Class 1 - Monday, January 23

• Set up C++ environment
• Compile "Hello World"

Variables

Arrays

Static allocation when array size is known at compile time

const int N = 5;

double x[N];
for (int i = 0; i < N; i++)
   x[i] = i;

Loops

Conditionals

Scoping

What is the output of this code?

double a = 5;
for (int i = 0; i < 10; i++) {
   double a = 10+i;
}
cout << a << endl;

Functions

Assignment 1

Class 2 - Monday, January 30

• File reading/writing
• Equation solvers, Cholesky decomposition

GitHub Classroom

• Navigate to Files Input Output on GitHub Classroom.
• Clone the repository into git clone <HTTPS copied from GitHub> using the handy-dandy GitHub tool of your choice.
• Move to and print directory to check (e.g., in PowerShell). cd, dir
• Open Local Folder in Visual Studio.
• Build All! (to make your compiled C++ executable): Ctrl+Shift+B

Demo

• basic stuff #include <iostream>
• read/write files #include <ifstream>
• help with characters #include <string>

File reading

Dynamically allocated matrix storage and read from file:

• Dynamically allocate storage during run time (do not know N at compile time)

double *A = new double[N*N];

• Read N and filename from external file

string filename = "filename.txt";
ifstream infile(filename);

• error checking!!!!!! (especially important for file reading / writing, dividing by zero, etc.)

if (infile.fail()) {
   cerr << "error opening file " << filename << endl;
   return -1;
}

• Move across the rows, but store by the column:

for (int r = 0; r < N; r++)
   for (int c = 0; c < N; c++) {
      infile >> A[N*c + r];
   }
}

Note: infile was defined by the ifstream. Similar to cin.

• Need a delete for every new

delete [] A;

Note: if pointer to a variable: delete A deletes only pointer to beginning of array. Note: if pointer to an array: delete [] A deletes all of memory allocation of the array.

Alternative reading in

Alternative methods other than cout and argv:

• look to your main file!

int main (int argc, const char **argv) {
   int N;
         
   // argv[0] program name
   // argv[1] inputs N
   // argv[2] inputs filename
   if (argc < 3) {
      cerr << "insufficient inputs: requires 2 args" << endl;
      return -1;
   }
   
   N = atoi(argv[1]);
   string infilename = argv[2];
   
   //
   //
}

File writing

Writing to a file ofstream v. ifstream

• add a new argv[3] with outfilename
• name your variable: string outfilename = argv[3]
• read in the file: ofstream(outfilename)
• error check!!

if (outfile.fail()) {
   cerr << "error opening file " << outfilename << endl;
   return -1;
}

• write out the files:

for (int r = 0; r < N; r++)
   for (int c = 0; c < N; c++) {
      outfile << A[N*c + r] << ' ';
   }
}

Assignment

Cholesky Decomposition:

Ax = b
A = L L^T // Factorization
L L^T x = b
y = L^T x // Backward substitution
Ly = b // Forward substitution

• Cholesky decomposition can be used to solve $Ax = b$
• where $L$ is a lower triangular matrix (with real and positive diagonal entries and $A$ is symmetric, positive-definite)
• So $L$ represents the upper and lower triangles where everything else is zero.
• $Ly = b$ can be solved for $y$ by forward substitution. $Lx = y$ can be solved for $x$ by backward substitution. these two halves of repeated substitutions can be coded easily.
• Be careful of the many zeroes! This is slow and counts as an operation in C++. You can find solvers to exploit sparsity, symmetry, bandwidth, etc.
• Direct solvers and iterative solvers depend on the number of dofs. Topic for future assignment
• OpenSees uses third party libraries for its solvers.

\begin{figure}[!htbp] \centering \includegraphics[width=1.0\textwidth]{Figs/Assignment 2.PNG} \caption{\label{fig:frog}Some stuff about Cholesky factorization.} \end{figure}

Questions

• Does the memory reset upon shutdown? yes
• Statically allocated arrays do not need to be "freed" (i.e., deleted); e.g., double B[100*100]. Can see this in size of compiled program
• Can you get the length from the file? Yes, perhaps using a "scan" method, but in C++ you often define the length explicitly, especially if you already know the length of the number of values you want to read. For example, first line of the .txt file can be the length.
• ifstream Reads file one value by one value and skipping white space.
• Inputted text file can be relative (e.g., using ../../filename.txt)
• ofstream makes new file or overrides existing file
• .json is a nice way to read/write files, check out: https://github.com/nlohmann/json Topic for future session
• Many solvers available.
• In julia, there's ways to see whether it's column major. may be something similar in c++ (e.g., via #define, operator overloading, inline functions, macros).
• #include as you said is used to include a file before the actual compilation. #define is used to define a Macro that is replaced by its value just before compilation.
• Make sure you initialize your data to all zeros (because you never know what's already there to start, could be junk).
• Initialization

// Defaut Initialization of a arbitrary object   
int i{};                // i becomes 0
std::string s{};        // s becomes ""
std::vector<float> v{}; // v becomes an empty vector
double d{};             // d becomes 0.0

\begin{figure}[!htbp] \centering \includegraphics[width=0.3\textwidth]{Figs/Capture.PNG} \caption{\label{fig:frog}iterative (purple) v. direct (red) solvers.} \end{figure}

Class 3 - Monday, February 6

• Basic command line parser
• BennyFrame 1.0 assignment
• BennyFrame 1.0 input and output file formats
• Read input file
• Store data in 1D arrays
• Multiple load cases

Questions

• Null pointers, why initialize to null (0)
• Garbage collections, memory leaks, dangling pointers
• How to deal with mixed input types, e.g., strings and numbers