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---
:name: zgegv
:md5sum: 96caca0b338719751521b432c1b15a00
:category: :subroutine
:arguments:
- jobvl:
:type: char
:intent: input
- jobvr:
:type: char
:intent: input
- n:
:type: integer
:intent: input
- a:
:type: doublecomplex
:intent: input/output
:dims:
- lda
- n
- lda:
:type: integer
:intent: input
- b:
:type: doublecomplex
:intent: input/output
:dims:
- ldb
- n
- ldb:
:type: integer
:intent: input
- alpha:
:type: doublecomplex
:intent: output
:dims:
- n
- beta:
:type: doublecomplex
:intent: output
:dims:
- n
- vl:
:type: doublecomplex
:intent: output
:dims:
- ldvl
- n
- ldvl:
:type: integer
:intent: input
- vr:
:type: doublecomplex
:intent: output
:dims:
- ldvr
- n
- ldvr:
:type: integer
:intent: input
- work:
:type: doublecomplex
:intent: output
:dims:
- MAX(1,lwork)
- lwork:
:type: integer
:intent: input
:option: true
:default: 2*n
- rwork:
:type: doublereal
:intent: output
:dims:
- 8*n
- info:
:type: integer
:intent: output
:substitutions:
ldvr: "lsame_(&jobvr,\"V\") ? n : 1"
ldvl: "lsame_(&jobvl,\"V\") ? n : 1"
:fortran_help: " SUBROUTINE ZGEGV( JOBVL, JOBVR, N, A, LDA, B, LDB, ALPHA, BETA, VL, LDVL, VR, LDVR, WORK, LWORK, RWORK, INFO )\n\n\
* Purpose\n\
* =======\n\
*\n\
* This routine is deprecated and has been replaced by routine ZGGEV.\n\
*\n\
* ZGEGV computes the eigenvalues and, optionally, the left and/or right\n\
* eigenvectors of a complex matrix pair (A,B).\n\
* Given two square matrices A and B,\n\
* the generalized nonsymmetric eigenvalue problem (GNEP) is to find the\n\
* eigenvalues lambda and corresponding (non-zero) eigenvectors x such\n\
* that\n\
* A*x = lambda*B*x.\n\
*\n\
* An alternate form is to find the eigenvalues mu and corresponding\n\
* eigenvectors y such that\n\
* mu*A*y = B*y.\n\
*\n\
* These two forms are equivalent with mu = 1/lambda and x = y if\n\
* neither lambda nor mu is zero. In order to deal with the case that\n\
* lambda or mu is zero or small, two values alpha and beta are returned\n\
* for each eigenvalue, such that lambda = alpha/beta and\n\
* mu = beta/alpha.\n\
*\n\
* The vectors x and y in the above equations are right eigenvectors of\n\
* the matrix pair (A,B). Vectors u and v satisfying\n\
* u**H*A = lambda*u**H*B or mu*v**H*A = v**H*B\n\
* are left eigenvectors of (A,B).\n\
*\n\
* Note: this routine performs \"full balancing\" on A and B -- see\n\
* \"Further Details\", below.\n\
*\n\n\
* Arguments\n\
* =========\n\
*\n\
* JOBVL (input) CHARACTER*1\n\
* = 'N': do not compute the left generalized eigenvectors;\n\
* = 'V': compute the left generalized eigenvectors (returned\n\
* in VL).\n\
*\n\
* JOBVR (input) CHARACTER*1\n\
* = 'N': do not compute the right generalized eigenvectors;\n\
* = 'V': compute the right generalized eigenvectors (returned\n\
* in VR).\n\
*\n\
* N (input) INTEGER\n\
* The order of the matrices A, B, VL, and VR. N >= 0.\n\
*\n\
* A (input/output) COMPLEX*16 array, dimension (LDA, N)\n\
* On entry, the matrix A.\n\
* If JOBVL = 'V' or JOBVR = 'V', then on exit A\n\
* contains the Schur form of A from the generalized Schur\n\
* factorization of the pair (A,B) after balancing. If no\n\
* eigenvectors were computed, then only the diagonal elements\n\
* of the Schur form will be correct. See ZGGHRD and ZHGEQZ\n\
* for details.\n\
*\n\
* LDA (input) INTEGER\n\
* The leading dimension of A. LDA >= max(1,N).\n\
*\n\
* B (input/output) COMPLEX*16 array, dimension (LDB, N)\n\
* On entry, the matrix B.\n\
* If JOBVL = 'V' or JOBVR = 'V', then on exit B contains the\n\
* upper triangular matrix obtained from B in the generalized\n\
* Schur factorization of the pair (A,B) after balancing.\n\
* If no eigenvectors were computed, then only the diagonal\n\
* elements of B will be correct. See ZGGHRD and ZHGEQZ for\n\
* details.\n\
*\n\
* LDB (input) INTEGER\n\
* The leading dimension of B. LDB >= max(1,N).\n\
*\n\
* ALPHA (output) COMPLEX*16 array, dimension (N)\n\
* The complex scalars alpha that define the eigenvalues of\n\
* GNEP.\n\
*\n\
* BETA (output) COMPLEX*16 array, dimension (N)\n\
* The complex scalars beta that define the eigenvalues of GNEP.\n\
* \n\
* Together, the quantities alpha = ALPHA(j) and beta = BETA(j)\n\
