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);
SquareMatrix U = SVD.LeftTransformMatrix();
Assert.IsTrue(U.Dimension == R.RowCount);
Assert.IsTrue(TestUtilities.IsNearlyEqual(U.Transpose() * U, TestUtilities.CreateSquareUnitMatrix(U.Dimension)));
SquareMatrix V = SVD.RightTransformMatrix();
Assert.IsTrue(V.Dimension == R.ColumnCount);
Assert.IsTrue(TestUtilities.IsNearlyEqual(V.Transpose() * V, TestUtilities.CreateSquareUnitMatrix(V.Dimension)));
RectangularMatrix S = U.Transpose() * R * V;
for (int i = 0; i < SVD.Dimension; i++)
{
double w = SVD.SingularValue(i);
Console.WriteLine(" {0} {1}", w, S[i, i]);
Assert.IsTrue(w >= 0.0);
Assert.IsTrue(TestUtilities.IsNearlyEqual(S[i, i], w));
Assert.IsTrue(TestUtilities.IsNearlyEqual(R * SVD.RightSingularVector(i), w * SVD.LeftSingularVector(i)));
}
}
}