1 SUBROUTINE PDSYNTRD( UPLO, N, A, IA, JA, DESCA, D, E, TAU, WORK, 2 $ 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 25, 2001 8* 9* .. Scalar Arguments .. 10 CHARACTER UPLO 11 INTEGER IA, INFO, JA, LWORK, N 12* .. 13* .. Array Arguments .. 14 INTEGER DESCA( * ) 15 DOUBLE PRECISION A( * ), D( * ), E( * ), TAU( * ), WORK( * ) 16* .. 17* Bugs 18* ==== 19* 20* 21* Support for UPLO='U' is limited to calling the old, slow, PDSYTRD 22* code. 23* 24* 25* Purpose 26* 27* ======= 28* 29* PDSYNTRD is a prototype version of PDSYTRD which uses tailored 30* codes (either the serial, DSYTRD, or the parallel code, PDSYTTRD) 31* when the workspace provided by the user is adequate. 32* 33* 34* PDSYNTRD reduces a real symmetric matrix sub( A ) to symmetric 35* tridiagonal form T by an orthogonal similarity transformation: 36* Q' * sub( A ) * Q = T, where sub( A ) = A(IA:IA+N-1,JA:JA+N-1). 37* 38* Features 39* ======== 40* 41* PDSYNTRD is faster than PDSYTRD on almost all matrices, 42* particularly small ones (i.e. N < 500 * sqrt(P) ), provided that 43* enough workspace is available to use the tailored codes. 44* 45* The tailored codes provide performance that is essentially 46* independent of the input data layout. 47* 48* The tailored codes place no restrictions on IA, JA, MB or NB. 49* At present, IA, JA, MB and NB are restricted to those values allowed 50* by PDSYTRD to keep the interface simple. These restrictions are 51* documented below. (Search for "restrictions".) 52* 53* Notes 54* ===== 55* 56* 57* Each global data object is described by an associated description 58* vector. This vector stores the information required to establish 59* the mapping between an object element and its corresponding process 60* and memory location. 61* 62* Let A be a generic term for any 2D block cyclicly distributed array. 63* Such a global array has an associated description vector DESCA. 64* In the following comments, the character _ should be read as 65* "of the global array". 66* 67* NOTATION STORED IN EXPLANATION 68* --------------- -------------- -------------------------------------- 69* DTYPE_A(global) DESCA( DTYPE_ )The descriptor type. In this case, 70* DTYPE_A = 1. 71* CTXT_A (global) DESCA( CTXT_ ) The BLACS context handle, indicating 72* the BLACS process grid A is distribu- 73* ted over. The context itself is glo- 74* bal, but the handle (the integer 75* value) may vary. 76* M_A (global) DESCA( M_ ) The number of rows in the global 77* array A. 78* N_A (global) DESCA( N_ ) The number of columns in the global 79* array A. 80* MB_A (global) DESCA( MB_ ) The blocking factor used to distribute 81* the rows of the array. 82* NB_A (global) DESCA( NB_ ) The blocking factor used to distribute 83* the columns of the array. 84* RSRC_A (global) DESCA( RSRC_ ) The process row over which the first 85* row of the array A is distributed. 86* CSRC_A (global) DESCA( CSRC_ ) The process column over which the 87* first column of the array A is 88* distributed. 