///<summary>Calculates the inverse of the matrix.</summary>
///<returns>the inverse of the matrix.</returns>
///<exception cref="NotPositiveDefiniteException">A is not positive definite.</exception>
public ComplexDoubleMatrix GetInverse()
{
Compute();
if (!ispd)
{
throw new NotPositiveDefiniteException();
}
else
{
#if MANAGED
var ret = ComplexDoubleMatrix.CreateIdentity(order);
ret = Solve(ret);
return(ret);
#else
Complex[] inverse = new Complex[l.data.Length];
Array.Copy(l.data, inverse, l.data.Length);
Lapack.Potri.Compute(Lapack.UpLo.Lower, order, inverse, order);
ComplexDoubleMatrix ret = new ComplexDoubleMatrix(order, order);
ret.data = inverse;
for (int i = 0; i < order; i++)
{
for (int j = 0; j < order; j++)
{
if (j > i)
{
ret.data[j * order + i] = ComplexMath.Conjugate(ret.data[i * order + j]);
}
}
}
return(ret);
#endif
}
}
public void SquareDecomp()
{
ComplexDoubleMatrix a = new ComplexDoubleMatrix(3);
a[0, 0] = new Complex(1.1, 1.1);
a[0, 1] = new Complex(2.2, -2.2);
a[0, 2] = new Complex(3.3, 3.3);
a[1, 0] = new Complex(4.4, -4.4);
a[1, 1] = new Complex(5.5, 5.5);
a[1, 2] = new Complex(6.6, -6.6);
a[2, 0] = new Complex(7.7, 7.7);
a[2, 1] = new Complex(8.8, -8.8);
a[2, 2] = new Complex(9.9, 9.9);
ComplexDoubleQRDecomp qrd = new ComplexDoubleQRDecomp(a);
ComplexDoubleMatrix qq = qrd.Q.GetConjugateTranspose() * qrd.Q;
ComplexDoubleMatrix qr = qrd.Q * qrd.R;
ComplexDoubleMatrix I = ComplexDoubleMatrix.CreateIdentity(3);
// determine the maximum relative error
double MaxError = 0.0;
for (int i = 0; i < 3; i++)
{
for (int j = 0; i < 3; i++)
{
double E = ComplexMath.Absolute((qq[i, j] - I[i, j]));
if (E > MaxError)
{
MaxError = E;
}
}
}
Assert.IsTrue(MaxError < 1.0E-14);
MaxError = 0.0;
for (int i = 0; i < 3; i++)
{
for (int j = 0; i < 3; i++)
{
double E = ComplexMath.Absolute((qr[i, j] - a[i, j]) / a[i, j]);
if (E > MaxError)
{
MaxError = E;
}
}
}
Assert.IsTrue(MaxError < 1.0E-14);
}
///<summary>Calculates the inverse of the matrix.</summary>
///<returns>the inverse of the matrix.</returns>
///<exception cref="SingularMatrixException">matrix is singular.</exception>
public ComplexDoubleMatrix GetInverse()
{
Compute();
if (singular)
{
throw new SingularMatrixException();
}
else
{
#if MANAGED
ComplexDoubleMatrix ret = ComplexDoubleMatrix.CreateIdentity(order);
ret = Solve(ret);
return(ret);
#else
Complex[] inverse = new Complex[factor.Length];
Array.Copy(factor, inverse, factor.Length);
Lapack.Getri.Compute(order, inverse, order, pivots);
ComplexDoubleMatrix ret = new ComplexDoubleMatrix(order, order);
ret.data = inverse;
return(ret);
#endif
}
}
/// <summary>Performs the QR factorization.</summary>
protected override void InternalCompute()
{
int m = matrix.Rows;
int n = matrix.Columns;
#if MANAGED
int minmn = m < n ? m : n;
r_ = new ComplexDoubleMatrix(matrix); // create a copy
ComplexDoubleVector[] u = new ComplexDoubleVector[minmn];
for (int i = 0; i < minmn; i++)
{
u[i] = Householder.GenerateColumn(r_, i, m - 1, i);
Householder.UA(u[i], r_, i, m - 1, i + 1, n - 1);
}
q_ = ComplexDoubleMatrix.CreateIdentity(m);
for (int i = minmn - 1; i >= 0; i--)
{
Householder.UA(u[i], q_, i, m - 1, i, m - 1);
}
#else
qr = ComplexDoubleMatrix.ToLinearComplexArray(matrix);
jpvt = new int[n];
jpvt[0] = 1;
Lapack.Geqp3.Compute(m, n, qr, m, jpvt, out tau);
r_ = new ComplexDoubleMatrix(m, n);
// Populate R
for (int i = 0; i < m; i++)
{
for (int j = 0; j < n; j++)
{
if (i <= j)
{
r_.data[j * m + i] = qr[(jpvt[j] - 1) * m + i];
}
else
{
r_.data[j * m + i] = Complex.Zero;
}
}
}
q_ = new ComplexDoubleMatrix(m, m);
for (int i = 0; i < m; i++)
{
for (int j = 0; j < m; j++)
{
if (j < n)
{
q_.data[j * m + i] = qr[j * m + i];
}
else
{
q_.data[j * m + i] = Complex.Zero;
}
}
}
if (m < n)
{
Lapack.Ungqr.Compute(m, m, m, q_.data, m, tau);
}
else
{
Lapack.Ungqr.Compute(m, m, n, q_.data, m, tau);
}
#endif
for (int i = 0; i < m; i++)
{
if (q_[i, i] == 0)
{
isFullRank = false;
}
}
}
