ScaLAPACK 2.1  2.1 ScaLAPACK: Scalable Linear Algebra PACKage
psormtr.f
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1  SUBROUTINE psormtr( SIDE, UPLO, TRANS, M, N, A, IA, JA, DESCA,
2  \$ TAU, C, IC, JC, DESCC, WORK, LWORK, 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 SIDE, TRANS, UPLO
11  INTEGER IA, IC, INFO, JA, JC, LWORK, M, N
12 * ..
13 * .. Array Arguments ..
14  INTEGER DESCA( * ), DESCC( * )
15  REAL A( * ), C( * ), TAU( * ), WORK( * )
16 * ..
17 *
18 * Purpose
19 * =======
20 *
21 * PSORMTR overwrites the general real M-by-N distributed matrix
22 * sub( C ) = C(IC:IC+M-1,JC:JC+N-1) with
23 *
24 * SIDE = 'L' SIDE = 'R'
25 * TRANS = 'N': Q * sub( C ) sub( C ) * Q
26 * TRANS = 'T': Q**T * sub( C ) sub( C ) * Q**T
27 *
28 * where Q is a real orthogonal distributed matrix of order nq, with
29 * nq = m if SIDE = 'L' and nq = n if SIDE = 'R'. Q is defined as the
30 * product of nq-1 elementary reflectors, as returned by PSSYTRD:
31 *
32 * if UPLO = 'U', Q = H(nq-1) . . . H(2) H(1);
33 *
34 * if UPLO = 'L', Q = H(1) H(2) . . . H(nq-1).
35 *
36 * Notes
37 * =====
38 *
39 * Each global data object is described by an associated description
40 * vector. This vector stores the information required to establish
41 * the mapping between an object element and its corresponding process
42 * and memory location.
43 *
44 * Let A be a generic term for any 2D block cyclicly distributed array.
45 * Such a global array has an associated description vector DESCA.
46 * In the following comments, the character _ should be read as
47 * "of the global array".
48 *
49 * NOTATION STORED IN EXPLANATION
50 * --------------- -------------- --------------------------------------
51 * DTYPE_A(global) DESCA( DTYPE_ )The descriptor type. In this case,
52 * DTYPE_A = 1.
53 * CTXT_A (global) DESCA( CTXT_ ) The BLACS context handle, indicating
54 * the BLACS process grid A is distribu-
55 * ted over. The context itself is glo-
56 * bal, but the handle (the integer
57 * value) may vary.
58 * M_A (global) DESCA( M_ ) The number of rows in the global
59 * array A.
60 * N_A (global) DESCA( N_ ) The number of columns in the global
61 * array A.
62 * MB_A (global) DESCA( MB_ ) The blocking factor used to distribute
63 * the rows of the array.
64 * NB_A (global) DESCA( NB_ ) The blocking factor used to distribute
65 * the columns of the array.
66 * RSRC_A (global) DESCA( RSRC_ ) The process row over which the first
67 * row of the array A is distributed.
68 * CSRC_A (global) DESCA( CSRC_ ) The process column over which the
69 * first column of the array A is
70 * distributed.
71 * LLD_A (local) DESCA( LLD_ ) The leading dimension of the local
72 * array. LLD_A >= MAX(1,LOCr(M_A)).
73 *
74 * Let K be the number of rows or columns of a distributed matrix,
75 * and assume that its process grid has dimension p x q.
76 * LOCr( K ) denotes the number of elements of K that a process
77 * would receive if K were distributed over the p processes of its
78 * process column.
79 * Similarly, LOCc( K ) denotes the number of elements of K that a
80 * process would receive if K were distributed over the q processes of
81 * its process row.
82 * The values of LOCr() and LOCc() may be determined via a call to the
83 * ScaLAPACK tool function, NUMROC:
84 * LOCr( M ) = NUMROC( M, MB_A, MYROW, RSRC_A, NPROW ),
85 * LOCc( N ) = NUMROC( N, NB_A, MYCOL, CSRC_A, NPCOL ).
86 * An upper bound for these quantities may be computed by:
87 * LOCr( M ) <= ceil( ceil(M/MB_A)/NPROW )*MB_A
88 * LOCc( N ) <= ceil( ceil(N/NB_A)/NPCOL )*NB_A
89 *
90 * Arguments
91 * =========
92 *
93 * SIDE (global input) CHARACTER
94 * = 'L': apply Q or Q**T from the Left;
95 * = 'R': apply Q or Q**T from the Right.