* represent the j-th eigenvalue of the matrix pair (A,B), in\n\
* one of the forms lambda = alpha/beta or mu = beta/alpha.\n\
* Since either lambda or mu may overflow, they should not,\n\
* in general, be computed.\n\
*\n\
* VL (output) COMPLEX*16 array, dimension (LDVL,N)\n\
* If JOBVL = 'V', the left eigenvectors u(j) are stored\n\
* in the columns of VL, in the same order as their eigenvalues.\n\
* Each eigenvector is scaled so that its largest component has\n\
* abs(real part) + abs(imag. part) = 1, except for eigenvectors\n\
* corresponding to an eigenvalue with alpha = beta = 0, which\n\
* are set to zero.\n\
* Not referenced if JOBVL = 'N'.\n\
*\n\
* LDVL (input) INTEGER\n\
* The leading dimension of the matrix VL. LDVL >= 1, and\n\
* if JOBVL = 'V', LDVL >= N.\n\
*\n\
* VR (output) COMPLEX*16 array, dimension (LDVR,N)\n\
* If JOBVR = 'V', the right eigenvectors x(j) are stored\n\
* in the columns of VR, in the same order as their eigenvalues.\n\
* Each eigenvector is scaled so that its largest component has\n\
* abs(real part) + abs(imag. part) = 1, except for eigenvectors\n\
* corresponding to an eigenvalue with alpha = beta = 0, which\n\
* are set to zero.\n\
* Not referenced if JOBVR = 'N'.\n\
*\n\
* LDVR (input) INTEGER\n\
* The leading dimension of the matrix VR. LDVR >= 1, and\n\
* if JOBVR = 'V', LDVR >= N.\n\
*\n\
* WORK (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK))\n\
* On exit, if INFO = 0, WORK(1) returns the optimal LWORK.\n\
*\n\
* LWORK (input) INTEGER\n\
* The dimension of the array WORK. LWORK >= max(1,2*N).\n\
* For good performance, LWORK must generally be larger.\n\
* To compute the optimal value of LWORK, call ILAENV to get\n\
* blocksizes (for ZGEQRF, ZUNMQR, and ZUNGQR.) Then compute:\n\
* NB -- MAX of the blocksizes for ZGEQRF, ZUNMQR, and ZUNGQR;\n\
* The optimal LWORK is MAX( 2*N, N*(NB+1) ).\n\
*\n\
* If LWORK = -1, then a workspace query is assumed; the routine\n\
* only calculates the optimal size of the WORK array, returns\n\
* this value as the first entry of the WORK array, and no error\n\
* message related to LWORK is issued by XERBLA.\n\
*\n\
* RWORK (workspace/output) DOUBLE PRECISION array, dimension (8*N)\n\
*\n\
* INFO (output) INTEGER\n\
* = 0: successful exit\n\
* < 0: if INFO = -i, the i-th argument had an illegal value.\n\
* =1,...,N:\n\
* The QZ iteration failed. No eigenvectors have been\n\
* calculated, but ALPHA(j) and BETA(j) should be\n\
* correct for j=INFO+1,...,N.\n\
* > N: errors that usually indicate LAPACK problems:\n\
* =N+1: error return from ZGGBAL\n\
* =N+2: error return from ZGEQRF\n\
* =N+3: error return from ZUNMQR\n\
* =N+4: error return from ZUNGQR\n\
* =N+5: error return from ZGGHRD\n\
* =N+6: error return from ZHGEQZ (other than failed\n\
* iteration)\n\
* =N+7: error return from ZTGEVC\n\
* =N+8: error return from ZGGBAK (computing VL)\n\
* =N+9: error return from ZGGBAK (computing VR)\n\
* =N+10: error return from ZLASCL (various calls)\n\
*\n\n\
* Further Details\n\
* ===============\n\
*\n\
* Balancing\n\
* ---------\n\
*\n\
* This driver calls ZGGBAL to both permute and scale rows and columns\n\
* of A and B. The permutations PL and PR are chosen so that PL*A*PR\n\
* and PL*B*R will be upper triangular except for the diagonal blocks\n\
* A(i:j,i:j) and B(i:j,i:j), with i and j as close together as\n\
* possible. The diagonal scaling matrices DL and DR are chosen so\n\
* that the pair DL*PL*A*PR*DR, DL*PL*B*PR*DR have elements close to\n\
* one (except for the elements that start out zero.)\n\
*\n\
* After the eigenvalues and eigenvectors of the balanced matrices\n\
* have been computed, ZGGBAK transforms the eigenvectors back to what\n\
* they would have been (in perfect arithmetic) if they had not been\n\
* balanced.\n\
*\n\
* Contents of A and B on Exit\n\
* -------- -- - --- - -- ----\n\
*\n\
* If any eigenvectors are computed (either JOBVL='V' or JOBVR='V' or\n\
* both), then on exit the arrays A and B will contain the complex Schur\n\
* form[*] of the \"balanced\" versions of A and B. If no eigenvectors\n\
* are computed, then only the diagonal blocks will be correct.\n\
*\n\
* [*] In other words, upper triangular form.\n\
*\n\
* =====================================================================\n\
*\n"
|
