\(\newcommand{\W}[1]{ \; #1 \; }\) \(\newcommand{\R}[1]{ {\rm #1} }\) \(\newcommand{\B}[1]{ {\bf #1} }\) \(\newcommand{\D}[2]{ \frac{\partial #1}{\partial #2} }\) \(\newcommand{\DD}[3]{ \frac{\partial^2 #1}{\partial #2 \partial #3} }\) \(\newcommand{\Dpow}[2]{ \frac{\partial^{#1}}{\partial {#2}^{#1}} }\) \(\newcommand{\dpow}[2]{ \frac{ {\rm d}^{#1}}{{\rm d}\, {#2}^{#1}} }\)
det_by_minor¶
View page sourceDeterminant Using Expansion by Minors¶
Syntax¶
# include <cppad/speed/det_by_minor.hpp>
det_by_minor
< Scalar > det ( n )Inclusion¶
The template class det_by_minor
is defined in the CppAD
namespace by including the file cppad/speed/det_by_minor.hpp
.
Constructor¶
The syntax
det_by_minor
< Scalar > det ( n )
constructs the object det which can be used for evaluating the determinant of n by n matrices using expansion by minors.
Scalar¶
The type Scalar must satisfy the same conditions as in the function det_of_minor .
n¶
The argument n has prototype
size_t
n
det¶
The syntax
d = det ( a )
returns the determinant of the matrix A using expansion by minors.
a¶
The argument a has prototype
const
Vector & a
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
d¶
The return value d has prototype
Scalar d
It is equal to the determinant of \(A\).
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_minor.cpp
contains an example and test of det_by_minor.hpp
.
Source Code¶
The file det_by_minor.hpp contains the source for this template function.