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
|
SUBROUTINE PSLAED0( N, D, E, Q, IQ, JQ, DESCQ, WORK, IWORK, INFO )
*
* -- ScaLAPACK auxiliary routine (version 1.7) --
* University of Tennessee, Knoxville, Oak Ridge National Laboratory,
* and University of California, Berkeley.
* December 31, 1998
*
* .. Scalar Arguments ..
INTEGER INFO, IQ, JQ, N
* ..
* .. Array Arguments ..
INTEGER DESCQ( * ), IWORK( * )
REAL D( * ), E( * ), Q( * ), WORK( * )
* ..
*
* Purpose
* =======
*
* PSLAED0 computes all eigenvalues and corresponding eigenvectors of a
* symmetric tridiagonal matrix using the divide and conquer method.
*
*
* Arguments
* =========
*
* 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,
* global dimension (N, N),
* 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 ) REAL array, dimension (LWORK)
* LWORK = 6*N + 2*NP*NQ, with
* NP = NUMROC( N, MB_Q, MYROW, IQROW, NPROW )
* NQ = NUMROC( N, NB_Q, MYCOL, IQCOL, NPCOL )
* IQROW = INDXG2P( IQ, NB_Q, MYROW, RSRC_Q, NPROW )
* IQCOL = INDXG2P( JQ, MB_Q, MYCOL, CSRC_Q, NPCOL )
*
* IWORK (local workspace/output) INTEGER array, dimension (LIWORK)
* 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).
*
* =====================================================================
*
* .. 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 )
* ..
* .. Local Scalars ..
INTEGER I, ID, IDCOL, IDROW, IID, IINFO, IIQ, IM1, IM2,
$ IPQ, IQCOL, IQROW, J, JJD, JJQ, LDQ, MATSIZ,
$ MYCOL, MYROW, N1, NB, NBL, NBL1, NPCOL, NPROW,
$ SUBPBS, TSUBPBS
* ..
* .. External Subroutines ..
EXTERNAL BLACS_GRIDINFO, INFOG2L, PSLAED1, PXERBLA,
$ SGEBR2D, SGEBS2D, SGERV2D, SGESD2D, SSTEQR
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS, MIN
* ..
* .. 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 )
INFO = 0
IF( DESCQ( NB_ ).GT.N .OR. N.LT.2 )
$ INFO = -1
IF( INFO.NE.0 ) THEN
CALL PXERBLA( DESCQ( CTXT_ ), 'PSLAED0', -INFO )
RETURN
END IF
*
NB = DESCQ( NB_ )
LDQ = DESCQ( LLD_ )
CALL INFOG2L( IQ, JQ, DESCQ, NPROW, NPCOL, MYROW, MYCOL, IIQ, JJQ,
$ IQROW, IQCOL )
*
* Determine the size and placement of the submatrices, and save in
* the leading elements of IWORK.
*
TSUBPBS = ( N-1 ) / NB + 1
IWORK( 1 ) = TSUBPBS
SUBPBS = 1
10 CONTINUE
IF( IWORK( SUBPBS ).GT.1 ) THEN
DO 20 J = SUBPBS, 1, -1
IWORK( 2*J ) = ( IWORK( J )+1 ) / 2
IWORK( 2*J-1 ) = IWORK( J ) / 2
20 CONTINUE
SUBPBS = 2*SUBPBS
GO TO 10
END IF
DO 30 J = 2, SUBPBS
IWORK( J ) = IWORK( J ) + IWORK( J-1 )
30 CONTINUE
*
* Divide the matrix into TSUBPBS submatrices of size at most NB
* using rank-1 modifications (cuts).
*
DO 40 I = NB + 1, N, NB
IM1 = I - 1
D( IM1 ) = D( IM1 ) - ABS( E( IM1 ) )
D( I ) = D( I ) - ABS( E( IM1 ) )
40 CONTINUE
*
* Solve each submatrix eigenproblem at the bottom of the divide and
* conquer tree. D is the same on each process.
*
DO 50 ID = 1, N, NB
CALL INFOG2L( IQ-1+ID, JQ-1+ID, DESCQ, NPROW, NPCOL, MYROW,
$ MYCOL, IID, JJD, IDROW, IDCOL )
MATSIZ = MIN( NB, N-ID+1 )
IF( MYROW.EQ.IDROW .AND. MYCOL.EQ.IDCOL ) THEN
IPQ = IID + ( JJD-1 )*LDQ
CALL SSTEQR( 'I', MATSIZ, D( ID ), E( ID ), Q( IPQ ), LDQ,
$ WORK, INFO )
IF( INFO.NE.0 ) THEN
CALL PXERBLA( DESCQ( CTXT_ ), 'SSTEQR', -INFO )
RETURN
END IF
IF( MYROW.NE.IQROW .OR. MYCOL.NE.IQCOL ) THEN
CALL SGESD2D( DESCQ( CTXT_ ), MATSIZ, 1, D( ID ), MATSIZ,
$ IQROW, IQCOL )
END IF
ELSE IF( MYROW.EQ.IQROW .AND. MYCOL.EQ.IQCOL ) THEN
CALL SGERV2D( DESCQ( CTXT_ ), MATSIZ, 1, D( ID ), MATSIZ,
$ IDROW, IDCOL )
END IF
50 CONTINUE
*
IF( MYROW.EQ.IQROW .AND. MYCOL.EQ.IQCOL ) THEN
CALL SGEBS2D( DESCQ( CTXT_ ), 'A', ' ', N, 1, D, N )
ELSE
CALL SGEBR2D( DESCQ( CTXT_ ), 'A', ' ', N, 1, D, N, IQROW,
$ IQCOL )
END IF
*
* Successively merge eigensystems of adjacent submatrices
* into eigensystem for the corresponding larger matrix.
*
* while ( SUBPBS > 1 )
*
60 CONTINUE
IF( SUBPBS.GT.1 ) THEN
IM2 = SUBPBS - 2
DO 80 I = 0, IM2, 2
IF( I.EQ.0 ) THEN
NBL = IWORK( 2 )
NBL1 = IWORK( 1 )
IF( NBL1.EQ.0 )
$ GO TO 70
ID = 1
MATSIZ = MIN( N, NBL*NB )
N1 = NBL1*NB
ELSE
NBL = IWORK( I+2 ) - IWORK( I )
NBL1 = NBL / 2
IF( NBL1.EQ.0 )
$ GO TO 70
ID = IWORK( I )*NB + 1
MATSIZ = MIN( NB*NBL, N-ID+1 )
N1 = NBL1*NB
END IF
*
* Merge lower order eigensystems (of size N1 and MATSIZ - N1)
* into an eigensystem of size MATSIZ.
*
CALL PSLAED1( MATSIZ, N1, D( ID ), ID, Q, IQ, JQ, DESCQ,
$ E( ID+N1-1 ), WORK, IWORK( SUBPBS+1 ), IINFO )
IF( IINFO.NE.0 ) THEN
INFO = IINFO*( N+1 ) + ID
END IF
70 CONTINUE
IWORK( I / 2+1 ) = IWORK( I+2 )
80 CONTINUE
SUBPBS = SUBPBS / 2
GO TO 60
END IF
*
* end while
*
90 CONTINUE
RETURN
*
* End of PSLAED0
*
END
|
