public static void QRDecomposition()
{
SquareMatrix A = new SquareMatrix(new double[, ] {
{ 1, -2, 3 },
{ 2, -5, 12 },
{ 0, 2, -10 }
});
ColumnVector b = new ColumnVector(2, 8, -4);
SquareQRDecomposition qrd = A.QRDecomposition();
ColumnVector x = qrd.Solve(b);
PrintMatrix("x", x);
SquareMatrix Q = qrd.QMatrix;
SquareMatrix R = qrd.RMatrix;
PrintMatrix("QR", Q * R);
PrintMatrix("Q Q^T", Q.MultiplySelfByTranspose());
SquareMatrix AI = qrd.Inverse();
PrintMatrix("A^{-1}", AI);
PrintMatrix("A^{-1} A", AI * A);
}
public void SquareRandomMatrixQRDecomposition()
{
for (int d = 1; d <= 100; d += 11)
{
Console.WriteLine("d={0}", d);
SquareMatrix M = CreateSquareRandomMatrix(d);
// QR decompose the matrix.
SquareQRDecomposition QRD = M.QRDecomposition();
// The dimension should be right.
Assert.IsTrue(QRD.Dimension == M.Dimension);
// Test that the decomposition works.
SquareMatrix Q = QRD.QMatrix;
SquareMatrix R = QRD.RMatrix;
Assert.IsTrue(TestUtilities.IsNearlyEqual(Q * R, M));
// Check that the inverse works.
SquareMatrix MI = QRD.Inverse();
Assert.IsTrue(TestUtilities.IsNearlyEqual(M * MI, UnitMatrix.OfDimension(d)));
// Test that a solution works.
ColumnVector t = new ColumnVector(d);
for (int i = 0; i < d; i++)
{
t[i] = i;
}
ColumnVector s = QRD.Solve(t);
Assert.IsTrue(TestUtilities.IsNearlyEqual(M * s, t));
}
}