Question

I was trying to understand how to store a band matrix, I found an example in the book “C++ and Object Oriented Numeric Computing” but I cannot figure out what’s the purpose of the line bda[i] += P; and this also gives me problems when trying to print the band matrix. Here it is:

int N = 5; //Matrix of NxN
int P = 1; //Left bandwidth
int R = 2; //Right bandwidth

//Matrix A
double A[5][5] = { { 1, 6, 10, 0, 0 },
        { 13, 2, 0, 11, 0 },
        { 0, 14, 3, 8, 12 },
        { 0, 0, 0, 4, 9 },
        { 0, 0, 0, 16, 5 } };

//Allocate memory for rows
double** bda = new double*[N];
for (int i = 0; i < N; i++) {
    bda[i] = new double[P + R + 1]; //Allocate memory for cols
    bda[i] += P; //What's the purpose of this?
}

Answer 1

This is used for a compact way to store a matrix that has P nonzero diagonals to the left of the main diagonal, and R nonzero diagonals to the right, with all other elements being zero. For each row, we only allocate space for the P+R+1 elements around the main diagonal.

The bda[i] += P line makes bda[i] point to an element on the main diagonal. This can make it more convenient to use the matrix: bda[i][0] is on the main diagonal for every i, bda[i][1] is on the first diagonal to the right, bda[i][-1] is on the first diagonal to the left, etc. This allows you to find elements on the main diagonal or near it without having to add P each time. Whether this is helpful depends on how you use the matrix.

Note that if you do this, you will need to subtract P from bda[i] before you delete[] it.