1 DOUBLE PRECISION FUNCTION PZLANSY( NORM, UPLO, N, A, IA, JA, 2 $ DESCA, WORK ) 3 IMPLICIT NONE 4* 5* -- ScaLAPACK auxiliary routine (version 1.7) -- 6* University of Tennessee, Knoxville, Oak Ridge National Laboratory, 7* and University of California, Berkeley. 8* May 1, 1997 9* 10* .. Scalar Arguments .. 11 CHARACTER NORM, UPLO 12 INTEGER IA, JA, N 13* .. 14* .. Array Arguments .. 15 INTEGER DESCA( * ) 16 DOUBLE PRECISION WORK( * ) 17 COMPLEX*16 A( * ) 18* .. 19* 20* Purpose 21* ======= 22* 23* PZLANSY returns the value of the one norm, or the Frobenius norm, 24* or the infinity norm, or the element of largest absolute value of a 25* real symmetric distributed matrix sub( A ) = A(IA:IA+N-1,JA:JA+N-1). 26* 27* PZLANSY returns the value 28* 29* ( max(abs(A(i,j))), NORM = 'M' or 'm' with IA <= i <= IA+N-1, 30* ( and JA <= j <= JA+N-1, 31* ( 32* ( norm1( sub( A ) ), NORM = '1', 'O' or 'o' 33* ( 34* ( normI( sub( A ) ), NORM = 'I' or 'i' 35* ( 36* ( normF( sub( A ) ), NORM = 'F', 'f', 'E' or 'e' 37* 38* where norm1 denotes the one norm of a matrix (maximum column sum), 39* normI denotes the infinity norm of a matrix (maximum row sum) and 40* normF denotes the Frobenius norm of a matrix (square root of sum of 41* squares). Note that max(abs(A(i,j))) is not a matrix norm. 42* 43* Notes 44* ===== 45* 46* Each global data object is described by an associated description 47* vector. This vector stores the information required to establish 48* the mapping between an object element and its corresponding process 49* and memory location. 50* 51* Let A be a generic term for any 2D block cyclicly distributed array. 52* Such a global array has an associated description vector DESCA. 53* In the following comments, the character _ should be read as 54* "of the global array". 55* 56* NOTATION STORED IN EXPLANATION 57* --------------- -------------- -------------------------------------- 58* DTYPE_A(global) DESCA( DTYPE_ )The descriptor type. In this case, 59* DTYPE_A = 1. 60* CTXT_A (global) DESCA( CTXT_ ) The BLACS context handle, indicating 61* the BLACS process grid A is distribu- 62* ted over. The context itself is glo- 63* bal, but the handle (the integer 64* value) may vary. 65* M_A (global) DESCA( M_ ) The number of rows in the global 66* array A. 67* N_A (global) DESCA( N_ ) The number of columns in the global 68* array A. 69* MB_A (global) DESCA( MB_ ) The blocking factor used to distribute 70* the rows of the array. 71* NB_A (global) DESCA( NB_ ) The blocking factor used to distribute 72* the columns of the array. 73* RSRC_A (global) DESCA( RSRC_ ) The process row over which the first 74* row of the array A is distributed. 75* CSRC_A (global) DESCA( CSRC_ ) The process column over which the 76* first column of the array A is 77* distributed. 