
NAMEzgegs.f SYNOPSISFunctions/Subroutinessubroutine zgegs (JOBVSL, JOBVSR, N, A, LDA, B, LDB, ALPHA, BETA, VSL, LDVSL, VSR, LDVSR, WORK, LWORK, RWORK, INFO) Function/Subroutine Documentationsubroutine zgegs (characterJOBVSL, characterJOBVSR, integerN, complex*16, dimension( lda, * )A, integerLDA, complex*16, dimension( ldb, * )B, integerLDB, complex*16, dimension( * )ALPHA, complex*16, dimension( * )BETA, complex*16, dimension( ldvsl, * )VSL, integerLDVSL, complex*16, dimension( ldvsr, * )VSR, integerLDVSR, complex*16, dimension( * )WORK, integerLWORK, double precision, dimension( * )RWORK, integerINFO)ZGEEVX computes the eigenvalues and, optionally, the left and/or right eigenvectors for GE matrices Purpose:This routine is deprecated and has been replaced by routine ZGGES. ZGEGS computes the eigenvalues, Schur form, and, optionally, the left and or/right Schur vectors of a complex matrix pair (A,B). Given two square matrices A and B, the generalized Schur factorization has the form A = Q*S*Z**H, B = Q*T*Z**H where Q and Z are unitary matrices and S and T are upper triangular. The columns of Q are the left Schur vectors and the columns of Z are the right Schur vectors. If only the eigenvalues of (A,B) are needed, the driver routine ZGEGV should be used instead. See ZGEGV for a description of the eigenvalues of the generalized nonsymmetric eigenvalue problem (GNEP). JOBVSL
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JOBVSL is CHARACTER*1 = 'N': do not compute the left Schur vectors; = 'V': compute the left Schur vectors (returned in VSL).JOBVSR JOBVSR is CHARACTER*1 = 'N': do not compute the right Schur vectors; = 'V': compute the right Schur vectors (returned in VSR).N N is INTEGER The order of the matrices A, B, VSL, and VSR. N >= 0.A A is COMPLEX*16 array, dimension (LDA, N) On entry, the matrix A. On exit, the upper triangular matrix S from the generalized Schur factorization.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. On exit, the upper triangular matrix T from the generalized Schur factorization.LDB LDB is INTEGER The leading dimension of B. LDB >= max(1,N).ALPHA ALPHA is COMPLEX*16 array, dimension (N) The complex scalars alpha that define the eigenvalues of GNEP. ALPHA(j) = S(j,j), the diagonal element of the Schur form of A.BETA BETA is COMPLEX*16 array, dimension (N) The nonnegative real scalars beta that define the eigenvalues of GNEP. BETA(j) = T(j,j), the diagonal element of the triangular factor T. Together, the quantities alpha = ALPHA(j) and beta = BETA(j) represent the jth eigenvalue of the matrix pair (A,B), in one of the forms lambda = alpha/beta or mu = beta/alpha. Since either lambda or mu may overflow, they should not, in general, be computed.VSL VSL is COMPLEX*16 array, dimension (LDVSL,N) If JOBVSL = 'V', the matrix of left Schur vectors Q. Not referenced if JOBVSL = 'N'.LDVSL LDVSL is INTEGER The leading dimension of the matrix VSL. LDVSL >= 1, and if JOBVSL = 'V', LDVSL >= N.VSR VSR is COMPLEX*16 array, dimension (LDVSR,N) If JOBVSR = 'V', the matrix of right Schur vectors Z. Not referenced if JOBVSR = 'N'.LDVSR LDVSR is INTEGER The leading dimension of the matrix VSR. LDVSR >= 1, and if JOBVSR = 'V', LDVSR >= N.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). For good performance, LWORK must generally be larger. To compute the optimal value of LWORK, call ILAENV to get blocksizes (for ZGEQRF, ZUNMQR, and CUNGQR.) Then compute: NB  MAX of the blocksizes for ZGEQRF, ZUNMQR, and CUNGQR; the optimal LWORK is N*(NB+1). 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 (3*N)INFO INFO is INTEGER = 0: successful exit < 0: if INFO = i, the ith argument had an illegal value. =1,...,N: The QZ iteration failed. (A,B) are not in Schur form, but ALPHA(j) and BETA(j) should be correct for j=INFO+1,...,N. > N: errors that usually indicate LAPACK problems: =N+1: error return from ZGGBAL =N+2: error return from ZGEQRF =N+3: error return from ZUNMQR =N+4: error return from ZUNGQR =N+5: error return from ZGGHRD =N+6: error return from ZHGEQZ (other than failed iteration) =N+7: error return from ZGGBAK (computing VSL) =N+8: error return from ZGGBAK (computing VSR) =N+9: error return from ZLASCL (various places) Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
Definition at line 224 of file zgegs.f.
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