ScaLAPACK 2.1  2.1
ScaLAPACK: Scalable Linear Algebra PACKage
pdsytdrv.f
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1  SUBROUTINE pdsytdrv( UPLO, N, A, IA, JA, DESCA, D, E, TAU, WORK,
2  $ INFO )
3 *
4 * -- ScaLAPACK routine (version 1.7) --
5 * University of Tennessee, Knoxville, Oak Ridge National Laboratory,
6 * and University of California, Berkeley.
7 * May 1, 1997
8 *
9 * .. Scalar Arguments ..
10  CHARACTER UPLO
11  INTEGER IA, INFO, JA, N
12 * ..
13 * .. Array Arguments ..
14  INTEGER DESCA( * )
15  DOUBLE PRECISION A( * ), D( * ), E( * ), TAU( * ), WORK( * )
16 * ..
17 *
18 * Purpose
19 * =======
20 *
21 * PDSYTDRV computes sub( A ) = A(IA:IA+N-1,JA:JA+N-1) from Q, the
22 * symmetric tridiagonal matrix T (or D and E), and TAU, which were
23 * computed by PDSYTRD: sub( A ) := Q * T * Q'.
24 *
25 * Notes
26 * =====
27 *
28 * Each global data object is described by an associated description
29 * vector. This vector stores the information required to establish
30 * the mapping between an object element and its corresponding process
31 * and memory location.
32 *
33 * Let A be a generic term for any 2D block cyclicly distributed array.
34 * Such a global array has an associated description vector DESCA.
35 * In the following comments, the character _ should be read as
36 * "of the global array".
37 *
38 * NOTATION STORED IN EXPLANATION
39 * --------------- -------------- --------------------------------------
40 * DTYPE_A(global) DESCA( DTYPE_ )The descriptor type. In this case,
41 * DTYPE_A = 1.
42 * CTXT_A (global) DESCA( CTXT_ ) The BLACS context handle, indicating
43 * the BLACS process grid A is distribu-
44 * ted over. The context itself is glo-
45 * bal, but the handle (the integer
46 * value) may vary.
47 * M_A (global) DESCA( M_ ) The number of rows in the global
48 * array A.
49 * N_A (global) DESCA( N_ ) The number of columns in the global
50 * array A.
51 * MB_A (global) DESCA( MB_ ) The blocking factor used to distribute
52 * the rows of the array.
53 * NB_A (global) DESCA( NB_ ) The blocking factor used to distribute
54 * the columns of the array.
55 * RSRC_A (global) DESCA( RSRC_ ) The process row over which the first
56 * row of the array A is distributed.
57 * CSRC_A (global) DESCA( CSRC_ ) The process column over which the
58 * first column of the array A is
59 * distributed.
60 * LLD_A (local) DESCA( LLD_ ) The leading dimension of the local
61 * array. LLD_A >= MAX(1,LOCr(M_A)).
62 *
63 * Let K be the number of rows or columns of a distributed matrix,
64 * and assume that its process grid has dimension p x q.
65 * LOCr( K ) denotes the number of elements of K that a process
66 * would receive if K were distributed over the p processes of its
67 * process column.
68 * Similarly, LOCc( K ) denotes the number of elements of K that a
69 * process would receive if K were distributed over the q processes of
70 * its process row.
71 * The values of LOCr() and LOCc() may be determined via a call to the
72 * ScaLAPACK tool function, NUMROC:
73 * LOCr( M ) = NUMROC( M, MB_A, MYROW, RSRC_A, NPROW ),
74 * LOCc( N ) = NUMROC( N, NB_A, MYCOL, CSRC_A, NPCOL ).
75 * An upper bound for these quantities may be computed by:
76 * LOCr( M ) <= ceil( ceil(M/MB_A)/NPROW )*MB_A
77 * LOCc( N ) <= ceil( ceil(N/NB_A)/NPCOL )*NB_A
78 *
79 * Arguments
80 * =========
81 *
82 * UPLO (global input) CHARACTER
83 * Specifies whether the upper or lower triangular part of the
84 * symmetric matrix sub( A ) is stored:
85 * = 'U': Upper triangular
86 * = 'L': Lower triangular
87 *
88 * N (global input) INTEGER
89 * The number of rows and columns to be operated on, i.e. the
90 * order of the distributed submatrix sub( A ). N >= 0.
