compute error from linear system - extract every column - c++

Question

I want to compute the error in linear least squares method.
I have matrices A,B and X. (AX=B).
Sizes are : A(NxN) , B(NxNRHS) , X(N,NRHS) ,where NRHS is number of right hand side.
The error is computed as sqrt(sum(B-AX)).
But I must take into account every column of B and X in order to make the substraction.
I must substract B[i]-A[..]X[i] -> where i is every column of B and X.
I can't figure how to do it ,hence how to extract every column.I can't find the right indices for B and X matrices (I think) ,because I must go beyond whole A matrix and only beyond every column of B and X.
I am doing something like this (using column major order):
int N=128;
int NRHS =1;
int Asize=N*N;
int Bsize=N*NRHS;
int Xsize=N*NRHS;
A=(double*)malloc(Asize*sizeof(double));
B=(double*)malloc(Bsize*sizeof(double));
X=(double*)malloc(Xsize*sizeof(double));
...
for(int i = 0; i < N; i++)
{
for (int j=0;j<NRHS; j++){
diff[i+j*N] = fabs(B[i+j*N] - A[i+j*N]*X[i+j*N]);
abs_error=sqrt(sums(diff,N));
}
}
I thought of adding some statement using the modulo operator but I couldn't figure.
sums is just a function which gives the sum of an array where the second argument is the number of elements.

Answer 1

You could first do a matrix multiplication of A and X using loops.
Then you could write another 2 loops to compute the difference (B - AX). This would simply your problem.
Edit
After you compute the product of A and X, assuming that you store the product in a variable named AX,the following code will give you the difference between corresponding elements.
differenceMatrix = (double*)malloc(Bsize*sizeof(double));
for(int i = 0; i < N; i++)
{
for (int j = 0; j < NRHS; j++){
differenceMatrix[i+j*N] = fabs(B[i+j*N] - AX[i+j*N]);
}
}
Each column of the differenceMatrix contains the difference between corresponding elements.
Edit
To obtain the sum of difference of each column
double sumOfDifferencePerColumn;
for(int i = 0; i < N; i++)
{
sumOfDifferencePerColumn = 0.0;
for (int j = 0; j < NRHS; j++){
sumOfDifferencePerColumn += ( fabs(B[i+j*N] - AX[i+j*N]) );
}
// add code to take square root or use the sum of difference of each column
}