d01pa_a1w_f (md_simplex_a1w)

Note: _a1w_ denotes that first order adjoints are computed in working precision; this has the corresponding argument type nagad_a1w_w_rtype. Further implementations, for example for higher order differentiation or using the tangent linear approach, may become available at later marks of the NAG AD Library. The method of codifying AD implementations in routine name and corresponding argument types is described in the NAG AD Library Introduction.

1Purpose

d01pa_a1w_f is the adjoint version of the primal routine d01paf .

2Specification

Fortran Interface
 Subroutine d01pa_a1w_f ( ad_handle, ndim, vert, ldvert, sdvert, functn, minord, maxord, finvls, esterr, iuser, ruser, ifail)
 Integer, Intent (In) :: ndim, ldvert, sdvert, maxord Integer, Intent (Inout) :: minord, iuser(*), ifail External :: functn Type (nagad_a1w_w_rtype), Intent (Inout) :: vert(ldvert,sdvert), finvls(maxord), ruser(*) Type (nagad_a1w_w_rtype), Intent (Out) :: esterr Type (c_ptr), Intent (In) :: ad_handle
 Subroutine functn ( ad_handle, ndim, x, ret, iuser, ruser)
 Integer, Intent (In) :: ndim Integer, Intent (Inout) :: iuser(*) Type (nagad_a1w_w_rtype), Intent (Inout) :: x(ndim), ruser(*) Type (nagad_a1w_w_rtype), Intent (Out) :: ret Type (c_ptr), Intent (In) :: ad_handle

3Description

d01paf returns a sequence of approximations to the integral of a function over a multidimensional simplex, together with an error estimate for the last approximation. For further information see Section 3 in the documentation for d01paf .

None.

5Arguments

d01pa_a1w_f provides access to all the arguments available in the primal routine. There are also additional arguments specific to AD. A tooltip popup for each argument can be found by hovering over the argument name in Section 2 and a summary of the arguments are provided below:
• ad_handle – a handle to the AD configuration data object, as created by x10aa_a1w_f.
• ndim$n$, the number of dimensions of the integral.
• vert – on entry: $\mathbf{vert}\left(\mathit{i},\mathit{j}\right)$ must be set to the $\mathit{j}$th component of the $\mathit{i}$th vertex for the simplex integration region, for $\mathit{j}=\mathrm{1},2, \dots ,n$, for $\mathit{i}=\mathrm{1},2, \dots ,n+\mathrm{1}$. on exit: these values are unchanged.
• ldvert – the first dimension of the array vert.
• sdvert – the second dimension of the array vert.
• functnfunctn must return the value of the integrand $f$ at a given point.
• minord – on entry: must specify the highest order of the approximations currently available in the array finvls. on exit: $\mathbf{minord}=\mathbf{maxord}$.
• maxord – the highest order of approximation to the integral to be computed.
• finvls – on entry: if $\mathbf{minord}>\mathrm{0}$, $\mathbf{finvls}\left(\mathrm{1}\right),\mathbf{finvls}\left(\mathrm{2}\right),\dots ,\mathbf{finvls}\left(\mathbf{minord}\right)$ must contain approximations to the integral previously computed by routine. on exit: contains these values unchanged, and the newly computed values $\mathbf{finvls}\left(\mathbf{minord}+\mathrm{1}\right),\mathbf{finvls}\left(\mathbf{minord}+\mathrm{2}\right),\dots ,\mathbf{finvls}\left(\mathbf{maxord}\right)$.
• esterr – on exit: an absolute error estimate for $\mathbf{finvls}\left(\mathbf{maxord}\right)$.
• iuser – may be used to pass information to user-supplied argument(s).
• ruser – may be used to pass information to user-supplied argument(s).
• ifail – on entry: ifail must be set to $\mathrm{0}$, $-\mathrm{1}\text{ or }\mathrm{1}$. on exit: ifail = 0 unless the routine detects an error or a warning has been flagged (see Section 6).

6Error Indicators and Warnings

d01pa_a1w_f preserves all error codes from d01paf and in addition can return:
$\mathbf{ifail}=-89$
See Section 5.2 in the NAG AD Library Introduction for further information.
$\mathbf{ifail}=-899$
Dynamic memory allocation failed for AD.
See Section 5.1 in the NAG AD Library Introduction for further information.

Not applicable.

8Parallelism and Performance

d01pa_a1w_f is not threaded in any implementation.