1SSYGV(1) LAPACK driver routine (version 3.2) SSYGV(1)
2
6 SSYGV - computes all the eigenvalues, and optionally, the eigenvectors
7 of a real generalized symmetric-definite eigenproblem, of the form
8 A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x
9
11 SUBROUTINE SSYGV( ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W, WORK, LWORK,
12 INFO )
13 CHARACTER JOBZ, UPLO
15 INTEGER INFO, ITYPE, LDA, LDB, LWORK, N
17 REAL A( LDA, * ), B( LDB, * ), W( * ), WORK( * )
19
21 SSYGV computes all the eigenvalues, and optionally, the eigenvectors of
22 a real generalized symmetric-definite eigenproblem, of the form
23 A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A and B
24 are assumed to be symmetric and B is also
25 positive definite.
26
28 ITYPE (input) INTEGER
29 Specifies the problem type to be solved:
30 = 1: A*x = (lambda)*B*x
31 = 2: A*B*x = (lambda)*x
32 = 3: B*A*x = (lambda)*x
33 JOBZ (input) CHARACTER*1
35 = 'N': Compute eigenvalues only;
36 = 'V': Compute eigenvalues and eigenvectors.
37 UPLO (input) CHARACTER*1
39 = 'U': Upper triangles of A and B are stored;
40 = 'L': Lower triangles of A and B are stored.
41 N (input) INTEGER
43 The order of the matrices A and B. N >= 0.
44 A (input/output) REAL array, dimension (LDA, N)
46 On entry, the symmetric matrix A. If UPLO = 'U', the leading
47 N-by-N upper triangular part of A contains the upper triangular
48 part of the matrix A. If UPLO = 'L', the leading N-by-N lower
49 triangular part of A contains the lower triangular part of the
50 matrix A. On exit, if JOBZ = 'V', then if INFO = 0, A contains
51 the matrix Z of eigenvectors. The eigenvectors are normalized
52 as follows: if ITYPE = 1 or 2, Z**T*B*Z = I; if ITYPE = 3,
53 Z**T*inv(B)*Z = I. If JOBZ = 'N', then on exit the upper tri‐
54 angle (if UPLO='U') or the lower triangle (if UPLO='L') of A,
55 including the diagonal, is destroyed.
56 LDA (input) INTEGER
58 The leading dimension of the array A. LDA >= max(1,N).
59 B (input/output) REAL array, dimension (LDB, N)
61 On entry, the symmetric positive definite matrix B. If UPLO =
62 'U', the leading N-by-N upper triangular part of B contains the
63 upper triangular part of the matrix B. If UPLO = 'L', the
64 leading N-by-N lower triangular part of B contains the lower
65 triangular part of the matrix B. On exit, if INFO <= N, the
66 part of B containing the matrix is overwritten by the triangu‐
67 lar factor U or L from the Cholesky factorization B = U**T*U or
68 B = L*L**T.
69 LDB (input) INTEGER
71 The leading dimension of the array B. LDB >= max(1,N).
72 W (output) REAL array, dimension (N)
74 If INFO = 0, the eigenvalues in ascending order.
75 WORK (workspace/output) REAL array, dimension (MAX(1,LWORK))
77 On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
78 LWORK (input) INTEGER
80 The length of the array WORK. LWORK >= max(1,3*N-1). For
81 optimal efficiency, LWORK >= (NB+2)*N, where NB is the block‐
82 size for SSYTRD returned by ILAENV. If LWORK = -1, then a
83 workspace query is assumed; the routine only calculates the
84 optimal size of the WORK array, returns this value as the first
85 entry of the WORK array, and no error message related to LWORK
86 is issued by XERBLA.
87 INFO (output) INTEGER
89 = 0: successful exit
90 < 0: if INFO = -i, the i-th argument had an illegal value
91 > 0: SPOTRF or SSYEV returned an error code:
92 <= N: if INFO = i, SSYEV failed to converge; i off-diagonal
93 elements of an intermediate tridiagonal form did not converge
94 to zero; > N: if INFO = N + i, for 1 <= i <= N, then the
95 leading minor of order i of B is not positive definite. The
96 factorization of B could not be completed and no eigenvalues or
97 eigenvectors were computed.
98 LAPACK driver routine (version 3.N2o)vember 2008 SSYGV(1)