Performs SVD and back substitute to solve equations. More...
#include <TooN/GR_SVD.h>
Public Member Functions | |
| template<class Precision2 , class Base > | |
| GR_SVD (const Matrix< M, N, Precision2, Base > &A) | |
| const Matrix< M, N, Precision > & | get_U () |
| const Matrix< N, N, Precision > & | get_V () |
| const Vector< N, Precision > & | get_diagonal () |
| Precision | get_largest_singular_value () |
| Precision | get_smallest_singular_value () |
| int | get_smallest_singular_value_index () |
| void | get_inv_diag (Vector< N > &inv_diag, const Precision condition) |
| Return the pesudo-inverse diagonal. More... | |
| template<int Rows2, int Cols2, typename P2 , typename B2 > | |
| Matrix< N, Cols2, typename Internal::MultiplyType< Precision, P2 >::type > | backsub (const Matrix< Rows2, Cols2, P2, B2 > &rhs, const Precision condition=1e9) |
| Calculate result of multiplying the (pseudo-)inverse of M by another matrix. More... | |
| template<int Size, typename P2 , typename B2 > | |
| Vector< N, typename Internal::MultiplyType< Precision, P2 >::type > | backsub (const Vector< Size, P2, B2 > &rhs, const Precision condition=1e9) |
| Calculate result of multiplying the (pseudo-)inverse of M by a vector. More... | |
| Matrix< N, M, Precision > | get_pinv (const Precision condition=1e9) |
| Get the pseudo-inverse \(M^{\dagger}\). | |
| void | reorder () |
| Reorder the components so the singular values are in descending order. | |
Static Public Attributes | |
| static const int | BigDim = M>N?M:N |
| static const int | SmallDim = M<N?M:N |
Protected Member Functions | |
| void | Bidiagonalize () |
| void | Accumulate_RHS () |
| void | Accumulate_LHS () |
| void | Diagonalize () |
| bool | Diagonalize_SubLoop (int k, Precision &z) |
Protected Attributes | |
| Vector< N, Precision > | vDiagonal |
| Vector< BigDim, Precision > | vOffDiagonal |
| Matrix< M, N, Precision > | mU |
| Matrix< N, N, Precision > | mV |
| int | nError |
| int | nIterations |
| Precision | anorm |
Detailed Description
template<int M, int N = M, class Precision = DefaultPrecision, bool WANT_U = 1, bool WANT_V = 1>
class TooN::GR_SVD< M, N, Precision, WANT_U, WANT_V >
Performs SVD and back substitute to solve equations.
This code is a c++ translation of the FORTRAN routine give in George E. Forsythe et al, Computer Methods for Mathematical Computations, Prentice-Hall 1977. That code itself is a translation of the ALGOL routine by Golub and Reinsch, Num. Math. 14, 403-420, 1970.
N.b. the singular values returned by this routine are not sorted. N.b. this also means that even for MxN matrices with M<N, N singular values are computed and used.
The template parameters WANT_U and WANT_V may be set to false to indicate that U and/or V are not needed for a minor speed-up.
Member Function Documentation
◆ backsub() [1/2]
|
inline |
Calculate result of multiplying the (pseudo-)inverse of M by another matrix.
For a matrix \(A\), this calculates \(M^{\dagger}A\) by back substitution (i.e. without explictly calculating the (pseudo-)inverse). See the detailed description for a description of condition variables.
◆ backsub() [2/2]
|
inline |
Calculate result of multiplying the (pseudo-)inverse of M by a vector.
For a vector \(b\), this calculates \(M^{\dagger}b\) by back substitution (i.e. without explictly calculating the (pseudo-)inverse). See the detailed description for a description of condition variables.
◆ get_inv_diag()
|
inline |
Return the pesudo-inverse diagonal.
The reciprocal of the diagonal elements is returned if the elements are well scaled with respect to the largest element, otherwise 0 is returned.
- Parameters
-
inv_diag Vector in which to return the inverse diagonal. condition Elements must be larger than this factor times the largest diagonal element to be considered well scaled.
The documentation for this class was generated from the following file:
- TooN/GR_SVD.h
