DGEMM and DGEMV give different results - c

Question

I want to implement the following equation in C:
C[l,q,m] = A[m,q,k] * B[k,l]
where the repeated index k is being summed over.
I implemented this in three ways:
Naive implementation with loops
Using the BLAS routine DGEMV (matrix-vector multiplication)
Using the BLAS routine DGEMM (matrix-matrix multiplication)
This is the minimal not-working code:
#include <stdio.h>
#include <stdint.h>
#include <stdlib.h>
#include <string.h>
#include <cblas.h>
void main()
{
const size_t n = 3;
const size_t n2 = n*n;
const size_t n3 = n*n*n;
/* Fill rank 3 tensor with random numbers */
double a[n3];
for (size_t i = 0; i < n3; i++) {
a[i] = (double) rand() / RAND_MAX;
}
/* Fill matrix with random numbers */
double b[n2];
for (size_t i = 0; i < n2; i++) {
b[i] = (double) rand() / RAND_MAX;
}
/* All loops */
double c_exact[n3];
memset(c_exact, 0, n3 * sizeof(double));
for (size_t l = 0; l < n; l++) {
for (size_t q = 0; q < n; q++) {
for (size_t m = 0; m < n; m++) {
for (size_t k = 0; k < n; k++) {
c_exact[l*n2+q*n+m] += a[m*n2+q*n+k] * b[k*n+l];
}
}
}
}
/* Matrix-vector */
double c_mv[n3];
memset(c_mv, 0, n3 * sizeof(double));
for (size_t m = 0; m < n; m++) {
for (size_t l = 0; l < n; l++) {
cblas_dgemv(
CblasRowMajor, CblasNoTrans, n, n, 1.0, &a[m*n2],
n, &b[l], n, 0.0, &c_mv[l*n2+m], n);
}
}
/* Matrix-matrix */
double c_mm[n3];
memset(c_mm, 0, n3 * sizeof(double));
for (size_t m = 0; m < n; m++) {
cblas_dgemm(
CblasRowMajor, CblasTrans, CblasTrans, n, n, n, 1.0, b, n,
&a[m*n2], n, 0.0, &c_mm[m], n2);
}
/* Compute difference */
double diff_mv = 0.0;
double diff_mm = 0.0;
for (size_t idx = 0; idx < n3; idx++) {
diff_mv += c_mv[idx] - c_exact[idx];
diff_mm += c_mm[idx] - c_exact[idx];
}
printf("Difference matrix-vector: %e\n", diff_mv);
printf("Difference matrix-matrix: %e\n", diff_mm);
}
And this the output:
Difference matrix-vector: 0.000000e+00
Difference matrix-matrix: -1.188678e+01
i.e. the DGEMV implementation is correct, the DGEMM not - I really don't understand this. I switched around the multiplication (matrix-matrix multiplication is non commutative) and transposed both to get the right order C[l,q,m] instead of C[q,l,m], but I also tried it without switching/transposing and it does not work.
Can anyone please help?
Thanks.
edit: I thought about it a bit and feel like I'm trying to do something that DGEMM doe not support? Namely I try to insert a submatrix into C[:,:,m], which means that both the leading and trailing index are not contiguous in memory. DGEMM allows me to set the parameter LDC, which in this case needs to be n^2, but it does not know that also the second index is non-contiguous with a stride of n (and there is no parameter to tell it?). So why does DGEMM not support a second parameter for the stride of the trailing dimension?