1: SUBROUTINE ZSTEGR( JOBZ, RANGE, N, D, E, VL, VU, IL, IU,
2: $ ABSTOL, M, W, Z, LDZ, ISUPPZ, WORK, LWORK, IWORK,
3: $ LIWORK, INFO )
4:
5: IMPLICIT NONE
6: *
7: *
8: * -- LAPACK computational routine (version 3.2) --
9: * -- LAPACK is a software package provided by Univ. of Tennessee, --
10: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
11: * November 2006
12: *
13: * .. Scalar Arguments ..
14: CHARACTER JOBZ, RANGE
15: INTEGER IL, INFO, IU, LDZ, LIWORK, LWORK, M, N
16: DOUBLE PRECISION ABSTOL, VL, VU
17: * ..
18: * .. Array Arguments ..
19: INTEGER ISUPPZ( * ), IWORK( * )
20: DOUBLE PRECISION D( * ), E( * ), W( * ), WORK( * )
21: COMPLEX*16 Z( LDZ, * )
22: * ..
23: *
24: * Purpose
25: * =======
26: *
27: * ZSTEGR computes selected eigenvalues and, optionally, eigenvectors
28: * of a real symmetric tridiagonal matrix T. Any such unreduced matrix has
29: * a well defined set of pairwise different real eigenvalues, the corresponding
30: * real eigenvectors are pairwise orthogonal.
31: *
32: * The spectrum may be computed either completely or partially by specifying
33: * either an interval (VL,VU] or a range of indices IL:IU for the desired
34: * eigenvalues.
35: *
36: * ZSTEGR is a compatability wrapper around the improved ZSTEMR routine.
37: * See DSTEMR for further details.
38: *
39: * One important change is that the ABSTOL parameter no longer provides any
40: * benefit and hence is no longer used.
41: *
42: * Note : ZSTEGR and ZSTEMR work only on machines which follow
43: * IEEE-754 floating-point standard in their handling of infinities and
44: * NaNs. Normal execution may create these exceptiona values and hence
45: * may abort due to a floating point exception in environments which
46: * do not conform to the IEEE-754 standard.
47: *
48: * Arguments
49: * =========
50: *
51: * JOBZ (input) CHARACTER*1
52: * = 'N': Compute eigenvalues only;
53: * = 'V': Compute eigenvalues and eigenvectors.
54: *
55: * RANGE (input) CHARACTER*1
56: * = 'A': all eigenvalues will be found.
57: * = 'V': all eigenvalues in the half-open interval (VL,VU]
58: * will be found.
59: * = 'I': the IL-th through IU-th eigenvalues will be found.
60: *
61: * N (input) INTEGER
62: * The order of the matrix. N >= 0.
63: *
64: * D (input/output) DOUBLE PRECISION array, dimension (N)
65: * On entry, the N diagonal elements of the tridiagonal matrix
66: * T. On exit, D is overwritten.
67: *
68: * E (input/output) DOUBLE PRECISION array, dimension (N)
69: * On entry, the (N-1) subdiagonal elements of the tridiagonal
70: * matrix T in elements 1 to N-1 of E. E(N) need not be set on
71: * input, but is used internally as workspace.
72: * On exit, E is overwritten.
73: *
74: * VL (input) DOUBLE PRECISION
75: * VU (input) DOUBLE PRECISION
76: * If RANGE='V', the lower and upper bounds of the interval to
77: * be searched for eigenvalues. VL < VU.
78: * Not referenced if RANGE = 'A' or 'I'.
79: *
80: * IL (input) INTEGER
81: * IU (input) INTEGER
82: * If RANGE='I', the indices (in ascending order) of the
83: * smallest and largest eigenvalues to be returned.
84: * 1 <= IL <= IU <= N, if N > 0.
85: * Not referenced if RANGE = 'A' or 'V'.
86: *
87: * ABSTOL (input) DOUBLE PRECISION
88: * Unused. Was the absolute error tolerance for the
89: * eigenvalues/eigenvectors in previous versions.
90: *
91: * M (output) INTEGER
92: * The total number of eigenvalues found. 0 <= M <= N.
93: * If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1.
