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---
:name: zgeesx
:md5sum: c664e00d89738fc39bde317d2585291e
:category: :subroutine
:arguments:
- jobvs:
:type: char
:intent: input
- sort:
:type: char
:intent: input
- select:
:intent: external procedure
:block_type: logical
:block_arg_num: 1
:block_arg_type: doublecomplex
- sense:
:type: char
:intent: input
- n:
:type: integer
:intent: input
- a:
:type: doublecomplex
:intent: input/output
:dims:
- lda
- n
- lda:
:type: integer
:intent: input
- sdim:
:type: integer
:intent: output
- w:
:type: doublecomplex
:intent: output
:dims:
- n
- vs:
:type: doublecomplex
:intent: output
:dims:
- ldvs
- n
- ldvs:
:type: integer
:intent: input
- rconde:
:type: doublereal
:intent: output
- rcondv:
:type: doublereal
:intent: output
- work:
:type: doublecomplex
:intent: output
:dims:
- MAX(1,lwork)
- lwork:
:type: integer
:intent: input
:option: true
:default: "(lsame_(&sense,\"E\")||lsame_(&sense,\"V\")||lsame_(&sense,\"B\")) ? n*n/2 : 2*n"
- rwork:
:type: doublereal
:intent: workspace
:dims:
- n
- bwork:
:type: logical
:intent: workspace
:dims:
- "lsame_(&sort,\"N\") ? 0 : n"
- info:
:type: integer
:intent: output
:substitutions:
ldvs: "lsame_(&jobvs,\"V\") ? n : 1"
:fortran_help: " SUBROUTINE ZGEESX( JOBVS, SORT, SELECT, SENSE, N, A, LDA, SDIM, W, VS, LDVS, RCONDE, RCONDV, WORK, LWORK, RWORK, BWORK, INFO )\n\n\
* Purpose\n\
* =======\n\
*\n\
* ZGEESX computes for an N-by-N complex nonsymmetric matrix A, the\n\
* eigenvalues, the Schur form T, and, optionally, the matrix of Schur\n\
* vectors Z. This gives the Schur factorization A = Z*T*(Z**H).\n\
*\n\
* Optionally, it also orders the eigenvalues on the diagonal of the\n\
* Schur form so that selected eigenvalues are at the top left;\n\
* computes a reciprocal condition number for the average of the\n\
* selected eigenvalues (RCONDE); and computes a reciprocal condition\n\
* number for the right invariant subspace corresponding to the\n\
* selected eigenvalues (RCONDV). The leading columns of Z form an\n\
* orthonormal basis for this invariant subspace.\n\
*\n\
* For further explanation of the reciprocal condition numbers RCONDE\n\
* and RCONDV, see Section 4.10 of the LAPACK Users' Guide (where\n\
* these quantities are called s and sep respectively).\n\
*\n\
* A complex matrix is in Schur form if it is upper triangular.\n\
*\n\n\
* Arguments\n\
* =========\n\
*\n\
* JOBVS (input) CHARACTER*1\n\
* = 'N': Schur vectors are not computed;\n\
* = 'V': Schur vectors are computed.\n\
*\n\
* SORT (input) CHARACTER*1\n\
* Specifies whether or not to order the eigenvalues on the\n\
* diagonal of the Schur form.\n\
* = 'N': Eigenvalues are not ordered;\n\
* = 'S': Eigenvalues are ordered (see SELECT).\n\
*\n\
* SELECT (external procedure) LOGICAL FUNCTION of one COMPLEX*16 argument\n\
* SELECT must be declared EXTERNAL in the calling subroutine.\n\
* If SORT = 'S', SELECT is used to select eigenvalues to order\n\
* to the top left of the Schur form.\n\
* If SORT = 'N', SELECT is not referenced.\n\
* An eigenvalue W(j) is selected if SELECT(W(j)) is true.\n\
*\n\
* SENSE (input) CHARACTER*1\n\
* Determines which reciprocal condition numbers are computed.\n\
* = 'N': None are computed;\n\
* = 'E': Computed for average of selected eigenvalues only;\n\
