naginterfaces.library.quad.dim1_​gen_​vec_​multi_​dimreq

naginterfaces.library.quad.dim1_gen_vec_multi_dimreq(ni, iopts, opts)

The dimension of the arrays that must be passed as actual arguments to dim1_gen_vec_multi_rcomm() are dependent upon a number of factors. dim1_gen_vec_multi_dimreq returns the correct size of these arrays enabling dim1_gen_vec_multi_rcomm() to be called successfully.

For full information please refer to the NAG Library document for d01rc

https://support.nag.com/numeric/nl/nagdoc_30/flhtml/d01/d01rcf.html

Parameters

niint

$n_i$, the number of integrals which will be approximated in the subsequent call to dim1_gen_vec_multi_rcomm().

ioptsint, array-like, shape $\left(100\right)$

The integer option array as returned by opt_set().

optsfloat, array-like, shape $\left(100\right)$

The real option array as returned by opt_set().

Returns

lenxrqint

$\text{lenxrq}$, the minimum dimension of the array $\text{x}$ that can be used in a subsequent call to dim1_gen_vec_multi_rcomm().

ldfmrqint

$\text{ldfmrq}$, the minimum leading dimension of the array $\text{fm}$ that can be used in a subsequent call to dim1_gen_vec_multi_rcomm().

sdfmrqint

$\text{sdfmrq}$, the minimum second dimension of the array $\text{fm}$ that can be used in a subsequent call to dim1_gen_vec_multi_rcomm().

Note: the minimum dimension of the array $\text{fm}$ is $\text{ldfmrq}\times \text{sdfmrq}$.

licminint

$\text{licmin}$, the minimum dimension of the array $\text{icom}$ that must be passed to dim1_gen_vec_multi_rcomm() to enable it to calculate a single approximation to all the $n_i$ integrals over the interval $[a,b]$ with $s_{\text{pri}}$ initial segments.

licmaxint

$\text{licmax}$ the dimension of the array $\text{icom}$ that must be passed to dim1_gen_vec_multi_rcomm() to enable it to exhaust the adaptive process controlled by the currently set options for the $n_i$ integrals over the interval $[a,b]$ with $s_{\text{pri}}$ initial segments.

lcminint

$\text{lcmin}$, the minimum dimension of the array $\text{com}$ that must be passed to dim1_gen_vec_multi_rcomm() to enable it to calculate a single approximation to all the $n_i$ integrals over the interval $[a,b]$ with $s_{\text{pri}}$ initial segments.

lcmaxint

$\text{lcmax}$, the dimension of the array $\text{com}$ that must be passed to dim1_gen_vec_multi_rcomm() to enable it to exhaust the adaptive process controlled by the currently set options for the $n_i$ integrals over the interval $[a,b]$ with $s_{\text{pri}}$ initial segments.

Raises

NagValueError

(errno $21$)

On entry, $ni=⟨value⟩$.

Constraint: $ni>0$.

(errno $1001$)

One of the option arrays $iopts$ or $opts$ has become corrupted. Re-initialize the arrays using opt_set().

Notes

dim1_gen_vec_multi_dimreq returns the minimum dimension of the arrays $\text{x}$ ($\text{lenxrq}$), $\text{fm}$ ($\text{ldfmrq}\times \text{sdfmrq}$), $\text{icom}$ ($\text{licmin}$) and $\text{com}$ ($\text{lcmin}$) that must be passed to dim1_gen_vec_multi_rcomm() to enable the integration to commence given options currently set for the $ni$ integrands. dim1_gen_vec_multi_dimreq also returns the upper bounds $\text{licmax}$ and $\text{lcmax}$ for the dimension of the arrays $\text{icom}$ and $\text{com}$, that could possibly be required with the chosen options.

All the minimum values $\text{lenxrq}$, $\text{ldfmrq}$, $\text{sdfmrq}$, $\text{licmin}$ and $\text{lcmin}$, and subsequently all the maximum values $\text{licmax}$ and $\text{lcmax}$ may be affected if different options are set, and hence dim1_gen_vec_multi_dimreq should be called after any options are set, and before the first call to dim1_gen_vec_multi_rcomm().

A segment is here defined as a (possibly maximal) subset of the domain of integration. During subdivision, a segment is bisected into two new segments.