91 *
92 * A (local input/local output) DOUBLE PRECISION pointer into the
93 * local memory to an array of dimension (LLD_A,LOCc(JA+N-1)).
94 * This array contains the local pieces of sub( A ). On entry,
95 * if UPLO='U', the diagonal and first superdiagonal of sub( A )
96 * have the corresponding elements of the tridiagonal matrix T,
97 * and the elements above the first superdiagonal, with the
98 * array TAU, represent the orthogonal matrix Q as a product of
99 * elementary reflectors, and the strictly lower triangular part
100 * of sub( A ) is not referenced. If UPLO='L', the diagonal and
101 * first subdiagonal of sub( A ) have the corresponding elements
102 * of the tridiagonal matrix T, and the elements below the first
103 * subdiagonal, with the array TAU, represent the orthogonal
104 * matrix Q as a product of elementary reflectors, and the
105 * strictly upper triangular part of sub( A ) is not referenced.
106 * On exit, if UPLO = 'U', the upper triangular part of the
107 * distributed symmetric matrix sub( A ) is recovered.
108 * If UPLO='L', the lower triangular part of the distributed
109 * symmetric matrix sub( A ) is recovered.
110 *
111 * IA (global input) INTEGER
112 * The row index in the global array A indicating the first
113 * row of sub( A ).
114 *
115 * JA (global input) INTEGER
116 * The column index in the global array A indicating the
117 * first column of sub( A ).
118 *
119 * DESCA (global and local input) INTEGER array of dimension DLEN_.
120 * The array descriptor for the distributed matrix A.
121 *
122 * D (local input) DOUBLE PRECISION array, dimension LOCc(JA+N-1)
123 * The diagonal elements of the tridiagonal matrix T:
124 * D(i) = A(i,i). D is tied to the distributed matrix A.
125 *
126 * E (local input) DOUBLE PRECISION array, dimension LOCc(JA+N-1)
127 * if UPLO = 'U', LOCc(JA+N-2) otherwise. The off-diagonal
128 * elements of the tridiagonal matrix T: E(i) = A(i,i+1) if
129 * UPLO = 'U', E(i) = A(i+1,i) if UPLO = 'L'. E is tied to the
130 * distributed matrix A.
131 *
132 * TAU (local input) DOUBLE PRECISION, array, dimension
133 * LOCc(JA+N-1). This array contains the scalar factors TAU of
134 * the elementary reflectors. TAU is tied to the distributed
135 * matrix A.
136 *
137 * WORK (local workspace) DOUBLE PRECISION array, dimension (LWORK)
138 * LWORK >= 2 * NB *( NB + NP )
139 *
140 * where NB = MB_A = NB_A,
141 * NP = NUMROC( N, NB, MYROW, IAROW, NPROW ),
142 * IAROW = INDXG2P( IA, NB, MYROW, RSRC_A, NPROW ).
143 *
144 * INDXG2P and NUMROC are ScaLAPACK tool functions;
145 * MYROW, MYCOL, NPROW and NPCOL can be determined by calling
146 * the subroutine BLACS_GRIDINFO.
147 *
148 * INFO (global output) INTEGER
149 * On exit, if INFO <> 0, a discrepancy has been found between
150 * the diagonal and off-diagonal elements of A and the copies
151 * contained in the arrays D and E.
152 *
153 * =====================================================================
154 *
155 * .. Parameters ..
156  INTEGER BLOCK_CYCLIC_2D, CSRC_, CTXT_, DLEN_, DTYPE_,
157  $ lld_, mb_, m_, nb_, n_, rsrc_
158  parameter( block_cyclic_2d = 1, dlen_ = 9, dtype_ = 1,
159  $ ctxt_ = 2, m_ = 3, n_ = 4, mb_ = 5, nb_ = 6,
160  $ rsrc_ = 7, csrc_ = 8, lld_ = 9 )
161  DOUBLE PRECISION EIGHT, HALF, ONE, ZERO
162  parameter( eight = 8.0d+0, half = 0.5d+0, one = 1.0d+0,
163  $ zero = 0.0d+0 )
164 * ..
165 * .. Local Scalars ..
166  LOGICAL UPPER
167  INTEGER I, IACOL, IAROW, ICTXT, II, IPT, IPV, IPX,
168  $ ipy, j, jb, jj, jl, k, mycol, myrow, nb, np,
169  $ npcol, nprow
170  DOUBLE PRECISION ADDBND, D1, D2, E1, E2
171 * ..
