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

det_grad_33

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Check Gradient of Determinant of 3 by 3 matrix

Syntax

# include <cppad/speed/det_grad_33.hpp>

ok = det_grad_33 ( x , g )

Purpose

This routine can be used to check a method for computing the gradient of the determinant of a matrix.

Inclusion

The template function det_grad_33 is defined in the CppAD namespace by including the file cppad/speed/det_grad_33.hpp (relative to the CppAD distribution directory).

x

The argument x has prototype

const Vector & x

. It contains the elements of the matrix \(X\) in row major order; i.e.,

\[X_{i,j} = x [ i * 3 + j ]\]

g

The argument g has prototype

const Vector & g

. It contains the elements of the gradient of \(\det ( X )\) in row major order; i.e.,

\[\D{\det (X)}{X(i,j)} = g [ i * 3 + j ]\]

Vector

If y is a Vector object, it must support the syntax

y [ i ]

where i has type size_t with value less than 9. This must return a double value corresponding to the i-th element of the vector y . This is the only requirement of the type Vector .

ok

The return value ok has prototype

bool ok

It is true, if the gradient g passes the test and false otherwise.

Source Code

The file det_grad_33.hpp contains the source code for this template function.