DGGES(1) LAPACK driver routine (version 3.2) DGGES(1)[top]NAMEDGGES - computes for a pair of N-by-N real nonsymmetric matrices (A,B),SYNOPSISSUBROUTINE DGGES( JOBVSL, JOBVSR, SORT, SELCTG, N, A, LDA, B, LDB, SDIM, ALPHAR, ALPHAI, BETA, VSL, LDVSL, VSR, LDVSR, WORK, LWORK, BWORK, INFO ) CHARACTER JOBVSL, JOBVSR, SORT INTEGER INFO, LDA, LDB, LDVSL, LDVSR, LWORK, N, SDIM LOGICAL BWORK( * ) DOUBLE PRECISION A( LDA, * ), ALPHAI( * ), ALPHAR( * ), B( LDB, * ), BETA( * ), VSL( LDVSL, * ), VSR( LDVSR, * ), WORK( * ) LOGICAL SELCTG EXTERNAL SELCTGPURPOSEDGGES computes for a pair of N-by-N real nonsymmetric matrices (A,B), the generalized eigenvalues, the generalized real Schur form (S,T), optionally, the left and/or right matrices of Schur vectors (VSL and VSR). This gives the generalized Schur factorization (A,B) = ( (VSL)*S*(VSR)**T, (VSL)*T*(VSR)**T ) Optionally, it also orders the eigenvalues so that a selected cluster of eigenvalues appears in the leading diagonal blocks of the upper quasi-triangular matrix S and the upper triangular matrix T.The leading columns of VSL and VSR then form an orthonormal basis for the corre‐ sponding left and right eigenspaces (deflating subspaces). (If only the generalized eigenvalues are needed, use the driver DGGEV instead, which is faster.) A generalized eigenvalue for a pair of matrices (A,B) is a scalar w or a ratio alpha/beta = w, such that A - w*B is singular. It is usually represented as the pair (alpha,beta), as there is a reasonable inter‐ pretation for beta=0 or both being zero. A pair of matrices (S,T) is in generalized real Schur form if T is upper triangular with non-negative diagonal and S is block upper trian‐ gular with 1-by-1 and 2-by-2 blocks. 1-by-1 blocks correspond to real generalized eigenvalues, while 2-by-2 blocks of S will be "standard‐ ized" by making the corresponding elements of T have the form: [ a 0 ] [ 0 b ] and the pair of corresponding 2-by-2 blocks in S and T will have a com‐ plex conjugate pair of generalized eigenvalues.ARGUMENTSJOBVSL (input) CHARACTER*1 = 'N': do not compute the left Schur vectors; = 'V': compute the left Schur vectors. JOBVSR (input) CHARACTER*1 = 'N': do not compute the right Schur vectors; = 'V': compute the right Schur vectors. SORT (input) CHARACTER*1 Specifies whether or not to order the eigenvalues on the diago‐ nal of the generalized Schur form. = 'N': Eigenvalues are not ordered; = 'S': Eigenvalues are ordered (see SELCTG); SELCTG (external procedure) LOGICAL FUNCTION of three DOUBLE PRECISION arguments SELCTG must be declared EXTERNAL in the calling subroutine. If SORT = 'N', SELCTG is not referenced. If SORT = 'S', SELCTG is used to select eigenvalues to sort to the top left of the Schur form. An eigenvalue (ALPHAR(j)+ALPHAI(j))/BETA(j) is selected if SELCTG(ALPHAR(j),ALPHAI(j),BETA(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 in the ill-conditioned case, a selected complex eigenvalue may no longer satisfy SELCTG(ALPHAR(j),ALPHAI(j), BETA(j)) = .TRUE. after ordering. INFO is to be set to N+2 in this case. N (input) INTEGER The order of the matrices A, B, VSL, and VSR. N >= 0. A (input/output) DOUBLE PRECISION array, dimension (LDA, N) On entry, the first of the pair of matrices. On exit, A has been overwritten by its generalized Schur form S. LDA (input) INTEGER The leading dimension of A. LDA >= max(1,N). B (input/output) DOUBLE