NAG Library Function Document

nag_quad_1d_fin_gonnet_vec (d01rgc)

1  Purpose

2  Specification

3  Description

4  References

5  Arguments

1:     a – doubleInput

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

2:     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:     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:     x[nx] – const doubleInput

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

2:     nx – IntegerInput

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

3:     fv[nx] – 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:     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:     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 3.2.1.1 in the Essential Introduction).

4:     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:     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:     dinest – double *Output

On exit: the estimate of the definite integral f.

7:     errest – double *Output

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

8:     nevals – Integer *Output

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

9:     comm – Nag_Comm *Communication Structure

The NAG communication argument (see Section 3.2.1.1 in the Essential Introduction).

10:   fail – NagError *Input/Output

The NAG error argument (see Section 3.6 in the Essential Introduction).

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.

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.

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)