public Matrix <double> SingulerValueDecomposition(Matrix <double> A, Matrix <double> b)
{
/*
* Svd<double> svd = A.Svd(true);
* double ConditionMumber = svd.ConditionNumber;
* Debug.WriteLine("Cond: {0}", svd.ConditionNumber);
*
* if((svd.ConditionNumber == double.PositiveInfinity) || (svd.ConditionNumber == double.NegativeInfinity)) {
* Debug.WriteLine("Condition number is infinity");
* return null;
* }
*
* // get matrix of left singular vectors with first n columns of U
* Matrix<double> U1 = svd.U.SubMatrix(0, A.RowCount, 0, A.ColumnCount);
*
* // get matrix of singular values
* Matrix<double> S = new DiagonalMatrix(A.ColumnCount, A.ColumnCount, svd.S.ToArray());
*
* // get matrix of right singular vectors
* Matrix<double> V = svd.VT.Transpose();
*
* return V.Multiply(S.Inverse()).Multiply(U1.Transpose().Multiply(b));
*/
Svd <double> svd = A.Svd(true);
double ConditionMumber = svd.ConditionNumber;
Debug.WriteLine("Rank, Det, Cond: {0},{1},{2}", svd.Rank, svd.Determinant, svd.ConditionNumber);
if ((svd.ConditionNumber == double.PositiveInfinity) || (svd.ConditionNumber == double.NegativeInfinity))
{
Debug.WriteLine("Condition number is infinity");
return(null);
}
return(svd.Solve(b));
}
/// <summary>
///
/// </summary>
/// <param name="stiffnessMatrix"></param>
/// <param name="forceVector"></param>
/// <returns></returns>
protected override KeyedVector<NodalDegreeOfFreedom> Solve(StiffnessMatrix stiffnessMatrix, KeyedVector<NodalDegreeOfFreedom> forceVector)
{
Svd<NodalDegreeOfFreedom, NodalDegreeOfFreedom> svd = new Svd<NodalDegreeOfFreedom, NodalDegreeOfFreedom>(stiffnessMatrix, true);
return svd.Solve(forceVector);
}
private static void FindFit(X[] x, double[] y, double[] sig, int cFuncs, BasisFuncs funcs, out double[] coeff, out double[,] u, out double[,] v, out double[] w, out double chiSq)
{
int cData = x.Length;
// - evaluate basis functions over domain set (x)
// - scale the basis by the significance
u = new double[cData, cFuncs];
double[] b = new double[cData];
double[] funcY = new double[cFuncs];
for (int i = 0; i < cData; i++)
{
funcs(x[i], funcY, cFuncs);
double sigInv = 1 / sig[i];
for (int j = 0; j < cFuncs; j++)
{
u[i, j] = funcY[j] * sigInv;
}
b[i] = y[i] * sigInv;
}
// singular value decomposition
Matrix <double> U = Matrix <double> .Build.DenseOfArray(u);
Svd <double> SVD = U.Svd();
w = SVD.S.ToArray();
Debug.Assert((SVD.VT.RowCount == cFuncs) && (SVD.VT.ColumnCount == cFuncs));
v = SVD.VT.Transpose().ToArray();
// Math.Net computes full mxm U matrix but we're using only the first n columns. (like LAPACK DGESVD() with JOBU='O')
for (int i = 0; i < cData; i++)
{
for (int j = 0; j < cFuncs; j++)
{
u[i, j] = SVD.U.At(i, j);
}
}
// zero out insignificant values
double wMax = 0;
for (int j = 0; j < cFuncs; j++)
{
wMax = Math.Max(wMax, w[j]);
}
const double Tolerance = 1e-5;
double cutoff = Tolerance * wMax;
for (int j = 0; j < cFuncs; j++)
{
if (w[j] < cutoff)
{
w[j] = 0;
}
}
// solve for coefficients (uses backsubstitution)
Vector <double> X = SVD.Solve(Vector <double> .Build.DenseOfArray(b));
coeff = X.ToArray();
// compute quality of fit
chiSq = 0;
for (int i = 0; i < cData; i++)
{
funcs(x[i], funcY, cFuncs);
double sum = 0;
for (int j = 0; j < cFuncs; j++)
{
sum += coeff[j] * funcY[j];
}
double diff = (y[i] - sum) / sig[i];
chiSq += diff * diff;
}
}
/// <summary>
///
/// </summary>
/// <param name="stiffnessMatrix"></param>
/// <param name="forceVector"></param>
/// <returns></returns>
protected override KeyedVector <NodalDegreeOfFreedom> Solve(StiffnessMatrix stiffnessMatrix, KeyedVector <NodalDegreeOfFreedom> forceVector)
{
Svd <NodalDegreeOfFreedom, NodalDegreeOfFreedom> svd = new Svd <NodalDegreeOfFreedom, NodalDegreeOfFreedom>(stiffnessMatrix, true);
return(svd.Solve(forceVector));
}