C, matrix transposed multiplication using dynamic memory allocation - c

Question

I'm trying to transpose and multiply some matrices, basically
I get 2 matrices, matrixA and matrixB the action to be performed is trace(transpose(matrixA)*matrixB).
I managed to get this working for nxn matrices but I can't get it to work with mxn where (n>m or m>n).
I've looked online for solutions but I can't implement theirs solution into mine.
I removed almost all the code to simplify reading, if you prefer the entire code I linked it here.
If you do want to run the entire code, to recreate the problem use the following commands:
zeroes matrixA 2 3
zeroes matrixB 2 3
set matrixA
1 2 3 4 5 6
set matrixB
6 5 4 3 2 1
frob matrixA matrixB
The above commands should return Sum 56 but instead I get Sum 18
int* matrixATransposed = (int*) malloc(matrixARowLenght * matrixAColLenght * sizeof(int));
for (int i = 0; i < matrixARowLenght; i++)
{
for (int j = 0; j < matrixAColLenght; j++)
{
*(matrixATransposed + i * matrixAColLenght + j) = *(matrixA + j * matrixAColLenght + i);
}
}
// Multiply
int* mulRes = (int*)malloc(matrixARowLenght * matrixAColLenght * sizeof(int));
for (int i = 0; i < matrixAColLenght; i++) {
for (int j = 0; j < matrixBColLenght; j++) {
*(mulRes + i * matrixARowLenght + j) = 0;
for (int k = 0; k < matrixARowLenght; k++)
*(mulRes + i * matrixAColLenght + j) += *(matrixATransposed + i * matrixAColLenght + k) * *(matrixB + k * matrixBColLenght + j);
}
}
// Sum the trace
int trace = 0;
for (int i = 0; i < matrixARowLenght; i++) {
for (int j = 0; j < matrixAColLenght; j++) {
if (i == j) {
trace += *(mulRes + i * matrixAColLenght + j);
}
}
}
printf_s("Sum: %d\n", trace);

Answer 1

Your array indices for calculating the transpose, multiplication, and the trace seem to be incorrect. I've corrected them in the following program:
#include <stdlib.h>
#include <stdio.h>
int main(int argc, char **argv) {
int matrixARowLenght = 2;
int matrixAColLenght = 3;
int matrixA[] = {1,2,3,4,5,6};
int matrixBRowLenght = 2;
int matrixBColLenght = 3;
int matrixB[] = {6,5,4,3,2,1};
// Transpose
int* matrixATransposed = (int *) malloc(matrixARowLenght * matrixAColLenght * sizeof(int));
for (int i = 0; i < matrixAColLenght; i++) {
for (int j = 0; j < matrixARowLenght; j++) {
*(matrixATransposed + i * matrixARowLenght + j) = *(matrixA + j * matrixAColLenght + i);
}
}
// Multiply
int *mulRes = (int *) malloc(matrixARowLenght * matrixAColLenght * sizeof(int));
for (int i = 0; i < matrixAColLenght; ++i) {
for (int j = 0; j < matrixAColLenght; ++j) {
*(mulRes + (i * matrixAColLenght) + j) = 0;
for (int k = 0; k < matrixARowLenght; ++k) {
*(mulRes + (i * matrixAColLenght) + j) += *(matrixATransposed + (i * matrixARowLenght) + k) * *(matrixB + (k * matrixAColLenght) + j);
}
}
}
free(matrixATransposed);
// Sum the trace
int trace = 0;
for (int i = 0; i < matrixAColLenght; i++) {
for (int j = 0; j < matrixAColLenght; j++) {
if (i == j) {
trace += *(mulRes + i * matrixAColLenght + j);
}
}
}
printf("Sum: %d\n", trace);
free(mulRes);
return 0;
}
The above program will output your expected value:
Sum: 56
** UPDATE **
As pointed by MFisherKDX, the above code will not work if the result matrix is not a square matrix. The following code fixes this issue:
#include <stdlib.h>
#include <stdio.h>
int main(int argc, char **argv) {
int matrixARowLenght = 2;
int matrixAColLenght = 3;
int matrixA[] = {1,2,3,4,5,6};
int matrixBRowLenght = 2;
int matrixBColLenght = 4;
int matrixB[] = {8,7,6,5,4,3,2,1};
// Transpose
int* matrixATransposed = (int *) malloc(matrixARowLenght * matrixAColLenght * sizeof(int));
for (int i = 0; i < matrixAColLenght; i++) {
for (int j = 0; j < matrixARowLenght; j++) {
*(matrixATransposed + i * matrixARowLenght + j) = *(matrixA + j * matrixAColLenght + i);
}
}
// Multiply
int *mulRes = (int *) malloc(matrixAColLenght * matrixBColLenght * sizeof(int));
for (int i = 0; i < matrixAColLenght; ++i) {
for (int j = 0; j < matrixBColLenght; ++j) {
*(mulRes + (i * matrixBColLenght) + j) = 0;
for (int k = 0; k < matrixARowLenght; ++k) {
*(mulRes + (i * matrixBColLenght) + j) += *(matrixATransposed + (i * matrixARowLenght) + k) * *(matrixB + (k * matrixBColLenght) + j);
}
}
}
free(matrixATransposed);
// Sum the trace
int trace = 0;
for (int i = 0; i < matrixAColLenght; i++) {
for (int j = 0; j < matrixBColLenght; j++) {
if (i == j) {
trace += *(mulRes + i * matrixBColLenght + j);
}
}
}
printf("Sum: %d\n", trace);
free(mulRes);
return 0;
}
This code will output the following as expected:
Sum: 83