public static float Determinant(MatrixFixed M, bool balance)
{
int n = M.Rows;
//assert(M.Columns() == n);
switch (n)
{
case 1: return M[0, 0];
case 2: return Determinant(M[0], M[1]);
case 3: return Determinant(M[0], M[1], M[2]);
case 4: return Determinant(M[0], M[1], M[2], M[3]);
default:
if (balance)
{
MatrixFixed tmp = new MatrixFixed(M);
float scalings = 1;
for (int t = 0; t < 5; ++t)
{
float rn;
// normalize rows.
for (uint i = 0; i < n; ++i)
{
rn = tmp.GetRow((int)i).RMS();
if (rn > 0)
{
scalings *= rn;
tmp.ScaleRow((int)i, 1.0f / rn);
}
}
// normalize columns.
for (uint i = 0; i < n; ++i)
{
rn = tmp.GetColumn((int)i).RMS();
if (rn > 0)
{
scalings *= rn;
tmp.ScaleColumn((int)i, 1.0f / rn);
}
}
/*
#if 0
// pivot
for (int k=0; k<n-1; ++k) {
// find largest element after (k, k):
int i0 = k, j0 = k;
abs_t v0(0);
for (int i=k; i<n; ++i) {
for (int j=k; j<n; ++j) {
abs_t v = std::abs(tmp[i][j]);
if (v > v0) {
i0 = i;
j0 = j;
v0 = v;
}
}
}
// largest element is in position (i0, j0).
if (i0 != k) {
for (int j=0; j<n; ++j)
std::swap(tmp[k][j], tmp[i0][j]);
scalings = -scalings;
}
if (j0 != k) {
for (int i=0; i<n; ++i)
std::swap(tmp[i][k], tmp[i][j0]);
scalings = -scalings;
}
}
#endif
*/
}
float balanced_det = (new QR(tmp)).Determinant();
//std::clog << __FILE__ ": scalings, balanced_det = " << scalings << ", " << balanced_det << std::endl;
return (float)(scalings) * balanced_det;
}
else
return (new QR(M)).Determinant();
}
}