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---
:name: sgeesx
:md5sum: 64fcd2b5803aefdf7af907e57f81fd53
:category: :subroutine
:arguments:
- jobvs:
:type: char
:intent: input
- sort:
:type: char
:intent: input
- select:
:intent: external procedure
:block_type: logical
:block_arg_num: 2
:block_arg_type: real
- sense:
:type: char
:intent: input
- n:
:type: integer
:intent: input
- a:
:type: real
:intent: input/output
:dims:
- lda
- n
- lda:
:type: integer
:intent: input
- sdim:
:type: integer
:intent: output
- wr:
:type: real
:intent: output
:dims:
- n
- wi:
:type: real
:intent: output
:dims:
- n
- vs:
:type: real
:intent: output
:dims:
- ldvs
- n
- ldvs:
:type: integer
:intent: input
- rconde:
:type: real
:intent: output
- rcondv:
:type: real
:intent: output
- work:
:type: real
: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*n/2 : 3*n"
- iwork:
:type: integer
:intent: output
:dims:
- MAX(1,liwork)
- liwork:
:type: integer
:intent: input
- 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 SGEESX( JOBVS, SORT, SELECT, SENSE, N, A, LDA, SDIM, WR, WI, VS, LDVS, RCONDE, RCONDV, WORK, LWORK, IWORK, LIWORK, BWORK, INFO )\n\n\
* Purpose\n\
* =======\n\
*\n\
* SGEESX computes for an N-by-N real nonsymmetric matrix A, the\n\
* eigenvalues, the real Schur form T, and, optionally, the matrix of\n\
* Schur vectors Z. This gives the Schur factorization A = Z*T*(Z**T).\n\
*\n\
* Optionally, it also orders the eigenvalues on the diagonal of the\n\
* real 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 real matrix is in real Schur form if it is upper quasi-triangular\n\
* with 1-by-1 and 2-by-2 blocks. 2-by-2 blocks will be standardized in\n\
* the form\n\
* [ a b ]\n\
* [ c a ]\n\
*\n\
* where b*c < 0. The eigenvalues of such a block are a +- sqrt(bc).\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 two REAL arguments\n\
* SELECT must be declared EXTERNAL in the calling subroutine.\n\
* If SORT = 'S', SELECT is used to select eigenvalues to sort\n\
* to the top left of the Schur form.\n\
* If SORT = 'N', SELECT is not referenced.\n\
* An eigenvalue WR(j)+sqrt(-1)*WI(j) is selected if\n\
* SELECT(WR(j),WI(j)) is true; i.e., if either one of a\n\
* complex conjugate pair of eigenvalues is selected, then both\n\
* are. Note that a selected complex eigenvalue may no longer\n\
* satisfy SELECT(WR(j),WI(j)) = .TRUE. after ordering, since\n\
* ordering may change the value of complex eigenvalues\n\
* (especially if the eigenvalue is ill-conditioned); in this\n\
* case INFO may be set to N+3 (see INFO below).\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) REAL array, dimension (LDA, N)\n\
* On entry, the N-by-N matrix A.\n\
* On exit, A is overwritten by its real 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 (after sorting)\n\
* for which SELECT is true. (Complex conjugate\n\
* pairs for which SELECT is true for either\n\
* eigenvalue count as 2.)\n\
*\n\
* WR (output) REAL array, dimension (N)\n\
* WI (output) REAL array, dimension (N)\n\
* WR and WI contain the real and imaginary parts, respectively,\n\
* of the computed eigenvalues, in the same order that they\n\
* appear on the diagonal of the output Schur form T. Complex\n\
* conjugate pairs of eigenvalues appear consecutively with the\n\
* eigenvalue having the positive imaginary part first.\n\
*\n\
* VS (output) REAL array, dimension (LDVS,N)\n\
* If JOBVS = 'V', VS contains the orthogonal 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) REAL\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) REAL\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) REAL 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(1,3*N).\n\
* Also, if SENSE = 'E' or 'V' or 'B',\n\
* LWORK >= N+2*SDIM*(N-SDIM), where SDIM is the number of\n\
* selected eigenvalues computed by this routine. Note that\n\
* N+2*SDIM*(N-SDIM) <= N+N*N/2. Note also that an error is only\n\
* returned if LWORK < max(1,3*N), but if SENSE = 'E' or 'V' or\n\
* '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 bounds on the optimal sizes of the\n\
* arrays WORK and IWORK, returns these values as the first\n\
* entries of the WORK and IWORK arrays, and no error messages\n\
* related to LWORK or LIWORK are issued by XERBLA.\n\
*\n\
* IWORK (workspace/output) INTEGER array, dimension (MAX(1,LIWORK))\n\
* On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.\n\
*\n\
* LIWORK (input) INTEGER\n\
* The dimension of the array IWORK.\n\
* LIWORK >= 1; if SENSE = 'V' or 'B', LIWORK >= SDIM*(N-SDIM).\n\
* Note that SDIM*(N-SDIM) <= N*N/4. Note also that an error is\n\
* only returned if LIWORK < 1, but if SENSE = 'V' or 'B' this\n\
* may not be large enough.\n\
*\n\
* If LIWORK = -1, then a workspace query is assumed; the\n\
* routine only calculates upper bounds on the optimal sizes of\n\
* the arrays WORK and IWORK, returns these values as the first\n\
* entries of the WORK and IWORK arrays, and no error messages\n\
* related to LWORK or LIWORK are issued by XERBLA.\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 WR and WI\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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