* = 'V': Computed for selected right invariant subspace only;\n\
* = 'B': Computed for both.\n\
* If SENSE = 'E', 'V' or 'B', SORT must equal 'S'.\n\
*\n\
* N (input) INTEGER\n\
* The order of the matrix A. N >= 0.\n\
*\n\
* A (input/output) COMPLEX*16 array, dimension (LDA, N)\n\
* On entry, the N-by-N matrix A.\n\
* On exit, A is overwritten by its Schur form T.\n\
*\n\
* LDA (input) INTEGER\n\
* The leading dimension of the array A. LDA >= max(1,N).\n\
*\n\
* SDIM (output) INTEGER\n\
* If SORT = 'N', SDIM = 0.\n\
* If SORT = 'S', SDIM = number of eigenvalues for which\n\
* SELECT is true.\n\
*\n\
* W (output) COMPLEX*16 array, dimension (N)\n\
* W contains the computed eigenvalues, in the same order\n\
* that they appear on the diagonal of the output Schur form T.\n\
*\n\
* VS (output) COMPLEX*16 array, dimension (LDVS,N)\n\
* If JOBVS = 'V', VS contains the unitary matrix Z of Schur\n\
* vectors.\n\
* If JOBVS = 'N', VS is not referenced.\n\
*\n\
* LDVS (input) INTEGER\n\
* The leading dimension of the array VS. LDVS >= 1, and if\n\
* JOBVS = 'V', LDVS >= N.\n\
*\n\
* RCONDE (output) DOUBLE PRECISION\n\
* If SENSE = 'E' or 'B', RCONDE contains the reciprocal\n\
* condition number for the average of the selected eigenvalues.\n\
* Not referenced if SENSE = 'N' or 'V'.\n\
*\n\
* RCONDV (output) DOUBLE PRECISION\n\
* If SENSE = 'V' or 'B', RCONDV contains the reciprocal\n\
* condition number for the selected right invariant subspace.\n\
* Not referenced if SENSE = 'N' or 'E'.\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\
* Also, if SENSE = 'E' or 'V' or 'B', LWORK >= 2*SDIM*(N-SDIM),\n\
* where SDIM is the number of selected eigenvalues computed by\n\
* this routine. Note that 2*SDIM*(N-SDIM) <= N*N/2. Note also\n\
* that an error is only returned if LWORK < max(1,2*N), but if\n\
* SENSE = 'E' or 'V' or 'B' this may not be large enough.\n\
* For good performance, LWORK must generally be larger.\n\
*\n\
* If LWORK = -1, then a workspace query is assumed; the routine\n\
* only calculates upper bound on the optimal size of the\n\
* array WORK, returns this value as the first entry of the WORK\n\
* array, and no error message related to LWORK is issued by\n\
* XERBLA.\n\
*\n\
* RWORK (workspace) DOUBLE PRECISION array, dimension (N)\n\
*\n\
* BWORK (workspace) LOGICAL array, dimension (N)\n\
* Not referenced if SORT = 'N'.\n\
*\n\
* INFO (output) INTEGER\n\
* = 0: successful exit\n\
* < 0: if INFO = -i, the i-th argument had an illegal value.\n\
* > 0: if INFO = i, and i is\n\
* <= N: the QR algorithm failed to compute all the\n\
* eigenvalues; elements 1:ILO-1 and i+1:N of W\n\
* contain those eigenvalues which have converged; if\n\
* JOBVS = 'V', VS contains the transformation which\n\
* reduces A to its partially converged Schur form.\n\
* = N+1: the eigenvalues could not be reordered because some\n\
* eigenvalues were too close to separate (the problem\n\
* is very ill-conditioned);\n\
* = N+2: after reordering, roundoff changed values of some\n\
* complex eigenvalues so that leading eigenvalues in\n\
* the Schur form no longer satisfy SELECT=.TRUE. This\n\
* could also be caused by underflow due to scaling.\n\
*\n\n\
* =====================================================================\n\
*\n"
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