The Simplex Parameters for CUBATR.

We describe only those parameters that are specific for the simplex (and some additional ones to make the description selfcontained). For all parameters we refer to [10].

Input Parameters

$n$

Integer number of variables in the integrand(s). We require $n > 0$.

$l$

Integer number of components in the vector integrand function.

$V$

A real array of dimension $(n,0:n,m)$. V($i,j,k$) must contain the $i^{th}$ component of the $j^{th}$ vertex of the $k^{th}$ input simplex region, for $i = 1,...,n$, $j = 0,...,n$, $k = 1,...,m$.

$m$

Integer number of subregions.

RGTYPE

An integer vector of length $m$.
For integration over simplices all components of RGTYPE must be set to 1.

KEY

An optional integer parameter that selects the integration rule. KEY must satisfy $0 \leq$ KEY $\leq 4$.
This is an optional parameter with default value 0.
The following table gives the polynomial degrees of the different integration rules for the possible values of KEY and for $n = 2$, $n = 3$ and $n > 3$.

KEY $\backslash n$	2	3	$>$ 3
0	13	8	7
1	3	3	3
2	5	5	5
3	7	7	7
4	9	9	9

JOB

An optional integer memory allocation parameter. This is an optional parameter with default value 1.
If JOB = 0, no integration is done and all previously allocated memory is freed.
If JOB = 1, the global adaptive integration is done as requested.
If JOB = 12, the same algorithm is used but a simplex is always divided in 2 parts.
The default is JOB = 1.

TUNE

A real error estimate tuning parameter. TUNE must satisfy $0 \leq$ TUNE $\leq 1$.
This is an optional parameter with default value 1.
For TUNE = 0, a liberal error estimate is used.
For TUNE = 1, a conservative error estimate is used; this is the most reliable case.