24 January 2020 01:09:20 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 ) = 4.44089e-16 Matrix order N = 2 Maxtrix nullity NULLTY = 0 RMS ( A - U'*U ) = 4.44089e-16 Matrix order N = 3 Maxtrix nullity NULLTY = 0 RMS ( A - U'*U ) = 0 Matrix order N = 4 Maxtrix nullity NULLTY = 0 RMS ( A - U'*U ) = 8.88178e-16 Matrix order N = 5 Maxtrix nullity NULLTY = 0 RMS ( A - U'*U ) = 8.88178e-16 Matrix order N = 6 Maxtrix nullity NULLTY = 0 RMS ( A - U'*U ) = 8.88178e-16 Matrix order N = 7 Maxtrix nullity NULLTY = 0 RMS ( A - U'*U ) = 2.80867e-15 Matrix order N = 8 Maxtrix nullity NULLTY = 0 RMS ( A - U'*U ) = 3.76822e-15 Matrix order N = 9 Maxtrix nullity NULLTY = 0 RMS ( A - U'*U ) = 7.32411e-15 Matrix order N = 10 Maxtrix nullity NULLTY = 0 RMS ( A - U'*U ) = 5.61733e-15 Matrix order N = 11 Maxtrix nullity NULLTY = 0 RMS ( A - U'*U ) = 5.61733e-15 Matrix order N = 12 Maxtrix nullity NULLTY = 0 RMS ( A - U'*U ) = 1.05091e-14 Matrix order N = 13 Maxtrix nullity NULLTY = 0 RMS ( A - U'*U ) = 8.51911e-15 Matrix order N = 14 Maxtrix nullity NULLTY = 0 RMS ( A - U'*U ) = 1.36445e-14 Matrix order N = 15 Maxtrix nullity NULLTY = 0 RMS ( A - U'*U ) = 1.74951e-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 Matrix order N = 2 Maxtrix nullity NULLTY = 0 RMS ( A - U'*U ) = 0 Matrix order N = 3 Maxtrix nullity NULLTY = 0 RMS ( A - U'*U ) = 0 Matrix order N = 4 Maxtrix nullity NULLTY = 0 RMS ( A - U'*U ) = 0 Matrix order N = 5 Maxtrix nullity NULLTY = 0 RMS ( A - U'*U ) = 1.38778e-17 Matrix order N = 6 Maxtrix nullity NULLTY = 0 RMS ( A - U'*U ) = 1.38778e-17 Matrix order N = 7 Maxtrix nullity NULLTY = 0 RMS ( A - U'*U ) = 2.4037e-17 Matrix order N = 8 Maxtrix nullity NULLTY = 0 RMS ( A - U'*U ) = 3.10317e-17 Matrix order N = 9 Maxtrix nullity NULLTY = 0 RMS ( A - U'*U ) = 3.80059e-17 Matrix order N = 10 Maxtrix nullity NULLTY = 1 RMS ( A - U'*U ) = 2.22673e-11 Matrix order N = 11 Maxtrix nullity NULLTY = 1 RMS ( A - U'*U ) = 1.09934 Matrix order N = 12 Maxtrix nullity NULLTY = 1 RMS ( A - U'*U ) = 16.7193 Matrix order N = 13 Maxtrix nullity NULLTY = 1 RMS ( A - U'*U ) = 27.9614 Matrix order N = 14 Maxtrix nullity NULLTY = 1 RMS ( A - U'*U ) = 38.8361 Matrix order N = 15 Maxtrix nullity NULLTY = 1 RMS ( A - U'*U ) = 49.5867 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 RMS ( A - U'*U ) = 0 Matrix order N = 2 Maxtrix nullity NULLTY = 0 Matrix determinant DET = 0.0833333 RMS ( A - U'*U ) = 0 Matrix order N = 3 Maxtrix nullity NULLTY = 0 Matrix determinant DET = 0.000462963 RMS ( A - U'*U ) = 0 Matrix order N = 4 Maxtrix nullity NULLTY = 0 Matrix determinant DET = 1.65344e-07 RMS ( A - U'*U ) = 0 Matrix order N = 5 Maxtrix nullity NULLTY = 0 Matrix determinant DET = 3.7493e-12 RMS ( A - U'*U ) = 1.38778e-17 Matrix order N = 6 Maxtrix nullity NULLTY = 0 Matrix determinant DET = 5.3673e-18 RMS ( A - U'*U ) = 1.38778e-17 Matrix order N = 7 Maxtrix nullity NULLTY = 0 Matrix determinant DET = 4.8358e-25 RMS ( A - U'*U ) = 2.4037e-17 Matrix order N = 8 Maxtrix nullity NULLTY = 0 Matrix determinant DET = 2.73705e-33 RMS ( A - U'*U ) = 3.10317e-17 Matrix order N = 9 Maxtrix nullity NULLTY = 0 Matrix determinant DET = 9.72027e-43 RMS ( A - U'*U ) = 3.80059e-17 Matrix order N = 10 Maxtrix nullity NULLTY = 1 Matrix determinant DET = 0 RMS ( A - U'*U ) = 2.22673e-11 Matrix order N = 11 Maxtrix nullity NULLTY = 1 Matrix determinant DET = 0 RMS ( A - U'*U ) = 1.09934 Matrix order N = 12 Maxtrix nullity NULLTY = 1 Matrix determinant DET = 0 RMS ( A - U'*U ) = 16.7193 Matrix order N = 13 Maxtrix nullity NULLTY = 1 Matrix determinant DET = 0 RMS ( A - U'*U ) = 27.9614 Matrix order N = 14 Maxtrix nullity NULLTY = 1 Matrix determinant DET = 0 RMS ( A - U'*U ) = 38.8361 Matrix order N = 15 Maxtrix nullity NULLTY = 1 Matrix determinant DET = 0 RMS ( A - U'*U ) = 49.5867 ASA006_TEST: Normal end of execution. 24 January 2020 01:09:20 PM