1 SUBROUTINE PZLASE2( UPLO, M, N, ALPHA, BETA, A, IA, JA, DESCA ) 2* 3* -- ScaLAPACK auxiliary routine (version 1.7) -- 4* University of Tennessee, Knoxville, Oak Ridge National Laboratory, 5* and University of California, Berkeley. 6* May 1, 1997 7* 8* .. Scalar Arguments .. 9 CHARACTER UPLO 10 INTEGER IA, JA, M, N 11 COMPLEX*16 ALPHA, BETA 12* .. 13* .. Array Arguments .. 14 INTEGER DESCA( * ) 15 COMPLEX*16 A( * ) 16* .. 17* 18* Purpose 19* ======= 20* 21* PZLASE2 initializes an M-by-N distributed matrix sub( A ) denoting 22* A(IA:IA+M-1,JA:JA+N-1) to BETA on the diagonal and ALPHA on the 23* offdiagonals. PZLASE2 requires that only dimension of the matrix 24* operand is distributed. 25* 26* Notes 27* ===== 28* 29* Each global data object is described by an associated description 30* vector. This vector stores the information required to establish 31* the mapping between an object element and its corresponding process 32* and memory location. 33* 34* Let A be a generic term for any 2D block cyclicly distributed array. 35* Such a global array has an associated description vector DESCA. 36* In the following comments, the character _ should be read as 37* "of the global array". 38* 39* NOTATION STORED IN EXPLANATION 40* --------------- -------------- -------------------------------------- 41* DTYPE_A(global) DESCA( DTYPE_ )The descriptor type. In this case, 42* DTYPE_A = 1. 43* CTXT_A (global) DESCA( CTXT_ ) The BLACS context handle, indicating 44* the BLACS process grid A is distribu- 45* ted over. The context itself is glo- 46* bal, but the handle (the integer 47* value) may vary. 48* M_A (global) DESCA( M_ ) The number of rows in the global 49* array A. 50* N_A (global) DESCA( N_ ) The number of columns in the global 51* array A. 52* MB_A (global) DESCA( MB_ ) The blocking factor used to distribute 53* the rows of the array. 54* NB_A (global) DESCA( NB_ ) The blocking factor used to distribute 55* the columns of the array. 56* RSRC_A (global) DESCA( RSRC_ ) The process row over which the first 57* row of the array A is distributed. 58* CSRC_A (global) DESCA( CSRC_ ) The process column over which the 59* first column of the array A is 60* distributed. 61* LLD_A (local) DESCA( LLD_ ) The leading dimension of the local 62* array. LLD_A >= MAX(1,LOCr(M_A)). 63* 64* Let K be the number of rows or columns of a distributed matrix, 65* and assume that its process grid has dimension p x q. 66* LOCr( K ) denotes the number of elements of K that a process 67* would receive if K were distributed over the p processes of its 68* process column. 69* Similarly, LOCc( K ) denotes the number of elements of K that a 70* process would receive if K were distributed over the q processes of 71* its process row. 72* The values of LOCr() and LOCc() may be determined via a call to the 73* ScaLAPACK tool function, NUMROC: 74* LOCr( M ) = NUMROC( M, MB_A, MYROW, RSRC_A, NPROW ), 75* LOCc( N ) = NUMROC( N, NB_A, MYCOL, CSRC_A, NPCOL ). 