NAG C Library Function Document

nag_quad_1d_inf_exp_wt (d01ubc)

1
Purpose

nag_quad_1d_inf_exp_wt (d01ubc) returns the Gaussian quadrature approximation for the specific problem 0exp-x2fx dx. The degrees of precision catered for are: 1, 3, 5, 7, 9, 19, 29, 39 and 49, corresponding to values of n=1, 2, 3, 4, 5, 10, 15, 20 and 25, where n is the number of weights.

2
Specification

#include <nag.h>
#include <nagd01.h>
void  nag_quad_1d_inf_exp_wt (
void (*fun)(const double x[], double f[], Integer n, Nag_Comm *comm, Integer *istop),
Integer n, double *ans, Nag_Comm *comm, NagError *fail)

3
Description

nag_quad_1d_inf_exp_wt (d01ubc) uses the weights wi and the abscissae xi such that 0exp-x2fx is approximated by i=1 n wifxi to maximum precision i.e., it is exact when fx is a polynomial of degree 2n-1.

4
References

Golub G H and Welsch J H (1969) Calculation of Gauss quadrature rules Math. Comput. 23 221–230

5
Arguments

1:     fun function, supplied by the userExternal Function
fun must return the integrands fxi in fi for each xi in xi, for i=1,2,,n at a given point.
The specification of fun is:
void  fun (const double x[], double f[], Integer n, Nag_Comm *comm, Integer *istop)
1:     x[n] const doubleInput
On entry: the points at which the integrand function f must be evaluated.
2:     f[n] doubleOutput
On exit: fi must contain the value of the integrand fxi evaluated at the point xi, for i=1,2,,n.
3:     n IntegerInput
On entry: n specifies the number of weights and abscissae to be used.
4:     comm Nag_Comm *
Pointer to structure of type Nag_Comm; the following members are relevant to fun.
userdouble *
iuserInteger *
pPointer 
The type Pointer will be void *. Before calling nag_quad_1d_inf_exp_wt (d01ubc) you may allocate memory and initialize these pointers with various quantities for use by fun when called from nag_quad_1d_inf_exp_wt (d01ubc) (see Section 3.3.1.1 in How to Use the NAG Library and its Documentation).
5:     istop Integer *Input/Output
On entry: istop=0.
On exit: you may set istop to a negative number if at any time it is impossible to evaluate the function fx. In this case nag_quad_1d_inf_exp_wt (d01ubc) halts with fail set to the value of istop and the value returned in ans will be that of a non-signalling NaN.
2:     n IntegerInput
On entry: n specifies the number of weights and abscissae to be used.
Constraint: n=1, 2, 3, 4, 5, 10, 15, 20 or 25.
3:     ans double *Output
On exit: if fail.code=0, ans contains an approximation to the integral. Otherwise, ans will be a non-signalling NaN.
4:     comm Nag_Comm *
The NAG communication argument (see Section 3.3.1.1 in How to Use the NAG Library and its Documentation).
5:     fail NagError *Input/Output
The NAG error argument (see Section 3.7 in How to Use the NAG Library and its Documentation).

6
Error Indicators and Warnings

NE_ALLOC_FAIL
Dynamic memory allocation failed.
See Section 2.3.1.2 in How to Use the NAG Library and its Documentation for further information.
NE_BAD_PARAM
On entry, argument value had an illegal value.
NE_INT
On entry, n=value.
Constraint: 1n25.
On entry, n=value.
n is not one of the allowed values.
NE_INTERNAL_ERROR
An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.
See Section 2.7.6 in How to Use the NAG Library and its Documentation for further information.
NE_NO_LICENCE
Your licence key may have expired or may not have been installed correctly.
See Section 2.7.5 in How to Use the NAG Library and its Documentation for further information.
NE_USER_STOP
The user has halted the calculation.

7
Accuracy

The weights and abscissae have been calculated using quadruple precision arithmetic.

8
Parallelism and Performance

nag_quad_1d_inf_exp_wt (d01ubc) is not threaded in any implementation.

9
Further Comments

None.

10
Example

This example computes an approximation to 0exp-x2x dx.

10.1
Program Text

Program Text (d01ubce.c)

10.2
Program Data

None.

10.3
Program Results

Program Results (d01ubce.r)