94: *
95: * W (output) DOUBLE PRECISION array, dimension (N)
96: * The first M elements contain the selected eigenvalues in
97: * ascending order.
98: *
99: * Z (output) COMPLEX*16 array, dimension (LDZ, max(1,M) )
100: * If JOBZ = 'V', and if INFO = 0, then the first M columns of Z
101: * contain the orthonormal eigenvectors of the matrix T
102: * corresponding to the selected eigenvalues, with the i-th
103: * column of Z holding the eigenvector associated with W(i).
104: * If JOBZ = 'N', then Z is not referenced.
105: * Note: the user must ensure that at least max(1,M) columns are
106: * supplied in the array Z; if RANGE = 'V', the exact value of M
107: * is not known in advance and an upper bound must be used.
108: * Supplying N columns is always safe.
109: *
110: * LDZ (input) INTEGER
111: * The leading dimension of the array Z. LDZ >= 1, and if
112: * JOBZ = 'V', then LDZ >= max(1,N).
113: *
114: * ISUPPZ (output) INTEGER ARRAY, dimension ( 2*max(1,M) )
115: * The support of the eigenvectors in Z, i.e., the indices
116: * indicating the nonzero elements in Z. The i-th computed eigenvector
117: * is nonzero only in elements ISUPPZ( 2*i-1 ) through
118: * ISUPPZ( 2*i ). This is relevant in the case when the matrix
119: * is split. ISUPPZ is only accessed when JOBZ is 'V' and N > 0.
120: *
121: * WORK (workspace/output) DOUBLE PRECISION array, dimension (LWORK)
122: * On exit, if INFO = 0, WORK(1) returns the optimal
123: * (and minimal) LWORK.
124: *
125: * LWORK (input) INTEGER
126: * The dimension of the array WORK. LWORK >= max(1,18*N)
127: * if JOBZ = 'V', and LWORK >= max(1,12*N) if JOBZ = 'N'.
128: * If LWORK = -1, then a workspace query is assumed; the routine
129: * only calculates the optimal size of the WORK array, returns
130: * this value as the first entry of the WORK array, and no error
131: * message related to LWORK is issued by XERBLA.
132: *
133: * IWORK (workspace/output) INTEGER array, dimension (LIWORK)
134: * On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.
135: *
136: * LIWORK (input) INTEGER
137: * The dimension of the array IWORK. LIWORK >= max(1,10*N)
138: * if the eigenvectors are desired, and LIWORK >= max(1,8*N)
139: * if only the eigenvalues are to be computed.
140: * If LIWORK = -1, then a workspace query is assumed; the
141: * routine only calculates the optimal size of the IWORK array,
142: * returns this value as the first entry of the IWORK array, and
143: * no error message related to LIWORK is issued by XERBLA.
144: *
145: * INFO (output) INTEGER
146: * On exit, INFO
147: * = 0: successful exit
148: * < 0: if INFO = -i, the i-th argument had an illegal value
149: * > 0: if INFO = 1X, internal error in DLARRE,
150: * if INFO = 2X, internal error in ZLARRV.
151: * Here, the digit X = ABS( IINFO ) < 10, where IINFO is
152: * the nonzero error code returned by DLARRE or
153: * ZLARRV, respectively.
154: *
155: * Further Details
156: * ===============
157: *
158: * Based on contributions by
159: * Inderjit Dhillon, IBM Almaden, USA
160: * Osni Marques, LBNL/NERSC, USA
161: * Christof Voemel, LBNL/NERSC, USA
162: *
163: * =====================================================================
164: *
165: * .. Local Scalars ..
166: LOGICAL TRYRAC
167: * ..
168: * .. External Subroutines ..
169: EXTERNAL ZSTEMR
170: * ..
171: * .. Executable Statements ..
172: INFO = 0
173: TRYRAC = .FALSE.
174:
175: CALL ZSTEMR( JOBZ, RANGE, N, D, E, VL, VU, IL, IU,
176: $ M, W, Z, LDZ, N, ISUPPZ, TRYRAC, WORK, LWORK,
177: $ IWORK, LIWORK, INFO )
178: *
179: * End of ZSTEGR
180: *
181: END
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