89* LLD_A (local) DESCA( LLD_ ) The leading dimension of the local 90* array. LLD_A >= MAX(1,LOCr(M_A)). 91* 92* Let K be the number of rows or columns of a distributed matrix, 93* and assume that its process grid has dimension p x q. 94* LOCr( K ) denotes the number of elements of K that a process 95* would receive if K were distributed over the p processes of its 96* process column. 97* Similarly, LOCc( K ) denotes the number of elements of K that a 98* process would receive if K were distributed over the q processes of 99* its process row. 100* The values of LOCr() and LOCc() may be determined via a call to the 101* ScaLAPACK tool function, NUMROC: 102* LOCr( M ) = NUMROC( M, MB_A, MYROW, RSRC_A, NPROW ), 103* LOCc( N ) = NUMROC( N, NB_A, MYCOL, CSRC_A, NPCOL ). 104* An upper bound for these quantities may be computed by: 105* LOCr( M ) <= ceil( ceil(M/MB_A)/NPROW )*MB_A 106* LOCc( N ) <= ceil( ceil(N/NB_A)/NPCOL )*NB_A 107* 108* 109* Arguments 110* ========= 111* 112* UPLO (global input) CHARACTER 113* Specifies whether the upper or lower triangular part of the 114* symmetric matrix sub( A ) is stored: 115* = 'U': Upper triangular 116* = 'L': Lower triangular 117* 118* N (global input) INTEGER 119* The number of rows and columns to be operated on, i.e. the 120* order of the distributed submatrix sub( A ). N >= 0. 121* 122* A (local input/local output) DOUBLE PRECISION pointer into the 123* local memory to an array of dimension (LLD_A,LOCc(JA+N-1)). 124* On entry, this array contains the local pieces of the 125* symmetric distributed matrix sub( A ). If UPLO = 'U', the 126* leading N-by-N upper triangular part of sub( A ) contains 127* the upper triangular part of the matrix, and its strictly 128* lower triangular part is not referenced. If UPLO = 'L', the 129* leading N-by-N lower triangular part of sub( A ) contains the 130* lower triangular part of the matrix, and its strictly upper 131* triangular part is not referenced. On exit, if UPLO = 'U', 132* the diagonal and first superdiagonal of sub( A ) are over- 133* written by the corresponding elements of the tridiagonal 134* matrix T, and the elements above the first superdiagonal, 135* with the array TAU, represent the orthogonal matrix Q as a 136* product of elementary reflectors; if UPLO = 'L', the diagonal 137* and first subdiagonal of sub( A ) are overwritten by the 138* corresponding elements of the tridiagonal matrix T, and the 139* elements below the first subdiagonal, with the array TAU, 140* represent the orthogonal matrix Q as a product of elementary 141* reflectors. See Further Details. 142* 143* IA (global input) INTEGER 144* The row index in the global array A indicating the first 145* row of sub( A ). 146* 147* JA (global input) INTEGER 148* The column index in the global array A indicating the 149* first column of sub( A ). 150* 151* DESCA (global and local input) INTEGER array of dimension DLEN_. 