zggevx.f - Online Linux Manual PageSection : 3
Updated : Tue Nov 14 2017
Source : Version 3.8.0
Note : LAPACK
NAMEzggevx.f
SYNOPSIS
Functions/Subroutinessubroutine zggevx (BALANC, JOBVL, JOBVR, SENSE, N, A, LDA, B, LDB, ALPHA, BETA, VL, LDVL, VR, LDVR, ILO, IHI, LSCALE, RSCALE, ABNRM, BBNRM, RCONDE, RCONDV, WORK, LWORK, RWORK, IWORK, BWORK, INFO)
ZGGEVX computes the eigenvalues and, optionally, the left and/or right eigenvectors for GE matrices
Function/Subroutine Documentation
subroutine zggevx (character BALANC, character JOBVL, character JOBVR, character SENSE, integer N, complex*16, dimension( lda, * ) A, integer LDA, complex*16, dimension( ldb, * ) B, integer LDB, complex*16, dimension( * ) ALPHA, complex*16, dimension( * ) BETA, complex*16, dimension( ldvl, * ) VL, integer LDVL, complex*16, dimension( ldvr, * ) VR, integer LDVR, integer ILO, integer IHI, double precision, dimension( * ) LSCALE, double precision, dimension( * ) RSCALE, double precision ABNRM, double precision BBNRM, double precision, dimension( * ) RCONDE, double precision, dimension( * ) RCONDV, complex*16, dimension( * ) WORK, integer LWORK, double precision, dimension( * ) RWORK, integer, dimension( * ) IWORK, logical, dimension( * ) BWORK, integer INFO) ZGGEVX computes the eigenvalues and, optionally, the left and/or right eigenvectors for GE matrices Purpose: ZGGEVX computes for a pair of N-by-N complex nonsymmetric matrices
(A,B) the generalized eigenvalues, and optionally, the left and/or
right generalized eigenvectors.
Optionally, it also computes a balancing transformation to improve
the conditioning of the eigenvalues and eigenvectors (ILO, IHI,
LSCALE, RSCALE, ABNRM, and BBNRM), reciprocal condition numbers for
the eigenvalues (RCONDE), and reciprocal condition numbers for the
right eigenvectors (RCONDV).
A generalized eigenvalue for a pair of matrices (A,B) is a scalar
lambda or a ratio alpha/beta = lambda, such that A - lambda*B is
singular. It is usually represented as the pair (alpha,beta), as
there is a reasonable interpretation for beta=0, and even for both
being zero.
The right eigenvector v(j) corresponding to the eigenvalue lambda(j)
of (A,B) satisfies
A * v(j) = lambda(j) * B * v(j) .
The left eigenvector u(j) corresponding to the eigenvalue lambda(j)
of (A,B) satisfies
u(j)**H * A = lambda(j) * u(j)**H * B.
where u(j)**H is the conjugate-transpose of u(j).Parameters: BALANC BALANC is CHARACTER*1
Specifies the balance option to be performed:
= 'N': do not diagonally scale or permute;
= 'P': permute only;
= 'S': scale only;
= 'B': both permute and scale.
Computed reciprocal condition numbers will be for the
matrices after permuting and/or balancing. Permuting does
not change condition numbers (in exact arithmetic), but
balancing does.
JOBVL JOBVL is CHARACTER*1
= 'N': do not compute the left generalized eigenvectors;
= 'V': compute the left generalized eigenvectors.
JOBVR JOBVR is CHARACTER*1
= 'N': do not compute the right generalized eigenvectors;
= 'V': compute the right generalized eigenvectors.
SENSE SENSE is CHARACTER*1
Determines which reciprocal condition numbers are computed.
= 'N': none are computed;
= 'E': computed for eigenvalues only;
= 'V': computed for eigenvectors only;
= 'B': computed for eigenvalues and eigenvectors.
N N is INTEGER
The order of the matrices A, B, VL, and VR. N >= 0.
A A is COMPLEX*16 array, dimension (LDA, N)
On entry, the matrix A in the pair (A,B).
