1ZGEGS(1) LAPACK driver routine (version 3.1) ZGEGS(1)
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6 ZGEGS - i deprecated and has been replaced by routine ZGGES
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9 SUBROUTINE ZGEGS( JOBVSL, JOBVSR, N, A, LDA, B, LDB, ALPHA, BETA, VSL,
10 LDVSL, VSR, LDVSR, WORK, LWORK, RWORK, INFO )
11 CHARACTER JOBVSL, JOBVSR
13 INTEGER INFO, LDA, LDB, LDVSL, LDVSR, LWORK, N
15 DOUBLE PRECISION RWORK( * )
17 COMPLEX*16 A( LDA, * ), ALPHA( * ), B( LDB, * ), BETA( * ), VSL(
19 LDVSL, * ), VSR( LDVSR, * ), WORK( * )
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22 This routine is deprecated and has been replaced by routine ZGGES.
23 ZGEGS computes the eigenvalues, Schur form, and, optionally, the left
25 and or/right Schur vectors of a complex matrix pair (A,B). Given two
26 square matrices A and B, the generalized Schur
27 factorization has the form
28 A = Q*S*Z**H, B = Q*T*Z**H
30 where Q and Z are unitary matrices and S and T are upper triangular.
32 The columns of Q are the left Schur vectors
33 and the columns of Z are the right Schur vectors.
34 If only the eigenvalues of (A,B) are needed, the driver routine ZGEGV
36 should be used instead. See ZGEGV for a description of the eigenvalues
37 of the generalized nonsymmetric eigenvalue problem (GNEP).
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41 JOBVSL (input) CHARACTER*1
42 = 'N': do not compute the left Schur vectors;
43 = 'V': compute the left Schur vectors (returned in VSL).
44 JOBVSR (input) CHARACTER*1
46 = 'N': do not compute the right Schur vectors;
47 = 'V': compute the right Schur vectors (returned in VSR).
48 N (input) INTEGER
50 The order of the matrices A, B, VSL, and VSR. N >= 0.
51 A (input/output) COMPLEX*16 array, dimension (LDA, N)
53 On entry, the matrix A. On exit, the upper triangular matrix S
54 from the generalized Schur factorization.
55 LDA (input) INTEGER
57 The leading dimension of A. LDA >= max(1,N).
58 B (input/output) COMPLEX*16 array, dimension (LDB, N)
60 On entry, the matrix B. On exit, the upper triangular matrix T
61 from the generalized Schur factorization.
62 LDB (input) INTEGER
64 The leading dimension of B. LDB >= max(1,N).
65 ALPHA (output) COMPLEX*16 array, dimension (N)
67 The complex scalars alpha that define the eigenvalues of GNEP.
68 ALPHA(j) = S(j,j), the diagonal element of the Schur form of A.
69 BETA (output) COMPLEX*16 array, dimension (N)
71 The non-negative real scalars beta that define the eigenvalues
72 of GNEP. BETA(j) = T(j,j), the diagonal element of the trian‐
73 gular factor T.
74 Together, the quantities alpha = ALPHA(j) and beta = BETA(j)
76 represent the j-th eigenvalue of the matrix pair (A,B), in one
77 of the forms lambda = alpha/beta or mu = beta/alpha. Since
78 either lambda or mu may overflow, they should not, in general,
79 be computed.
80 VSL (output) COMPLEX*16 array, dimension (LDVSL,N)
82 If JOBVSL = 'V', the matrix of left Schur vectors Q. Not ref‐
83 erenced if JOBVSL = 'N'.
84 LDVSL (input) INTEGER
86 The leading dimension of the matrix VSL. LDVSL >= 1, and if
87 JOBVSL = 'V', LDVSL >= N.
88 VSR (output) COMPLEX*16 array, dimension (LDVSR,N)
90 If JOBVSR = 'V', the matrix of right Schur vectors Z. Not ref‐
91 erenced if JOBVSR = 'N'.
92 LDVSR (input) INTEGER
94 The leading dimension of the matrix VSR. LDVSR >= 1, and if
95 JOBVSR = 'V', LDVSR >= N.
96 WORK (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK))
98 On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
99 LWORK (input) INTEGER
101 The dimension of the array WORK. LWORK >= max(1,2*N). For
102 good performance, LWORK must generally be larger. To compute
103 the optimal value of LWORK, call ILAENV to get blocksizes (for
104 ZGEQRF, ZUNMQR, and CUNGQR.) Then compute: NB -- MAX of the
105 blocksizes for ZGEQRF, ZUNMQR, and CUNGQR; the optimal LWORK is
106 N*(NB+1).
107 If LWORK = -1, then a workspace query is assumed; the routine
109 only calculates the optimal size of the WORK array, returns
110 this value as the first entry of the WORK array, and no error
111 message related to LWORK is issued by XERBLA.
112 RWORK (workspace) DOUBLE PRECISION array, dimension (3*N)
114 INFO (output) INTEGER
116 = 0: successful exit
117 < 0: if INFO = -i, the i-th argument had an illegal value.
118 =1,...,N: The QZ iteration failed. (A,B) are not in Schur
119 form, but ALPHA(j) and BETA(j) should be correct for
120 j=INFO+1,...,N. > N: errors that usually indicate LAPACK
121 problems:
122 =N+1: error return from ZGGBAL
123 =N+2: error return from ZGEQRF
124 =N+3: error return from ZUNMQR
125 =N+4: error return from ZUNGQR
126 =N+5: error return from ZGGHRD
127 =N+6: error return from ZHGEQZ (other than failed iteration)
128 =N+7: error return from ZGGBAK (computing VSL)
129 =N+8: error return from ZGGBAK (computing VSR)
130 =N+9: error return from ZLASCL (various places)
131 LAPACK driver routine (version 3.N1o)vember 2006 ZGEGS(1)