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

det_by_lu

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Determinant Using Expansion by Lu Factorization

Syntax

# include <cppad/speed/det_by_lu.hpp>

det_by_lu < Scalar > det ( n )

d = det ( a )

Inclusion

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

Constructor

The syntax

det_by_lu < Scalar > det ( n )

constructs the object det which can be used for evaluating the determinant of n by n matrices using LU factorization.

Scalar

The type Scalar can be any NumericType

n

The argument n has prototype

size_t n

det

The syntax

d = det ( a )

returns the determinant of the matrix \(A\) using LU factorization.

a

The argument a has prototype

const Vector & a

It must be a Vector with length \(n * n\) and with It must be a Vector with length \(n * n\) and with elements of type Scalar . The elements of the \(n \times n\) matrix \(A\) are defined, for \(i = 0 , \ldots , n-1\) and \(j = 0 , \ldots , n-1\), by

\[A_{i,j} = a[ i * m + j]\]

d

The return value d has prototype

Scalar d

Vector

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

y [ i ]

where i has type size_t with value less than \(n * n\). This must return a Scalar value corresponding to the i-th element of the vector y . This is the only requirement of the type Vector .

Example

The file det_by_lu.cpp contains an example and test of det_by_lu.hpp .

Source Code

The file det_by_lu.hpp contains the source for this template function.