn','objective','Algorithm','trust-region','MaxFunctionEvaluations',10000,'MaxIterations',10000,'FunctionTolerance',1e-7); + +if runoptim + x_guess = [0,0,0.5,0,-3]; + [x_opt,~,exitflag,params] = IP_DDFT(tdata,ydata,params,kernelSize,Cspace,options,x_guess,'Nmu',3,'discrete',true,'cutoff',k0); +else + modelfunc.C = @(k) exp(-(k-k0).^2/(2*alpha^2))*0.95; + modelfunc.mu = @(x) x - x.^2/2 + x.^3/3; + arg.C = linspace(0,2,500); + arg.mu = linspace(min(ydata(:)),max(ydata(:)),100); + history_production(resultpath,[1,21,38,1797],modelfunc,arg,tdata-tdata(1),ydata,params,kernelSize,Cspace,'IP_DDFT_arg',{'Nmu',3},'yyaxisLim',[-0.5,1.5;-1,1.2],'k0',k0,'xlim',[min(ydata(:)),2]); + f = gcf; + f.Position = [680 337 522 641]; +end From c726c253c17ad75cc868bddea9ba73efd65cf478 Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Wed, 31 Jul 2019 14:39:38 -0400 Subject: [PATCH 096/149] add Cspace=isotropic_laguerre_scale --- solver/IP_DDFT.m | 7 +++++++ 1 file changed, 7 insertions(+) diff --git a/solver/IP_DDFT.m b/solver/IP_DDFT.m index b1b70c6..6ee3e8f 100644 --- a/solver/IP_DDFT.m +++ b/solver/IP_DDFT.m @@ -108,6 +108,13 @@ [k2,~] = formk(params.N,params.L); k = sqrt(k2)/cutoff; params.Csensval = hermitefunction(k,NC,[],1); +case 'isotropic_laguerre_scale' + %|k| scaled by cutoff + NC = kernelSize; + meta.C.exp = false; + [k2,~] = formk(params.N,params.L); + k = sqrt(k2)/cutoff; + params.Csensval = laguerrepoly(k,NC,[],0,1) .* exp(-k/2); case 'isotropic_CmE' %constant minus exponential NC = kernelSize; From 5c4c0224abc672c9416a7d5b685cb04d844e7b7e Mon Sep 17 00:00:00 2001 From: hbozhao Date: Wed, 31 Jul 2019 17:08:48 -0400 Subject: [PATCH 097/149] DDFT_nucleation36, sensitivity analysis using isotropic_hermite_scale --- solver/DDFT_nucleation36.m | 57 ++++++++++++++++++++++++++++++++++++++ 1 file changed, 57 insertions(+) create mode 100644 solver/DDFT_nucleation36.m diff --git a/solver/DDFT_nucleation36.m b/solver/DDFT_nucleation36.m new file mode 100644 index 0000000..aae7846 --- /dev/null +++ b/solver/DDFT_nucleation36.m @@ -0,0 +1,57 @@ +%based on DDFT_nucleation29 +%5 snapshots. kernelSize = 10 +addpath('../../CHACR/GIP') +runoptim = true; + +tic; +L = [5,5]; +N = [256,256]; +n = prod(N); + +params.N = N; +params.L = L; + +[k2,k] = formk(N,L); +k0 = 10; +alpha = 5; +params.C = exp(-(sqrt(k2)-k0).^2/(2*alpha^2))*0.95; + +[t1,y1,params] = solver_DDFT([],[],params); + +xx = linspace(0,L(1),N(1)); +yy = linspace(0,L(2),N(2)); +[xx,yy] = ndgrid(xx,yy); +center = L/2; +radius = 0.06*L(1); +thickness = 0.01*L(1); +roi = roi_circle(xx,yy,center,radius,thickness); + +%nucleus +y0 = y1(end,:)'; +roi = roi(:); +y02 = 0.045; +rho = (y02*n - sum(roi.*y0)) / sum(1-roi); +y0 = roi.*y0 + (1-roi)*rho; + +tspan2 = linspace(0,2.5,100); +[t2,y2] = solver_DDFT(tspan2,y0,params); + +ind = 1:20:100; +tdata = t2(ind); +ydata = y2(ind,:); +toc + + +kernelSize = 50; +Cspace = 'isotropic_hermite_scale'; +params.moreoptions = moreodeset('gmresTol',1e-5); + + +resultpath = [largedatapath,'DDFT_nucleation36.mat']; + +if runoptim + [hessian,hessian_t,dy] = IP_DDFT(tdata,ydata,params,kernelSize,Cspace,[],[],'discrete',true,'cutoff',k0,'assign_suppress',{'C'},'mode','sens'); + save(resultpath,'hessian','hessian_t','dy'); +else + load(resultpath); +end From 9d2e6638ddc340460631376b821dac96ba3b4974 Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Wed, 31 Jul 2019 19:31:51 -0400 Subject: [PATCH 098/149] update IP_DDFT, now cutoff can be used for all Cspace=isotropic*, add relevant Cfunc output pp --- solver/IP_DDFT.m | 32 +++++++++++++++++++++----------- 1 file changed, 21 insertions(+), 11 deletions(-) diff --git a/solver/IP_DDFT.m b/solver/IP_DDFT.m index 6ee3e8f..43cfca5 100644 --- a/solver/IP_DDFT.m +++ b/solver/IP_DDFT.m @@ -10,7 +10,7 @@ addParameter(ps,'mu_positive',true); %set the higher order polynomial of mu to be positive (exponentiated) addParameter(ps,'D',false); %setting this to true turns on optimizing over D addParameter(ps,'discrete',false); -addParameter(ps,'cutoff',[]); %must be provided if Cspace = isotropic_*_cutoff/scale (cutoff or scale value), optional for Cspace = isotropic +addParameter(ps,'cutoff',1); %used by Cspace = isotropic_* addParameter(ps,'isotropic_even',false); %set to true if even polynomials are used (Cspace = isotropic_poly_*) addParameter(ps,'assign_suppress',{}); %when mode='sens', use this to suppress the reassignment of certain parameters, however parameters of interest is still stored in meta. Be careful, this only works for things whose senstivity doesn't depend on the parameters themselves @@ -38,9 +38,7 @@ meta.C.exp = false(1,NC); meta.C.exp(end) = true; [k2,~] = formk(params.N,params.L); - if ~isempty(cutoff) - k2 = k2/cutoff^2; - end + k2 = k2/cutoff^2; p = custom_Poly; if Nmu>0 %throw the constant term to mu, note that kernelSize is now the number of non-constant polynomials @@ -120,6 +118,7 @@ NC = kernelSize; meta.C.exp = false; [k2,~] = formk(params.N,params.L); + k2 = k2/cutoff^2; if isempty(ps.Results.bound) bound = [0,max(k2(:))]; else @@ -212,19 +211,30 @@ end if nargout > 3 - %post processing - if isequal(Cspace,'isotropic') + %post processing, isotropic_*_cutoff not yet supported + switch Cspace + case 'isotropic' + if Nmu>0 + params.Cfunc.func = @(x,coeff) p.func((x/cutoff).^2,[0,coeff(1:end-1),-coeff(end)]); + else + params.Cfunc.func = @(x,coeff) p.func((x/cutoff).^2,[coeff(1:end-1),-coeff(end)]); + end + case 'isotropic_CmE' if Nmu>0 - params.Cfunc.func = @(x,coeff) p.func(x.^2,[0,coeff(1:end-1),-coeff(end)]); + params.Cfunc.func = @(x,coeff) -expleg.func((x/cutoff).^2,coeff); else - params.Cfunc.func = @(x,coeff) p.func(x.^2,[coeff(1:end-1),-coeff(end)]); + params.Cfunc.func = @(x,coeff) coeff(1)-expleg.func((x/cutoff).^2,coeff(2:end)); end - elseif isequal(Cspace,'isotropic_CmE') + case 'isotropic_poly_scale' if Nmu>0 - params.Cfunc.func = @(x,coeff) -expleg.func(x.^2,coeff); + params.Cfunc.func = @(x,coeff) legendrepoly(x/cutoff,[],[0,coeff]); else - params.Cfunc.func = @(x,coeff) coeff(1)-expleg.func(x.^2,coeff(2:end)); + params.Cfunc.func = @(x,coeff) legendrepoly(x/cutoff,[],coeff); end + case 'isotropic_hermite_scale' + params.Cfunc.func = @(x,coeff) hermitefunction(x/cutoff,[],coeff); + case 'isotropic_laguerre_scale' + params.Cfunc.func = @(x,coeff) laguerrepoly(x/cutoff,[],coeff) .* exp(-x/cutoff/2); end pp.params = params; pp.meta = meta; From ff857f83c24e10e7a3fc37765ec885769a029954 Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Wed, 31 Jul 2019 19:32:41 -0400 Subject: [PATCH 099/149] in history_production, generalize C to all isotropic*, fix bugs --- solver/history_production.m | 15 +++++++++------ 1 file changed, 9 insertions(+), 6 deletions(-) diff --git a/solver/history_production.m b/solver/history_production.m index 3123f31..b23fb41 100644 --- a/solver/history_production.m +++ b/solver/history_production.m @@ -13,6 +13,7 @@ function history_production(resultpath,ind,modelfunc,arg,tdata,ydata,params,kern %If there is more than one functions to plot, modelfunc should be a struct, whose field names match those in the meta. If there is only one function to plot, modelfunc can either be a struct or simply a function handle %the result file can also contain y, the solution to the PDE at each step, in which case we don't need to recompute %IP_DDFT_arg, varargin for IP_DDFT +addpath('../../CHACR') addpath('../../CHACR/IP') ps = inputParser; addParameter(ps,'label',true); @@ -112,7 +113,7 @@ function history_production(resultpath,ind,modelfunc,arg,tdata,ydata,params,kern ax.YTick = []; ax.Box = 'off'; else - if isequal(name,'C') && ismember(Cspace,{'isotropic','isotropic_CmE'}) + if isequal(name,'C') && ~isempty(regexp(Cspace,'isotropic*')) customfunc = pp.params.Cfunc.func; customparams = pp.params.Cfunc.params; yoffset = offset; @@ -121,13 +122,15 @@ function history_production(resultpath,ind,modelfunc,arg,tdata,ydata,params,kern customparams = pp.params.(name).params; yoffset = - customfunc(0,customparams); end - if j==1 - yyaxis left - elseif j==2 - yyaxis right + if numFunc>1 + if j==1 + yyaxis left + elseif j==2 + yyaxis right + end end argj = arg.(name); - if isequal(name,'C') && ismember(Cspace,{'isotropic','isotropic_CmE'}) + if isequal(name,'C') && ~isempty(regexp(Cspace,'isotropic*')) xscale = ps.k0; else xscale = 1; From 6d41919c9e9c21f8ebebc4c4f0dd2f34ef53167f Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Wed, 31 Jul 2019 19:33:37 -0400 Subject: [PATCH 100/149] add DDFT_nucleation30 visualization --- solver/DDFT_nucleation30.m | 16 ++++++++++++---- 1 file changed, 12 insertions(+), 4 deletions(-) diff --git a/solver/DDFT_nucleation30.m b/solver/DDFT_nucleation30.m index 6f02b84..8505e48 100644 --- a/solver/DDFT_nucleation30.m +++ b/solver/DDFT_nucleation30.m @@ -1,7 +1,7 @@ %based on DDFT_nucleation29 %5 snapshots. kernelSize = 10 addpath('../../CHACR/GIP') -runoptim = true; +runoptim = false; tic; L = [5,5]; @@ -52,6 +52,14 @@ options = optimoptions('fminunc','OutputFcn', @(x,optimvalues,state) save_opt_history(x,optimvalues,state,resultpath)); options = optimoptions(options,'HessianFcn','objective','Algorithm','trust-region','MaxFunctionEvaluations',10000,'MaxIterations',10000); -x_guess = zeros(1,kernelSize); - -[x_opt,~,exitflag,params] = IP_DDFT(tdata,ydata,params,kernelSize,Cspace,options,x_guess,'Nmu',0,'discrete',true,'cutoff',k0); +if runoptim + x_guess = zeros(1,kernelSize); + [x_opt,~,exitflag,params] = IP_DDFT(tdata,ydata,params,kernelSize,Cspace,options,x_guess,'Nmu',0,'discrete',true,'cutoff',k0); +else + modelfunc.C = @(k) exp(-(k-k0).^2/(2*alpha^2))*0.95; + Crange = [0,4]; + arg.C = linspace(Crange(1),Crange(2),500); + history_production(resultpath,[1,11,21,36],modelfunc,arg,tdata-tdata(1),ydata,params,kernelSize,Cspace,'IP_DDFT_arg',{'Nmu',0,'discrete',true,'cutoff',k0},'yyaxisLim',[-0.5,1.5;-1,1.2],'k0',k0,'xlim',Crange); + % f = gcf; + % f.Position = [680 337 522 641]; +end From b0436390075d3b88df669a0a4266f1297843ad5c Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Wed, 31 Jul 2019 19:36:01 -0400 Subject: [PATCH 101/149] small updates to DDFT_nucleation files --- solver/DDFT_nucleation31.m | 2 +- solver/DDFT_nucleation33.m | 4 ++-- solver/DDFT_nucleation36.m | 3 ++- 3 files changed, 5 insertions(+), 4 deletions(-) diff --git a/solver/DDFT_nucleation31.m b/solver/DDFT_nucleation31.m index 362cc95..2d701ad 100644 --- a/solver/DDFT_nucleation31.m +++ b/solver/DDFT_nucleation31.m @@ -36,7 +36,7 @@ tspan2 = linspace(0,2.5,100); [t2,y2] = solver_DDFT(tspan2,y0,params); -ind = 1:100; +ind = 1:20:100; tdata = t2(ind); ydata = y2(ind,:); toc diff --git a/solver/DDFT_nucleation33.m b/solver/DDFT_nucleation33.m index 5360317..6371b57 100644 --- a/solver/DDFT_nucleation33.m +++ b/solver/DDFT_nucleation33.m @@ -52,6 +52,6 @@ options = optimoptions('fminunc','OutputFcn', @(x,optimvalues,state) save_opt_history(x,optimvalues,state,resultpath)); options = optimoptions(options,'HessianFcn','objective','Algorithm','trust-region','MaxFunctionEvaluations',10000,'MaxIterations',10000); -x_guess = [zeros(1,kernelSize),0.5,0,0]; +x_guess = [zeros(1,kernelSize),0.5,0,-4]; -[x_opt,~,exitflag,params] = IP_DDFT(tdata,ydata,params,kernelSize,Cspace,options,x_guess,'Nmu',3,'discrete',true,'cutoff',k0,'mu_positive',false); +[x_opt,~,exitflag,params] = IP_DDFT(tdata,ydata,params,kernelSize,Cspace,options,x_guess,'Nmu',3,'discrete',true,'cutoff',k0); diff --git a/solver/DDFT_nucleation36.m b/solver/DDFT_nucleation36.m index aae7846..13506c2 100644 --- a/solver/DDFT_nucleation36.m +++ b/solver/DDFT_nucleation36.m @@ -42,8 +42,9 @@ toc -kernelSize = 50; +kernelSize = 150; Cspace = 'isotropic_hermite_scale'; +%note 100 is about where hermitefunction still approaches zero as k approaches kmax (N/L*pi) params.moreoptions = moreodeset('gmresTol',1e-5); From b686b2563cd59995c6943997b3cb31086a3292a7 Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Thu, 1 Aug 2019 20:01:00 -0400 Subject: [PATCH 102/149] add isotropic_fourier_scale in IP_DDFT --- solver/IP_DDFT.m | 25 ++++++++++++++++++++++++- 1 file changed, 24 insertions(+), 1 deletion(-) diff --git a/solver/IP_DDFT.m b/solver/IP_DDFT.m index 43cfca5..88cc9e3 100644 --- a/solver/IP_DDFT.m +++ b/solver/IP_DDFT.m @@ -50,7 +50,7 @@ %let the basis of the last derivative be negative Csensval(:,:,end) = -Csensval(:,:,end); params.Csensval = Csensval; -case 'isotropic_cos_cutoff' +case {'isotropic_cos_cutoff','isotropic_cos_scale'} NC = kernelSize; meta.C.exp = false; [k2,~] = formk(params.N,params.L); @@ -68,6 +68,29 @@ end mask = 1*(k<=1); params.Csensval = Csensval .* mask; +case {'isotropic_fourier_scale'} + NC = kernelSize; + meta.C.exp = false; + [k2,~] = formk(params.N,params.L); + k = sqrt(k2)/cutoff; + Csensval = ones(size(k,1),size(k,2),NC); + if Nmu > 0 + Ncos = ceil((NC-1)/2); + Nsin = NC-1-Ncos; + NcosInd(1,1,:) = 1:Ncos; + NsinInd(1,1,:) = 1:Nsin; + Csensval(:,:,2:2:(2*Ncos)) = cos(NcosInd*pi*k); + Csensval(:,:,3:2:(2*Nsin+1)) = sin(NsinInd*pi*k); + else + Ncos = ceil(NC/2); + Nsin = NC-Ncos; + NcosInd(1,1,:) = 1:Ncos; + NsinInd(1,1,:) = 1:Nsin; + Csensval(:,:,1:2:(2*Ncos-1)) = cos(NcosInd*pi*k); + Csensval(:,:,2:2:(2*Nsin)) = sin(NsinInd*pi*k); + end + mask = 1*(k<=1); + params.Csensval = Csensval .* mask; case {'isotropic_poly_cutoff','isotropic_poly_scale'} %NB: we use |k| as the argument of Legenre polynomials %scale k by cutoff, if using poly_cutoff, beyond cutoff, C is set to zero. From 3aaeeba1b6b814d715a756f3b2c2f21aadcd08b7 Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Thu, 1 Aug 2019 20:01:36 -0400 Subject: [PATCH 103/149] update IP_DDFT, add mode='pp' --- solver/IP_DDFT.m | 19 ++++++++++--------- 1 file changed, 10 insertions(+), 9 deletions(-) diff --git a/solver/IP_DDFT.m b/solver/IP_DDFT.m index 88cc9e3..a431c7f 100644 --- a/solver/IP_DDFT.m +++ b/solver/IP_DDFT.m @@ -202,12 +202,12 @@ end end +forwardHandle = @(tdata,y0,FSA,meta,params) forwardSolver(tdata,y0,FSA,meta,params,tspan,ybound); +assignHandle = @(name,xparam,params) assign(name,xparam,params,Cspace,kernelSize); switch mode case 'eval' [x_opt,~,params] = IP(tdata,ydata,x_guess,meta,params, ... - @(tdata,y0,FSA,meta,params) forwardSolver(tdata,y0,FSA,meta,params,tspan,ybound), ... - [], [], [],... - @(name,xparam,params) assign(name,xparam,params,Cspace,kernelSize),'eval',true); + forwardHandle, [], [], [], assignHandle,'eval',true); fval = []; exitflag = []; case 'IP' @@ -219,18 +219,19 @@ options = optimoptions('fminunc','SpecifyObjectiveGradient',true,'Display','iter-detailed'); end [x_opt,fval,exitflag] = fminunc(@(x) IP(tdata,ydata,x,meta,params, ... - @(tdata,y0,FSA,meta,params) forwardSolver(tdata,y0,FSA,meta,params,tspan,ybound), ... - @adjointSolver, ... - loss,lossHess, ... - @(name,xparam,params) assign(name,xparam,params,Cspace,kernelSize),'discrete',discrete), ... + forwardHandle, @adjointSolver,loss,lossHess, assignHandle,'discrete',discrete), ... x_guess, options); case 'sens' loss = @(y,ydata,~) MSE(y,ydata,prod(params.dx)); lossHess = @(dy,~,~,~) MSE([],[],prod(params.dx),dy); [~,~,x_opt,exitflag,fval] = IP(tdata,ydata,x_guess,meta,params, ... - @(tdata,y0,FSA,meta,params) forwardSolver(tdata,y0,FSA,meta,params,tspan,ybound), ... - [],loss,lossHess, ... + forwardHandle, [],loss,lossHess, ... @(name,xparam,params) assign(name,xparam,params,Cspace,kernelSize,suppress),'discrete',discrete); +case 'pp' + x_opt = []; + fval = []; + exitflag = []; + params = paramsTransfer(x_guess,meta,params,assignHandle,ydata,false); end if nargout > 3 From 2825717a5c5b317494f64abe359eb1461807949a Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Thu, 1 Aug 2019 20:02:41 -0400 Subject: [PATCH 104/149] add history_func, copied from history_production to plot functions in history only --- solver/history_func.m | 114 ++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 114 insertions(+) create mode 100644 solver/history_func.m diff --git a/solver/history_func.m b/solver/history_func.m new file mode 100644 index 0000000..2231c6e --- /dev/null +++ b/solver/history_func.m @@ -0,0 +1,114 @@ +function history_func(ind,modelfunc,arg,Cspace,pp,property,varargin) + %show the functional forms of history + %pp is the post-processing output from IP_DDFT + %property can be provided directly, if not, through varargin + %ind is the index + if isempty(property) + ps = inputParser; + ps.KeepUnmatched = true; + addParameter(ps,'xlabel','on'); + addParameter(ps,'dmu_at_0',1); %when meta has both mu and C, rescale so that dmu/dx at 0 has this value + addParameter(ps,'k0',1); %used to scale k + addParameter(ps,'yyaxisLim',[]); + addParameter(ps,'xlim',[]); + addParameter(ps,'legend',[]); + addParameter(ps,'label',true); + addParameter(ps,'labelHorizontalAlignment','left'); + parse(ps,varargin{:}); + ps = ps.Results; + else + ps = property; + end + + meta = pp.meta; + names = fieldnames(meta); + namesflag = ismember({'mu','C'},names); + numFunc = numel(names); + + if all(namesflag) + %calculate current gradient of mu at x=0 + grad0 = customizeFunGrad(pp.params,'mu','grad',0); + %gradient of the first order basis function of mu + [~,grad1] = feval(pp.params.mu.func,0,1); + %set the gradient of mu at x=0 to be 1. The offset is + offset = (ps.dmu_at_0-grad0)/grad1; + pp.params.mu.params(1) = pp.params.mu.params(1) + offset; + else + offset = 0; + end + ax = gca; + for j=1:numFunc + name = names{j}; + if ismember(name,{'D','extdata'}) + continue; + end + if isequal(name,'C') && ismember(Cspace,{'k','real'}) + imagesc(pp.params.C-offset); + caxis([0,1]); + axis(ax,'image'); + ax.XTick = []; + ax.YTick = []; + ax.Box = 'off'; + else + if isequal(name,'C') && ~isempty(regexp(Cspace,'isotropic*')) + customfunc = pp.params.Cfunc.func; + customparams = pp.params.Cfunc.params; + yoffset = offset; + elseif isequal(name,'mu') + customfunc = pp.params.(name).func; + customparams = pp.params.(name).params; + yoffset = - customfunc(0,customparams); + end + if numFunc>1 + if j==1 + yyaxis left + elseif j==2 + yyaxis right + end + end + argj = arg.(name); + if isequal(name,'C') && ~isempty(regexp(Cspace,'isotropic*')) + xscale = ps.k0; + else + xscale = 1; + end + if numFunc==1 + ax.ColorOrderIndex = j; + end + plot(argj,modelfunc.