76* An upper bound for these quantities may be computed by: 77* LOCr( M ) <= ceil( ceil(M/MB_A)/NPROW )*MB_A 78* LOCc( N ) <= ceil( ceil(N/NB_A)/NPCOL )*NB_A 79* 80* Arguments 81* ========= 82* 83* UPLO (global input) CHARACTER 84* Specifies the part of the distributed matrix sub( A ) to be 85* set: 86* = 'U': Upper triangular part is set; the strictly lower 87* triangular part of sub( A ) is not changed; 88* = 'L': Lower triangular part is set; the strictly upper 89* triangular part of sub( A ) is not changed; 90* Otherwise: All of the matrix sub( A ) is set. 91* 92* M (global input) INTEGER 93* The number of rows to be operated on i.e the number of rows 94* of the distributed submatrix sub( A ). M >= 0. 95* 96* N (global input) INTEGER 97* The number of columns to be operated on i.e the number of 98* columns of the distributed submatrix sub( A ). N >= 0. 99* 100* ALPHA (global input) COMPLEX*16 101* The constant to which the offdiagonal elements are to be 102* set. 103* 104* BETA (global input) COMPLEX*16 105* The constant to which the diagonal elements are to be set. 106* 107* A (local output) COMPLEX*16 pointer into the local memory 108* to an array of dimension (LLD_A,LOCc(JA+N-1)). This array 109* contains the local pieces of the distributed matrix sub( A ) 110* to be set. On exit, the leading M-by-N submatrix sub( A ) 111* is set as follows: 112* 113* if UPLO = 'U', A(IA+i-1,JA+j-1) = ALPHA, 1<=i<=j-1, 1<=j<=N, 114* if UPLO = 'L', A(IA+i-1,JA+j-1) = ALPHA, j+1<=i<=M, 1<=j<=N, 115* otherwise, A(IA+i-1,JA+j-1) = ALPHA, 1<=i<=M, 1<=j<=N, 116* IA+i.NE.JA+j, 117* and, for all UPLO, A(IA+i-1,JA+i-1) = BETA, 1<=i<=min(M,N). 118* 119* IA (global input) INTEGER 120* The row index in the global array A indicating the first 121* row of sub( A ). 122* 123* JA (global input) INTEGER 124* The column index in the global array A indicating the 125* first column of sub( A ). 126* 127* DESCA (global and local input) INTEGER array of dimension DLEN_. 128* The array descriptor for the distributed matrix A. 129* 130* ===================================================================== 131* 132* .. Parameters .. 133 INTEGER BLOCK_CYCLIC_2D, CSRC_, CTXT_, DLEN_, DTYPE_, 134 $ LLD_, MB_, M_, NB_, N_, RSRC_ 135 PARAMETER ( BLOCK_CYCLIC_2D = 1, DLEN_ = 9, DTYPE_ = 1, 136 $ CTXT_ = 2, M_ = 3, N_ = 4, MB_ = 5, NB_ = 6, 137 $ RSRC_ = 7, CSRC_ = 8, LLD_ = 9 ) 138* .. 139* .. Local Scalars .. 140 INTEGER HEIGHT, IACOL, IAROW, IBASE, ICOFFA, II, IIA, 141 $ IIBEG, IIEND, IINXT, ILEFT, IRIGHT, IROFFA, 142 $ ITOP, JJ, JJA, JJBEG, JJEND, JJNXT, LDA, MBA, 143 $ MP, MPA, MYCOL, MYDIST, MYROW, NBA, NPCOL, 144 $ NPROW, NQ, NQA, WIDE 145* .. 146* .. External Subroutines .. 147 EXTERNAL BLACS_GRIDINFO, INFOG2L, ZLASET 148* .. 149* .. External Functions .. 150 LOGICAL LSAME 151 INTEGER ICEIL, NUMROC 152 EXTERNAL ICEIL, LSAME, NUMROC 153* .. 154* .. Intrinsic Functions .. 155 INTRINSIC MAX, MIN, MOD 156* .. 157* .. Executable Statements .. 