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
|
SUBROUTINE PDGEHDRV( N, ILO, IHI, A, IA, JA, DESCA, TAU, WORK )
*
* -- ScaLAPACK routine (version 1.7) --
* University of Tennessee, Knoxville, Oak Ridge National Laboratory,
* and University of California, Berkeley.
* May 28, 2001
*
* .. Scalar Arguments ..
INTEGER IA, IHI, ILO, JA, N
* ..
* .. Array Arguments ..
INTEGER DESCA( * )
DOUBLE PRECISION A( * ), TAU( * ), WORK( * )
* ..
*
* Purpose
* =======
*
* PDGEHDRV computes sub( A ) = A(IA:IA+N-1,JA:JA+N-1) from the
* orthogonal matrix Q, the Hessenberg matrix, and the array TAU
* returned by PDGEHRD:
* sub( A ) := Q * H * Q'
*
* Arguments
* =========
*
* N (global input) INTEGER
* The number of rows and columns to be operated on, i.e. the
* order of the distributed submatrix sub( A ). N >= 0.
*
* ILO (global input) INTEGER
* IHI (global input) INTEGER
* It is assumed that sub( A ) is already upper triangular in
* rows and columns 1:ILO-1 and IHI+1:N. If N > 0,
* 1 <= ILO <= IHI <= N; otherwise set ILO = 1, IHI = N.
*
* A (local input/local output) DOUBLE PRECISION pointer into the
* local memory to an array of dimension (LLD_A,LOCc(JA+N-1)).
* On entry, this array contains the local pieces of the N-by-N
* general distributed matrix sub( A ) reduced to Hessenberg
* form by PDGEHRD. The upper triangle and the first sub-
* diagonal of sub( A ) contain the upper Hessenberg matrix H,
* and the elements below the first subdiagonal, with the array
* TAU, represent the orthogonal matrix Q as a product of
* elementary reflectors. On exit, the original distributed
* N-by-N matrix sub( A ) is recovered.
*
* IA (global input) INTEGER
* The row index in the global array A indicating the first
* row of sub( A ).
*
* JA (global input) INTEGER
* The column index in the global array A indicating the
* first column of sub( A ).
*
* DESCA (global and local input) INTEGER array of dimension DLEN_.
* The array descriptor for the distributed matrix A.
*
* TAU (local input) DOUBLE PRECISION array, dimension LOCc(JA+N-2)
* The scalar factors of the elementary reflectors returned by
* PDGEHRD. TAU is tied to the distributed matrix A.
*
* WORK (local workspace) DOUBLE PRECISION array, dimension (LWORK).
* LWORK >= NB*NB + NB*IHLP + MAX[ NB*( IHLP+INLQ ),
* NB*( IHLQ + MAX[ IHIP,
* IHLP+NUMROC( NUMROC( IHI-ILO+LOFF+1, NB, 0, 0,
* NPCOL ), NB, 0, 0, LCMQ ) ] ) ]
*
* where NB = MB_A = NB_A,
* LCM is the least common multiple of NPROW and NPCOL,
* LCM = ILCM( NPROW, NPCOL ), LCMQ = LCM / NPCOL,
*
* IROFFA = MOD( IA-1, NB ),
* IAROW = INDXG2P( IA, NB, MYROW, RSRC_A, NPROW ),
* IHIP = NUMROC( IHI+IROFFA, NB, MYROW, IAROW, NPROW ),
*
* ILROW = INDXG2P( IA+ILO-1, NB, MYROW, RSRC_A, NPROW ),
* ILCOL = INDXG2P( JA+ILO-1, NB, MYCOL, CSRC_A, NPCOL ),
* IHLP = NUMROC( IHI-ILO+IROFFA+1, NB, MYROW, ILROW, NPROW ),
* IHLQ = NUMROC( IHI-ILO+IROFFA+1, NB, MYCOL, ILCOL, NPCOL ),
* INLQ = NUMROC( N-ILO+IROFFA+1, NB, MYCOL, ILCOL, NPCOL ).
*
* ILCM, INDXG2P and NUMROC are ScaLAPACK tool functions;
* MYROW, MYCOL, NPROW and NPCOL can be determined by calling
* the subroutine BLACS_GRIDINFO.
*
* =====================================================================
*
* .. Parameters ..
INTEGER BLOCK_CYCLIC_2D, CSRC_, CTXT_, DLEN_, DTYPE_,
$ LLD_, MB_, M_, NB_, N_, RSRC_
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 )
DOUBLE PRECISION ZERO
PARAMETER ( ZERO = 0.0D+0 )
* ..
* .. Local Scalars ..
INTEGER I, IACOL, IAROW, ICTXT, IHLP, II, IOFF, IPT,
$ IPV, IPW, IV, J, JB, JJ, JL, K, MYCOL, MYROW,
$ NB, NPCOL, NPROW
* ..
* .. Local Arrays ..
INTEGER DESCV( DLEN_ )
* ..
