1CSTEDC(1) LAPACK routine (version 3.1) CSTEDC(1)
2
6 CSTEDC - all eigenvalues and, optionally, eigenvectors of a symmetric
7 tridiagonal matrix using the divide and conquer method
8
10 SUBROUTINE CSTEDC( 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 REAL D( * ), E( * ), RWORK( * )
20 COMPLEX WORK( * ), Z( LDZ, * )
22
24 CSTEDC 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 CHETRD or CHPTRD or CHBTRD 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 SLAED3 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) REAL 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) REAL 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 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 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) REAL array, dimension (MAX(1,LRWORK))
86 On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK.
87 LRWORK (input) INTEGER
89 The dimension of the array RWORK. If COMPZ = 'N' or N <= 1,
90 LRWORK must be at least 1. If COMPZ = 'V' and N > 1, LRWORK
91 must be at least 1 + 3*N + 2*N*lg N + 3*N**2 , where lg( N ) =
92 smallest integer k such that 2**k >= N. If COMPZ = 'I' and N >
93 1, LRWORK must be at least 1 + 4*N + 2*N**2 . Note that for
94 COMPZ = 'I' or 'V', then if N is less than or equal to the min‐
95 imum divide size, usually 25, then LRWORK need only be
96 max(1,2*(N-1)).
97 If LRWORK = -1, then a workspace query is assumed; the routine
99 only calculates the optimal sizes of the WORK, RWORK and IWORK
100 arrays, returns these values as the first entries of the WORK,
101 RWORK and IWORK arrays, and no error message related to LWORK
102 or LRWORK or LIWORK is issued by XERBLA.
103 IWORK (workspace/output) INTEGER array, dimension (MAX(1,LIWORK))
105 On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.
106 LIWORK (input) INTEGER
108 The dimension of the array IWORK. If COMPZ = 'N' or N <= 1,
109 LIWORK must be at least 1. If COMPZ = 'V' or N > 1, LIWORK
110 must be at least 6 + 6*N + 5*N*lg N. If COMPZ = 'I' or N > 1,
111 LIWORK must be at least 3 + 5*N . Note that for COMPZ = 'I' or
112 'V', then if N is less than or equal to the minimum divide
113 size, usually 25, then LIWORK need only be 1.
114 If LIWORK = -1, then a workspace query is assumed; the routine
116 only calculates the optimal sizes of the WORK, RWORK and IWORK
117 arrays, returns these values as the first entries of the WORK,
118 RWORK and IWORK arrays, and no error message related to LWORK
119 or LRWORK or LIWORK is issued by XERBLA.
120 INFO (output) INTEGER
122 = 0: successful exit.
123 < 0: if INFO = -i, the i-th argument had an illegal value.
124 > 0: The algorithm failed to compute an eigenvalue while work‐
125 ing on the submatrix lying in rows and columns INFO/(N+1)
126 through mod(INFO,N+1).
127
129 Based on contributions by
130 Jeff Rutter, Computer Science Division, University of California
131 at Berkeley, USA
132 LAPACK routine (version 3.1) November 2006 CSTEDC(1)