#include "amatrix.h"
#include "realavector.h"
#include "settings.h"

Data Structures
struct	_tridiag
	Real tridiagonal matrix , represented by vectors containing the diagonal, sub- and superdiagonal. More...

Typedefs
typedef struct _tridiag	tridiag
	Tridiagonal matrix.

typedef tridiag *	ptridiag
	Pointer to a tridiag object.

typedef const tridiag *	pctridiag
	Pointer to a constant tridiag object.

Functions
ptridiag	init_tridiag (ptridiag T, uint size)
	Initialize a tridiag object. More...

ptridiag	init_sub_tridiag (ptridiag T, ptridiag src, uint size, uint off)
	Initialize a tridiag object to represent a submatrix. More...

ptridiag	init_vec_tridiag (ptridiag T, prealavector src, uint size)
	Initialize a tridiag object using pre-allocated storage. More...

void	uninit_tridiag (ptridiag T)
	Uninitialize a tridiag object. More...

ptridiag	new_tridiag (uint size)
	Create a new tridiag object. More...

void	del_tridiag (ptridiag T)
	Delete a tridiag object. More...

void	copy_tridiag (pctridiag T, ptridiag Tcopy)
	Copy a matrix into another matrix, $T_{\rm copy} \gets T$ . More...

real	check_tridiag (pctridiag T, pcamatrix Ts)
	Compute the Frobenius norm $\\|T - T_s\\|_F$ of the difference of a tridiagonal matrix and a general matrix . More...

real	check_lower_tridiag (pctridiag T, pcamatrix Ts)
	Compute the Frobenius norm $\\|T - T_s\\|_F$ of the difference of a lower bidiagonal matrix and a general matrix . More...

void	diageval_tridiag_amatrix (field alpha, bool atrans, pctridiag a, bool xtrans, pamatrix x)
	Multiply a matrix by the diagonal part of a tridiagonal matrix, $X \gets \alpha A X$ . More...

void	lowereval_tridiag_amatrix (field alpha, bool atrans, pctridiag a, bool xtrans, pamatrix x)
	Multiply a matrix by the lower bidiagonal part of a tridiagonal matrix, $X \gets \alpha A X$ . More...

void	qrstep_tridiag (ptridiag T, field shift, pamatrix Q)
	Perform one implicit QR step on a self-adjoint tridiagonal matrix. More...

uint	sb_muleig_tridiag (ptridiag T, pamatrix Q, uint maxiter)
	Solve a self-adjoint tridiagonal eigenproblem, self-made implementation without BLAS or LAPACK. More...

uint	muleig_tridiag (ptridiag T, pamatrix Q)
	Solve a self-adjoint tridiagonal eigenproblem. More...

uint	eig_tridiag (ptridiag T, pamatrix Q)
	Solve a self-adjoint tridiagonal eigenproblem. More...

void	sb_tridiagonalize_amatrix (pamatrix A, ptridiag T, pamatrix Q)
	Hessenberg tridiagonalization of a self-adjoint matrix, self-made implementation without BLAS or LAPACK. More...

void	tridiagonalize_amatrix (pamatrix A, ptridiag T, pamatrix Q)
	Hessenberg tridiagonalization of a self-adjoint matrix. More...

uint	sb_eig_amatrix (pamatrix A, prealavector lambda, pamatrix Q, uint maxiter)
	Solve a self-adjoint eigenproblem, self-made implementation without BLAS or LAPACK. More...

uint	eig_amatrix (pamatrix A, prealavector lambda, pamatrix Q)
	Solve a self-adjoint eigenproblem, $A e = \lambda e$ . More...

uint	geig_amatrix (pamatrix A, pamatrix M, prealavector lambda, pamatrix Q)
	Solve self-adjoint generalized eigenproblem, $A e = \lambda M e$ . More...

void	svdstep_tridiag (ptridiag T, field shift, pamatrix U, pamatrix Vt)
	Perform one step of the Golub-Kahan iteration on a lower bidiagonal matrix. More...

uint	sb_mulsvd_tridiag (ptridiag T, pamatrix U, pamatrix Vt, uint maxiter)
	Compute the SVD of a bidiagonal matrix, self-made implementation without BLAS or LAPACK. More...

uint	mulsvd_tridiag (ptridiag T, pamatrix U, pamatrix Vt)
	Compute the SVD of a bidiagonal matrix. More...

uint	svd_tridiag (ptridiag T, pamatrix U, pamatrix Vt)
	Compute the SVD of a bidiagonal matrix. More...

void	sb_bidiagonalize_amatrix (pamatrix A, ptridiag T, pamatrix U, pamatrix Vt)
	Golub-Kahan bidiagonalization of a matrix, self-made implementation without BLAS or LAPACK. More...

void	bidiagonalize_amatrix (pamatrix A, ptridiag T, pamatrix U, pamatrix Vt)
	Golub-Kahan bidiagonalization of a matrix. More...

uint	sb_svd_amatrix (pamatrix A, prealavector sigma, pamatrix U, pamatrix Vt, uint maxiter)
	Compute the SVD of a matrix, self-made implementation without BLAS or LAPACK. More...

uint	svd_amatrix (pamatrix A, prealavector sigma, pamatrix U, pamatrix Vt)
	Compute the SVD of a matrix. More...

Detailed Description

Author: Steffen Börm

Data Structures

Typedefs

Functions

Detailed Description