(name)(argj*xscale),'--','LineWidth',2); + ylimtemp = ax.YLim; + hold on; + if numFunc==1 + ax.ColorOrderIndex = j; + end + plot(argj,customfunc(argj*xscale,customparams)+yoffset,'LineWidth',2); + if isempty(ps.yyaxisLim) + ax.YLim = ylimtemp; + else + ax.YLim = ps.yyaxisLim(j,:); + end + if ~isempty(ps.xlim) + ax.XLim = ps.xlim; + end + axis square + if ~isequal(ps.xlabel,'on') + ax.XTick = []; + else + if namesflag(1) && ~namesflag(2) + xl = '\psi'; + elseif ~namesflag(1) && namesflag(2) + xl = 'k/k_0'; + elseif all(namesflag) + xl = '\psi or k/k_0'; + end + xlabel(xl); + if ~isempty(ps.legend) + legend(ps.legend{:}); + legend('boxoff'); + end + end + end + if ps.label && j==1 && ~isempty(ind) + text(0.1,1.2,['Iter. ',num2str(ind-1)],'Units','normalized','HorizontalAlignment',ps.labelHorizontalAlignment); + end + end From ab3dd92aeeee635336da7ba28a5ce493f8fb997b Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Thu, 1 Aug 2019 20:03:01 -0400 Subject: [PATCH 105/149] begin working on mainFigure --- solver/mainFig.m | 91 ++++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 91 insertions(+) create mode 100644 solver/mainFig.m diff --git a/solver/mainFig.m b/solver/mainFig.m new file mode 100644 index 0000000..296d33c --- /dev/null +++ b/solver/mainFig.m @@ -0,0 +1,91 @@ +%the script for the main figure for DDFT +addpath('../../CHACR/GIP') + +L = [5,5]; +N = [256,256]; +n = prod(N); + +params.N = N; +params.L = L; + +[k2,k] = formk(N,L); +k0 = 10; +alpha = 5; +params.C = exp(-(sqrt(k2)-k0).^2/(2*alpha^2))*0.95; + +if ~exist('t2','var') + [t1,y1,params] = solver_DDFT([],[],params); + + xx = linspace(0,L(1),N(1)); + yy = linspace(0,L(2),N(2)); + [xx,yy] = ndgrid(xx,yy); + center = L/2; + radius = 0.06*L(1); + thickness = 0.01*L(1); + roi = roi_circle(xx,yy,center,radius,thickness); + + %nucleus + y0 = y1(end,:)'; + roi = roi(:); + y02 = 0.045; + rho = (y02*n - sum(roi.*y0)) / sum(1-roi); + y0 = roi.*y0 + (1-roi)*rho; + + tspan2 = linspace(0,2.5,100); + [t2,y2] = solver_DDFT(tspan2,y0,params); + + ind = 1:20:100; + tdata = t2(ind); + ydata = y2(ind,:); +end + +rowtotal = 5; +columntotal = 5; +stparg = {0.05,[0.05,0.08],0.05}; +clim = [min(min(ydata(:))),max(max(ydata(:)))]; +%first row: data +h = visualize([],[],[],ydata,'c',false,'ImageSize',params.N,'caxis','auto','GridSize',[1,NaN],'OuterGridSize',[rowtotal,1],'OuterSubplot',[1,1],'subtightplot',stparg); +for j = 1:length(h) + title(h(j),['t = ',num2str(tdata(j),2)]); +end +axes(h(1)); +text(0.1,1.5,'(a). Data','Units','normalized','HorizontalAlignment','left'); +%second row: history of DDFT_nucleation23 +kernelSize = 2; +Cspace = 'isotropic'; +params.moreoptions = moreodeset('gmresTol',1e-5); +IP_DDFT_arg = {'Nmu',3}; +figprop = {'IP_DDFT_arg',IP_DDFT_arg,'yyaxisLim',[-0.5,1.5;-1,1.2],'k0',k0,'xlim',[min(ydata(:)),2]}; +resultpath = [largedatapath,'DDFT_nucleation23']; +varload = load(resultpath); +history = varload.history; +modelfunc.C = @(k) exp(-(k-k0).^2/(2*alpha^2))*0.95; +modelfunc.mu = @(x) x - x.^2/2 + x.^3/3; +arg.C = linspace(0,2,500); +arg.mu = linspace(min(ydata(:)),max(ydata(:)),100); +ind = [1,19,25,31,1797]; +for i = 1:length(ind) + subtightplot(rowtotal,columntotal,columntotal+i,stparg{:}); + [~,~,~,pp] = IP_DDFT(tdata,ydata,params,kernelSize,Cspace,[],history(ind(i),:),'mode','pp',IP_DDFT_arg{:}); + history_func(ind(i),modelfunc,arg,Cspace,pp,[],figprop{:}); +end +%third row: final result of DDFT_nucleation23 +[yhistory,~,~,pp] = IP_DDFT(tdata,ydata,params,kernelSize,Cspace,[],history(end,:),'mode','eval',IP_DDFT_arg{:}); +visualize([],[],[],yhistory,'c',false,'ImageSize',params.N,'caxis',clim,'GridSize',[1,NaN],'OuterGridSize',[rowtotal,1],'OuterSubplot',[3,1],'subtightplot',stparg); + +%fourth row: history of DDFT_nucleation30 +kernelSize = 10; +Cspace = 'isotropic_hermite_scale'; +Crange = [0,4]; +IP_DDFT_arg = {'Nmu',0,'discrete',true,'cutoff',k0}; +figprop = {'IP_DDFT_arg',IP_DDFT_arg,'yyaxisLim',[-0.5,1.5],'k0',k0,'xlim',Crange}; +resultpath = [largedatapath,'DDFT_nucleation30']; +varload = load(resultpath); +history = varload.history; +arg.C = linspace(Crange(1),Crange(2),500); +ind = [1,11,16,21,36]; +for i = 1:length(ind) + subtightplot(rowtotal,columntotal,columntotal*3+i,stparg{:}); + [~,~,~,pp] = IP_DDFT(tdata,ydata,params,kernelSize,Cspace,[],history(ind(i),:),'mode','pp',IP_DDFT_arg{:}); + history_func(ind(i),modelfunc,arg,Cspace,pp,[],figprop{:}); +end From b8005e6ebfc0548d7e3e5543d172686388e3dd32 Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Thu, 1 Aug 2019 20:04:01 -0400 Subject: [PATCH 106/149] update DDFT_nucleation, add 35: laguerre poly (failed), 37: sensitivity using fourier_ --- solver/DDFT_nucleation35.m | 58 ++++++++++++++++++++++++++++++++++++++ solver/DDFT_nucleation36.m | 2 +- solver/DDFT_nucleation37.m | 58 ++++++++++++++++++++++++++++++++++++++ 3 files changed, 117 insertions(+), 1 deletion(-) create mode 100644 solver/DDFT_nucleation35.m create mode 100644 solver/DDFT_nucleation37.m diff --git a/solver/DDFT_nucleation35.m b/solver/DDFT_nucleation35.m new file mode 100644 index 0000000..02206cd --- /dev/null +++ b/solver/DDFT_nucleation35.m @@ -0,0 +1,58 @@ +%based on DDFT_nucleation30 +%5 snapshots. kernelSize = 10. Cspace=isotropic_laguerre_scale +%failed +addpath('../../CHACR/GIP') +runoptim = true; + +tic; +L = [5,5]; +N = [256,256]; +n = prod(N); + +params.N = N; +params.L = L; + +[k2,k] = formk(N,L); +k0 = 10; +alpha = 5; +params.C = exp(-(sqrt(k2)-k0).^2/(2*alpha^2))*0.95; + +[t1,y1,params] = solver_DDFT([],[],params); + +xx = linspace(0,L(1),N(1)); +yy = linspace(0,L(2),N(2)); +[xx,yy] = ndgrid(xx,yy); +center = L/2; +radius = 0.06*L(1); +thickness = 0.01*L(1); +roi = roi_circle(xx,yy,center,radius,thickness); + +%nucleus +y0 = y1(end,:)'; +roi = roi(:); +y02 = 0.045; +rho = (y02*n - sum(roi.*y0)) / sum(1-roi); +y0 = roi.*y0 + (1-roi)*rho; + +tspan2 = linspace(0,2.5,100); +[t2,y2] = solver_DDFT(tspan2,y0,params); + +ind = 1:20:100; +tdata = t2(ind); +ydata = y2(ind,:); +toc + + +kernelSize = 6; +Cspace = 'isotropic_laguerre_scale'; +params.moreoptions = moreodeset('gmresTol',1e-5); + + +resultpath = [largedatapath,'DDFT_nucleation35.mat']; + +options = optimoptions('fminunc','OutputFcn', @(x,optimvalues,state) save_opt_history(x,optimvalues,state,resultpath)); +options = optimoptions(options,'HessianFcn','objective','Algorithm','trust-region','MaxFunctionEvaluations',10000,'MaxIterations',10000); + +x_guess = zeros(1,kernelSize); + +[x_opt,~,exitflag,params] = IP_DDFT(tdata,ydata,params,kernelSize,Cspace,options,x_guess,'Nmu',0,'discrete',true,'cutoff',k0); diff --git a/solver/DDFT_nucleation36.m b/solver/DDFT_nucleation36.m index 13506c2..1881319 100644 --- a/solver/DDFT_nucleation36.m +++ b/solver/DDFT_nucleation36.m @@ -42,7 +42,7 @@ toc -kernelSize = 150; +kernelSize = 300; Cspace = 'isotropic_hermite_scale'; %note 100 is about where hermitefunction still approaches zero as k approaches kmax (N/L*pi) params.moreoptions = moreodeset('gmresTol',1e-5); diff --git a/solver/DDFT_nucleation37.m b/solver/DDFT_nucleation37.m new file mode 100644 index 0000000..d979efa --- /dev/null +++ b/solver/DDFT_nucleation37.m @@ -0,0 +1,58 @@ +%based on DDFT_nucleation29 +%5 snapshots. kernelSize = 10 +addpath('../../CHACR/GIP') +runoptim = true; + +tic; +L = [5,5]; +N = [256,256]; +n = prod(N); + +params.N = N; +params.L = L; + +[k2,k] = formk(N,L); +k0 = 10; +alpha = 5; +params.C = exp(-(sqrt(k2)-k0).^2/(2*alpha^2))*0.95; + +[t1,y1,params] = solver_DDFT([],[],params); + +xx = linspace(0,L(1),N(1)); +yy = linspace(0,L(2),N(2)); +[xx,yy] = ndgrid(xx,yy); +center = L/2; +radius = 0.06*L(1); +thickness = 0.01*L(1); +roi = roi_circle(xx,yy,center,radius,thickness); + +%nucleus +y0 = y1(end,:)'; +roi = roi(:); +y02 = 0.045; +rho = (y02*n - sum(roi.*y0)) / sum(1-roi); +y0 = roi.*y0 + (1-roi)*rho; + +tspan2 = linspace(0,2.5,100); +[t2,y2] = solver_DDFT(tspan2,y0,params); + +ind = 1:20:100; +tdata = t2(ind); +ydata = y2(ind,:); +toc + + +kernelSize = 300; +Cspace = 'isotropic_fourier_scale'; +params.moreoptions = moreodeset('gmresTol',1e-5); + + +resultpath = [largedatapath,'DDFT_nucleation37.mat']; + +kmax = floor(params.N(1)/2+1)/params.L(1)*2*pi; +if runoptim + [hessian,hessian_t,dy] = IP_DDFT(tdata,ydata,params,kernelSize,Cspace,[],[],'discrete',true,'cutoff',kmax,'assign_suppress',{'C'},'mode','sens'); + save(resultpath,'hessian','hessian_t','dy'); +else + load(resultpath); +end From fe826c09717e961f042f083af9afe56ad1d75edd Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Thu, 1 Aug 2019 20:06:54 -0400 Subject: [PATCH 107/149] fix bug in IP_DDFT regarding isotropic_fourier_scale --- solver/IP_DDFT.m | 8 ++++---- 1 file changed, 4 insertions(+), 4 deletions(-) diff --git a/solver/IP_DDFT.m b/solver/IP_DDFT.m index a431c7f..d38b817 100644 --- a/solver/IP_DDFT.m +++ b/solver/IP_DDFT.m @@ -79,15 +79,15 @@ Nsin = NC-1-Ncos; NcosInd(1,1,:) = 1:Ncos; NsinInd(1,1,:) = 1:Nsin; - Csensval(:,:,2:2:(2*Ncos)) = cos(NcosInd*pi*k); - Csensval(:,:,3:2:(2*Nsin+1)) = sin(NsinInd*pi*k); + Csensval(:,:,2:2:(2*Ncos)) = cos(NcosInd*pi.*k); + Csensval(:,:,3:2:(2*Nsin+1)) = sin(NsinInd*pi.*k); else Ncos = ceil(NC/2); Nsin = NC-Ncos; NcosInd(1,1,:) = 1:Ncos; NsinInd(1,1,:) = 1:Nsin; - Csensval(:,:,1:2:(2*Ncos-1)) = cos(NcosInd*pi*k); - Csensval(:,:,2:2:(2*Nsin)) = sin(NsinInd*pi*k); + Csensval(:,:,1:2:(2*Ncos-1)) = cos(NcosInd*pi.*k); + Csensval(:,:,2:2:(2*Nsin)) = sin(NsinInd*pi.*k); end mask = 1*(k<=1); params.Csensval = Csensval .* mask; From 230a877a2d1fe854a8ce2308bd5e3180b835f390 Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Fri, 2 Aug 2019 03:09:31 -0400 Subject: [PATCH 108/149] update history_production, use history_func --- solver/history_production.m | 89 ++----------------------------------- 1 file changed, 3 insertions(+), 86 deletions(-) diff --git a/solver/history_production.m b/solver/history_production.m index b23fb41..f3ee16a 100644 --- a/solver/history_production.m +++ b/solver/history_production.m @@ -83,94 +83,11 @@ function history_production(resultpath,ind,modelfunc,arg,tdata,ydata,params,kern [yhistory,~,~,pp] = IP_DDFT(tdata,ydata,params,kernelSize,Cspace,[],history(ind(i),:),'mode','eval',ps.IP_DDFT_arg{:}); visualize([],[],[],yhistory(frameindex_model,:),'c',false,'ImageSize',params.N,'caxis',clim,'GridSize',[1,NaN],'OuterGridSize',[rowtotal,1],'OuterSubplot',[i+1,1],'ColumnTotal',columntotal,'StarterInd',i*columntotal+1,'subtightplot',stparg); end - meta = pp.meta; - names = fieldnames(meta); - namesflag = ismember({'mu','C'},names); - numFunc = numel(names); + subtightplot(rowtotal,columntotal,i*columntotal+1,stparg{:}); - if all(namesflag) - %calculate current gradient of mu at x=0 - grad0 = customizeFunGrad(pp.params,'mu','grad',0); - %gradient of the first order basis function of mu - [~,grad1] = feval(pp.params.mu.func,0,1); - %set the gradient of mu at x=0 to be 1. The offset is - offset = (ps.dmu_at_0-grad0)/grad1; - pp.params.mu.params(1) = pp.params.mu.params(1) + offset; - else - offset = 0; - end - for j=1:numFunc - name = names{j}; - if ismember(name,{'D','extdata'}) - continue; - end - if isequal(name,'C') && ismember(Cspace,{'k','real'}) - imagesc(pp.params.C-offset); - caxis([0,1]); - ax = gca; - axis(ax,'image'); - ax.XTick = []; - ax.YTick = []; - ax.Box = 'off'; - else - if isequal(name,'C') && ~isempty(regexp(Cspace,'isotropic*')) - customfunc = pp.params.Cfunc.func; - customparams = pp.params.Cfunc.params; - yoffset = offset; - elseif isequal(name,'mu') - customfunc = pp.params.(name).func; - customparams = pp.params.(name).params; - yoffset = - customfunc(0,customparams); - end - if numFunc>1 - if j==1 - yyaxis left - elseif j==2 - yyaxis right - end - end - argj = arg.(name); - if isequal(name,'C') && ~isempty(regexp(Cspace,'isotropic*')) - xscale = ps.k0; - else - xscale = 1; - end - plot(argj,modelfunc.(name)(argj*xscale),'--','LineWidth',2); - ax = gca; - ylimtemp = ax.YLim; - hold on; - plot(argj,customfunc(argj*xscale,customparams)+yoffset,'LineWidth',2); - if isempty(ps.yyaxisLim) - ax.YLim = ylimtemp; - else - ax.YLim = ps.yyaxisLim(j,:); - end - if ~isempty(ps.xlim) - ax.XLim = ps.xlim; - end - axis square - if i~=numIter - ax.XTick = []; - else - if namesflag(1) && ~namesflag(2) - xl = '\psi'; - elseif ~namesflag(1) && namesflag(2) - xl = 'k/k_0'; - elseif all(namesflag) - xl = '\psi or k/k_0'; - end - xlabel(xl); - if ~isempty(ps.legend) - legend(ps.legend{:}); - legend('boxoff'); - end - end - end - if ps.label && j==1 - text(0.1,1.2,['Iter. ',num2str(ind(i)-1)],'Units','normalized','HorizontalAlignment',ps.labelHorizontalAlignment); - end - end + history_func(ind(i),modelfunc,arg,Cspace,pp,ps); end + if isfield(meta,'C') && ismember(Cspace,{'k','real'}) && ~isempty(ps.CtruthSubplot) axC = subtightplot(rowtotal,columntotal,columntotal*(ps.CtruthSubplot(1)-1)+ps.CtruthSubplot(2),stparg{:}); CC = params.C; From 7c2960864c288dee4c895cbfcdf891463e9b8ec3 Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Fri, 2 Aug 2019 03:13:21 -0400 Subject: [PATCH 109/149] DDFT_nucleation38 try Laguerre polynomials for sensitivity analysis --- solver/DDFT_nucleation38.m | 56 ++++++++++++++++++++++++++++++++++++++ 1 file changed, 56 insertions(+) create mode 100644 solver/DDFT_nucleation38.m diff --git a/solver/DDFT_nucleation38.m b/solver/DDFT_nucleation38.m new file mode 100644 index 0000000..1c461ba --- /dev/null +++ b/solver/DDFT_nucleation38.m @@ -0,0 +1,56 @@ +%based on DDFT_nucleation37, sensitivity analysis, use Laguerre +addpath('../../CHACR/GIP') +runoptim = true; + +tic; +L = [5,5]; +N = [256,256]; +n = prod(N); + +params.N = N; +params.L = L; + +[k2,k] = formk(N,L); +k0 = 10; +alpha = 5; +params.C = exp(-(sqrt(k2)-k0).^2/(2*alpha^2))*0.95; + +[t1,y1,params] = solver_DDFT([],[],params); + +xx = linspace(0,L(1),N(1)); +yy = linspace(0,L(2),N(2)); +[xx,yy] = ndgrid(xx,yy); +center = L/2; +radius = 0.06*L(1); +thickness = 0.01*L(1); +roi = roi_circle(xx,yy,center,radius,thickness); + +%nucleus +y0 = y1(end,:)'; +roi = roi(:); +y02 = 0.045; +rho = (y02*n - sum(roi.*y0)) / sum(1-roi); +y0 = roi.*y0 + (1-roi)*rho; + +tspan2 = linspace(0,2.5,100); +[t2,y2] = solver_DDFT(tspan2,y0,params); + +ind = 1:20:100; +tdata = t2(ind); +ydata = y2(ind,:); +toc + + +kernelSize = 300; +Cspace = 'isotropic_laguerre_scale'; +params.moreoptions = moreodeset('gmresTol',1e-5); + + +resultpath = [largedatapath,'DDFT_nucleation38.mat']; + +if runoptim + [hessian,hessian_t,dy] = IP_DDFT(tdata,ydata,params,kernelSize,Cspace,[],[],'discrete',true,'cutoff',k0,'assign_suppress',{'C'},'mode','sens'); + save(resultpath,'hessian','hessian_t','dy'); +else + load(resultpath); +end From a9b7b34d752477eecb5de87cc162bd5320f890ed Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Fri, 2 Aug 2019 20:59:09 -0400 Subject: [PATCH 110/149] update DDFT_nucleation26/38 to show C2 error bar --- solver/DDFT_nucleation36.m | 7 +++++++ solver/DDFT_nucleation38.m | 9 ++++++++- 2 files changed, 15 insertions(+), 1 deletion(-) diff --git a/solver/DDFT_nucleation36.m b/solver/DDFT_nucleation36.m index 1881319..99727e8 100644 --- a/solver/DDFT_nucleation36.m +++ b/solver/DDFT_nucleation36.m @@ -55,4 +55,11 @@ save(resultpath,'hessian','hessian_t','dy'); else load(resultpath); + numBasis = 100; + x = linspace(0,10,1000)'; + psi = hermitefunction(x,numBasis); + C = psi * (hessian(1:numBasis,1:numBasis)\psi'); + dev = diag(C); + y = exp(-(x-k0).^2/(2*alpha^2))*0.95; + boundedline(x,y,dev); end diff --git a/solver/DDFT_nucleation38.m b/solver/DDFT_nucleation38.m index 1c461ba..2e28d3f 100644 --- a/solver/DDFT_nucleation38.m +++ b/solver/DDFT_nucleation38.m @@ -1,6 +1,6 @@ %based on DDFT_nucleation37, sensitivity analysis, use Laguerre addpath('../../CHACR/GIP') -runoptim = true; +runoptim = false; tic; L = [5,5]; @@ -53,4 +53,11 @@ save(resultpath,'hessian','hessian_t','dy'); else load(resultpath); + numBasis = 10; + x = linspace(0,10,1000)'; + psi = laguerrepoly(x,numBasis) .* exp(-x/2); + C = psi * (hessian(1:numBasis,1:numBasis)\psi'); + dev = diag(C); + y = exp(-(x-k0).^2/(2*alpha^2))*0.95; + boundedline(x,y,dev); end From e9781a5b60016442f5eda5f7bee58ff6c7252d70 Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Mon, 5 Aug 2019 03:16:25 -0400 Subject: [PATCH 111/149] calculate sensitivity (eigenvalue etc) using 1D approx --- solver/sens1D.m | 32 ++++++++++++++++++++++++++++++++ 1 file changed, 32 insertions(+) create mode 100644 solver/sens1D.m diff --git a/solver/sens1D.m b/solver/sens1D.m new file mode 100644 index 0000000..54d1ef0 --- /dev/null +++ b/solver/sens1D.m @@ -0,0 +1,32 @@ +addpath('../../CHACR/GIP') +Nbasis = 5000; +t = 1; +k = linspace(0,100,10000)'; +k2 = k.^2; +k0 = 10; +alpha = 5; +C = exp(-(k-k0).^2/(2*alpha^2))*0.95; +y0 = 0.06; +dmu = (1-y0+y0^2); +sigma = - k2 .* (dmu - C); + +bound = [k(1),k(end)]; +kscale = (k-mean(bound))/diff(bound); +psi = legendrepoly(kscale,Nbasis) .* sqrt(2*(1:Nbasis)-1); +% psi = laguerrepoly(k,Nbasis) .* exp(-k/2); +deta = k .* k2 .* exp(sigma*t) .* psi; +scale = (k .* k2 .* exp(sigma*t)).^2; +hessian = deta' * deta; +[V,D] = eig(hessian); + +xx = linspace(0,20,1000)'; +figure; +for i = 1:3 + subplot(1,3,i); + % plot(xx,laguerrepoly(xx,[],V(:,end-i+1)).*exp(-xx/2)); + % plot(k,psi*V(:,end-i+1)); + plot(xx,legendrepoly((xx-mean(bound))/diff(bound),[],V(:,end-i+1) .