Wed May 17 09:51:20 2023

chebyshev1_exactness_test():
  Python version: 3.8.10
  Test chebyshev1_exactness().

chebyshev1_exactness():
  Investigate the polynomial exactness of a Gauss-Chebyshev1
  type 1 quadrature rule by integrating all monomials up to a given
  degree over the [-1,+1] interval.

chebyshev1_exactness: User input:
  Quadrature rule X file = "cheby1_o4_x.txt".
  Quadrature rule W file = "cheby1_o4_w.txt".
  Quadrature rule R file = "cheby1_o4_r.txt".
  Maximum degree to check = 10

  Number of points  = 4

  The quadrature rule to be tested is
  a Gauss-Chebyshev type 1 rule
  ORDER = #d 4

  Standard rule:
    Integral ( -1 <= x <= +1 ) f(x) / ( 1 - x^2 ) dx
    is to be approximated by
    sum ( 1 <= I <= ORDER ) w(i) * f(x(i)).

  Weights W:

[0.78539816 0.78539816 0.78539816 0.78539816]

  Abscissas X:

[-0.92387953 -0.38268343  0.38268343  0.92387953]

  Region R:

[-1.  1.]

  A Gauss-Chebyshev type 1 rule would be able to exactly
  integrate monomials up to and including 
  degree =  7

      Error    Degree

        0.0000000000000000    0
        0.0000000000000001    1
        0.0000000000000000    2
        0.0000000000000000    3
        0.0000000000000000    4
        0.0000000000000000    5
        0.0000000000000001    6
        0.0000000000000000    7
        0.0285714285714287    8
        0.0000000000000000    9
        0.0793650793650795   10

chebyshev1_exactness():
  Normal end of execution.

chebyshev1_exactness_test():
  Normal end of execution.
Wed May 17 09:51:20 2023