PRECISION array, dimension (LDB, N) On entry, the second of the pair of matrices. On exit, B has been overwritten by its generalized Schur form T. LDB (input) INTEGER The leading dimension of B. LDB >= max(1,N). SDIM (output) INTEGER If SORT = 'N', SDIM = 0. If SORT = 'S', SDIM = number of ei‐ genvalues (after sorting) for which SELCTG is true. (Complex conjugate pairs for which SELCTG is true for either eigenvalue count as 2.) ALPHAR (output) DOUBLE PRECISION array, dimension (N) ALPHAI (output) DOUBLE PRECISION array, dimension (N) BETA (output) DOUBLE PRECISION array, dimension (N) On exit, (ALPHAR(j) + ALPHAI(j)*i)/BETA(j), j=1,...,N, will be the gen‐ eralized eigenvalues. ALPHAR(j) + ALPHAI(j)*i, and BETA(j),j=1,...,N are the diagonals of the complex Schur form (S,T) that would result if the 2-by-2 diagonal blocks of the real Schur form of (A,B) were further reduced to triangular form using 2-by-2 complex unitary transformations. If ALPHAI(j) is zero, then the j-th eigenvalue is real; if posi‐ tive, then the j-th and (j+1)-st eigenvalues are a complex con‐ jugate pair, with ALPHAI(j+1) negative. Note: the quotients ALPHAR(j)/BETA(j) and ALPHAI(j)/BETA(j) may easily over- or underflow, and BETA(j) may even be zero. Thus, the user should avoid naively computing the ratio. However, ALPHAR and ALPHAI will be always less than and usually comparable with norm(A) in magnitude, and BETA always less than and usually comparable with norm(B). VSL (output) DOUBLE PRECISION array, dimension (LDVSL,N) If JOBVSL = 'V', VSL will contain the left Schur vectors. Not referenced if JOBVSL = 'N'. LDVSL (input) INTEGER The leading dimension of the matrix VSL. LDVSL >=1, and if JOB‐ VSL = 'V', LDVSL >= N. VSR (output) DOUBLE PRECISION array, dimension (LDVSR,N) If JOBVSR = 'V', VSR will contain the right Schur vectors. Not referenced if JOBVSR = 'N'. LDVSR (input) INTEGER The leading dimension of the matrix VSR. LDVSR >= 1, and if JOBVSR = 'V', LDVSR >= N. WORK (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK(1) returns the optimal LWORK. LWORK (input) INTEGER The dimension of the array WORK. If N = 0, LWORK >= 1, else LWORK >= 8*N+16. For good performance , LWORK must generally be larger. If LWORK =, 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. BWORK (workspace) LOGICAL array, dimension (N) Not referenced if SORT = 'N'. INFO (output) INTEGER = 0: successful exit < 0: if INFO =-1, the i-th argument had an illegal value. = 1,...,N: The QZ iteration failed. (A,B) are not in Schur form, but ALPHAR(j), ALPHAI(j), and BETA(j) should be correct for j=INFO+1,...,N. > N: =N+1: other than QZ iteration failed in DHGEQZ. =N+2: after reordering, roundoff changed values of some complex eigenvalues so that leading eigenvalues in the Generalized Schur form no longer satisfy SELCTG=.TRUE. This could also be caused due to scaling. =N+3: reordering failed in DTGSEN. LAPACK driver routine (version 3November 2008 DGGES(1)-i

List of man pages available for

Copyright (c) for man pages and the logo by the respective OS vendor.

For those who want to learn more, the polarhome community provides shell access and support.

[legal] [privacy] [GNU] [policy] [cookies] [netiquette] [sponsors] [FAQ]

Polar

Member of Polar

Based on Fawad Halim's script.

....................................................................

Vote for polarhome |