* sqrt(2*(1:Nbasis)-1)')); +end + +figure; +plot(k,psi*V(:,end)); \ No newline at end of file From 9420010743de76da5a1e1a3dfc72c48a35a8428b Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Mon, 5 Aug 2019 03:16:38 -0400 Subject: [PATCH 112/149] update mainFig and history_func --- solver/history_func.m | 4 ++-- solver/mainFig.m | 49 ++++++++++++++++++++++++++++++++++++------- 2 files changed, 44 insertions(+), 9 deletions(-) diff --git a/solver/history_func.m b/solver/history_func.m index 2231c6e..b94f70f 100644 --- a/solver/history_func.m +++ b/solver/history_func.m @@ -95,11 +95,11 @@ function history_func(ind,modelfunc,arg,Cspace,pp,property,varargin) ax.XTick = []; else if namesflag(1) && ~namesflag(2) - xl = '\psi'; + xl = '\eta'; elseif ~namesflag(1) && namesflag(2) xl = 'k/k_0'; elseif all(namesflag) - xl = '\psi or k/k_0'; + xl = '\eta or k/k_0'; end xlabel(xl); if ~isempty(ps.legend) diff --git a/solver/mainFig.m b/solver/mainFig.m index 296d33c..993b97d 100644 --- a/solver/mainFig.m +++ b/solver/mainFig.m @@ -39,17 +39,17 @@ ydata = y2(ind,:); end -rowtotal = 5; +rowtotal = 4; columntotal = 5; -stparg = {0.05,[0.05,0.08],0.05}; +stparg = {0.05,[0.08,0.06],[0.07,0.03]}; clim = [min(min(ydata(:))),max(max(ydata(:)))]; %first row: data -h = visualize([],[],[],ydata,'c',false,'ImageSize',params.N,'caxis','auto','GridSize',[1,NaN],'OuterGridSize',[rowtotal,1],'OuterSubplot',[1,1],'subtightplot',stparg); +h = visualize([],[],[],ydata,'c',false,'ImageSize',params.N,'caxis',clim,'GridSize',[1,NaN],'OuterGridSize',[rowtotal,1],'OuterSubplot',[1,1],'subtightplot',stparg); for j = 1:length(h) title(h(j),['t = ',num2str(tdata(j),2)]); end axes(h(1)); -text(0.1,1.5,'(a). Data','Units','normalized','HorizontalAlignment','left'); +text(0.01,1.55,'(a) Data','Units','normalized','HorizontalAlignment','left'); %second row: history of DDFT_nucleation23 kernelSize = 2; Cspace = 'isotropic'; @@ -68,17 +68,32 @@ subtightplot(rowtotal,columntotal,columntotal+i,stparg{:}); [~,~,~,pp] = IP_DDFT(tdata,ydata,params,kernelSize,Cspace,[],history(ind(i),:),'mode','pp',IP_DDFT_arg{:}); history_func(ind(i),modelfunc,arg,Cspace,pp,[],figprop{:}); + if i~=1 + xlabel([]); + yyaxis left + yticklabels([]); + yyaxis right + yticklabels([]); + else + text(0.01,1.55,'(b) Quartic approximation','Units','normalized','HorizontalAlignment','left'); + legend({'$\hat{C_2}(k)$ (truth)','$\hat{C_2}(k)$','$\mu_h(\eta)$ (truth)','$\mu_h(\eta)$'},... + 'Orientation','horizontal','Position',[0.225 0.025 0.7228 0.0533],'Interpreter','latex'); + legend('boxoff'); + end end %third row: final result of DDFT_nucleation23 -[yhistory,~,~,pp] = IP_DDFT(tdata,ydata,params,kernelSize,Cspace,[],history(end,:),'mode','eval',IP_DDFT_arg{:}); -visualize([],[],[],yhistory,'c',false,'ImageSize',params.N,'caxis',clim,'GridSize',[1,NaN],'OuterGridSize',[rowtotal,1],'OuterSubplot',[3,1],'subtightplot',stparg); +if ~exist('yhistory','var') + [yhistory,~,~,pp] = IP_DDFT(tdata,ydata,params,kernelSize,Cspace,[],history(end,:),'mode','eval',IP_DDFT_arg{:}); +end +h = visualize([],[],[],yhistory,'c',false,'ImageSize',params.N,'caxis',clim,'GridSize',[1,NaN],'OuterGridSize',[rowtotal,1],'OuterSubplot',[3,1],'subtightplot',stparg); +text(h(1),0.01,1.2,'(c) Quartic approximation result','Units','normalized','HorizontalAlignment','left'); %fourth row: history of DDFT_nucleation30 kernelSize = 10; Cspace = 'isotropic_hermite_scale'; Crange = [0,4]; IP_DDFT_arg = {'Nmu',0,'discrete',true,'cutoff',k0}; -figprop = {'IP_DDFT_arg',IP_DDFT_arg,'yyaxisLim',[-0.5,1.5],'k0',k0,'xlim',Crange}; +figprop = {'IP_DDFT_arg',IP_DDFT_arg,'yyaxisLim',[-0.5,1.2],'k0',k0,'xlim',Crange}; resultpath = [largedatapath,'DDFT_nucleation30']; varload = load(resultpath); history = varload.history; @@ -86,6 +101,26 @@ ind = [1,11,16,21,36]; for i = 1:length(ind) subtightplot(rowtotal,columntotal,columntotal*3+i,stparg{:}); + if i==length(ind) + DDFT_nucleation36; + delete(hl); + hold on; + end [~,~,~,pp] = IP_DDFT(tdata,ydata,params,kernelSize,Cspace,[],history(ind(i),:),'mode','pp',IP_DDFT_arg{:}); history_func(ind(i),modelfunc,arg,Cspace,pp,[],figprop{:}); + if i~=1 + xlabel([]); + yyaxis left + yticklabels([]); + yyaxis right + yticklabels([]); + else + text(0.01,1.55,'(d) Hermite function basis function','Units','normalized','HorizontalAlignment','left'); + end end +f = gcf; +set(findall(f,'-property','FontName'),'FontName','Arial'); +set(findall(f,'-property','FontWeight'),'FontWeight','normal'); +set(findall(f,'-property','FontSize'),'FontSize',12); +f.Position = [680 298 560 680]; +% print(f,'C:\Users\zhbkl\Dropbox (MIT)\Research\Report 6\figure\DDFT_mainFig','-dtiff','-r400'); From aee2537eb8f2a522481760f39ec655d40d340cf6 Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Mon, 5 Aug 2019 03:16:59 -0400 Subject: [PATCH 113/149] update DDFT_nucleation36/38 (sensitivity) visualization --- solver/DDFT_nucleation36.m | 92 ++++++++++++++++++++------------------ solver/DDFT_nucleation38.m | 90 +++++++++++++++++++------------------ 2 files changed, 95 insertions(+), 87 deletions(-) diff --git a/solver/DDFT_nucleation36.m b/solver/DDFT_nucleation36.m index 99727e8..a700f10 100644 --- a/solver/DDFT_nucleation36.m +++ b/solver/DDFT_nucleation36.m @@ -1,65 +1,69 @@ %based on DDFT_nucleation29 %5 snapshots. kernelSize = 10 addpath('../../CHACR/GIP') -runoptim = true; +runoptim = false; -tic; -L = [5,5]; -N = [256,256]; -n = prod(N); +resultpath = [largedatapath,'DDFT_nucleation36.mat']; -params.N = N; -params.L = L; +if runoptim + tic; + L = [5,5]; + N = [256,256]; + n = prod(N); -[k2,k] = formk(N,L); -k0 = 10; -alpha = 5; -params.C = exp(-(sqrt(k2)-k0).^2/(2*alpha^2))*0.95; + params.N = N; + params.L = L; -[t1,y1,params] = solver_DDFT([],[],params); + [k2,k] = formk(N,L); + k0 = 10; + alpha = 5; + params.C = exp(-(sqrt(k2)-k0).^2/(2*alpha^2))*0.95; -xx = linspace(0,L(1),N(1)); -yy = linspace(0,L(2),N(2)); -[xx,yy] = ndgrid(xx,yy); -center = L/2; -radius = 0.06*L(1); -thickness = 0.01*L(1); -roi = roi_circle(xx,yy,center,radius,thickness); + [t1,y1,params] = solver_DDFT([],[],params); -%nucleus -y0 = y1(end,:)'; -roi = roi(:); -y02 = 0.045; -rho = (y02*n - sum(roi.*y0)) / sum(1-roi); -y0 = roi.*y0 + (1-roi)*rho; + xx = linspace(0,L(1),N(1)); + yy = linspace(0,L(2),N(2)); + [xx,yy] = ndgrid(xx,yy); + center = L/2; + radius = 0.06*L(1); + thickness = 0.01*L(1); + roi = roi_circle(xx,yy,center,radius,thickness); -tspan2 = linspace(0,2.5,100); -[t2,y2] = solver_DDFT(tspan2,y0,params); + %nucleus + y0 = y1(end,:)'; + roi = roi(:); + y02 = 0.045; + rho = (y02*n - sum(roi.*y0)) / sum(1-roi); + y0 = roi.*y0 + (1-roi)*rho; -ind = 1:20:100; -tdata = t2(ind); -ydata = y2(ind,:); -toc + tspan2 = linspace(0,2.5,100); + [t2,y2] = solver_DDFT(tspan2,y0,params); + ind = 1:20:100; + tdata = t2(ind); + ydata = y2(ind,:); + toc -kernelSize = 300; -Cspace = 'isotropic_hermite_scale'; -%note 100 is about where hermitefunction still approaches zero as k approaches kmax (N/L*pi) -params.moreoptions = moreodeset('gmresTol',1e-5); + kernelSize = 300; + Cspace = 'isotropic_hermite_scale'; + %note 100 is about where hermitefunction still approaches zero as k approaches kmax (N/L*pi) + params.moreoptions = moreodeset('gmresTol',1e-5); -resultpath = [largedatapath,'DDFT_nucleation36.mat']; - -if runoptim [hessian,hessian_t,dy] = IP_DDFT(tdata,ydata,params,kernelSize,Cspace,[],[],'discrete',true,'cutoff',k0,'assign_suppress',{'C'},'mode','sens'); save(resultpath,'hessian','hessian_t','dy'); else - load(resultpath); + addpath('../../External/boundedline-pkg') + if ~exist('hessian','var') + load(resultpath); + end numBasis = 100; - x = linspace(0,10,1000)'; + epsilon = 0.01*prod(params.L); + x = linspace(0,4,1000)'; psi = hermitefunction(x,numBasis); - C = psi * (hessian(1:numBasis,1:numBasis)\psi'); - dev = diag(C); - y = exp(-(x-k0).^2/(2*alpha^2))*0.95; - boundedline(x,y,dev); + C = psi * ((hessian(1:numBasis,1:numBasis)+epsilon*eye(numBasis))\psi'); + dev = diag(C)/50; + y = exp(-(x-1).^2/(2*(alpha/k0)^2))*0.95; + [hl,hp] = boundedline(x,y,dev); + ylim([-0.5,1.5]) end diff --git a/solver/DDFT_nucleation38.m b/solver/DDFT_nucleation38.m index 2e28d3f..40f6ce5 100644 --- a/solver/DDFT_nucleation38.m +++ b/solver/DDFT_nucleation38.m @@ -2,62 +2,66 @@ addpath('../../CHACR/GIP') runoptim = false; -tic; -L = [5,5]; -N = [256,256]; -n = prod(N); - -params.N = N; -params.L = L; - -[k2,k] = formk(N,L); -k0 = 10; -alpha = 5; -params.C = exp(-(sqrt(k2)-k0).^2/(2*alpha^2))*0.95; +resultpath = [largedatapath,'DDFT_nucleation38.mat']; -[t1,y1,params] = solver_DDFT([],[],params); +if runoptim + tic; + L = [5,5]; + N = [256,256]; + n = prod(N); -xx = linspace(0,L(1),N(1)); -yy = linspace(0,L(2),N(2)); -[xx,yy] = ndgrid(xx,yy); -center = L/2; -radius = 0.06*L(1); -thickness = 0.01*L(1); -roi = roi_circle(xx,yy,center,radius,thickness); + params.N = N; + params.L = L; + [k2,k] = formk(N,L); + k0 = 10; + alpha = 5; + params.C = exp(-(sqrt(k2)-k0).^2/(2*alpha^2))*0.95; -%nucleus -y0 = y1(end,:)'; -roi = roi(:); -y02 = 0.045; -rho = (y02*n - sum(roi.*y0)) / sum(1-roi); -y0 = roi.*y0 + (1-roi)*rho; + [t1,y1,params] = solver_DDFT([],[],params); -tspan2 = linspace(0,2.5,100); -[t2,y2] = solver_DDFT(tspan2,y0,params); + xx = linspace(0,L(1),N(1)); + yy = linspace(0,L(2),N(2)); + [xx,yy] = ndgrid(xx,yy); + center = L/2; + radius = 0.06*L(1); + thickness = 0.01*L(1); + roi = roi_circle(xx,yy,center,radius,thickness); -ind = 1:20:100; -tdata = t2(ind); -ydata = y2(ind,:); -toc + %nucleus + y0 = y1(end,:)'; + roi = roi(:); + y02 = 0.045; + rho = (y02*n - sum(roi.*y0)) / sum(1-roi); + y0 = roi.*y0 + (1-roi)*rho; + tspan2 = linspace(0,2.5,100); + [t2,y2] = solver_DDFT(tspan2,y0,params); -kernelSize = 300; -Cspace = 'isotropic_laguerre_scale'; -params.moreoptions = moreodeset('gmresTol',1e-5); + ind = 1:20:100; + tdata = t2(ind); + ydata = y2(ind,:); + toc -resultpath = [largedatapath,'DDFT_nucleation38.mat']; + kernelSize = 300; + Cspace = 'isotropic_laguerre_scale'; + params.moreoptions = moreodeset('gmresTol',1e-5); -if runoptim [hessian,hessian_t,dy] = IP_DDFT(tdata,ydata,params,kernelSize,Cspace,[],[],'discrete',true,'cutoff',k0,'assign_suppress',{'C'},'mode','sens'); save(resultpath,'hessian','hessian_t','dy'); else - load(resultpath); - numBasis = 10; - x = linspace(0,10,1000)'; + addpath('../../External/boundedline-pkg') + if ~exist('hessian','var') + load(resultpath); + end + numBasis = 150; + epsilon = 0.004*prod(params.L); + x = linspace(0,5,1000)'; psi = laguerrepoly(x,numBasis) .* exp(-x/2); - C = psi * (hessian(1:numBasis,1:numBasis)\psi'); + C = psi * ((hessian(1:numBasis,1:numBasis)+epsilon*eye(numBasis))\psi'); dev = diag(C); - y = exp(-(x-k0).^2/(2*alpha^2))*0.95; - boundedline(x,y,dev); + y = exp(-(x-1).^2/(2*(alpha/k0)^2))*0.95; + figure; + boundedline(x,y,dev/50); + ylim([-0.5,1.5]) end From d0a790f2fedd77e3824a44699b25d06e3cffd5e3 Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Tue, 13 Aug 2019 00:49:12 -0400 Subject: [PATCH 114/149] update mainFig and utility function --- solver/history_func.m | 3 ++- solver/history_production.m | 1 + solver/mainFig.m | 2 +- 3 files changed, 4 insertions(+), 2 deletions(-) diff --git a/solver/history_func.m b/solver/history_func.m index b94f70f..3b41169 100644 --- a/solver/history_func.m +++ b/solver/history_func.m @@ -14,6 +14,7 @@ function history_func(ind,modelfunc,arg,Cspace,pp,property,varargin) addParameter(ps,'legend',[]); addParameter(ps,'label',true); addParameter(ps,'labelHorizontalAlignment','left'); + addParameter(ps,'targetLineStyle','-.'); parse(ps,varargin{:}); ps = ps.Results; else @@ -75,7 +76,7 @@ function history_func(ind,modelfunc,arg,Cspace,pp,property,varargin) if numFunc==1 ax.ColorOrderIndex = j; end - plot(argj,modelfunc.(name)(argj*xscale),'--','LineWidth',2); + plot(argj,modelfunc.(name)(argj*xscale),ps.targetLineStyle,'LineWidth',2); ylimtemp = ax.YLim; hold on; if numFunc==1 diff --git a/solver/history_production.m b/solver/history_production.m index f3ee16a..e9e8998 100644 --- a/solver/history_production.m +++ b/solver/history_production.m @@ -34,6 +34,7 @@ function history_production(resultpath,ind,modelfunc,arg,tdata,ydata,params,kern addParameter(ps,'k0',1); %used to scale k addParameter(ps,'dmu_at_0',1); %when meta has both mu and C, rescale so that dmu/dx at 0 has this value addParameter(ps,'mu_at_0',0); %offset mu so that mu at 0 has this value +addParameter(ps,'targetLineStyle','-.'); parse(ps,varargin{:}); ps = ps.Results; diff --git a/solver/mainFig.m b/solver/mainFig.m index 993b97d..aeebd5f 100644 --- a/solver/mainFig.m +++ b/solver/mainFig.m @@ -77,7 +77,7 @@ else text(0.01,1.55,'(b) Quartic approximation','Units','normalized','HorizontalAlignment','left'); legend({'$\hat{C_2}(k)$ (truth)','$\hat{C_2}(k)$','$\mu_h(\eta)$ (truth)','$\mu_h(\eta)$'},... - 'Orientation','horizontal','Position',[0.225 0.025 0.7228 0.0533],'Interpreter','latex'); + 'Orientation','horizontal','Position',[0.10 0 0.8169 0.0374],'Interpreter','latex'); legend('boxoff'); end end From f7b4006a489c7b62cf8ed830b8c4cd3ccf6b13df Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Tue, 13 Aug 2019 23:23:18 -0400 Subject: [PATCH 115/149] DDFT_nucleation39, using initial and final frames only --- solver/DDFT_nucleation39.m | 65 ++++++++++++++++++++++++++++++++++++++ 1 file changed, 65 insertions(+) create mode 100644 solver/DDFT_nucleation39.m diff --git a/solver/DDFT_nucleation39.m b/solver/DDFT_nucleation39.m new file mode 100644 index 0000000..6295c26 --- /dev/null +++ b/solver/DDFT_nucleation39.m @@ -0,0 +1,65 @@ +%based on DDFT_nucleation30 +%2 snapshots. kernelSize = 10 +addpath('../../CHACR/GIP') +runoptim = true; + +tic; +L = [5,5]; +N = [256,256]; +n = prod(N); + +params.N = N; +params.L = L; + +[k2,k] = formk(N,L); +k0 = 10; +alpha = 5; +params.C = exp(-(sqrt(k2)-k0).^2/(2*alpha^2))*0.95; + +[t1,y1,params] = solver_DDFT([],[],params); + +xx = linspace(0,L(1),N(1)); +yy = linspace(0,L(2),N(2)); +[xx,yy] = ndgrid(xx,yy); +center = L/2; +radius = 0.06*L(1); +thickness = 0.01*L(1); +roi = roi_circle(xx,yy,center,radius,thickness); + +%nucleus +y0 = y1(end,:)'; +roi = roi(:); +y02 = 0.045; +rho = (y02*n - sum(roi.*y0)) / sum(1-roi); +y0 = roi.*y0 + (1-roi)*rho; + +tspan2 = linspace(0,2.5,100); +[t2,y2] = solver_DDFT(tspan2,y0,params); + +ind = [1,41]; +tdata = t2(ind); +ydata = y2(ind,:); +toc + + +kernelSize = 10; +Cspace = 'isotropic_hermite_scale'; +params.moreoptions = moreodeset('gmresTol',1e-5); + + +resultpath = [largedatapath,'DDFT_nucleation39.mat']; + +options = optimoptions('fminunc','OutputFcn', @(x,optimvalues,state) save_opt_history(x,optimvalues,state,resultpath)); +options = optimoptions(options,'HessianFcn','objective','Algorithm','trust-region','MaxFunctionEvaluations',10000,'MaxIterations',10000); + +if runoptim + x_guess = zeros(1,kernelSize); + [x_opt,~,exitflag,params] = IP_DDFT(tdata,ydata,params,kernelSize,Cspace,options,x_guess,'Nmu',0,'discrete',true,'cutoff',k0); +else + modelfunc.C = @(k) exp(-(k-k0).^2/(2*alpha^2))*0.95; + Crange = [0,4]; + arg.C = linspace(Crange(1),Crange(2),500); + history_production(resultpath,[1,11,21,36],modelfunc,arg,tdata-tdata(1),ydata,params,kernelSize,Cspace,'IP_DDFT_arg',{'Nmu',0,'discrete',true,'cutoff',k0},'yyaxisLim',[-0.5,1.5;-1,1.2],'k0',k0,'xlim',Crange); + % f = gcf; + % f.Position = [680 337 522 641]; +end From 34701fe48409672f35df1a95baf333fb85d4fea6 Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Wed, 14 Aug 2019 02:08:26 -0400 Subject: [PATCH 116/149] critical bug in ASA (adjoint jacobian) for solver_DDFT (reconfirm), Laplacian and mu' don't commute --- solver/solver_DDFT.m | 47 ++++++++++++++++++++++++++++---------------- 1 file changed, 30 insertions(+), 17 deletions(-) diff --git a/solver/solver_DDFT.m b/solver/solver_DDFT.m index ae8a04b..415399b 100644 --- a/solver/solver_DDFT.m +++ b/solver/solver_DDFT.m @@ -138,7 +138,7 @@ options = odeset(options,'Jacobian',@(t,y) jacobian(t,sol,params), ... 'mass', -speye(prod(params.N)),'MassSingular','yes','MStateDependence','none'); moreoptions = moreodeset(moreoptions, ... - 'jacMult',@(xi,t,y,info) jacobian_mult(params,xi,t,sol,info), ... + 'jacMult',@(xi,t,y,info) jacobian_mult(params,xi,t,sol,info,true), ... 'pencil',@(xi,t,y,hinvGak,info) pencil(params,xi,t,sol,hinvGak,info,true), ... 'KrylovDecomp',@(~,~,dfdy,hinvGak) KrylovDecomp(L,dfdy,hinvGak,true), ... 'KrylovPrecon',@(x,L,U,hinvGak,~,~,~) KrylovPrecon(LK,params,x,L,U,hinvGak,true)); @@ -221,13 +221,12 @@ function Pargs = KrylovDecomp(L,dfdy,hinvGak,adjoint) %here dfdy comes from Jacobian %L is the finite-difference Laplacian operator + n = length(L); if nargin>3 && adjoint - msign = -1; + J = -speye(n) - hinvGak*sparse(1:n,1:n,dfdy).*L; else - msign = 1; + J = speye(n) - hinvGak*L.*sparse(1:n,1:n,dfdy); end - n = length(L); - J = msign*speye(n) - hinvGak*L.*sparse(1:n,1:n,dfdy); [L,U] = ilu(J); Pargs = {L,U}; end @@ -248,10 +247,13 @@ yy = U \ (L \ yy); end -function yy = jacobian_mult(params,xi,t,y,info) +function yy = jacobian_mult(params,xi,t,y,info,adjoint) + if nargin<6 + adjoint = false; + end if isequal(info,'force') - yy = jacobian_mult(params,xi,t,y,[]); - yy = jacobian_mult(params,xi,t,y,yy); + yy = jacobian_mult(params,xi,t,y,[],adjoint); + yy = jacobian_mult(params,xi,t,y,yy,adjoint); elseif isempty(info) if isstruct(y) y = sol_interp(y,t); @@ -263,10 +265,18 @@ dx = params.dx; C = params.C; xi = reshape(xi,N(1),N(2),[]); - mu = info .* xi - ifft2(C .* fft2(xi), 'symmetric'); - yy = 0; - for i = 1:length(N) - yy = yy + (circshift(mu,1,i)+circshift(mu,-1,i)-2*mu)/dx(i)^2; + if ~adjoint + mu = info .* xi - ifft2(C .* fft2(xi), 'symmetric'); + yy = 0; + for i = 1:length(N) + yy = yy + (circshift(mu,1,i)+circshift(mu,-1,i)-2*mu)/dx(i)^2; + end + else + yy = 0; + for i = 1:length(N) + yy = yy + (circshift(xi,1,i)+circshift(xi,-1,i)-2*xi)/dx(i)^2; + end + yy = info .* yy - ifft2(C .* fft2(yy), 'symmetric'); end yy = reshape(yy,prod(N),[]); yy = params.D * yy; @@ -275,9 +285,9 @@ function yy = ASA_mult(t,xi,sol,info,params,varargin) if isempty(info) - yy = jacobian_mult(params,[],t,sol,[]); + yy = jacobian_mult(params,[],t,sol,[],true); else - yy = jacobian_mult(params,xi,[],[],info); + yy = jacobian_mult(params,xi,[],[],info,true); if ~isempty(varargin) tdata = varargin{1}; error = varargin{2}; @@ -295,12 +305,15 @@ end function yy = pencil(params,xi,t,y,hinvGak,info,adjoint) - if nargin>6 && adjoint + if nargin < 7 + adjoint = false; + end + if adjoint msign = -1; else msign = 1; end - yy = jacobian_mult(params,xi,t,y,info); + yy = jacobian_mult(params,xi,t,y,info,adjoint); if ~isempty(info) yy = msign*xi - hinvGak*yy; end @@ -392,7 +405,7 @@ yp0 = F0; if discrete y0 = yp0; - yp0 = jacobian_mult(params,y0,t0,sol,'force'); + yp0 = jacobian_mult(params,y0,t0,sol,'force',true); end end From 0d5958ae814904edfb44439b7587169a52e5c96f Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Wed, 14 Aug 2019 02:10:09 -0400 Subject: [PATCH 117/149] add DDFT_nucleation40, try Cspace = k again after fixing ASA bug --- solver/DDFT_nucleation40.m | 69 ++++++++++++++++++++++++++++++++++++++ 1 file changed, 69 insertions(+) create mode 100644 solver/DDFT_nucleation40.m diff --git a/solver/DDFT_nucleation40.m b/solver/DDFT_nucleation40.m new file mode 100644 index 0000000..d2d8800 --- /dev/null +++ b/solver/DDFT_nucleation40.m @@ -0,0 +1,69 @@ +%based on DDFT_nucleation30 +%5 snapshots. Cspace = 'k' +addpath('../../CHACR/GIP') +runoptim = true; + +tic; +L = [5,5]; +N = [256,256]; +n = prod(N); + +params.N = N; +params.L = L; + +[k2,k] = formk(N,L); +k0 = 10; +alpha = 5; +params.C = exp(-(sqrt(k2)-k0).^2/(2*alpha^2))*0.95; + +[t1,y1,params] = solver_DDFT([],[],params); + +xx = linspace(0,L(1),N(1)); +yy = linspace(0,L(2),N(2)); +[xx,yy] = ndgrid(xx,yy); +center = L/2; +radius = 0.06*L(1); +thickness = 0.01*L(1); +roi = roi_circle(xx,yy,center,radius,thickness); + +%nucleus +y0 = y1(end,:)'; +roi = roi(:); +y02 = 0.045; +rho = (y02*n - sum(roi.*y0)) / sum(1-roi); +y0 = roi.