28 February 2022 06:12:04 PM

quadrature_golub_welsch_():
  C++ version
  Test quadrature_golub_welsch().

TEST01:
  Compute points and weights for Gauss quadrature
  with the Chebyshev Type 1 weight w(x) = 1/sqrt(1-x^2).
  Order N = 5
  Interval = [-1,1]

  Abscissas:

         0       -0.951057
         1       -0.587785
         2     2.26221e-18
         3        0.587785
         4        0.951057

  Weights:

         0        0.628319
         1        0.628319
         2        0.628319
         3        0.628319
         4        0.628319

TEST02:
  Compute points and weights for Gauss quadrature
  with the Chebyshev Type 2 weight w(x) = sqrt(1-x^2).
  Order N = 5
  Interval = [-1,1]

  Abscissas:

         0       -0.866025
         1            -0.5
         2     5.95249e-17
         3             0.5
         4        0.866025

  Weights:

         0          0.1309
         1        0.392699
         2        0.523599
         3        0.392699
         4          0.1309

TEST03:
  Compute points and weights for Gauss quadrature
  with the Gegenbauer weight w(x) = (1-x^2)^alpha.
  Order N = 5
  ALPHA = 0.25
  Interval = [-1,1]

  Abscissas:

         0       -0.885526
         1       -0.518146
         2     6.84469e-18
         3        0.518146
         4        0.885526

  Weights:

         0        0.171047
         1         0.43055
         2        0.544843
         3         0.43055
         4        0.171047

TEST04:
  Compute points and weights for Gauss quadrature
  with the generalized Hermite weight w(x) = |x|^alpha * exp(-x^2).
  ALPHA = 2
  Order N = 5
  Interval = (-oo,+oo)

  Abscissas:

         0         -2.3175
         1        -1.27639
         2     5.11203e-16
         3         1.27639
         4          2.3175

  Weights:

         0       0.0288027
         1        0.313028
         2        0.202566
         3        0.313028
         4       0.0288027

TEST05:
  Compute points and weights for Gauss quadrature
  with the generalized Laguerre weight w(x) = x^alpha * exp(-x).
  Order N = 5
  ALPHA = 2
  Interval = [0,+oo)

  Abscissas:

         0         1.03111
         1         2.83721
         2         5.62029
         3         9.68291
         4         15.8285

  Weights:

         0        0.520917
         1         1.06671
         2         0.38355
         3       0.0285642
         4     0.000262713

TEST06:
  Compute points and weights for Gauss quadrature
  with the Hermite weight w(x) = exp(-x^2).
  Order N = 5
  Interval = (-oo,+oo)

  Abscissas:

         0        -2.02018
         1       -0.958572
         2     2.40258e-16
         3        0.958572
         4         2.02018

  Weights:

         0       0.0199532
         1        0.393619
         2        0.945309
         3        0.393619
         4       0.0199532

TEST07:
  Compute points and weights for Gauss quadrature
  with the Jacobi weight w(x) = (1-x^2)^alpha*(1+x)^beta
  Order N = 5
  ALPHA = 0.25
  BETA =  0.75
  Interval = [-1,1]

  Abscissas:

         0       -0.835553
         1       -0.446113
         2        0.062007
         3        0.552614
         4        0.894318

  Weights:

         0       0.0874589
         1        0.330899
         2        0.538382
         3        0.495706
         4        0.213635

TEST08:
  Compute points and weights for Gauss quadrature
  with the Laguerre weight w(x) = exp(-x).
  Order N = 5
  Interval = [0,+oo)

  Abscissas:

         0         0.26356
         1          1.4134
         2         3.59643
         3         7.08581
         4         12.6408

  Weights:

         0        0.521756
         1        0.398667
         2       0.0759424
         3      0.00361176
         4       2.337e-05

TEST09:
  Compute points and weights for Gauss quadrature
  with the Legendre weight w(x) = 1.
  Order N = 5
  Interval = [-1,1]

  Abscissas:

         0        -0.90618
         1       -0.538469
         2    -1.08185e-16
         3        0.538469
         4         0.90618

  Weights:

         0        0.236927
         1        0.478629
         2        0.568889
         3        0.478629
         4        0.236927

QWGW_TEST:
  Normal end of execution.

28 February 2022 06:12:04 PM