Wed Oct  5 20:59:52 2022

differ_test():
  Python version: 3.6.9
  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    5.71219e-15
   2    1.31575e-15
   2    1.41799e-15
   2    5.42359e-16
   2    1.21904e-14

   3    6.71369e-15
   3    1.05448e-14
   3    9.18134e-15
   3    4.56659e-15
   3    1.5285e-12

   4    4.39716e-14
   4    1.29445e-13
   4    1.91224e-13
   4    4.61235e-14
   4    2.41589e-13

   5    7.91301e-13
   5    1.03321e-12
   5    3.7174e-13
   5    8.97897e-12
   5    2.91276e-13

   6    7.26911e-10
   6    4.7275e-12
   6    1.20371e-10
   6    1.08178e-10
   6    8.94186e-12

   7    5.67335e-10
   7    6.1611e-11
   7    2.45349e-10
   7    4.67434e-10
   7    1.063e-09

   8    1.4603e-10
   8    7.05095e-10
   8    1.24804e-08
   8    1.27583e-07
   8    5.90913e-07

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.
  Forward difference coefficients, O =  3 , P =  1
[[ 0. -1.]
 [ 1.  3.]
 [ 2. -3.]
 [ 3.  1.]]
  Backward difference coefficients, O =  3 , P =  1
[[-3. -1.]
 [-2.  3.]
 [-1. -3.]
 [ 0.  1.]]
  Central difference coefficients, O =  3 , P =  2
[[-2.  -0.5]
 [-1.   1. ]
 [ 0.   0. ]
 [ 1.  -1. ]
 [ 2.   0.5]]
  Central difference coefficients, O =  3 , P =  4
[[-3.00000000e+00  1.25000000e-01]
 [-2.00000000e+00 -1.00000000e+00]
 [-1.00000000e+00  1.62500000e+00]
 [ 0.00000000e+00  3.38175542e-15]
 [ 1.00000000e+00 -1.62500000e+00]
 [ 2.00000000e+00  1.00000000e+00]
 [ 3.00000000e+00 -1.25000000e-01]]
  Forward difference coefficients, O =  4 , P =  1
[[ 0.  1.]
 [ 1. -4.]
 [ 2.  6.]
 [ 3. -4.]
 [ 4.  1.]]
  Backward difference coefficients, O =  4 , P =  1
[[-4.  1.]
 [-3. -4.]
 [-2.  6.]
 [-1. -4.]
 [ 0.  1.]]
  Central difference coefficients, O =  4 , P =  3
[[-3.         -0.16666667]
 [-2.          2.        ]
 [-1.         -6.5       ]
 [ 0.          9.33333333]
 [ 1.         -6.5       ]
 [ 2.          2.        ]
 [ 3.         -0.16666667]]

differ_test05():
  differ_stencil() produces coefficients for difference
  approximations of the O-th derivative, 
  using arbitrarily spaced data, with maximum spacing H
  with error of order H^P.

  For all tests, let X0 =  0.0
  and use a uniformly spacing of  1.0 , so we can compare
  with previous forward, backward and central differences.
  Finite difference coefficients, O =  3 , P =  1
[[ 0. -1.]
 [ 1.  3.]
 [ 2. -3.]
 [ 3.  1.]]
  Backward difference coefficients, O =  3 , P =  1
[[-3. -1.]
 [-2.  3.]
 [-1. -3.]
 [ 0.  1.]]
  Central difference coefficients, O =  3 , P =  2
[[-2.  -0.5]
 [-1.   1. ]
 [ 0.   0. ]
 [ 1.  -1. ]
 [ 2.   0.5]]
  Central difference coefficients, O =  3 , P =  4
[[-3.00000000e+00  1.25000000e-01]
 [-2.00000000e+00 -1.00000000e+00]
 [-1.00000000e+00  1.62500000e+00]
 [ 0.00000000e+00  3.38175542e-15]
 [ 1.00000000e+00 -1.62500000e+00]
 [ 2.00000000e+00  1.00000000e+00]
 [ 3.00000000e+00 -1.25000000e-01]]
  Finite difference coefficients, O =  4 , P =  1
[[ 0.  1.]
 [ 1. -4.]
 [ 2.  6.]
 [ 3. -4.]
 [ 4.  1.]]
  Backward difference coefficients, O =  4 , P =  1
[[-4.  1.]
 [-3. -4.]
 [-2.  6.]
 [-1. -4.]
 [ 0.  1.]]
  Central difference coefficients, O =  4 , P =  3
[[-3.         -0.16666667]
 [-2.          2.        ]
 [-1.         -6.5       ]
 [ 0.          9.33333333]
 [ 1.         -6.5       ]
 [ 2.          2.        ]
 [ 3.         -0.16666667]]

differ_test():
  Normal end of execution.
Wed Oct  5 20:59:52 2022