1DSYGV(1) LAPACK driver routine (version 3.1) DSYGV(1)
2
6 DSYGV - all the eigenvalues, and optionally, the eigenvectors of a real
7 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( * )
19
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
29 ITYPE (input) INTEGER
30 Specifies the problem type to be solved:
31 = 1: A*x = (lambda)*B*x
32 = 2: A*B*x = (lambda)*x
33 = 3: B*A*x = (lambda)*x
34 JOBZ (input) CHARACTER*1
36 = 'N': Compute eigenvalues only;
37 = 'V': Compute eigenvalues and eigenvectors.
38 UPLO (input) CHARACTER*1
40 = 'U': Upper triangles of A and B are stored;
41 = 'L': Lower triangles of A and B are stored.
42 N (input) INTEGER
44 The order of the matrices A and B. N >= 0.
45 A (input/output) DOUBLE PRECISION array, dimension (LDA, N)
47 On entry, the symmetric matrix A. If UPLO = 'U', the leading
48 N-by-N upper triangular part of A contains the upper triangular
49 part of the matrix A. If UPLO = 'L', the leading N-by-N lower
50 triangular part of A contains the lower triangular part of the
51 matrix A.
52 On exit, if JOBZ = 'V', then if INFO = 0, A contains the matrix
54 Z of eigenvectors. The eigenvectors are normalized as follows:
55 if ITYPE = 1 or 2, Z**T*B*Z = I; if ITYPE = 3, Z**T*inv(B)*Z =
56 I. If JOBZ = 'N', then on exit the upper triangle (if
57 UPLO='U') or the lower triangle (if UPLO='L') of A, including
58 the diagonal, is destroyed.
59 LDA (input) INTEGER
61 The leading dimension of the array A. LDA >= max(1,N).
62 B (input/output) DOUBLE PRECISION array, dimension (LDB, N)
64 On entry, the symmetric positive definite matrix B. If UPLO =
65 'U', the leading N-by-N upper triangular part of B contains the
66 upper triangular part of the matrix B. If UPLO = 'L', the
67 leading N-by-N lower triangular part of B contains the lower
68 triangular part of the matrix B.
69 On exit, if INFO <= N, the part of B containing the matrix is
71 overwritten by the triangular factor U or L from the Cholesky
72 factorization B = U**T*U or B = L*L**T.
73 LDB (input) INTEGER
75 The leading dimension of the array B. LDB >= max(1,N).
76 W (output) DOUBLE PRECISION array, dimension (N)
78 If INFO = 0, the eigenvalues in ascending order.
79 WORK (workspace/output) DOUBLE PRECISION array, dimension
81 (MAX(1,LWORK))
82 On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
83 LWORK (input) INTEGER
85 The length of the array WORK. LWORK >= max(1,3*N-1). For
86 optimal efficiency, LWORK >= (NB+2)*N, where NB is the block‐
87 size for DSYTRD returned by ILAENV.
88 If LWORK = -1, then a workspace query is assumed; the routine
90 only calculates the optimal size of the WORK array, returns
91 this value as the first entry of the WORK array, and no error
92 message related to LWORK is issued by XERBLA.
93 INFO (output) INTEGER
95 = 0: successful exit
96 < 0: if INFO = -i, the i-th argument had an illegal value
97 > 0: DPOTRF or DSYEV returned an error code:
98 <= N: if INFO = i, DSYEV failed to converge; i off-diagonal
99 elements of an intermediate tridiagonal form did not converge
100 to zero; > N: if INFO = N + i, for 1 <= i <= N, then the
101 leading minor of order i of B is not positive definite. The
102 factorization of B could not be completed and no eigenvalues or
103 eigenvectors were computed.
104 LAPACK driver routine (version 3.N1o)vember 2006 DSYGV(1)