1 SUBROUTINE DSTEGR( 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 DOUBLE PRECISION Z( LDZ, * )
22 * ..
23 *
24 * Purpose
25 * =======
26 *
27 * DSTEGR 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 * DSTEGR is a compatability wrapper around the improved DSTEMR 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 : DSTEGR and DSTEMR 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) DOUBLE PRECISION 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 DLARRV.
151 * Here, the digit X = ABS( IINFO ) < 10, where IINFO is
152 * the nonzero error code returned by DLARRE or
153 * DLARRV, 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 DSTEMR
170 * ..
171 * .. Executable Statements ..
172 INFO = 0
173 TRYRAC = .FALSE.
174
175 CALL DSTEMR( 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 DSTEGR
180 *
181 END
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 DOUBLE PRECISION Z( LDZ, * )
22 * ..
23 *
24 * Purpose
25 * =======
26 *
27 * DSTEGR 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 * DSTEGR is a compatability wrapper around the improved DSTEMR 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 : DSTEGR and DSTEMR 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) DOUBLE PRECISION 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 DLARRV.
151 * Here, the digit X = ABS( IINFO ) < 10, where IINFO is
152 * the nonzero error code returned by DLARRE or
153 * DLARRV, 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 DSTEMR
170 * ..
171 * .. Executable Statements ..
172 INFO = 0
173 TRYRAC = .FALSE.
174
175 CALL DSTEMR( 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 DSTEGR
180 *
181 END