152* The array descriptor for the distributed matrix A. 153* 154* D (local output) DOUBLE PRECISION array, dimension LOCc(JA+N-1) 155* The diagonal elements of the tridiagonal matrix T: 156* D(i) = A(i,i). D is tied to the distributed matrix A. 157* 158* E (local output) DOUBLE PRECISION array, dimension LOCc(JA+N-1) 159* if UPLO = 'U', LOCc(JA+N-2) otherwise. The off-diagonal 160* elements of the tridiagonal matrix T: E(i) = A(i,i+1) if 161* UPLO = 'U', E(i) = A(i+1,i) if UPLO = 'L'. E is tied to the 162* distributed matrix A. 163* 164* TAU (local output) DOUBLE PRECISION array, dimension 165* LOCc(JA+N-1). This array contains the scalar factors TAU of 166* the elementary reflectors. TAU is tied to the distributed 167* matrix A. 168* 169* WORK (local workspace/local output) DOUBLE PRECISION array, 170* dimension (LWORK) 171* On exit, WORK( 1 ) returns the optimal LWORK. 172* 173* LWORK (local or global input) INTEGER 174* The dimension of the array WORK. 175* LWORK is local input and must be at least 176* LWORK >= MAX( NB * ( NP +1 ), 3 * NB ) 177* 178* For optimal performance, greater workspace is needed, i.e. 179* LWORK >= 2*( ANB+1 )*( 4*NPS+2 ) + ( NPS + 4 ) * NPS 180* ICTXT = DESCA( CTXT_ ) 181* ANB = PJLAENV( ICTXT, 3, 'PDSYTTRD', 'L', 0, 0, 0, 0 ) 182* SQNPC = INT( SQRT( DBLE( NPROW * NPCOL ) ) ) 183* NPS = MAX( NUMROC( N, 1, 0, 0, SQNPC ), 2*ANB ) 184* 185* NUMROC is a ScaLAPACK tool functions; 186* PJLAENV is a ScaLAPACK envionmental inquiry function 187* MYROW, MYCOL, NPROW and NPCOL can be determined by calling 188* the subroutine BLACS_GRIDINFO. 189* 190* 191* INFO (global output) INTEGER 192* = 0: successful exit 193* < 0: If the i-th argument is an array and the j-entry had 194* an illegal value, then INFO = -(i*100+j), if the i-th 195* argument is a scalar and had an illegal value, then 196* INFO = -i. 197* 198* Further Details 199* =============== 200* 201* If UPLO = 'U', the matrix Q is represented as a product of elementary 202* reflectors 203* 204* Q = H(n-1) . . . H(2) H(1). 205* 206* Each H(i) has the form 207* 208* H(i) = I - tau * v * v' 209* 210* where tau is a real scalar, and v is a real vector with 211* v(i+1:n) = 0 and v(i) = 1; v(1:i-1) is stored on exit in 212* A(ia:ia+i-2,ja+i), and tau in TAU(ja+i-1). 213* 214* If UPLO = 'L', the matrix Q is represented as a product of elementary 215* reflectors 216* 217* Q = H(1) H(2) . . . H(n-1). 218* 219* Each H(i) has the form 220* 221* H(i) = I - tau * v * v' 222* 223* where tau is a real scalar, and v is a real vector with 224* v(1:i) = 0 and v(i+1) = 1; v(i+2:n) is stored on exit in 225* A(ia+i+1:ia+n-1,ja+i-1), and tau in TAU(ja+i-1). 226* 227* The contents of sub( A ) on exit are illustrated by the following 228* examples with n = 5: 229* 230* if UPLO = 'U': if UPLO = 'L': 231* 232* ( d e v2 v3 v4 ) ( d ) 233* ( d e v3 v4 ) ( e d ) 234* ( d e v4 ) ( v1 e d ) 235* ( d e ) ( v1 v2 e d ) 236* ( d ) ( v1 v2 v3 e d ) 237* 238* where d and e denote diagonal and off-diagonal elements of T, and vi 239* denotes an element of the vector defining H(i). 