PARP Research Group Universidad de Murcia

src/qvmath/qvmatrixalgebra.cpp File Reference

File from the QVision library. More...

#include <limits>
#include <iostream>
#include <qvmath.h>
#include <qvdefines.h>
#include <qvmath/qvmatrixalgebra.h>
#include <QVPermutation>

Go to the source code of this file.

Functions

void singularValueDecomposition (const QVMatrix &M, QVMatrix &U, QVVector &s, QVMatrix &V, const TQVSVD_Method method)
 Obtains the Singular Value Decomposition (SVD) of a rectangular $ m \times n $ matrix M.
void solveFromSingularValueDecomposition (const QVMatrix &U, const QVVector &s, const QVMatrix &V, QVMatrix &X, const QVMatrix &B)
 Solves the linear system $M X = B$ for the unknown matrix $X$, using the previously obtained singular value decomposition $M = U diag(s) V^T$.
void solveFromSingularValueDecomposition (const QVMatrix &U, const QVVector &s, const QVMatrix &V, QVVector &x, const QVVector &b)
 Solves the linear system $M x = b$ for the unknown vector $x$, using the previously obtained singular value decomposition $M = U diag(s) V^T$.
void solveBySingularValueDecomposition (const QVMatrix &M, QVVector &x, const QVVector &b, const TQVSVD_Method method)
 Solves the linear system $M x = b$ for the unknown vector $x$, using the singular value decomposition $M = U diag(s) V^T$.
void solveBySingularValueDecomposition (const QVMatrix &M, QVMatrix &X, const QVMatrix &B, const TQVSVD_Method method)
 Solves the linear system $M X = B$ for the unknown matrix $X$, using the singular value decomposition $M = U diag(s) V^T$.
void solveBySingularValueDecomposition (const QVMatrix &M, QVVector &x, const QVVector &b, QVMatrix &U, QVVector &s, QVMatrix &V, const TQVSVD_Method method)
 Solves the linear system $M x = b$ for the unknown vector $x$, using the singular value decomposition $M = U diag(s) V^T$.
void solveBySingularValueDecomposition (const QVMatrix &M, QVMatrix &X, const QVMatrix &B, QVMatrix &U, QVVector &s, QVMatrix &V, const TQVSVD_Method method)
 Solves the linear system $M X = B$ for the unknown matrix $X$, using the singular value decomposition $M = U diag(s) V^T$.
double singularValueDecompositionResidual (const QVMatrix &M, const QVMatrix &U, const QVVector &s, const QVMatrix &V)
 Checks for correctness of the SVD of a matrix.
void singularValues (const QVMatrix &M, QVVector &s, const TQVSV_Method method)
 Gets the singular values of a matrix.
double singularValuesResidual (const QVMatrix &M, const QVVector &s)
 Checks for correctness of the singular values of a matrix.
void CholeskyDecomposition (const QVMatrix &M, QVMatrix &L, const TQVCholesky_Method method)
 Obtains the Cholesky decomposition of a symmetric and positive definite matrix.
void solveFromCholeskyDecomposition (const QVMatrix &L, QVMatrix &X, const QVMatrix &B)
 Solves the linear system $M X = B$ for the unknown matrix $X$, using the previously obtained Cholesky decomposition $ M = L L^{T} $.
void solveFromCholeskyDecomposition (const QVMatrix &L, QVVector &x, const QVVector &b)
 Solves the linear system $M x = b$ for the unknown vector $x$, using the previously obtained Cholesky decomposition $ M = L L^{T} $.
void solveByCholeskyDecomposition (const QVMatrix &M, QVMatrix &X, const QVMatrix &B, const TQVCholesky_Method method)
 Solves the linear system $M X = B$ for the unknown matrix $X$, using the Cholesky decomposition $ M = L L^{T} $.
void solveByCholeskyDecomposition (const QVMatrix &M, QVVector &x, const QVVector &b, const TQVCholesky_Method method)
 Solves the linear system $M x = b$ for the unknown vector $x$, using the Cholesky decomposition $ M = L L^{T} $.