172 * .. Local Arrays ..
173  INTEGER DESCD( DLEN_ ), DESCE( DLEN_ ), DESCV( DLEN_ ),
174  $ desct( dlen_ )
175 * ..
176 * .. External Functions ..
177  LOGICAL LSAME
178  INTEGER INDXG2P, NUMROC
179  DOUBLE PRECISION PDLAMCH
180  EXTERNAL indxg2p, lsame, numroc, pdlamch
181 * ..
182 * .. External Subroutines ..
183  EXTERNAL blacs_gridinfo, descset, infog2l, igsum2d,
184  $ pdelget, pdgemm, pdlacpy,
185  $ pdlarft, pdlaset, pdsymm,
186  $ pdsyr2k, pdtrmm
187 * ..
188 * .. Intrinsic Functions ..
189  INTRINSIC abs, max, min, mod
190 * ..
191 * .. Executable statements ..
192 *
193  ictxt = desca( ctxt_ )
194  CALL blacs_gridinfo( ictxt, nprow, npcol, myrow, mycol )
195 *
196  info = 0
197  nb = desca( mb_ )
198  upper = lsame( uplo, 'U' )
199  CALL infog2l( ia, ja, desca, nprow, npcol, myrow, mycol, ii, jj,
200  $ iarow, iacol )
201  np = numroc( n, nb, myrow, iarow, nprow )
202 *
203  ipt = 1
204  ipv = nb * nb + ipt
205  ipx = nb * np + ipv
206  ipy = nb * np + ipx
207 *
208  CALL descset( descd, 1, ja+n-1, 1, desca( nb_ ), myrow,
209  $ desca( csrc_ ), desca( ctxt_ ), 1 )
210 *
211  addbnd = eight * pdlamch( ictxt, 'eps' )
212 *
213  IF( upper ) THEN
214 *
215  CALL descset( desce, 1, ja+n-1, 1, desca( nb_ ), myrow,
216  $ desca( csrc_ ), desca( ctxt_ ), 1 )
217 *
218  DO 10 j = 0, n-1
219  d1 = zero
220  e1 = zero
221  d2 = zero
222  e2 = zero
223  CALL pdelget( ' ', ' ', d2, d, 1, ja+j, descd )
224  CALL pdelget( 'Columnwise', ' ', d1, a, ia+j, ja+j, desca )
225  IF( j.LT.(n-1) ) THEN
226  CALL pdelget( ' ', ' ', e2, e, 1, ja+j+1, desce )
227  CALL pdelget( 'Columnwise', ' ', e1, a, ia+j, ja+j+1,
228  $ desca )
229  END IF
230 *
231  IF( ( abs( d1 - d2 ).GT.( abs( d2 ) * addbnd ) ) .OR.
232  $ ( abs( e1 - e2 ).GT.( abs( e2 ) * addbnd ) ) )
233  $ info = info + 1
234  10 CONTINUE
235 *
236 * Compute the upper triangle of sub( A ).
237 *
238  CALL descset( descv, n, nb, nb, nb, iarow, iacol, ictxt,
239  $ max( 1, np ) )
240  CALL descset( desct, nb, nb, nb, nb, iarow, iacol, ictxt, nb )
241 *
242  DO 20 k = 0, n-1, nb
243  jb = min( nb, n-k )
244  i = ia + k
245  j = ja + k
246 *
247 * Compute the lower triangular matrix T.
248 *
249  CALL pdlarft( 'Backward', 'Columnwise', k+jb-1, jb, a, ia,
250  $ j, desca, tau, work( ipt ), work( ipv ) )
251 *
252 * Copy Householder vectors into WORK( IPV ).
253 *
254  CALL pdlacpy( 'All', k+jb-1, jb, a, ia, j, desca,
255  $ work( ipv ), 1, 1, descv )
256 *
257  IF( k.GT.0 ) THEN
258  CALL pdlaset( 'Lower', jb+1, jb, zero, one, work( ipv ),
259  $ k, 1, descv )
260  ELSE
261  CALL pdlaset( 'Lower', jb, jb-1, zero, one, work( ipv ),
262  $ 1, 2, descv )
263  CALL pdlaset( 'Ge', jb, 1, zero, zero, work( ipv ), 1,
264  $ 1, descv )
265  END IF
266 *
267 * Zero out the strict upper triangular part of A.