240* 241* Alignment requirements 242* ====================== 243* 244* The distributed submatrix sub( A ) must verify some alignment proper- 245* ties, namely the following expression should be true: 246* ( MB_A.EQ.NB_A .AND. IROFFA.EQ.ICOFFA .AND. IROFFA.EQ.0 ) with 247* IROFFA = MOD( IA-1, MB_A ) and ICOFFA = MOD( JA-1, NB_A ). 248* 249* ===================================================================== 250* 251* .. Parameters .. 252 INTEGER BLOCK_CYCLIC_2D, DLEN_, DTYPE_, CTXT_, M_, N_, 253 $ MB_, NB_, RSRC_, CSRC_, LLD_ 254 PARAMETER ( BLOCK_CYCLIC_2D = 1, DLEN_ = 9, DTYPE_ = 1, 255 $ CTXT_ = 2, M_ = 3, N_ = 4, MB_ = 5, NB_ = 6, 256 $ RSRC_ = 7, CSRC_ = 8, LLD_ = 9 ) 257 DOUBLE PRECISION ONE 258 PARAMETER ( ONE = 1.0D+0 ) 259* .. 260* .. Local Scalars .. 261 LOGICAL LQUERY, UPPER 262 CHARACTER COLCTOP, ROWCTOP 263 INTEGER ANB, CTXTB, I, IACOL, IAROW, ICOFFA, ICTXT, 264 $ IINFO, INDB, INDD, INDE, INDTAU, INDW, IPW, 265 $ IROFFA, J, JB, JX, K, KK, LLWORK, LWMIN, MINSZ, 266 $ MYCOL, MYCOLB, MYROW, MYROWB, NB, NP, NPCOL, 267 $ NPCOLB, NPROW, NPROWB, NPS, NQ, ONEPMIN, SQNPC, 268 $ TTLWMIN 269* .. 270* .. Local Arrays .. 271 INTEGER DESCB( DLEN_ ), DESCW( DLEN_ ), IDUM1( 2 ), 272 $ IDUM2( 2 ) 273* .. 274* .. External Subroutines .. 275 EXTERNAL BLACS_GET, BLACS_GRIDEXIT, BLACS_GRIDINFO, 276 $ BLACS_GRIDINIT, CHK1MAT, DESCSET, DSYTRD, 277 $ IGAMN2D, PCHK1MAT, PDELSET, PDLAMR1D, PDLATRD, 278 $ PDSYR2K, PDSYTD2, PDSYTTRD, PDTRMR2D, 279 $ PB_TOPGET, PB_TOPSET, PXERBLA 280* .. 281* .. External Functions .. 282 LOGICAL LSAME 283 INTEGER INDXG2L, INDXG2P, NUMROC, PJLAENV 284 EXTERNAL LSAME, INDXG2L, INDXG2P, NUMROC, PJLAENV 285* .. 286* .. Intrinsic Functions .. 287 INTRINSIC DBLE, ICHAR, INT, MAX, MIN, MOD, SQRT 288* .. 289* .. Executable Statements .. 290* 291* This is just to keep ftnchek and toolpack/1 happy 292 IF( BLOCK_CYCLIC_2D*CSRC_*CTXT_*DLEN_*DTYPE_*LLD_*MB_*M_*NB_*N_* 293 $ RSRC_.LT.0 )RETURN 294* Get grid parameters 295* 296 ICTXT = DESCA( CTXT_ ) 297 CALL BLACS_GRIDINFO( ICTXT, NPROW, NPCOL, MYROW, MYCOL ) 298* 299* Test the input parameters 300* 301 INFO = 0 302 IF( NPROW.EQ.-1 ) THEN 303 INFO = -( 600+CTXT_ ) 304 ELSE 305 CALL CHK1MAT( N, 2, N, 2, IA, JA, DESCA, 6, INFO ) 306 UPPER = LSAME( UPLO, 'U' ) 307 IF( INFO.EQ.0 ) THEN 308 NB = DESCA( NB_ ) 309 IROFFA = MOD( IA-1, DESCA( MB_ ) ) 310 ICOFFA = MOD( JA-1, DESCA( NB_ ) ) 311 IAROW = INDXG2P( IA, NB, MYROW, DESCA( RSRC_ ), NPROW ) 312 IACOL = INDXG2P( JA, NB, MYCOL, DESCA( CSRC_ ), NPCOL ) 313 NP = NUMROC( N, NB, MYROW, IAROW, NPROW ) 314 NQ = MAX( 1, NUMROC( N+JA-1, NB, MYCOL, DESCA( CSRC_ ), 315 $ NPCOL ) ) 316 LWMIN = MAX( ( NP+1 )*NB, 3*NB ) 317 ANB = PJLAENV( ICTXT, 3, 'PDSYTTRD', 'L', 0, 0, 0, 0 ) 318 MINSZ = PJLAENV( ICTXT, 5, 'PDSYTTRD', 'L', 0, 0, 0, 0 ) 319 SQNPC = INT( SQRT( DBLE( NPROW*NPCOL ) ) ) 320 NPS = MAX( NUMROC( N, 1, 0, 0, SQNPC ), 2*ANB ) 321 TTLWMIN = 2*( ANB+1 )*( 4*NPS+2 ) + ( NPS+4 )*NPS 322* 323 WORK( 1 ) = DBLE( TTLWMIN ) 324 LQUERY = ( LWORK.EQ.