qz.cc File Reference

#include <cfloat>
#include <iostream>
#include <iomanip>
#include "CmplxQRP.h"
#include "CmplxQR.h"
#include "dbleQR.h"
#include "f77-fcn.h"
#include "lo-math.h"
#include "quit.h"
#include "defun-dld.h"
#include "error.h"
#include "gripes.h"
#include "oct-obj.h"
#include "oct-map.h"
#include "ov.h"
#include "pager.h"
#include "symtab.h"
#include "utils.h"
#include "variables.h"

Include dependency graph for qz.cc:

Typedefs
typedef octave_idx_type(*	sort_function )(const octave_idx_type &LSIZE, const double &ALPHA, const double &BETA, const double &S, const double &P)
Functions
F77_RET_T	F77_FUNC (dggbal, DGGBAL)(F77_CONST_CHAR_ARG_DECL
F77_RET_T	F77_FUNC (zggbal, ZGGBAL)(F77_CONST_CHAR_ARG_DECL
F77_RET_T	F77_FUNC (dggbak, DGGBAK)(F77_CONST_CHAR_ARG_DECL
F77_RET_T	F77_FUNC (zggbak, ZGGBAK)(F77_CONST_CHAR_ARG_DECL
F77_RET_T	F77_FUNC (dgghrd, DGGHRD)(F77_CONST_CHAR_ARG_DECL
F77_RET_T	F77_FUNC (zgghrd, ZGGHRD)(F77_CONST_CHAR_ARG_DECL
F77_RET_T	F77_FUNC (dhgeqz, DHGEQZ)(F77_CONST_CHAR_ARG_DECL
F77_RET_T	F77_FUNC (zhgeqz, ZHGEQZ)(F77_CONST_CHAR_ARG_DECL
F77_RET_T	F77_FUNC (dlag2, DLAG2)(const double *A
F77_RET_T	F77_FUNC (dsubsp, DSUBSP)(const octave_idx_type &NMAX
F77_RET_T	F77_FUNC (dtgevc, DTGEVC)(F77_CONST_CHAR_ARG_DECL
F77_RET_T	F77_FUNC (ztgevc, ZTGEVC)(F77_CONST_CHAR_ARG_DECL
F77_RET_T	F77_FUNC (xdlamch, XDLAMCH)(F77_CONST_CHAR_ARG_DECL
F77_RET_T	F77_FUNC (xdlange, XDLANGE)(F77_CONST_CHAR_ARG_DECL
	DEFUN_DLD (qz, args, nargout,"-*- texinfo -*-\n\ @deftypefn {Loadable Function} {@var{lambda} =} qz (@var{A}, @var{B})\n\ @deftypefnx {Loadable Function} {@var{lambda} =} qz (@var{A}, @var{B}, @var{opt})\n\ QZ@tie{}decomposition of the generalized eigenvalue problem\n\ (@math{A x = s B x}). There are three ways to call this function:\n\ @enumerate\n\ @item @code{@var{lambda} = qz (@var{A}, @var{B})}\n\ \n\ Computes the generalized eigenvalues\n\ @tex\n\ $\\lambda$\n\ @end tex\n\ @ifnottex\n\ @var{lambda}\n\ @end ifnottex\n\ of @math{(A - s B)}.\n\ \n\ @item @code{[AA, BB, Q, Z, V, W, @var{lambda}] = qz (@var{A}, @var{B})}\n\ \n\ Computes QZ@tie{}decomposition, generalized eigenvectors, and \n\ generalized eigenvalues of @math{(A - s B)}\n\ @tex\n\ $$ AV = BV{ \\rm diag }(\\lambda) $$\n\ $$ W^T A = { \\rm diag }(\\lambda)W^T B $$\n\ $$ AA = Q^T AZ, BB = Q^T BZ $$\n\ @end tex\n\ @ifnottex\n\ \n\ @example\n\ @group\n\ \n\ A * V = B * V * diag (@var{lambda})\n\ W' * A = diag (@var{lambda}) * W' * B\n\ AA = Q * A * Z, BB = Q * B * Z\n\ \n\ @end group\n\ @end example\n\ \n\ @end ifnottex\n\ with @var{Q} and @var{Z} orthogonal (unitary)= @var{I}\n\ \n\ @item @code{[AA,BB,Z@{, @var{lambda}@}] = qz (@var{A}, @var{B}, @var{opt})}\n\ \n\ As in form [2], but allows ordering of generalized eigenpairs\n\ for (e.g.) solution of discrete time algebraic Riccati equations.\n\ Form 3 is not available for complex matrices, and does not compute\n\ the generalized eigenvectors @var{V}, @var{W}, nor the orthogonal matrix\n\ @var{Q}.