*y0 + (1-roi)*rho; + +tspan2 = linspace(0,2.5,100); +[t2,y2] = solver_DDFT(tspan2,y0,params); + +ind = 1:20:100; +tdata = t2(ind); +ydata = y2(ind,:); +toc + + +kernelSize = [41,41]; +NC = floor((prod(kernelSize)+1)/2); +Cspace = 'k'; +params.moreoptions = moreodeset('gmresTol',1e-5); + + +resultpath = [largedatapath,'DDFT_nucleation40.mat']; + +options = optimoptions('fminunc','OutputFcn', @(x,optimvalues,state) save_opt_history(x,optimvalues,state,resultpath,[],true)); +options = optimoptions(options,'MaxFunctionEvaluations',10000,'MaxIterations',10000); + +if runoptim + x_opt = zeros(1,NC); + exitflag = 5; + while (exitflag==5) + [x_opt,~,exitflag,params] = IP_DDFT(tdata,ydata,params,kernelSize,Cspace,options,x_opt,'Nmu',0,'discrete',true); + end +else + modelfunc.C = @(k) exp(-(k-k0).^2/(2*alpha^2))*0.95; + Crange = [0,4]; + arg.C = linspace(Crange(1),Crange(2),500); + history_production(resultpath,[1,11,21,36],modelfunc,arg,tdata-tdata(1),ydata,params,kernelSize,Cspace,'IP_DDFT_arg',{'Nmu',0,'discrete',true,'cutoff',k0},'yyaxisLim',[-0.5,1.5;-1,1.2],'k0',k0,'xlim',Crange); + % f = gcf; + % f.Position = [680 337 522 641]; +end From 6470f69088110d0a38f1a3ea2dcf26442392706e Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Wed, 14 Aug 2019 02:10:27 -0400 Subject: [PATCH 118/149] update mainFig, (remove yyaxis right in the bottom row) --- solver/mainFig.m | 3 --- 1 file changed, 3 deletions(-) diff --git a/solver/mainFig.m b/solver/mainFig.m index aeebd5f..df5fe5a 100644 --- a/solver/mainFig.m +++ b/solver/mainFig.m @@ -110,9 +110,6 @@ history_func(ind(i),modelfunc,arg,Cspace,pp,[],figprop{:}); if i~=1 xlabel([]); - yyaxis left - yticklabels([]); - yyaxis right yticklabels([]); else text(0.01,1.55,'(d) Hermite function basis function','Units','normalized','HorizontalAlignment','left'); From 817f41222bc3f3dcf77e085b7fd96a38810e0f27 Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Sun, 22 Sep 2019 19:26:30 -0400 Subject: [PATCH 119/149] update mainFig's subplot spacing, figure saved as DDFT_mainFig_v4 --- solver/mainFig.m | 8 ++++++-- 1 file changed, 6 insertions(+), 2 deletions(-) diff --git a/solver/mainFig.m b/solver/mainFig.m index df5fe5a..1cfa820 100644 --- a/solver/mainFig.m +++ b/solver/mainFig.m @@ -65,7 +65,8 @@ arg.mu = linspace(min(ydata(:)),max(ydata(:)),100); ind = [1,19,25,31,1797]; for i = 1:length(ind) - subtightplot(rowtotal,columntotal,columntotal+i,stparg{:}); + ax = subtightplot(rowtotal,columntotal,columntotal+i,stparg{:}); + ax.Position(2) = ax.Position(2) + 0.01; [~,~,~,pp] = IP_DDFT(tdata,ydata,params,kernelSize,Cspace,[],history(ind(i),:),'mode','pp',IP_DDFT_arg{:}); history_func(ind(i),modelfunc,arg,Cspace,pp,[],figprop{:}); if i~=1 @@ -86,6 +87,9 @@ [yhistory,~,~,pp] = IP_DDFT(tdata,ydata,params,kernelSize,Cspace,[],history(end,:),'mode','eval',IP_DDFT_arg{:}); end h = visualize([],[],[],yhistory,'c',false,'ImageSize',params.N,'caxis',clim,'GridSize',[1,NaN],'OuterGridSize',[rowtotal,1],'OuterSubplot',[3,1],'subtightplot',stparg); +for i = 1:length(h) + h(i).Position(2) = h(i).Position(2) - 0.01; +end text(h(1),0.01,1.2,'(c) Quartic approximation result','Units','normalized','HorizontalAlignment','left'); %fourth row: history of DDFT_nucleation30 @@ -119,5 +123,5 @@ set(findall(f,'-property','FontName'),'FontName','Arial'); set(findall(f,'-property','FontWeight'),'FontWeight','normal'); set(findall(f,'-property','FontSize'),'FontSize',12); -f.Position = [680 298 560 680]; +f.Position = [680 321 560 657]; % print(f,'C:\Users\zhbkl\Dropbox (MIT)\Research\Report 6\figure\DDFT_mainFig','-dtiff','-r400'); From 6e4d6f4d090c3350d71fdd8382ecb457aab44c73 Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Sat, 23 Nov 2019 18:12:18 -0500 Subject: [PATCH 120/149] add DDFT_nucleation41, redo DDFT_nucleation32 with a different x_guess --- solver/DDFT_nucleation41.m | 69 ++++++++++++++++++++++++++++++++++++++ 1 file changed, 69 insertions(+) create mode 100644 solver/DDFT_nucleation41.m diff --git a/solver/DDFT_nucleation41.m b/solver/DDFT_nucleation41.m new file mode 100644 index 0000000..972c7be --- /dev/null +++ b/solver/DDFT_nucleation41.m @@ -0,0 +1,69 @@ +%based on DDFT_nucleation32 +%change x_guess(1) to 0.1 +addpath('../../CHACR/GIP') +runoptim = true; + +tic; +L = [5,5]; +N = [256,256]; +n = prod(N); + +params.N = N; +params.L = L; + +[k2,k] = formk(N,L); +k0 = 10; +alpha = 5; +params.C = exp(-(sqrt(k2)-k0).^2/(2*alpha^2))*0.95; + +[t1,y1,params] = solver_DDFT([],[],params); + +xx = linspace(0,L(1),N(1)); +yy = linspace(0,L(2),N(2)); +[xx,yy] = ndgrid(xx,yy); +center = L/2; +radius = 0.06*L(1); +thickness = 0.01*L(1); +roi = roi_circle(xx,yy,center,radius,thickness); + +%nucleus +y0 = y1(end,:)'; +roi = roi(:); +y02 = 0.045; +rho = (y02*n - sum(roi.*y0)) / sum(1-roi); +y0 = roi.*y0 + (1-roi)*rho; + +tspan2 = linspace(0,2.5,100); +[t2,y2] = solver_DDFT(tspan2,y0,params); + +ind = 1:20:100; +tdata = t2(ind); +ydata = y2(ind,:); +toc + + +kernelSize = 10; +Cspace = 'isotropic_hermite_scale'; +params.moreoptions = moreodeset('gmresTol',1e-5); + + +resultpath = [largedatapath,'DDFT_nucleation32.mat']; + +options = optimoptions('fminunc','OutputFcn', @(x,optimvalues,state) save_opt_history(x,optimvalues,state,resultpath)); +options = optimoptions(options,'HessianFcn','objective','Algorithm','trust-region','MaxFunctionEvaluations',10000,'MaxIterations',10000); + +x_guess = [zeros(1,kernelSize),0.5,0,-3]; +x_guess(1) = 0.1; + +if runoptim + [x_opt,~,exitflag,params] = IP_DDFT(tdata,ydata,params,kernelSize,Cspace,options,x_guess,'Nmu',3,'discrete',true,'cutoff',k0); +else + modelfunc.C = @(k) exp(-(k-k0).^2/(2*alpha^2))*0.95; + modelfunc.mu = @(x) x - x.^2/2 + x.^3/3; + Crange = [0,4]; + arg.C = linspace(Crange(1),Crange(2),500); + arg.mu = linspace(min(ydata(:)),max(ydata(:)),100); + history_production(resultpath,[1,10,20,30,40,65],modelfunc,arg,tdata-tdata(1),ydata,params,kernelSize,Cspace,'IP_DDFT_arg',{'Nmu',3,'discrete',true,'cutoff',k0},'yyaxisLim',[-0.5,1.5;-1,1.2],'k0',k0,'xlim',Crange,'showModelSolution',false); + % f = gcf; + % f.Position = [680 337 522 641]; +end From 56aebdccc07b1db5f86d48e329733a9494eb66e0 Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Mon, 25 Nov 2019 01:48:40 -0500 Subject: [PATCH 121/149] add option of (commented now) shifting C2 such that C2(0) matches the truth --- solver/history_func.m | 4 ++++ 1 file changed, 4 insertions(+) diff --git a/solver/history_func.m b/solver/history_func.m index 3b41169..6e4fc89 100644 --- a/solver/history_func.m +++ b/solver/history_func.m @@ -34,6 +34,10 @@ function history_func(ind,modelfunc,arg,Cspace,pp,property,varargin) %set the gradient of mu at x=0 to be 1. The offset is offset = (ps.dmu_at_0-grad0)/grad1; pp.params.mu.params(1) = pp.params.mu.params(1) + offset; + + % shift C2 such that C2(0) matches the truth + % offset = modelfunc.C(0) - customizeFunGrad(pp.params,'Cfunc','fun',0); + % pp.params.mu.params(1) = pp.params.mu.params(1) + offset/grad1; else offset = 0; end From bbfa6de4b917198cb589293fcc2db6953eed8c41 Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Mon, 25 Nov 2019 01:50:00 -0500 Subject: [PATCH 122/149] highlight the difference between row 3 (model) and row 1 (data) using mydecorrstretch (based on decorrstretch) --- solver/mainFig.m | 19 +++- solver/mydecorrstretch.m | 197 +++++++++++++++++++++++++++++++++++++++ 2 files changed, 214 insertions(+), 2 deletions(-) create mode 100644 solver/mydecorrstretch.m diff --git a/solver/mainFig.m b/solver/mainFig.m index 1cfa820..29990fe 100644 --- a/solver/mainFig.m +++ b/solver/mainFig.m @@ -86,7 +86,22 @@ if ~exist('yhistory','var') [yhistory,~,~,pp] = IP_DDFT(tdata,ydata,params,kernelSize,Cspace,[],history(end,:),'mode','eval',IP_DDFT_arg{:}); end -h = visualize([],[],[],yhistory,'c',false,'ImageSize',params.N,'caxis',clim,'GridSize',[1,NaN],'OuterGridSize',[rowtotal,1],'OuterSubplot',[3,1],'subtightplot',stparg); +%highlight the difference between model and data in the last image +Ntime = size(yhistory,1); +for i = 1:Ntime + h(i) = subtightplot(rowtotal,columntotal,columntotal*2+i,stparg{:}); + if i >= Ntime - 1 + C = imfuse(mat2gray(reshape(yhistory(i,:),params.N),flip(clim)),mat2gray(reshape(ydata(i,:),params.N),flip(clim)),'Scaling','none'); + C = mydecorrstretch(C,[1,0.2,0.2]); + imshow(C); + else + imshow(mat2gray(reshape(yhistory(i,:),params.N),flip(clim))); + end +end +%show all model plots (without difference) +% h = visualize([],[],[],yhistory,'c',false,'ImageSize',params.N,'caxis',clim,'GridSize',[1,NaN],'OuterGridSize',[rowtotal,1],'OuterSubplot',[3,1],'subtightplot',stparg); +%show difference between model and data only +% h = visualize([],[],[],yhistory-ydata,'c',false,'ImageSize',params.N,'caxis','auto','GridSize',[1,NaN],'OuterGridSize',[rowtotal,1],'OuterSubplot',[3,1],'subtightplot',stparg); for i = 1:length(h) h(i).Position(2) = h(i).Position(2) - 0.01; end @@ -102,7 +117,7 @@ varload = load(resultpath); history = varload.history; arg.C = linspace(Crange(1),Crange(2),500); -ind = [1,11,16,21,36]; +ind = [1,4,11,26,35]; for i = 1:length(ind) subtightplot(rowtotal,columntotal,columntotal*3+i,stparg{:}); if i==length(ind) diff --git a/solver/mydecorrstretch.m b/solver/mydecorrstretch.m new file mode 100644 index 0000000..f274c31 --- /dev/null +++ b/solver/mydecorrstretch.m @@ -0,0 +1,197 @@ +function S = mydecorrstretch(A, relativeStretch, useCorr) +%use relative stretch (a three-valued array) to specify the magnitude of stretching in each principle components +if nargin < 2 + relativeStretch = ones(3,1); +end +if nargin < 3 + useCorr = true; +end +% Decorrelation stretch for a multiband image of class double. +inputClass = class(A); +if ~strcmp(inputClass,'double') + A = im2double(A); +end + +[r c nbands] = size(A); % Save the shape +npixels = r * c; % Number of pixels +A = reshape(A,[npixels nbands]); % Reshape to numPixels-by-numBands +B = A; + +meanB = mean(B,1); % Mean pixel value in each spectral band +targetMean = meanB; + +n = size(B,1); % Equals npixels if rowsubs is empty +if n == 1 + cov = zeros(nbands); +else + cov = (B' * B - (n * meanB') * meanB)/(n - 1); % Sample covariance matrix +end + +[T, offset] = fitdecorrtrans(meanB, cov, useCorr, targetMean, [], relativeStretch); + +S = bsxfun(@plus, A*T, offset); +S = reshape(S, [r c nbands]); + +S = images.internal.changeClass(inputClass,S); +end + +function [T, offset] = fitdecorrtrans(means, Cov, useCorr, targetMean, targetSigma, relativeStretch) +% FITDECORRTRANS Fit decorrelating transformation to image statistics. +% +% Given MEANS, a 1-by-NBANDS vector of band means, and COV, an NBANDS-by-NBANDS +% band covariance matrix, calculate an NBANDS-by-NBANDS linear transformation +% matrix, T, and 1-by-NBANDS offset vector, OFFSET, that will decorrelate +% an image with those statistics. If A is such an image, reshaped to size +% NPIXELS-by-NBANDS, then A is decorrelated as follows: +% +% A * T + repmat(OFFSET,[NPIXELS 1]). +% +% Set USECORR=true to use the correlation matrix to derive T, or set +% USECORR=false to use the covariance matrix. T is scaled to either (1) +% achieve the target standard deviation specified by TARGETSIGMA (either +% a scalar or an NBANDS-by-NBANDS diagonal matrix) or (2), if TARGETSIGMA=[], +% to preserve the variances on the diagonal of COV. Likewise, OFFSET +% includes a shift to either (1) set the mean of each output band to +% a specified target (TARGETMEAN, either a scalar or a 1-by-NBANDS vector) +% or (2), if TARGETMEAN=[], to preserve the band-means specified in MEANS. +% +% It's easy to verify that FITDECORRTRANS has worked by checking that +% +% T' * Cov * T +% +% equals diag(COV), TARGETSIGMA^2, or TARGETSIGMA^2 * eye(NBANDS). +% Likewise, one can check that +% +% means * T + OFFSET +% +% equals either MEANS or TARGETMEANS. +% +% Even in the case of perfectly or nearly correlated bands, FITDECORRTRANS +% remains stable. T and OFFSET continue to provide a reasonable-looking +% result when applied to an image with the appropriate statistics. However, +% +% T' * Cov * T +% +% will no longer be diagonal, and its diagonal elements corresponding to +% zero-variance bands will be zero. +% +% Notes +% ----- +% In general, T is not unique, because once an image has been decorrelated +% (via left multiplication by T = V * inv(sqrt(D)) * V') it can be +% rotated arbitrarily in band space without reintroducing correlations. +% All these different choices will give the same value of T' * Cov * T. +% +% The correlation and covariance methods each produce a different, but +% valid T. Those particular choices for T also have the desirable property +% of preserving, roughly, the hue of a given pixel. +% +% The correlation method may be understood as follows. Consider the image +% that is derived by scaling the original image, band by band, to have +% unit variance in each band. The correlation matrix of the original +% image is the covariance matrix of this derived image. That is, +% if S is a diagonal matrix containing the square-root band-variances, +% of image A, then Corr is the covariance of A / S (assuming that A has +% been reshaped to size NPIXELS-by-NBANDS). Thus the expression +% below, T = pinv(S) * V * decorrWeight(D) * V' * targetSigma, can be +% understood as follows when applied to A step by step: +% +% Scale A band-wise to achieve unit variance in each band: +% A * pinv(S) +% +% Transform the scaled A to the eigenvector basis: +% A * pinv(S) * V +% +% Decorrelate: +% A * pinv(S) * V * decorrWeight(D) +% +% Transform back (resulting in unit variance in each band): +% A * pinv(S) * V * decorrWeight(D) * V' +% +% Scale each band to achieve the desired standard deviation: +% A * pinv(S) * V * decorrWeight(D) * V' * targetSigma +% +% (The covariance method works the same, but because there's no need for an +% initial scaling to unit variance the pinv(S) factor is omitted.) +% +% Robustness is achieved by: +% 1. Ensuring that the correlation matrix has ones on the diagonal +% (even in the event of one or more uniform bands) +% 2. Through the use of PINV in place of INV +% 3. By forcing any small negative eigenvalues to zero +% 4. By rescaling T as needed to compensate for the +% effects of a rank-deficient covariance matrix. +% +% References +% ---------- +% +% Alley, Ronald E., Algorithm Theoretical Basis Document for Decorrelation +% Stretch, Version 2.2, Jet Propulsion Laboratory, Pasadena, CA, +% August 15,1996. +% +% Mather, Paul M., Computer Processing of Remotely-Sensed Images: An +% Introduction, 2nd Edition, John Wiley & Sons, 1999. + +% Copyright 2002 The MathWorks, Inc. + +% Square-root variances in a diagonal matrix. +S = diag(sqrt(diag(Cov))); + +if isempty(targetSigma) + % Restore original sample variances. + targetSigma = S; +end + +if useCorr + Corr = pinv(S) * Cov * pinv(S); + Corr(logical(eye(size(Corr,1)))) = 1; + [V D] = eig(Corr); + T = pinv(S) * V * decorrWeight(D, relativeStretch) * V' * targetSigma; +else + [V D] = eig(Cov); + T = V * decorrWeight(D, relativeStretch) * V' * targetSigma; +end + +% Get the output variances right even for correlated bands, except +% for zero-variance bands---which can't be stretched at all. +T = T * pinv(diag(sqrt(diag(T' * Cov * T)))) * targetSigma; + +if isempty(targetMean) + % Restore original sample means. + targetMean = means; +end + +offset = targetMean - means * T; +end + +%-------------------------------------------------------------------------- +function W = decorrWeight(D, relativeStretch) + +% Given the diagonal eigenvalue matrix D, compute the decorrelating +% weights W. In the full rank, well-conditioned case, decorrWeight(D) +% returns the same result as sqrt(inv(D)). In addition, it provides +% a graceful way to handle rank-deficient or near-rank-deficient +% (ill-conditioned) cases resulting from situations of perfect or +% near-perfect band-to-band correlation and/or bands with zero variance. + +D(D < 0) = 0; +W = sqrt(pinv(D)) .* diag(relativeStretch); +end + +%-------------------------------------------------------------------------- +function S = pinv(D) + +% Pseudoinverse of a diagonal matrix, with a larger-than-standard +% tolerance to help in handling edge cases. We've provided our +% own in order to: (1) Avoid replacing all calls to PINV with calls to +% PINV(...,TOL) and (2) Take advantage of the fact that our input is +% always diagonal so we don't need to call SVD. + +d = diag(D); +tol =length(d) * max(d) * sqrt(eps); +keep = d > tol; +s = ones(size(d)); +s(keep) = s(keep) ./ d(keep); +s(~keep) = 0; +S = diag(s); +end From 9c9197855ee6db47ef2c110779d2e89a7d368f63 Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Mon, 25 Nov 2019 01:51:40 -0500 Subject: [PATCH 123/149] fix bug in history_production, add the option of showModelSolution, now you can turn off showing model prediction (which takes too long if not saved) --- solver/history_production.m | 36 +++++++++++++++++++++++++----------- 1 file changed, 25 insertions(+), 11 deletions(-) diff --git a/solver/history_production.m b/solver/history_production.m index e9e8998..c158844 100644 --- a/solver/history_production.m +++ b/solver/history_production.m @@ -16,6 +16,7 @@ function history_production(resultpath,ind,modelfunc,arg,tdata,ydata,params,kern addpath('../../CHACR') addpath('../../CHACR/IP') ps = inputParser; +addParameter(ps,'xlabel','on'); addParameter(ps,'label',true); addParameter(ps,'labelPosition','top'); addParameter(ps,'labelxpos',0.1); @@ -35,6 +36,7 @@ function history_production(resultpath,ind,modelfunc,arg,tdata,ydata,params,kern addParameter(ps,'dmu_at_0',1); %when meta has both mu and C, rescale so that dmu/dx at 0 has this value addParameter(ps,'mu_at_0',0); %offset mu so that mu at 0 has this value addParameter(ps,'targetLineStyle','-.'); +addParameter(ps,'showModelSolution',true); %plot the model solution at each iteration parse(ps,varargin{:}); ps = ps.Results; @@ -59,10 +61,15 @@ function history_production(resultpath,ind,modelfunc,arg,tdata,ydata,params,kern else column = length(frameindex); end -rowtotal = numIter+1; -columntotal = column; -frameindex_model = frameindex; -frameindex_model(frameindex==1) = []; %remove the initial condition +if ps.showModelSolution + rowtotal = numIter+1; + columntotal = column; + frameindex_model = frameindex; + frameindex_model(frameindex==1) = []; %remove the initial condition +else + rowtotal = ceil(numIter/column) + 1; + columntotal = column; +end % 'color',[0.8500,0.3250,0.0980] stparg = {0.05,[0.05,0.08],0.05}; @@ -77,19 +84,26 @@ function history_production(resultpath,ind,modelfunc,arg,tdata,ydata,params,kern text(0.1,1.5,'Data','Units','normalized','HorizontalAlignment',ps.labelHorizontalAlignment); end for i = 1:numIter - if isfield(varload,'y') - y = varload.y; - visualize([],[],[],y{ind(i)}(frameindex_model,:),'c',false,'ImageSize',params.N,'caxis',clim,'GridSize',[1,NaN],'OuterGridSize',[rowtotal,1],'OuterSubplot',[i+1,1],'ColumnTotal',columntotal,'StarterInd',i*columntotal+1,'subtightplot',stparg); + if ~ps.showModelSolution || (ps.showModelSolution && isfield(varload,'y')) + [~,~,~,pp] = IP_DDFT(tdata,ydata,params,kernelSize,Cspace,[],history(ind(i),:),'mode','pp',ps.IP_DDFT_arg{:}); + end + if ps.showModelSolution + if isfield(varload,'y') + y = varload.y; + visualize([],[],[],y{ind(i)}(frameindex_model,:),'c',false,'ImageSize',params.N,'caxis',clim,'GridSize',[1,NaN],'OuterGridSize',[rowtotal,1],'OuterSubplot',[i+1,1],'ColumnTotal',columntotal,'StarterInd',i*columntotal+1,'subtightplot',stparg); + else + [yhistory,~,~,pp] = IP_DDFT(tdata,ydata,params,kernelSize,Cspace,[],history(ind(i),:),'mode','eval',ps.IP_DDFT_arg{:}); + visualize([],[],[],yhistory(frameindex_model,:),'c',false,'ImageSize',params.N,'caxis',clim,'GridSize',[1,NaN],'OuterGridSize',[rowtotal,1],'OuterSubplot',[i+1,1],'ColumnTotal',columntotal,'StarterInd',i*columntotal+1,'subtightplot',stparg); + end + subtightplot(rowtotal,columntotal,i*columntotal+1,stparg{:}); else - [yhistory,~,~,pp] = IP_DDFT(tdata,ydata,params,kernelSize,Cspace,[],history(ind(i),:),'mode','eval',ps.IP_DDFT_arg{:}); - visualize([],[],[],yhistory(frameindex_model,:),'c',false,'ImageSize',params.N,'caxis',clim,'GridSize',[1,NaN],'OuterGridSize',[rowtotal,1],'OuterSubplot',[i+1,1],'ColumnTotal',columntotal,'StarterInd',i*columntotal+1,'subtightplot',stparg); + subtightplot(rowtotal,columntotal,columntotal+i,stparg{:}); end - subtightplot(rowtotal,columntotal,i*columntotal+1,stparg{:}); history_func(ind(i),modelfunc,arg,Cspace,pp,ps); end -if isfield(meta,'C') && ismember(Cspace,{'k','real'}) && ~isempty(ps.CtruthSubplot) +if ismember(Cspace,{'k','real'}) && ~isempty(ps.CtruthSubplot) axC = subtightplot(rowtotal,columntotal,columntotal*(ps.CtruthSubplot(1)-1)+ps.CtruthSubplot(2),stparg{:}); CC = params.C; halfSize = (kernelSize-1)/2; From 4acb8fdcca11c35ade67788a045b2433882236a4 Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Mon, 25 Nov 2019 01:52:36 -0500 Subject: [PATCH 124/149] plot the result of DDFT_nucleation32 and 41 --- solver/DDFT_nucleation32.m | 15 +++++++++++++-- solver/DDFT_nucleation41.m | 4 ++-- 2 files changed, 15 insertions(+), 4 deletions(-) diff --git a/solver/DDFT_nucleation32.m b/solver/DDFT_nucleation32.m index f1b4937..fd0fabd 100644 --- a/solver/DDFT_nucleation32.m +++ b/solver/DDFT_nucleation32.m @@ -1,7 +1,7 @@ %based on DDFT_nucleation29 %5 snapshots. optimize mu, kernelSize = 10 addpath('../../CHACR/GIP') -runoptim = true; +runoptim = false; tic; L = [5,5]; @@ -54,4 +54,15 @@ x_guess = [zeros(1,kernelSize),0.5,0,-3]; -[x_opt,~,exitflag,params] = IP_DDFT(tdata,ydata,params,kernelSize,Cspace,options,x_guess,'Nmu',3,'discrete',true,'cutoff',k0); +if runoptim + [x_opt,~,exitflag,params] = IP_DDFT(tdata,ydata,params,kernelSize,Cspace,options,x_guess,'Nmu',3,'discrete',true,'cutoff',k0); +else + modelfunc.C = @(k) exp(-(k-k0).^2/(2*alpha^2))*0.95; + modelfunc.mu = @(x) x - x.^2/2 + x.^3/3; + Crange = [0,4]; + arg.C = linspace(Crange(1),Crange(2),500); + arg.mu = linspace(min(ydata(:)),max(ydata(:)),100); + history_production(resultpath,[1,10,20,30,40,65],modelfunc,arg,tdata-tdata(1),ydata,params,kernelSize,Cspace,'IP_DDFT_arg',{'Nmu',3,'discrete',true,'cutoff',k0},'yyaxisLim',[-0.5,1.5;-1,1.2],'k0',k0,'xlim',Crange,'showModelSolution',false); + % f = gcf; + % f.Position = [680 337 522 641]; +end diff --git a/solver/DDFT_nucleation41.m b/solver/DDFT_nucleation41.m index 972c7be..7a7c0e7 100644 --- a/solver/DDFT_nucleation41.m +++ b/solver/DDFT_nucleation41.m @@ -47,7 +47,7 @@ params.moreoptions = moreodeset('gmresTol',1e-5); -resultpath = [largedatapath,'DDFT_nucleation32.mat']; +resultpath = [largedatapath,'DDFT_nucleation41.mat']; options = optimoptions('fminunc','OutputFcn', @(x,optimvalues,state) save_opt_history(x,optimvalues,state,resultpath)); options = optimoptions(options,'HessianFcn','objective','Algorithm','trust-region','MaxFunctionEvaluations',10000,'MaxIterations',10000); @@ -63,7 +63,7 @@ Crange = [0,4]; arg.C = linspace(Crange(1),Crange(2),500); arg.mu = linspace(min(ydata(:)),max(ydata(:)),100); - history_production(resultpath,[1,10,20,30,40,65],modelfunc,arg,tdata-tdata(1),ydata,params,kernelSize,Cspace,'IP_DDFT_arg',{'Nmu',3,'discrete',true,'cutoff',k0},'yyaxisLim',[-0.5,1.5;-1,1.2],'k0',k0,'xlim',Crange,'showModelSolution',false); + history_production(resultpath,[1,10,20,30,40,58],modelfunc,arg,tdata-tdata(1),ydata,params,kernelSize,Cspace,'IP_DDFT_arg',{'Nmu',3,'discrete',true,'cutoff',k0},'yyaxisLim',[-0.5,1.5;-1,1.2],'k0',k0,'xlim',Crange,'showModelSolution',false); % f = gcf; % f.Position = [680 337 522 641]; end From 3225464f7595b8983465cd126aa5ce94323ac8b5 Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Mon, 25 Nov 2019 22:33:31 -0500 Subject: [PATCH 125/149] in history_production, save nonexistent model prediction to result as y --- solver/history_production.m | 20 ++++++++++++++++++-- 1 file changed, 18 insertions(+), 2 deletions(-) diff --git a/solver/history_production.m b/solver/history_production.m index c158844..dbc115e 100644 --- a/solver/history_production.m +++ b/solver/history_production.m @@ -40,8 +40,12 @@ function history_production(resultpath,ind,modelfunc,arg,tdata,ydata,params,kern parse(ps,varargin{:}); ps = ps.Results; -varload = load(resultpath); +varload = matfile(resultpath); history = varload.history; +savey = isempty(who(varload,'y')); +if savey + varload.Properties.Writable = true; +end if isempty(ind) ind = 1:size(history,1); elseif isequal(ind,'end') @@ -83,16 +87,24 @@ function history_production(resultpath,ind,modelfunc,arg,tdata,ydata,params,kern axes(h(1)); text(0.1,1.5,'Data','Units','normalized','HorizontalAlignment',ps.labelHorizontalAlignment); end + +if savey + y = {}; +else + y = varload.y; +end + for i = 1:numIter if ~ps.showModelSolution || (ps.showModelSolution && isfield(varload,'y')) [~,~,~,pp] = IP_DDFT(tdata,ydata,params,kernelSize,Cspace,[],history(ind(i),:),'mode','pp',ps.IP_DDFT_arg{:}); end if ps.showModelSolution - if isfield(varload,'y') + if ~savey y = varload.y; visualize([],[],[],y{ind(i)}(frameindex_model,:),'c',false,'ImageSize',params.N,'caxis',clim,'GridSize',[1,NaN],'OuterGridSize',[rowtotal,1],'OuterSubplot',[i+1,1],'ColumnTotal',columntotal,'StarterInd',i*columntotal+1,'subtightplot',stparg); else [yhistory,~,~,pp] = IP_DDFT(tdata,ydata,params,kernelSize,Cspace,[],history(ind(i),:),'mode','eval',ps.IP_DDFT_arg{:}); + y{ind(i)} = yhistory; visualize([],[],[],yhistory(frameindex_model,:),'c',false,'ImageSize',params.N,'caxis',clim,'GridSize',[1,NaN],'OuterGridSize',[rowtotal,1],'OuterSubplot',[i+1,1],'ColumnTotal',columntotal,'StarterInd',i*columntotal+1,'subtightplot',stparg); end subtightplot(rowtotal,columntotal,i*columntotal+1,stparg{:}); @@ -121,6 +133,10 @@ function history_production(resultpath,ind,modelfunc,arg,tdata,ydata,params,kern set(findall(gcf,'-property','FontWeight'),'FontWeight','normal'); set(findall(gcf,'-property','FontSize'),'FontSize',ps.FontSize); +if savey + varload.y = y; +end + end function hOut = TextLocation(textString,varargin) From 8ebd5964b93645f72ab7ab5593a9b1f3a5e703c8 Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Tue, 26 Nov 2019 00:51:04 -0500 Subject: [PATCH 126/149] update mainFig subplot positions, used to produce DDFT_mainFig_v5 on 11/25/2019 --- solver/mainFig.m | 19 +++++++++++-------- 1 file changed, 11 insertions(+), 8 deletions(-) diff --git a/solver/mainFig.m b/solver/mainFig.m index 29990fe..daa551b 100644 --- a/solver/mainFig.m +++ b/solver/mainFig.m @@ -43,13 +43,15 @@ columntotal = 5; stparg = {0.05,[0.08,0.06],[0.07,0.03]}; clim = [min(min(ydata(:))),max(max(ydata(:)))]; +figure; %first row: data h = visualize([],[],[],ydata,'c',false,'ImageSize',params.N,'caxis',clim,'GridSize',[1,NaN],'OuterGridSize',[rowtotal,1],'OuterSubplot',[1,1],'subtightplot',stparg); for j = 1:length(h) title(h(j),['t = ',num2str(tdata(j),2)]); + h(j).Position(2) = h(j).Position(2) + 0.02; end axes(h(1)); -text(0.01,1.55,'(a) Data','Units','normalized','HorizontalAlignment','left'); +text(0.01,1.46,'(a) Data','Units','normalized','HorizontalAlignment','left'); %second row: history of DDFT_nucleation23 kernelSize = 2; Cspace = 'isotropic'; @@ -66,7 +68,7 @@ ind = [1,19,25,31,1797]; for i = 1:length(ind) ax = subtightplot(rowtotal,columntotal,columntotal+i,stparg{:}); - ax.Position(2) = ax.Position(2) + 0.01; + ax.Position(2) = ax.Position(2) + 0.025; [~,~,~,pp] = IP_DDFT(tdata,ydata,params,kernelSize,Cspace,[],history(ind(i),:),'mode','pp',IP_DDFT_arg{:}); history_func(ind(i),modelfunc,arg,Cspace,pp,[],figprop{:}); if i~=1 @@ -76,7 +78,7 @@ yyaxis right yticklabels([]); else - text(0.01,1.55,'(b) Quartic approximation','Units','normalized','HorizontalAlignment','left'); + text(0.01,1.53,'(b) Quartic approximation','Units','normalized','HorizontalAlignment','left'); legend({'$\hat{C_2}(k)$ (truth)','$\hat{C_2}(k)$','$\mu_h(\eta)$ (truth)','$\mu_h(\eta)$'},... 'Orientation','horizontal','Position',[0.10 0 0.8169 0.0374],'Interpreter','latex'); legend('boxoff'); @@ -103,7 +105,7 @@ %show difference between model and data only % h = visualize([],[],[],yhistory-ydata,'c',false,'ImageSize',params.N,'caxis','auto','GridSize',[1,NaN],'OuterGridSize',[rowtotal,1],'OuterSubplot',[3,1],'subtightplot',stparg); for i = 1:length(h) - h(i).Position(2) = h(i).Position(2) - 0.01; + h(i).Position(2) = h(i).Position(2) - 0; end text(h(1),0.01,1.2,'(c) Quartic approximation result','Units','normalized','HorizontalAlignment','left'); @@ -119,7 +121,8 @@ arg.C = linspace(Crange(1),Crange(2),500); ind = [1,4,11,26,35]; for i = 1:length(ind) - subtightplot(rowtotal,columntotal,columntotal*3+i,stparg{:}); + ax = subtightplot(rowtotal,columntotal,columntotal*3+i,stparg{:}); + ax.Position(2) = ax.Position(2) + 0.01; if i==length(ind) DDFT_nucleation36; delete(hl); @@ -131,12 +134,12 @@ xlabel([]); yticklabels([]); else - text(0.01,1.55,'(d) Hermite function basis function','Units','normalized','HorizontalAlignment','left'); + text(0.01,1.54,'(d) Hermite function basis function','Units','normalized','HorizontalAlignment','left'); end end f = gcf; set(findall(f,'-property','FontName'),'FontName','Arial'); set(findall(f,'-property','FontWeight'),'FontWeight','normal'); -set(findall(f,'-property','FontSize'),'FontSize',12); -f.Position = [680 321 560 657]; +set(findall(f,'-property','FontSize'),'FontSize',13); +f.Position = [680 321 588 657]; % print(f,'C:\Users\zhbkl\Dropbox (MIT)\Research\Report 6\figure\DDFT_mainFig','-dtiff','-r400'); From dd3f5df179682c85f453d74852fb4b36e8b6dda1 Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Tue, 26 Nov 2019 03:48:26 -0500 Subject: [PATCH 127/149] update history_production, add stparg option, fix xlabel --- solver/history_production.m | 17 +++++++++++++---- 1 file changed, 13 insertions(+), 4 deletions(-) diff --git a/solver/history_production.m b/solver/history_production.m index dbc115e..23b3575 100644 --- a/solver/history_production.m +++ b/solver/history_production.m @@ -37,6 +37,7 @@ function history_production(resultpath,ind,modelfunc,arg,tdata,ydata,params,kern addParameter(ps,'mu_at_0',0); %offset mu so that mu at 0 has this value addParameter(ps,'targetLineStyle','-.'); addParameter(ps,'showModelSolution',true); %plot the model solution at each iteration +addParameter(ps,'stparg',{0.05,[0.05,0.08],0.05}); %argument for subtightplot parse(ps,varargin{:}); ps = ps.Results; @@ -76,7 +77,7 @@ function history_production(resultpath,ind,modelfunc,arg,tdata,ydata,params,kern end % 'color',[0.8500,0.3250,0.0980] -stparg = {0.05,[0.05,0.08],0.05}; +stparg = ps.stparg; figure; clim = [min(min(ydata(frameindex,:))),max(max(ydata(frameindex,:)))]; h = visualize([],[],[],ydata(frameindex,:),'c',false,'ImageSize',params.N,'caxis',clim,'GridSize',[1,NaN],'OuterGridSize',[rowtotal,1],'OuterSubplot',[1,1],'ColumnTotal',columntotal,'StarterInd',0,'subtightplot',stparg); @@ -95,7 +96,7 @@ function history_production(resultpath,ind,modelfunc,arg,tdata,ydata,params,kern end for i = 1:numIter - if ~ps.showModelSolution || (ps.showModelSolution && isfield(varload,'y')) + if ~ps.showModelSolution || (ps.showModelSolution && ~savey) [~,~,~,pp] = IP_DDFT(tdata,ydata,params,kernelSize,Cspace,[],history(ind(i),:),'mode','pp',ps.IP_DDFT_arg{:}); end if ps.showModelSolution @@ -107,12 +108,20 @@ function history_production(resultpath,ind,modelfunc,arg,tdata,ydata,params,kern y{ind(i)} = yhistory; visualize([],[],[],yhistory(frameindex_model,:),'c',false,'ImageSize',params.N,'caxis',clim,'GridSize',[1,NaN],'OuterGridSize',[rowtotal,1],'OuterSubplot',[i+1,1],'ColumnTotal',columntotal,'StarterInd',i*columntotal+1,'subtightplot',stparg); end - subtightplot(rowtotal,columntotal,i*columntotal+1,stparg{:}); + ax = subtightplot(rowtotal,columntotal,i*columntotal+1,stparg{:}); else - subtightplot(rowtotal,columntotal,columntotal+i,stparg{:}); + ax = subtightplot(rowtotal,columntotal,columntotal+i,stparg{:}); + end + + + if (ps.showModelSolution && i==numIter) || (~ps.showModelSolution && i==1) + ps.xlabel = 'on'; + else + ps.xlabel = []; end history_func(ind(i),modelfunc,arg,Cspace,pp,ps); + end if ismember(Cspace,{'k','real'}) && ~isempty(ps.CtruthSubplot) From 38ddee6d97372ef9a5e1c4f9840da213023a3218 Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Tue, 26 Nov 2019 03:48:42 -0500 Subject: [PATCH 128/149] visualize DDFT_nucleation41 result --- solver/DDFT_nucleation41.m | 13 +++++++++---- 1 file changed, 9 insertions(+), 4 deletions(-) diff --git a/solver/DDFT_nucleation41.m b/solver/DDFT_nucleation41.m index 7a7c0e7..bb8c997 100644 --- a/solver/DDFT_nucleation41.m +++ b/solver/DDFT_nucleation41.m @@ -1,7 +1,7 @@ %based on DDFT_nucleation32 %change x_guess(1) to 0.1 addpath('../../CHACR/GIP') -runoptim = true; +runoptim = false; tic; L = [5,5]; @@ -63,7 +63,12 @@ Crange = [0,4]; arg.C = linspace(Crange(1),Crange(2),500); arg.mu = linspace(min(ydata(:)),max(ydata(:)),100); - history_production(resultpath,[1,10,20,30,40,58],modelfunc,arg,tdata-tdata(1),ydata,params,kernelSize,Cspace,'IP_DDFT_arg',{'Nmu',3,'discrete',true,'cutoff',k0},'yyaxisLim',[-0.5,1.5;-1,1.2],'k0',k0,'xlim',Crange,'showModelSolution',false); - % f = gcf; - % f.Position = [680 337 522 641]; + history_production(resultpath,[1,11,36,58],modelfunc,arg,tdata-tdata(1),ydata,params,kernelSize,Cspace,... + 'IP_DDFT_arg',{'Nmu',3,'discrete',true,'cutoff',k0},'yyaxisLim',[-0.5,1.5;-1,1.2],... + 'k0',k0,'xlim',[min(ydata(:)),Crange(2)],'showModelSolution',true,... + 'legend',{{'$\hat{C_2}(k)$ (truth)','$\hat{C_2}(k)$','$\mu_h(\eta)$ (truth)','$\mu_h(\eta)$'},... + 'Orientation','horizontal','Position',[0.2051 0.001 0.7874 0.0566],'Interpreter','latex'},... + 'FontSize',13,'stparg',{0.05,[0.1,0.08],[0.08,0.04]}); + f = gcf; + f.Position = [680 368 588 610]; end From 693b6ec117ffac590320c7d4f6b11a4c726f9554 Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Sun, 17 May 2020 02:13:06 -0400 Subject: [PATCH 129/149] add user-defined option in Cspace 'user' --- solver/IP_DDFT.m | 5 +++++ 1 file changed, 5 insertions(+) diff --git a/solver/IP_DDFT.m b/solver/IP_DDFT.m index d38b817..485f9d9 100644 --- a/solver/IP_DDFT.m +++ b/solver/IP_DDFT.m @@ -14,6 +14,9 @@ addParameter(ps,'isotropic_even',false); %set to true if even polynomials are used (Cspace = isotropic_poly_*) addParameter(ps,'assign_suppress',{}); %when mode='sens', use this to suppress the reassignment of certain parameters, however parameters of interest is still stored in meta. Be careful, this only works for things whose senstivity doesn't depend on the parameters themselves + +%Cspace: +%another option 'user', user-defined Csensval, in which case Csensval must be provided in params ps.CaseSensitive = false; parse(ps,varargin{:}); tspan = ps.Results.tspan; @@ -161,6 +164,8 @@ meta.C.exp = false(1,NC); meta.C.exp(end) = true; params = FD2otf(NC,params); +case 'user' + meta.C.exp = false; otherwise NC = floor((prod(kernelSize)+1)/2); params.Csens = @(y,i) Csens_ASA(y,i,Cspace,kernelSize); From 28fc08153270de80248e4436700a8e164103f7d9 Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Sun, 17 May 2020 02:16:07 -0400 Subject: [PATCH 130/149] add DDFT_nucleation30_DILI, perform DILI based on nucleation30, (mainFig d), C only --- solver/DDFT_nucleation30_DILI.m | 94 +++++++++++++++++++++++++++++++++ 1 file changed, 94 insertions(+) create mode 100644 solver/DDFT_nucleation30_DILI.m diff --git a/solver/DDFT_nucleation30_DILI.m b/solver/DDFT_nucleation30_DILI.m new file mode 100644 index 0000000..2306481 --- /dev/null +++ b/solver/DDFT_nucleation30_DILI.m @@ -0,0 +1,94 @@ +%based on DDFT_nucleation29 +%5 snapshots. kernelSize = 10 +addpath('../../CHACR/GIP') +runoptim = false; + +tic; +L = [5,5]; +N = [256,256]; +n = prod(N); + +params.N = N; +params.L = L; + +[k2,k] = formk(N,L); +k0 = 10; +alpha = 5; +modelfunc = @(x) exp(-(x-k0).^2/(2*alpha^2))*0.95; +params.C = modelfunc(sqrt(k2)); + +[t1,y1,params] = solver_DDFT([],[],params); + +xx = linspace(0,L(1),N(1)); +yy = linspace(0,L(2),N(2)); +[xx,yy] = ndgrid(xx,yy); +center = L/2; +radius = 0.06*L(1); +thickness = 0.01*L(1); +roi = roi_circle(xx,yy,center,radius,thickness); + +%nucleus +y0 = y1(end,:)'; +roi = roi(:); +y02 = 0.045; +rho = (y02*n - sum(roi.*y0)) / sum(1-roi); +y0 = roi.