SGEES (3)  Linux Manuals
NAME
sgees.f 
SYNOPSIS
Functions/Subroutines
subroutine sgees (JOBVS, SORT, SELECT, N, A, LDA, SDIM, WR, WI, VS, LDVS, WORK, LWORK, BWORK, INFO)
SGEES computes the eigenvalues, the Schur form, and, optionally, the matrix of Schur vectors for GE matrices
Function/Subroutine Documentation
subroutine sgees (characterJOBVS, characterSORT, logical, externalSELECT, integerN, real, dimension( lda, * )A, integerLDA, integerSDIM, real, dimension( * )WR, real, dimension( * )WI, real, dimension( ldvs, * )VS, integerLDVS, real, dimension( * )WORK, integerLWORK, logical, dimension( * )BWORK, integerINFO)
SGEES computes the eigenvalues, the Schur form, and, optionally, the matrix of Schur vectors for GE matrices
Purpose:

SGEES computes for an NbyN real nonsymmetric matrix A, the eigenvalues, the real Schur form T, and, optionally, the matrix of Schur vectors Z. This gives the Schur factorization A = Z*T*(Z**T). Optionally, it also orders the eigenvalues on the diagonal of the real Schur form so that selected eigenvalues are at the top left. The leading columns of Z then form an orthonormal basis for the invariant subspace corresponding to the selected eigenvalues. A matrix is in real Schur form if it is upper quasitriangular with 1by1 and 2by2 blocks. 2by2 blocks will be standardized in the form [ a b ] [ c a ] where b*c < 0. The eigenvalues of such a block are a + sqrt(bc).
Parameters:

JOBVS
JOBVS is CHARACTER*1 = 'N': Schur vectors are not computed; = 'V': Schur vectors are computed.
SORTSORT is CHARACTER*1 Specifies whether or not to order the eigenvalues on the diagonal of the Schur form. = 'N': Eigenvalues are not ordered; = 'S': Eigenvalues are ordered (see SELECT).
SELECTSELECT is LOGICAL FUNCTION of two REAL arguments SELECT must be declared EXTERNAL in the calling subroutine. If SORT = 'S', SELECT is used to select eigenvalues to sort to the top left of the Schur form. If SORT = 'N', SELECT is not referenced. An eigenvalue WR(j)+sqrt(1)*WI(j) is selected if SELECT(WR(j),WI(j)) is true; i.e., if either one of a complex conjugate pair of eigenvalues is selected, then both complex eigenvalues are selected. Note that a selected complex eigenvalue may no longer satisfy SELECT(WR(j),WI(j)) = .TRUE. after ordering, since ordering may change the value of complex eigenvalues (especially if the eigenvalue is illconditioned); in this case INFO is set to N+2 (see INFO below).
NN is INTEGER The order of the matrix A. N >= 0.
AA is REAL array, dimension (LDA,N) On entry, the NbyN matrix A. On exit, A has been overwritten by its real Schur form T.
LDALDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).
SDIMSDIM is INTEGER If SORT = 'N', SDIM = 0. If SORT = 'S', SDIM = number of eigenvalues (after sorting) for which SELECT is true. (Complex conjugate pairs for which SELECT is true for either eigenvalue count as 2.)
WRWR is REAL array, dimension (N)
WIWI is REAL array, dimension (N) WR and WI contain the real and imaginary parts, respectively, of the computed eigenvalues in the same order that they appear on the diagonal of the output Schur form T. Complex conjugate pairs of eigenvalues will appear consecutively with the eigenvalue having the positive imaginary part first.
VSVS is REAL array, dimension (LDVS,N) If JOBVS = 'V', VS contains the orthogonal matrix Z of Schur vectors. If JOBVS = 'N', VS is not referenced.
LDVSLDVS is INTEGER The leading dimension of the array VS. LDVS >= 1; if JOBVS = 'V', LDVS >= N.
WORKWORK is REAL array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK(1) contains the optimal LWORK.
LWORKLWORK is INTEGER The dimension of the array WORK. LWORK >= max(1,3*N). For good performance, LWORK must generally be larger. If LWORK = 1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA.
BWORKBWORK is LOGICAL array, dimension (N) Not referenced if SORT = 'N'.
INFOINFO is INTEGER = 0: successful exit < 0: if INFO = i, the ith argument had an illegal value. > 0: if INFO = i, and i is <= N: the QR algorithm failed to compute all the eigenvalues; elements 1:ILO1 and i+1:N of WR and WI contain those eigenvalues which have converged; if JOBVS = 'V', VS contains the matrix which reduces A to its partially converged Schur form. = N+1: the eigenvalues could not be reordered because some eigenvalues were too close to separate (the problem is very illconditioned); = N+2: after reordering, roundoff changed values of some complex eigenvalues so that leading eigenvalues in the Schur form no longer satisfy SELECT=.TRUE. This could also be caused by underflow due to scaling.
Author:

Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
 November 2011
Definition at line 216 of file sgees.f.
Author
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