NAG Library Function Document

nag_quad_1d_fin_gonnet_vec (d01rgc)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

1:    $\mathbf{a}$ – doubleInput

On entry: $a$, the lower limit of integration.

2:    $\mathbf{b}$ – doubleInput

On entry: $b$, the upper limit of integration. It is not necessary that $a<b$.

Note: if $\mathbf{a}=\mathbf{b}$, the function will immediately return $\mathbf{dinest}=0.0$, $\mathbf{errest}=0.0$ and $\mathbf{nevals}=0$.

3:    $\mathbf{f}$ – function, supplied by the userExternal Function

f must return the value of the integrand $f$ at a set of points.

The specification of f is:

void  f (const double x[], Integer nx, double fv[], Integer *iflag, Nag_Comm *comm)

1:    $\mathbf{x}\left[\mathbf{nx}\right]$ – const doubleInput

On entry: the abscissae, $x_i$, for $\mathit{i}=1,2,\dots ,\mathbf{nx}$, at which function values are required.

2:    $\mathbf{nx}$ – IntegerInput

On entry: the number of abscissae at which a function value is required.

3:    $\mathbf{fv}\left[\mathbf{nx}\right]$ – doubleOutput

On exit: fv must contain the values of the integrand $f$. $\mathbf{fv}\left[i-1\right]=f\left(x_i\right)$ for all $i=1,2,\dots ,\mathbf{nx}$.

4:    $\mathbf{iflag}$ – Integer *Input/Output

On entry: $\mathbf{iflag}=0$.

On exit: set $\mathbf{iflag}<0$ to force an immediate exit with $\mathbf{fail}\mathbf{.}\mathbf{code}=$ NE_USER_STOP.

5:    $\mathbf{comm}$ – Nag_Comm *

Pointer to structure of type Nag_Comm; the following members are relevant to f.

user – double *

iuser – Integer *

p – Pointer 

The type Pointer will be void *. Before calling nag_quad_1d_fin_gonnet_vec (d01rgc) you may allocate memory and initialize these pointers with various quantities for use by f when called from nag_quad_1d_fin_gonnet_vec (d01rgc) (see Section 3.3.1.1 in How to Use the NAG Library and its Documentation).

4:    $\mathbf{epsabs}$ – doubleInput

On entry: the absolute accuracy required.

If epsabs is negative, $\left|\mathbf{epsabs}\right|$ is used. See Section 7.

If $\mathbf{epsabs}=0.0$, only the relative error will be used.

5:    $\mathbf{epsrel}$ – doubleInput

On entry: the relative accuracy required.

If epsrel is negative, $\left|\mathbf{epsrel}\right|$ is used. See Section 7.

If $\mathbf{epsrel}=0.0$, only the absolute error will be used otherwise the actual value of epsrel used by nag_quad_1d_fin_gonnet_vec (d01rgc) is $\max \left(\mathit{machine precision},\left|\mathbf{epsrel}\right|\right)$.

Constraint: at least one of epsabs and epsrel must be nonzero.

6:    $\mathbf{dinest}$ – double *Output

On exit: the estimate of the definite integral f.

7:    $\mathbf{errest}$ – double *Output

On exit: the error estimate of the definite integral f.

8:    $\mathbf{nevals}$ – Integer *Output

On exit: the total number of points at which the integrand, $f$, has been evaluated.

9:    $\mathbf{comm}$ – Nag_Comm *

The NAG communication argument (see Section 3.3.1.1 in How to Use the NAG Library and its Documentation).

10:  $\mathbf{fail}$ – 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_ACCURACY

The requested accuracy was not achieved. Consider using larger values of epsabs and epsrel.

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 $〈\mathit{\text{value}}〉$ had an illegal value.

NE_CONVERGENCE

The integral is probably divergent or slowly convergent.

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_TOO_SMALL

Both $\mathbf{epsabs}=0.0$ and $\mathbf{epsrel}=0.0$.

NE_USER_STOP

Exit requested from f with $\mathbf{iflag}=〈\mathit{\text{value}}〉$.

7

Accuracy

8

Parallelism and Performance

9

Further Comments

10

Example

10.1

Program Text

Program Text (d01rgce.c)

10.2

Program Data

10.3

Program Results

Program Results (d01rgce.r)