96 *
97 * UPLO (global input) CHARACTER
98 * = 'U': Upper triangle of A(IA:*,JA:*) contains elementary
99 * reflectors from PSSYTRD;
100 * = 'L': Lower triangle of A(IA:*,JA:*) contains elementary
101 * reflectors from PSSYTRD.
102 *
103 * TRANS (global input) CHARACTER
104 * = 'N': No transpose, apply Q;
105 * = 'T': Transpose, apply Q**T.
106 *
107 * M (global input) INTEGER
108 * The number of rows to be operated on i.e the number of rows
109 * of the distributed submatrix sub( C ). M >= 0.
110 *
111 * N (global input) INTEGER
112 * The number of columns to be operated on i.e the number of
113 * columns of the distributed submatrix sub( C ). N >= 0.
114 *
115 * A (local input) REAL pointer into the local memory
116 * to an array of dimension (LLD_A,LOCc(JA+M-1)) if SIDE='L',
117 * or (LLD_A,LOCc(JA+N-1)) if SIDE = 'R'. The vectors which
118 * define the elementary reflectors, as returned by PSSYTRD.
119 * If SIDE = 'L', LLD_A >= max(1,LOCr(IA+M-1));
120 * if SIDE = 'R', LLD_A >= max(1,LOCr(IA+N-1)).
121 *
122 * IA (global input) INTEGER
123 * The row index in the global array A indicating the first
124 * row of sub( A ).
125 *
126 * JA (global input) INTEGER
127 * The column index in the global array A indicating the
128 * first column of sub( A ).
129 *
130 * DESCA (global and local input) INTEGER array of dimension DLEN_.
131 * The array descriptor for the distributed matrix A.
132 *
133 * TAU (local input) REAL array, dimension LTAU, where
134 * if SIDE = 'L' and UPLO = 'U', LTAU = LOCc(M_A),
135 * if SIDE = 'L' and UPLO = 'L', LTAU = LOCc(JA+M-2),
136 * if SIDE = 'R' and UPLO = 'U', LTAU = LOCc(N_A),
137 * if SIDE = 'R' and UPLO = 'L', LTAU = LOCc(JA+N-2).
138 * TAU(i) must contain the scalar factor of the elementary
139 * reflector H(i), as returned by PSSYTRD. TAU is tied to the
140 * distributed matrix A.
141 *
142 * C (local input/local output) REAL pointer into the
143 * local memory to an array of dimension (LLD_C,LOCc(JC+N-1)).
144 * On entry, the local pieces of the distributed matrix sub(C).
145 * On exit, sub( C ) is overwritten by Q*sub( C ) or Q'*sub( C )
146 * or sub( C )*Q' or sub( C )*Q.
147 *
148 * IC (global input) INTEGER
149 * The row index in the global array C indicating the first
150 * row of sub( C ).
151 *
152 * JC (global input) INTEGER
153 * The column index in the global array C indicating the
154 * first column of sub( C ).
155 *
156 * DESCC (global and local input) INTEGER array of dimension DLEN_.
157 * The array descriptor for the distributed matrix C.
158 *
159 * WORK (local workspace/local output) REAL array,
160 * dimension (LWORK)
161 * On exit, WORK(1) returns the minimal and optimal LWORK.
162 *
163 * LWORK (local or global input) INTEGER
164 * The dimension of the array WORK.
