cggev-f(3)

cggev.f –

Synopsis

Functions/Subroutines

subroutine cggev (JOBVL, JOBVR, N, A, LDA, B, LDB, ALPHA, BETA, VL, LDVL, VR, LDVR, WORK, LWORK, RWORK, INFO)
CGGEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for GE matrices

Function/Subroutine Documentation

subroutine cggev (characterJOBVL, characterJOBVR, integerN, complex, dimension( lda, * )A, integerLDA, complex, dimension( ldb, * )B, integerLDB, complex, dimension( * )ALPHA, complex, dimension( * )BETA, complex, dimension( ldvl, * )VL, integerLDVL, complex, dimension( ldvr, * )VR, integerLDVR, complex, dimension( * )WORK, integerLWORK, real, dimension( * )RWORK, integerINFO)

CGGEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for GE matrices

Purpose:

 CGGEV 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.
 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 generalized eigenvector v(j) corresponding to the
 generalized eigenvalue lambda(j) of (A,B) satisfies
 A * v(j) = lambda(j) * B * v(j).
 The left generalized eigenvector u(j) corresponding to the
 generalized eigenvalues 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:

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.

 N is INTEGER
 The order of the matrices A, B, VL, and VR. N >= 0.

 A is COMPLEX array, dimension (LDA, N)
 On entry, the matrix A in the pair (A,B).
 On exit, A has been overwritten.

LDA

 LDA is INTEGER
 The leading dimension of A. LDA >= max(1,N).

 B is COMPLEX array, dimension (LDB, N)
 On entry, the matrix B in the pair (A,B).
 On exit, B has been overwritten.

LDB

 LDB is INTEGER
 The leading dimension of B. LDB >= max(1,N).

ALPHA

 ALPHA is COMPLEX array, dimension (N)

BETA

 BETA is COMPLEX array, dimension (N)
 On exit, ALPHA(j)/BETA(j), j=1,...,N, will be the
 generalized eigenvalues.
 Note: the quotients 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 is COMPLEX 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 is scaled so the largest component has
 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 is COMPLEX 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 is scaled so the largest component has
 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.

WORK

 WORK is COMPLEX 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).
 For good performance, LWORK must generally be larger.
 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 REAL array, dimension (8*N)

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 then QZ iteration failed in SHGEQZ,
 =N+2: error return from STGEVC.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

April 2012

Definition at line 217 of file cggev.f.

Author

Generated automatically by Doxygen for LAPACK from the source code.