On exit, A has been overwritten. If JOBVL='V' or JOBVR='V'
or both, then A contains the first part of the complex Schur
form of the "balanced" versions of the input A and B.
LDA LDA is INTEGER
The leading dimension of A. LDA >= max(1,N).
B B is COMPLEX*16 array, dimension (LDB, N)
On entry, the matrix B in the pair (A,B).
On exit, B has been overwritten. If JOBVL='V' or JOBVR='V'
or both, then B contains the second part of the complex
Schur form of the "balanced" versions of the input A and B.
LDB LDB is INTEGER
The leading dimension of B. LDB >= max(1,N).
ALPHA ALPHA is COMPLEX*16 array, dimension (N)
BETA BETA is COMPLEX*16 array, dimension (N)
On exit, ALPHA(j)/BETA(j), j=1,...,N, will be the generalized
eigenvalues.
Note: the quotient ALPHA(j)/BETA(j) ) may easily over- or
underflow, and BETA(j) may even be zero. Thus, the user
should avoid naively computing the ratio ALPHA/BETA.
However, ALPHA will be always less than and usually
comparable with norm(A) in magnitude, and BETA always less
than and usually comparable with norm(B).
VL VL is COMPLEX*16 array, dimension (LDVL,N)
If JOBVL = 'V', the left generalized eigenvectors u(j) are
stored one after another in the columns of VL, in the same
order as their eigenvalues.
Each eigenvector will be scaled so the largest component
will have abs(real part) + abs(imag. part) = 1.
Not referenced if JOBVL = 'N'.
LDVL LDVL is INTEGER
The leading dimension of the matrix VL. LDVL >= 1, and
if JOBVL = 'V', LDVL >= N.
VR VR is COMPLEX*16 array, dimension (LDVR,N)
If JOBVR = 'V', the right generalized eigenvectors v(j) are
stored one after another in the columns of VR, in the same
order as their eigenvalues.
Each eigenvector will be scaled so the largest component
will have abs(real part) + abs(imag. part) = 1.
Not referenced if JOBVR = 'N'.
LDVR LDVR is INTEGER
The leading dimension of the matrix VR. LDVR >= 1, and
if JOBVR = 'V', LDVR >= N.
ILO ILO is INTEGER
IHI IHI is INTEGER
ILO and IHI are integer values such that on exit
A(i,j) = 0 and B(i,j) = 0 if i > j and
j = 1,...,ILO-1 or i = IHI+1,...,N.
If BALANC = 'N' or 'S', ILO = 1 and IHI = N.
LSCALE LSCALE is DOUBLE PRECISION array, dimension (N)
Details of the permutations and scaling factors applied
to the left side of A and B. If PL(j) is the index of the
row interchanged with row j, and DL(j) is the scaling
factor applied to row j, then
LSCALE(j) = PL(j) for j = 1,...,ILO-1
= DL(j) for j = ILO,...,IHI
= PL(j) for j = IHI+1,...,N.
The order in which the interchanges are made is N to IHI+1,
then 1 to ILO-1.
RSCALE RSCALE is DOUBLE PRECISION array, dimension (N)
Details of the permutations and scaling factors applied
to the right side of A and B. If PR(j) is the index of the
column interchanged with column j, and DR(j) is the scaling
factor applied to column j, then
RSCALE(j) = PR(j) for j = 1,...,ILO-1
= DR(j) for j = ILO,...,IHI
= PR(j) for j = IHI+1,...,N
The order in which the interchanges are made is N to IHI+1,
then 1 to ILO-1.
ABNRM ABNRM is DOUBLE PRECISION
The one-norm of the balanced matrix A.
BBNRM BBNRM is DOUBLE PRECISION
The one-norm of the balanced matrix B.
RCONDE RCONDE is DOUBLE PRECISION array, dimension (N)
If SENSE = 'E' or 'B', the reciprocal condition numbers of
the eigenvalues, stored in consecutive elements of the array.
If SENSE = 'N' or 'V', RCONDE is not referenced.
