# NAG AD Library Routine Document

## f07ce_a1w_f (dgttrs_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

f07ce_a1w_f is the adjoint version of the primal routine f07cef (dgttrs).

## 2Specification

Fortran Interface
 Subroutine f07ce_a1w_f ( ad_handle, trans, n, nrhs, dl, d, du, du2, ipiv, b, ldb, ifail)
 Integer, Intent (In) :: n, nrhs, ipiv(*), ldb Integer, Intent (Out) :: info Type (nagad_a1w_w_rtype), Intent (In) :: dl(*), d(*), du(*), du2(*) Type (nagad_a1w_w_rtype), Intent (Inout) :: b(ldb,*) Character (1), Intent (In) :: trans Type (c_ptr), Intent (In) :: ad_handle
 void f07ce_a1w_f_ ( void *&ad_handle, const char *trans, const Integer &n, const Integer &nrhs, nagad_a1w_w_rtype dl[], nagad_a1w_w_rtype d[], nagad_a1w_w_rtype du[], nagad_a1w_w_rtype du2[], Integer ipiv[], nagad_a1w_w_rtype b[], const Integer &ldb, Integer &ifail, const Charlen length_trans)

## 3Description

f07cef (dgttrs) computes the solution to a real system of linear equations $AX=B$ or ${A}^{\mathrm{T}}X=B$, where $A$ is an $n$ by $n$ tridiagonal matrix and $X$ and $B$ are $n$ by $r$ matrices, using the $LU$ factorization returned by f07cdf (dgttrf). For further information see Section 3 in the documentation for f07cef (dgttrs).

None.

## 5Arguments

f07ce_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.
• trans – specifies the equations to be solved as follows.
• n$n$, the order of the matrix $A$.
• nrhs$r$, the number of right-hand sides, i.e., the number of columns of the matrix $B$.
• dl – must contain the $\left(n-\mathrm{1}\right)$ multipliers that define the matrix $L$ of the $LU$ factorization of $A$.
• d – must contain the $n$ diagonal elements of the upper triangular matrix $U$ from the $LU$ factorization of $A$.
• du – must contain the $\left(n-\mathrm{1}\right)$ elements of the first superdiagonal of $U$.
• du2 – must contain the $\left(n-\mathrm{2}\right)$ elements of the second superdiagonal of $U$.
• ipiv – must contain the $n$ pivot indices that define the permutation matrix $P$.
• b – on entry: the $n$ by $r$ matrix of right-hand sides $B$. on exit: the $n$ by $r$ solution matrix $X$.
• ldb – the first dimension of the array b.
• ifail – on exit: $\mathbf{ifail}=\mathrm{0}$ unless the routine detects an error (see Section 6).

## 6Error Indicators and Warnings

f07ce_a1w_f uses the standard NAG ifail mechanism. Any errors indicated via info values returned by f07cef may be indicated with the same value returned by ifail. In addition, this routine may 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

f07ce_a1w_f is not threaded in any implementation.