78* LLD_A (local) DESCA( LLD_ ) The leading dimension of the local 79* array. LLD_A >= MAX(1,LOCr(M_A)). 80* 81* Let K be the number of rows or columns of a distributed matrix, 82* and assume that its process grid has dimension p x q. 83* LOCr( K ) denotes the number of elements of K that a process 84* would receive if K were distributed over the p processes of its 85* process column. 86* Similarly, LOCc( K ) denotes the number of elements of K that a 87* process would receive if K were distributed over the q processes of 88* its process row. 89* The values of LOCr() and LOCc() may be determined via a call to the 90* ScaLAPACK tool function, NUMROC: 91* LOCr( M ) = NUMROC( M, MB_A, MYROW, RSRC_A, NPROW ), 92* LOCc( N ) = NUMROC( N, NB_A, MYCOL, CSRC_A, NPCOL ). 93* An upper bound for these quantities may be computed by: 94* LOCr( M ) <= ceil( ceil(M/MB_A)/NPROW )*MB_A 95* LOCc( N ) <= ceil( ceil(N/NB_A)/NPCOL )*NB_A 96* 97* Arguments 98* ========= 99* 100* NORM (global input) CHARACTER 101* Specifies the value to be returned in PZLANSY as described 102* above. 103* 104* UPLO (global input) CHARACTER 105* Specifies whether the upper or lower triangular part of the 106* symmetric matrix sub( A ) is to be referenced. 107* = 'U': Upper triangular part of sub( A ) is referenced, 108* = 'L': Lower triangular part of sub( A ) is referenced. 109* 110* N (global input) INTEGER 111* The number of rows and columns to be operated on i.e the 112* number of rows and columns of the distributed submatrix 113* sub( A ). When N = 0, PZLANSY is set to zero. N >= 0. 114* 115* A (local input) COMPLEX*16 pointer into the local memory 116* to an array of dimension (LLD_A, LOCc(JA+N-1)) containing the 117* local pieces of the symmetric distributed matrix sub( A ). 118* If UPLO = 'U', the leading N-by-N upper triangular part of 119* sub( A ) contains the upper triangular matrix which norm is 120* to be computed, and the strictly lower triangular part of 121* this matrix is not referenced. If UPLO = 'L', the leading 122* N-by-N lower triangular part of sub( A ) contains the lower 123* triangular matrix which norm is to be computed, and the 124* strictly upper triangular part of sub( A ) is not referenced. 125* 126* IA (global input) INTEGER 127* The row index in the global array A indicating the first 128* row of sub( A ). 129* 130* JA (global input) INTEGER 131* The column index in the global array A indicating the 132* first column of sub( A ). 133* 134* DESCA (global and local input) INTEGER array of dimension DLEN_. 135* The array descriptor for the distributed matrix A. 136* 137* WORK (local workspace) DOUBLE PRECISION array dimension (LWORK) 138* LWORK >= 0 if NORM = 'M' or 'm' (not referenced), 139* 2*Nq0+Np0+LDW if NORM = '1', 'O', 'o', 'I' or 'i', 140* where LDW is given by: 141* IF( NPROW.NE.NPCOL ) THEN 142* LDW = MB_A*CEIL(CEIL(Np0/MB_A)/(LCM/NPROW)) 143* ELSE 144* LDW = 0 145* END IF 146* 0 if NORM = 'F', 'f', 'E' or 'e' (not referenced), 147* 148* where LCM is the least common multiple of NPROW and NPCOL 149* LCM = ILCM( NPROW, NPCOL ) and CEIL denotes the ceiling 150* operation (ICEIL). 