20 May 2009 12:50:32 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 = 1 OUTPUT = "C++". // // Weights W, abscissas X and range R // for a Gauss-Hermite quadrature rule // ORDER = 4 // // OPTION = 1, physicist weighted rule: // Integral ( -oo < x < +oo ) exp(-x*x) f(x) dx // is to be approximated by // sum ( 1 <= I <= ORDER ) w(i) * f(x(i)). // w[0] = 0.08131283544699208; w[1] = 0.8049140900030078; w[2] = 0.8049140900030078; w[3] = 0.08131283544699208; x[0] = -1.650680123885785; x[1] = -0.5246476232752904; x[2] = 0.5246476232752904; x[3] = 1.650680123885785; r[0] = -1e+30; r[1] = 1e+30; HERMITE_RULE: Normal end of execution. 20 May 2009 12:50:32 AM