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---
:name: cgegs
:md5sum: 0d915b089b60c924c71d32fe45a153c2
:category: :subroutine
:arguments:
- jobvsl:
:type: char
:intent: input
- jobvsr:
:type: char
:intent: input
- n:
:type: integer
:intent: input
- a:
:type: complex
:intent: input/output
:dims:
- lda
- n
- lda:
:type: integer
:intent: input
- b:
:type: complex
:intent: input/output
:dims:
- ldb
- n
- ldb:
:type: integer
:intent: input
- alpha:
:type: complex
:intent: output
:dims:
- n
- beta:
:type: complex
:intent: output
:dims:
- n
- vsl:
:type: complex
:intent: output
:dims:
- ldvsl
- n
- ldvsl:
:type: integer
:intent: input
- vsr:
:type: complex
:intent: output
:dims:
- ldvsr
- n
- ldvsr:
:type: integer
:intent: input
- work:
:type: complex
:intent: output
:dims:
- MAX(1,lwork)
- lwork:
:type: integer
:intent: input
:option: true
:default: 2*n
- rwork:
:type: real
:intent: workspace
:dims:
- 3*n
- info:
:type: integer
:intent: output
:substitutions:
ldvsl: "lsame_(&jobvsl,\"V\") ? n : 1"
ldvsr: "lsame_(&jobvsr,\"V\") ? n : 1"
:fortran_help: " SUBROUTINE CGEGS( JOBVSL, JOBVSR, N, A, LDA, B, LDB, ALPHA, BETA, VSL, LDVSL, VSR, LDVSR, WORK, LWORK, RWORK, INFO )\n\n\
* Purpose\n\
* =======\n\
*\n\
* This routine is deprecated and has been replaced by routine CGGES.\n\
*\n\
* CGEGS computes the eigenvalues, Schur form, and, optionally, the\n\
* left and or/right Schur vectors of a complex matrix pair (A,B).\n\
* Given two square matrices A and B, the generalized Schur\n\
* factorization has the form\n\
* \n\
* A = Q*S*Z**H, B = Q*T*Z**H\n\
* \n\
* where Q and Z are unitary matrices and S and T are upper triangular.\n\
* The columns of Q are the left Schur vectors\n\
* and the columns of Z are the right Schur vectors.\n\
* \n\
* If only the eigenvalues of (A,B) are needed, the driver routine\n\
* CGEGV should be used instead. See CGEGV for a description of the\n\
* eigenvalues of the generalized nonsymmetric eigenvalue problem\n\
* (GNEP).\n\
*\n\n\
* Arguments\n\
* =========\n\
*\n\
* JOBVSL (input) CHARACTER*1\n\
* = 'N': do not compute the left Schur vectors;\n\
* = 'V': compute the left Schur vectors (returned in VSL).\n\
*\n\
* JOBVSR (input) CHARACTER*1\n\
* = 'N': do not compute the right Schur vectors;\n\
* = 'V': compute the right Schur vectors (returned in VSR).\n\
*\n\
* N (input) INTEGER\n\
* The order of the matrices A, B, VSL, and VSR. N >= 0.\n\
*\n\
* A (input/output) COMPLEX array, dimension (LDA, N)\n\
* On entry, the matrix A.\n\
* On exit, the upper triangular matrix S from the generalized\n\
* Schur factorization.\n\
*\n\
* LDA (input) INTEGER\n\
* The leading dimension of A. LDA >= max(1,N).\n\
*\n\
* B (input/output) COMPLEX array, dimension (LDB, N)\n\
* On entry, the matrix B.\n\
* On exit, the upper triangular matrix T from the generalized\n\
* Schur factorization.\n\
*\n\
* LDB (input) INTEGER\n\
* The leading dimension of B. LDB >= max(1,N).\n\
*\n\
* ALPHA (output) COMPLEX array, dimension (N)\n\
* The complex scalars alpha that define the eigenvalues of\n\
* GNEP. ALPHA(j) = S(j,j), the diagonal element of the Schur\n\
* form of A.\n\
*\n\
* BETA (output) COMPLEX array, dimension (N)\n\
* The non-negative real scalars beta that define the\n\
* eigenvalues of GNEP. BETA(j) = T(j,j), the diagonal element\n\
* of the triangular factor T.\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\
* VSL (output) COMPLEX array, dimension (LDVSL,N)\n\
* If JOBVSL = 'V', the matrix of left Schur vectors Q.\n\
* Not referenced if JOBVSL = 'N'.\n\
*\n\
* LDVSL (input) INTEGER\n\
* The leading dimension of the matrix VSL. LDVSL >= 1, and\n\
* if JOBVSL = 'V', LDVSL >= N.\n\
*\n\
* VSR (output) COMPLEX array, dimension (LDVSR,N)\n\
* If JOBVSR = 'V', the matrix of right Schur vectors Z.\n\
* Not referenced if JOBVSR = 'N'.\n\
*\n\
* LDVSR (input) INTEGER\n\
* The leading dimension of the matrix VSR. LDVSR >= 1, and\n\
* if JOBVSR = 'V', LDVSR >= N.\n\
*\n\
* WORK (workspace/output) COMPLEX 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 CGEQRF, CUNMQR, and CUNGQR.) Then compute:\n\
* NB -- MAX of the blocksizes for CGEQRF, CUNMQR, and CUNGQR;\n\
* the optimal LWORK is 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) REAL array, dimension (3*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. (A,B) are not in Schur\n\
* form, but ALPHA(j) and BETA(j) should be correct for\n\
* j=INFO+1,...,N.\n\
* > N: errors that usually indicate LAPACK problems:\n\
* =N+1: error return from CGGBAL\n\
* =N+2: error return from CGEQRF\n\
* =N+3: error return from CUNMQR\n\
* =N+4: error return from CUNGQR\n\
* =N+5: error return from CGGHRD\n\
* =N+6: error return from CHGEQZ (other than failed\n\
* iteration)\n\
* =N+7: error return from CGGBAK (computing VSL)\n\
* =N+8: error return from CGGBAK (computing VSR)\n\
* =N+9: error return from CLASCL (various places)\n\
*\n\n\
* =====================================================================\n\
*\n"
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