*y0 + (1-roi)*rho; + +tspan2 = linspace(0,2.5,100); +[t2,y2] = solver_DDFT(tspan2,y0,params); + +ind = 1:20:100; +tdata = t2(ind); +ydata = y2(ind,:); +toc + + +kernelSize = 10; +Cspace = 'user'; +params.moreoptions = moreodeset('gmresTol',1e-5); + +%basis function here is hermitefunction scaled by 1/sqrt(eigenvalue), where eigenvalue is (2n+1) as in x^2 y(x) - y''_n(x) = (2n+1) y_n(x) +customfunc = @(x) hermitefunction(x/k0,kernelSize,[],1) ./ sqrt(1:2:(2*kernelSize-1)); +%get mu parameters at truth +% xfit = linspace(0,3*k0,20)'; +% x_start = customfunc(xfit) \ modelfunc(xfit); +%provide Csensval +k = sqrt(k2); +params.Csensval = reshape(customfunc(k(:)), [size(k),kernelSize]); + +logpdf = @(x) IP_DDFT(tdata,ydata,params,kernelSize,Cspace,options,x,'Nmu',0,'discrete',true,'cutoff',k0,'mode','eval'); + +name = 'DDFT_nucleation30_DILI_MAP'; +resultpath = [largedatapath,name,'.mat']; +if ~exist(resultpath,'file') + %find MAP + x_guess = zeros(1,kernelSize); + optoptions = optimoptions('fminunc','SpecifyObjectiveGradient',true,'Display','iter-detailed','MaxIterations',50,'StepTolerance',1e-6,'FunctionTolerance',1e-6,'HessianFcn','objective','Algorithm','trust-region'); + optoptions = optimoptions(optoptions,'OutputFcn',@(x,optimvalues,state) save_opt_history(x,optimvalues,state,resultpath)); + [x_start, Smin] = IP_DDFT(tdata,ydata,params,kernelSize,Cspace,options,x_guess,'Nmu',0,'discrete',true,'cutoff',k0); +else + varload = load(resultpath); + x_start = varload.history(end,:); +end + +options = []; +options.init = x_start; +options.N = 20000; +options.logpdf = logpdf; +options.eigthresh = 0.1; +options.eigthresh_local = 1e-4; +options.tLIS = 0.1; +options.tCS = 1; +options.nlag = 100; +options.nb = 50; %have nlag and nb when constr is used, try see if less infeasible samples are taken +options.nmax = 100; +options.verbose = true; +options.proposal = 'LI_Prior'; +options.sigmae = 1e-4; +options.resultpath = [largedatapath,'DDFT_nucleation30_DILI']; +options.saveperstep = 100; + +rng(1); +if rundili + [chain,result] = mcmc_DILI(options); +end From 680b8da184b2551f82d333643893fd0a07d53c7f Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Sun, 17 May 2020 02:51:52 -0400 Subject: [PATCH 131/149] DDFT_nucleation30_DILI, fix bug, change back to normalized hermite function (not scaled by eigenvalue) --- solver/DDFT_nucleation30_DILI.m | 37 ++++++++++++++++++++------------- 1 file changed, 22 insertions(+), 15 deletions(-) diff --git a/solver/DDFT_nucleation30_DILI.m b/solver/DDFT_nucleation30_DILI.m index 2306481..8c95645 100644 --- a/solver/DDFT_nucleation30_DILI.m +++ b/solver/DDFT_nucleation30_DILI.m @@ -48,28 +48,35 @@ params.moreoptions = moreodeset('gmresTol',1e-5); %basis function here is hermitefunction scaled by 1/sqrt(eigenvalue), where eigenvalue is (2n+1) as in x^2 y(x) - y''_n(x) = (2n+1) y_n(x) -customfunc = @(x) hermitefunction(x/k0,kernelSize,[],1) ./ sqrt(1:2:(2*kernelSize-1)); +% customfunc = @(x) hermitefunction(x/k0,kernelSize,[],1) ./ sqrt(1:2:(2*kernelSize-1)); %get mu parameters at truth % xfit = linspace(0,3*k0,20)'; % x_start = customfunc(xfit) \ modelfunc(xfit); %provide Csensval + +%I changed my mind, just use normalized hermitefunction, so prior is just exp(-||C(k)||_2^2/2) +customfunc = @(x) hermitefunction(x/k0,kernelSize,[],1); k = sqrt(k2); params.Csensval = reshape(customfunc(k(:)), [size(k),kernelSize]); -logpdf = @(x) IP_DDFT(tdata,ydata,params,kernelSize,Cspace,options,x,'Nmu',0,'discrete',true,'cutoff',k0,'mode','eval'); - -name = 'DDFT_nucleation30_DILI_MAP'; -resultpath = [largedatapath,name,'.mat']; -if ~exist(resultpath,'file') - %find MAP - x_guess = zeros(1,kernelSize); - optoptions = optimoptions('fminunc','SpecifyObjectiveGradient',true,'Display','iter-detailed','MaxIterations',50,'StepTolerance',1e-6,'FunctionTolerance',1e-6,'HessianFcn','objective','Algorithm','trust-region'); - optoptions = optimoptions(optoptions,'OutputFcn',@(x,optimvalues,state) save_opt_history(x,optimvalues,state,resultpath)); - [x_start, Smin] = IP_DDFT(tdata,ydata,params,kernelSize,Cspace,options,x_guess,'Nmu',0,'discrete',true,'cutoff',k0); -else - varload = load(resultpath); - x_start = varload.history(end,:); -end +logpdf = @(x) IP_DDFT(tdata,ydata,params,kernelSize,Cspace,[],x,'Nmu',0,'discrete',true,'cutoff',k0,'mode','eval'); + +% name = 'DDFT_nucleation30_DILI_MAP'; +% resultpath = [largedatapath,name,'.mat']; +% if ~exist(resultpath,'file') +% %find MAP +% x_guess = zeros(1,kernelSize); +% optoptions = optimoptions('fminunc','SpecifyObjectiveGradient',true,'Display','iter-detailed','MaxIterations',50,'StepTolerance',1e-6,'FunctionTolerance',1e-6,'HessianFcn','objective','Algorithm','trust-region'); +% optoptions = optimoptions(optoptions,'OutputFcn',@(x,optimvalues,state) save_opt_history(x,optimvalues,state,resultpath)); +% [x_start, Smin] = IP_DDFT(tdata,ydata,params,kernelSize,Cspace,optoptions,x_guess,'Nmu',0,'discrete',true,'cutoff',k0); +% else +% varload = load(resultpath); +% x_start = varload.history(end,:); +% end + +%use result from DDFT_nucleation30 directly +varload = load([largedatapath,'DDFT_nucleation30']); +x_start = varload.history(end,:); options = []; options.init = x_start; From ab57b75e4d9ec6a25e7d2dafd691041516f8783a Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Sun, 17 May 2020 04:01:00 -0400 Subject: [PATCH 132/149] add mode='fgh' in IP_DDFT (for DILI) --- solver/IP_DDFT.m | 16 +++++++++++++++- 1 file changed, 15 insertions(+), 1 deletion(-) diff --git a/solver/IP_DDFT.m b/solver/IP_DDFT.m index 485f9d9..2e2317d 100644 --- a/solver/IP_DDFT.m +++ b/solver/IP_DDFT.m @@ -3,6 +3,7 @@ addParameter(ps,'mode','IP'); %IP, eval, pp (walks through the function without eval or IP) %set mode = 'eval' to only do the forward solve and return the solution as x_opt, fval and exitflag will be empty %set mode = 'sens' to perform sensitivity analysis at x_guess, x_opt, fval, exitflag are hessian, hessian_t (hessian at eqch time step), and dy, respectively +% set mode = 'fgh' to output {fval, grad and hess} addParameter(ps,'tspan',100); %set tspan to a positive integer or 'sol' to specify the number of time points returned for solution history. Inactive and automatically set to 'discrete' if discrete = true addParameter(ps,'bound',[]); %this is more Cspace = isotropic_CmE @@ -16,7 +17,7 @@ %when mode='sens', use this to suppress the reassignment of certain parameters, however parameters of interest is still stored in meta. Be careful, this only works for things whose senstivity doesn't depend on the parameters themselves %Cspace: -%another option 'user', user-defined Csensval, in which case Csensval must be provided in params +%another option 'user', user-defined Csensval, in which case Csensval must be provided in params, NC=kernelSize, meta.C.exp=false ps.CaseSensitive = false; parse(ps,varargin{:}); tspan = ps.Results.tspan; @@ -165,6 +166,7 @@ meta.C.exp(end) = true; params = FD2otf(NC,params); case 'user' + NC = kernelSize; meta.C.exp = false; otherwise NC = floor((prod(kernelSize)+1)/2); @@ -215,6 +217,18 @@ forwardHandle, [], [], [], assignHandle,'eval',true); fval = []; exitflag = []; +case 'fgh' + switch nargout + case 1 + x_opt = IP(tdata,ydata,x_guess,meta,params, ... + forwardHandle, @adjointSolver,loss,lossHess, assignHandle, varargin{:}); + case 2 + [x_opt,fval] = IP(tdata,ydata,x_guess,meta,params, ... + forwardHandle, @adjointSolver,loss,lossHess, assignHandle, 'ASA',false,varargin{:}); + case 3 + [x_opt,fval,exitflag] = IP(tdata,ydata,x_guess,meta,params, ... + forwardHandle, @adjointSolver,loss,lossHess, assignHandle, 'ASA',false,varargin{:}); + end case 'IP' loss = @(y,ydata,~) MSE(y,ydata,prod(params.dx)*100); lossHess = @(dy,~,~,~) MSE([],[],prod(params.dx)*100,dy); From ded8b761d9cfe4f52261bdbcd84ffe6a70bb5d07 Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Thu, 28 May 2020 00:22:09 -0400 Subject: [PATCH 133/149] update DDFT_nucleation30_DILI visualization to generate Fig. 2 in expip_v0.tex, for meeting with Martin on 05/26 --- solver/DDFT_nucleation30_DILI.m | 78 +++++++++++++++++++++++---------- 1 file changed, 56 insertions(+), 22 deletions(-) diff --git a/solver/DDFT_nucleation30_DILI.m b/solver/DDFT_nucleation30_DILI.m index 8c95645..0537d5d 100644 --- a/solver/DDFT_nucleation30_DILI.m +++ b/solver/DDFT_nucleation30_DILI.m @@ -1,7 +1,7 @@ %based on DDFT_nucleation29 %5 snapshots. kernelSize = 10 addpath('../../CHACR/GIP') -runoptim = false; +rundili = false; tic; L = [5,5]; @@ -17,25 +17,27 @@ modelfunc = @(x) exp(-(x-k0).^2/(2*alpha^2))*0.95; params.C = modelfunc(sqrt(k2)); -[t1,y1,params] = solver_DDFT([],[],params); - -xx = linspace(0,L(1),N(1)); -yy = linspace(0,L(2),N(2)); -[xx,yy] = ndgrid(xx,yy); -center = L/2; -radius = 0.06*L(1); -thickness = 0.01*L(1); -roi = roi_circle(xx,yy,center,radius,thickness); - -%nucleus -y0 = y1(end,:)'; -roi = roi(:); -y02 = 0.045; -rho = (y02*n - sum(roi.*y0)) / sum(1-roi); -y0 = roi.*y0 + (1-roi)*rho; - -tspan2 = linspace(0,2.5,100); -[t2,y2] = solver_DDFT(tspan2,y0,params); +if ~exist('y1','var') + [t1,y1,params] = solver_DDFT([],[],params); + + xx = linspace(0,L(1),N(1)); + yy = linspace(0,L(2),N(2)); + [xx,yy] = ndgrid(xx,yy); + center = L/2; + radius = 0.06*L(1); + thickness = 0.01*L(1); + roi = roi_circle(xx,yy,center,radius,thickness); + + %nucleus + y0 = y1(end,:)'; + roi = roi(:); + y02 = 0.045; + rho = (y02*n - sum(roi.*y0)) / sum(1-roi); + y0 = roi.*y0 + (1-roi)*rho; + + tspan2 = linspace(0,2.5,100); + [t2,y2] = solver_DDFT(tspan2,y0,params); +end ind = 1:20:100; tdata = t2(ind); @@ -59,7 +61,7 @@ k = sqrt(k2); params.Csensval = reshape(customfunc(k(:)), [size(k),kernelSize]); -logpdf = @(x) IP_DDFT(tdata,ydata,params,kernelSize,Cspace,[],x,'Nmu',0,'discrete',true,'cutoff',k0,'mode','eval'); +% logpdf = @(x) IP_DDFT(tdata,ydata,params,kernelSize,Cspace,[],x,'Nmu',0,'discrete',true,'cutoff',k0,'mode','eval'); % name = 'DDFT_nucleation30_DILI_MAP'; % resultpath = [largedatapath,name,'.mat']; @@ -81,7 +83,6 @@ options = []; options.init = x_start; options.N = 20000; -options.logpdf = logpdf; options.eigthresh = 0.1; options.eigthresh_local = 1e-4; options.tLIS = 0.1; @@ -97,5 +98,38 @@ rng(1); if rundili + options.logpdf = logpdf; [chain,result] = mcmc_DILI(options); +else + f = figure('Position',[680 642 392 336]); + burnin = 100; + p = 0.95; %confidence level + xplot = linspace(0,5*k0,200)'; + varload = load(options.resultpath); + cf.func = @(x,coeff) hermitefunction(x/k0,[],coeff,1); + cf.sens = @(x,coeff) customfunc(x); + yy = linearfuncEval(cf,xplot,varload.chain(burnin:end,:)); + mu = mean(yy,1); + upper = quantile(yy,1-(1-p)/2) - mu; + lower = mu - quantile(yy,(1-p)/2); + + main = axes('Position',[0.18,0.2,0.6,0.7]); + [hl,hp] = boundedline(xplot/k0,mu',[lower;upper].'); + hl.LineWidth = 2; + xlabel('k/k_0'); + ylabel('$\hat{C}_2(k)$','Interpreter','latex'); + xlim([0,5]); + + ymin = min(ydata(:)); + ymax = max(ydata(:)); + for i = 1:5 + axes('Position',[0.82,0.1+0.18*(5-i),0.15,0.15]); + imshow((reshape(ydata(i,:),N)-ymin)/(ymax-ymin)); + colormap(flip(gray)); + end + + set(findall(f,'-property','FontName'),'FontName','Arial'); + set(findall(f,'-property','FontWeight'),'FontWeight','normal'); + set(findall(f,'-property','FontSize'),'FontSize',13); + print(f,['C:\Users\zhbkl\Dropbox (MIT)\Research\Report 6\PaperIPExpand\DDFT_nucleation30_DILI'],'-dpng','-r500'); end From 9389b61fb5d49b4faa7ccfc425218bf038559d0c Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Mon, 4 Jan 2021 03:05:32 -0500 Subject: [PATCH 134/149] add presentation_RD, to generate figure for slide --- solver/presentation_RD.m | 24 ++++++++++++++++++++++++ 1 file changed, 24 insertions(+) create mode 100644 solver/presentation_RD.m diff --git a/solver/presentation_RD.m b/solver/presentation_RD.m new file mode 100644 index 0000000..e816501 --- /dev/null +++ b/solver/presentation_RD.m @@ -0,0 +1,24 @@ +L = [5,5]; +N = [1000,1000]; +L = [10,10]; +N = [2000,2000]; +n = prod(N); + +params.N = N; +params.L = L; + +[k2,k] = formk(N,L); +k0 = 50; +alpha = 5; +params.C = exp(-(sqrt(k2)-k0).^2/(2*alpha^2))*0.95; + + +tspan = 0:0.1:5; +[t1,y1,params] = solver_DDFT(tspan,[],params); + + +save([largedatapath,'presentation_RD'],'y'); +% im = circshift(circshift(y(:,:,18),300,2),250,1); +% im = (im-min(im(:)))/(max(im(:))-min(im(:))); +% im = ind2rgb(floor(im*255),cmocean('thermal')); +% imwrite(im,'C:\Users\zhbkl\Dropbox (MIT)\Research\Report 6\figure\presentation_RD.png'); \ No newline at end of file From 91034b8611fe109eb5db485e97f8c71777a9855e Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Mon, 4 Jan 2021 16:53:45 -0500 Subject: [PATCH 135/149] fux bugs in solver_DDFT --- solver/solver_DDFT.m | 10 +++++----- 1 file changed, 5 insertions(+), 5 deletions(-) diff --git a/solver/solver_DDFT.m b/solver/solver_DDFT.m index 415399b..efceeac 100644 --- a/solver/solver_DDFT.m +++ b/solver/solver_DDFT.m @@ -62,7 +62,7 @@ ND = N(i); I = speye(NI); E = sparse(2:ND,1:ND-1,1,ND,ND); - D = E+E'-2*I; + D = E+E'-2*speye(ND); %circulant D, periodic boundary condition D(1,ND) = 1; D(ND,1) = 1; @@ -170,7 +170,7 @@ yp0_list = y0_list; for ind = 2:length(tdata) t0 = tdata(ind); - F0 = error(end,:)'; + F0 = error(ind,:)'; [y0_list(:,ind-1),yp0_list(:,ind-1)] = ASAinit(F0,discrete,params,t0,sol); end %serial @@ -402,10 +402,10 @@ function [y0,yp0] = ASAinit(F0,discrete,params,t0,sol) y0 = zeros(size(F0)); - yp0 = F0; + yp0 = -F0; if discrete - y0 = yp0; - yp0 = jacobian_mult(params,y0,t0,sol,'force',true); + y0 = -yp0; + yp0 = -jacobian_mult(params,y0,t0,sol,'force',true); end end From c7f2837f605413b3832bb29688520f7d8950b584 Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Tue, 5 Jan 2021 03:52:02 -0500 Subject: [PATCH 136/149] fix bug in solver_DDFT about user options setting --- solver/solver_DDFT.m | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/solver/solver_DDFT.m b/solver/solver_DDFT.m index efceeac..acd0406 100644 --- a/solver/solver_DDFT.m +++ b/solver/solver_DDFT.m @@ -84,7 +84,7 @@ end options = odeset; if isfield(params,'options') && ~isempty(params.options) - options = moreodeset(options,params.options); + options = odeset(options,params.options); end if ~ASA From 00c201563b400e752044a007d1551f0fef2956cd Mon Sep 17 00:00:00 2001 From: Hongbo Date: Fri, 15 Jan 2021 18:56:47 -0500 Subject: [PATCH 137/149] update presentation_RD.m --- solver/presentation_RD.m | 25 ++++++++++++++++++++----- 1 file changed, 20 insertions(+), 5 deletions(-) diff --git a/solver/presentation_RD.m b/solver/presentation_RD.m index e816501..b04efc7 100644 --- a/solver/presentation_RD.m +++ b/solver/presentation_RD.m @@ -1,7 +1,12 @@ -L = [5,5]; -N = [1000,1000]; +%L = [5,5]; +%N = [1000,1000]; L = [10,10]; N = [2000,2000]; +%N = [256*2,256*2]; +%L = [2.5,10]; +%N = [500,2000]; +%L = [5,5]; +%N = [2000,2000]; n = prod(N); params.N = N; @@ -9,16 +14,26 @@ [k2,k] = formk(N,L); k0 = 50; +%R_D5 +%k0 = 100; alpha = 5; params.C = exp(-(sqrt(k2)-k0).^2/(2*alpha^2))*0.95; tspan = 0:0.1:5; -[t1,y1,params] = solver_DDFT(tspan,[],params); +tspan = linspace(0,0.2,101); +params.options = odeset('OutputFcn',@(t,y,flag) simOutput(t,y,flag,true,[])); +y0 = randomfield(N,L,'RBF',2*pi/k0/10,1); +y0 = y0(:); +y0 = []; +[t1,y1,params] = solver_DDFT(tspan,y0,params); -save([largedatapath,'presentation_RD'],'y'); +y = permute(reshape(y1,[length(tspan),N]),[2,3,1]); + + +%save([largedatapath,'presentation_RD_4'],'y'); % im = circshift(circshift(y(:,:,18),300,2),250,1); % im = (im-min(im(:)))/(max(im(:))-min(im(:))); % im = ind2rgb(floor(im*255),cmocean('thermal')); -% imwrite(im,'C:\Users\zhbkl\Dropbox (MIT)\Research\Report 6\figure\presentation_RD.png'); \ No newline at end of file +% imwrite(im,'C:\Users\zhbkl\Dropbox (MIT)\Research\Report 6\figure\presentation_RD.png'); From e8c66d46b8ed2297f8ec9194b709c0e30bd58b75 Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Fri, 15 Jan 2021 19:37:52 -0500 Subject: [PATCH 138/149] add presentation_RD_nucleus, present crystallization starting from a nucleus --- solver/presentation_RD_nucleus.m | 48 ++++++++++++++++++++++++++++++++ 1 file changed, 48 insertions(+) create mode 100644 solver/presentation_RD_nucleus.m diff --git a/solver/presentation_RD_nucleus.m b/solver/presentation_RD_nucleus.m new file mode 100644 index 0000000..f69e540 --- /dev/null +++ b/solver/presentation_RD_nucleus.m @@ -0,0 +1,48 @@ +%based on presentation_RD and DDFT_nucleation, start from a nucleus +L = [5,5]; +N = [1024,1024]; +% L = [10,10]; +% N = [2000,2000]; +n = prod(N); + +params.N = N; +params.L = L; + +[k2,k] = formk(N,L); +k0 = 50; +alpha = 5; +params.C = exp(-(sqrt(k2)-k0).^2/(2*alpha^2))*0.95; + +params.options = odeset('OutputFcn',@(t,y,flag) simOutput(t,y,flag,true,[])); + +tspan = linspace(0,0.2,3); + +y0 = []; +[t1,y1,params] = solver_DDFT(tspan,y0,params); + +y1 = y1(end,:); +y1 = reshape(y1,N); +%% +imcenter = y1((N(1)/2-50):(N(1)/2+50),(N(2)/2-50):(N(2)/2+50)); +[ii,jj] = find(imcenter==max(imcenter(:))); +xx = 1:size(imcenter,1); +yy = 1:size(imcenter,2); +[xx,yy]=ndgrid(xx,yy); +%mask around the nucleus +mask = ((xx-ii).^2+(yy-jj).^2)<(pi/k0*N(1)/L(1))^2; +roi = zeros(N); +roi((N(1)/2-50):(N(1)/2+50),(N(2)/2-50):(N(2)/2+50)) = mask; + +%initial condition for the crystallization from a nuclues +y0 = y1(:); +roi = roi(:); +y02 = 0.08; +rho = (y02*n - sum(roi.*y0)) / sum(1-roi); +y0 = roi.*y0 + (1-roi)*rho; + +tspan = linspace(0,0.4,601); +[t2,y2,params] = solver_DDFT(tspan,y0,params); +y2 = permute(reshape(y2,[length(t2),N]),[2,3,1]); + +ysample = y2(:,:,1:60:end); +% imwrite((y2-min(y2(:)))/(max(y2(:))-min(y2(:))),[largedatapath,'presentation_RD_nucleus.png']); From c6ad2192fa223617469e87d56d3436ce40ade8ac Mon Sep 17 00:00:00 2001 From: Hongbo Date: Sat, 16 Jan 2021 18:22:51 -0500 Subject: [PATCH 139/149] update presentation_RD_nucleus, running model and exporting --- solver/presentation_RD_nucleus.m | 33 +++++++++++++++++++++++++++++--- 1 file changed, 30 insertions(+), 3 deletions(-) diff --git a/solver/presentation_RD_nucleus.m b/solver/presentation_RD_nucleus.m index f69e540..a4c865a 100644 --- a/solver/presentation_RD_nucleus.m +++ b/solver/presentation_RD_nucleus.m @@ -22,19 +22,30 @@ y1 = y1(end,:); y1 = reshape(y1,N); -%% + imcenter = y1((N(1)/2-50):(N(1)/2+50),(N(2)/2-50):(N(2)/2+50)); +imcenter = y1(1:101,1:101); [ii,jj] = find(imcenter==max(imcenter(:))); xx = 1:size(imcenter,1); yy = 1:size(imcenter,2); [xx,yy]=ndgrid(xx,yy); %mask around the nucleus mask = ((xx-ii).^2+(yy-jj).^2)<(pi/k0*N(1)/L(1))^2; +nucleus = imcenter .* mask; +ind1 = find(any(mask,2)); +ind2 = find(any(mask,1)); +nucleus = nucleus(ind1,ind2); +mask = mask(ind1,ind2); +shift = floor(size(mask)/2); roi = zeros(N); -roi((N(1)/2-50):(N(1)/2+50),(N(2)/2-50):(N(2)/2+50)) = mask; +y0 = zeros(N); +xind = N(1)/2-shift(1)-1 + (1:size(mask,1)); +yind = N(2)/2-shift(2)-1 + (1:size(mask,2)); %indices for placing nucleus in the center +roi(xind,yind) = mask; +y0(xind,yind) = nucleus; %initial condition for the crystallization from a nuclues -y0 = y1(:); +y0 = y0(:); roi = roi(:); y02 = 0.08; rho = (y02*n - sum(roi.*y0)) / sum(1-roi); @@ -46,3 +57,19 @@ ysample = y2(:,:,1:60:end); % imwrite((y2-min(y2(:)))/(max(y2(:))-min(y2(:))),[largedatapath,'presentation_RD_nucleus.png']); + +mv = VideoWriter([largedatapath,'presentation_RD_nucleus']); +open(mv); +writeVideo(mv,(permute(y2,[1,2,4,3])-min(y2(:)))/(max(y2(:))-min(y2(:)))); +close(mv); + +mv = VideoWriter([largedatapath,'presentation_RD_nucleus']); +open(mv); +yk = abs(fft2(y2)); +yk(1,1,:) = 0; +yk = fftshift(fftshift(yk,1),2); +Ncutoff = k0.