Wed Oct 12 00:18:09 2022

gram_polynomial_test():
  Python version: 3.6.9
  Test gram_polynomial()

gram_abscissas_test():
  Test gram_abscissas()

  x = gram_abscissas( 3 )
[-6.66666667e-01 -5.55111512e-17  6.66666667e-01]

  x = gram_abscissas( 4 )
[-0.75 -0.25  0.25  0.75]

  x = gram_abscissas( 5 )
[-8.00000000e-01 -4.00000000e-01  5.55111512e-17  4.00000000e-01
  8.00000000e-01]

  x = gram_abscissas( 10 )
[-0.9 -0.7 -0.5 -0.3 -0.1  0.1  0.3  0.5  0.7  0.9]

gram_beta_test():
  Test gram_beta()

       M = 
         0         1         2         3         4         5
  N =  0:    --------   -0.0000   -0.0000   -0.0000   -0.0000   -0.0000
  N =  1:    --------  --------    0.2500    0.2963    0.3125    0.3200
  N =  2:    --------  --------  --------    0.1481    0.2000    0.2240
  N =  3:    --------  --------  --------  --------    0.1125    0.1646
  N =  4:    --------  --------  --------  --------  --------    0.0914
  N =  5:    --------  --------  --------  --------  --------  --------

gram_polynomial_coefficients_test():
  Test polynomial_coefficients_beta()

Gram polynomial g(0,10)

  p(x) =     1

Gram polynomial g(1,10)

  p(x) =     1 * x

Gram polynomial g(2,10)

  p(x) =     1 * x^2
           - 0.33

Gram polynomial g(3,10)

  p(x) =     1 * x^3
           - 0.586 * x

Gram polynomial g(4,10)

  p(x) =     1 * x^4
           - 0.82 * x^2
           + 0.07722

Gram polynomial g(5,10)

  p(x) =     1 * x^5
           - 1.03333 * x^3
           + 0.202233 * x
  Graphics saved as "gram_0_10.png"
  Graphics saved as "gram_1_10.png"
  Graphics saved as "gram_2_10.png"
  Graphics saved as "gram_3_10.png"
  Graphics saved as "gram_4_10.png"
  Graphics saved as "gram_5_10.png"

  Orthogonality matrix:
[[ 1.00000000e+00  1.77635684e-17  2.66453526e-17  1.33226763e-17
  -5.55111512e-18  2.77555756e-18]
 [ 1.77635684e-17  3.32800000e-01  2.20782681e-17 -2.12933514e-18
   5.82755110e-18 -1.80399330e-18]
 [ 2.66453526e-17  2.20782681e-17  8.81786880e-02  5.08812805e-18
  -1.16604771e-18 -2.83073520e-19]
 [ 1.33226763e-17 -2.12933514e-18  5.08812805e-18  2.23480067e-02
  -4.99763613e-19 -1.23407568e-18]
 [-5.55111512e-18  5.82755110e-18 -1.16604771e-18 -4.99763613e-19
   5.53038672e-03 -4.80581810e-20]
 [ 2.77555756e-18 -1.80399330e-18 -2.83073520e-19 -1.23407568e-18
  -4.80581810e-20  1.34069981e-03]]

  Orthogonal projection of f=exp(x)
[1.17512285e+00 1.10353613e+00 5.36655555e-01 1.76111843e-01
 4.35892821e-02 8.65733830e-03 1.43550936e-03 2.04267418e-04
 2.54539747e-05 2.82106991e-06 2.81515560e-07]

r8poly_print_test
  Python version: 3.6.9
  r8poly_print prints an R8POLY.

  The R8POLY:

  p(x) =     9 * x^5
           + 0.78 * x^4
           + 56 * x^2
           - 3.4 * x
           + 12

  The R8POLY:

  p(x) =     0.78 * x^4
           + 56 * x^2
           - 3.4 * x
           + 12

  The R8POLY:

  p(x) =     12

  The R8POLY:

  p(x) = 0

gram_polynomial_test():
  Normal end of execution.
Wed Oct 12 00:18:10 2022