\n\ \n\ @table @var\n\ @item opt\n\ for ordering eigenvalues of the GEP pencil. The leading block\n\ of the revised pencil contains all eigenvalues that satisfy:\n\ @table @asis\n\ @item \"N\"\n\ = unordered (default) \n\ \n\ @item \"S\"\n\ = small: leading block has all |lambda| @leq{} 1 \n\ \n\ @item \"B\"\n\ = big: leading block has all |lambda| @geq{} 1 \n\ \n\ @item \"-\"\n\ = negative real part: leading block has all eigenvalues\n\ in the open left half-plane\n\ \n\ @item \"+\"\n\ = non-negative real part: leading block has all eigenvalues\n\ in the closed right half-plane\n\ @end table\n\ @end table\n\ @end enumerate\n\ \n\ Note: @code{qz} performs permutation balancing, but not scaling\n\ (@pxref{doc-balance}). The order of output arguments was selected for\n\ compatibility with @sc{matlab}.\n\ @seealso{balance, eig, schur}\n\ @end deftypefn")
Variables
F77_RET_T const octave_idx_type &	N
F77_RET_T const octave_idx_type double *	A
F77_RET_T const octave_idx_type double const octave_idx_type &	LDA
F77_RET_T const octave_idx_type double const octave_idx_type double *	B
F77_RET_T const octave_idx_type double const octave_idx_type double const octave_idx_type &	LDB
F77_RET_T const octave_idx_type double const octave_idx_type double const octave_idx_type octave_idx_type &	ILO
F77_RET_T const octave_idx_type double const octave_idx_type double const octave_idx_type octave_idx_type octave_idx_type &	IHI
F77_RET_T const octave_idx_type double const octave_idx_type double const octave_idx_type octave_idx_type octave_idx_type double *	LSCALE
F77_RET_T const octave_idx_type double const octave_idx_type double const octave_idx_type octave_idx_type octave_idx_type double double *	RSCALE
F77_RET_T const octave_idx_type double const octave_idx_type double const octave_idx_type octave_idx_type octave_idx_type double double double *	WORK
F77_RET_T const octave_idx_type double const octave_idx_type double const octave_idx_type octave_idx_type octave_idx_type double double double octave_idx_type &INFO	F77_CHAR_ARG_LEN_DECL
F77_RET_T	F77_CONST_CHAR_ARG_DECL
F77_RET_T const octave_idx_type const octave_idx_type const octave_idx_type const double const double octave_idx_type &	M
F77_RET_T const octave_idx_type const octave_idx_type const octave_idx_type const double const double octave_idx_type double *	V
F77_RET_T const octave_idx_type const octave_idx_type const octave_idx_type const double const double octave_idx_type double const octave_idx_type &	LDV
F77_RET_T const octave_idx_type const octave_idx_type const octave_idx_type double const octave_idx_type double const octave_idx_type double *	Q
F77_RET_T const octave_idx_type const octave_idx_type const octave_idx_type double const octave_idx_type double const octave_idx_type double const octave_idx_type &	LDQ
F77_RET_T const octave_idx_type const octave_idx_type const octave_idx_type double const octave_idx_type double const octave_idx_type double const octave_idx_type double *	Z
F77_RET_T const octave_idx_type const octave_idx_type const octave_idx_type double const octave_idx_type double const octave_idx_type double const octave_idx_type double const octave_idx_type &	LDZ
F77_RET_T const octave_idx_type const octave_idx_type const octave_idx_type double const octave_idx_type double const octave_idx_type double *	ALPHAR
F77_RET_T const octave_idx_type const octave_idx_type const octave_idx_type double const octave_idx_type double const octave_idx_type double double *	ALPHAI
F77_RET_T const octave_idx_type const octave_idx_type const octave_idx_type double const octave_idx_type double const octave_idx_type double double double *	BETA