165 * LWORK is local input and must be at least
166 *
167 * If UPLO = 'U',
168 * IAA = IA, JAA = JA+1, ICC = IC, JCC = JC;
169 * else UPLO = 'L',
170 * IAA = IA+1, JAA = JA;
171 * if SIDE = 'L',
172 * ICC = IC+1; JCC = JC;
173 * else
174 * ICC = IC; JCC = JC+1;
175 * end if
176 * end if
177 *
178 * If SIDE = 'L',
179 * MI = M-1; NI = N;
180 * LWORK >= MAX( (NB_A*(NB_A-1))/2, (NqC0 + MpC0)*NB_A ) +
181 * NB_A * NB_A
182 * else if SIDE = 'R',
183 * MI = M; MI = N-1;
184 * LWORK >= MAX( (NB_A*(NB_A-1))/2, ( NqC0 + MAX( NpA0 +
185 * NUMROC( NUMROC( NI+ICOFFC, NB_A, 0, 0, NPCOL ),
186 * NB_A, 0, 0, LCMQ ), MpC0 ) )*NB_A ) +
187 * NB_A * NB_A
188 * end if
189 *
190 * where LCMQ = LCM / NPCOL with LCM = ICLM( NPROW, NPCOL ),
191 *
192 * IROFFA = MOD( IAA-1, MB_A ), ICOFFA = MOD( JAA-1, NB_A ),
193 * IAROW = INDXG2P( IAA, MB_A, MYROW, RSRC_A, NPROW ),
194 * NpA0 = NUMROC( NI+IROFFA, MB_A, MYROW, IAROW, NPROW ),
195 *
196 * IROFFC = MOD( ICC-1, MB_C ), ICOFFC = MOD( JCC-1, NB_C ),
197 * ICROW = INDXG2P( ICC, MB_C, MYROW, RSRC_C, NPROW ),
198 * ICCOL = INDXG2P( JCC, NB_C, MYCOL, CSRC_C, NPCOL ),
199 * MpC0 = NUMROC( MI+IROFFC, MB_C, MYROW, ICROW, NPROW ),
200 * NqC0 = NUMROC( NI+ICOFFC, NB_C, MYCOL, ICCOL, NPCOL ),
201 *
202 * ILCM, INDXG2P and NUMROC are ScaLAPACK tool functions;
203 * MYROW, MYCOL, NPROW and NPCOL can be determined by calling
204 * the subroutine BLACS_GRIDINFO.
205 *
206 * If LWORK = -1, then LWORK is global input and a workspace
207 * query is assumed; the routine only calculates the minimum
208 * and optimal size for all work arrays. Each of these
209 * values is returned in the first entry of the corresponding
210 * work array, and no error message is issued by PXERBLA.
211 *
212 *
213 * INFO (global output) INTEGER
214 * = 0: successful exit
215 * < 0: If the i-th argument is an array and the j-entry had
216 * an illegal value, then INFO = -(i*100+j), if the i-th
217 * argument is a scalar and had an illegal value, then
218 * INFO = -i.
219 *
220 * Alignment requirements
221 * ======================
222 *
223 * The distributed submatrices A(IA:*, JA:*) and C(IC:IC+M-1,JC:JC+N-1)
224 * must verify some alignment properties, namely the following
225 * expressions should be true:
226 *
227 * If SIDE = 'L',
228 * ( MB_A.EQ.MB_C .AND. IROFFA.EQ.IROFFC .AND. IAROW.EQ.ICROW )
229 * If SIDE = 'R',
230 * ( MB_A.EQ.NB_C .AND. IROFFA.EQ.ICOFFC )
231 *
232 * =====================================================================
233 *
234 * .. Parameters ..
235  INTEGER BLOCK_CYCLIC_2D, CSRC_, CTXT_, DLEN_, DTYPE_,
236  \$ lld_, mb_, m_, nb_, n_, rsrc_
237  parameter( block_cyclic_2d = 1, dlen_ = 9, dtype_ = 1,
238  \$ ctxt_ = 2, m_ = 3, n_ = 4, mb_ = 5, nb_ = 6,
239  \$ rsrc_ = 7, csrc_ = 8, lld_ = 9 )
240 * ..
241 * .. Local Scalars ..
242  LOGICAL LEFT, LQUERY, NOTRAN, UPPER
243  INTEGER IAA, IAROW, ICC, ICCOL, ICOFFC, ICROW, ICTXT,
244  \$ iinfo, iroffa, iroffc, jaa, jcc, lcm, lcmq,
245  \$ lwmin, mi, mpc0, mycol, myrow, ni, npa0, npcol,
246  \$ nprow, nq, nqc0
247 * ..
248 * .. Local Arrays ..
249  INTEGER IDUM1( 4 ), IDUM2( 4 )
250 * ..
251 * .. External Subroutines ..
252  EXTERNAL blacs_gridinfo, chk1mat, pchk2mat, psormql,
253  \$ psormqr, pxerbla
254 * ..
255 * .. External Functions ..
256  LOGICAL LSAME
257  INTEGER ILCM, INDXG2P, NUMROC
258  EXTERNAL ilcm, indxg2p, lsame, numroc
259 * ..