*L/2/pi; +Ncutoff = floor(Ncutoff * 4); +yk = yk((N(1)/2-Ncutoff):(N(1)/2+Ncutoff),(N(2)/2-Ncutoff):(N(2)/2+Ncutoff),:); +writeVideo(mv,permute(min(yk./max(yk,[],[1,2])*10,1),[1,2,4,3])); +close(mv); From bcd99bb4b54a0e823694e746d622737b6fbc4b37 Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Sat, 16 Jan 2021 18:37:58 -0500 Subject: [PATCH 140/149] write C3 into an image in presentation_RD_nucleus --- solver/presentation_RD_nucleus.m | 7 +++++++ 1 file changed, 7 insertions(+) diff --git a/solver/presentation_RD_nucleus.m b/solver/presentation_RD_nucleus.m index a4c865a..1d8fa24 100644 --- a/solver/presentation_RD_nucleus.m +++ b/solver/presentation_RD_nucleus.m @@ -73,3 +73,10 @@ yk = yk((N(1)/2-Ncutoff):(N(1)/2+Ncutoff),(N(2)/2-Ncutoff):(N(2)/2+Ncutoff),:); writeVideo(mv,permute(min(yk./max(yk,[],[1,2])*10,1),[1,2,4,3])); close(mv); + +%write the C2 function into an image +c=fftshift(ifft2(params.C)); +cl=linspecer(2); +cc=divergentColormap(cl(1,:),cl(2,:),c,true,max(c(:))*[-1,1],[0,0,0]); +alpha = abs(c)/max(abs(c(:))); +imwrite(cc,'C:\Users\zhbkl\Dropbox (MIT)\Research\Report 6\figure\presentation_RD_nucleus_C2.png','Alpha',alpha.^0.7); \ No newline at end of file From 4912d8a19e3b2d25b20b97204640ed47642deb29 Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Sat, 16 Jan 2021 18:38:20 -0500 Subject: [PATCH 141/149] add history_production and history_func, add offset and muderiv options --- solver/history_func.m | 18 +++++++++++++++--- solver/history_production.m | 2 ++ 2 files changed, 17 insertions(+), 3 deletions(-) diff --git a/solver/history_func.m b/solver/history_func.m index 6e4fc89..b9d460e 100644 --- a/solver/history_func.m +++ b/solver/history_func.m @@ -15,6 +15,8 @@ function history_func(ind,modelfunc,arg,Cspace,pp,property,varargin) addParameter(ps,'label',true); addParameter(ps,'labelHorizontalAlignment','left'); addParameter(ps,'targetLineStyle','-.'); + addParameter(ps,'offset',true); %if both C and mu are optimized. Whether to offset C with a constant term and offset mu with a the linear term + addParameter(ps,'muderiv',false); %plot mu'(c) instead of mu parse(ps,varargin{:}); ps = ps.Results; else @@ -26,7 +28,7 @@ function history_func(ind,modelfunc,arg,Cspace,pp,property,varargin) namesflag = ismember({'mu','C'},names); numFunc = numel(names); - if all(namesflag) + if all(namesflag) && ps.offset %calculate current gradient of mu at x=0 grad0 = customizeFunGrad(pp.params,'mu','grad',0); %gradient of the first order basis function of mu @@ -80,13 +82,23 @@ function history_func(ind,modelfunc,arg,Cspace,pp,property,varargin) if numFunc==1 ax.ColorOrderIndex = j; end - plot(argj,modelfunc.(name)(argj*xscale),ps.targetLineStyle,'LineWidth',2); + if isequal(name,'mu') && ps.muderiv + [~,yarg] = modelfunc.(name)(argj*xscale); + else + yarg = modelfunc.(name)(argj*xscale); + end + plot(argj,yarg,ps.targetLineStyle,'LineWidth',2); ylimtemp = ax.YLim; hold on; if numFunc==1 ax.ColorOrderIndex = j; end - plot(argj,customfunc(argj*xscale,customparams)+yoffset,'LineWidth',2); + if isequal(name,'mu') && ps.muderiv + [~,yarg] = customfunc(argj*xscale,customparams); + else + yarg = customfunc(argj*xscale,customparams)+yoffset; + end + plot(argj,yarg,'-','LineWidth',2); if isempty(ps.yyaxisLim) ax.YLim = ylimtemp; else diff --git a/solver/history_production.m b/solver/history_production.m index 23b3575..53f3155 100644 --- a/solver/history_production.m +++ b/solver/history_production.m @@ -36,6 +36,8 @@ function history_production(resultpath,ind,modelfunc,arg,tdata,ydata,params,kern addParameter(ps,'dmu_at_0',1); %when meta has both mu and C, rescale so that dmu/dx at 0 has this value addParameter(ps,'mu_at_0',0); %offset mu so that mu at 0 has this value addParameter(ps,'targetLineStyle','-.'); +addParameter(ps,'offset',true); %if both C and mu are optimized. Whether to offset C with a constant term and offset mu with a the linear term +addParameter(ps,'muderiv',false); %plot mu'(c) instead of mu addParameter(ps,'showModelSolution',true); %plot the model solution at each iteration addParameter(ps,'stparg',{0.05,[0.05,0.08],0.05}); %argument for subtightplot parse(ps,varargin{:}); From 39afacc9c17706e7a3931ae018b8d18530cc0298 Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Sat, 16 Jan 2021 18:38:35 -0500 Subject: [PATCH 142/149] add history_movie, turn history into a movie --- solver/history_movie.m | 234 +++++++++++++++++++++++++++++++++++++++++ 1 file changed, 234 insertions(+) create mode 100644 solver/history_movie.m diff --git a/solver/history_movie.m b/solver/history_movie.m new file mode 100644 index 0000000..0c3fde4 --- /dev/null +++ b/solver/history_movie.m @@ -0,0 +1,234 @@ +function history_movie(resultpath,vid,ind,modelfunc,arg,tdata,ydata,params,kernelSize,Cspace, varargin) +%based on history_movie in CHACR/IP and history_production in RD/solver , produce a movie. +%must create a figure outside and a movie writer outside and pass the video object (vid) +%below are instructions from history_production, which may or may not be relevant here +%Two figures for figure handle +%note that ind is the indices of the optimization steps to be plotted. ind can also be 'end', in order to quickly visualize the final result. +%Use name value pair; +%'label'=true (default) to label the iteration number somewhere according to 'labelPosition'(= 'best' by default) for the first figure and to the left of each row for the second figure +%'labelxpos', coordinate of the x position of the label +%'labelHorizontalAlignment', 'left' (default), 'center','right' +%'ExchangeCurrentFieldColorScale', +%FrameIndex: selectively plot frames of c field by their index. ':' by default, meaning plotting all frames. +%Orientation: horizontal (default) arranges iterations (specified by ind) horizontally and different functions vertically; vertical does the other way +%yyaxisLim: each row corresponds to the ylim of each curve +%columntotal and rowtotal, overwrite the total number of columns and rows +%If there is more than one functions to plot, modelfunc should be a struct, whose field names match those in the meta. If there is only one function to plot, modelfunc can either be a struct or simply a function handle +%the result file can also contain y, the solution to the PDE at each step, in which case we don't need to recompute +%vararagout{1} is the all the subplots handles in 2D array form +ps = inputParser; +addParameter(ps,'funclabel',false); %label for functions +addParameter(ps,'funcxlabel',true); %xlabel for functions +addParameter(ps,'label',true); %label for iteration +addParameter(ps,'labelPosition','top'); +addParameter(ps,'labelpos',[0,1.2]); +addParameter(ps,'labelHorizontalAlignment','left'); +addParameter(ps,'ExchangeCurrentFieldColorScale',[]); +addParameter(ps,'FrameIndex',':'); +addParameter(ps,'Orientation','horizontal'); +addParameter(ps,'yyaxisLim',[]); +addParameter(ps,'timeLabel',true); %time is shifted such that t for the first frame is 0 +addParameter(ps,'timeLabelManual',[]); %replace the default time label above, must be a cell of char arrays +addParameter(ps,'FontSize',12); +addParameter(ps,'scale',[]); +addParameter(ps,'targetLineStyle','--'); +addParameter(ps,'title',[]); %left aligned, on top of the first data row +addParameter(ps,'stparg',{0.05,[0.1,0.08],0.05}); %argument for subtightplot +addParameter(ps,'visualizeArgs',{}); %additional arguments for visualize +addParameter(ps,'color',linspecer(2)); %color for lines +addParameter(ps,'save',true); %whether to save the ymodel result in resultpath +addParameter(ps,'use_saved',true); %whether to use saved ymodel result in resultpath +addParameter(ps,'darkmode',true); %generate darkmode movies +addParameter(ps,'offset',true); %if both C and mu are optimized. Whether to offset C with a constant term and offset mu with a the linear term +addParameter(ps,'muderiv',false); %plot mu'(c) instead of mu +addParameter(ps,'component',[]); %specify what functions to plot and in what order, only two allowed +addParameter(ps,'IP_DDFT_arg',{}); +addParameter(ps,'k0',1); %used to scale k +addParameter(ps,'dmu_at_0',1); %when meta has both mu and C, rescale so that dmu/dx at 0 has this value +addParameter(ps,'mu_at_0',0); %offset mu so that mu at 0 has this value + +parse(ps,varargin{:}); +ps = ps.Results; + +varload = matfile(resultpath); +history = varload.history; +has_y = ~isempty(who(varload,'y')); + +if isempty(ind) + ind = 1:size(history,1); +end + +%plot target and fitted function +if isempty(ps.component) + names = fieldnames(modelfunc); + names = names(1:2); + names = flip(sort(names)); +else + names = ps.component; +end +numFunc = numel(names); +numIter = length(ind); + + +frameindex = ps.FrameIndex; +if isequal(frameindex,':') + column = size(ydata,1); + frameindex = 1:column; +else + column = length(frameindex); +end +columntotal = column + 1; +rowtotal = 2; + +frameindex_model = frameindex; + +stparg = ps.stparg; + +clim = [min(min(ydata(frameindex,:))),max(max(ydata(frameindex,:)))]; + +hdata = visualize([],[],[],ydata(frameindex,:),'c',false,'ImageSize',params.N,'caxis',clim,'GridSize',[1,NaN],'OuterGridSize',[rowtotal,1],'OuterSubplot',[1,1],'ColumnTotal',columntotal,'StarterInd',1,'subtightplot',stparg,ps.visualizeArgs{:}); +data_cm = hdata(1).Colormap; + +if has_y && ps.use_saved + y = varload.y; +else + y = {}; +end + +open(vid); +for i = 1:numIter + if has_y && ps.use_saved + ymodel = y{ind(i)}; + [~,~,~,pp] = IP_DDFT(tdata,ydata,params,kernelSize,Cspace,[],history(ind(i),:),'mode','pp',ps.IP_DDFT_arg{:}); + else + [ymodel,~,~,pp] = IP_DDFT(tdata,ydata,params,kernelSize,Cspace,[],history(ind(i),:),'mode','eval',ps.IP_DDFT_arg{:}); + if ps.save + y{ind(i)} = ymodel; + end + end + hmodel = visualize([],[],[],ymodel(frameindex_model,:),'c',false,'ImageSize',params.N,'caxis',clim,'GridSize',[1,NaN],'OuterGridSize',[rowtotal,1],'OuterSubplot',[1,1],'ColumnTotal',columntotal,'StarterInd',columntotal+1,'subtightplot',stparg,ps.visualizeArgs{:}); + if all(ismember({'mu','C'},names)) && ps.offset + %calculate current gradient of mu at x=0 + grad0 = customizeFunGrad(pp.params,'mu','grad',0); + %gradient of the first order basis function of mu + [~,grad1] = feval(pp.params.mu.func,0,1); + %set the gradient of mu at x=0 to be 1. The offset is + offset = (ps.dmu_at_0-grad0)/grad1; + pp.params.mu.params(1) = pp.params.mu.params(1) + offset; + else + offset = 0; + end + + for j=1:numFunc + hfunc(j) = subtightplot(rowtotal,columntotal,(j-1)*columntotal+1,stparg{:}); + name = names{j}; + if isequal(name,'C') && ~isempty(regexp(Cspace,'isotropic*')) + customfunc = pp.params.Cfunc.func; + customparams = pp.params.Cfunc.params; + yoffset = offset; + elseif isequal(name,'mu') + customfunc = pp.params.(name).func; + customparams = pp.params.(name).params; + yoffset = - customfunc(0,customparams); + end + argj = arg.(name); + if isequal(name,'C') && ~isempty(regexp(Cspace,'isotropic*')) + xscale = ps.k0; + else + xscale = 1; + end + if isequal(name,'mu') && ps.muderiv + [~,yarg] = modelfunc.(name)(argj*xscale); + else + yarg = modelfunc.(name)(argj*xscale); + end + plot(argj,yarg,ps.targetLineStyle,'LineWidth',2,'Color',ps.color(j,:)); + ax = gca; + ylimtemp = ax.YLim; + hold on; + if isequal(name,'mu') && ps.muderiv + [~,yarg] = customfunc(argj*xscale,customparams); + else + yarg = customfunc(argj*xscale,customparams)+yoffset; + end + plot(argj,yarg,'-','LineWidth',2,'Color',ps.color(j,:)); + if isempty(ps.yyaxisLim) + ax.YLim = ylimtemp; + elseif all(isfinite(ps.yyaxisLim(j,:))) + ax.YLim = ps.yyaxisLim(j,:); + end + axis square + switch name + case 'mu' + ax.XTick = []; + clb = colorbar('southoutside','Position',[ax.Position(1),ax.Position(2)+0.04,ax.Position(3),0.03],'LineWidth',1); + if ps.darkmode + clb.Color = [1,1,1]; + end + case 'C' + if ps.funcxlabel + xlabel('k/k_0'); + end + end + if ps.darkmode + ax.Color = [0,0,0]; + ax.XColor = [1,1,1]; + ax.YColor = [1,1,1]; + end + ax.Colormap = data_cm; + if ps.funclabel + switch name + case 'mu' + if ps.muderiv + lab = "\mu_h'(c)"; + else + lab = '\mu_h(c)'; + end + case 'C' + lab = 'C_2(k)'; + end + tx = title(lab,'FontWeight','normal'); + if ps.darkmode + tx.Color = [1,1,1]; + end + end + end + if ps.label + tx = text(hfunc(1),ps.labelpos(1),ps.labelpos(2),['Iteration ',num2str(ind(i)-1)],'Units','normalized','HorizontalAlignment',ps.labelHorizontalAlignment); + if ps.darkmode + tx.Color = [1,1,1]; + end + end + set(findall(gcf,'-property','FontName'),'FontName','Arial'); + set(findall(gcf,'-property','FontWeight'),'FontWeight','normal'); + set(findall(gcf,'-property','FontSize'),'FontSize',ps.FontSize); + F = print('-RGBImage'); + writeVideo(vid,F); + delete(hfunc); + delete(hmodel); + if ps.label + delete(tx); + end +end +close(vid); + +if ps.save + varload.Properties.Writable = true; + varload.y = y; +end + +end + +function hOut = TextLocation(textString,varargin) + +l = legend(textString,varargin{:}); +t = annotation('textbox'); +t.String = textString; +t.Position = l.Position; +delete(l); +% t.LineStyle = 'None'; + +if nargout + hOut = t; +end +end From 4bd5f7c205e14fccadb2127b8f57c02253d15d4e Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Sat, 16 Jan 2021 18:39:10 -0500 Subject: [PATCH 143/149] update IP_DDFT, add loss in fgh mode --- solver/IP_DDFT.m | 2 ++ 1 file changed, 2 insertions(+) diff --git a/solver/IP_DDFT.m b/solver/IP_DDFT.m index 2e2317d..3117420 100644 --- a/solver/IP_DDFT.m +++ b/solver/IP_DDFT.m @@ -218,6 +218,8 @@ fval = []; exitflag = []; case 'fgh' + loss = @(y,ydata,~) MSE(y,ydata,prod(params.dx)); + lossHess = @(dy,~,~,~) MSE([],[],prod(params.dx),dy); switch nargout case 1 x_opt = IP(tdata,ydata,x_guess,meta,params, ... From b35cdaf2aee0e9b3eb595f54c9ecac1157d1afa1 Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Sat, 16 Jan 2021 18:39:28 -0500 Subject: [PATCH 144/149] update visualization, generate history movie, dark mode --- solver/DDFT_nucleation30_DILI.m | 20 +++++++++++++++++-- solver/DDFT_nucleation41.m | 35 +++++++++++++++++++++++---------- 2 files changed, 43 insertions(+), 12 deletions(-) diff --git a/solver/DDFT_nucleation30_DILI.m b/solver/DDFT_nucleation30_DILI.m index 0537d5d..5dcec72 100644 --- a/solver/DDFT_nucleation30_DILI.m +++ b/solver/DDFT_nucleation30_DILI.m @@ -101,7 +101,12 @@ options.logpdf = logpdf; [chain,result] = mcmc_DILI(options); else - f = figure('Position',[680 642 392 336]); + darkmode = true; + if darkmode + f = figure('Position',[680 642 392 336],'Color',[0,0,0],'InvertHardCopy','off'); + else + f = figure('Position',[680 642 392 336]); + end burnin = 100; p = 0.95; %confidence level xplot = linspace(0,5*k0,200)'; @@ -116,9 +121,20 @@ main = axes('Position',[0.18,0.2,0.6,0.7]); [hl,hp] = boundedline(xplot/k0,mu',[lower;upper].'); hl.LineWidth = 2; + hold on; + htruth = plot(xplot/k0,modelfunc(xplot),'--k'); xlabel('k/k_0'); ylabel('$\hat{C}_2(k)$','Interpreter','latex'); xlim([0,5]); + if darkmode + htruth.Color = [1,1,1]; + hp.FaceColor=hl.Color*0.4; + end + if darkmode + main.Color = [0,0,0]; + main.XColor = [1,1,1]; + main.YColor = [1,1,1]; + end ymin = min(ydata(:)); ymax = max(ydata(:)); @@ -131,5 +147,5 @@ set(findall(f,'-property','FontName'),'FontName','Arial'); set(findall(f,'-property','FontWeight'),'FontWeight','normal'); set(findall(f,'-property','FontSize'),'FontSize',13); - print(f,['C:\Users\zhbkl\Dropbox (MIT)\Research\Report 6\PaperIPExpand\DDFT_nucleation30_DILI'],'-dpng','-r500'); + % print(f,['C:\Users\zhbkl\Dropbox (MIT)\Research\Report 6\PaperIPExpand\DDFT_nucleation30_DILI'],'-dpng','-r500'); end diff --git a/solver/DDFT_nucleation41.m b/solver/DDFT_nucleation41.m index bb8c997..ce0b665 100644 --- a/solver/DDFT_nucleation41.m +++ b/solver/DDFT_nucleation41.m @@ -47,7 +47,7 @@ params.moreoptions = moreodeset('gmresTol',1e-5); -resultpath = [largedatapath,'DDFT_nucleation41.mat']; +resultpath = [largedatapath,'DDFT_nucleation41_ally.mat']; options = optimoptions('fminunc','OutputFcn', @(x,optimvalues,state) save_opt_history(x,optimvalues,state,resultpath)); options = optimoptions(options,'HessianFcn','objective','Algorithm','trust-region','MaxFunctionEvaluations',10000,'MaxIterations',10000); @@ -59,16 +59,31 @@ [x_opt,~,exitflag,params] = IP_DDFT(tdata,ydata,params,kernelSize,Cspace,options,x_guess,'Nmu',3,'discrete',true,'cutoff',k0); else modelfunc.C = @(k) exp(-(k-k0).^2/(2*alpha^2))*0.95; - modelfunc.mu = @(x) x - x.^2/2 + x.^3/3; + modelfunc.mu = @mu; Crange = [0,4]; arg.C = linspace(Crange(1),Crange(2),500); arg.mu = linspace(min(ydata(:)),max(ydata(:)),100); - history_production(resultpath,[1,11,36,58],modelfunc,arg,tdata-tdata(1),ydata,params,kernelSize,Cspace,... - 'IP_DDFT_arg',{'Nmu',3,'discrete',true,'cutoff',k0},'yyaxisLim',[-0.5,1.5;-1,1.2],... - 'k0',k0,'xlim',[min(ydata(:)),Crange(2)],'showModelSolution',true,... - 'legend',{{'$\hat{C_2}(k)$ (truth)','$\hat{C_2}(k)$','$\mu_h(\eta)$ (truth)','$\mu_h(\eta)$'},... - 'Orientation','horizontal','Position',[0.2051 0.001 0.7874 0.0566],'Interpreter','latex'},... - 'FontSize',13,'stparg',{0.05,[0.1,0.08],[0.08,0.04]}); - f = gcf; - f.Position = [680 368 588 610]; + % history_production(resultpath,[],modelfunc,arg,tdata-tdata(1),ydata,params,kernelSize,Cspace,... + % 'IP_DDFT_arg',{'Nmu',3,'discrete',true,'cutoff',k0},'yyaxisLim',[-0.5,1.5;0,2],... + % 'k0',k0,'xlim',[min(ydata(:)),Crange(2)],'showModelSolution',true,'offset',true,'muderiv',true,... + % 'legend',{{'$\hat{C_2}(k)$ (truth)','$\hat{C_2}(k)$','$\mu_h(\eta)$ (truth)','$\mu_h(\eta)$'},... + % 'Orientation','horizontal','Position',[0.2051 0.001 0.7874 0.0566],'Interpreter','latex'},... + % 'FontSize',13,'stparg',{0.05,[0.1,0.08],[0.08,0.04]}); + % f = gcf; + % f.Position = [680 368 588 610]; + + figure('Color',[0,0,0],'Position',[593 189 1036 610],'InvertHardCopy','off'); + mv = VideoWriter('DDFT_nucleation41','MPEG-4'); + mv.FrameRate = 1; + history_movie(resultpath,mv,[],modelfunc,arg,tdata-tdata(1),ydata,params,kernelSize,Cspace,... + 'yyaxisLim',[0.6,1.7;-0.2,1.2],'funcxlabel',false,'FontSize',14,... + 'visualizeArgs',{'edgeColor',[1,1,1],'edgeWidth',1,'colormap',colormap(gray)},... + 'k0',k0,'IP_DDFT_arg',{'Nmu',3,'discrete',true,'cutoff',k0},... + 'use_saved',true,'save',false,'muderiv',true,'offset',true,... + 'stparg',{[0.03,0.03],[0.05,0.15],0.08},'labelpos',[-0.3,1.6]); +end + +function [y,dy] = mu(x) + y = x - x.^2/2 + x.^3/3; + dy = 1 - x + x.^2; end From 730e6c8f29530d8d8ae67a9cd9b863daa940f987 Mon Sep 17 00:00:00 2001 From: Hongbo Date: Thu, 30 Dec 2021 01:49:22 -0500 Subject: [PATCH 145/149] add DDFT_nucleation42 created on bgs --- solver/DDFT_nucleation42_bgs.m | 80 ++++++++++++++++++++++++++++++++++ 1 file changed, 80 insertions(+) create mode 100644 solver/DDFT_nucleation42_bgs.m diff --git a/solver/DDFT_nucleation42_bgs.m b/solver/DDFT_nucleation42_bgs.m new file mode 100644 index 0000000..a3c46c4 --- /dev/null +++ b/solver/DDFT_nucleation42_bgs.m @@ -0,0 +1,80 @@ +%based on DDFT_nucleation41 +%change mu third order guess to 0 +addpath('../../CHACR/GIP') +runoptim = true; + +tic; +L = [5,5]; +N = [256,256]; +n = prod(N); + +params.N = N; +params.L = L; + +[k2,k] = formk(N,L); +k0 = 10; +alpha = 5; +params.C = exp(-(sqrt(k2)-k0).