F77_RET_T const octave_idx_type const octave_idx_type const octave_idx_type double const octave_idx_type double const octave_idx_type double double double double const octave_idx_type double const octave_idx_type double const octave_idx_type &	LWORK
F77_RET_T const octave_idx_type const octave_idx_type const octave_idx_type Complex const octave_idx_type Complex const octave_idx_type Complex *	ALPHA
F77_RET_T const octave_idx_type const octave_idx_type const octave_idx_type Complex const octave_idx_type Complex const octave_idx_type Complex Complex Complex *	CQ
F77_RET_T const octave_idx_type const octave_idx_type const octave_idx_type Complex const octave_idx_type Complex const octave_idx_type Complex Complex Complex const octave_idx_type Complex *	CZ
F77_RET_T const octave_idx_type const octave_idx_type const octave_idx_type Complex const octave_idx_type Complex const octave_idx_type Complex Complex Complex const octave_idx_type Complex const octave_idx_type Complex const octave_idx_type double *	RWORK
F77_RET_T const octave_idx_type const double const octave_idx_type const double &	SAFMIN
F77_RET_T const octave_idx_type const double const octave_idx_type const double double &	SCALE1
F77_RET_T const octave_idx_type const double const octave_idx_type const double double double &	SCALE2
F77_RET_T const octave_idx_type const double const octave_idx_type const double double double double &	WR1
F77_RET_T const octave_idx_type const double const octave_idx_type const double double double double double &	WR2
F77_RET_T const octave_idx_type const double const octave_idx_type const double double double double double double &	WI
F77_RET_T const octave_idx_type double double double const double &	EPS
F77_RET_T const octave_idx_type double double double const double octave_idx_type &	NDIM
F77_RET_T const octave_idx_type double double double const double octave_idx_type octave_idx_type &	FAIL
F77_RET_T const octave_idx_type double double double const double octave_idx_type octave_idx_type octave_idx_type *	IND
F77_RET_T octave_idx_type *	SELECT
F77_RET_T octave_idx_type const octave_idx_type double const octave_idx_type double const octave_idx_type double *	VL
F77_RET_T octave_idx_type const octave_idx_type double const octave_idx_type double const octave_idx_type double const octave_idx_type &	LDVL
F77_RET_T octave_idx_type const octave_idx_type double const octave_idx_type double const octave_idx_type double const octave_idx_type double *	VR
F77_RET_T octave_idx_type const octave_idx_type double const octave_idx_type double const octave_idx_type double const octave_idx_type double const octave_idx_type &	LDVR
F77_RET_T octave_idx_type const octave_idx_type double const octave_idx_type double const octave_idx_type double const octave_idx_type double const octave_idx_type const octave_idx_type &	MM
F77_RET_T octave_idx_type const octave_idx_type const Complex const octave_idx_type const Complex const octave_idx_type Complex *	xVL
F77_RET_T octave_idx_type const octave_idx_type const Complex const octave_idx_type const Complex const octave_idx_type Complex const octave_idx_type Complex *	xVR
F77_RET_T octave_idx_type const octave_idx_type const Complex const octave_idx_type const Complex const octave_idx_type Complex const octave_idx_type Complex const octave_idx_type const octave_idx_type octave_idx_type Complex *	CWORK

