///////////////////////////////////////////////////////////////////////////////
// return determinant of 4x4 matrix
///////////////////////////////////////////////////////////////////////////////
float Matrix4::getDeterminant()
{
return m[0] * getCofactor(m[5],m[6],m[7], m[9],m[10],m[11], m[13],m[14],m[15]) -
m[1] * getCofactor(m[4],m[6],m[7], m[8],m[10],m[11], m[12],m[14],m[15]) +
m[2] * getCofactor(m[4],m[5],m[7], m[8],m[9], m[11], m[12],m[13],m[15]) -
m[3] * getCofactor(m[4],m[5],m[6], m[8],m[9], m[10], m[12],m[13],m[14]);
}
void minverse(double ***im, int n, double ***om)
{
int i, j, s = 0;
double d = det(im, n);
printf("cofactor of [%d][%d] : %lf\n", 2, 2, getCofactor(im, 1, 1, n));
printf("det : %lf\n", d);
for (i = 0; i < n; i++)
for (j = 0; j < n; j++, s++)
(*om)[i][j] = getCofactor(im, i, j, n) * (s % 2 == 0 ? 1. : -1.) / d;
madjugate(om, n);
}
int main() {
int M[MAXITEM][MAXITEM],
C[MAXITEM][MAXITEM],
T[MAXITEM][MAXITEM];
int i, j;
printf("Enter a 3x3 matrix and the program will produce the adjoint:\n");
for(i = 0 ; i < 3 ; i++) {
for(j = 0 ; j < 3 ; j++) {
scanf("%d", &M[i][j]);
}
}
//-- Producing the cofactor matrix
for(i = 0 ; i < 3 ; i++) {
for(j = 0 ; j < 3 ; j++) {
C[i][j] = getCofactor(M, i, j);
}
}
//-- Generate the transpose of the cofactor matrix
for(i = 0 ; i < 3 ; i++) {
for(j = 0 ; j < 3 ; j++) {
T[i][j] = C[j][i];
}
}
//-- Display the final matrix
printf("The adjoint is:\n");
for(i = 0 ; i < 3 ; i++) {
for(j = 0 ; j < 3 ; j++) {
printf("%4d ", T[i][j]);
}
printf("\n");
}
return 0;
}
///////////////////////////////////////////////////////////////////////////////
// compute the inverse of a general 4x4 matrix using Cramer's Rule
// If cannot find inverse, return indentity matrix
// M^-1 = adj(M) / det(M)
///////////////////////////////////////////////////////////////////////////////
Matrix4& Matrix4::invertGeneral()
{
// get cofactors of minor matrices
float cofactor0 = getCofactor(m[5],m[6],m[7], m[9],m[10],m[11], m[13],m[14],m[15]);
float cofactor1 = getCofactor(m[4],m[6],m[7], m[8],m[10],m[11], m[12],m[14],m[15]);
float cofactor2 = getCofactor(m[4],m[5],m[7], m[8],m[9], m[11], m[12],m[13],m[15]);
float cofactor3 = getCofactor(m[4],m[5],m[6], m[8],m[9], m[10], m[12],m[13],m[14]);
// get determinant
float determinant = m[0] * cofactor0 - m[1] * cofactor1 + m[2] * cofactor2 - m[3] * cofactor3;
if(fabs(determinant) <= 0.00001f)
{
return identity();
}
// get rest of cofactors for adj(M)
float cofactor4 = getCofactor(m[1],m[2],m[3], m[9],m[10],m[11], m[13],m[14],m[15]);
float cofactor5 = getCofactor(m[0],m[2],m[3], m[8],m[10],m[11], m[12],m[14],m[15]);
float cofactor6 = getCofactor(m[0],m[1],m[3], m[8],m[9], m[11], m[12],m[13],m[15]);
float cofactor7 = getCofactor(m[0],m[1],m[2], m[8],m[9], m[10], m[12],m[13],m[14]);
float cofactor8 = getCofactor(m[1],m[2],m[3], m[5],m[6], m[7], m[13],m[14],m[15]);
float cofactor9 = getCofactor(m[0],m[2],m[3], m[4],m[6], m[7], m[12],m[14],m[15]);
float cofactor10= getCofactor(m[0],m[1],m[3], m[4],m[5], m[7], m[12],m[13],m[15]);
float cofactor11= getCofactor(m[0],m[1],m[2], m[4],m[5], m[6], m[12],m[13],m[14]);
float cofactor12= getCofactor(m[1],m[2],m[3], m[5],m[6], m[7], m[9], m[10],m[11]);
float cofactor13= getCofactor(m[0],m[2],m[3], m[4],m[6], m[7], m[8], m[10],m[11]);
float cofactor14= getCofactor(m[0],m[1],m[3], m[4],m[5], m[7], m[8], m[9], m[11]);
float cofactor15= getCofactor(m[0],m[1],m[2], m[4],m[5], m[6], m[8], m[9], m[10]);
// build inverse matrix = adj(M) / det(M)
// adjugate of M is the transpose of the cofactor matrix of M
float invDeterminant = 1.0f / determinant;
m[0] = invDeterminant * cofactor0;
m[1] = -invDeterminant * cofactor4;
m[2] = invDeterminant * cofactor8;
m[3] = -invDeterminant * cofactor12;
m[4] = -invDeterminant * cofactor1;
m[5] = invDeterminant * cofactor5;
m[6] = -invDeterminant * cofactor9;
m[7] = invDeterminant * cofactor13;
m[8] = invDeterminant * cofactor2;
m[9] = -invDeterminant * cofactor6;
m[10]= invDeterminant * cofactor10;
m[11]= -invDeterminant * cofactor14;
m[12]= -invDeterminant * cofactor3;
m[13]= invDeterminant * cofactor7;
m[14]= -invDeterminant * cofactor11;
m[15]= invDeterminant * cofactor15;
return *this;
}