void solveByCholeskyDecomposition (const QVMatrix &M, QVMatrix &X, const QVMatrix &B, QVMatrix &L, const TQVCholesky_Method method)
 Solves the linear system $M X = B$ for the unknown matrix $X$, using the Cholesky decomposition $ M = L L^{T} $.
void solveByCholeskyDecomposition (const QVMatrix &M, QVVector &x, const QVVector &b, QVMatrix &L, const TQVCholesky_Method method)
 Solves the linear system $M x = b$ for the unknown vector $x$, using the Cholesky decomposition $ M = L L^{T} $.
double CholeskyDecompositionResidual (const QVMatrix &M, const QVMatrix &L)
 Checks for correctness of the Cholesky decomposition of a matrix.
void LUDecomposition (const QVMatrix &M, QVMatrix &P, QVMatrix &L, QVMatrix &U, const TQVLU_Method method)
 Obtains the LU decomposition of a rectangular $ m \times n $ matrix.
void solveFromLUDecomposition (const QVMatrix &P, const QVMatrix &L, const QVMatrix &U, QVMatrix &X, const QVMatrix &B)
 Solves the linear system $M X = B$ for the unknown matrix $X$, using the previously obtained LU decomposition of M:
void solveFromLUDecomposition (const QVMatrix &P, const QVMatrix &L, const QVMatrix &U, QVVector &x, const QVVector &b)
 Solves the linear system $M x = b$ for the unknown vector $x$, using the previously obtained LU decomposition $ M = P L U $.
void solveByLUDecomposition (const QVMatrix &M, QVMatrix &X, const QVMatrix &B, const TQVLU_Method method)
 Solves the linear system $M X = B$ for the unknown matrix $X$, using the LU decomposition $ M = P L U $.
void solveByLUDecomposition (const QVMatrix &M, QVVector &x, const QVVector &b, const TQVLU_Method method)
 Solves the linear system $M x = b$ for the unknown vector $x$, using the LU decomposition $ M = P L U $.
void solveByLUDecomposition (const QVMatrix &M, QVMatrix &X, const QVMatrix &B, QVMatrix &P, QVMatrix &L, QVMatrix &U, const TQVLU_Method method)
 Solves the linear system $M X = B$ for the unknown matrix $X$, using the LU decomposition $ M = P L U $.
void solveByLUDecomposition (const QVMatrix &M, QVVector &x, const QVVector &b, QVMatrix &P, QVMatrix &L, QVMatrix &U, const TQVLU_Method method)
 Solves the linear system $M x = b$ for the unknown vector $x$, using the LU decomposition $ M = P L U $.
double LUDecompositionResidual (const QVMatrix &M, const QVMatrix &P, const QVMatrix &L, const QVMatrix &U)
 Checks for correctness of the LU decomposition of a matrix.
void QRDecomposition (const QVMatrix &M, QVMatrix &Q, QVMatrix &R, const TQVQR_Method method)
 Obtains the QR decomposition of a rectangular $ m \times n $ matrix.
double QRDecompositionResidual (const QVMatrix &M, const QVMatrix &Q, const QVMatrix &R)
 Checks for correctness of the QR decomposition of a matrix.
void QLDecomposition (const QVMatrix &M, QVMatrix &Q, QVMatrix &L, const TQVQR_Method method)
 Obtains the QL decomposition of a rectangular $ m \times n $ matrix.
double QLDecompositionResidual (const QVMatrix &M, const QVMatrix &Q, const QVMatrix &L)
 Checks for correctness of the QL decomposition of a matrix.
void RQDecomposition (const QVMatrix &M, QVMatrix &R, QVMatrix &Q, const TQVQR_Method method)
 Obtains the RQ decomposition of a rectangular $ m \times n $ matrix.
double RQDecompositionResidual (const QVMatrix &M, const QVMatrix &R, const QVMatrix &Q)
 Checks for correctness of the RQ decomposition of a matrix.
void LQDecomposition (const QVMatrix &M, QVMatrix &L, QVMatrix &Q, const TQVQR_Method method)
 Obtains the LQ decomposition of a rectangular $ m \times n $ matrix.
double LQDecompositionResidual (const QVMatrix &M, const QVMatrix &L, const QVMatrix &Q)
 Checks for correctness of the LQ decomposition of a matrix.
