15-Feb-2019 09:04:31

quadmom_test
  MATLAB version
  Test quadmom.

QUADMOM_TEST01:
  Compute the points and weights of a quadrature rule
  for the Legendre weight, rho(x)=1, over [-1,+1],
  using Golub and Welsch's moment method.
  Compare with a standard calculation.

  Points from GW moment and orthogonal polynomial methods:

       1:       -0.90618      -0.90618
       2:      -0.538469     -0.538469
       3:    7.74299e-17  -1.08185e-16
       4:       0.538469      0.538469
       5:        0.90618       0.90618

  Weights from GW moment and orthogonal polynomial methods:

       1:       0.236927      0.236927
       2:       0.478629      0.478629
       3:       0.568889      0.568889
       4:       0.478629      0.478629
       5:       0.236927      0.236927

QUADMOM_TEST02:
  Compute the points and weights of a quadrature rule for
  the standard Gaussian weight, rho(x)=exp(-x^2/2)/sqrt(2pi),
  over (-oo,+oo), using Golub and Welsch's moment method.
  Compare with a standard calculation.

  Points from GW moment and orthogonal polynomial methods:

       1:       -2.85697      -2.85697
       2:       -1.35563      -1.35563
       3:    1.40971e-16   3.39776e-16
       4:        1.35563       1.35563
       5:        2.85697       2.85697

  Weights from GW moment and orthogonal polynomial methods:

       1:      0.0112574     0.0112574
       2:       0.222076      0.222076
       3:       0.533333      0.533333
       4:       0.222076      0.222076
       5:      0.0112574     0.0112574

QUADMOM_TEST03:
  Compute the points and weights of a quadrature rule for
  a general Gaussian weight,
  rho(mu,s;x)=exp(-((x-mu)/sigma)^2/2)/sigma^2/sqrt(2pi),
  over (-oo,+oo), using Golub and Welsch's moment method.
  Compare with a standard calculation.

  MU = 1
  SIGMA = 2

  Points from GW moment and orthogonal polynomial methods:

       1:       -4.71394      -4.71394
       2:       -1.71125      -1.71125
       3:              1             1
       4:        3.71125       3.71125
       5:        6.71394       6.71394

  Weights from GW moment and orthogonal polynomial methods:

       1:      0.0112574     0.0112574
       2:       0.222076      0.222076
       3:       0.533333      0.533333
       4:       0.222076      0.222076
       5:      0.0112574     0.0112574

QUADMOM_TEST04:
  Compute the points and weights of a quadrature rule for
  the Laguerre weight, rho(x)=exp(-x),
  over [0,+oo), using Golub and Welsch's moment method.
  Compare with a standard calculation.

  Points from GW moment and orthogonal polynomial methods:

       1:        0.26356       0.26356
       2:         1.4134        1.4134
       3:        3.59643       3.59643
       4:        7.08581       7.08581
       5:        12.6408       12.6408

  Weights from GW moment and orthogonal polynomial methods:

       1:       0.521756      0.521756
       2:       0.398667      0.398667
       3:      0.0759424     0.0759424
       4:     0.00361176    0.00361176
       5:      2.337e-05     2.337e-05

QUADMOM_TEST05:
  Compute the points and weights of a quadrature rule for
  a truncated normal weight,
  rho(mu,s;x)=exp(-((x-mu)/sigma)^2/2)/sigma^2/sqrt(2pi),
  over [a,b], using Golub and Welsch's moment method.

  MU = 100
  SIGMA = 25
  A = 50
  B = 150

  Points from GW moment method:

     1:      56.4761
     2:      76.3469
     3:          100
     4:      123.653
     5:      143.524

  Weights from GW moment method:

     1:    0.0558883
     2:     0.242951
     3:     0.402322
     4:     0.242951
     5:    0.0558883

QUADMOM_TEST06:
  Compute the points and weights of a quadrature rule for
  a lower truncated normal weight,
  rho(mu,s;x)=exp(-((x-mu)/sigma)^2/2)/sigma^2/sqrt(2pi),
  over [a,+00), using Golub and Welsch's moment method.

  MU = 2
  SIGMA = 0.5
  A = 0

  Points from GW moment method:

     1:     0.181699
     2:     0.642168
     3:      1.13382
     4:      1.62238
     5:      2.10999
     6:       2.6048
     7:      3.11888
     8:      3.67288
     9:      4.31747

  Weights from GW moment method:

     1:  0.000423601
     2:   0.00977395
     3:    0.0873217
     4:     0.292167
     5:     0.381303
     6:     0.192724
     7:    0.0345414
     8:   0.00173334
     9:   1.2624e-05

QUADMOM_TEST07:
  Compute the points and weights of a quadrature rule for
  an upper truncated normal weight,
  rho(mu,s;x)=exp(-((x-mu)/sigma)^2/2)/sigma^2/sqrt(2pi),
  over (-oo,b], using Golub and Welsch's moment method.

  MU = 2
  SIGMA = 0.5
  B = 3

  Points from GW moment method:

     1:    -0.496847
     2:     0.120141
     3:     0.642855
     4:      1.11849
     5:      1.56329
     6:      1.98198
     7:      2.36954
     8:      2.70492
     9:      2.93754

  Weights from GW moment method:

     1:  2.21114e-06
     2:  0.000387457
     3:    0.0101584
     4:     0.079157
     5:     0.240686
     6:     0.330417
     7:     0.227969
     8:    0.0893336
     9:    0.0218891

QUADMOM_TEST08:
  Integrate sin(x) against a lower truncated normal weight.

  MU = 0
  SIGMA = 1
  A = -3

   N    Estimate

   1      0.00443782
   2     -0.00295694
   3     0.000399622
   4     -0.00023654
   5    -0.000173932
   6    -0.000177684
   7    -0.000177529
   8    -0.000177534
   9    -0.000177534

quadmom_test
  Normal end of execution.

15-Feb-2019 09:04:31