public void SingularValueDecompositionConstructorTest2()
{
// test for m-x-n matrices where m > n (4 > 2)
double[,] value = new double[,]
{
{ 1, 2 },
{ 3, 4 },
{ 5, 6 },
{ 7, 8 }
}; // value is 4x2, thus having more rows than columns
SingularValueDecomposition target = new SingularValueDecomposition(value, true, true, false);
double[,] actual = Matrix.Multiply(Matrix.Multiply(target.LeftSingularVectors,
Matrix.Diagonal(target.Diagonal)), target.RightSingularVectors.Transpose());
// Checking the decomposition
Assert.IsTrue(Matrix.IsEqual(actual, value, 0.01));
Assert.IsTrue(Matrix.IsEqual(target.Reverse(), value, 1e-2));
double[,] U = // economy svd
{
{ 0.152483233310201, 0.822647472225661, },
{ 0.349918371807964, 0.421375287684580, },
{ 0.547353510305727, 0.0201031031435023, },
{ 0.744788648803490, -0.381169081397574, },
};
// U should be equal except for some sign changes
Assert.IsTrue(Matrix.IsEqual(target.LeftSingularVectors, U, 0.001));
// Checking values
double[,] V =
{
{ 0.641423027995072, -0.767187395072177 },
{ 0.767187395072177, 0.641423027995072 },
};
// V should be equal except for some sign changes
Assert.IsTrue(Matrix.IsEqual(target.RightSingularVectors, V, 0.0001));
double[,] S =
{
{ 14.2690954992615, 0.000000000000000 },
{ 0.0000000000000, 0.626828232417543 },
};
// The diagonal values should be equal
Assert.IsTrue(Matrix.IsEqual(target.Diagonal, Matrix.Diagonal(S), 0.001));
}