1SGEGS(1) LAPACK driver routine (version 3.1) SGEGS(1)
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6 SGEGS - i deprecated and has been replaced by routine SGGES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21 This routine is deprecated and has been replaced by routine SGGES.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
24 and or/right Schur vectors of a real matrix pair (A,B). Given two
25 square matrices A and B, the generalized real Schur factorization has
26 the form
27 A = Q*S*Z**T, B = Q*T*Z**T
29 where Q and Z are orthogonal matrices, T is upper triangular, and S is
31 an upper quasi-triangular matrix with 1-by-1 and 2-by-2 diagonal
32 blocks, the 2-by-2 blocks corresponding to complex conjugate pairs of
33 eigenvalues of (A,B). The columns of Q are the left Schur vectors and
34 the columns of Z are the right Schur vectors.
35 If only the eigenvalues of (A,B) are needed, the driver routine SGEGV
37 should be used instead. See SGEGV for a description of the eigenvalues
38 of the generalized nonsymmetric eigenvalue problem (GNEP).
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42 JOBVSL (input) CHARACTER*1
43 = 'N': do not compute the left Schur vectors;
44 = 'V': compute the left Schur vectors (returned in VSL).
45 JOBVSR (input) CHARACTER*1
47 = 'N': do not compute the right Schur vectors;
48 = 'V': compute the right Schur vectors (returned in VSR).
49 N (input) INTEGER
51 The order of the matrices A, B, VSL, and VSR. N >= 0.
52 A (input/output) REAL array, dimension (LDA, N)
54 On entry, the matrix A. On exit, the upper quasi-triangular
55 matrix S from the generalized real Schur factorization.
56 LDA (input) INTEGER
58 The leading dimension of A. LDA >= max(1,N).
59 B (input/output) REAL array, dimension (LDB, N)
61 On entry, the matrix B. On exit, the upper triangular matrix T
62 from the generalized real Schur factorization.
63 LDB (input) INTEGER
65 The leading dimension of B. LDB >= max(1,N).
66 ALPHAR (output) REAL array, dimension (N)
68 The real parts of each scalar alpha defining an eigenvalue of
69 GNEP.
70 ALPHAI (output) REAL array, dimension (N)
72 The imaginary parts of each scalar alpha defining an eigenvalue
73 of GNEP. If ALPHAI(j) is zero, then the j-th eigenvalue is
74 real; if positive, then the j-th and (j+1)-st eigenvalues are a
75 complex conjugate pair, with ALPHAI(j+1) = -ALPHAI(j).
76 BETA (output) REAL array, dimension (N)
78 The scalars beta that define the eigenvalues of GNEP.
79 Together, the quantities alpha = (ALPHAR(j),ALPHAI(j)) and beta
80 = BETA(j) represent the j-th eigenvalue of the matrix pair
81 (A,B), in one of the forms lambda = alpha/beta or mu =
82 beta/alpha. Since either lambda or mu may overflow, they
83 should not, in general, be computed.
84 VSL (output) REAL array, dimension (LDVSL,N)
86 If JOBVSL = 'V', the matrix of left Schur vectors Q. Not ref‐
87 erenced if JOBVSL = 'N'.
88 LDVSL (input) INTEGER
90 The leading dimension of the matrix VSL. LDVSL >=1, and if JOB‐
91 VSL = 'V', LDVSL >= N.
92 VSR (output) REAL array, dimension (LDVSR,N)
94 If JOBVSR = 'V', the matrix of right Schur vectors Z. Not ref‐
95 erenced if JOBVSR = 'N'.
96 LDVSR (input) INTEGER
98 The leading dimension of the matrix VSR. LDVSR >= 1, and if
99 JOBVSR = 'V', LDVSR >= N.
100 WORK (workspace/output) REAL array, dimension (MAX(1,LWORK))
102 On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
103 LWORK (input) INTEGER
105 The dimension of the array WORK. LWORK >= max(1,4*N). For
106 good performance, LWORK must generally be larger. To compute
107 the optimal value of LWORK, call ILAENV to get blocksizes (for
108 SGEQRF, SORMQR, and SORGQR.) Then compute: NB -- MAX of the
109 blocksizes for SGEQRF, SORMQR, and SORGQR The optimal LWORK is
110 2*N + N*(NB+1).
111 If LWORK = -1, then a workspace query is assumed; the routine
113 only calculates the optimal size of the WORK array, returns
114 this value as the first entry of the WORK array, and no error
115 message related to LWORK is issued by XERBLA.
116 INFO (output) INTEGER
118 = 0: successful exit
119 < 0: if INFO = -i, the i-th argument had an illegal value.
120 = 1,...,N: The QZ iteration failed. (A,B) are not in Schur
121 form, but ALPHAR(j), ALPHAI(j), and BETA(j) should be correct
122 for j=INFO+1,...,N. > N: errors that usually indicate LAPACK
123 problems:
124 =N+1: error return from SGGBAL
125 =N+2: error return from SGEQRF
126 =N+3: error return from SORMQR
127 =N+4: error return from SORGQR
128 =N+5: error return from SGGHRD
129 =N+6: error return from SHGEQZ (other than failed iteration)
130 =N+7: error return from SGGBAK (computing VSL)
131 =N+8: error return from SGGBAK (computing VSR)
132 =N+9: error return from SLASCL (various places)
133 LAPACK driver routine (version 3.N1o)vember 2006 SGEGS(1)