static void SymmInv(MultidimensionalArray M, MultidimensionalArray L, MultidimensionalArray R)
{
L.Clear();
R.Clear();
L.AccEye(1.0);
#if DEBUG
var Mbefore = M.CloneAs();
#endif
int n = M.NoOfRows;
for (int i = 0; i < n; i++)
{
double M_ii = M[i, i];
if (M_ii == 0.0)
{
throw new ArithmeticException("Zero diagonal element at " + i + "-th row.");
}
double scl = 1.0 / Math.Sqrt(Math.Abs(M_ii));
M.RowScale(i, scl);
L.RowScale(i, scl);
M.ColScale(i, scl);
double diagsign = Math.Sign(M[i, i]);
if (diagsign == 0.0)
{
throw new ArithmeticException("Zero diagonal element at " + i + "-th row.");
}
if (Math.Abs(Math.Abs(M[i, i]) - 1.0) > 1.0e-8)
{
throw new ArithmeticException("Unable to create diagonal 1.0.");
}
for (int k = i + 1; k < n; k++)
{
double M_ki = M[k, i];
M.RowAdd(i, k, -M_ki * diagsign);
L.RowAdd(i, k, -M_ki * diagsign);
M.ColAdd(i, k, -M_ki * diagsign);
Debug.Assert(Math.Abs(M[k, i]) < 1.0e-8);
Debug.Assert(Math.Abs(M[i, k]) < 1.0e-8);
}
}
L.TransposeTo(R);
#if DEBUG
var Test = MultidimensionalArray.Create(M.Lengths);
//var Q = MultidimensionalArray.Create(M.Lengths);
//Test.AccEye(1.0);
Test.Multiply(-1.0, L, Mbefore, R, 1.0, "ij", "ik", "kl", "lj");
for (int i = 0; i < n; i++)
{
//Debug.Assert((Test[i, i].Abs() - 1.0).Abs() < 1.0e-8);
//Test[i, i] -= Math.Sign(Test[i, i]);
Test[i, i] = 0;
}
double TestNorm = Test.InfNorm();
double scale = Math.Max(Mbefore.InfNorm(), R.InfNorm());
Debug.Assert(TestNorm / scale < 1.0e-4);
/*
* if(TestNorm / scale >= 1.0e-8) {
* var MM = Mbefore.CloneAs();
* MultidimensionalArray Lo = MultidimensionalArray.Create(n, n);
*
* for(int j = 0; j < n; j++) {
* double Lo_jj = MM[j, j];
* for(int k = 0; k < j; k++) {
* Lo_jj -= Lo[j, k].Pow2();
* }
*
* double sig = Math.Abs(Lo_jj);
* Lo[j, j] = Math.Sqrt(Lo_jj * sig);
*
*
* for(int i = j; i < n; i++) {
* double acc = MM[i, j];
* for(int k = 0; k < j; k++) {
* acc -= Lo[i, k] * Lo[j, k];
* }
*
* Lo[i, j] = (1 / (Lo[j, j] * sig)) * acc;
* }
* }
*
* int info = 0;
* unsafe {
* fixed(double* B_entries = Lo.Storage) {
*
* int UPLO = 'L', DIAG = 'N';
* LAPACK.F77_LAPACK.DTRTRI_(ref UPLO, ref DIAG, ref n, B_entries, ref n, out info);
* }
* }
*
* MultidimensionalArray Up = MultidimensionalArray.Create(n, n);
* Lo.TransposeTo(Up);
* Test.Clear();
* Test.Multiply(-1.0, Lo, Mbefore, R, 1.0, "ij", "ik", "kl", "lj");
*
*
* for(int i = 0; i < n; i++) {
* //Debug.Assert((Test[i, i].Abs() - 1.0).Abs() < 1.0e-8);
* Test[i, i] -= Math.Sign(Test[i, i]);
* }
*
* double TestNorm1 = Test.InfNorm();
* //double scale = Math.Max(Mbefore.InfNorm(), R.InfNorm());
* Console.WriteLine(TestNorm1);
*
* }
*/
#endif
}