void solve(size_t n, real **A, real *x, real *b)
{
size_t *P;
/* Construct LUP decomposition */
P = safeMalloc(n*sizeof(size_t));
decomposeLUP(n, A, P);
/* Solve by forward and backward substitution */
LUPsolve(n, A, P, x, b);
free(P);
}
// based on LUP algorithm from Cormen et al "Introduction to Algorithms"
Matrix4 Matrix4::inverse() const {
double lu[4][4];
int perm[4];
decomposeLUP(lu, perm);
double result[4][4];
for (int i = 0; i < 4; i++) {
double x[4];
double b[4] = {0};
b[i] = 1.0;
solveLUP(x, lu, perm, b);
for (int j=0; j < 4; j++) {
result[j][i] = x[j];
}
}
return Matrix4(result);
}