14 October 2018 07:18:17 PM ASA006_TEST: C version Test the ASA006 library. TEST01: CHOLESKY computes the Cholesky factorization of a positive definite symmetric matrix. A compressed storage format is used Here we look at the matrix A which is N+1 on the diagonal and N on the off diagonals. Matrix order N = 1 Maxtrix nullity NULLTY = 0 RMS ( A - U'*U ) = 4.440892e-16 Matrix order N = 2 Maxtrix nullity NULLTY = 0 RMS ( A - U'*U ) = 4.440892e-16 Matrix order N = 3 Maxtrix nullity NULLTY = 0 RMS ( A - U'*U ) = 0.000000e+00 Matrix order N = 4 Maxtrix nullity NULLTY = 0 RMS ( A - U'*U ) = 8.881784e-16 Matrix order N = 5 Maxtrix nullity NULLTY = 0 RMS ( A - U'*U ) = 8.881784e-16 Matrix order N = 6 Maxtrix nullity NULLTY = 0 RMS ( A - U'*U ) = 8.881784e-16 Matrix order N = 7 Maxtrix nullity NULLTY = 0 RMS ( A - U'*U ) = 2.808667e-15 Matrix order N = 8 Maxtrix nullity NULLTY = 0 RMS ( A - U'*U ) = 3.768222e-15 Matrix order N = 9 Maxtrix nullity NULLTY = 0 RMS ( A - U'*U ) = 7.324107e-15 Matrix order N = 10 Maxtrix nullity NULLTY = 0 RMS ( A - U'*U ) = 5.617334e-15 Matrix order N = 11 Maxtrix nullity NULLTY = 0 RMS ( A - U'*U ) = 5.617334e-15 Matrix order N = 12 Maxtrix nullity NULLTY = 0 RMS ( A - U'*U ) = 1.050907e-14 Matrix order N = 13 Maxtrix nullity NULLTY = 0 RMS ( A - U'*U ) = 8.519108e-15 Matrix order N = 14 Maxtrix nullity NULLTY = 0 RMS ( A - U'*U ) = 1.364446e-14 Matrix order N = 15 Maxtrix nullity NULLTY = 0 RMS ( A - U'*U ) = 1.749509e-14 TEST02: CHOLESKY computes the Cholesky factorization of a positive definite symmetric matrix. A compressed storage format is used Here we look at the Hilbert matrix A(I,J) = 1/(I+J-1) For this matrix, we expect errors to grow quickly. Matrix order N = 1 Maxtrix nullity NULLTY = 0 RMS ( A - U'*U ) = 0.000000e+00 Matrix order N = 2 Maxtrix nullity NULLTY = 0 RMS ( A - U'*U ) = 0.000000e+00 Matrix order N = 3 Maxtrix nullity NULLTY = 0 RMS ( A - U'*U ) = 0.000000e+00 Matrix order N = 4 Maxtrix nullity NULLTY = 0 RMS ( A - U'*U ) = 0.000000e+00 Matrix order N = 5 Maxtrix nullity NULLTY = 0 RMS ( A - U'*U ) = 1.387779e-17 Matrix order N = 6 Maxtrix nullity NULLTY = 0 RMS ( A - U'*U ) = 1.387779e-17 Matrix order N = 7 Maxtrix nullity NULLTY = 0 RMS ( A - U'*U ) = 2.403703e-17 Matrix order N = 8 Maxtrix nullity NULLTY = 0 RMS ( A - U'*U ) = 3.103168e-17 Matrix order N = 9 Maxtrix nullity NULLTY = 0 RMS ( A - U'*U ) = 3.800589e-17 Matrix order N = 10 Maxtrix nullity NULLTY = 0 RMS ( A - U'*U ) = 4.496917e-17 Matrix order N = 11 Maxtrix nullity NULLTY = 0 RMS ( A - U'*U ) = 4.955361e-17 Matrix order N = 12 Maxtrix nullity NULLTY = 0 RMS ( A - U'*U ) = 5.463691e-17 Matrix order N = 13 Maxtrix nullity NULLTY = 0 RMS ( A - U'*U ) = 5.594315e-17 Matrix order N = 14 Maxtrix nullity NULLTY = 0 RMS ( A - U'*U ) = 1.076531e+00 Matrix order N = 15 Maxtrix nullity NULLTY = 0 RMS ( A - U'*U ) = 1.674980e+01 TEST03: SUBCHL computes the Cholesky factor of a submatrix of a positive definite symmetric matrix. A compressed storage format is used. Here we look at the Hilbert matrix A(I,J) = 1/(I+J-1). For this particular matrix, we expect the errors to grow rapidly. Matrix order N = 1 Maxtrix nullity NULLTY = 0 Matrix determinant DET = 1.000000 RMS ( A - U'*U ) = 0.000000e+00 Matrix order N = 2 Maxtrix nullity NULLTY = 0 Matrix determinant DET = 0.083333 RMS ( A - U'*U ) = 0.000000e+00 Matrix order N = 3 Maxtrix nullity NULLTY = 0 Matrix determinant DET = 0.000463 RMS ( A - U'*U ) = 0.000000e+00 Matrix order N = 4 Maxtrix nullity NULLTY = 0 Matrix determinant DET = 0.000000 RMS ( A - U'*U ) = 0.000000e+00 Matrix order N = 5 Maxtrix nullity NULLTY = 0 Matrix determinant DET = 0.000000 RMS ( A - U'*U ) = 1.387779e-17 Matrix order N = 6 Maxtrix nullity NULLTY = 0 Matrix determinant DET = 0.000000 RMS ( A - U'*U ) = 1.387779e-17 Matrix order N = 7 Maxtrix nullity NULLTY = 0 Matrix determinant DET = 0.000000 RMS ( A - U'*U ) = 2.403703e-17 Matrix order N = 8 Maxtrix nullity NULLTY = 0 Matrix determinant DET = 0.000000 RMS ( A - U'*U ) = 3.103168e-17 Matrix order N = 9 Maxtrix nullity NULLTY = 0 Matrix determinant DET = 0.000000 RMS ( A - U'*U ) = 3.800589e-17 Matrix order N = 10 Maxtrix nullity NULLTY = 0 Matrix determinant DET = 0.000000 RMS ( A - U'*U ) = 4.496917e-17 Matrix order N = 11 Maxtrix nullity NULLTY = 0 Matrix determinant DET = 0.000000 RMS ( A - U'*U ) = 4.955361e-17 Matrix order N = 12 Maxtrix nullity NULLTY = 0 Matrix determinant DET = 0.000000 RMS ( A - U'*U ) = 5.463691e-17 Matrix order N = 13 Maxtrix nullity NULLTY = 0 Matrix determinant DET = 0.000000 RMS ( A - U'*U ) = 5.594315e-17 Matrix order N = 14 Maxtrix nullity NULLTY = 0 Matrix determinant DET = 0.000000 RMS ( A - U'*U ) = 1.076531e+00 Matrix order N = 15 Maxtrix nullity NULLTY = 0 Matrix determinant DET = 0.000000 RMS ( A - U'*U ) = 1.674980e+01 ASA006_TEST: Normal end of execution. 14 October 2018 07:18:17 PM