Fri Aug 12 16:11:47 2022

asa006_test():
  Python version: 3.6.9
  Test asa006()

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.

   N   Null  RMS error

   1   0    0.0000
   2   0    0.0000
   3   0    0.0000
   4   0    0.0000
   5   0    0.0000
   6   0    0.0000
   7   0    0.0000
   8   0    0.0000
   9   0    0.0000
  10   0    0.0000
  11   0    0.0000
  12   0    0.0000
  13   0    0.0000
  14   0    0.0000

asa006_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 )

  We expect errors to grow quickly with N.

   N   Null  RMS error

   1   0    0.0000
   2   0    0.0000
   3   0    0.0000
   4   0    0.0000
   5   0    0.0000
   6   0    0.0000
   7   0    0.0000
   8   0    0.0000
   9   0    0.0000
  10   1    0.0000
  11   1    0.0000
  12   1    0.2106
  13   1    0.2917
  14   1    0.3504

asa006_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.

  N  NSUB  NULLTY  DET  RMS

  15   1   0  1.0000e+00  0.0000e+00
  15   2   0  8.3333e-02  0.0000e+00
  15   3   0  4.6296e-04  0.0000e+00
  15   4   0  1.6534e-07  0.0000e+00
  15   5   0  3.7493e-12  1.3878e-17
  15   6   0  5.3673e-18  1.3878e-17
  15   7   0  4.8358e-25  2.4037e-17
  15   8   0  2.7371e-33  3.1032e-17
  15   9   0  9.7203e-43  3.8006e-17
  15  10   1  0.0000e+00  2.2267e-11
  15  11  Numerical singularity!
  15  12  Numerical singularity!
  15  13  Numerical singularity!
  15  14  Numerical singularity!
  15  15  Numerical singularity!

asa006_test():
  Normal end of execution.
Fri Aug 12 16:11:47 2022