20 May 2009 12:51:43 AM

HERMITE_RULE
  C++ version

  Compiled on May 20 2009 at 00:45:39.

  Compute a Gauss-Hermite quadrature rule for approximating

    Integral ( -oo < x < +oo ) w(x) f(x) dx

  of order ORDER.

  The user specifies ORDER, OPTION, and OUTPUT.

  OPTION specifies the weight function w(x):

    0, the unweighted rule for:
      Integral ( -oo < x < +oo )             f(x) dx

    1, the physicist weighted rule for:
      Integral ( -oo < x < +oo ) exp(-x*x)   f(x) dx

    2, the probabilist weighted rule for:
      Integral ( -oo < x < +oo ) exp(-x*x/2) f(x) dx

  OUTPUT is:

  "C++" for printed C++ output;
  "F77" for printed Fortran77 output;
  "F90" for printed Fortran90 output;
  "MAT" for printed MATLAB output;

  or:

  "filename" to generate 3 files:

    filename_w.txt - the weight file
    filename_x.txt - the abscissa file.
    filename_r.txt - the region file.

  ORDER =  4
  OPTION = 2
  OUTPUT = "F90".
!
!  Weights W, abscissas X and range R
!  for a Gauss-Hermite quadrature rule
!  ORDER = 4
!
!  OPTION = 2, probabilist weighted rule:
!    Integral ( -oo < x < +oo ) exp(-x*x/2) f(x) dx
!    is to be approximated by
!    sum ( 1 <= I <= ORDER ) w(i) * f(x(i)).
!
  w(1) = 0.3175630296981958
  w(2) = 0.9236776208083954
  w(3) = 0.9236776208083954
  w(4) = 0.3175630296981958

  x(1) = -1.650680123885785
  x(2) = -0.5246476232752904
  x(3) = 0.5246476232752904
  x(4) = 1.650680123885785

  r(1) = -1e+30
  r(2) = 1e+30

HERMITE_RULE:
  Normal end of execution.

20 May 2009 12:51:43 AM