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);
}
public void NullTest()
{
ComplexDoubleQRDecomp test = new ComplexDoubleQRDecomp(null);
}
public void SolveMatrix()
{
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 qr = new ComplexDoubleQRDecomp(a);
ComplexDoubleMatrix b = new ComplexDoubleMatrix(3);
b[0, 0] = new Complex(2.3, -3.2);
b[0, 1] = new Complex(2.3, -3.2);
b[0, 2] = new Complex(2.3, -3.2);
b[1, 0] = new Complex(6.7, 7.8);
b[1, 1] = new Complex(6.7, 7.8);
b[1, 2] = new Complex(6.7, 7.8);
b[2, 0] = new Complex(1.3, -9.7);
b[2, 1] = new Complex(1.3, -9.7);
b[2, 2] = new Complex(1.3, -9.7);
ComplexDoubleMatrix X = qr.Solve(b);
Assert.IsTrue(Comparer.AreEqual(X[0, 0], new Complex(-0.57, 1.14), .01));
Assert.IsTrue(Comparer.AreEqual(X[0, 1], new Complex(-0.57, 1.14), .01));
Assert.IsTrue(Comparer.AreEqual(X[0, 2], new Complex(-0.57, 1.14), .01));
Assert.IsTrue(Comparer.AreEqual(X[1, 0], new Complex(1.03, -0.16), .01));
Assert.IsTrue(Comparer.AreEqual(X[1, 1], new Complex(1.03, -0.16), .01));
Assert.IsTrue(Comparer.AreEqual(X[1, 2], new Complex(1.03, -0.16), .01));
Assert.IsTrue(Comparer.AreEqual(X[2, 0], new Complex(0.16, -0.52), .01));
Assert.IsTrue(Comparer.AreEqual(X[2, 1], new Complex(0.16, -0.52), .01));
Assert.IsTrue(Comparer.AreEqual(X[2, 2], new Complex(0.16, -0.52), .01));
a = new ComplexDoubleMatrix(3, 2);
a[0, 0] = new Complex(1.1, 1.1);
a[0, 1] = new Complex(2.2, -2.2);
a[1, 0] = new Complex(4.4, -4.4);
a[1, 1] = new Complex(5.5, 5.5);
a[2, 0] = new Complex(7.7, 7.7);
a[2, 1] = new Complex(8.8, -8.8);
qr = new ComplexDoubleQRDecomp(a);
b = new ComplexDoubleMatrix(3);
b[0, 0] = new Complex(2.3, -3.2);
b[0, 1] = new Complex(2.3, -3.2);
b[0, 2] = new Complex(2.3, -3.2);
b[1, 0] = new Complex(6.7, 7.8);
b[1, 1] = new Complex(6.7, 7.8);
b[1, 2] = new Complex(6.7, 7.8);
b[2, 0] = new Complex(1.3, -9.7);
b[2, 1] = new Complex(1.3, -9.7);
b[2, 2] = new Complex(1.3, -9.7);
X = qr.Solve(b);
Assert.IsTrue(Comparer.AreEqual(X[0, 0], new Complex(-0.344, 0.410), .01));
Assert.IsTrue(Comparer.AreEqual(X[0, 1], new Complex(-0.344, 0.410), .01));
Assert.IsTrue(Comparer.AreEqual(X[0, 2], new Complex(-0.344, 0.410), .01));
Assert.IsTrue(Comparer.AreEqual(X[1, 0], new Complex(1.01, -0.170), .01));
Assert.IsTrue(Comparer.AreEqual(X[1, 1], new Complex(1.01, -0.170), .01));
Assert.IsTrue(Comparer.AreEqual(X[1, 2], new Complex(1.01, -0.170), .01));
}