18 January 2008 09:38:33 AM
GEN_LAGUERRE_RULE
C++ version
Compiled on Jan 18 2008 at 09:36:44.
Compute a generalized Gauss-Laguerre rule for approximating
Integral ( A <= x < oo ) x^ALPHA exp(-x) f(x) dx
of order ORDER and parameter ALPHA.
For now, A is fixed at 0.0.
The user specifies ORDER, ALPHA, OPTION, and OUTPUT.
OPTION is:
0 to get the standard rule for handling:
Integral ( A <= x < oo ) x^ALPHA exp(-x) f(x) dx
1 to get the modified rule for handling:
Integral ( A <= x < oo ) f(x) dx
For OPTION = 1, the weights of the standard rule
are multiplied by x^(-ALPHA) * exp(+x).
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.
The requested order of the rule is = 4
The requested ALPHA = 0
The requested value of OPTION = 0
OUTPUT option is "F90".
!
! Weights W, abscissas X and range R
! for a generalized Gauss-Laguerre quadrature rule
! ORDER = 4
! A = 0
! ALPHA = 0
!
! OPTION = 0, Standard rule:
! Integral ( A <= x < oo ) x^ALPHA exp(-x) f(x) dx
! is to be approximated by
! sum ( 1 <= I <= ORDER ) w(i) * f(x(i)).
!
w(1) = 0.6031541043416347
w(2) = 0.3574186924377997
w(3) = 0.03888790851500539
w(4) = 0.0005392947055613274
x(1) = 0.3225476896193922
x(2) = 1.745761101158347
x(3) = 4.536620296921128
x(4) = 9.395070912301133
r(1) = 0
r(2) = 1e+30
GEN_LAGUERRE_RULE:
Normal end of execution.
18 January 2008 09:38:33 AM