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13-May-2025 17:52:29

sphere_exactness_test():
  MATLAB/Octave version 9.11.0.2358333 (R2021b) Update 7
  Test sphere_exactness().
13-May-2025 17:52:29

sphere_exactness():
  MATLAB/Octave version 9.11.0.2358333 (R2021b) Update 7

  Investigate the polynomial exactness of a quadrature
  rule for the unit sphere by integrating all monomials
  of a given degree.

sphere_exactness: User input:
  File structure = "xyz1".
  Filename prefix = "design_04".
  Maximum degree = 5
  Number of points = 14

      Error    Degree  Exponents

        0.0000000000000000    0    0  0  0

        0.0000000000000004    1    1  0  0
        0.0000000000000001    1    0  1  0
        0.0000000000000000    1    0  0  1

        0.0000000000000000    2    2  0  0
        0.0000000000000000    2    1  1  0
        0.0000000000000009    2    0  2  0
        0.0000000000000001    2    1  0  1
        0.0000000000000000    2    0  1  1
        0.0000000000000009    2    0  0  2

        0.0000000000000001    3    3  0  0
        0.0000000000000001    3    2  1  0
        0.0000000000000001    3    1  2  0
        0.0000000000000007    3    0  3  0
        0.0000000000000000    3    2  0  1
        0.0000000000000002    3    1  1  1
        0.0000000000000001    3    0  2  1
        0.0000000000000001    3    1  0  2
        0.0000000000000007    3    0  1  2
        0.0000000000000000    3    0  0  3

        0.0000000000000000    4    4  0  0
        0.0000000000000000    4    3  1  0
        0.0000000000000000    4    2  2  0
        0.0000000000000000    4    1  3  0
        0.0000000000000009    4    0  4  0
        0.0000000000000000    4    3  0  1
        0.0000000000000000    4    2  1  1
        0.0000000000000001    4    1  2  1
        0.0000000000000000    4    0  3  1
        0.0000000000000001    4    2  0  2
        0.0000000000000000    4    1  1  2
        0.0000000000000003    4    0  2  2
        0.0000000000000002    4    1  0  3
        0.0000000000000000    4    0  1  3
        0.0000000000000013    4    0  0  4

        0.0000000000000000    5    5  0  0
        0.0000000000000000    5    4  1  0
        0.0000000000000000    5    3  2  0
        0.1140044293477214    5    2  3  0
        0.0000000000000001    5    1  4  0
        0.1425055366846508    5    0  5  0
        0.0000000000000000    5    4  0  1
        0.0000000000000000    5    3  1  1
        0.0000000000000000    5    2  2  1
        0.0000000000000000    5    1  3  1
        0.0000000000000001    5    0  4  1
        0.0000000000000000    5    3  0  2
        0.1140044293477214    5    2  1  2
        0.0000000000000000    5    1  2  2
        0.0285011073369301    5    0  3  2
        0.0000000000000000    5    2  0  3
        0.0000000000000001    5    1  1  3
        0.0000000000000000    5    0  2  3
        0.0000000000000000    5    1  0  4
        0.0855033220107906    5    0  1  4
        0.0000000000000001    5    0  0  5

sphere_exactness():
  Normal end of execution.

13-May-2025 17:52:29
13-May-2025 17:52:29

sphere_exactness():
  MATLAB/Octave version 9.11.0.2358333 (R2021b) Update 7

  Investigate the polynomial exactness of a quadrature
  rule for the unit sphere by integrating all monomials
  of a given degree.

sphere_exactness: User input:
  File structure = "dtpw".
  Filename prefix = "lebedev_013".
  Maximum degree = 5
  Number of points = 74

      Error    Degree  Exponents

        0.0000000000000000    0    0  0  0

        0.0000000000000000    1    1  0  0
        0.0000000000000001    1    0  1  0
        0.0000000000000009    1    0  0  1

        0.0000000000000000    2    2  0  0
        0.0000000000000000    2    1  1  0
        0.0000000000000000    2    0  2  0
        0.0000000000000002    2    1  0  1
        0.0000000000000000    2    0  1  1
        0.0000000000000009    2    0  0  2

        0.0000000000000002    3    3  0  0
        0.0000000000000000    3    2  1  0
        0.0000000000000001    3    1  2  0
        0.0000000000000001    3    0  3  0
        0.0000000000000004    3    2  0  1
        0.0000000000000000    3    1  1  1
        0.0000000000000003    3    0  2  1
        0.0000000000000001    3    1  0  2
        0.0000000000000001    3    0  1  2
        0.0000000000000006    3    0  0  3

        0.0000000000000178    4    4  0  0
        0.0000000000000000    4    3  1  0
        0.0000000000000091    4    2  2  0
        0.0000000000000000    4    1  3  0
        0.0000000000000178    4    0  4  0
        0.0000000000000001    4    3  0  1
        0.0000000000000000    4    2  1  1
        0.0000000000000000    4    1  2  1
        0.0000000000000001    4    0  3  1
        0.0000000000000093    4    2  0  2
        0.0000000000000000    4    1  1  2
        0.0000000000000093    4    0  2  2
        0.0000000000000001    4    1  0  3
        0.0000000000000000    4    0  1  3
        0.0000000000000169    4    0  0  4

        0.0000000000000000    5    5  0  0
        0.0000000000000001    5    4  1  0
        0.0000000000000001    5    3  2  0
        0.0000000000000000    5    2  3  0
        0.0000000000000001    5    1  4  0
        0.0000000000000000    5    0  5  0
        0.0000000000000001    5    4  0  1
        0.0000000000000000    5    3  1  1
        0.0000000000000000    5    2  2  1
        0.0000000000000000    5    1  3  1
        0.0000000000000001    5    0  4  1
        0.0000000000000000    5    3  0  2
        0.0000000000000000    5    2  1  2
        0.0000000000000000    5    1  2  2
        0.0000000000000000    5    0  3  2
        0.0000000000000002    5    2  0  3
        0.0000000000000000    5    1  1  3
        0.0000000000000002    5    0  2  3
        0.0000000000000000    5    1  0  4
        0.0000000000000000    5    0  1  4
        0.0000000000000003    5    0  0  5

sphere_exactness():
  Normal end of execution.

13-May-2025 17:52:30

sphere_exactness_test():
  Normal end of execution.

13-May-2025 17:52:30