260 * .. Intrinsic Functions ..
261  INTRINSIC ichar, max, mod, real
262 * ..
263 * .. Executable Statements ..
264 *
265 * Get grid parameters
266 *
267  ictxt = desca( ctxt_ )
268  CALL blacs_gridinfo( ictxt, nprow, npcol, myrow, mycol )
269 *
270 * Test the input parameters
271 *
272  info = 0
273  IF( nprow.EQ.-1 ) THEN
274  info = -(900+ctxt_)
275  ELSE
276  left = lsame( side, 'L' )
277  notran = lsame( trans, 'N' )
278  upper = lsame( uplo, 'U' )
279 *
280  IF( upper ) THEN
281  iaa = ia
282  jaa = ja+1
283  icc = ic
284  jcc = jc
285  ELSE
286  iaa = ia+1
287  jaa = ja
288  IF( left ) THEN
289  icc = ic + 1
290  jcc = jc
291  ELSE
292  icc = ic
293  jcc = jc + 1
294  END IF
295  END IF
296 *
297 * NQ is the order of Q
298 *
299  IF( left ) THEN
300  nq = m
301  mi = m - 1
302  ni = n
303  CALL chk1mat( mi, 4, nq-1, 4, iaa, jaa, desca, 9, info )
304  ELSE
305  nq = n
306  mi = m
307  ni = n - 1
308  CALL chk1mat( ni, 5, nq-1, 5, iaa, jaa, desca, 9, info )
309  END IF
310  CALL chk1mat( mi, 4, ni, 5, icc, jcc, descc, 14, info )
311  IF( info.EQ.0 ) THEN
312  iroffa = mod( iaa-1, desca( mb_ ) )
313  iroffc = mod( icc-1, descc( mb_ ) )
314  icoffc = mod( jcc-1, descc( nb_ ) )
315  iarow = indxg2p( iaa, desca( mb_ ), myrow, desca( rsrc_ ),
316  \$ nprow )
317  icrow = indxg2p( icc, descc( mb_ ), myrow, descc( rsrc_ ),
318  \$ nprow )
319  iccol = indxg2p( jcc, descc( nb_ ), mycol, descc( csrc_ ),
320  \$ npcol )
321  mpc0 = numroc( mi+iroffc, descc( mb_ ), myrow, icrow,
322  \$ nprow )
323  nqc0 = numroc( ni+icoffc, descc( nb_ ), mycol, iccol,
324  \$ npcol )
325 *
326  IF( left ) THEN
327  lwmin = max( ( desca( nb_ ) * ( desca( nb_ ) - 1 ) ) / 2,
328  \$ ( mpc0 + nqc0 ) * desca( nb_ ) ) +
329  \$ desca( nb_ ) * desca( nb_ )
330  ELSE
331  npa0 = numroc( ni+iroffa, desca( mb_ ), myrow, iarow,
332  \$ nprow )
333  lcm = ilcm( nprow, npcol )
334  lcmq = lcm / npcol
335  lwmin = max( ( desca( nb_ ) * ( desca( nb_ ) - 1 ) )
336  \$ / 2, ( nqc0 + max( npa0 + numroc( numroc(
337  \$ ni+icoffc, desca( nb_ ), 0, 0, npcol ),
338  \$ desca( nb_ ), 0, 0, lcmq ), mpc0 ) ) *
339  \$ desca( nb_ ) ) + desca( nb_ ) * desca( nb_ )
340  END IF
341 *
342  work( 1 ) = real( lwmin )
343  lquery = ( lwork.EQ.-1 )
