So this code:

void CLASS cam_xyz_coeff(float _rgb_cam[3][4], double cam_xyz[4][3])
{
double cam_rgb[4][3], inverse[4][3], num;
int i, j, k;

for (i = 0; i < colors; i++) /* Multiply out XYZ colorspace */
for (j = 0; j < 3; j++)
for (cam_rgb[i][j] = k = 0; k < 3; k++)
cam_rgb[i][j] += cam_xyz[i][k] * xyz_rgb[k][j];

for (i = 0; i < colors; i++)
{ /* Normalize cam_rgb so that */
for (num = j = 0; j < 3; j++) /* cam_rgb * (1,1,1) is (1,1,1,1) */
num += cam_rgb[i][j];
if (num > 0.00001)
{
for (j = 0; j < 3; j++)
cam_rgb[i][j] /= num;
pre_mul[i] = 1 / num;
}