Unexpected result with cblas_dgemv

Question

I have a question regarding cblas_dgemv. I am trying to understand how it works. And what I am possibly doing wrong. I have an array Matrix and then I try to read that matrix RowMajor and ColumnMajor.

I am getting the expected result in the RowMajor Case; [6, 2, 4, 6]'.

However for the ColMajor, I am getting [-7, 3, 0, 5]' when the answer should be [6, 3, 2, 3]'

Here is my code. I am using Intel MKL.

#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <mkl.h>


#define NCols 5
#define Nrows 4

double A[] = { 8, 4, 7, 3, 5, 1, 1, 3, 2, 1, 2, 3, 2, 0, 1, 1 , 2, 3, 4, 1};

double x[] = { -1, 2, -1, 1, 2 };

double y[Nrows];
double alpha = 1.0, beta = 0.0;
char tbuf[1024];
int main() {
    int i, j;

    // Print original matrix

    // y = Ax
    cblas_dgemv(CblasRowMajor, CblasNoTrans, Nrows, NCols, alpha, A, NCols, x, 1, beta, y, 1);
    // Print resulting vector
    for (j = 0; j < Nrows; j++) {
        printf(" %f\n", y[j]);
    }

    cblas_dgemv(CblasColMajor, CblasNoTrans, Nrows, NCols, alpha, A, NCols, x, 1, beta, y, 1);
    // Print resulting vector
    for (j = 0; j < Nrows; j++) {
        printf(" %f\n", y[j]);
    }

    return 0;
}

Answer 1

The issue is on the lda. From the reference we get that

lda: The size of the first dimension of matrix A

The CblasRowMajor and CblasColMajor describe the memory storage sequence of a two dimensional matrix.

The CblasRowMajor storage of a matrix A(nrow,ncol) means that first are stored the ncol values of the first row of matrix A, then the ncol values of second row of A and so on.

The CblasColMajor storage of a matrix A(nrow,ncol) means that first are stored the nrow values of the first column of matrix A, then the nrow values of second column of A and so on.

So in CblasRowMajor storage the LDA (first dimension of matrix A) is the ncol while in CblasColMajor the nrow.

In your example you just have to change lda of the second cblas_dgemv

cblas_dgemv(CblasColMajor, CblasNoTrans, Nrows, NCols, alpha, A, Nrows, x, 1, beta, y, 1);