NAG CL Interface
d01rgc (dim1_​fin_​gonnet_​vec)

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

1: $\mathbf{a}$ – double Input

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

2: $\mathbf{b}$ – double Input

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 user External 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: $\mathbf{x}\left[\mathit{dim}\right]$ – const double Input

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

2: $\mathbf{nx}$ – Integer Input

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

3: $\mathbf{fv}\left[\mathit{dim}\right]$ – double Output

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 d01rgc you may allocate memory and initialize these pointers with various quantities for use by f when called from d01rgc (see Section 3.1.1 in the Introduction to the NAG Library CL Interface).

4: $\mathbf{epsabs}$ – double Input

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: $\mathbf{epsrel}$ – double Input

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 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 3.1.1 in the Introduction to the NAG Library CL Interface).

10: $\mathbf{fail}$ – 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_ACCURACY

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

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 $〈\mathit{\text{value}}〉$ 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 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_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

10.2 Program Data

10.3 Program Results