1CHPEVD(1) LAPACK driver routine (version 3.2) CHPEVD(1)
2
6 CHPEVD - computes all the eigenvalues and, optionally, eigenvectors of
7 a complex Hermitian matrix A in packed storage
8
10 SUBROUTINE CHPEVD( JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, LWORK, RWORK,
11 LRWORK, IWORK, LIWORK, INFO )
12 CHARACTER JOBZ, UPLO
14 INTEGER INFO, LDZ, LIWORK, LRWORK, LWORK, N
16 INTEGER IWORK( * )
18 REAL RWORK( * ), W( * )
20 COMPLEX AP( * ), WORK( * ), Z( LDZ, * )
22
24 CHPEVD computes all the eigenvalues and, optionally, eigenvectors of a
25 complex Hermitian matrix A in packed storage. If eigenvectors are
26 desired, it uses a divide and conquer algorithm.
27 The divide and conquer algorithm makes very mild assumptions about
28 floating point arithmetic. It will work on machines with a guard digit
29 in add/subtract, or on those binary machines without guard digits which
30 subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2. It could
31 conceivably fail on hexadecimal or decimal machines without guard dig‐
32 its, but we know of none.
33
35 JOBZ (input) CHARACTER*1
36 = 'N': Compute eigenvalues only;
37 = 'V': Compute eigenvalues and eigenvectors.
38 UPLO (input) CHARACTER*1
40 = 'U': Upper triangle of A is stored;
41 = 'L': Lower triangle of A is stored.
42 N (input) INTEGER
44 The order of the matrix A. N >= 0.
45 AP (input/output) COMPLEX array, dimension (N*(N+1)/2)
47 On entry, the upper or lower triangle of the Hermitian matrix
48 A, packed columnwise in a linear array. The j-th column of A
49 is stored in the array AP as follows: if UPLO = 'U', AP(i +
50 (j-1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i +
51 (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n. On exit, AP is over‐
52 written by values generated during the reduction to tridiagonal
53 form. If UPLO = 'U', the diagonal and first superdiagonal of
54 the tridiagonal matrix T overwrite the corresponding elements
55 of A, and if UPLO = 'L', the diagonal and first subdiagonal of
56 T overwrite the corresponding elements of A.
57 W (output) REAL array, dimension (N)
59 If INFO = 0, the eigenvalues in ascending order.
60 Z (output) COMPLEX array, dimension (LDZ, N)
62 If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal
63 eigenvectors of the matrix A, with the i-th column of Z holding
64 the eigenvector associated with W(i). If JOBZ = 'N', then Z is
65 not referenced.
66 LDZ (input) INTEGER
68 The leading dimension of the array Z. LDZ >= 1, and if JOBZ =
69 'V', LDZ >= max(1,N).
70 WORK (workspace/output) COMPLEX array, dimension (MAX(1,LWORK))
72 On exit, if INFO = 0, WORK(1) returns the required LWORK.
73 LWORK (input) INTEGER
75 The dimension of array WORK. If N <= 1, LWORK
76 must be at least 1. If JOBZ = 'N' and N > 1, LWORK must be at
77 least N. If JOBZ = 'V' and N > 1, LWORK must be at least 2*N.
78 If LWORK = -1, then a workspace query is assumed; the routine
79 only calculates the required sizes of the WORK, RWORK and IWORK
80 arrays, returns these values as the first entries of the WORK,
81 RWORK and IWORK arrays, and no error message related to LWORK
82 or LRWORK or LIWORK is issued by XERBLA.
83 RWORK (workspace/output) REAL array, dimension (MAX(1,LRWORK))
85 On exit, if INFO = 0, RWORK(1) returns the required LRWORK.
86 LRWORK (input) INTEGER
88 The dimension of array RWORK. If N <= 1, LRWORK
89 must be at least 1. If JOBZ = 'N' and N > 1, LRWORK must be at
90 least N. If JOBZ = 'V' and N > 1, LRWORK must be at least 1 +
91 5*N + 2*N**2. If LRWORK = -1, then a workspace query is
92 assumed; the routine only calculates the required sizes of the
93 WORK, RWORK and IWORK arrays, returns these values as the first
94 entries of the WORK, RWORK and IWORK arrays, and no error mes‐
95 sage related to LWORK or LRWORK or LIWORK is issued by XERBLA.
96 IWORK (workspace/output) INTEGER array, dimension (MAX(1,LIWORK))
98 On exit, if INFO = 0, IWORK(1) returns the required LIWORK.
99 LIWORK (input) INTEGER
101 The dimension of array IWORK. If JOBZ = 'N' or N <= 1, LIWORK
102 must be at least 1. If JOBZ = 'V' and N > 1, LIWORK must be
103 at least 3 + 5*N. If LIWORK = -1, then a workspace query is
104 assumed; the routine only calculates the required sizes of the
105 WORK, RWORK and IWORK arrays, returns these values as the first
106 entries of the WORK, RWORK and IWORK arrays, and no error mes‐
107 sage related to LWORK or LRWORK or LIWORK is issued by XERBLA.
108 INFO (output) INTEGER
110 = 0: successful exit
111 < 0: if INFO = -i, the i-th argument had an illegal value.
112 > 0: if INFO = i, the algorithm failed to converge; i off-
113 diagonal elements of an intermediate tridiagonal form did not
114 converge to zero.
115 LAPACK driver routine (version 3.N2o)vember 2008 CHPEVD(1)