NAG AD Library Routine Document

f07ca_a1w_f (dgtsv_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.


f07ca_a1w_f is the adjoint version of the primal routine f07caf (dgtsv). Depending on the value of ad_handle, f07ca_a1w_f uses algorithmic differentiation or symbolic adjoints to compute adjoints of the primal.


Fortran Interface
Subroutine f07ca_a1w_f (ad_handle, n, nrhs, dl, d, du, b, ldb, ifail)
Integer, Intent (In):: n, nrhs, ldb
Integer, Intent (Out):: info
Type (nagad_a1w_w_rtype), Intent (Inout):: dl(*), d(*), du(*), b(ldb,*)
Type (c_ptr), Intent (In):: ad_handle
C++ Header Interface
#include <nagad.h>
void f07ca_a1w_f_ (void *&ad_handle, 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 b[], const Integer &ldb, Integer &ifail)


f07caf (dgtsv) computes the solution to a real system of linear equations
AX=B ,  
where A is an n by n tridiagonal matrix and X and B are n by r matrices. For further information see Section 3 in the documentation for f07caf (dgtsv).

Symbolic Adjoint

f07ca_a1w_f can provide symbolic adjoints by setting the symbolic mode as described in Section 3.2.2 in the X10 Chapter Introduction. Please see Section 4 in NAG AD Library Introduction for API description on how to use symbolic adjoints.

Mathematical Background

The symbolic adjoint uses the LU decomposition computed by the primal routine to obtain the adjoint of the right-hand side B by solving
AT· B i,1 = X i,1 , (1)
where B i,1  and X i,1  denote the ith column of the matrices B 1  and X 1  respectively. The adjoint of the matrix A is then computed according to
A 1 = i=1 r - B i,1 · XiT , (2)
where B i,1 and Xi denote the ith column of the matrices B 1 and X respectively.
Please see Du Toit and Naumann (2017).

Usable Adjoints

You can set or access the adjoints of output argument b. The adjoints of all other output arguments are ignored.
f07ca_a1w_f increments the adjoints of input arguments b, d, du and dl according to the first order adjoint model.


Du Toit J, Naumann U (2017) Adjoint Algorithmic Differentiation Tool Support for Typical Numerical Patterns in Computational Finance


f07ca_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:

Error Indicators and Warnings

f07ca_a1w_f uses the standard NAG ifail mechanism. Any errors indicated via info values returned by f07caf may be indicated with the same value returned by ifail. In addition, this routine may return:
An unexpected AD error has been triggered by this routine. Please contact NAG.
See Section 5.2 in the NAG AD Library Introduction for further information.
Dynamic memory allocation failed for AD.
See Section 5.1 in the NAG AD Library Introduction for further information.


Not applicable.

Parallelism and Performance

f07ca_a1w_f is not threaded in any implementation.

Further Comments



The following examples are variants of the example for f07caf (dgtsv), modified to demonstrate calling the NAG AD Library.
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