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---
:name: dgegs
:md5sum: c49c4cd3c8469332e43b4d911700e384
:category: :subroutine
:arguments:
- jobvsl:
:type: char
:intent: input
- jobvsr:
:type: char
:intent: input
- n:
:type: integer
:intent: input
- a:
:type: doublereal
:intent: input/output
:dims:
- lda
- n
- lda:
:type: integer
:intent: input
- b:
:type: doublereal
:intent: input/output
:dims:
- ldb
- n
- ldb:
:type: integer
:intent: input
- alphar:
:type: doublereal
:intent: output
:dims:
- n
- alphai:
:type: doublereal
:intent: output
:dims:
- n
- beta:
:type: doublereal
:intent: output
:dims:
- n
- vsl:
:type: doublereal
:intent: output
:dims:
- ldvsl
- n
- ldvsl:
:type: integer
:intent: input
- vsr:
:type: doublereal
:intent: output
:dims:
- ldvsr
- n
- ldvsr:
:type: integer
:intent: input
- work:
:type: doublereal
:intent: output
:dims:
- MAX(1,lwork)
- lwork:
:type: integer
:intent: input
:option: true
:default: 4*n
- info:
:type: integer
:intent: output
:substitutions:
ldvsl: "lsame_(&jobvsl,\"V\") ? n : 1"
ldvsr: "lsame_(&jobvsr,\"V\") ? n : 1"
:fortran_help: " SUBROUTINE DGEGS( JOBVSL, JOBVSR, N, A, LDA, B, LDB, ALPHAR, ALPHAI, BETA, VSL, LDVSL, VSR, LDVSR, WORK, LWORK, INFO )\n\n\
* Purpose\n\
* =======\n\
*\n\
* This routine is deprecated and has been replaced by routine DGGES.\n\
*\n\
* DGEGS computes the eigenvalues, real Schur form, and, optionally,\n\
* left and or/right Schur vectors of a real matrix pair (A,B).\n\
* Given two square matrices A and B, the generalized real Schur\n\
* factorization has the form\n\
*\n\
* A = Q*S*Z**T, B = Q*T*Z**T\n\
*\n\
* where Q and Z are orthogonal matrices, T is upper triangular, and S\n\
* is an upper quasi-triangular matrix with 1-by-1 and 2-by-2 diagonal\n\
* blocks, the 2-by-2 blocks corresponding to complex conjugate pairs\n\
* of eigenvalues of (A,B). 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\
* DGEGV should be used instead. See DGEGV 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) DOUBLE PRECISION array, dimension (LDA, N)\n\
* On entry, the matrix A.\n\
* On exit, the upper quasi-triangular matrix S from the\n\
* generalized real Schur factorization.\n\
*\n\
* LDA (input) INTEGER\n\
* The leading dimension of A. LDA >= max(1,N).\n\
*\n\
* B (input/output) DOUBLE PRECISION array, dimension (LDB, N)\n\
* On entry, the matrix B.\n\
* On exit, the upper triangular matrix T from the generalized\n\
* real Schur factorization.\n\
*\n\
* LDB (input) INTEGER\n\
* The leading dimension of B. LDB >= max(1,N).\n\
*\n\
* ALPHAR (output) DOUBLE PRECISION array, dimension (N)\n\
* The real parts of each scalar alpha defining an eigenvalue\n\
* of GNEP.\n\
*\n\
* ALPHAI (output) DOUBLE PRECISION array, dimension (N)\n\
* The imaginary parts of each scalar alpha defining an\n\
* eigenvalue of GNEP. If ALPHAI(j) is zero, then the j-th\n\
* eigenvalue is real; if positive, then the j-th and (j+1)-st\n\
* eigenvalues are a complex conjugate pair, with\n\
* ALPHAI(j+1) = -ALPHAI(j).\n\
*\n\
* BETA (output) DOUBLE PRECISION array, dimension (N)\n\
* The scalars beta that define the eigenvalues of GNEP.\n\
* Together, the quantities alpha = (ALPHAR(j),ALPHAI(j)) and\n\
* beta = BETA(j) represent the j-th eigenvalue of the matrix\n\
* pair (A,B), in one of the forms lambda = alpha/beta or\n\
* mu = beta/alpha. Since either lambda or mu may overflow,\n\
* they should not, in general, be computed.\n\
*\n\
* VSL (output) DOUBLE PRECISION 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) DOUBLE PRECISION 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) DOUBLE PRECISION 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(1,4*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 DGEQRF, DORMQR, and DORGQR.) Then compute:\n\
* NB -- MAX of the blocksizes for DGEQRF, DORMQR, and DORGQR\n\
* The optimal LWORK is 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\
* 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 ALPHAR(j), ALPHAI(j), and BETA(j) should\n\
* be correct for j=INFO+1,...,N.\n\
* > N: errors that usually indicate LAPACK problems:\n\
* =N+1: error return from DGGBAL\n\
* =N+2: error return from DGEQRF\n\
* =N+3: error return from DORMQR\n\
* =N+4: error return from DORGQR\n\
* =N+5: error return from DGGHRD\n\
* =N+6: error return from DHGEQZ (other than failed\n\
* iteration)\n\
* =N+7: error return from DGGBAK (computing VSL)\n\
* =N+8: error return from DGGBAK (computing VSR)\n\
* =N+9: error return from DLASCL (various places)\n\
*\n\n\
* =====================================================================\n\
*\n"
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