Tue May 20 21:22:26 2025

differ_test():
  python version: 3.10.12
  numpy version:  1.26.4
  Test differ().

differ_matrix_test():
  Demonstrate that the DIFFER matrix is "really"
  a Vandermonde matrix.
  Stencil matrix:
[[ 2.500000e+00  3.300000e+00 -1.300000e+00  5.000000e-01]
 [ 6.250000e+00  1.089000e+01  1.690000e+00  2.500000e-01]
 [ 1.562500e+01  3.593700e+01 -2.197000e+00  1.250000e-01]
 [ 3.906250e+01  1.185921e+02  2.856100e+00  6.250000e-02]]
  Solution of DIFFER system:
[1. 2. 3. 4.]
  Solution of VANDERMONDE system:
[ 2.5  6.6 -3.9  2. ]
  Transformed solution of VANDERMONDE system:
[1. 2. 3. 4.]

differ_test02():
  differ_inverse() returns the inverse of a DIFFER matrix

   N    Inverse error

   2    2.32397e-15
   2    6.24881e-15
   2    2.1667e-15
   2    1.00785e-14
   2    1.69925e-15

   3    4.14817e-15
   3    5.65009e-15
   3    9.34235e-15
   3    2.4436e-12
   3    2.14513e-15

   4    5.84205e-13
   4    5.3416e-12
   4    5.09672e-14
   4    3.60836e-14
   4    8.68432e-14

   5    3.01256e-12
   5    2.03061e-13
   5    2.01787e-11
   5    3.53339e-12
   5    5.34077e-13

   6    4.41244e-12
   6    1.79654e-12
   6    4.34416e-12
   6    2.74226e-09
   6    8.22611e-12

   7    8.77739e-11
   7    1.06128e-11
   7    1.89043e-11
   7    3.91327e-10
   7    1.92777e-10

   8    2.30039e-10
   8    8.11524e-09
   8    2.37383e-10
   8    1.35787e-10
   8    2.85619e-08

differ_test03():
  Reproduce a specific example.
  Solution of DIFFER system:
[-0.08333333  0.5        -1.5         0.25      ]

  DFDX =          3.669313568906812
  d exp(x) /dx =  3.6692966676192444

differ_test04():
  differ_forward(),
  differ_backward(), and
  differ_central() produce coefficients for difference
  approximations of the O-th derivative, 
  with error of order H^P, for a uniform spacing of H.

  Use a spacing of H =  1.0 for all examples.