1ZHPGV(1) LAPACK driver routine (version 3.1) ZHPGV(1)
2
6 ZHPGV - all the eigenvalues and, optionally, the eigenvectors of a com‐
7 plex generalized Hermitian-definite eigenproblem, of the form
8 A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x
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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
31 ITYPE (input) INTEGER
32 Specifies the problem type to be solved:
33 = 1: A*x = (lambda)*B*x
34 = 2: A*B*x = (lambda)*x
35 = 3: B*A*x = (lambda)*x
36 JOBZ (input) CHARACTER*1
38 = 'N': Compute eigenvalues only;
39 = 'V': Compute eigenvalues and eigenvectors.
40 UPLO (input) CHARACTER*1
42 = 'U': Upper triangles of A and B are stored;
43 = 'L': Lower triangles of A and B are stored.
44 N (input) INTEGER
46 The order of the matrices A and B. N >= 0.
47 AP (input/output) COMPLEX*16 array, dimension (N*(N+1)/2)
49 On entry, the upper or lower triangle of the Hermitian matrix
50 A, packed columnwise in a linear array. The j-th column of A
51 is stored in the array AP as follows: if UPLO = 'U', AP(i +
52 (j-1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i +
53 (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.
54 On exit, the contents of AP are destroyed.
56 BP (input/output) COMPLEX*16 array, dimension (N*(N+1)/2)
58 On entry, the upper or lower triangle of the Hermitian matrix
59 B, packed columnwise in a linear array. The j-th column of B
60 is stored in the array BP as follows: if UPLO = 'U', BP(i +
61 (j-1)*j/2) = B(i,j) for 1<=i<=j; if UPLO = 'L', BP(i +
62 (j-1)*(2*n-j)/2) = B(i,j) for j<=i<=n.
63 On exit, the triangular factor U or L from the Cholesky factor‐
65 ization B = U**H*U or B = L*L**H, in the same storage format as
66 B.
67 W (output) DOUBLE PRECISION array, dimension (N)
69 If INFO = 0, the eigenvalues in ascending order.
70 Z (output) COMPLEX*16 array, dimension (LDZ, N)
72 If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of
73 eigenvectors. The eigenvectors are normalized as follows: if
74 ITYPE = 1 or 2, Z**H*B*Z = I; if ITYPE = 3, Z**H*inv(B)*Z = I.
75 If JOBZ = 'N', then Z is not referenced.
76 LDZ (input) INTEGER
78 The leading dimension of the array Z. LDZ >= 1, and if JOBZ =
79 'V', LDZ >= max(1,N).
80 WORK (workspace) COMPLEX*16 array, dimension (max(1, 2*N-1))
82 RWORK (workspace) DOUBLE PRECISION array, dimension (max(1, 3*N-2))
84 INFO (output) INTEGER
86 = 0: successful exit
87 < 0: if INFO = -i, the i-th argument had an illegal value
88 > 0: ZPPTRF or ZHPEV returned an error code:
89 <= N: if INFO = i, ZHPEV failed to converge; i off-diagonal
90 elements of an intermediate tridiagonal form did not convergeto
91 zero; > N: if INFO = N + i, for 1 <= i <= n, then the leading
92 minor of order i of B is not positive definite. The factoriza‐
93 tion of B could not be completed and no eigenvalues or eigen‐
94 vectors were computed.
95 LAPACK driver routine (version 3.N1o)vember 2006 ZHPGV(1)