# NAG AD Library Routine Document

## d01fb_a1w_f (md_gauss_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

d01fb_a1w_f is the adjoint version of the primal routine d01fbf .

## 2Specification

Fortran Interface
 Subroutine d01fb_a1w_f ( ad_handle, ndim, nptvec, lwa, weight, abscis, fun, ret, iuser, ruser, ifail)
 Integer, Intent (In) :: ndim, nptvec(ndim), lwa Integer, Intent (Inout) :: iuser(*), ifail External :: fun Type (nagad_a1w_w_rtype), Intent (In) :: weight(lwa), abscis(lwa) Type (nagad_a1w_w_rtype), Intent (Inout) :: ruser(*) Type (nagad_a1w_w_rtype), Intent (Out) :: ret Type (c_ptr), Intent (In) :: ad_handle
 Subroutine fun ( 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

d01fbf computes an estimate of a multidimensional integral (from $1$ to $20$ dimensions), given the analytic form of the integrand and suitable Gaussian weights and abscissae. For further information see Section 3 in the documentation for d01fbf .

None.

## 5Arguments

d01fb_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.
• nptvec$\mathbf{nptvec}\left(\mathit{j}\right)$ must specify the number of points in the $\mathit{j}$th dimension of the summation, for $\mathit{j}=\mathrm{1},2, \dots ,n$.
• lwa – the dimension of the arrays weight and abscis.
• weight – must contain in succession the weights for the various dimensions, i.e., $\mathbf{weight}\left(k\right)$ contains the $i$th weight for the $j$th dimension, with. $k=\mathbf{nptvec}\left(\mathrm{1}\right)+\mathbf{nptvec}\left(\mathrm{2}\right)+\cdots +\mathbf{nptvec}\left(j-\mathrm{1}\right)+i\text{.}$.
• abscis – must contain in succession the abscissae for the various dimensions, i.e., $\mathbf{abscis}\left(k\right)$ contains the $i$th abscissa for the $j$th dimension, with. $k=\mathbf{nptvec}\left(\mathrm{1}\right)+\mathbf{nptvec}\left(\mathrm{2}\right)+\cdots +\mathbf{nptvec}\left(j-\mathrm{1}\right)+i\text{.}$.
• fun – this argument must return the value of the integrand $f$ at a specified point.
• ret – routine computes an estimate of a multidimensional integral (from $\mathrm{1}$ to $\mathrm{20}$ dimensions), given the analytic form of the integrand and suitable Gaussian weights and abscissae..
• 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

d01fb_a1w_f preserves all error codes from d01fbf 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

d01fb_a1w_f is not threaded in any implementation.