1DSYGV(1) LAPACK driver routine (version 3.2) DSYGV(1)
2
6 DSYGV - 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 DSYGV( 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 DOUBLE PRECISION A( LDA, * ), B( LDB, * ), W( * ), WORK( * )
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21 DSYGV 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) DOUBLE PRECISION 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) DOUBLE PRECISION 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) DOUBLE PRECISION array, dimension (N)
74 If INFO = 0, the eigenvalues in ascending order.
75 WORK (workspace/output) DOUBLE PRECISION array, dimension
77 (MAX(1,LWORK))
78 On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
79 LWORK (input) INTEGER
81 The length of the array WORK. LWORK >= max(1,3*N-1). For
82 optimal efficiency, LWORK >= (NB+2)*N, where NB is the block‐
83 size for DSYTRD returned by ILAENV. If LWORK = -1, then a
84 workspace query is assumed; the routine only calculates the
85 optimal size of the WORK array, returns this value as the first
86 entry of the WORK array, and no error message related to LWORK
87 is issued by XERBLA.
88 INFO (output) INTEGER
90 = 0: successful exit
91 < 0: if INFO = -i, the i-th argument had an illegal value
92 > 0: DPOTRF or DSYEV returned an error code:
93 <= N: if INFO = i, DSYEV failed to converge; i off-diagonal
94 elements of an intermediate tridiagonal form did not converge
95 to zero; > N: if INFO = N + i, for 1 <= i <= N, then the
96 leading minor of order i of B is not positive definite. The
97 factorization of B could not be completed and no eigenvalues or
98 eigenvectors were computed.
99 LAPACK driver routine (version 3.N2o)vember 2008 DSYGV(1)