344  IF( .NOT.left .AND. .NOT.lsame( side, 'R' ) ) THEN
345  info = -1
346  ELSE IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
347  info = -2
348  ELSE IF( .NOT.lsame( trans, 'N' ) .AND.
349  \$ .NOT.lsame( trans, 'T' ) ) THEN
350  info = -3
351  ELSE IF( .NOT.left .AND. desca( mb_ ).NE.descc( nb_ ) ) THEN
352  info = -(900+nb_)
353  ELSE IF( left .AND. iroffa.NE.iroffc ) THEN
354  info = -12
355  ELSE IF( left .AND. iarow.NE.icrow ) THEN
356  info = -12
357  ELSE IF( .NOT.left .AND. iroffa.NE.icoffc ) THEN
358  info = -13
359  ELSE IF( left .AND. desca( mb_ ).NE.descc( mb_ ) ) THEN
360  info = -(1400+mb_)
361  ELSE IF( ictxt.NE.descc( ctxt_ ) ) THEN
362  info = -(1400+ctxt_)
363  ELSE IF( lwork.LT.lwmin .AND. .NOT.lquery ) THEN
364  info = -16
365  END IF
366  END IF
367 *
368  IF( left ) THEN
369  idum1( 1 ) = ichar( 'L' )
370  ELSE
371  idum1( 1 ) = ichar( 'R' )
372  END IF
373  idum2( 1 ) = 1
374  IF( upper ) THEN
375  idum1( 2 ) = ichar( 'U' )
376  ELSE
377  idum1( 2 ) = ichar( 'L' )
378  END IF
379  idum2( 2 ) = 2
380  IF( notran ) THEN
381  idum1( 3 ) = ichar( 'N' )
382  ELSE
383  idum1( 3 ) = ichar( 'T' )
384  END IF
385  idum2( 3 ) = 3
386  IF( lwork.EQ.-1 ) THEN
387  idum1( 4 ) = -1
388  ELSE
389  idum1( 4 ) = 1
390  END IF
391  idum2( 4 ) = 16
392  IF( left ) THEN
393  CALL pchk2mat( mi, 4, nq-1, 4, iaa, jaa, desca, 9, mi, 4,
394  \$ ni, 5, icc, jcc, descc, 14, 4, idum1, idum2,
395  \$ info )
396  ELSE
397  CALL pchk2mat( ni, 5, nq-1, 5, iaa, jaa, desca, 9, mi, 4,
398  \$ ni, 5, icc, jcc, descc, 14, 4, idum1, idum2,
399  \$ info )
400  END IF
401  END IF
402 *
403  IF( info.NE.0 ) THEN
404  CALL pxerbla( ictxt, 'PSORMTR', -info )
405  RETURN
406  ELSE IF( lquery ) THEN
407  RETURN
408  END IF
409 *
410 * Quick return if possible
411 *
412  IF( m.EQ.0 .OR. n.EQ.0 .OR. nq.EQ.1 )
413  \$ RETURN
414 *
415  IF( upper ) THEN
416 *
417 * Q was determined by a call to PSSYTRD with UPLO = 'U'
418 *
419  CALL psormql( side, trans, mi, ni, nq-1, a, iaa, jaa, desca,
420  \$ tau, c, icc, jcc, descc, work, lwork, iinfo )
421 *
422  ELSE
423 *
424 * Q was determined by a call to PSSYTRD with UPLO = 'L'
425 *
426  CALL psormqr( side, trans, mi, ni, nq-1, a, iaa, jaa, desca,
427  \$ tau, c, icc, jcc, descc, work, lwork, iinfo )
428 *
429  END IF
430 *
431  work( 1 ) = real( lwmin )
432 *
433  RETURN
434 *
435 * End of PSORMTR
436 *
437  END
max
#define max(A, B)
Definition: pcgemr.c:180
psormqr
subroutine psormqr(SIDE, TRANS, M, N, K, A, IA, JA, DESCA, TAU, C, IC, JC, DESCC, WORK, LWORK, INFO)
Definition: psormqr.f:3
pchk2mat
subroutine pchk2mat(MA, MAPOS0, NA, NAPOS0, IA, JA, DESCA, DESCAPOS0, MB, MBPOS0, NB, NBPOS0, IB, JB, DESCB, DESCBPOS0, NEXTRA, EX, EXPOS, INFO)
Definition: pchkxmat.f:175
psormtr
subroutine psormtr(SIDE, UPLO, TRANS, M, N, A, IA, JA, DESCA, TAU, C, IC, JC, DESCC, WORK, LWORK, INFO)
Definition: psormtr.f:3
psormql
subroutine psormql(SIDE, TRANS, M, N, K, A, IA, JA, DESCA, TAU, C, IC, JC, DESCC, WORK, LWORK, INFO)
Definition: psormql.f:3
chk1mat
subroutine chk1mat(MA, MAPOS0, NA, NAPOS0, IA, JA, DESCA, DESCAPOS0, INFO)
Definition: chk1mat.f:3
pxerbla
subroutine pxerbla(ICTXT, SRNAME, INFO)
Definition: pxerbla.f:2