// Crout's LU decomposition for matrix determinant and inverse
// stores combined lower & upper in lum[][]
// stores row permuations into perm[]
// returns +1 or -1 according to even or odd number of row permutations
// lower gets dummy 1.0s on diagonal (0.0s above)
// upper gets lum values on diagonal (0.0s below)
public static int decompose(Matrix m, out Matrix lum, out int[] perm)
{
int toggle = +1; // even (+1) or odd (-1) row permutatuions
int n = m.rows_;
// Make a copy of Matrix m into result Matrix lu
lum = new Matrix(n, n);
for (int i = 0; i < n; ++i)
{
for (int j = 0; j < n; ++j)
{
lum[i, j] = m[i, j];
}
}
// make perm[]
perm = new int[n];
for (int i = 0; i < n; ++i)
{
perm[i] = i;
}
for (int j = 0; j < n - 1; ++j) // process by column. note n-1
{
double max = Math.Abs(lum[j, j]);
int piv = j;
for (int i = j + 1; i < n; ++i) // find pivot index
{
double xij = Math.Abs(lum[i, j]);
if (xij > max)
{
max = xij;
piv = i;
}
} // i
if (piv != j)
{
lum.swapRow(piv, j);
int t = perm[piv]; // swap perm elements
perm[piv] = perm[j];
perm[j] = t;
toggle = -toggle;
}
double xjj = lum[j, j];
if (xjj != 0.0)
{
for (int i = j + 1; i < n; ++i)
{
double xij = lum[i, j] / xjj;
lum[i, j] = xij;
for (int k = j + 1; k < n; ++k)
{
lum[i, k] -= xij * lum[j, k];
}
}
}
} // j
return(toggle);
}