---

Typedef Documentation

F77_RET_T const octave_idx_type double double double sort_function

---

Function Documentation

DEFUN_DLD	(	qz	,
		args	,
		nargout
	)

F77_RET_T F77_FUNC	(	dlag2	,
		DLAG2
	)			const

F77_RET_T F77_FUNC	(	dggbal	,
		DGGBAL
	)

F77_RET_T F77_FUNC	(	zggbal	,
		ZGGBAL
	)

F77_RET_T F77_FUNC	(	zhgeqz	,
		ZHGEQZ
	)

F77_RET_T F77_FUNC	(	zggbak	,
		ZGGBAK
	)

F77_RET_T F77_FUNC	(	xdlange	,
		XDLANGE
	)

F77_RET_T F77_FUNC	(	xdlamch	,
		XDLAMCH
	)

F77_RET_T F77_FUNC	(	ztgevc	,
		ZTGEVC
	)

F77_RET_T F77_FUNC	(	dtgevc	,
		DTGEVC
	)

F77_RET_T F77_FUNC	(	dgghrd	,
		DGGHRD
	)

F77_RET_T F77_FUNC	(	dsubsp	,
		DSUBSP
	)			const

F77_RET_T F77_FUNC	(	dggbak	,
		DGGBAK
	)

F77_RET_T F77_FUNC	(	dhgeqz	,
		DHGEQZ
	)

F77_RET_T F77_FUNC	(	zgghrd	,
		ZGGHRD
	)

---

Variable Documentation

F77_RET_T octave_idx_type const octave_idx_type const Complex* A

F77_RET_T const octave_idx_type const octave_idx_type const octave_idx_type Complex const octave_idx_type Complex const octave_idx_type Complex* ALPHA

F77_RET_T const octave_idx_type const octave_idx_type const octave_idx_type double const octave_idx_type double const octave_idx_type double double* ALPHAI

F77_RET_T const octave_idx_type const octave_idx_type const octave_idx_type double const octave_idx_type double const octave_idx_type double* ALPHAR

F77_RET_T octave_idx_type const octave_idx_type const Complex const octave_idx_type const Complex* B

F77_RET_T const octave_idx_type const octave_idx_type const octave_idx_type Complex const octave_idx_type Complex const octave_idx_type Complex Complex * BETA

F77_RET_T const octave_idx_type const octave_idx_type const octave_idx_type Complex const octave_idx_type Complex const octave_idx_type Complex Complex Complex* CQ

F77_RET_T octave_idx_type const octave_idx_type const Complex const octave_idx_type const Complex const octave_idx_type Complex const octave_idx_type Complex const octave_idx_type const octave_idx_type octave_idx_type Complex* CWORK

F77_RET_T const octave_idx_type const octave_idx_type const octave_idx_type Complex const octave_idx_type Complex const octave_idx_type Complex Complex Complex const octave_idx_type Complex* CZ

F77_RET_T const octave_idx_type double double double const double& EPS

F77_RET_T const octave_idx_type const octave_idx_type const double const octave_idx_type double double& F77_CHAR_ARG_LEN_DECL

F77_RET_T F77_CONST_CHAR_ARG_DECL

F77_RET_T const octave_idx_type double double double const double octave_idx_type octave_idx_type& FAIL

F77_RET_T const octave_idx_type const octave_idx_type const octave_idx_type& IHI

F77_RET_T const octave_idx_type const octave_idx_type& ILO

F77_RET_T const octave_idx_type double double double const double octave_idx_type octave_idx_type octave_idx_type* IND

F77_RET_T octave_idx_type const octave_idx_type const Complex const octave_idx_type& LDA

F77_RET_T octave_idx_type const octave_idx_type const Complex const octave_idx_type const Complex const octave_idx_type& LDB

