public void QrDecompositionConstructorTest()
{
double[,] value =
{
{ 2, -1, 0 },
{ -1, 2, -1 },
{ 0, -1, 2 }
};
var target = new QrDecomposition(value);
// Decomposition Identity
var Q = target.OrthogonalFactor;
var QQt = Q.DotWithTransposed(Q);
Assert.IsTrue(Matrix.IsEqual(QQt, Matrix.Identity(3), 1e-6));
Assert.IsTrue(Matrix.IsEqual(value, target.Reverse(), 1e-6));
// Linear system solving
double[,] B = Matrix.ColumnVector(new double[] { 1, 2, 3 });
double[,] expected = Matrix.ColumnVector(new double[] { 2.5, 4.0, 3.5 });
double[,] actual = target.Solve(B);
Assert.IsTrue(Matrix.IsEqual(expected, actual, 0.0000000000001));
}
public void SolveTransposeTest()
{
double[,] a =
{
{ 2, 1, 4 },
{ 6, 2, 2 },
{ 0, 1, 6 },
};
double[,] b =
{
{ 1, 0, 7 },
{ 5, 2, 1 },
{ 1, 5, 2 },
};
double[,] expected =
{
{ 0.5062, 0.2813, 0.0875 },
{ 0.1375, 1.1875, -0.0750 },
{ 0.8063, -0.2188, 0.2875 },
};
var target = new QrDecomposition(b, true);
double[,] actual = target.SolveTranspose(a);
Assert.IsTrue(Matrix.IsEqual(expected, actual, 1e-3));
Assert.IsTrue(Matrix.IsEqual(b.Transpose(), target.Reverse(), 1e-6));
}
public void SolveTest2()
{
// Example from Lecture notes for MATHS 370: Advanced Numerical Methods
// http://www.math.auckland.ac.nz/~sharp/370/qr-solving.pdf
double[,] value =
{
{ 1, 0, 0 },
{ 1, 7, 49 },
{ 1, 14, 196 },
{ 1, 21, 441 },
{ 1, 28, 784 },
{ 1, 35, 1225 },
};
// Matrices
{
double[,] b =
{
{ 4 },
{ 1 },
{ 0 },
{ 0 },
{ 2 },
{ 5 },
};
double[,] expected =
{
{ 3.9286 },
{ -0.5031 },
{ 0.0153 },
};
var target = new QrDecomposition(value);
double[,] actual = target.Solve(b);
Assert.IsTrue(Matrix.IsEqual(expected, actual, atol: 1e-4));
Assert.IsTrue(Matrix.IsEqual(value, target.Reverse(), 1e-6));
var target2 = new JaggedQrDecomposition(value.ToJagged());
double[][] actual2 = target2.Solve(b.ToJagged());
Assert.IsTrue(Matrix.IsEqual(expected, actual2, atol: 1e-4));
Assert.IsTrue(Matrix.IsEqual(value, target2.Reverse(), 1e-6));
}
// Vectors
{
double[] b = { 4, 1, 0, 0, 2, 5 };
double[] expected = { 3.9286, -0.5031, 0.0153 };
var target = new QrDecomposition(value);
double[] actual = target.Solve(b);
Assert.IsTrue(Matrix.IsEqual(expected, actual, atol: 1e-4));
}
}
public void InverseTest()
{
int n = 5;
var I = Matrix.Identity(n);
for (int i = 0; i < n; i++)
{
for (int j = 0; j < n; j++)
{
double[,] value = Matrix.Magic(n);
var target = new QrDecomposition(value);
var solution = target.Solve(I);
var inverse = target.Inverse();
var reverse = target.Reverse();
Assert.IsTrue(Matrix.IsEqual(solution, inverse, 1e-4));
Assert.IsTrue(Matrix.IsEqual(value, reverse, 1e-4));
}
}
}