24 January 2020 02:34:26 PM ASA007_TEST: C++ version Test the ASA007 library. TEST01: SYMINV computes the inverse 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 ( C * A - I ) = 1.11022e-16 Matrix order N = 2 Maxtrix nullity NULLTY = 0 RMS ( C * A - I ) = 3.84593e-16 Matrix order N = 3 Maxtrix nullity NULLTY = 0 RMS ( C * A - I ) = 3.14018e-16 Matrix order N = 4 Maxtrix nullity NULLTY = 0 RMS ( C * A - I ) = 1.20089e-15 Matrix order N = 5 Maxtrix nullity NULLTY = 0 RMS ( C * A - I ) = 1.27071e-15 Matrix order N = 6 Maxtrix nullity NULLTY = 0 RMS ( C * A - I ) = 1.66163e-15 Matrix order N = 7 Maxtrix nullity NULLTY = 0 RMS ( C * A - I ) = 3.87307e-15 Matrix order N = 8 Maxtrix nullity NULLTY = 0 RMS ( C * A - I ) = 3.82504e-15 Matrix order N = 9 Maxtrix nullity NULLTY = 0 RMS ( C * A - I ) = 3.73537e-15 Matrix order N = 10 Maxtrix nullity NULLTY = 0 RMS ( C * A - I ) = 6.78236e-15 Matrix order N = 11 Maxtrix nullity NULLTY = 0 RMS ( C * A - I ) = 1.69439e-14 Matrix order N = 12 Maxtrix nullity NULLTY = 0 RMS ( C * A - I ) = 9.82093e-15 Matrix order N = 13 Maxtrix nullity NULLTY = 0 RMS ( C * A - I ) = 2.33081e-14 Matrix order N = 14 Maxtrix nullity NULLTY = 0 RMS ( C * A - I ) = 2.1177e-14 Matrix order N = 15 Maxtrix nullity NULLTY = 0 RMS ( C * A - I ) = 1.54843e-14 TEST02: SYMINV computes the inverse 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 ( C * A - I ) = 0 Matrix order N = 2 Maxtrix nullity NULLTY = 0 RMS ( C * A - I ) = 6.28037e-16 Matrix order N = 3 Maxtrix nullity NULLTY = 0 RMS ( C * A - I ) = 1.00486e-14 Matrix order N = 4 Maxtrix nullity NULLTY = 0 RMS ( C * A - I ) = 3.45765e-13 Matrix order N = 5 Maxtrix nullity NULLTY = 0 RMS ( C * A - I ) = 6.38268e-12 Matrix order N = 6 Maxtrix nullity NULLTY = 0 RMS ( C * A - I ) = 1.49865e-10 Matrix order N = 7 Maxtrix nullity NULLTY = 0 RMS ( C * A - I ) = 3.65951e-09 Matrix order N = 8 Maxtrix nullity NULLTY = 0 RMS ( C * A - I ) = 1.57231e-07 Matrix order N = 9 Maxtrix nullity NULLTY = 0 RMS ( C * A - I ) = 4.40683e-06 Matrix order N = 10 Maxtrix nullity NULLTY = 1 RMS ( C * A - I ) = 1 Matrix order N = 11 Maxtrix nullity NULLTY = 1 RMS ( C * A - I ) = 3.29587 Matrix order N = 12 Maxtrix nullity NULLTY = 1 RMS ( C * A - I ) = 3.443 Matrix order N = 13 Maxtrix nullity NULLTY = 1 RMS ( C * A - I ) = 3.5882 Matrix order N = 14 Maxtrix nullity NULLTY = 1 RMS ( C * A - I ) = 3.73148 Matrix order N = 15 Maxtrix nullity NULLTY = 1 RMS ( C * A - I ) = 3.87289 ASA007_TEST: Normal end of execution. 24 January 2020 02:34:26 PM