public void testSVD()
{
//BOOST_MESSAGE("Testing singular value decomposition...");
setup();
double tol = 1.0e-12;
Matrix[] testMatrices = { M1, M2, M3, M4 };
for (int j = 0; j < testMatrices.Length; j++) {
// m >= n required (rows >= columns)
Matrix A = testMatrices[j];
SVD svd = new SVD(A);
// U is m x n
Matrix U = svd.U();
// s is n long
Vector s = svd.singularValues();
// S is n x n
Matrix S = svd.S();
// V is n x n
Matrix V = svd.V();
for (int i=0; i < S.rows(); i++) {
if (S[i,i] != s[i])
Assert.Fail("S not consistent with s");
}
// tests
Matrix U_Utranspose = Matrix.transpose(U)*U;
if (norm(U_Utranspose-I) > tol)
Assert.Fail("U not orthogonal (norm of U^T*U-I = " + norm(U_Utranspose-I) + ")");
Matrix V_Vtranspose = Matrix.transpose(V) * V;
if (norm(V_Vtranspose-I) > tol)
Assert.Fail("V not orthogonal (norm of V^T*V-I = " + norm(V_Vtranspose-I) + ")");
Matrix A_reconstructed = U * S * Matrix.transpose(V);
if (norm(A_reconstructed-A) > tol)
Assert.Fail("Product does not recover A: (norm of U*S*V^T-A = " + norm(A_reconstructed-A) + ")");
}
}
public void testQRSolve()
{
// Testing QR solve...
setup();
double tol = 1.0e-12;
MersenneTwisterUniformRng rng = new MersenneTwisterUniformRng( 1234 );
Matrix bigM = new Matrix( 50, 100, 0.0 );
for ( int i = 0; i < Math.Min( bigM.rows(), bigM.columns() ); ++i )
{
bigM[i, i] = i + 1.0;
}
Matrix[] testMatrices = { M1, M2, M3, Matrix.transpose(M3),
M4, Matrix.transpose(M4), M5, I, M7, bigM, Matrix.transpose(bigM) };
for ( int j = 0; j < testMatrices.Length; j++ )
{
Matrix A = testMatrices[j];
Vector b = new Vector( A.rows() );
for ( int k = 0; k < 10; ++k )
{
for ( int i = 0; i < b.Count; ++i )
{
b[i] = rng.next().value;
}
Vector x = MatrixUtilities.qrSolve( A, b, true );
if ( A.columns() >= A.rows() )
{
if ( norm( A * x - b ) > tol )
Assert.Fail( "A*x does not match vector b (norm = "
+ norm( A * x - b ) + ")" );
}
else
{
// use the SVD to calculate the reference values
int n = A.columns();
Vector xr = new Vector( n, 0.0 );
SVD svd = new SVD( A );
Matrix V = svd.V();
Matrix U = svd.U();
Vector w = svd.singularValues();
double threshold = n * Const.QL_EPSILON;
for ( int i = 0; i < n; ++i )
{
if ( w[i] > threshold )
{
double u = 0;
int zero = 0;
for ( int kk = 0; kk < U.rows(); kk++ )
u += ( U[kk, i] * b[zero++] ) / w[i];
for ( int jj = 0; jj < n; ++jj )
{
xr[jj] += u * V[jj, i];
}
}
}
if ( norm( xr - x ) > tol )
{
Assert.Fail( "least square solution does not match (norm = "
+ norm( x - xr ) + ")" );
}
}
}
}
}