-1 ) 325 IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN 326 INFO = -1 327* 328* The following two restrictions are not necessary provided 329* that either of the tailored codes are used. 330* 331 ELSE IF( IROFFA.NE.ICOFFA .OR. ICOFFA.NE.0 ) THEN 332 INFO = -5 333 ELSE IF( DESCA( MB_ ).NE.DESCA( NB_ ) ) THEN 334 INFO = -( 600+NB_ ) 335 ELSE IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN 336 INFO = -11 337 END IF 338 END IF 339 IF( UPPER ) THEN 340 IDUM1( 1 ) = ICHAR( 'U' ) 341 ELSE 342 IDUM1( 1 ) = ICHAR( 'L' ) 343 END IF 344 IDUM2( 1 ) = 1 345 IF( LWORK.EQ.-1 ) THEN 346 IDUM1( 2 ) = -1 347 ELSE 348 IDUM1( 2 ) = 1 349 END IF 350 IDUM2( 2 ) = 11 351 CALL PCHK1MAT( N, 2, N, 2, IA, JA, DESCA, 6, 2, IDUM1, IDUM2, 352 $ INFO ) 353 END IF 354* 355 IF( INFO.NE.0 ) THEN 356 CALL PXERBLA( ICTXT, 'PDSYNTRD', -INFO ) 357 RETURN 358 ELSE IF( LQUERY ) THEN 359 RETURN 360 END IF 361* 362* Quick return if possible 363* 364 IF( N.EQ.0 ) 365 $ RETURN 366* 367* 368 ONEPMIN = N*N + 3*N + 1 369 LLWORK = LWORK 370 CALL IGAMN2D( ICTXT, 'A', ' ', 1, 1, LLWORK, 1, 1, -1, -1, -1, 371 $ -1 ) 372* 373* 374* 375* Use the serial, LAPACK, code: DTRD on small matrices if we 376* we have enough space. 377* 378 NPROWB = 0 379 IF( ( N.LT.MINSZ .OR. SQNPC.EQ.1 ) .AND. LLWORK.GE.ONEPMIN .AND. 380 $ .NOT.UPPER ) THEN 381 NPROWB = 1 382 NPS = N 383 ELSE 384 IF( LLWORK.GE.TTLWMIN .AND. .NOT.UPPER ) THEN 385 NPROWB = SQNPC 386 END IF 387 END IF 388* 389 IF( NPROWB.GE.1 ) THEN 390 NPCOLB = NPROWB 391 SQNPC = NPROWB 392 INDB = 1 393 INDD = INDB + NPS*NPS 394 INDE = INDD + NPS 395 INDTAU = INDE + NPS 396 INDW = INDTAU + NPS 397 LLWORK = LLWORK - INDW + 1 398* 399 CALL BLACS_GET( ICTXT, 10, CTXTB ) 400 CALL BLACS_GRIDINIT( CTXTB, 'Row major', SQNPC, SQNPC ) 401 CALL BLACS_GRIDINFO( CTXTB, NPROWB, NPCOLB, MYROWB, MYCOLB ) 402 CALL DESCSET( DESCB, N, N, 1, 1, 0, 0, CTXTB, NPS ) 403* 404 CALL PDTRMR2D( UPLO, 'N', N, N, A, IA, JA, DESCA, WORK( INDB ), 405 $ 1, 1, DESCB, ICTXT ) 406* 407* 408* Only those processors in context CTXTB are needed for a while 409* 410 IF( NPROWB.GT.0 ) THEN 411* 412 IF( NPROWB.EQ.1 ) THEN 413 CALL DSYTRD( UPLO, N, WORK( INDB ), NPS, WORK( INDD ), 414 $ WORK( INDE ), WORK( INDTAU ), WORK( INDW ), 415 $ LLWORK, INFO ) 416 ELSE 417* 418 CALL PDSYTTRD( 'L', N, WORK( INDB ), 1, 1, DESCB, 419 $ WORK( INDD ), WORK( INDE ), 420 $ WORK( INDTAU ), WORK( INDW ), LLWORK, 421 $ INFO ) 422* 423 END IF 424 END IF 425* 426* All processors participate in moving the data back to the 427* way that PDSYNTRD expects it. 428* 429 CALL PDLAMR1D( N-1, WORK( INDE ), 1, 1, DESCB, E, 1, JA, 430 $ DESCA ) 431* 432 CALL PDLAMR1D( N, WORK( INDD ), 1, 1, DESCB, D, 1, JA, DESCA ) 433* 434 CALL PDLAMR1D( N, WORK( INDTAU ), 1, 1, DESCB, TAU, 1, JA, 435 $ DESCA ) 436* 437 CALL PDTRMR2D( UPLO, 'N', N, N, WORK( INDB ), 1, 1, DESCB, A, 438 $ IA, JA, DESCA, ICTXT ) 439* 440 IF( MYROWB.GE.0 ) 441 $ CALL BLACS_GRIDEXIT( CTXTB ) 442* 443 ELSE 444* 445 CALL PB_TOPGET( ICTXT, 'Combine', 'Columnwise', COLCTOP ) 446 CALL PB_TOPGET( ICTXT, 'Combine', 'Rowwise', ROWCTOP ) 447 CALL PB_TOPSET( ICTXT, 'Combine', 'Columnwise', '1-tree' ) 448 CALL PB_TOPSET( ICTXT, 'Combine', 'Rowwise', '1-tree' ) 449* 450 IPW = NP*NB + 1 451* 452 IF( UPPER ) THEN 453* 454* Reduce the upper triangle of sub( A ). 