\(\newcommand{\W}[1]{ \; #1 \; }\) \(\newcommand{\R}[1]{ {\rm #1} }\) \(\newcommand{\B}[1]{ {\bf #1} }\) \(\newcommand{\D}[2]{ \frac{\partial #1}{\partial #2} }\) \(\newcommand{\DD}[3]{ \frac{\partial^2 #1}{\partial #2 \partial #3} }\) \(\newcommand{\Dpow}[2]{ \frac{\partial^{#1}}{\partial {#2}^{#1}} }\) \(\newcommand{\dpow}[2]{ \frac{ {\rm d}^{#1}}{{\rm d}\, {#2}^{#1}} }\)

link_det_lu

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Speed Testing Gradient of Determinant Using Lu Factorization

Prototype

extern bool link_det_lu(
    size_t                     size      ,
    size_t                     repeat    ,
    CppAD::vector<double>&     matrix    ,
    CppAD::vector<double>&     gradient
);

Purpose

Each package must define a version of this routine as specified below. This is used by the speed_main program to run the corresponding speed and correctness tests.

Method

The same template routine det_by_lu is used by the different AD packages.

Return Value

If this speed test is not yet supported by a particular package , the corresponding return value for link_det_lu should be false .

size

The argument size is the number of rows and columns in the matrix.

repeat

The argument repeat is the number of different matrices that the gradient (or determinant) is computed for.

matrix

The argument matrix is a vector with size * size elements. The input value of its elements does not matter. The output value of its elements is the last matrix that the gradient (or determinant) is computed for.

gradient

The argument gradient is a vector with size * size elements. The input value of its elements does not matter. The output value of its elements is the gradient of the determinant of matrix with respect to its elements.

double

In the case where package is double , only the first element of gradient is used and it is actually the determinant value (the gradient value is not computed).