158* 159 IF( M.EQ.0 .OR. N.EQ.0 ) 160 $ RETURN 161* 162* Get grid parameters 163* 164 CALL BLACS_GRIDINFO( DESCA( CTXT_ ), NPROW, NPCOL, MYROW, MYCOL ) 165* 166 CALL INFOG2L( IA, JA, DESCA, NPROW, NPCOL, MYROW, MYCOL, IIA, JJA, 167 $ IAROW, IACOL ) 168 MBA = DESCA( MB_ ) 169 NBA = DESCA( NB_ ) 170 LDA = DESCA( LLD_ ) 171 IROFFA = MOD( IA-1, MBA ) 172 ICOFFA = MOD( JA-1, NBA ) 173* 174 IF( N.LE.( NBA-ICOFFA ) ) THEN 175* 176* It is assumed that the local columns JJA:JJA+N-1 of the matrix 177* A are in the same process column (IACOL). 178* 179* N 180* JJA JJA+N-1 181* / --------------------- \ 182* IROFFA| | | | 183* \ |...................| | ( IAROW ) 184* IIA |x | | MB_A 185* | x | | 186* |--x----------------| / 187* | x | 188* | x | ITOP 189* | x | | 190* | x | /-------\ 191* |-------x-----------| |-------x-----------| 192* | x | | x | 193* | x | | x | 194* | x | | x | 195* | x | | x | 196* |------------x------| |------------x------| 197* | x | \____________/ 198* | x | | 199* | x | IBASE 200* | x | 201* |-----------------x-| Local picture 202* | x| 203* | | 204* | | 205* | | 206* |-------------------| 207* | | 208* . . 209* . . 210* . (IACOL) . 211* 212 IF( MYCOL.EQ.IACOL ) THEN 213* 214 MPA = NUMROC( M+IROFFA, MBA, MYROW, IAROW, NPROW ) 215 IF( MPA.LE.0 ) 216 $ RETURN 217 IF( MYROW.EQ.IAROW ) 218 $ MPA = MPA - IROFFA 219 MYDIST = MOD( MYROW-IAROW+NPROW, NPROW ) 220 ITOP = MYDIST * MBA - IROFFA 221* 222 IF( LSAME( UPLO, 'U' ) ) THEN 223* 224 ITOP = MAX( 0, ITOP ) 225 IIBEG = IIA 226 IIEND = IIA + MPA - 1 227 IINXT = MIN( ICEIL( IIBEG, MBA ) * MBA, IIEND ) 228* 229 10 CONTINUE 230 IF( ( N-ITOP ).GT.0 ) THEN 231 CALL ZLASET( UPLO, IINXT-IIBEG+1, N-ITOP, ALPHA, BETA, 232 $ A( IIBEG+(JJA+ITOP-1)*LDA ), LDA ) 233 MYDIST = MYDIST + NPROW 234 ITOP = MYDIST * MBA - IROFFA 235 IIBEG = IINXT +1 236 IINXT = MIN( IINXT+MBA, IIEND ) 237 GO TO 10 238 END IF 239* 240 ELSE IF( LSAME( UPLO, 'L' ) ) THEN 241* 242 II = IIA 243 JJ = JJA 244 MP = MPA 245 IBASE = MIN( ITOP+MBA, N ) 246 ITOP = MIN( MAX( 0, ITOP ), N ) 247* 248 20 CONTINUE 249 IF( JJ.LE.( JJA+N-1 ) ) THEN 250 HEIGHT = IBASE - ITOP 251 CALL ZLASET( 'All', MP, ITOP-JJ+JJA, ALPHA, ALPHA, 252 $ A( II+(JJ-1)*LDA ), LDA ) 253 CALL ZLASET( UPLO, MP, HEIGHT, ALPHA, BETA, 254 $ A( II+(JJA+ITOP-1)*LDA ), LDA ) 255 MP = MAX( 0, MP - HEIGHT ) 256 II = II + HEIGHT 257 JJ = JJA + IBASE 258 MYDIST = MYDIST + NPROW 259 ITOP = MYDIST * MBA - IROFFA 260 IBASE = MIN( ITOP + MBA, N ) 261 ITOP = MIN( ITOP, N ) 262 GO TO 20 263 END IF 264* 265 ELSE 266* 267 II = IIA 268 JJ = JJA 269 MP = MPA 270 IBASE = MIN( ITOP+MBA, N ) 271 ITOP = MIN( MAX( 0, ITOP ), N ) 272* 273 30 CONTINUE 274 IF( JJ.LE.( JJA+N-1 ) ) THEN 275 HEIGHT = IBASE - ITOP 276 CALL ZLASET( 'All', MPA, ITOP-JJ+JJA, ALPHA, ALPHA, 277 $ A( IIA+(JJ-1)*LDA ), LDA ) 278 CALL ZLASET( 'All', MPA-MP, HEIGHT, ALPHA, ALPHA, 279 $ A( IIA+(JJA+ITOP-1)*LDA ), LDA ) 280 CALL ZLASET( 'All', MP, HEIGHT, ALPHA, BETA, 281 $ A( II+(JJA+ITOP-1)*LDA ), LDA ) 282 MP = MAX( 0, MP - HEIGHT ) 283 II = II + HEIGHT 284 JJ = JJA + IBASE 285 MYDIST = MYDIST + NPROW 286 ITOP = MYDIST * MBA - IROFFA 287 IBASE = MIN( ITOP + MBA, N ) 288 ITOP = MIN( ITOP, N ) 289 GO TO 30 290 END IF 291* 292 END IF 293* 294 END IF 295* 296 ELSE IF( M.LE.