public void RandomRectangularSVD()
{
for (int c = 1; c < 64; c += 11)
{
Console.WriteLine(c);
RectangularMatrix R = GenerateRandomMatrix(64, c);
SingularValueDecomposition SVD = R.SingularValueDecomposition();
Assert.IsTrue(SVD.RowCount == R.RowCount);
Assert.IsTrue(SVD.ColumnCount == SVD.ColumnCount);
Assert.IsTrue(SVD.Dimension == SVD.ColumnCount);
// U has right dimensions and is orthogonal
SquareMatrix U = SVD.LeftTransformMatrix;
Assert.IsTrue(U.Dimension == R.RowCount);
Assert.IsTrue(TestUtilities.IsNearlyEqual(U.Transpose * U, UnitMatrix.OfDimension(U.Dimension)));
// V has right dimensions and is orthogonal
SquareMatrix V = SVD.RightTransformMatrix;
Assert.IsTrue(V.Dimension == R.ColumnCount);
Assert.IsTrue(TestUtilities.IsNearlyEqual(V.Transpose * V, UnitMatrix.OfDimension(V.Dimension)));
// The transforms decompose the matrix with the claimed singular values
RectangularMatrix S = U.Transpose * R * V;
for (int i = 0; i < SVD.Contributors.Count; i++)
{
SingularValueContributor t = SVD.Contributors[i];
Assert.IsTrue(t.SingularValue >= 0.0);
Assert.IsTrue(TestUtilities.IsNearlyEqual(S[i, i], t.SingularValue));
Assert.IsTrue(TestUtilities.IsNearlyEqual(R * t.RightSingularVector, t.SingularValue * t.LeftSingularVector));
}
// We can reconstruct the original matrix from the claimed singular values
RectangularMatrix R2 = new RectangularMatrix(SVD.RowCount, SVD.ColumnCount);
foreach (SingularValueContributor t in SVD.Contributors)
{
R2 += t.SingularValue * t.LeftSingularVector * t.RightSingularVector.Transpose;
}
Assert.IsTrue(TestUtilities.IsNearlyEqual(R, R2));
}
}
public void SquareMatrixSVD()
{
for (int d = 4; d < 64; d += 7)
{
SquareMatrix A = CreateSquareRandomMatrix(d, d);
SingularValueDecomposition SVD = A.SingularValueDecomposition();
Assert.IsTrue(SVD.Dimension == A.Dimension);
// U has right dimensions and is orthogonal
SquareMatrix U = SVD.LeftTransformMatrix;
Assert.IsTrue(U.Dimension == A.Dimension);
Assert.IsTrue(TestUtilities.IsNearlyEqual(U.MultiplyTransposeBySelf(), UnitMatrix.OfDimension(U.Dimension)));
// V has right dimensions and is orthogonal
SquareMatrix V = SVD.RightTransformMatrix;
Assert.IsTrue(V.Dimension == A.Dimension);
Assert.IsTrue(TestUtilities.IsNearlyEqual(V.MultiplyTransposeBySelf(), UnitMatrix.OfDimension(V.Dimension)));
Assert.IsTrue(SVD.Dimension == A.Dimension);
// The transforms decompose the matrix with the claimed singular values
SquareMatrix S = U.Transpose * A * V;
for (int i = 0; i < SVD.Contributors.Count; i++)
{
SingularValueContributor t = SVD.Contributors[i];
Assert.IsTrue(t.SingularValue >= 0.0);
Assert.IsTrue(TestUtilities.IsNearlyEqual(S[i, i], t.SingularValue));
}
// We can solve a rhs using the SVD
ColumnVector x = new ColumnVector(d);
for (int i = 0; i < d; i++)
{
x[i] = i;
}
ColumnVector b = A * x;
ColumnVector y = SVD.Solve(b);
Assert.IsTrue(TestUtilities.IsNearlyEqual(x, y));
}
}
