3D identity matrix to correctly set vertices - c

Question

Im playing around with matrices, with a view to doing 3D transformation in GDI (for the fun of it). At the moment i'm checking that im getting the right values from identity matrix given a representation of four vertices arranged in a square. I've been scratching my head as to why it's not giving expected output. I have done my research but can't see what i am doing wrong here.
Here's my definition of matrix.
typedef struct m{
float _m01, _m05, _m09, _m13;
float _m02, _m06, _m10, _m14;
float _m03, _m07, _m11, _m15;
float _m04, _m08, _m12, _m16;
}mat;
struct m matIdentity(struct m *m1){
m1->_m01 = 1.0; m1->_m05 = 0.0; m1->_m09 = 0.0; m1->_m13 = 0.0;
m1->_m02 = 0.0; m1->_m06 = 1.0; m1->_m10 = 0.0; m1->_m14 = 0.0;
m1->_m03 = 0.0; m1->_m07 = 0.0; m1->_m11 = 1.0; m1->_m15 = 0.0;
m1->_m04 = 0.0; m1->_m08 = 0.0; m1->_m12 = 0.0; m1->_m16 = 1.0;
}
Here's making use of matrix with
struct m matrix;
matIdentity(&matrix);
//represent 4 vertices(x,y,z,w);
float square[4][4] = {
{0.0, 0.0, 0.0, 1.0},
{0.0, 20.0, 0.0, 1.0},
{20.0, 20.0, 0.0, 1.0},
{20.0, 0.0, 0.0, 1.0}
};
float result[4][4];
int i = 0;
for(i = 0; i < 4; i++){
result[i][1] = (matrix._m01 * square[i][0]) + (matrix._m05 * square[i][1]) + (matrix._m09 * square[i][2]) + (matrix._m13 * square[i][3]);
result[i][2] = (matrix._m02 * square[i][0]) + (matrix._m06 * square[i][1]) + (matrix._m10 * square[i][2]) + (matrix._m14 * square[i][3]);
result[i][3] = (matrix._m03 * square[i][0]) + (matrix._m07 * square[i][1]) + (matrix._m11 * square[i][2]) + (matrix._m15 * square[i][3]);
result[i][4] = (matrix._m04 * square[i][0]) + (matrix._m08 * square[i][1]) + (matrix._m12 * square[i][2]) + (matrix._m16 * square[i][3]);
}
char strOutput[500];
sprintf(strOutput,"%f %f %f %f\n %f %f %f %f\n %f %f %f %f\n %f %f %f %f\n ",
result[0][0], result[0][1], result[0][2], result[0][3],
result[1][0], result[1][1], result[1][2], result[1][3],
result[2][0], result[2][1], result[2][2], result[2][3],
result[3][0], result[3][1], result[3][2], result[3][3]
);
I have a feeling the problem is somewhere to do with multiplying a row based representation of vertices using a column major matrix. Can anyone please suggest how i should be doing this.

Answer 1

I don't understand why you don't use array first, then start to use array and iteration, and in the end give up iteration. Please, such program can only cause confusion.
The correct formula is C(i, j)=sigma(A(i, k)*B(k, j), k=1..n), where C=AB and n is 4 for your case.
(e.g., this line should be like: result[i][0] = (matrix._m01 * square[0][i]) + (matrix._m02 * square[1][i]) + (matrix._m03 * square[2][i]) + (matrix._m04 * square[3][i]); )Write a simple nested for-iteration to calculate this...
This is not for one vector, but n vectors....

Answer 2

This is not matrix multiplication. Multiplying a vector by a matrix goes like this:
float mat[4][4];
float vec_in[4];
float vec_out[4];
// todo: initialize values
for (int j = 0; j < 4; ++j)
{
vec_out[j] = 0.0f;
for (int i = 0; i < 4; ++i)
{
vec_out[j] += vec_in[i] * mat[i][j];
}
}