1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
|
SUBROUTINE PSSTEDC( COMPZ, N, D, E, Q, IQ, JQ, DESCQ, WORK, LWORK,
$ IWORK, LIWORK, INFO )
*
* -- ScaLAPACK routine (version 1.7) --
* University of Tennessee, Knoxville, Oak Ridge National Laboratory,
* and University of California, Berkeley.
* March 13, 2000
*
* .. Scalar Arguments ..
CHARACTER COMPZ
INTEGER INFO, IQ, JQ, LIWORK, LWORK, N
* ..
* .. Array Arguments ..
INTEGER DESCQ( * ), IWORK( * )
REAL D( * ), E( * ), Q( * ), WORK( * )
* ..
*
* Purpose
* =======
* PSSTEDC computes all eigenvalues and eigenvectors of a
* symmetric tridiagonal matrix in parallel, using the divide and
* conquer algorithm.
*
* This code makes very mild assumptions about floating point
* arithmetic. It will work on machines with a guard digit in
* add/subtract, or on those binary machines without guard digits
* which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2.
* It could conceivably fail on hexadecimal or decimal machines
* without guard digits, but we know of none. See SLAED3 for details.
*
* Arguments
* =========
*
* COMPZ (input) CHARACTER*1
* = 'N': Compute eigenvalues only. (NOT IMPLEMENTED YET)
* = 'I': Compute eigenvectors of tridiagonal matrix also.
* = 'V': Compute eigenvectors of original dense symmetric
* matrix also. On entry, Z contains the orthogonal
* matrix used to reduce the original matrix to
* tridiagonal form. (NOT IMPLEMENTED YET)
*
* N (global input) INTEGER
* The order of the tridiagonal matrix T. N >= 0.
*
* D (global input/output) REAL array, dimension (N)
* On entry, the diagonal elements of the tridiagonal matrix.
* On exit, if INFO = 0, the eigenvalues in descending order.
*
* E (global input/output) REAL array, dimension (N-1)
* On entry, the subdiagonal elements of the tridiagonal matrix.
* On exit, E has been destroyed.
*
* Q (local output) REAL array,
* local dimension ( LLD_Q, LOCc(JQ+N-1))
* Q contains the orthonormal eigenvectors of the symmetric
* tridiagonal matrix.
* On output, Q is distributed across the P processes in block
* cyclic format.
*
* IQ (global input) INTEGER
* Q's global row index, which points to the beginning of the
* submatrix which is to be operated on.
*
* JQ (global input) INTEGER
* Q's global column index, which points to the beginning of
* the submatrix which is to be operated on.
*
* DESCQ (global and local input) INTEGER array of dimension DLEN_.
* The array descriptor for the distributed matrix Z.
*
*
* WORK (local workspace/output) REAL array,
* dimension (LWORK)
* On output, WORK(1) returns the workspace needed.
*
* LWORK (local input/output) INTEGER,
* the dimension of the array WORK.
* LWORK = 6*N + 2*NP*NQ
* NP = NUMROC( N, NB, MYROW, DESCQ( RSRC_ ), NPROW )
* NQ = NUMROC( N, NB, MYCOL, DESCQ( CSRC_ ), NPCOL )
*
* If LWORK = -1, the LWORK is global input and a workspace
* query is assumed; the routine only calculates the minimum
* size for the WORK array. The required workspace is returned
* as the first element of WORK and no error message is issued
* by PXERBLA.
*
* IWORK (local workspace/output) INTEGER array, dimension (LIWORK)
* On exit, if LIWORK > 0, IWORK(1) returns the optimal LIWORK.
*
* LIWORK (input) INTEGER
* The dimension of the array IWORK.
* LIWORK = 2 + 7*N + 8*NPCOL
*
* INFO (global output) INTEGER
* = 0: successful exit
* < 0: If the i-th argument is an array and the j-entry had
* an illegal value, then INFO = -(i*100+j), if the i-th
* argument is a scalar and had an illegal value, then
* INFO = -i.
* > 0: The algorithm failed to compute the INFO/(N+1) th
* eigenvalue while working on the submatrix lying in
* global rows and columns mod(INFO,N+1).
*
* Further Details
* ======= =======
*
* Contributed by Francoise Tisseur, University of Manchester.
*
* Reference: F. Tisseur and J. Dongarra, "A Parallel Divide and
* Conquer Algorithm for the Symmetric Eigenvalue Problem
* on Distributed Memory Architectures",
* SIAM J. Sci. Comput., 6:20 (1999), pp. 2223--2236.
* (see also LAPACK Working Note 132)
* http://www.netlib.org/lapack/lawns/lawn132.ps
*
* =====================================================================
*
* .. Parameters ..
INTEGER BLOCK_CYCLIC_2D, DLEN_, DTYPE_, CTXT_, M_, N_,
$ MB_, NB_, RSRC_, CSRC_, LLD_
PARAMETER ( BLOCK_CYCLIC_2D = 1, DLEN_ = 9, DTYPE_ = 1,
$ CTXT_ = 2, M_ = 3, N_ = 4, MB_ = 5, NB_ = 6,
$ RSRC_ = 7, CSRC_ = 8, LLD_ = 9 )
REAL ZERO, ONE
PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 )
* ..
* .. Local Scalars ..
LOGICAL LQUERY
INTEGER ICOFFQ, IIQ, IPQ, IQCOL, IQROW, IROFFQ, JJQ,
$ LDQ, LIWMIN, LWMIN, MYCOL, MYROW, NB, NP,
$ NPCOL, NPROW, NQ
REAL ORGNRM
* ..
* .. External Functions ..
LOGICAL LSAME
INTEGER INDXG2P, NUMROC
REAL SLANST
EXTERNAL INDXG2P, LSAME, NUMROC, SLANST
* ..
