1ZHPGV(1) LAPACK driver routine (version 3.2) ZHPGV(1)
2
6 ZHPGV - computes all the eigenvalues and, optionally, the eigenvectors
7 of a complex generalized Hermitian-definite eigenproblem, of the form
8 A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x
9
11 SUBROUTINE ZHPGV( ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK, RWORK,
12 INFO )
13 CHARACTER JOBZ, UPLO
15 INTEGER INFO, ITYPE, LDZ, N
17 DOUBLE PRECISION RWORK( * ), W( * )
19 COMPLEX*16 AP( * ), BP( * ), WORK( * ), Z( LDZ, * )
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23 ZHPGV computes all the eigenvalues and, optionally, the eigenvectors of
24 a complex generalized Hermitian-definite eigenproblem, of the form
25 A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A and B
26 are assumed to be Hermitian, stored in packed format, and B is also
27 positive definite.
28
30 ITYPE (input) INTEGER
31 Specifies the problem type to be solved:
32 = 1: A*x = (lambda)*B*x
33 = 2: A*B*x = (lambda)*x
34 = 3: B*A*x = (lambda)*x
35 JOBZ (input) CHARACTER*1
37 = 'N': Compute eigenvalues only;
38 = 'V': Compute eigenvalues and eigenvectors.
39 UPLO (input) CHARACTER*1
41 = 'U': Upper triangles of A and B are stored;
42 = 'L': Lower triangles of A and B are stored.
43 N (input) INTEGER
45 The order of the matrices A and B. N >= 0.
46 AP (input/output) COMPLEX*16 array, dimension (N*(N+1)/2)
48 On entry, the upper or lower triangle of the Hermitian matrix
49 A, packed columnwise in a linear array. The j-th column of A
50 is stored in the array AP as follows: if UPLO = 'U', AP(i +
51 (j-1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i +
52 (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n. On exit, the contents
53 of AP are destroyed.
54 BP (input/output) COMPLEX*16 array, dimension (N*(N+1)/2)
56 On entry, the upper or lower triangle of the Hermitian matrix
57 B, packed columnwise in a linear array. The j-th column of B
58 is stored in the array BP as follows: if UPLO = 'U', BP(i +
59 (j-1)*j/2) = B(i,j) for 1<=i<=j; if UPLO = 'L', BP(i +
60 (j-1)*(2*n-j)/2) = B(i,j) for j<=i<=n. On exit, the triangular
61 factor U or L from the Cholesky factorization B = U**H*U or B =
62 L*L**H, in the same storage format as B.
63 W (output) DOUBLE PRECISION array, dimension (N)
65 If INFO = 0, the eigenvalues in ascending order.
66 Z (output) COMPLEX*16 array, dimension (LDZ, N)
68 If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of
69 eigenvectors. The eigenvectors are normalized as follows: if
70 ITYPE = 1 or 2, Z**H*B*Z = I; if ITYPE = 3, Z**H*inv(B)*Z = I.
71 If JOBZ = 'N', then Z is not referenced.
72 LDZ (input) INTEGER
74 The leading dimension of the array Z. LDZ >= 1, and if JOBZ =
75 'V', LDZ >= max(1,N).
76 WORK (workspace) COMPLEX*16 array, dimension (max(1, 2*N-1))
78 RWORK (workspace) DOUBLE PRECISION array, dimension (max(1, 3*N-2))
80 INFO (output) INTEGER
82 = 0: successful exit
83 < 0: if INFO = -i, the i-th argument had an illegal value
84 > 0: ZPPTRF or ZHPEV returned an error code:
85 <= N: if INFO = i, ZHPEV failed to converge; i off-diagonal
86 elements of an intermediate tridiagonal form did not convergeto
87 zero; > N: if INFO = N + i, for 1 <= i <= n, then the leading
88 minor of order i of B is not positive definite. The factoriza‐
89 tion of B could not be completed and no eigenvalues or eigen‐
90 vectors were computed.
91 LAPACK driver routine (version 3.N2o)vember 2008 ZHPGV(1)