void solveFromQRDecomposition (const QVMatrix &Q, const QVMatrix &R, QVMatrix &X, const QVMatrix &B)
 Solves the linear system $M X = B$ for the unknown matrix $X$, using the previously obtained QR decomposition of M:
void solveFromQRDecomposition (const QVMatrix &Q, const QVMatrix &R, QVVector &x, const QVVector &b)
 Solves the linear system $M x = b$ for the unknown vector $x$, using the previously obtained QR decomposition of M:
void solveByQRDecomposition (const QVMatrix &M, QVVector &x, const QVVector &b, const TQVQR_Method method)
 Solves the linear system $M x = b$ for the unknown vector $x$, using the QR decomposition of M:
void solveByQRDecomposition (const QVMatrix &M, QVMatrix &X, const QVMatrix &B, const TQVQR_Method method)
 Solves the linear system $M X = B$ for the unknown matrix $X$, using the QR decomposition of M:
void solveByQRDecomposition (const QVMatrix &M, QVVector &x, const QVVector &b, QVMatrix &Q, QVMatrix &R, const TQVQR_Method method)
 Solves the linear system $M x = b$ for the unknown vector $x$, using the QR decomposition of M:
void solveByQRDecomposition (const QVMatrix &M, QVMatrix &X, const QVMatrix &B, QVMatrix &Q, QVMatrix &R, const TQVQR_Method method)
 Solves the linear system $M X = B$ for the unknown matrix $X$, using the QR decomposition of M:
void eigenDecomposition (const QVMatrix &M, QVVector &lambda, QVMatrix &Q, const TQVEigenDecomposition_Method method)
 Obtains the eigen-decomposition of a symmetric matrix.
double eigenDecompositionResidual (const QVMatrix &M, const QVVector &lambda, const QVMatrix &Q)
 Checks for correctness of the eigendecomposition of a matrix.
void eigenValues (const QVMatrix &M, QVVector &lambda, const TQVEigenValues_Method method)
 Gets the eigenvalues of a matrix.
double eigenValuesResidual (const QVMatrix &M, const QVVector &lambda)
 Checks for correctness of the eigenvalues of a symmetric matrix.
QVMatrix pseudoInverse (const QVMatrix &M, const TQVSVD_Method method, double epsilon)
 Obtains the Moore–Penrose pseudoinverse of a matrix.
double determinant (const QVMatrix &M, const TQVLU_Method method)
 Obtains the determinant of a square matrix.
void solveHomogeneous (const QVMatrix &A, QVector< double > &x, const TQVSVD_Method method)
 Solves an homogeneous linear system of equations.
double solveResidual (const QVMatrix &M, const QVMatrix &X, const QVMatrix &B)
 Returns the residual of the solution to a linear matrix equation.
double solveResidual (const QVMatrix &M, const QVVector &x, const QVVector &b)
 Returns the residual of the solution to a linear vector equation.
double sparseSolve (const QVSparseBlockMatrix &qvspmatrixPre, QVVector &x, const QVVector &bPre, const bool isSymmetric, const bool isPosDefinite, const TQVSparseSolve_Method method, const bool start_from_x, const bool iters_or_resid, const int iters, const double resid, int &final_iter_count)
 Solves a sparse system of linear equations, taking advantage of sparseness to accelerate the computation.
bool solveHomogeneous (const QVSparseBlockMatrix &A, QVVector &x, const int maxIterations, const double minRelativeError, const TQVSparseSolve_Method method)
 Solves a sparse homogeneous linear system using the inverse iteration algorithm and the MKL sparse routines.
QVVector regressionLine (const QVMatrix &points)

Detailed Description

File from the QVision library.

Author:
PARP Research Group. University of Murcia, Spain.

Definition in file qvmatrixalgebra.cpp.

Function Documentation

QVVector regressionLine ( const QVMatrix &  points  ) 

Todo:
esto no funciona.

Definition at line 1887 of file qvmatrixalgebra.cpp.



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