linalg Namespace Reference

Namespace for Linear Algebra functions based on BLAS, LAPACK, Lanczos and related algorithms. More...

Data Structures
class	CArpack
	Finder of a few eigenvalues of eigenvectors via Arnoldi method. More...
class	RArpack
	Finder of a few eigenvalues of eigenvectors via Arnoldi method. More...

Enumerations
enum	EigType {   LargestMagnitude = 0, SmallestMagnitude = 1, LargestReal = 2, LargestAlgebraic = 2,   SmallestReal = 3, SmallestAlgebraic = 3, LargestImaginary = 4, SmallestImaginary = 5 }
	Type of eigenvalues that eigs and Arpack compute. More...

Functions
const CTensor	eig (const RTensor &A, CTensor *R=0, CTensor *L=0)
	Eigenvalue decomposition of a real matrix. More...
const CTensor	eig (const CTensor &A, CTensor *R=0, CTensor *L=0)
	Eigenvalue decomposition of a complex matrix. More...
double	eig_power_left (const RTensor &O, RTensor *vector, size_t iter, double tol)
	Left eigenvalue and eigenvector with the largest absolute value, computed using the power method.
tensor::cdouble	eig_power_left (const CTensor &O, CTensor *vector, size_t iter, double tol)
	Left eigenvalue and eigenvector with the largest absolute value, computed using the power method.
double	eig_power_right (const RTensor &O, RTensor *vector, size_t iter, double tol)
	Right eigenvalue and eigenvector with the largest absolute value, computed using the power method.
tensor::cdouble	eig_power_right (const CTensor &O, CTensor *vector, size_t iter, double tol)
	Right eigenvalue and eigenvector with the largest absolute value, computed using the power method.
RTensor	eig_sym (const RTensor &A, RTensor *V)
	Eigenvalue decomposition of a real matrix. More...
RTensor	eig_sym (const CTensor &A, CTensor *V)
	Eigenvalue decomposition of a complex matrix. More...
CTensor	eigs (const CTensor &A, int eig_type, size_t neig, CTensor *vectors=NULL, const tensor::cdouble *initial_guess=NULL)
	Find out a few eigenvalues and eigenvectors of a complex nonsymmetric matrix. More...
CTensor	eigs (const CSparse &A, int eig_type, size_t neig, CTensor *vectors=NULL, const tensor::cdouble *initial_guess=NULL)
	Find out a few eigenvalues and eigenvectors of a nonsymmetric complex sparse matrix. More...
RTensor	eigs (const RTensor &A, int eig_type, size_t neig, RTensor *vectors=NULL, const double *initial_guess=NULL)
	Find out a few eigenvalues and eigenvectors of a real nonsymmetric matrix. More...
RTensor	eigs (const RSparse &A, int eig_type, size_t neig, RTensor *vectors=NULL, const double *initial_guess=NULL)
	Find out a few eigenvalues and eigenvectors of a nonsymmetric real sparse matrix. More...
RTensor	eigs_sym (const RTensor &A, int eig_type, size_t neig, RTensor *vectors=NULL, const double *initial_guess=NULL)
	Find out a few eigenvalues and eigenvectors of a symmetric real matrix. More...
RTensor	eigs_sym (const CTensor &A, int eig_type, size_t neig, CTensor *vectors=NULL, const tensor::cdouble *initial_guess=NULL)
	Find out a few eigenvalues and eigenvectors of a symmetric real matrix. More...
RTensor	eigs_sym (const RSparse &A, int eig_type, size_t neig, RTensor *vectors=NULL, const double *initial_guess=NULL)
	Find out a few eigenvalues and eigenvectors of a symmetric real sparse matrix. More...
RTensor	eigs_sym (const CSparse &A, int eig_type, size_t neig, CTensor *vectors=NULL, const tensor::cdouble *initial_guess=NULL)
	Find out a few eigenvalues and eigenvectors of a hermitian complex sparse matrix. More...
const RTensor	expm (const RTensor &Aunorm, unsigned int order)
	Compute the exponential of a real matrix. More...
const CTensor	expm (const CTensor &Aunorm, unsigned int order)
	Compute the exponential of a real matrix. More...
const RTensor	solve (const RTensor &A, const RTensor &B)
	Solve a real linear system of equations by Gauss-Seidel method. More...
const CTensor	solve (const CTensor &A, const CTensor &B)
	Solve a complex linear system of equations by Gauss-Seidel method.
const RTensor	solve_with_svd (const RTensor &A, const RTensor &B, double tol)
	Solution of a linear system of equations using Penrose's pseudoinvese. More...
const CTensor	solve_with_svd (const CTensor &A, const CTensor &B, double tol)
	Solution of a linear system of equations using Penrose's pseudoinvese. More...
RTensor	svd (RTensor A, RTensor *U, RTensor *VT, bool economic)
	Singular value decomposition of a real matrix. More...
RTensor	svd (CTensor A, CTensor *U, CTensor *VT, bool economic)
	Singular value decomposition of a complex matrix. More...

