matrix.h File Reference

#include <core/ManagedMemory.h>
#include <core/scaled.h>
#include <core/matrix3.h>
#include <gsl/gsl_cblas.h>

Classes
class	diagMatrix
	Real diagonal matrix. More...
class	matrix
	General complex matrix. More...
struct	matrixScaledTransOp
	Matrix with pending scale, submatrix and/or transpose operations. More...
class	tiledBlockMatrix
	A block matrix formed by repeating (tiling) a dense matrix along the diagonal. More...

Functions
matrix	conj (const scaled< matrix > &A)
	return element-wise complex conjugate of A
matrixScaledTransOp	dagger (const matrixScaledTransOp &A)
	return hermitian adjoint of A
matrixScaledTransOp	transpose (const matrixScaledTransOp &A)
	return transpose of A
matrix	dagger_symmetrize (const matrixScaledTransOp &A)
matrix	transpose_symmetrize (const matrixScaledTransOp &A)
	return adjoint symmetric part: (A + Adag)/2
double	nrm2 (const matrixScaledTransOp &A)
	return transpose symmetric part: (A + AT)/2 More...
matrix &	operator*= (matrix &m, double s)
scaled< matrix >	operator* (double s, const matrix &m)
scaled< matrix >	operator* (const matrix &m, double s)
scaled< matrix >	operator- (const matrix &m)
matrix &	operator*= (matrix &m, complex s)
matrix	operator* (complex s, const matrix &m)
matrix	operator* (const matrix &m, complex s)
diagMatrix	operator* (double s, const diagMatrix &m)
diagMatrix	operator* (const diagMatrix &m, double s)
diagMatrix	operator- (const diagMatrix &m)
matrix	operator* (const matrixScaledTransOp &, const matrixScaledTransOp &)
matrix	operator* (const diagMatrix &, const matrix &)
matrix	operator* (const matrix &, const diagMatrix &)
matrix	operator* (const std::vector< complex > &d, const matrix &m)
matrix	operator* (const matrix &m, const std::vector< complex > &d)
diagMatrix	operator* (const diagMatrix &, const diagMatrix &)
matrix &	operator+= (matrix &m1, const matrix &m2)
matrix &	operator-= (matrix &m1, const matrix &m2)
matrix	operator+ (const matrix &m1, const matrix &m2)
matrix	operator- (const matrix &m1, const matrix &m2)
void	axpy (double alpha, const diagMatrix &x, matrix &y)
matrix &	operator+= (matrix &m, const diagMatrix &d)
matrix &	operator-= (matrix &m, const diagMatrix &d)
matrix	operator+ (const matrix &m, const diagMatrix &d)
matrix	operator+ (const diagMatrix &d, const matrix &m)
matrix	operator- (const matrix &m, const diagMatrix &d)
matrix	operator- (const diagMatrix &d, const matrix &m)
void	axpy (double alpha, const diagMatrix &x, diagMatrix &y)
diagMatrix &	operator+= (diagMatrix &d1, const diagMatrix &d2)
diagMatrix &	operator-= (diagMatrix &d1, const diagMatrix &d2)
diagMatrix	operator+ (const diagMatrix &d1, const diagMatrix &d2)
diagMatrix	operator- (const diagMatrix &d1, const diagMatrix &d2)
diagMatrix	clone (const diagMatrix &x)
matrix	clone (const matrix &x)
double	dot (const diagMatrix &x, const diagMatrix &y)
double	dot (const matrix &x, const matrix &y)
void	randomize (diagMatrix &x)
void	randomize (matrix &x)
diagMatrix	diagDot (const matrix &X, const matrix &Y)
	Compute diag(dagger(X)*Y) efficiently (avoid the off-diagonals)
matrix	inv (const matrix &A)
	Compute / apply inverse: More...
diagMatrix	inv (const diagMatrix &A)
	inverse of diagonal matrix
matrix	invTriangular (const matrix &T, bool upper)
	return inv(T) for triangular matrix T (upper/lower for upper=true/false)
matrix	invApply (const matrix &A, const matrix &b)
	return inv(A) * b (A must be hermitian, positive-definite)
matrix	LU (const matrix &A)
	Compute the LU decomposition of the matrix.
matrix	cholesky (const matrix &A, bool upper)
complex	det (const matrix &A)
double	det (const diagMatrix &A)
	Compute the determinant of an diagonal matrix A.
matrix	pow (const matrix &A, double exponent, matrix *Aevecs=0, diagMatrix *Aeigs=0, bool *isSingular=0)
matrix	invsqrt (const matrix &A, matrix *Aevecs=0, diagMatrix *Aeigs=0, bool *isSingular=0)
matrix	orthoMatrix (const matrix &A)
matrix	cis (const matrix &A, matrix *Aevecs=0, diagMatrix *Aeigs=0)
	Compute cis(A) = exp(iota A) and optionally the eigensystem of A (if non-null)
matrix	cisInv (const matrix &A, matrix *Bevecs=0, diagMatrix *Beigs=0)
matrix	sqrt_grad (const matrix &grad_sqrtA, const matrix &Aevecs, const diagMatrix &Aeigs)
	Return gradient w.r.t A given gradient w.r.t sqrt(A) and A's eigensystem.
matrix	cis_grad (const matrix &grad_cisA, const matrix &Aevecs, const diagMatrix &Aeigs)
	Return gradient w.r.t A given gradient w.r.t cis(A) and A's eigensystem.
complex	trace (const matrix &m)
	trace of matrix
double	trace (const diagMatrix &m)
	trace of diagonal matrix
double	nrm2 (const diagMatrix &m)
	RMS of matrix entries.
diagMatrix	diag (const matrix &m)
	obtain the real diagonal part of a hermitian matrix
diagMatrix	eye (int N)
	identity
matrix	zeroes (int nRows, int nCols)
	a dense-matrix of zeroes
matrix	operator* (const matrix &m, const tiledBlockMatrix &tbm)
	multiply dense matrix by block matrix

Detailed Description

General size diagonal and dense matrices, and their operators