1DSTEDC(1) LAPACK driver routine (version 3.2) DSTEDC(1)
2
6 DSTEDC - computes all eigenvalues and, optionally, eigenvectors of a
7 symmetric tridiagonal matrix using the divide and conquer method
8
10 SUBROUTINE DSTEDC( COMPZ, N, D, E, Z, LDZ, WORK, LWORK, IWORK, LIWORK,
11 INFO )
12 CHARACTER COMPZ
14 INTEGER INFO, LDZ, LIWORK, LWORK, N
16 INTEGER IWORK( * )
18 DOUBLE PRECISION D( * ), E( * ), WORK( * ), Z( LDZ, * )
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22 DSTEDC computes all eigenvalues and, optionally, eigenvectors of a sym‐
23 metric tridiagonal matrix using the divide and conquer method. The
24 eigenvectors of a full or band real symmetric matrix can also be found
25 if DSYTRD or DSPTRD or DSBTRD has been used to reduce this matrix to
26 tridiagonal form.
27 This code makes very mild assumptions about floating point arithmetic.
28 It will work on machines with a guard digit in add/subtract, or on
29 those binary machines without guard digits which subtract like the Cray
30 X-MP, Cray Y-MP, Cray C-90, or Cray-2. It could conceivably fail on
31 hexadecimal or decimal machines without guard digits, but we know of
32 none. See DLAED3 for details.
33
35 COMPZ (input) CHARACTER*1
36 = 'N': Compute eigenvalues only.
37 = 'I': Compute eigenvectors of tridiagonal matrix also.
38 = 'V': Compute eigenvectors of original dense symmetric matrix
39 also. On entry, Z contains the orthogonal matrix used to
40 reduce the original matrix to tridiagonal form.
41 N (input) INTEGER
43 The dimension of the symmetric tridiagonal matrix. N >= 0.
44 D (input/output) DOUBLE PRECISION array, dimension (N)
46 On entry, the diagonal elements of the tridiagonal matrix. On
47 exit, if INFO = 0, the eigenvalues in ascending order.
48 E (input/output) DOUBLE PRECISION array, dimension (N-1)
50 On entry, the subdiagonal elements of the tridiagonal matrix.
51 On exit, E has been destroyed.
52 Z (input/output) DOUBLE PRECISION array, dimension (LDZ,N)
54 On entry, if COMPZ = 'V', then Z contains the orthogonal matrix
55 used in the reduction to tridiagonal form. On exit, if INFO =
56 0, then if COMPZ = 'V', Z contains the orthonormal eigenvectors
57 of the original symmetric matrix, and if COMPZ = 'I', Z con‐
58 tains the orthonormal eigenvectors of the symmetric tridiagonal
59 matrix. If COMPZ = 'N', then Z is not referenced.
60 LDZ (input) INTEGER
62 The leading dimension of the array Z. LDZ >= 1. If eigenvec‐
63 tors are desired, then LDZ >= max(1,N).
64 WORK (workspace/output) DOUBLE PRECISION array,
66 dimension (LWORK) On exit, if INFO = 0, WORK(1) returns the
67 optimal LWORK.
68 LWORK (input) INTEGER
70 The dimension of the array WORK. If COMPZ = 'N' or N <= 1 then
71 LWORK must be at least 1. If COMPZ = 'V' and N > 1 then LWORK
72 must be at least ( 1 + 3*N + 2*N*lg N + 3*N**2 ), where lg( N )
73 = smallest integer k such that 2**k >= N. If COMPZ = 'I' and N
74 > 1 then LWORK must be at least ( 1 + 4*N + N**2 ). Note that
75 for COMPZ = 'I' or 'V', then if N is less than or equal to the
76 minimum divide size, usually 25, then LWORK need only be
77 max(1,2*(N-1)). If LWORK = -1, then a workspace query is
78 assumed; the routine only calculates the optimal size of the
79 WORK array, returns this value as the first entry of the WORK
80 array, and no error message related to LWORK is issued by
81 XERBLA.
82 IWORK (workspace/output) INTEGER array, dimension (MAX(1,LIWORK))
84 On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.
85 LIWORK (input) INTEGER
87 The dimension of the array IWORK. If COMPZ = 'N' or N <= 1
88 then LIWORK must be at least 1. If COMPZ = 'V' and N > 1 then
89 LIWORK must be at least ( 6 + 6*N + 5*N*lg N ). If COMPZ = 'I'
90 and N > 1 then LIWORK must be at least ( 3 + 5*N ). Note that
91 for COMPZ = 'I' or 'V', then if N is less than or equal to the
92 minimum divide size, usually 25, then LIWORK need only be 1.
93 If LIWORK = -1, then a workspace query is assumed; the routine
94 only calculates the optimal size of the IWORK array, returns
95 this value as the first entry of the IWORK array, and no error
96 message related to LIWORK is issued by XERBLA.
97 INFO (output) INTEGER
99 = 0: successful exit.
100 < 0: if INFO = -i, the i-th argument had an illegal value.
101 > 0: The algorithm failed to compute an eigenvalue while work‐
102 ing on the submatrix lying in rows and columns INFO/(N+1)
103 through mod(INFO,N+1).
104
106 Based on contributions by
107 Jeff Rutter, Computer Science Division, University of California
108 at Berkeley, USA
109 Modified by Francoise Tisseur, University of Tennessee.
110 LAPACK driver routine (version 3.N2o)vember 2008 DSTEDC(1)