151* 152* IROFFA = MOD( IA-1, MB_A ), ICOFFA = MOD( JA-1, NB_A ), 153* IAROW = INDXG2P( IA, MB_A, MYROW, RSRC_A, NPROW ), 154* IACOL = INDXG2P( JA, NB_A, MYCOL, CSRC_A, NPCOL ), 155* Np0 = NUMROC( N+IROFFA, MB_A, MYROW, IAROW, NPROW ), 156* Nq0 = NUMROC( N+ICOFFA, NB_A, MYCOL, IACOL, NPCOL ), 157* 158* ICEIL, ILCM, INDXG2P and NUMROC are ScaLAPACK tool functions; 159* MYROW, MYCOL, NPROW and NPCOL can be determined by calling 160* the subroutine BLACS_GRIDINFO. 161* 162* ===================================================================== 163* 164* .. Parameters .. 165 INTEGER BLOCK_CYCLIC_2D, CSRC_, CTXT_, DLEN_, DTYPE_, 166 $ LLD_, MB_, M_, NB_, N_, RSRC_ 167 PARAMETER ( BLOCK_CYCLIC_2D = 1, DLEN_ = 9, DTYPE_ = 1, 168 $ CTXT_ = 2, M_ = 3, N_ = 4, MB_ = 5, NB_ = 6, 169 $ RSRC_ = 7, CSRC_ = 8, LLD_ = 9 ) 170 DOUBLE PRECISION ONE, ZERO 171 PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) 172* .. 173* .. Local Scalars .. 174 INTEGER I, IAROW, IACOL, IB, ICOFF, ICTXT, ICURCOL, 175 $ ICURROW, II, IIA, IN, IROFF, ICSR, ICSR0, 176 $ IOFFA, IRSC, IRSC0, IRSR, IRSR0, JJ, JJA, K, 177 $ LDA, LL, MYCOL, MYROW, NP, NPCOL, NPROW, NQ 178 DOUBLE PRECISION SUM, VALUE 179* .. 180* .. Local Arrays .. 181 DOUBLE PRECISION SSQ( 2 ), COLSSQ( 2 ) 182* .. 183* .. External Subroutines .. 184 EXTERNAL BLACS_GRIDINFO, DAXPY, DCOMBSSQ, 185 $ DGAMX2D, DGSUM2D, DGEBR2D, 186 $ DGEBS2D, PDCOL2ROW, PDTREECOMB, 187 $ ZLASSQ 188* .. 189* .. External Functions .. 190 LOGICAL LSAME 191 INTEGER ICEIL, IDAMAX, NUMROC 192 EXTERNAL ICEIL, IDAMAX, LSAME, NUMROC 193* .. 194* .. Intrinsic Functions .. 195 INTRINSIC ABS, MAX, MIN, MOD, SQRT 196* .. 197* .. Executable Statements .. 198* 199* Get grid parameters and local indexes. 200* 201 ICTXT = DESCA( CTXT_ ) 202 CALL BLACS_GRIDINFO( ICTXT, NPROW, NPCOL, MYROW, MYCOL ) 203 CALL INFOG2L( IA, JA, DESCA, NPROW, NPCOL, MYROW, MYCOL, 204 $ IIA, JJA, IAROW, IACOL ) 205* 206 IROFF = MOD( IA-1, DESCA( MB_ ) ) 207 ICOFF = MOD( JA-1, DESCA( NB_ ) ) 208 NP = NUMROC( N+IROFF, DESCA( MB_ ), MYROW, IAROW, NPROW ) 209 NQ = NUMROC( N+ICOFF, DESCA( NB_ ), MYCOL, IACOL, NPCOL ) 210 ICSR = 1 211 IRSR = ICSR + NQ 212 IRSC = IRSR + NQ 213 IF( MYROW.EQ.IAROW ) THEN 214 IRSC0 = IRSC + IROFF 215 NP = NP - IROFF 216 ELSE 217 IRSC0 = IRSC 218 END IF 219 IF( MYCOL.EQ.IACOL ) THEN 220 ICSR0 = ICSR + ICOFF 221 IRSR0 = IRSR + ICOFF 222 NQ = NQ - ICOFF 223 ELSE 224 ICSR0 = ICSR 225 IRSR0 = IRSR 226 END IF 227 IN = MIN( ICEIL( IA, DESCA( MB_ ) ) * DESCA( MB_ ), IA+N-1 ) 228 LDA = DESCA( LLD_ ) 229* 230* If the matrix is