1SGEGS(1) LAPACK driver routine (version 3.2) SGEGS(1)
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6 SGEGS - routine i deprecated and has been replaced by routine SGGES
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9 SUBROUTINE SGEGS( JOBVSL, JOBVSR, N, A, LDA, B, LDB, ALPHAR, ALPHAI,
10 BETA, VSL, LDVSL, VSR, LDVSR, WORK, LWORK, INFO )
11 CHARACTER JOBVSL, JOBVSR
13 INTEGER INFO, LDA, LDB, LDVSL, LDVSR, LWORK, N
15 REAL A( LDA, * ), ALPHAI( * ), ALPHAR( * ), B( LDB, * ),
17 BETA( * ), VSL( LDVSL, * ), VSR( LDVSR, * ), WORK( *
18 )
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21 This routine is deprecated and has been replaced by routine SGGES.
22 SGEGS computes the eigenvalues, real Schur form, and, optionally, left
23 and or/right Schur vectors of a real matrix pair (A,B). Given two
24 square matrices A and B, the generalized real Schur factorization has
25 the form
26 A = Q*S*Z**T, B = Q*T*Z**T
27 where Q and Z are orthogonal matrices, T is upper triangular, and S is
28 an upper quasi-triangular matrix with 1-by-1 and 2-by-2 diagonal
29 blocks, the 2-by-2 blocks corresponding to complex conjugate pairs of
30 eigenvalues of (A,B). The columns of Q are the left Schur vectors and
31 the columns of Z are the right Schur vectors.
32 If only the eigenvalues of (A,B) are needed, the driver routine SGEGV
33 should be used instead. See SGEGV for a description of the eigenvalues
34 of the generalized nonsymmetric eigenvalue problem (GNEP).
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37 JOBVSL (input) CHARACTER*1
38 = 'N': do not compute the left Schur vectors;
39 = 'V': compute the left Schur vectors (returned in VSL).
40 JOBVSR (input) CHARACTER*1
42 = 'N': do not compute the right Schur vectors;
43 = 'V': compute the right Schur vectors (returned in VSR).
44 N (input) INTEGER
46 The order of the matrices A, B, VSL, and VSR. N >= 0.
47 A (input/output) REAL array, dimension (LDA, N)
49 On entry, the matrix A. On exit, the upper quasi-triangular
50 matrix S from the generalized real Schur factorization.
51 LDA (input) INTEGER
53 The leading dimension of A. LDA >= max(1,N).
54 B (input/output) REAL array, dimension (LDB, N)
56 On entry, the matrix B. On exit, the upper triangular matrix T
57 from the generalized real Schur factorization.
58 LDB (input) INTEGER
60 The leading dimension of B. LDB >= max(1,N).
61 ALPHAR (output) REAL array, dimension (N)
63 The real parts of each scalar alpha defining an eigenvalue of
64 GNEP.
65 ALPHAI (output) REAL array, dimension (N)
67 The imaginary parts of each scalar alpha defining an eigenvalue
68 of GNEP. If ALPHAI(j) is zero, then the j-th eigenvalue is
69 real; if positive, then the j-th and (j+1)-st eigenvalues are a
70 complex conjugate pair, with ALPHAI(j+1) = -ALPHAI(j).
71 BETA (output) REAL array, dimension (N)
73 The scalars beta that define the eigenvalues of GNEP.
74 Together, the quantities alpha = (ALPHAR(j),ALPHAI(j)) and beta
75 = BETA(j) represent the j-th eigenvalue of the matrix pair
76 (A,B), in one of the forms lambda = alpha/beta or mu =
77 beta/alpha. Since either lambda or mu may overflow, they
78 should not, in general, be computed.
79 VSL (output) REAL array, dimension (LDVSL,N)
81 If JOBVSL = 'V', the matrix of left Schur vectors Q. Not ref‐
82 erenced if JOBVSL = 'N'.
83 LDVSL (input) INTEGER
85 The leading dimension of the matrix VSL. LDVSL >=1, and if JOB‐
86 VSL = 'V', LDVSL >= N.
87 VSR (output) REAL array, dimension (LDVSR,N)
89 If JOBVSR = 'V', the matrix of right Schur vectors Z. Not ref‐
90 erenced if JOBVSR = 'N'.
91 LDVSR (input) INTEGER
93 The leading dimension of the matrix VSR. LDVSR >= 1, and if
94 JOBVSR = 'V', LDVSR >= N.
95 WORK (workspace/output) REAL array, dimension (MAX(1,LWORK))
97 On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
98 LWORK (input) INTEGER
100 The dimension of the array WORK. LWORK >= max(1,4*N). For
101 good performance, LWORK must generally be larger. To compute
102 the optimal value of LWORK, call ILAENV to get blocksizes (for
103 SGEQRF, SORMQR, and SORGQR.) Then compute: NB -- MAX of the
104 blocksizes for SGEQRF, SORMQR, and SORGQR The optimal LWORK is
105 2*N + N*(NB+1). If LWORK = -1, then a workspace query is
106 assumed; the routine only calculates the optimal size of the
107 WORK array, returns this value as the first entry of the WORK
108 array, and no error message related to LWORK is issued by
109 XERBLA.
110 INFO (output) INTEGER
112 = 0: successful exit
113 < 0: if INFO = -i, the i-th argument had an illegal value.
114 = 1,...,N: The QZ iteration failed. (A,B) are not in Schur
115 form, but ALPHAR(j), ALPHAI(j), and BETA(j) should be correct
116 for j=INFO+1,...,N. > N: errors that usually indicate LAPACK
117 problems:
118 =N+1: error return from SGGBAL
119 =N+2: error return from SGEQRF
120 =N+3: error return from SORMQR
121 =N+4: error return from SORGQR
122 =N+5: error return from SGGHRD
123 =N+6: error return from SHGEQZ (other than failed iteration)
124 =N+7: error return from SGGBAK (computing VSL)
125 =N+8: error return from SGGBAK (computing VSR)
126 =N+9: error return from SLASCL (various places)
127 LAPACK driver routine (version 3.N2o)vember 2008 SGEGS(1)