268 *
269  IF( k.GT.0 ) THEN
270  CALL pdlaset( 'Ge', k-1, jb, zero, zero, a, ia, j,
271  $ desca )
272  CALL pdlaset( 'Upper', jb-1, jb-1, zero, zero, a, i-1,
273  $ j+1, desca )
274  ELSE IF( jb.GT.1 ) THEN
275  CALL pdlaset( 'Upper', jb-2, jb-2, zero, zero, a, ia,
276  $ j+2, desca )
277  END IF
278 *
279 * (1) X := A * V * T'
280 *
281  CALL pdsymm( 'Left', 'Upper', k+jb, jb, one, a, ia, ja,
282  $ desca, work( ipv ), 1, 1, descv, zero,
283  $ work( ipx ), 1, 1, descv )
284  CALL pdtrmm( 'Right', 'Lower', 'Transpose', 'Non-Unit',
285  $ k+jb, jb, one, work( ipt ), 1, 1, desct,
286  $ work( ipx ), 1, 1, descv )
287 *
288 * (2) X := X - 1/2 * V * (T * V' * X)
289 *
290  CALL pdgemm( 'Transpose', 'No transpose', jb, jb, k+jb, one,
291  $ work( ipv ), 1, 1, descv, work( ipx ), 1, 1,
292  $ descv, zero, work( ipy ), 1, 1, desct )
293  CALL pdtrmm( 'Left', 'Lower', 'No transpose', 'Non-Unit',
294  $ jb, jb, one, work( ipt ), 1, 1, desct,
295  $ work( ipy ), 1, 1, desct )
296  CALL pdgemm( 'No tranpose', 'No transpose', k+jb, jb, jb,
297  $ -half, work( ipv ), 1, 1, descv, work( ipy ),
298  $ 1, 1, desct, one, work( ipx ), 1, 1, descv )
299 *
300 * (3) A := A - X * V' - V * X'
301 *
302  CALL pdsyr2k( 'Upper', 'No transpose', k+jb, jb, -one,
303  $ work( ipv ), 1, 1, descv, work( ipx ), 1, 1,
304  $ descv, one, a, ia, ja, desca )
305 *
306  descv( csrc_ ) = mod( descv( csrc_ ) + 1, npcol )
307  desct( csrc_ ) = mod( desct( csrc_ ) + 1, npcol )
308 *
309  20 CONTINUE
310 *
311  ELSE
312 *
313  CALL descset( desce, 1, ja+n-2, 1, desca( nb_ ), myrow,
314  $ desca( csrc_ ), desca( ctxt_ ), 1 )
315 *
316  DO 30 j = 0, n-1
317  d1 = zero
318  e1 = zero
319  d2 = zero
320  e2 = zero
321  CALL pdelget( ' ', ' ', d2, d, 1, ja+j, descd )
322  CALL pdelget( 'Columnwise', ' ', d1, a, ia+j, ja+j, desca )
323  IF( j.LT.(n-1) ) THEN
324  CALL pdelget( ' ', ' ', e2, e, 1, ja+j, desce )
325  CALL pdelget( 'Columnwise', ' ', e1, a, ia+j+1, ja+j,
326  $ desca )
327  END IF
328 *
329  IF( ( abs( d1 - d2 ).GT.( abs( d2 ) * addbnd ) ) .OR.
330  $ ( abs( e1 - e2 ).GT.( abs( e2 ) * addbnd ) ) )
331  $ info = info + 1
332  30 CONTINUE
333 *
334 * Compute the lower triangle of sub( A ).
335 *
336  jl = max( ( ( ja+n-2 ) / nb ) * nb + 1, ja )
337  iacol = indxg2p( jl, nb, mycol, desca( csrc_ ), npcol )
338  CALL descset( descv, n, nb, nb, nb, iarow, iacol, ictxt,
339  $ max( 1, np ) )
340  CALL descset( desct, nb, nb, nb, nb, indxg2p( ia+jl-ja+1, nb,
341  $ myrow, desca( rsrc_ ), nprow ), iacol, ictxt,
342  $ nb )
343 *
344  DO 40 j = jl, ja, -nb
345  k = j - ja + 1
346  i = ia + k - 1
347  jb = min( n-k+1, nb )
348 *
349 * Compute upper triangular matrix T from TAU.
