Exemplo n.º 1
0
        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])
                    {
                        QAssert.Fail("S not consistent with s");
                    }
                }

                // tests
                Matrix U_Utranspose = Matrix.transpose(U) * U;
                if (norm(U_Utranspose - I) > tol)
                {
                    QAssert.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)
                {
                    QAssert.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)
                {
                    QAssert.Fail("Product does not recover A: (norm of U*S*V^T-A = " + norm(A_reconstructed - A) + ")");
                }
            }
        }
Exemplo n.º 2
0
        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)
                        {
                            QAssert.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)
                        {
                            QAssert.Fail("least square solution does not match (norm = "
                                         + norm(x - xr) + ")");
                        }
                    }
                }
            }
        }