29 March 2023   6:52:45.528 PM

quadmom_test():
  FORTRAN90 version
  Test QUADMOM().

QUADMOM_PRB01:
  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   -0.906180       -0.906180    
     2   -0.538469       -0.538469    
     3   -0.428238E-16   -0.108185E-15
     4    0.538469        0.538469    
     5    0.906180        0.906180    
 
  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_PRB02:
  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    0.423182E-16    0.339776E-15
     4     1.35563         1.35563    
     5     2.85697         2.85697    
 
  Weights from GW moment and orthogonal polynomial methods:
 
     1    0.112574E-01    0.112574E-01
     2    0.222076        0.222076    
     3    0.533333        0.533333    
     4    0.222076        0.222076    
     5    0.112574E-01    0.112574E-01

QUADMOM_PRB03:
  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 =    1.00000    
  SIGMA =    2.00000    
 
  Points from GW moment and orthogonal polynomial methods:
 
     1    -4.71394        -4.71394    
     2    -1.71125        -1.71125    
     3     1.00000         1.00000    
     4     3.71125         3.71125    
     5     6.71394         6.71394    
 
  Weights from GW moment and orthogonal polynomial methods:
 
     1    0.112574E-01    0.112574E-01
     2    0.222076        0.222076    
     3    0.533333        0.533333    
     4    0.222076        0.222076    
     5    0.112574E-01    0.112574E-01

QUADMOM_PRB04:
  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    0.263560        0.263560    
     2     1.41340         1.41340    
     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    0.759424E-01    0.759424E-01
     4    0.361176E-02    0.361176E-02
     5    0.233700E-04    0.233700E-04

QUADMOM_PRB05:
  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 =    100.000    
  SIGMA =    25.0000    
  A =    50.0000    
  B =    150.000    
 
  Points from GW moment method:
 
         1     56.476084    
         2     76.346920    
         3     100.00000    
         4     123.65308    
         5     143.52392    
 
  Weights from GW moment method:
 
         1    0.55888328E-01
         2    0.24295063    
         3    0.40232209    
         4    0.24295063    
         5    0.55888327E-01

QUADMOM_PRB06:
  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,+oo), using Golub and Welsch's moment method.
 
  MU =    2.00000    
  SIGMA =   0.500000    
  A =    0.00000    
 
  Points from GW moment method:
 
         1    0.18169948    
         2    0.64216831    
         3     1.1338184    
         4     1.6223789    
         5     2.1099868    
         6     2.6047994    
         7     3.1188781    
         8     3.6728811    
         9     4.3174715    
 
  Weights from GW moment method:
 
         1    0.42360153E-03
         2    0.97739754E-02
         3    0.87321885E-01
         4    0.29216726    
         5    0.38130253    
         6    0.19272352    
         7    0.34541269E-01
         8    0.17333322E-02
         9    0.12623975E-04

QUADMOM_PRB07:
  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 =    2.00000    
  SIGMA =   0.500000    
  B =    3.00000    
 
  Points from GW moment method:
 
         1   -0.49684145    
         2    0.12014505    
         3    0.64285833    
         4     1.1184951    
         5     1.5632870    
         6     1.9819832    
         7     2.3695417    
         8     2.7049194    
         9     2.9375393    
 
  Weights from GW moment method:
 
         1    0.22112580E-05
         2    0.38746776E-03
         3    0.10158593E-01
         4    0.79157574E-01
         5    0.24068699    
         6    0.33041617    
         7    0.22796853    
         8    0.89333369E-01
         9    0.21889097E-01

QUADMOM_PRB08:
  Integrate sin(x) against a lower truncated normal weight.
 
  MU =    0.00000    
  SIGMA =    1.00000    
  A =   -3.00000    
 
   N    Estimate
 
   1    0.443782E-02
   2   -0.295694E-02
   3    0.399622E-03
   4   -0.236540E-03
   5   -0.173932E-03
   6   -0.177684E-03
   7   -0.177529E-03
   8   -0.177534E-03
   9   -0.177534E-03

QUADMOM_TEST
  Normal end of execution.

29 March 2023   6:52:45.529 PM