350 *
351  CALL pdlarft( 'Forward', 'Columnwise', n-k, jb, a, i+1, j,
352  $ desca, tau, work( ipt ), work( ipv ) )
353 *
354 * Copy Householder vectors into WORK( IPV ).
355 *
356  CALL pdlacpy( 'Lower', n-k, jb, a, i+1, j, desca,
357  $ work( ipv ), k+1, 1, descv )
358  CALL pdlaset( 'Upper', n-k, jb, zero, one, work( ipv ),
359  $ k+1, 1, descv )
360  CALL pdlaset( 'Ge', 1, jb, zero, zero, work( ipv ), k, 1,
361  $ descv )
362 *
363 * Zero out the strict lower triangular part of A.
364 *
365  CALL pdlaset( 'Lower', n-k-1, jb, zero, zero, a, i+2, j,
366  $ desca )
367 *
368 * (1) X := A * V * T'
369 *
370  CALL pdsymm( 'Left', 'Lower', n-k+1, jb, one, a, i, j,
371  $ desca, work( ipv ), k, 1, descv, zero,
372  $ work( ipx ), k, 1, descv )
373  CALL pdtrmm( 'Right', 'Upper', 'Transpose', 'Non-Unit',
374  $ n-k+1, jb, one, work( ipt ), 1, 1, desct,
375  $ work( ipx ), k, 1, descv )
376 *
377 * (2) X := X - 1/2 * V * (T * V' * X)
378 *
379  CALL pdgemm( 'Transpose', 'No transpose', jb, jb, n-k+1,
380  $ one, work( ipv ), k, 1, descv, work( ipx ),
381  $ k, 1, descv, zero, work( ipy ), 1, 1, desct )
382  CALL pdtrmm( 'Left', 'Upper', 'No transpose', 'Non-Unit',
383  $ jb, jb, one, work( ipt ), 1, 1, desct,
384  $ work( ipy ), 1, 1, desct )
385  CALL pdgemm( 'No transpose', 'No transpose', n-k+1, jb, jb,
386  $ -half, work( ipv ), k, 1, descv, work( ipy ),
387  $ 1, 1, desct, one, work( ipx ), k, 1, descv )
388 *
389 * (3) A := A - X * V' - V * X'
390 *
391  CALL pdsyr2k( 'Lower', 'No tranpose', n-k+1, jb, -one,
392  $ work( ipv ), k, 1, descv, work( ipx ), k, 1,
393  $ descv, one, a, i, j, desca )
394 *
395  descv( csrc_ ) = mod( descv( csrc_ ) + npcol - 1, npcol )
396  desct( rsrc_ ) = mod( desct( rsrc_ ) + nprow - 1, nprow )
397  desct( csrc_ ) = mod( desct( csrc_ ) + npcol - 1, npcol )
398 *
399  40 CONTINUE
400 *
401  END IF
402 *
403  CALL igsum2d( ictxt, 'All', ' ', 1, 1, info, 1, -1, 0 )
404 *
405  RETURN
406 *
407 * End of PDSYTDRV
408 *
409  END
max
#define max(A, B)
Definition: pcgemr.c:180
infog2l
subroutine infog2l(GRINDX, GCINDX, DESC, NPROW, NPCOL, MYROW, MYCOL, LRINDX, LCINDX, RSRC, CSRC)
Definition: infog2l.f:3
pdlarft
subroutine pdlarft(DIRECT, STOREV, N, K, V, IV, JV, DESCV, TAU, T, WORK)
Definition: pdlarft.f:3
pdelget
subroutine pdelget(SCOPE, TOP, ALPHA, A, IA, JA, DESCA)
Definition: pdelget.f:2
pdsytdrv
subroutine pdsytdrv(UPLO, N, A, IA, JA, DESCA, D, E, TAU, WORK, INFO)
Definition: pdsytdrv.f:3
descset
subroutine descset(DESC, M, N, MB, NB, IRSRC, ICSRC, ICTXT, LLD)
Definition: descset.f:3
pdlaset
subroutine pdlaset(UPLO, M, N, ALPHA, BETA, A, IA, JA, DESCA)
Definition: pdblastst.f:6862
pdlacpy
subroutine pdlacpy(UPLO, M, N, A, IA, JA, DESCA, B, IB, JB, DESCB)
Definition: pdlacpy.f:3
min
#define min(A, B)
Definition: pcgemr.c:181