cv::SVD Class Reference

Singular Value Decomposition. More...

#include "core.hpp"

Public Types
enum	Flags {   MODIFY_A = 1,   NO_UV = 2,   FULL_UV = 4 }

Public Member Functions
	SVD ()
	the default constructor More...
	SVD (InputArray src, int flags=0)
void	backSubst (InputArray rhs, OutputArray dst) const
	performs a singular value back substitution. More...
SVD &	operator() (InputArray src, int flags=0)
	the operator that performs SVD. The previously allocated u, w and vt are released. More...

Static Public Member Functions
static void	backSubst (InputArray w, InputArray u, InputArray vt, InputArray rhs, OutputArray dst)
	performs back substitution More...
template<typename _Tp , int m, int n, int nm, int nb>
static void	backSubst (const Matx< _Tp, nm, 1 > &w, const Matx< _Tp, m, nm > &u, const Matx< _Tp, n, nm > &vt, const Matx< _Tp, m, nb > &rhs, Matx< _Tp, n, nb > &dst)
static void	compute (InputArray src, OutputArray w, OutputArray u, OutputArray vt, int flags=0)
	decomposes matrix and stores the results to user-provided matrices More...
static void	compute (InputArray src, OutputArray w, int flags=0)
template<typename _Tp , int m, int n, int nm>
static void	compute (const Matx< _Tp, m, n > &a, Matx< _Tp, nm, 1 > &w, Matx< _Tp, m, nm > &u, Matx< _Tp, n, nm > &vt)
template<typename _Tp , int m, int n, int nm>
static void	compute (const Matx< _Tp, m, n > &a, Matx< _Tp, nm, 1 > &w)
static void	solveZ (InputArray src, OutputArray dst)
	solves an under-determined singular linear system More...

Public Attributes
Mat	u
Mat	vt
Mat	w

Detailed Description

Singular Value Decomposition.

Class for computing Singular Value Decomposition of a floating-point matrix. The Singular Value Decomposition is used to solve least-square problems, under-determined linear systems, invert matrices, compute condition numbers, and so on.

If you want to compute a condition number of a matrix or an absolute value of its determinant, you do not need u and vt. You can pass flags=SVD::NO_UV|... . Another flag SVD::FULL_UV indicates that full-size u and vt must be computed, which is not necessary most of the time.

See also

invert, solve, eigen, determinant

Member Enumeration Documentation

Flags

enum cv::SVD::Flags

Enumerator
MODIFY_A	allow the algorithm to modify the decomposed matrix; it can save space and speed up processing. currently ignored.
NO_UV	indicates that only a vector of singular values w is to be processed, while u and vt will be set to empty matrices
FULL_UV	when the matrix is not square, by default the algorithm produces u and vt matrices of sufficiently large size for the further A reconstruction; if, however, FULL_UV flag is specified, u and vt will be full-size square orthogonal matrices.

Constructor & Destructor Documentation

SVD() [1/2]

cv::SVD::SVD

(

)

the default constructor

initializes an empty SVD structure

SVD() [2/2]

cv::SVD::SVD	(	InputArray	src,
		int	flags = 0
	)

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts. initializes an empty SVD structure and then calls SVD::operator()

Parameters

src	decomposed matrix. The depth has to be CV_32F or CV_64F.
flags	operation flags (SVD::Flags)

Member Function Documentation

backSubst() [1/3]

static void cv::SVD::backSubst ( InputArray  w, InputArray  u, InputArray  vt, InputArray  rhs, OutputArray  dst  )

static

performs back substitution

backSubst() [2/3]

void cv::SVD::backSubst	(	InputArray	rhs,
		OutputArray	dst
	)		const

performs a singular value back substitution.