F77_RET_T const octave_idx_type const octave_idx_type const octave_idx_type Complex const octave_idx_type Complex const octave_idx_type Complex Complex Complex const octave_idx_type & LDQ

F77_RET_T const octave_idx_type const octave_idx_type const octave_idx_type const double const double octave_idx_type Complex const octave_idx_type& LDV

F77_RET_T octave_idx_type const octave_idx_type const Complex const octave_idx_type const Complex const octave_idx_type Complex const octave_idx_type & LDVL

F77_RET_T octave_idx_type const octave_idx_type const Complex const octave_idx_type const Complex const octave_idx_type Complex const octave_idx_type Complex const octave_idx_type & LDVR

F77_RET_T const octave_idx_type const octave_idx_type const octave_idx_type Complex const octave_idx_type Complex const octave_idx_type Complex Complex Complex const octave_idx_type Complex const octave_idx_type & LDZ

F77_RET_T const octave_idx_type const octave_idx_type const octave_idx_type const double* LSCALE

F77_RET_T const octave_idx_type const octave_idx_type const octave_idx_type Complex const octave_idx_type Complex const octave_idx_type Complex Complex Complex const octave_idx_type Complex const octave_idx_type Complex const octave_idx_type & LWORK

F77_RET_T octave_idx_type const octave_idx_type const Complex const octave_idx_type const Complex const octave_idx_type Complex const octave_idx_type Complex const octave_idx_type const octave_idx_type octave_idx_type& M

F77_RET_T octave_idx_type const octave_idx_type const Complex const octave_idx_type const Complex const octave_idx_type Complex const octave_idx_type Complex const octave_idx_type const octave_idx_type & MM

F77_RET_T octave_idx_type const octave_idx_type& N

F77_RET_T const octave_idx_type double double double const double octave_idx_type& NDIM

F77_RET_T const octave_idx_type const octave_idx_type const octave_idx_type double const octave_idx_type double const octave_idx_type double double double double * Q

F77_RET_T const octave_idx_type const octave_idx_type const octave_idx_type const double const double* RSCALE

F77_RET_T octave_idx_type const octave_idx_type const Complex const octave_idx_type const Complex const octave_idx_type Complex const octave_idx_type Complex const octave_idx_type const octave_idx_type octave_idx_type Complex double * RWORK

F77_RET_T const octave_idx_type const double const octave_idx_type const double& SAFMIN

F77_RET_T const octave_idx_type const double const octave_idx_type const double double& SCALE1

F77_RET_T const octave_idx_type const double const octave_idx_type const double double double& SCALE2

F77_RET_T octave_idx_type * SELECT

F77_RET_T const octave_idx_type const octave_idx_type const octave_idx_type const double const double octave_idx_type Complex* V

F77_RET_T octave_idx_type const octave_idx_type double const octave_idx_type double const octave_idx_type double* VL

F77_RET_T octave_idx_type const octave_idx_type double const octave_idx_type double const octave_idx_type double const octave_idx_type double* VR

F77_RET_T const octave_idx_type const double const octave_idx_type const double double double double double double& WI

F77_RET_T octave_idx_type const octave_idx_type double const octave_idx_type double const octave_idx_type double const octave_idx_type double const octave_idx_type const octave_idx_type octave_idx_type double* WORK

F77_RET_T const octave_idx_type const double const octave_idx_type const double double double double& WR1

F77_RET_T const octave_idx_type const double const octave_idx_type const double double double double double& WR2

F77_RET_T octave_idx_type const octave_idx_type const Complex const octave_idx_type const Complex const octave_idx_type Complex* xVL

F77_RET_T octave_idx_type const octave_idx_type const Complex const octave_idx_type const Complex const octave_idx_type Complex const octave_idx_type Complex* xVR

F77_RET_T const octave_idx_type double double double * Z