RCONDV RCONDV is DOUBLE PRECISION array, dimension (N)
If JOB = 'V' or 'B', the estimated reciprocal condition
numbers of the eigenvectors, stored in consecutive elements
of the array. If the eigenvalues cannot be reordered to
compute RCONDV(j), RCONDV(j) is set to 0; this can only occur
when the true value would be very small anyway.
If SENSE = 'N' or 'E', RCONDV is not referenced.
WORK WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK LWORK is INTEGER
The dimension of the array WORK. LWORK >= max(1,2*N).
If SENSE = 'E', LWORK >= max(1,4*N).
If SENSE = 'V' or 'B', LWORK >= max(1,2*N*N+2*N).
If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal size of the WORK array, returns
this value as the first entry of the WORK array, and no error
message related to LWORK is issued by XERBLA.
RWORK RWORK is DOUBLE PRECISION array, dimension (lrwork)
lrwork must be at least max(1,6*N) if BALANC = 'S' or 'B',
and at least max(1,2*N) otherwise.
Real workspace.
IWORK IWORK is INTEGER array, dimension (N+2)
If SENSE = 'E', IWORK is not referenced.
BWORK BWORK is LOGICAL array, dimension (N)
If SENSE = 'N', BWORK is not referenced.
INFO INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value.
= 1,...,N:
The QZ iteration failed. No eigenvectors have been
calculated, but ALPHA(j) and BETA(j) should be correct
for j=INFO+1,...,N.
> N: =N+1: other than QZ iteration failed in ZHGEQZ.
=N+2: error return from ZTGEVC.Author: Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Date: April 2012 Further Details: Balancing a matrix pair (A,B) includes, first, permuting rows and
columns to isolate eigenvalues, second, applying diagonal similarity
transformation to the rows and columns to make the rows and columns
as close in norm as possible. The computed reciprocal condition
numbers correspond to the balanced matrix. Permuting rows and columns
will not change the condition numbers (in exact arithmetic) but
diagonal scaling will. For further explanation of balancing, see
section 4.11.1.2 of LAPACK Users' Guide.
An approximate error bound on the chordal distance between the i-th
computed generalized eigenvalue w and the corresponding exact
eigenvalue lambda is
chord(w, lambda) <= EPS * norm(ABNRM, BBNRM) / RCONDE(I)
An approximate error bound for the angle between the i-th computed
eigenvector VL(i) or VR(i) is given by
EPS * norm(ABNRM, BBNRM) / DIF(i).
For further explanation of the reciprocal condition numbers RCONDE
and RCONDV, see section 4.11 of LAPACK User's Guide.Definition at line 376 of file zggevx.f.
AuthorGenerated automatically by Doxygen for LAPACK from the source code. 0
Johanes Gumabo
Data Size : 36,258 byte
man-zggevx.f.3Build : 2024-12-05, 20:55 :
Visitor Screen : x
Visitor Counter ( page / site ) : 5 / 170,463
Visitor ID : :
Visitor IP : 3.146.206.87 :
Visitor Provider : AMAZON-02 :
Provider Position ( lat x lon ) : 39.962500 x -83.006100 : x
Provider Accuracy Radius ( km ) : 1000 :
Provider City : Columbus :
Provider Province : Ohio , : ,
Provider Country : United States :
Provider Continent : North America :
Visitor Recorder : Version :
Visitor Recorder : Library :
Online Linux Manual Page : Version : Online Linux Manual Page - Fedora.40 - march=x86-64 - mtune=generic - 24.12.05
Online Linux Manual Page : Library : lib_c - 24.10.03 - march=x86-64 - mtune=generic - Fedora.40
Online Linux Manual Page : Library : lib_m - 24.10.03 - march=x86-64 - mtune=generic - Fedora.40
Data Base : Version : Online Linux Manual Page Database - 24.04.13 - march=x86-64 - mtune=generic - fedora-38
Data Base : Library : lib_c - 23.02.07 - march=x86-64 - mtune=generic - fedora.36
Very long time ago, I have the best tutor, Wenzel Svojanovsky . If someone knows the email address of Wenzel Svojanovsky , please send an email to johanes_gumabo@yahoo.co.id .
If error, please print screen and send to johanes_gumabo@yahoo.co.id
Under development. Support me via PayPal.