symmetric, we address only a triangular portion 231* of the matrix. A sum of row (column) i of the complete matrix 232* can be obtained by adding along row i and column i of the the 233* triangular matrix, stopping/starting at the diagonal, which is 234* the point of reflection. The pictures below demonstrate this. 235* In the following code, the row sums created by --- rows below are 236* refered to as ROWSUMS, and the column sums shown by | are refered 237* to as COLSUMS. Infinity-norm = 1-norm = ROWSUMS+COLSUMS. 238* 239* UPLO = 'U' UPLO = 'L' 240* ____i______ ___________ 241* |\ | | |\ | 242* | \ | | | \ | 243* | \ | | | \ | 244* | \|------| i i|---\ | 245* | \ | | |\ | 246* | \ | | | \ | 247* | \ | | | \ | 248* | \ | | | \ | 249* | \ | | | \ | 250* | \ | | | \ | 251* |__________\| |___|______\| 252* i 253* 254* II, JJ : local indices into array A 255* ICURROW : process row containing diagonal block 256* ICURCOL : process column containing diagonal block 257* IRSC0 : pointer to part of work used to store the ROWSUMS while 258* they are stored along a process column 259* IRSR0 : pointer to part of work used to store the ROWSUMS after 260* they have been transposed to be along a process row 261* 262 II = IIA 263 JJ = JJA 264* 265 IF( N.EQ.0 ) THEN 266* 267 VALUE = ZERO 268* 269************************************************************************ 270* max norm 271* 272 ELSE IF( LSAME( NORM, 'M' ) ) THEN 273* 274* Find max(abs(A(i,j))). 275* 276 VALUE = ZERO 277* 278 IF( LSAME( UPLO, 'U' ) ) THEN 279* 280* Handle first block separately 281* 282 IB = IN-IA+1 283* 284* Find COLMAXS 285* 286 IF( MYCOL.EQ.IACOL ) THEN 287 DO 20 K = (JJ-1)*LDA, (JJ+IB-2)*LDA, LDA 288 IF( II.GT.IIA ) THEN 289 DO 10 LL = IIA, II-1 290 VALUE = MAX( VALUE, ABS( A( LL+K ) ) ) 291 10 CONTINUE 292 END IF 293 IF( MYROW.EQ.IAROW ) 294 $ II = II + 1 295 20 CONTINUE 296* 297* Reset local indices so we can find ROWMAXS 298* 299 IF( MYROW.EQ.IAROW ) 300 $ II = II - IB 301* 302 END IF 303* 304* Find ROWMAXS 305* 306 IF( MYROW.EQ.IAROW ) THEN 307 DO 40 K = II, II+IB-1 308 IF( JJ.LE.JJA+NQ-1 ) THEN 309 DO 30 LL = (JJ-1)*LDA, (JJA+NQ-2)*LDA, LDA 310 VALUE = MAX( VALUE, ABS( A( K+LL ) ) ) 311 30 CONTINUE 312 END IF 313 IF( MYCOL.EQ.IACOL ) 314 $ JJ = JJ + 1 315 40 CONTINUE 316 II = II + IB 317 ELSE IF( MYCOL.EQ.IACOL ) THEN 318 JJ = JJ + IB 319 END IF 320* 321 ICURROW = MOD( IAROW+1, NPROW ) 322 ICURCOL = MOD( IACOL+1, NPCOL ) 323* 324* Loop over the remaining rows/columns of the matrix. 