CsrMatrix Class Reference

Complex CSR matrix. More...

#include <matrix.h>

Data Structures
class	LUft
	LU factorization object. More...
class	PngGenerator

Public Member Functions
	CsrMatrix ()
	CsrMatrix (size_t m, size_t n)
	CsrMatrix (CsrMatrix const &A)
	CsrMatrix (size_t m, size_t n, lArrayView const &p, lArrayView const &i, cArrayView const &x)
	~CsrMatrix ()
void	drop ()
	Clear data. More...
cArray	dot (cArrayView const &b) const
size_t	size () const
size_t	rows () const
size_t	cols () const
lArray const &	p () const
lArray const &	i () const
cArray const &	x () const
double	norm () const
void	write (const char *filename) const
void	plot (const char *filename, double threshold=0.) const
LUft	factorize (double droptol=0) const
	Compute (incomplete) LU factorization. More...
cArray	solve (const cArrayView b, size_t eqs=1) const
	Solve the Ax = b problem, where "b" can be a matrix. More...
void	link (std::string name)
	Link to a disk file. More...
Complex	operator() (unsigned i, unsigned j) const
CsrMatrix &	operator*= (Complex r)
CsrMatrix &	operator&= (CsrMatrix const &B)
CsrMatrix &	operator^= (CsrMatrix const &B)
CsrMatrix	sparse_like (CsrMatrix const &B) const
cArray	diag () const
CooMatrix	tocoo () const
RowMatrix< Complex >	torow () const
cArray	upperSolve (cArrayView const &b) const
cArray	lowerSolve (cArrayView const &b) const
template<class Functor >
CsrMatrix	nzTransform (Functor f) const
bool	hdfsave () const
bool	hdfsave (std::string name) const
bool	hdfload ()
bool	hdfload (std::string name)

Detailed Description

Complex compressed-storage-row-major-ordered sparse matrix. The data are stored in four arrays,

* p, i, x, z
* 

Here, Ap is an array of N+1 elements, where N is the number of rows. It contains indices of beginnings of single rows in all remaining arrays. The last element contains one-past-end pointer, i.e. it should be aqual to the element count of the matrix (zero and nonzero). The array Ai holds column indices of elements, which are stored in Ax and Az, real ang imaginary part being separated.

Constructor & Destructor Documentation

CsrMatrix::CsrMatrix ( )

inline

CsrMatrix::CsrMatrix ( size_t  m, size_t  n  )

inline

CsrMatrix::CsrMatrix ( CsrMatrix const &  A )

inline

CsrMatrix::CsrMatrix ( size_t  m, size_t  n, lArrayView const &  p, lArrayView const &  i, cArrayView const &  x  )

inline

CsrMatrix::~CsrMatrix ( )

inline

Member Function Documentation

size_t CsrMatrix::cols ( ) const

inline

cArray CsrMatrix::diag

(

)

const

Return dense array with diagonal elements of the matrix.

cArray CsrMatrix::dot

(

cArrayView const &

b

)

const

Ordinary matrix-vector product, \( A\cdot b \).

Parameters

b	Vector to multiply with.

void CsrMatrix::drop ( )

inline

CsrMatrix::LUft CsrMatrix::factorize

(

double

droptol = 0

)

const

This function computes the LU factorization of the matrix. It uses the free UMFPACK library.

Parameters

droptol

Drop tolerance. If an element of the factorization matrices should be in absolute value smaller than "droptol" the library will omit it completely effectively making the result more sparse.

Returns

Special structure of the LUft type, holding opaque information about the factorization.

bool CsrMatrix::hdfload ( )

inline

Load matrix from HDF file.

bool CsrMatrix::hdfload

(

std::string

name

)

bool CsrMatrix::hdfsave ( ) const

inline

Save matrix to HDF file.

bool CsrMatrix::hdfsave

(

std::string

name

)

const

lArray const& CsrMatrix::i ( ) const

inline

void CsrMatrix::link

(

std::string

name

)

Set a default I/O file that will be used if any of the functions hdfload or hdfsave will be used without an explicit filename.

cArray CsrMatrix::lowerSolve

(

cArrayView const &

b

)

const

Solves lower triangular system of equations using backsubstitution. The matrix needs not be triangular, but elements above the diagonal won't be used or changed.

Parameters

b	Right-hand side.

double CsrMatrix::norm

(

)

const

template<class Functor >

CsrMatrix CsrMatrix::nzTransform ( Functor  f ) const

inline

Applies a user transformation on nonzero matrix elements.

Parameters

f	A functor compatible with following declaration: * Complex (*f) (size_t i, size_t j, Complex z); *

CsrMatrix & CsrMatrix::operator&=

(

CsrMatrix const &

B

)

Addition of another CSR matrix. The matrices MUST HAVE THE SAME SPARSE STRUCTURE, as no indices are checked.

Complex CsrMatrix::operator()	(	unsigned	i,
		unsigned	j
	)		const

Element-wise access (const). If a non-existing element is referenced, zero is returned.

CsrMatrix & CsrMatrix::operator*=

(

Complex

r

)

Multiplication by a number.

CsrMatrix & CsrMatrix::operator^=

(

CsrMatrix const &

B

)

Subtraction of another CSR matrix. The matrices MUST HAVE THE SAME SPARSE STRUCTURE, as no indices are checked.

lArray const& CsrMatrix::p ( ) const

inline

void CsrMatrix::plot	(	const char *	filename,
		double	threshold = 0.
	)		const

Save matrix structure as a black-and-white image.

Parameters

filename	File name.
threshold	Largest absolute value represented by white colour.

size_t CsrMatrix::rows ( ) const

inline

size_t CsrMatrix::size ( ) const

inline

cArray CsrMatrix::solve	(	const cArrayView	b,
		size_t	eqs = 1
	)		const

Uses UMFPACK through the LUft::solve function.

Parameters

b	Complex vector containing column-major ordered data; it may be a flattened matrix.
eqs	Number of columns.

Returns

Array of roots in the same shape as "b".

CsrMatrix CsrMatrix::sparse_like

(

CsrMatrix const &

B

)

const

Sets fill-in elements so that the storage structure of this matrix will be identical to that of the other CSR matrix. We can the use “fast” arithmetic operators & and ^.

Returns

self

CooMatrix CsrMatrix::tocoo

(

)

const

Convert to COO format.

RowMatrix< Complex > CsrMatrix::torow

(

)

const

Convert to dense matrix.

cArray CsrMatrix::upperSolve

(

cArrayView const &

b

)

const

Solves upper triangular system of equations using backsubstitution. The matrix needs not be triangular, but elements under the diagonal won't be used or changed.

Parameters

b	Right-hand side.

void CsrMatrix::write

(

const char *

filename

)

const

Write the matrix data to a file.

Parameters

filename

Filename.

Format of the fields i,j,x,z is:

* %d\t%d\t%g\t%g
* 

cArray const& CsrMatrix::x ( ) const

inline

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

• src/matrix.h
• src/matrix.cpp