^2/(2*alpha^2))*0.95; + +%[t1,y1,params] = solver_DDFT([],[],params); +% +%xx = linspace(0,L(1),N(1)); +%yy = linspace(0,L(2),N(2)); +%[xx,yy] = ndgrid(xx,yy); +%center = L/2; +%radius = 0.06*L(1); +%thickness = 0.01*L(1); +%roi = roi_circle(xx,yy,center,radius,thickness); +% +%%nucleus +%y0 = y1(end,:)'; +%roi = roi(:); +%y02 = 0.045; +%rho = (y02*n - sum(roi.*y0)) / sum(1-roi); +%y0 = roi.*y0 + (1-roi)*rho; +% +%tspan2 = linspace(0,2.5,100); +%[t2,y2] = solver_DDFT(tspan2,y0,params); +% +%ind = 1:20:100; +%tdata = t2(ind); +%ydata = y2(ind,:); +%toc + + +kernelSize = 10; +Cspace = 'isotropic_hermite_scale'; +params.moreoptions = moreodeset('gmresTol',1e-5); + + +resultpath = [largedatapath,'DDFT_nucleation41.mat']; + +options = optimoptions('fminunc','OutputFcn', @(x,optimvalues,state) save_opt_history(x,optimvalues,state,resultpath)); +options = optimoptions(options,'HessianFcn','objective','Algorithm','trust-region','MaxFunctionEvaluations',10000,'MaxIterations',10000); + +x_guess = [zeros(1,kernelSize),0.5,0,-6]; +x_guess(1) = 0.1; + +if runoptim + [x_opt,~,exitflag,params] = IP_DDFT(tdata,ydata,params,kernelSize,Cspace,options,x_guess,'Nmu',3,'discrete',true,'cutoff',k0); +else + modelfunc.C = @(k) exp(-(k-k0).^2/(2*alpha^2))*0.95; + modelfunc.mu = @mu; + Crange = [0,4]; + arg.C = linspace(Crange(1),Crange(2),500); + arg.mu = linspace(min(ydata(:)),max(ydata(:)),100); + history_production(resultpath,[1,11,36,58],modelfunc,arg,tdata-tdata(1),ydata,params,kernelSize,Cspace,... + 'IP_DDFT_arg',{'Nmu',3,'discrete',true,'cutoff',k0},'yyaxisLim',[-0.5,1.5;0,2],... + 'k0',k0,'xlim',[min(ydata(:)),Crange(2)],'showModelSolution',true,...%'offset',true,'muderiv',true,... + 'legend',{{'$\hat{C_2}(k)$ (truth)','$\hat{C_2}(k)$','$\mu_h(\eta)$ (truth)','$\mu_h(\eta)$'},... + 'Orientation','horizontal','Position',[0.2051 0.001 0.7874 0.0566],'Interpreter','latex'},... + 'FontSize',13,'stparg',{0.05,[0.1,0.08],[0.08,0.04]}); + f = gcf; + f.Position = [680 368 588 610]; +end + +function [y,dy] = mu(x) + y = x - x.^2/2 + x.^3/3; + dy = 1 - x + x.^2; +end + From 231476ee54e10a5477c3173c12542505f851468e Mon Sep 17 00:00:00 2001 From: Hongbo Zhao Date: Thu, 30 Dec 2021 02:41:58 -0500 Subject: [PATCH 146/149] add files on workstation --- solver/DDFT.m | 14 +++- solver/DDFT_nlin.m | 16 ++++- solver/DDFT_nucleation30_DILI.m | 6 +- solver/DDFT_nucleation34.m | 3 + solver/DDFT_nucleation40.m | 2 + solver/DDFT_nucleation42.m | 68 ++++++++++++++++++ solver/DDFT_nucleation43.m | 68 ++++++++++++++++++ solver/IP_DDFT_debug.m | 4 +- solver/bd_test.m | 18 +++++ solver/machta.m | 21 ++++++ solver/turing_ss_2_params.m | 118 ++++++++++++++++++++++++++++++++ solver/turing_video.m | 68 ++++++++++++++++++ 12 files changed, 396 insertions(+), 10 deletions(-) create mode 100644 solver/DDFT_nucleation42.m create mode 100644 solver/DDFT_nucleation43.m create mode 100644 solver/bd_test.m create mode 100644 solver/machta.m create mode 100644 solver/turing_ss_2_params.m create mode 100644 solver/turing_video.m diff --git a/solver/DDFT.m b/solver/DDFT.m index 357c076..496c57a 100644 --- a/solver/DDFT.m +++ b/solver/DDFT.m @@ -1,6 +1,6 @@ %parameter search -L = [5,5]; -N = [256,256]/2; +L = [5,5]*2; +N = [256,256]*2; n = prod(N); n0 = 0.07; sigma = 0.01; @@ -9,6 +9,8 @@ n0 = n0 + sigma*randn(N); y0 = fftn(n0); y0 = y0(:); +% y00 = y0(1); +% y0(1) = []; % %use image? % im = imread('cameraman.tif'); @@ -20,6 +22,8 @@ [k2,k] = formk(N,L); k2 = k2(:); +% k2(1) = []; + kind1 = k{1}; kind2 = k{2}; [kind1,kind2] = ndgrid(kind1(:),kind2(:)); theta = angle(kind1+i*kind2); @@ -35,9 +39,13 @@ J = -k2.*(-C22); tspan = linspace(0,0.14,100); -tspan = [0,1.1]; +tspan = [0,1.7]; +tspan = linspace(0,1.07,100); % tspan = [0,0.14]; options = odeset('AbsTol',1e-3); [tout,yout] = odeimex(@(t,y) DDFT_nlin(t,y,k2,N),J,tspan,y0); +% Nt = 10000; +% h = (tspan(end)-tspan(1))/Nt; +% [tout,yout] = odeimexez(@(t,y) DDFT_nlin(t,y,k2,N),J,h,Nt,y0,[],1:100:Nt); figure; k2real(yout(:,end),N); diff --git a/solver/DDFT_nlin.m b/solver/DDFT_nlin.m index bb6730b..53cf4b4 100644 --- a/solver/DDFT_nlin.m +++ b/solver/DDFT_nlin.m @@ -1,5 +1,17 @@ -function dy = DDFT_nlin(t,y,k2,N) +function dy = DDFT_nlin(t,y,k2,N,y00) + if nargin > 4 && ~isempty(y00) + %k=0 component is omitted + k0flag = true; + y = [y00;y(:)]; + else + k0flag = false; + end y = real(ifftn(reshape(y,N))); + % mu = y - y.^2/2 + y.^3/3; mu = log(1+y); - dy = -k2 .* reshape(fftn(mu,N),[],1); + fmu = reshape(fftn(mu,N),[],1); + if k0flag + fmu(1) = []; + end + dy = -k2 .* fmu; end diff --git a/solver/DDFT_nucleation30_DILI.m b/solver/DDFT_nucleation30_DILI.m index 5dcec72..fe2d214 100644 --- a/solver/DDFT_nucleation30_DILI.m +++ b/solver/DDFT_nucleation30_DILI.m @@ -1,7 +1,7 @@ %based on DDFT_nucleation29 %5 snapshots. kernelSize = 10 addpath('../../CHACR/GIP') -rundili = false; +rundili = true; tic; L = [5,5]; @@ -47,7 +47,7 @@ kernelSize = 10; Cspace = 'user'; -params.moreoptions = moreodeset('gmresTol',1e-5); +%params.moreoptions = moreodeset('gmresTol',1e-5); %basis function here is hermitefunction scaled by 1/sqrt(eigenvalue), where eigenvalue is (2n+1) as in x^2 y(x) - y''_n(x) = (2n+1) y_n(x) % customfunc = @(x) hermitefunction(x/k0,kernelSize,[],1) ./ sqrt(1:2:(2*kernelSize-1)); @@ -61,7 +61,7 @@ k = sqrt(k2); params.Csensval = reshape(customfunc(k(:)), [size(k),kernelSize]); -% logpdf = @(x) IP_DDFT(tdata,ydata,params,kernelSize,Cspace,[],x,'Nmu',0,'discrete',true,'cutoff',k0,'mode','eval'); +logpdf = @(x) IP_DDFT(tdata,ydata,params,kernelSize,Cspace,[],x,'Nmu',0,'discrete',true,'cutoff',k0,'mode','fgh'); % name = 'DDFT_nucleation30_DILI_MAP'; % resultpath = [largedatapath,name,'.mat']; diff --git a/solver/DDFT_nucleation34.m b/solver/DDFT_nucleation34.m index 6a1a58b..bc1b0a6 100644 --- a/solver/DDFT_nucleation34.m +++ b/solver/DDFT_nucleation34.m @@ -55,6 +55,9 @@ if runoptim x_guess = [0,0,0.5,0,-3]; [x_opt,~,exitflag,params] = IP_DDFT(tdata,ydata,params,kernelSize,Cspace,options,x_guess,'Nmu',3,'discrete',true,'cutoff',k0); + %below is modified on workstation + x_guess = [0,-9,0.5,0,-3]; + [x_opt,~,exitflag,params] = IP_DDFT(tdata,ydata,params,kernelSize,Cspace,options,x_guess,'Nmu',3,'discrete',true,'cutoff',1); else modelfunc.C = @(k) exp(-(k-k0).^2/(2*alpha^2))*0.95; modelfunc.mu = @(x) x - x.^2/2 + x.^3/3; diff --git a/solver/DDFT_nucleation40.m b/solver/DDFT_nucleation40.m index d2d8800..7840e53 100644 --- a/solver/DDFT_nucleation40.m +++ b/solver/DDFT_nucleation40.m @@ -58,6 +58,8 @@ exitflag = 5; while (exitflag==5) [x_opt,~,exitflag,params] = IP_DDFT(tdata,ydata,params,kernelSize,Cspace,options,x_opt,'Nmu',0,'discrete',true); + %below is used by workstation + [x_opt,~,exitflag] = IP_DDFT(tdata,ydata,params,kernelSize,Cspace,options,x_opt,'Nmu',0,'discrete',true); end else modelfunc.C = @(k) exp(-(k-k0).^2/(2*alpha^2))*0.95; diff --git a/solver/DDFT_nucleation42.m b/solver/DDFT_nucleation42.m new file mode 100644 index 0000000..f157895 --- /dev/null +++ b/solver/DDFT_nucleation42.m @@ -0,0 +1,68 @@ +%based on DDFT_nucleation32 +%change x_guess the first coeff for mu to 0.6 from 0.5 +addpath('../../CHACR/GIP') +runoptim = true; + +tic; +L = [5,5]; +N = [256,256]; +n = prod(N); + +params.N = N; +params.L = L; + +[k2,k] = formk(N,L); +k0 = 10; +alpha = 5; +params.C = exp(-(sqrt(k2)-k0).^2/(2*alpha^2))*0.95; + +[t1,y1,params] = solver_DDFT([],[],params); + +xx = linspace(0,L(1),N(1)); +yy = linspace(0,L(2),N(2)); +[xx,yy] = ndgrid(xx,yy); +center = L/2; +radius = 0.06*L(1); +thickness = 0.01*L(1); +roi = roi_circle(xx,yy,center,radius,thickness); + +%nucleus +y0 = y1(end,:)'; +roi = roi(:); +y02 = 0.045; +rho = (y02*n - sum(roi.*y0)) / sum(1-roi); +y0 = roi.*y0 + (1-roi)*rho; + +tspan2 = linspace(0,2.5,100); +[t2,y2] = solver_DDFT(tspan2,y0,params); + +ind = 1:20:100; +tdata = t2(ind); +ydata = y2(ind,:); +toc + + +kernelSize = 10; +Cspace = 'isotropic_hermite_scale'; +params.moreoptions = moreodeset('gmresTol',1e-5); + + +resultpath = [largedatapath,'DDFT_nucleation42.mat']; + +options = optimoptions('fminunc','OutputFcn', @(x,optimvalues,state) save_opt_history(x,optimvalues,state,resultpath)); +options = optimoptions(options,'HessianFcn','objective','Algorithm','trust-region','MaxFunctionEvaluations',10000,'MaxIterations',10000); + +x_guess = [zeros(1,kernelSize),0.6,0,-3]; + +if runoptim + [x_opt,~,exitflag,params] = IP_DDFT(tdata,ydata,params,kernelSize,Cspace,options,x_guess,'Nmu',3,'discrete',true,'cutoff',k0); +else + modelfunc.C = @(k) exp(-(k-k0).^2/(2*alpha^2))*0.95; + modelfunc.mu = @(x) x - x.^2/2 + x.^3/3; + Crange = [0,4]; + arg.C = linspace(Crange(1),Crange(2),500); + arg.mu = linspace(min(ydata(:)),max(ydata(:)),100); + history_production(resultpath,[1,10,20,30,40,65],modelfunc,arg,tdata-tdata(1),ydata,params,kernelSize,Cspace,'IP_DDFT_arg',{'Nmu',3,'discrete',true,'cutoff',k0},'yyaxisLim',[-0.5,1.5;-1,1.2],'k0',k0,'xlim',Crange,'showModelSolution',false); + % f = gcf; + % f.Position = [680 337 522 641]; +end diff --git a/solver/DDFT_nucleation43.m b/solver/DDFT_nucleation43.m new file mode 100644 index 0000000..4af2892 --- /dev/null +++ b/solver/DDFT_nucleation43.m @@ -0,0 +1,68 @@ +%based on DDFT_nucleation32 +%change x_guess the first coeff for mu to 0.4 from 0.5 +addpath('../../CHACR/GIP') +runoptim = true; + +tic; +L = [5,5]; +N = [256,256]; +n = prod(N); + +params.N = N; +params.L = L; + +[k2,k] = formk(N,L); +k0 = 10; +alpha = 5; +params.C = exp(-(sqrt(k2)-k0).^2/(2*alpha^2))*0.95; + +[t1,y1,params] = solver_DDFT([],[],params); + +xx = linspace(0,L(1),N(1)); +yy = linspace(0,L(2),N(2)); +[xx,yy] = ndgrid(xx,yy); +center = L/2; +radius = 0.06*L(1); +thickness = 0.01*L(1); +roi = roi_circle(xx,yy,center,radius,thickness); + +%nucleus +y0 = y1(end,:)'; +roi = roi(:); +y02 = 0.045; +rho = (y02*n - sum(roi.*y0)) / sum(1-roi); +y0 = roi.*y0 + (1-roi)*rho; + +tspan2 = linspace(0,2.5,100); +[t2,y2] = solver_DDFT(tspan2,y0,params); + +ind = 1:20:100; +tdata = t2(ind); +ydata = y2(ind,:); +toc + + +kernelSize = 10; +Cspace = 'isotropic_hermite_scale'; +params.moreoptions = moreodeset('gmresTol',1e-5); + + +resultpath = [largedatapath,'DDFT_nucleation43.mat']; + +options = optimoptions('fminunc','OutputFcn', @(x,optimvalues,state) save_opt_history(x,optimvalues,state,resultpath)); +options = optimoptions(options,'HessianFcn','objective','Algorithm','trust-region','MaxFunctionEvaluations',10000,'MaxIterations',10000); + +x_guess = [zeros(1,kernelSize),0.4,0,-3]; + +if runoptim + [x_opt,~,exitflag,params] = IP_DDFT(tdata,ydata,params,kernelSize,Cspace,options,x_guess,'Nmu',3,'discrete',true,'cutoff',k0); +else + modelfunc.C = @(k) exp(-(k-k0).^2/(2*alpha^2))*0.95; + modelfunc.mu = @(x) x - x.^2/2 + x.^3/3; + Crange = [0,4]; + arg.C = linspace(Crange(1),Crange(2),500); + arg.mu = linspace(min(ydata(:)),max(ydata(:)),100); + history_production(resultpath,[1,10,20,30,40,65],modelfunc,arg,tdata-tdata(1),ydata,params,kernelSize,Cspace,'IP_DDFT_arg',{'Nmu',3,'discrete',true,'cutoff',k0},'yyaxisLim',[-0.5,1.5;-1,1.2],'k0',k0,'xlim',Crange,'showModelSolution',false); + % f = gcf; + % f.Position = [680 337 522 641]; +end diff --git a/solver/IP_DDFT_debug.m b/solver/IP_DDFT_debug.m index 66f1bcf..46b9653 100644 --- a/solver/IP_DDFT_debug.m +++ b/solver/IP_DDFT_debug.m @@ -37,12 +37,12 @@ val = zeros(1,Nalpha); gradient = zeros(Nalpha,NC); -for i = 1:length(alpha) +parfor i = 1:length(alpha) [val(i),gradient(i,:)] = IP(tdata,ydata,x_opt*alpha(i),meta,params, ... @(tdata,y0,FSA,meta,params) forwardSolver(tdata,y0,FSA,meta,params,tspan), ... @adjointSolver, ... loss,lossHess, ... - @(name,xparam,params) assign(name,xparam,params,Cspace,kernelSize)); + @(name,xparam,params) assign(name,xparam,params,Cspace,kernelSize)); disp(i); end end diff --git a/solver/bd_test.m b/solver/bd_test.m new file mode 100644 index 0000000..06f3fa6 --- /dev/null +++ b/solver/bd_test.m @@ -0,0 +1,18 @@ +D = [0.02,0.5]; +A1 = [0.08,-0.08;0.1,0]; +A2 = -[0.03,0.08]; +mat_ss = matfile('/home/hbozhao/Dropbox (MIT)/2.168 Project/Data/turing_ss'); +A1_ss = mean(mat_ss.A1,1); +A1lb = [-0.5,A1_ss(3);-0.5,A1_ss(4)]; +A1ub = [1.5,A1_ss(3);1.5,A1_ss(4)]; +Anorm = norm(A1+diag(A2),inf); + +ind = 0; +while ind < 10000 + A1new = A1lb + (A1ub-A1lb).*rand(2); + Anew = A1new+diag(A2); + if LSA(Anew,D) && (norm(Anew,inf)<5*Anorm) + ind = ind+1; + Alist(ind,:) = reshape(A1new,1,[]); + end +end diff --git a/solver/machta.m b/solver/machta.m new file mode 100644 index 0000000..d30ebbe --- /dev/null +++ b/solver/machta.m @@ -0,0 +1,21 @@ +n = 7; +theta = ones(1,n)/n; + +ntime = n; +rholen = n^2; +theta = padarray(theta,[0,(rholen-n)/2],0,'both'); +n = rholen; +center = ceil(rholen/2); +rho = zeros(ntime,rholen); +drho = zeros(ntime,rholen,n); +hessian_t = zeros(n,n,ntime); +rho(1,center) = 1; +for i = 2:ntime + rho(i,:) = conv(rho(i-1,:),theta,'same'); + for j = 1:n + drho(i,:,j) = conv(drho(i-1,:,j),theta,'same') + circshift(rho(i-1,:),j); + end + drho_t = squeeze(drho(i,:,:)); + hessian_t(:,:,i) = drho_t' * drho_t; +end +[V,D] = eig(hessian_t(:,:,end)); diff --git a/solver/turing_ss_2_params.m b/solver/turing_ss_2_params.m new file mode 100644 index 0000000..fd766cc --- /dev/null +++ b/solver/turing_ss_2_params.m @@ -0,0 +1,118 @@ +%parameter search +L = [60,60]/2; +N = [256,256]/2; +n = prod(N); +D = [0.02,0.5]; +b = [0.04,-0.15]; +A1 = [0.08,-0.08;0.1,0]; +A2 = -[0.03,0.08]; +lb = [0,0]; +ub = [0.2,0.5]; +u0 = 5; +v0 = 5; +sigma = [0.01,0.01]; +mat_ss = matfile('/home/hbozhao/Dropbox (MIT)/2.168 Project/Data/turing_ss'); +A1_ss = mean(mat_ss.A1,1); +A1lb = [-0.5,A1_ss(3);-0.5,A1_ss(4)]; +A1ub = [1.5,A1_ss(3);1.5,A1_ss(4)]; + +rng(1); +reinitialize = true; +if ~reinitialize + u0 = u0 + sigma(1)*randn(N); + v0 = v0 + sigma(2)*randn(N); + yu0 = fftn(u0); + yv0 = fftn(v0); + y0 = [yu0(:); yv0(:)]; +end + +[k2,k] = formk(N,L); + +JD = -k2(:)*D; +J = JD(:) + reshape(ones(n,1)*A2,[],1); + + +saveresult = true; +if saveresult + filepath = '/home/hbozhao/Dropbox (MIT)/2.168 Project/Data/turing_ss_2_params'; + mat = matfile(filepath,'Writable',true); + mat.A1 = []; + mat.y = []; +end +Nbatch = 250; +nall = 10000; +%Nbatch = 2; +%nall = 16; +nbatch = nall/(Nbatch*4); %must be integer + +Nt = 10000; +dt = 1; +outputstep = Nt; +thresh(1) = n*1e-5; %threshold for L2 norm of gradient +thresh(2) = 2;%about n*1e-3/8; %threshold for L2 norm of time derivative +termination = @(t,y,yp) event_gradient_ss(t,y,yp,k2(:),thresh); +if saveresult + transform = @(y) [reshape(real(ifftn(reshape(y(1:n),N))),[],1);reshape(real(ifftn(reshape(y(n+(1:n)),N))),[],1)]; +else + transform = []; +end +Anorm = norm(A1+diag(A2),inf); +A1 = reshape(A1,1,[]); +nparams = length(A1); +sigma = 0.05*eye(nparams); + +rungpu = false; + +tic; +for batch = 1:nbatch + ybatchall = zeros(4,Nbatch,N(1),N(2),length(outputstep),2); + A1batchall = zeros(4,Nbatch,nparams); + parfor process = 1:4 + ind = 0; + ybatch = zeros(Nbatch,N(1),N(2),length(outputstep),2); + A1batch = zeros(Nbatch,nparams); + while ind < Nbatch + A1new = A1lb + (A1ub-A1lb).*rand(2); + Anew = A1new+diag(A2); + if LSA(Anew,D) && (norm(Anew,inf)<5*Anorm) + fnlin = @(t,y) turing_nlin_bd(t,y,A1new,b,lb,ub,N); + if reinitialize + y0 = [reshape(fftn(u0 + sigma(1)*randn(N)),[],1); reshape(fftn(v0 + sigma(2)*randn(N)),[],1)]; + end + [~,y,et] = odeimexez(fnlin,J,dt,Nt,y0,[],outputstep,termination,rungpu,transform); + if et ~= 1 + A1 = reshape(A1new,1,[]); + ind = ind + 1; + ybatch(ind,:,:,:,:) = permute(reshape(y,N(1),N(2),2,[]),[1,2,4,3]); + A1batch(ind,:) = A1; + end + end + end + A1batchall(process,:,:) = A1batch; + ybatchall(process,:,:,:,:,:) = ybatch; + end + if saveresult + if batch == 1 + mat.A1 = reshape(A1batchall,[],nparams); + mat.y = reshape(ybatchall,[],N(1),N(2),length(outputstep),2); + else + range = (batch-1)*Nbatch*4+(1:Nbatch*4); + mat.A1(range,:) = reshape(A1batchall,[],nparams); + mat.y(range,:,:,:,:) = reshape(ybatchall,[],N(1),N(2),length(outputstep),2); + end + runtime=toc; + disp(['batch ',num2str(batch),' of size ',num2str(Nbatch*4),' saved: Elapsed time (min): ',num2str(runtime/60),' ETA (min): ',num2str(runtime/60*(nbatch-batch)/batch)]); + end +end + +%plot 9 random realizations +% figure; +% for i=1:9 +% subplot(3,3,i); +% imagesc(squeeze(mat.y(randi(nall),1:N(1),1:N(2),length(outputstep),1))); +% colormap gray; +% axis equal; +% ax = gca; +% ax.XTick=[]; ax.YTick=[]; +% end +% saveas(gcf,[filepath,'_sample'],'png'); diff --git a/solver/turing_video.m b/solver/turing_video.m new file mode 100644 index 0000000..544c8e6 --- /dev/null +++ b/solver/turing_video.m @@ -0,0 +1,68 @@ +%parameter search +L = [60,60]/2; +N = [256,256]/2; +n = prod(N); +D = [0.02,0.5]; +b = [0.04,-0.15]; +A1 = [0.08,-0.08;0.1,0]; +A2 = -[0.03,0.08]; +lb = [0,0]; +ub = [0.2,0.5]; +u0 = 5; +v0 = 5; +sigma = [0.01,0.01]; +A1lb = [-0.5,-1.5;-0.5,-1.5]; +A1ub = [1.5,0.5;1.5,0.5]; +mat = matfile('/home/hbozhao/Dropbox (MIT)/2.168 Project/Data/turing_ss.mat'); + +rng(1); +u0 = u0 + sigma(1)*randn(N); +v0 = v0 + sigma(2)*randn(N); +yu0 = fftn(u0); +yv0 = fftn(v0); +y0 = [yu0(:); yv0(:)]; + +[k2,k] = formk(N,L); + +JD = -k2(:)*D; +J = JD(:) + reshape(ones(n,1)*A2,[],1); + +rungpu = false; +Nt = 1000; +dt = 1; +outputstep = floor(linspace(1,Nt,300)); +transform = @(y) [reshape(real(ifftn(reshape(y(1:n),N))),[],1);reshape(real(ifftn(reshape(y(n+(1:n)),N))),[],1)]; + +for ind = 2%1:2 + switch ind + case 1 + A1 = [0.08,-0.08;0.1,0]; + case 2 + A1 = reshape(mat.A1(1021,1:4),2,2); + end + fnlin = @(t,y) turing_nlin_bd(t,y,A1,b,lb,ub,N); + [t,y,et] = odeimexez(fnlin,J,dt,Nt,y0,[],outputstep,[],rungpu,transform); + y = reshape(y,N(1),N(2),2,[]); + ymax = max(max(max(y,[],1),[],2),[],4); + + video_file = ['/home/hbozhao/Dropbox (MIT)/MIT Courses/2.168/2.168 Project/Final/movie_',num2str(ind)]; + myMovie = VideoWriter(video_file); + set(myMovie,'FrameRate',30); + open(myMovie); + for i = 1:length(t) + for j = 1:2 + subplot(1,2,j) + imagesc(y(:,:,j,i)); + a = gca; + a.XTick = []; a.YTick = []; + axis tight; axis equal; + a.CLim = [0,ymax(j)]; + colormap('gray') + colorbar; + end + F = print('-RGBImage'); + writeVideo(myMovie,F); + delete(findall(gcf,'Type','Axes')); + end + close(myMovie); +end From 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