The method calculates a back substitution for the specified right-hand side:

\[\texttt{x} = \texttt{vt} ^T \cdot diag( \texttt{w} )^{-1} \cdot \texttt{u} ^T \cdot \texttt{rhs} \sim \texttt{A} ^{-1} \cdot \texttt{rhs}\]

Using this technique you can either get a very accurate solution of the convenient linear system, or the best (in the least-squares terms) pseudo-solution of an overdetermined linear system.

Parameters

rhs	right-hand side of a linear system (u*w*v')*dst = rhs to be solved, where A has been previously decomposed.
dst	found solution of the system.

Note

Explicit SVD with the further back substitution only makes sense if you need to solve many linear systems with the same left-hand side (for example, src ). If all you need is to solve a single system (possibly with multiple rhs immediately available), simply call solve add pass DECOMP_SVD there. It does absolutely the same thing.

backSubst() [3/3]

template<typename _Tp , int m, int n, int nm, int nb>

static void cv::SVD::backSubst ( const Matx< _Tp, nm, 1 > &  w, const Matx< _Tp, m, nm > &  u, const Matx< _Tp, n, nm > &  vt, const Matx< _Tp, m, nb > &  rhs, Matx< _Tp, n, nb > &  dst  )

static

Todo:

document

compute() [1/4]

static void cv::SVD::compute ( InputArray  src, OutputArray  w, OutputArray  u, OutputArray  vt, int  flags = 0  )

static

decomposes matrix and stores the results to user-provided matrices

The methods/functions perform SVD of matrix. Unlike SVD::SVD constructor and SVD::operator(), they store the results to the user-provided matrices:

Mat A, w, u, vt;
SVD::compute(A, w, u, vt);

Parameters

src	decomposed matrix. The depth has to be CV_32F or CV_64F.
w	calculated singular values
u	calculated left singular vectors
vt	transposed matrix of right singular vectors
flags	operation flags - see SVD::Flags.

compute() [2/4]

static void cv::SVD::compute ( InputArray  src, OutputArray  w, int  flags = 0  )

static

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts. computes singular values of a matrix

Parameters

src	decomposed matrix. The depth has to be CV_32F or CV_64F.
w	calculated singular values
flags	operation flags - see SVD::Flags.

compute() [3/4]

template<typename _Tp , int m, int n, int nm>

static void cv::SVD::compute ( const Matx< _Tp, m, n > &  a, Matx< _Tp, nm, 1 > &  w, Matx< _Tp, m, nm > &  u, Matx< _Tp, n, nm > &  vt  )

static

Todo:

document

compute() [4/4]

template<typename _Tp , int m, int n, int nm>

static void cv::SVD::compute ( const Matx< _Tp, m, n > &  a, Matx< _Tp, nm, 1 > &  w  )

static

Todo:

document

operator()()

SVD& cv::SVD::operator()	(	InputArray	src,
		int	flags = 0
	)

the operator that performs SVD. The previously allocated u, w and vt are released.

The operator performs the singular value decomposition of the supplied matrix. The u,vt , and the vector of singular values w are stored in the structure. The same SVD structure can be reused many times with different matrices. Each time, if needed, the previous u,vt , and w are reclaimed and the new matrices are created, which is all handled by Mat::create.

Parameters

src	decomposed matrix. The depth has to be CV_32F or CV_64F.
flags	operation flags (SVD::Flags)

solveZ()

static void cv::SVD::solveZ ( InputArray  src, OutputArray  dst  )

static

solves an under-determined singular linear system

The method finds a unit-length solution x of a singular linear system A*x = 0. Depending on the rank of A, there can be no solutions, a single solution or an infinite number of solutions. In general, the algorithm solves the following problem:

\[dst = \arg \min _{x: \| x \| =1} \| src \cdot x \|\]

Parameters

src	left-hand-side matrix.
dst	found solution.

Member Data Documentation

u

Mat cv::SVD::u

vt

Mat cv::SVD::vt

w

Mat cv::SVD::w

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The documentation for this class was generated from the following file:

• core/include/opencv2/core.hpp