Detailed Description

Namespace for Linear Algebra functions based on BLAS, LAPACK, Lanczos and related algorithms.

Enumeration Type Documentation

enum linalg::EigType

Type of eigenvalues that eigs and Arpack compute.

Enumerator
LargestMagnitude	Eigenvalues with smallest modulus.
SmallestMagnitude	Eigenvalues with largest modulus.
LargestReal	Eigenvalues with largest real part.
LargestAlgebraic	Eigenvalues with largest real part.
SmallestReal	Eigenvalues with smallest real part.
SmallestAlgebraic	Eigenvalues with smallest real part.
LargestImaginary	Eigenvalues with the largest imaginary part.
SmallestImaginary	Eigenvalues with the smallest imaginary part.

Definition at line 69 of file linalg.h.

Function Documentation

CTensor linalg::eigs	(	const CTensor &	A,
		int	eig_type,
		size_t	neig,
		CTensor *	vectors = NULL,
		const tensor::cdouble *	initial_guess = NULL
	)

Find out a few eigenvalues and eigenvectors of a complex nonsymmetric matrix.

CTensor linalg::eigs	(	const CSparse &	A,
		int	eig_type,
		size_t	neig,
		CTensor *	vectors = NULL,
		const tensor::cdouble *	initial_guess = NULL
	)

Find out a few eigenvalues and eigenvectors of a nonsymmetric complex sparse matrix.

RTensor linalg::eigs	(	const RTensor &	A,
		int	eig_type,
		size_t	neig,
		RTensor *	vectors = NULL,
		const double *	initial_guess = NULL
	)

Find out a few eigenvalues and eigenvectors of a real nonsymmetric matrix.

RTensor linalg::eigs	(	const RSparse &	A,
		int	eig_type,
		size_t	neig,
		RTensor *	vectors = NULL,
		const double *	initial_guess = NULL
	)

Find out a few eigenvalues and eigenvectors of a nonsymmetric real sparse matrix.

RTensor linalg::eigs_sym	(	const RTensor &	A,
		int	eig_type,
		size_t	neig,
		RTensor *	vectors = NULL,
		const double *	initial_guess = NULL
	)

Find out a few eigenvalues and eigenvectors of a symmetric real matrix.

RTensor linalg::eigs_sym	(	const CTensor &	A,
		int	eig_type,
		size_t	neig,
		CTensor *	vectors = NULL,
		const tensor::cdouble *	initial_guess = NULL
	)

Find out a few eigenvalues and eigenvectors of a symmetric real matrix.

RTensor linalg::eigs_sym	(	const RSparse &	A,
		int	eig_type,
		size_t	neig,
		RTensor *	vectors = NULL,
		const double *	initial_guess = NULL
	)

Find out a few eigenvalues and eigenvectors of a symmetric real sparse matrix.

RTensor linalg::eigs_sym	(	const CSparse &	A,
		int	eig_type,
		size_t	neig,
		CTensor *	vectors = NULL,
		const tensor::cdouble *	initial_guess = NULL
	)

Find out a few eigenvalues and eigenvectors of a hermitian complex sparse matrix.