1ZSTEDC(1) LAPACK routine (version 3.1) ZSTEDC(1)
2
6 ZSTEDC - all eigenvalues and, optionally, eigenvectors of a symmetric
7 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.
31 It will work on machines with a guard digit in add/subtract, or on
32 those binary machines without guard digits which subtract like the Cray
33 X-MP, Cray Y-MP, Cray C-90, or Cray-2. It could conceivably fail on
34 hexadecimal or decimal machines without guard digits, but we know of
35 none. See DLAED3 for details.
36
39 COMPZ (input) CHARACTER*1
40 = 'N': Compute eigenvalues only.
41 = 'I': Compute eigenvectors of tridiagonal matrix also.
42 = 'V': Compute eigenvectors of original Hermitian matrix also.
43 On entry, Z contains the unitary matrix used to reduce the
44 original matrix to tridiagonal form.
45 N (input) INTEGER
47 The dimension of the symmetric tridiagonal matrix. N >= 0.
48 D (input/output) DOUBLE PRECISION array, dimension (N)
50 On entry, the diagonal elements of the tridiagonal matrix. On
51 exit, if INFO = 0, the eigenvalues in ascending order.
52 E (input/output) DOUBLE PRECISION array, dimension (N-1)
54 On entry, the subdiagonal elements of the tridiagonal matrix.
55 On exit, E has been destroyed.
56 Z (input/output) COMPLEX*16 array, dimension (LDZ,N)
58 On entry, if COMPZ = 'V', then Z contains the unitary matrix
59 used in the reduction to tridiagonal form. On exit, if INFO =
60 0, then if COMPZ = 'V', Z contains the orthonormal eigenvectors
61 of the original Hermitian matrix, and if COMPZ = 'I', Z con‐
62 tains the orthonormal eigenvectors of the symmetric tridiagonal
63 matrix. If COMPZ = 'N', then Z is not referenced.
64 LDZ (input) INTEGER
66 The leading dimension of the array Z. LDZ >= 1. If eigenvec‐
67 tors are desired, then LDZ >= max(1,N).
68 WORK (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK))
70 On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
71 LWORK (input) INTEGER
73 The dimension of the array WORK. If COMPZ = 'N' or 'I', or N
74 <= 1, LWORK must be at least 1. If COMPZ = 'V' and N > 1,
75 LWORK must be at least N*N. Note that for COMPZ = 'V', then if
76 N is less than or equal to the minimum divide size, usually 25,
77 then LWORK need only be 1.
78 If LWORK = -1, then a workspace query is assumed; the routine
80 only calculates the optimal sizes of the WORK, RWORK and IWORK
81 arrays, returns these values as the first entries of the WORK,
82 RWORK and IWORK arrays, and no error message related to LWORK
83 or LRWORK or LIWORK is issued by XERBLA.
84 RWORK (workspace/output) DOUBLE PRECISION array,
86 dimension (LRWORK) On exit, if INFO = 0, RWORK(1) returns the
87 optimal LRWORK.
88 LRWORK (input) INTEGER
90 The dimension of the array RWORK. If COMPZ = 'N' or N <= 1,
91 LRWORK must be at least 1. If COMPZ = 'V' and N > 1, LRWORK
92 must be at least 1 + 3*N + 2*N*lg N + 3*N**2 , where lg( N ) =
93 smallest integer k such that 2**k >= N. If COMPZ = 'I' and N >
94 1, LRWORK must be at least 1 + 4*N + 2*N**2 . Note that for
95 COMPZ = 'I' or 'V', then if N is less than or equal to the min‐
96 imum divide size, usually 25, then LRWORK need only be
97 max(1,2*(N-1)).
98 If LRWORK = -1, then a workspace query is assumed; the routine
100 only calculates the optimal sizes of the WORK, RWORK and IWORK
101 arrays, returns these values as the first entries of the WORK,
102 RWORK and IWORK arrays, and no error message related to LWORK
103 or LRWORK or LIWORK is issued by XERBLA.
104 IWORK (workspace/output) INTEGER array, dimension (MAX(1,LIWORK))
106 On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.
107 LIWORK (input) INTEGER
109 The dimension of the array IWORK. If COMPZ = 'N' or N <= 1,
110 LIWORK must be at least 1. If COMPZ = 'V' or N > 1, LIWORK
111 must be at least 6 + 6*N + 5*N*lg N. If COMPZ = 'I' or N > 1,
112 LIWORK must be at least 3 + 5*N . Note that for COMPZ = 'I' or
113 'V', then if N is less than or equal to the minimum divide
114 size, usually 25, then LIWORK need only be 1.
115 If LIWORK = -1, then a workspace query is assumed; the routine
117 only calculates the optimal sizes of the WORK, RWORK and IWORK
118 arrays, returns these values as the first entries of the WORK,
119 RWORK and IWORK arrays, and no error message related to LWORK
120 or LRWORK or LIWORK is issued by XERBLA.
121 INFO (output) INTEGER
123 = 0: successful exit.
124 < 0: if INFO = -i, the i-th argument had an illegal value.
125 > 0: The algorithm failed to compute an eigenvalue while work‐
126 ing on the submatrix lying in rows and columns INFO/(N+1)
127 through mod(INFO,N+1).
128
130 Based on contributions by
131 Jeff Rutter, Computer Science Division, University of California
132 at Berkeley, USA
133 LAPACK routine (version 3.1) November 2006 ZSTEDC(1)