#include <cassert>
#include <complex>
#include <cstring>
#include <iostream>
#include <vector>
#include <png++/png.hpp>
#include <umfpack.h>
#include "arrays.h"
#include "complex.h"

Include dependency graph for matrix.h:

This graph shows which files directly or indirectly include this file:

Go to the source code of this file.

Data Structures
class	RowMatrix< T >
	Dense (row-oriented) matrix. More...

class	ColMatrix< T >
	Dense (column-oriented) matrix. More...

class	DenseMatrix< T >
	DenseMatrix. More...

class	ColMatrix< T >
	Dense (column-oriented) matrix. More...

class	RowMatrix< T >
	Dense (row-oriented) matrix. More...

class	CscMatrix
	Complex CSC matrix. More...

class	CsrMatrix
	Complex CSR matrix. More...

class	CsrMatrix::PngGenerator

class	CsrMatrix::LUft
	LU factorization object. More...

class	CooMatrix
	Complex COO matrix. More...

class	SymDiaMatrix
	Symmetric diagonal matrix. More...

Enumerations
enum	MatrixTriangle { none = 0, strict_lower = 1, strict_upper = 2, strict_both = 3, diagonal = 4, lower = 5, upper = 6, both = 7 }
	Matrix parts. More...

Functions
template<class T >
RowMatrix< T >	operator+ (RowMatrix< T > const &A, RowMatrix< T > const &B)

template<class T >
RowMatrix< T >	operator- (RowMatrix< T > const &A, RowMatrix< T > const &B)

template<class T >
RowMatrix< T >	operator* (T x, RowMatrix< T > const &A)

template<class T >
RowMatrix< T >	operator* (RowMatrix< T > const &A, T x)

template<class T >
RowMatrix< T >	operator/ (RowMatrix< T > const &A, T x)

template<class T >
RowMatrix< T >	operator* (RowMatrix< T > const &A, ColMatrix< T > const &B)

template<class Type >
RowMatrix< Type >	operator* (RowMatrix< Type > const &A, ColMatrix< Type > const &B)
	Dense matrix multiplication. More...

CsrMatrix	operator& (const CsrMatrix &A, const CsrMatrix &B)

CsrMatrix	operator^ (const CsrMatrix &A, const CsrMatrix &B)

CsrMatrix	operator* (Complex z, const CsrMatrix &B)

CsrMatrix	operator* (const CsrMatrix &A, double r)

CscMatrix	operator& (const CscMatrix &A, const CscMatrix &B)

CscMatrix	operator^ (const CscMatrix &A, const CscMatrix &B)

CscMatrix	operator* (double r, const CscMatrix &B)

CscMatrix	operator* (const CscMatrix &A, double r)

CooMatrix	operator+ (const CooMatrix &A, const CooMatrix &B)

CooMatrix	operator- (const CooMatrix &A, const CooMatrix &B)

CooMatrix	operator* (const Complex &z, const CooMatrix &B)

CooMatrix	operator* (CooMatrix const &A, const cArrayView B)

CooMatrix	operator* (const CooMatrix &A, const Complex &z)

SymDiaMatrix	operator+ (SymDiaMatrix const &A, SymDiaMatrix const &B)

SymDiaMatrix	operator- (SymDiaMatrix const &A, SymDiaMatrix const &B)

SymDiaMatrix	operator* (SymDiaMatrix const &A, SymDiaMatrix const &B)

SymDiaMatrix	operator* (double z, SymDiaMatrix const &A)

SymDiaMatrix	operator* (Complex z, SymDiaMatrix const &A)

CooMatrix	kron (const CooMatrix &A, const CooMatrix &B)
	Kronecker product. More...

CooMatrix	eye (size_t N)

CooMatrix	stairs (size_t N)

Enumeration Type Documentation

enum MatrixTriangle

This enumeration contains some matrix part identificators that can be used e.g. together with matrix-vector multiplication routines (if implemented). The multiplication is done, then, as if the other parts were zero. For example

y = A.dot(x, strict_upper | strict_lower)

will multiply vector x as if the diagonal of A were zero.

Enumerator
none
strict_lower
strict_upper
strict_both
diagonal
lower
upper
both

Function Documentation

CooMatrix eye ( size_t N )

Identity matrix.

Parameters

N	Dimension.

