NAG CL Interface
d01ubc (dim1_​inf_​exp_​wt)

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1 Purpose

d01ubc returns the Gaussian quadrature approximation for the specific problem 0exp(-x2)f(x) 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>
void  d01ubc (
void (*f)(const double x[], double fv[], Integer n, Nag_Comm *comm, Integer *istop),
Integer n, double *ans, Nag_Comm *comm, NagError *fail)
The function may be called by the names: d01ubc, nag_quad_dim1_inf_exp_wt or nag_quad_1d_inf_exp_wt.

3 Description

d01ubc uses the weights wi and the abscissae xi such that 0exp(-x2)f(x) is approximated by i=1 n wif(xi) to maximum precision i.e., it is exact when f(x) 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: f function, supplied by the user External Function
f must return the integrand function values f(xi) for the given xi, for i=1,2,,n.
The specification of f is:
void  f (const double x[], double fv[], Integer n, Nag_Comm *comm, Integer *istop)
1: x[n] const double Input
On entry: the points at which the integrand function f must be evaluated.
2: fv[n] double Output
On exit: fv[i-1] must contain the value of the integrand f(xi) evaluated at the point x[i-1], for i=1,2,,n.
3: n Integer Input
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 f.
userdouble *
iuserInteger *
pPointer 
The type Pointer will be void *. Before calling d01ubc you may allocate memory and initialize these pointers with various quantities for use by f when called from d01ubc (see Section 3.1.1 in the Introduction to the NAG Library CL Interface).
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 f(x). In this case 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 Integer Input
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= NE_NOERROR, 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 3.1.1 in the Introduction to the NAG Library CL Interface).
5: fail NagError * Input/Output
The NAG error argument (see Section 7 in the Introduction to the NAG Library CL Interface).

6 Error Indicators and Warnings

NE_ALLOC_FAIL
Dynamic memory allocation failed.
See Section 3.1.2 in the Introduction to the NAG Library CL Interface 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 7.5 in the Introduction to the NAG Library CL Interface for further information.
NE_NO_LICENCE
Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library CL Interface 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

d01ubc is not threaded in any implementation.

9 Further Comments

None.

10 Example

This example computes an approximation to 0exp(-x2)x dx.

10.1 Program Text

Program Text (d01ubce.c)

10.2 Program Data

None.

10.3 Program Results

Program Results (d01ubce.r)