455* 456 KK = MOD( JA+N-1, NB ) 457 IF( KK.EQ.0 ) 458 $ KK = NB 459 CALL DESCSET( DESCW, N, NB, NB, NB, IAROW, 460 $ INDXG2P( JA+N-KK, NB, MYCOL, DESCA( CSRC_ ), 461 $ NPCOL ), ICTXT, MAX( 1, NP ) ) 462* 463 DO 10 K = N - KK + 1, NB + 1, -NB 464 JB = MIN( N-K+1, NB ) 465 I = IA + K - 1 466 J = JA + K - 1 467* 468* Reduce columns I:I+NB-1 to tridiagonal form and form 469* the matrix W which is needed to update the unreduced part of 470* the matrix 471* 472 CALL PDLATRD( UPLO, K+JB-1, JB, A, IA, JA, DESCA, D, E, 473 $ TAU, WORK, 1, 1, DESCW, WORK( IPW ) ) 474* 475* Update the unreduced submatrix A(IA:I-1,JA:J-1), using an 476* update of the form: 477* A(IA:I-1,JA:J-1) := A(IA:I-1,JA:J-1) - V*W' - W*V' 478* 479 CALL PDSYR2K( UPLO, 'No transpose', K-1, JB, -ONE, A, IA, 480 $ J, DESCA, WORK, 1, 1, DESCW, ONE, A, IA, 481 $ JA, DESCA ) 482* 483* Copy last superdiagonal element back into sub( A ) 484* 485 JX = MIN( INDXG2L( J, NB, 0, IACOL, NPCOL ), NQ ) 486 CALL PDELSET( A, I-1, J, DESCA, E( JX ) ) 487* 488 DESCW( CSRC_ ) = MOD( DESCW( CSRC_ )+NPCOL-1, NPCOL ) 489* 490 10 CONTINUE 491* 492* Use unblocked code to reduce the last or only block 493* 494 CALL PDSYTD2( UPLO, MIN( N, NB ), A, IA, JA, DESCA, D, E, 495 $ TAU, WORK, LWORK, IINFO ) 496* 497 ELSE 498* 499* Reduce the lower triangle of sub( A ) 500* 501 KK = MOD( JA+N-1, NB ) 502 IF( KK.EQ.0 ) 503 $ KK = NB 504 CALL DESCSET( DESCW, N, NB, NB, NB, IAROW, IACOL, ICTXT, 505 $ MAX( 1, NP ) ) 506* 507 DO 20 K = 1, N - NB, NB 508 I = IA + K - 1 509 J = JA + K - 1 510* 511* Reduce columns I:I+NB-1 to tridiagonal form and form 512* the matrix W which is needed to update the unreduced part 513* of the matrix 514* 515 CALL PDLATRD( UPLO, N-K+1, NB, A, I, J, DESCA, D, E, TAU, 516 $ WORK, K, 1, DESCW, WORK( IPW ) ) 517* 518* Update the unreduced submatrix A(I+NB:IA+N-1,I+NB:IA+N-1), 519* using an update of the form: A(I+NB:IA+N-1,I+NB:IA+N-1) := 520* A(I+NB:IA+N-1,I+NB:IA+N-1) - V*W' - W*V' 521* 522 CALL PDSYR2K( UPLO, 'No transpose', N-K-NB+1, NB, -ONE, 523 $ A, I+NB, J, DESCA, WORK, K+NB, 1, DESCW, 524 $ ONE, A, I+NB, J+NB, DESCA ) 525* 526* Copy last subdiagonal element back into sub( A ) 527* 528 JX = MIN( INDXG2L( J+NB-1, NB, 0, IACOL, NPCOL ), NQ ) 529 CALL PDELSET( A, I+NB, J+NB-1, DESCA, E( JX ) ) 530* 531 DESCW( CSRC_ ) = MOD( DESCW( CSRC_ )+1, NPCOL ) 532* 533 20 CONTINUE 534* 535* Use unblocked code to reduce the last or only block 536* 537 CALL PDSYTD2( UPLO, KK, A, IA+K-1, JA+K-1, DESCA, D, E, TAU, 538 $ WORK, LWORK, IINFO ) 539 END IF 540* 541 CALL PB_TOPSET( ICTXT, 'Combine', 'Columnwise', COLCTOP ) 542 CALL PB_TOPSET( ICTXT, 'Combine', 'Rowwise', ROWCTOP ) 543* 544 END IF 545* 546 WORK( 1 ) = DBLE( TTLWMIN ) 547* 548 RETURN 549* 550* End of PDSYNTRD 551* 552 END 553