matrix2d.h File Reference

#include <complex>
#include "xmipp_random_mode.h"
#include "xmipp_macros.h"
#include "xmipp_error.h"
#include "xmipp_strings.h"
#include <sys/mman.h>

Include dependency graph for matrix2d.h:

Go to the source code of this file.

Classes
class	Matrix1D< T >
class	Matrix2D< T >
class	Matrix2D< T >

Functions
template<typename T >
void	ludcmp (const Matrix2D< T > &A, Matrix2D< T > &LU, Matrix1D< int > &indx, T &d)
template<typename T >
void	lubksb (const Matrix2D< T > &LU, Matrix1D< int > &indx, Matrix1D< T > &b)
template<typename T >
void	svdcmp (const Matrix2D< T > &a, Matrix2D< double > &u, Matrix1D< double > &w, Matrix2D< double > &v)
void	svbksb (Matrix2D< double > &u, Matrix1D< double > &w, Matrix2D< double > &v, Matrix1D< double > &b, Matrix1D< double > &x)
void	cholesky (const Matrix2D< double > &M, Matrix2D< double > &L)
void	schur (const Matrix2D< double > &M, Matrix2D< double > &O, Matrix2D< double > &T)

Matrices speed up macros
#define	MATRIX2D_ARRAY(m)   ((m).mdata)
#define	FOR_ALL_ELEMENTS_IN_MATRIX2D(m)
#define	MAT_ELEM(m, i, j)   ((m).mdata[((size_t)i)*(m).mdimx+((size_t)j)])
#define	MAT_XSIZE(m)   ((m).mdimx)
#define	MAT_YSIZE(m)   ((m).mdimy)
#define	MAT_SIZE(m)   ((m).mdim)
#define	dMij(m, i, j)   MAT_ELEM(m, i, j)
#define	dMn(m, n)   ((m).mdata[(n)])
#define	M3x3_BY_V3x1(a, M, b)
#define	M3x3_BY_M3x3(A, B, C)
#define	M2x2_BY_V2x1(a, M, b)
#define	M2x2_BY_CT(M2, M1, k)
#define	M3x3_BY_CT(M2, M1, k)
#define	M4x4_BY_CT(M2, M1, k)
#define	M2x2_INV(Ainv, A)
#define	M3x3_INV(Ainv, A)
#define	M4x4_INV(Ainv, A)
typedef Matrix2D< double >	DMatrix
typedef Matrix2D< int >	IMatrix
template<typename T >
bool	operator== (const Matrix2D< T > &op1, const Matrix2D< T > &op2)

Matrix Related functions
These functions are not methods of Matrix2D
#define	VIA_BILIB
void	generalizedEigs (const Matrix2D< double > &A, const Matrix2D< double > &B, Matrix1D< double > &D, Matrix2D< double > &P)
void	firstEigs (const Matrix2D< double > &A, size_t M, Matrix1D< double > &D, Matrix2D< double > &P, bool Pneeded=true)
void	lastEigs (const Matrix2D< double > &A, size_t M, Matrix1D< double > &D, Matrix2D< double > &P)
void	eigsBetween (const Matrix2D< double > &A, size_t I1, size_t I2, Matrix1D< double > &D, Matrix2D< double > &P)
void	allEigs (const Matrix2D< double > &A, std::vector< std::complex< double > > &eigs)
void	connectedComponentsOfUndirectedGraph (const Matrix2D< double > &G, Matrix1D< int > &component)
template<typename T1 , typename T2 >
void	typeCast (const Matrix2D< T1 > &v1, Matrix2D< T2 > &v2)
template<typename T1 >
void	typeCast (const Matrix2D< T1 > &v1, Matrix2D< T1 > &v2)
void	orthogonalizeColumnsGramSchmidt (Matrix2D< double > &M)
void	normalizeColumns (Matrix2D< double > &A)
void	normalizeColumnsBetween0and1 (Matrix2D< double > &A)
void	subtractColumnMeans (Matrix2D< double > &A)
void	matrixOperation_AtA (const Matrix2D< double > &A, Matrix2D< double > &B)
void	matrixOperation_AAt (const Matrix2D< double > &A, Matrix2D< double > &C)
void	matrixOperation_AB (const Matrix2D< double > &A, const Matrix2D< double > &B, Matrix2D< double > &C)
void	matrixOperation_Ax (const Matrix2D< double > &A, const Matrix1D< double > &x, Matrix1D< double > &y)
void	matrixOperation_ABt (const Matrix2D< double > &A, const Matrix2D< double > &B, Matrix2D< double > &C)
void	matrixOperation_AtB (const Matrix2D< double > &A, const Matrix2D< double > &B, Matrix2D< double > &C)
void	matrixOperation_Atx (const Matrix2D< double > &A, const Matrix1D< double > &x, Matrix1D< double > &y)
void	matrixOperation_AtBt (const Matrix2D< double > &A, const Matrix2D< double > &B, Matrix2D< double > &C)
void	matrixOperation_XtAX_symmetric (const Matrix2D< double > &X, const Matrix2D< double > &A, Matrix2D< double > &B)
void	matrixOperation_IplusA (Matrix2D< double > &A)
void	matrixOperation_IminusA (Matrix2D< double > &A)
void	eraseFirstColumn (Matrix2D< double > &A)
void	keepColumns (Matrix2D< double > &A, int j0, int jF)

Function Documentation

cholesky()

void cholesky	(	const Matrix2D< double > &	M,
		Matrix2D< double > &	L
	)

Cholesky decomposition. Given M, this function decomposes M as M=L*L^t where L is a lower triangular matrix. M must be positive semi-definite.

Definition at line 160 of file matrix2d.cpp.

{
    L=M;
    Matrix1D<double> p;
    p.initZeros(MAT_XSIZE(M));
    choldc(L.adaptForNumericalRecipes2(), MAT_XSIZE(M), p.adaptForNumericalRecipes());
    FOR_ALL_ELEMENTS_IN_MATRIX2D(L)
    if (i==j)
        MAT_ELEM(L,i,j)=VEC_ELEM(p,i);
    else if (i<j)
        MAT_ELEM(L,i,j)=0.0;
}

schur()

void schur	(	const Matrix2D< double > &	M,
		Matrix2D< double > &	O,
		Matrix2D< double > &	T
	)

Schur decomposition. Given M, this function decomposes M as M = O*T*O' where O is an orthogonal matrix.

Definition at line 251 of file matrix2d.cpp.

{
    alglib::real_2d_array a, s;
    a.setcontent(MAT_YSIZE(M),MAT_XSIZE(M),MATRIX2D_ARRAY(M));
    bool ok=rmatrixschur(a, MAT_YSIZE(M), s);
    if (!ok)
        REPORT_ERROR(ERR_NUMERICAL,"Could not perform Schur decomposition");
    O.resizeNoCopy(M);
    T.resizeNoCopy(M);
    FOR_ALL_ELEMENTS_IN_MATRIX2D(M)
    {
        MAT_ELEM(O,i,j)=s(i,j);
        MAT_ELEM(T,i,j)=a(i,j);
    }
}