CooMatrix kron	(	const CooMatrix &	A,
		const CooMatrix &	B
	)

This routine computes the Kronecker product (“flattened tensor product”)

\[ C = A \otimes B \ , \]

where the matrix \( C \) is of size \( mn \times rs \) (for matrix \( A \) of size \( m \times r \) and matrix \( B \) of size \( n \times s \)) and defined by

\[ c_{i,j} = a_{i \,\mathrm{div}\, m, j \,\mathrm{div}\, r} \cdot b_{i \,\mathrm{mod}\, m, j \,\mathrm{mod}\, r} \]

Parameters

A	First matrix
B	Second matrix.

CsrMatrix operator&	(	const CsrMatrix &	A,
		const CsrMatrix &	B
	)

inline

Computes a sum of two csr-matrices OF THE SAME SPARSE STRUCTURE.

CscMatrix operator&	(	const CscMatrix &	A,
		const CscMatrix &	B
	)

inline

Computes a sum of two csc-matrices OF THE SAME SPARSE STRUCTURE.

template<class T >

RowMatrix<T> operator*	(	T	x,
		RowMatrix< T > const &	A
	)

template<class T >

RowMatrix<T> operator*	(	RowMatrix< T > const &	A,
		T	x
	)

template<class T >

RowMatrix<T> operator*	(	RowMatrix< T > const &	A,
		ColMatrix< T > const &	B
	)

template<class Type >

RowMatrix<Type> operator*	(	RowMatrix< Type > const &	A,
		ColMatrix< Type > const &	B
	)

CsrMatrix operator*	(	Complex	z,
		const CsrMatrix &	B
	)

inline

Multiplication of csr-matrix by a number.

CsrMatrix operator*	(	const CsrMatrix &	A,
		double	r
	)

inline

Multiplication of csr-matrix by a number.

CscMatrix operator*	(	double	r,
		const CscMatrix &	B
	)

inline

Multiplication of csc-matrix by a number.

CscMatrix operator*	(	const CscMatrix &	A,
		double	r
	)

inline

Multiplication of csc-matrix by a number.

CooMatrix operator*	(	const Complex &	z,
		const CooMatrix &	B
	)

inline

Computes product of a matrix and a complex number.

Parameters

z	Number.
B	Matrix.

CooMatrix operator*	(	CooMatrix const &	A,
		const cArrayView	B
	)

inline

Computes product of a sparse matrix and a dense matrix.

Parameters

A	COO-Matrix.
B	Dense matrix (as a column-major ordered array).

CooMatrix operator*	(	const CooMatrix &	A,
		const Complex &	z
	)

inline

Computes product of a matrix and a complex number.

Parameters

A	COO-Matrix.
z	Number.

SymDiaMatrix operator*	(	SymDiaMatrix const &	A,
		SymDiaMatrix const &	B
	)

SymDiaMatrix operator*	(	double	z,
		SymDiaMatrix const &	A
	)

SymDiaMatrix operator*	(	Complex	z,
		SymDiaMatrix const &	A
	)

template<class T >

RowMatrix<T> operator+	(	RowMatrix< T > const &	A,
		RowMatrix< T > const &	B
	)

CooMatrix operator+	(	const CooMatrix &	A,
		const CooMatrix &	B
	)

inline

Computes a sum of two coo-matrices.

Parameters

A	COO-matrix.
B	COO-matrix.

SymDiaMatrix operator+	(	SymDiaMatrix const &	A,
		SymDiaMatrix const &	B
	)

template<class T >

RowMatrix<T> operator-	(	RowMatrix< T > const &	A,
		RowMatrix< T > const &	B
	)

CooMatrix operator-	(	const CooMatrix &	A,
		const CooMatrix &	B
	)

inline

Computes a difference of two coo-matrices.

Parameters

A	COO-matrix.
B	COO-matrix.

SymDiaMatrix operator-	(	SymDiaMatrix const &	A,
		SymDiaMatrix const &	B
	)

template<class T >

RowMatrix<T> operator/	(	RowMatrix< T > const &	A,
		T	x
	)

CsrMatrix operator^	(	const CsrMatrix &	A,
		const CsrMatrix &	B
	)

inline

Computes a difference of two csr-matrices OF THE SAME SPARSE STRUCTURE.

CscMatrix operator^	(	const CscMatrix &	A,
		const CscMatrix &	B
	)

inline

Computes a difference of two csc-matrices OF THE SAME SPARSE STRUCTURE.

CooMatrix stairs ( size_t N )

Diagonal matrix with diagonal consisting of 0, 1, 2, 3, ..., N - 1.

Parameters

N	Dimension.

Data Structures

Enumerations

Functions

Enumeration Type Documentation

Function Documentation