1ZSTEDC(1) LAPACK routine (version 3.2) ZSTEDC(1)
2
6 ZSTEDC - computes all eigenvalues and, optionally, eigenvectors of a
7 symmetric tridiagonal matrix using the divide and conquer method
8
10 SUBROUTINE ZSTEDC( COMPZ, N, D, E, Z, LDZ, WORK, LWORK, RWORK, LRWORK,
11 IWORK, LIWORK, INFO )
12 CHARACTER COMPZ
14 INTEGER INFO, LDZ, LIWORK, LRWORK, LWORK, N
16 INTEGER IWORK( * )
18 DOUBLE PRECISION D( * ), E( * ), RWORK( * )
20 COMPLEX*16 WORK( * ), Z( LDZ, * )
22
24 ZSTEDC computes all eigenvalues and, optionally, eigenvectors of a sym‐
25 metric tridiagonal matrix using the divide and conquer method. The
26 eigenvectors of a full or band complex Hermitian matrix can also be
27 found if ZHETRD or ZHPTRD or ZHBTRD has been used to reduce this matrix
28 to tridiagonal form.
29 This code makes very mild assumptions about floating point arithmetic.
30 It will work on machines with a guard digit in add/subtract, or on
31 those binary machines without guard digits which subtract like the Cray
32 X-MP, Cray Y-MP, Cray C-90, or Cray-2. It could conceivably fail on
33 hexadecimal or decimal machines without guard digits, but we know of
34 none. See DLAED3 for details.
35
37 COMPZ (input) CHARACTER*1
38 = 'N': Compute eigenvalues only.
39 = 'I': Compute eigenvectors of tridiagonal matrix also.
40 = 'V': Compute eigenvectors of original Hermitian matrix also.
41 On entry, Z contains the unitary matrix used to reduce the
42 original matrix to tridiagonal form.
43 N (input) INTEGER
45 The dimension of the symmetric tridiagonal matrix. N >= 0.
46 D (input/output) DOUBLE PRECISION array, dimension (N)
48 On entry, the diagonal elements of the tridiagonal matrix. On
49 exit, if INFO = 0, the eigenvalues in ascending order.
50 E (input/output) DOUBLE PRECISION array, dimension (N-1)
52 On entry, the subdiagonal elements of the tridiagonal matrix.
53 On exit, E has been destroyed.
54 Z (input/output) COMPLEX*16 array, dimension (LDZ,N)
56 On entry, if COMPZ = 'V', then Z contains the unitary matrix
57 used in the reduction to tridiagonal form. On exit, if INFO =
58 0, then if COMPZ = 'V', Z contains the orthonormal eigenvectors
59 of the original Hermitian matrix, and if COMPZ = 'I', Z con‐
60 tains the orthonormal eigenvectors of the symmetric tridiagonal
61 matrix. If COMPZ = 'N', then Z is not referenced.
62 LDZ (input) INTEGER
64 The leading dimension of the array Z. LDZ >= 1. If eigenvec‐
65 tors are desired, then LDZ >= max(1,N).
66 WORK (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK))
68 On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
69 LWORK (input) INTEGER
71 The dimension of the array WORK. If COMPZ = 'N' or 'I', or N
72 <= 1, LWORK must be at least 1. If COMPZ = 'V' and N > 1,
73 LWORK must be at least N*N. Note that for COMPZ = 'V', then if
74 N is less than or equal to the minimum divide size, usually 25,
75 then LWORK need only be 1. If LWORK = -1, then a workspace
76 query is assumed; the routine only calculates the optimal sizes
77 of the WORK, RWORK and IWORK arrays, returns these values as
78 the first entries of the WORK, RWORK and IWORK arrays, and no
79 error message related to LWORK or LRWORK or LIWORK is issued by
80 XERBLA.
81 RWORK (workspace/output) DOUBLE PRECISION array,
83 dimension (LRWORK) On exit, if INFO = 0, RWORK(1) returns the
84 optimal LRWORK.
85 LRWORK (input) INTEGER
87 The dimension of the array RWORK. If COMPZ = 'N' or N <= 1,
88 LRWORK must be at least 1. If COMPZ = 'V' and N > 1, LRWORK
89 must be at least 1 + 3*N + 2*N*lg N + 3*N**2 , where lg( N ) =
90 smallest integer k such that 2**k >= N. If COMPZ = 'I' and N >
91 1, LRWORK must be at least 1 + 4*N + 2*N**2 . Note that for
92 COMPZ = 'I' or 'V', then if N is less than or equal to the min‐
93 imum divide size, usually 25, then LRWORK need only be
94 max(1,2*(N-1)). If LRWORK = -1, then a workspace query is
95 assumed; the routine only calculates the optimal sizes of the
96 WORK, RWORK and IWORK arrays, returns these values as the first
97 entries of the WORK, RWORK and IWORK arrays, and no error mes‐
98 sage related to LWORK or LRWORK or LIWORK is issued by XERBLA.
99 IWORK (workspace/output) INTEGER array, dimension (MAX(1,LIWORK))
101 On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.
102 LIWORK (input) INTEGER
104 The dimension of the array IWORK. If COMPZ = 'N' or N <= 1,
105 LIWORK must be at least 1. If COMPZ = 'V' or N > 1, LIWORK
106 must be at least 6 + 6*N + 5*N*lg N. If COMPZ = 'I' or N > 1,
107 LIWORK must be at least 3 + 5*N . Note that for COMPZ = 'I' or
108 'V', then if N is less than or equal to the minimum divide
109 size, usually 25, then LIWORK need only be 1. If LIWORK = -1,
110 then a workspace query is assumed; the routine only calculates
111 the optimal sizes of the WORK, RWORK and IWORK arrays, returns
112 these values as the first entries of the WORK, RWORK and IWORK
113 arrays, and no error message related to LWORK or LRWORK or
114 LIWORK is issued by XERBLA.
115 INFO (output) INTEGER
117 = 0: successful exit.
118 < 0: if INFO = -i, the i-th argument had an illegal value.
119 > 0: The algorithm failed to compute an eigenvalue while work‐
120 ing on the submatrix lying in rows and columns INFO/(N+1)
121 through mod(INFO,N+1).
122
124 Based on contributions by
125 Jeff Rutter, Computer Science Division, University of California
126 at Berkeley, USA
127 LAPACK routine (version 3.2) November 2008 ZSTEDC(1)