( MBA-IROFFA ) ) THEN 297* 298* It is assumed that the local rows IIA:IIA+M-1 of the matrix A 299* are in the same process row (IAROW). 300* 301* ICOFFA 302* / \JJA 303* IIA ------------------ .... -------- 304* | .x | | | / | | \ 305* | . x | | | ILEFT| | | | 306* | . x | | | | | | 307* | . x | | \ x | | 308* | . |x | | |x | | IRIGHT 309* | . | x | | | x | | 310* (IAROW) | . | x | | | x | | 311* | . | x| | | x| | 312* | . | x | | x / 313* | . | |x | | | 314* | . | | x | | | 315* | . | | x | | | 316* | . | | x| | | 317* IIA+M-1 ------------------ .... ------- 318* NB_A 319* (IACOL) Local picture 320* 321 IF( MYROW.EQ.IAROW ) THEN 322* 323 NQA = NUMROC( N+ICOFFA, NBA, MYCOL, IACOL, NPCOL ) 324 IF( NQA.LE.0 ) 325 $ RETURN 326 IF( MYCOL.EQ.IACOL ) 327 $ NQA = NQA - ICOFFA 328 MYDIST = MOD( MYCOL-IACOL+NPCOL, NPCOL ) 329 ILEFT = MYDIST * NBA - ICOFFA 330* 331 IF( LSAME( UPLO, 'L' ) ) THEN 332* 333 ILEFT = MAX( 0, ILEFT ) 334 JJBEG = JJA 335 JJEND = JJA + NQA - 1 336 JJNXT = MIN( ICEIL( JJBEG, NBA ) * NBA, JJEND ) 337* 338 40 CONTINUE 339 IF( ( M-ILEFT ).GT.0 ) THEN 340 CALL ZLASET( UPLO, M-ILEFT, JJNXT-JJBEG+1, ALPHA, 341 $ BETA, A( IIA+ILEFT+(JJBEG-1)*LDA ), LDA ) 342 MYDIST = MYDIST + NPCOL 343 ILEFT = MYDIST * NBA - ICOFFA 344 JJBEG = JJNXT +1 345 JJNXT = MIN( JJNXT+NBA, JJEND ) 346 GO TO 40 347 END IF 348* 349 ELSE IF( LSAME( UPLO, 'U' ) ) THEN 350* 351 II = IIA 352 JJ = JJA 353 NQ = NQA 354 IRIGHT = MIN( ILEFT+NBA, M ) 355 ILEFT = MIN( MAX( 0, ILEFT ), M ) 356* 357 50 CONTINUE 358 IF( II.LE.( IIA+M-1 ) ) THEN 359 WIDE = IRIGHT - ILEFT 360 CALL ZLASET( 'All', ILEFT-II+IIA, NQ, ALPHA, ALPHA, 361 $ A( II+(JJ-1)*LDA ), LDA ) 362 CALL ZLASET( UPLO, WIDE, NQ, ALPHA, BETA, 363 $ A( IIA+ILEFT+(JJ-1)*LDA ), LDA ) 364 NQ = MAX( 0, NQ - WIDE ) 365 II = IIA + IRIGHT 366 JJ = JJ + WIDE 367 MYDIST = MYDIST + NPCOL 368 ILEFT = MYDIST * NBA - ICOFFA 369 IRIGHT = MIN( ILEFT + NBA, M ) 370 ILEFT = MIN( ILEFT, M ) 371 GO TO 50 372 END IF 373* 374 ELSE 375* 376 II = IIA 377 JJ = JJA 378 NQ = NQA 379 IRIGHT = MIN( ILEFT+NBA, M ) 380 ILEFT = MIN( MAX( 0, ILEFT ), M ) 381* 382 60 CONTINUE 383 IF( II.LE.( IIA+M-1 ) ) THEN 384 WIDE = IRIGHT - ILEFT 385 CALL ZLASET( 'All', ILEFT-II+IIA, NQA, ALPHA, ALPHA, 386 $ A( II+(JJA-1)*LDA ), LDA ) 387 CALL ZLASET( 'All', WIDE, NQA-NQ, ALPHA, ALPHA, 388 $ A( IIA+ILEFT+(JJA-1)*LDA ), LDA ) 389 CALL ZLASET( 'All', WIDE, NQ, ALPHA, BETA, 390 $ A( IIA+ILEFT+(JJ-1)*LDA ), LDA ) 391 NQ = MAX( 0, NQ - WIDE ) 392 II = IIA + IRIGHT 393 JJ = JJ + WIDE 394 MYDIST = MYDIST + NPCOL 395 ILEFT = MYDIST * NBA - ICOFFA 396 IRIGHT = MIN( ILEFT + NBA, M ) 397 ILEFT = MIN( ILEFT, M ) 398 GO TO 60 399 END IF 400* 401 END IF 402* 403 END IF 404* 405 END IF 406* 407 RETURN 408* 409* End of PZLASE2 410* 411 END 412