12 August 2022 2:16:53.896 PM asa006_test(): FORTRAN90 version Test asa006(). test01(): cholesky() computes the Cholesky factorization of a symmetric positive definite 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 ) = 0.444089E-15 Matrix order N = 2 Maxtrix nullity NULLTY = 0 RMS ( A - U'*U ) = 0.444089E-15 Matrix order N = 3 Maxtrix nullity NULLTY = 0 RMS ( A - U'*U ) = 0.00000 Matrix order N = 4 Maxtrix nullity NULLTY = 0 RMS ( A - U'*U ) = 0.888178E-15 Matrix order N = 5 Maxtrix nullity NULLTY = 0 RMS ( A - U'*U ) = 0.888178E-15 Matrix order N = 6 Maxtrix nullity NULLTY = 0 RMS ( A - U'*U ) = 0.888178E-15 Matrix order N = 7 Maxtrix nullity NULLTY = 0 RMS ( A - U'*U ) = 0.280867E-14 Matrix order N = 8 Maxtrix nullity NULLTY = 0 RMS ( A - U'*U ) = 0.376822E-14 Matrix order N = 9 Maxtrix nullity NULLTY = 0 RMS ( A - U'*U ) = 0.732411E-14 Matrix order N = 10 Maxtrix nullity NULLTY = 0 RMS ( A - U'*U ) = 0.561733E-14 Matrix order N = 11 Maxtrix nullity NULLTY = 0 RMS ( A - U'*U ) = 0.561733E-14 Matrix order N = 12 Maxtrix nullity NULLTY = 0 RMS ( A - U'*U ) = 0.105091E-13 Matrix order N = 13 Maxtrix nullity NULLTY = 0 RMS ( A - U'*U ) = 0.851911E-14 Matrix order N = 14 Maxtrix nullity NULLTY = 0 RMS ( A - U'*U ) = 0.136445E-13 Matrix order N = 15 Maxtrix nullity NULLTY = 0 RMS ( A - U'*U ) = 0.174951E-13 test02(): cholesky() computes the Cholesky factorization of a symmetric positive definite 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 RMS ( A - U'*U ) = 0.00000 Matrix order N = 2 Maxtrix nullity NULLTY = 0 RMS ( A - U'*U ) = 0.00000 Matrix order N = 3 Maxtrix nullity NULLTY = 0 RMS ( A - U'*U ) = 0.00000 Matrix order N = 4 Maxtrix nullity NULLTY = 0 RMS ( A - U'*U ) = 0.00000 Matrix order N = 5 Maxtrix nullity NULLTY = 0 RMS ( A - U'*U ) = 0.138778E-16 Matrix order N = 6 Maxtrix nullity NULLTY = 0 RMS ( A - U'*U ) = 0.138778E-16 Matrix order N = 7 Maxtrix nullity NULLTY = 0 RMS ( A - U'*U ) = 0.240370E-16 Matrix order N = 8 Maxtrix nullity NULLTY = 0 RMS ( A - U'*U ) = 0.310317E-16 Matrix order N = 9 Maxtrix nullity NULLTY = 0 RMS ( A - U'*U ) = 0.380059E-16 Matrix order N = 10 Maxtrix nullity NULLTY = 1 RMS ( A - U'*U ) = 0.222673E-10 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 symmetric positive definite 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 = 1.00000 RMS ( A - U'*U ) = 0.00000 Matrix order N = 2 Maxtrix nullity NULLTY = 0 Matrix determinant DET = 0.833333E-01 RMS ( A - U'*U ) = 0.00000 Matrix order N = 3 Maxtrix nullity NULLTY = 0 Matrix determinant DET = 0.462963E-03 RMS ( A - U'*U ) = 0.00000 Matrix order N = 4 Maxtrix nullity NULLTY = 0 Matrix determinant DET = 0.165344E-06 RMS ( A - U'*U ) = 0.00000 Matrix order N = 5 Maxtrix nullity NULLTY = 0 Matrix determinant DET = 0.374930E-11 RMS ( A - U'*U ) = 0.138778E-16 Matrix order N = 6 Maxtrix nullity NULLTY = 0 Matrix determinant DET = 0.536730E-17 RMS ( A - U'*U ) = 0.138778E-16 Matrix order N = 7 Maxtrix nullity NULLTY = 0 Matrix determinant DET = 0.483580E-24 RMS ( A - U'*U ) = 0.240370E-16 Matrix order N = 8 Maxtrix nullity NULLTY = 0 Matrix determinant DET = 0.273705E-32 RMS ( A - U'*U ) = 0.310317E-16 Matrix order N = 9 Maxtrix nullity NULLTY = 0 Matrix determinant DET = 0.972027E-42 RMS ( A - U'*U ) = 0.380059E-16 Matrix order N = 10 Maxtrix nullity NULLTY = 1 Matrix determinant DET = 0.00000 RMS ( A - U'*U ) = 0.222673E-10 Matrix order N = 11 Maxtrix nullity NULLTY = 1 Matrix determinant DET = 0.00000 RMS ( A - U'*U ) = 0.309714E-01 Matrix order N = 12 Maxtrix nullity NULLTY = 1 Matrix determinant DET = 0.00000 RMS ( A - U'*U ) = 15.8190 Matrix order N = 13 Maxtrix nullity NULLTY = 1 Matrix determinant DET = 0.00000 RMS ( A - U'*U ) = 27.5203 Matrix order N = 14 Maxtrix nullity NULLTY = 1 Matrix determinant DET = 0.00000 RMS ( A - U'*U ) = 38.9786 Matrix order N = 15 Maxtrix nullity NULLTY = 1 Matrix determinant DET = 0.00000 RMS ( A - U'*U ) = 50.3554 asa006_test(): Normal end of execution. 12 August 2022 2:16:53.897 PM