* .. External Functions ..
INTEGER INDXG2P, NUMROC
EXTERNAL INDXG2P, NUMROC
* ..
* .. External Subroutines ..
EXTERNAL BLACS_GRIDINFO, DESCSET, INFOG2L, PDLARFB,
$ PDLARFT, PDLACPY, PDLASET
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX, MIN, MOD
* ..
* .. Executable statements ..
*
* Get grid parameters
*
ICTXT = DESCA( CTXT_ )
CALL BLACS_GRIDINFO( ICTXT, NPROW, NPCOL, MYROW, MYCOL )
*
* Quick return if possible
*
IF( IHI-ILO.LE.0 )
$ RETURN
*
NB = DESCA( MB_ )
IOFF = MOD( IA+ILO-2, NB )
CALL INFOG2L( IA+ILO-1, JA+ILO-1, DESCA, NPROW, NPCOL, MYROW,
$ MYCOL, II, JJ, IAROW, IACOL )
IHLP = NUMROC( IHI-ILO+IOFF+1, NB, MYROW, IAROW, NPROW )
*
IPT = 1
IPV = IPT + NB * NB
IPW = IPV + IHLP * NB
JL = MAX( ( ( JA+IHI-2 ) / NB ) * NB + 1, JA + ILO - 1 )
CALL DESCSET( DESCV, IHI-ILO+IOFF+1, NB, NB, NB, IAROW,
$ INDXG2P( JL, DESCA( NB_ ), MYCOL, DESCA( CSRC_ ),
$ NPCOL ), ICTXT, MAX( 1, IHLP ) )
*
DO 10 J = JL, ILO+JA+NB-IOFF-1, -NB
JB = MIN( JA+IHI-J-1, NB )
I = IA + J - JA
K = I - IA + 1
IV = K - ILO + IOFF + 1
*
* Compute upper triangular matrix T from TAU.
*
CALL PDLARFT( 'Forward', 'Columnwise', IHI-K, JB, A, I+1, J,
$ DESCA, TAU, WORK( IPT ), WORK( IPW ) )
*
* Copy Householder vectors into workspace.
*
CALL PDLACPY( 'All', IHI-K, JB, A, I+1, J, DESCA, WORK( IPV ),
$ IV+1, 1, DESCV )
*
* Zero out the strict lower triangular part of A.
*
CALL PDLASET( 'Lower', IHI-K-1, JB, ZERO, ZERO, A, I+2, J,
$ DESCA )
*
* Apply block Householder transformation from Left.
*
CALL PDLARFB( 'Left', 'No transpose', 'Forward', 'Columnwise',
$ IHI-K, N-K+1, JB, WORK( IPV ), IV+1, 1, DESCV,
$ WORK( IPT ), A, I+1, J, DESCA, WORK( IPW ) )
*
* Apply block Householder transformation from Right.
*
CALL PDLARFB( 'Right', 'Transpose', 'Forward', 'Columnwise',
$ IHI, IHI-K, JB, WORK( IPV ), IV+1, 1, DESCV,
$ WORK( IPT ), A, IA, J+1, DESCA, WORK( IPW ) )
*
DESCV( CSRC_ ) = MOD( DESCV( CSRC_ ) + NPCOL - 1, NPCOL )
*
10 CONTINUE
*
* Handle the first block separately
*
IV = IOFF + 1
I = IA + ILO - 1
J = JA + ILO - 1
JB = MIN( NB-IOFF, JA+IHI-J-1 )
*
* Compute upper triangular matrix T from TAU.
*
CALL PDLARFT( 'Forward', 'Columnwise', IHI-ILO, JB, A, I+1, J,
$ DESCA, TAU, WORK( IPT ), WORK( IPW ) )
*
* Copy Householder vectors into workspace.
*
CALL PDLACPY( 'All', IHI-ILO, JB, A, I+1, J, DESCA, WORK( IPV ),
$ IV+1, 1, DESCV )
*
* Zero out the strict lower triangular part of A.
*
IF( IHI-ILO.GT.0 )
$ CALL PDLASET( 'Lower', IHI-ILO-1, JB, ZERO, ZERO, A, I+2, J,
$ DESCA )
*
* Apply block Householder transformation from Left.
*
CALL PDLARFB( 'Left', 'No transpose', 'Forward', 'Columnwise',
$ IHI-ILO, N-ILO+1, JB, WORK( IPV ), IV+1, 1, DESCV,
$ WORK( IPT ), A, I+1, J, DESCA, WORK( IPW ) )
*
* Apply block Householder transformation from Right.
*
CALL PDLARFB( 'Right', 'Transpose', 'Forward', 'Columnwise', IHI,
$ IHI-ILO, JB, WORK( IPV ), IV+1, 1, DESCV,
$ WORK( IPT ), A, IA, J+1, DESCA, WORK( IPW ) )
*
RETURN
*
* End of PDGEHDRV
*
END
|