* .. External Subroutines ..
EXTERNAL BLACS_GRIDINFO, CHK1MAT, INFOG2L, PSLAED0,
$ PSLASRT, PXERBLA, SLASCL, SSTEDC
* ..
* .. Intrinsic Functions ..
INTRINSIC MOD, REAL
* ..
* .. Executable Statements ..
*
* This is just to keep ftnchek and toolpack/1 happy
IF( BLOCK_CYCLIC_2D*CSRC_*CTXT_*DLEN_*DTYPE_*LLD_*MB_*M_*NB_*N_*
$ RSRC_.LT.0 )RETURN
*
* Test the input parameters.
*
CALL BLACS_GRIDINFO( DESCQ( CTXT_ ), NPROW, NPCOL, MYROW, MYCOL )
LDQ = DESCQ( LLD_ )
NB = DESCQ( NB_ )
NP = NUMROC( N, NB, MYROW, DESCQ( RSRC_ ), NPROW )
NQ = NUMROC( N, NB, MYCOL, DESCQ( CSRC_ ), NPCOL )
INFO = 0
IF( NPROW.EQ.-1 ) THEN
INFO = -( 600+CTXT_ )
ELSE
CALL CHK1MAT( N, 2, N, 2, IQ, JQ, DESCQ, 8, INFO )
IF( INFO.EQ.0 ) THEN
NB = DESCQ( NB_ )
IROFFQ = MOD( IQ-1, DESCQ( MB_ ) )
ICOFFQ = MOD( JQ-1, DESCQ( NB_ ) )
IQROW = INDXG2P( IQ, NB, MYROW, DESCQ( RSRC_ ), NPROW )
IQCOL = INDXG2P( JQ, NB, MYCOL, DESCQ( CSRC_ ), NPCOL )
LWMIN = 6*N + 2*NP*NQ
LIWMIN = 2 + 7*N + 8*NPCOL
WORK( 1 ) = REAL( LWMIN )
IWORK( 1 ) = LIWMIN
LQUERY = ( LWORK.EQ.-1 .OR. LIWORK.EQ.-1 )
IF( .NOT.LSAME( COMPZ, 'I' ) ) THEN
INFO = -1
ELSE IF( N.LT.0 ) THEN
INFO = -2
ELSE IF( IROFFQ.NE.ICOFFQ .OR. ICOFFQ.NE.0 ) THEN
INFO = -5
ELSE IF( DESCQ( MB_ ).NE.DESCQ( NB_ ) ) THEN
INFO = -( 700+NB_ )
ELSE IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN
INFO = -10
ELSE IF( LIWORK.LT.LIWMIN .AND. .NOT.LQUERY ) THEN
INFO = -12
END IF
END IF
END IF
IF( INFO.NE.0 ) THEN
CALL PXERBLA( DESCQ( CTXT_ ), 'PSSTEDC', -INFO )
RETURN
ELSE IF( LQUERY ) THEN
RETURN
END IF
*
* Quick return
*
IF( N.EQ.0 )
$ GO TO 10
CALL INFOG2L( IQ, JQ, DESCQ, NPROW, NPCOL, MYROW, MYCOL, IIQ, JJQ,
$ IQROW, IQCOL )
IF( N.EQ.1 ) THEN
IF( MYROW.EQ.IQROW .AND. MYCOL.EQ.IQCOL )
$ Q( 1 ) = ONE
GO TO 10
END IF
*
* If N is smaller than the minimum divide size NB, then
* solve the problem with the serial divide and conquer
* code locally.
*
IF( N.LE.NB ) THEN
IF( ( MYROW.EQ.IQROW ) .AND. ( MYCOL.EQ.IQCOL ) ) THEN
IPQ = IIQ + ( JJQ-1 )*LDQ
CALL SSTEDC( 'I', N, D, E, Q( IPQ ), LDQ, WORK, LWORK,
$ IWORK, LIWORK, INFO )
IF( INFO.NE.0 ) THEN
INFO = ( N+1 ) + N
GO TO 10
END IF
END IF
GO TO 10
END IF
*
* If P=NPROW*NPCOL=1, solve the problem with SSTEDC.
*
IF( NPCOL*NPROW.EQ.1 ) THEN
IPQ = IIQ + ( JJQ-1 )*LDQ
CALL SSTEDC( 'I', N, D, E, Q( IPQ ), LDQ, WORK, LWORK, IWORK,
$ LIWORK, INFO )
GO TO 10
END IF
*
* Scale matrix to allowable range, if necessary.
*
ORGNRM = SLANST( 'M', N, D, E )
IF( ORGNRM.NE.ZERO ) THEN
CALL SLASCL( 'G', 0, 0, ORGNRM, ONE, N, 1, D, N, INFO )
CALL SLASCL( 'G', 0, 0, ORGNRM, ONE, N-1, 1, E, N-1, INFO )
END IF
*
CALL PSLAED0( N, D, E, Q, IQ, JQ, DESCQ, WORK, IWORK, INFO )
*
* Sort eigenvalues and corresponding eigenvectors
*
CALL PSLASRT( 'I', N, D, Q, IQ, JQ, DESCQ, WORK, LWORK, IWORK,
$ LIWORK, INFO )
*
* Scale back.
*
IF( ORGNRM.NE.ZERO )
$ CALL SLASCL( 'G', 0, 0, ONE, ORGNRM, N, 1, D, N, INFO )
*
10 CONTINUE
*
IF( LWORK.GT.0 )
$ WORK( 1 ) = REAL( LWMIN )
IF( LIWORK.GT.0 )
$ IWORK( 1 ) = LIWMIN
RETURN
*
* End of PSSTEDC
*
END
|