325* 326 DO 90 I = IN+1, IA+N-1, DESCA( MB_ ) 327 IB = MIN( DESCA( MB_ ), IA+N-I ) 328* 329* Find COLMAXS 330* 331 IF( MYCOL.EQ.ICURCOL ) THEN 332 DO 60 K = (JJ-1)*LDA, (JJ+IB-2)*LDA, LDA 333 IF( II.GT.IIA ) THEN 334 DO 50 LL = IIA, II-1 335 VALUE = MAX( VALUE, ABS( A( LL+K ) ) ) 336 50 CONTINUE 337 END IF 338 IF( MYROW.EQ.ICURROW ) 339 $ II = II + 1 340 60 CONTINUE 341* 342* Reset local indices so we can find ROWMAXS 343* 344 IF( MYROW.EQ.ICURROW ) 345 $ II = II - IB 346 END IF 347* 348* Find ROWMAXS 349* 350 IF( MYROW.EQ.ICURROW ) THEN 351 DO 80 K = II, II+IB-1 352 IF( JJ.LE.JJA+NQ-1 ) THEN 353 DO 70 LL = (JJ-1)*LDA, (JJA+NQ-2)*LDA, LDA 354 VALUE = MAX( VALUE, ABS( A( K+LL ) ) ) 355 70 CONTINUE 356 END IF 357 IF( MYCOL.EQ.ICURCOL ) 358 $ JJ = JJ + 1 359 80 CONTINUE 360 II = II + IB 361 ELSE IF( MYCOL.EQ.ICURCOL ) THEN 362 JJ = JJ + IB 363 END IF 364 ICURROW = MOD( ICURROW+1, NPROW ) 365 ICURCOL = MOD( ICURCOL+1, NPCOL ) 366 90 CONTINUE 367* 368 ELSE 369* 370* Handle first block separately 371* 372 IB = IN-IA+1 373* 374* Find COLMAXS 375* 376 IF( MYCOL.EQ.IACOL ) THEN 377 DO 110 K = (JJ-1)*LDA, (JJ+IB-2)*LDA, LDA 378 IF( II.LE.IIA+NP-1 ) THEN 379 DO 100 LL = II, IIA+NP-1 380 VALUE = MAX( VALUE, ABS( A( LL+K ) ) ) 381 100 CONTINUE 382 END IF 383 IF( MYROW.EQ.IAROW ) 384 $ II = II + 1 385 110 CONTINUE 386* 387* Reset local indices so we can find ROWMAXS 388* 389 IF( MYROW.EQ.IAROW ) 390 $ II = II - IB 391 END IF 392* 393* Find ROWMAXS 394* 395 IF( MYROW.EQ.IAROW ) THEN 396 DO 130 K = 0, IB-1 397 IF( JJ.GT.JJA ) THEN 398 DO 120 LL = (JJA-1)*LDA, (JJ-2)*LDA, LDA 399 VALUE = MAX( VALUE, ABS( A( II+LL ) ) ) 400 120 CONTINUE 401 END IF 402 II = II + 1 403 IF( MYCOL.EQ.IACOL ) 404 $ JJ = JJ + 1 405 130 CONTINUE 406 ELSE IF( MYCOL.EQ.IACOL ) THEN 407 JJ = JJ + IB 408 END IF 409* 410 ICURROW = MOD( IAROW+1, NPROW ) 411 ICURCOL = MOD( IACOL+1, NPCOL ) 412* 413* Loop over rows/columns of global matrix. 414* 415 DO 180 I = IN+1, IA+N-1, DESCA( MB_ ) 416 IB = MIN( DESCA( MB_ ), IA+N-I ) 417* 418* Find COLMAXS 419* 420 IF( MYCOL.EQ.ICURCOL ) THEN 421 DO 150 K = (JJ-1)*LDA, (JJ+IB-2)*LDA, LDA 422 IF( II.LE.IIA+NP-1 ) THEN 423 DO 140 LL = II, IIA+NP-1 424 VALUE = MAX( VALUE, ABS( A( LL+K ) ) ) 425 140 CONTINUE 426 END IF 427 IF( MYROW.EQ.ICURROW ) 428 $ II = II + 1 429 150 CONTINUE 430* 431* Reset local indices so we can find ROWMAXS 432* 433 IF( MYROW.EQ.ICURROW ) 434 $ II = II - IB 435 END IF 436* 437* Find ROWMAXS 438* 439 IF( MYROW.EQ.ICURROW ) THEN 440 DO 170 K = 0, IB-1 441 IF( JJ.GT.JJA ) THEN 442 DO 160 LL = (JJA-1)*LDA, (JJ-2)*LDA, LDA 443 VALUE = MAX( VALUE, ABS( A( II+LL ) ) ) 444 160 CONTINUE 445 END IF 446 II = II + 1 447 IF( MYCOL.EQ.ICURCOL ) 448 $ JJ = JJ + 1 449 170 CONTINUE 450 ELSE IF( MYCOL.EQ.ICURCOL ) THEN 451 JJ = JJ + IB 452 END IF 453 ICURROW = MOD( ICURROW+1, NPROW ) 454 ICURCOL = MOD( ICURCOL+1, NPCOL ) 455* 456 180 CONTINUE 457* 458 END IF 459* 460* Gather the result on process (IAROW,IACOL). 461* 462 CALL DGAMX2D( ICTXT, 'All', ' ', 1, 1, VALUE, 1, I, K, -1, 463 $ IAROW, IACOL ) 464* 465************************************************************************ 466* one or inf norm 467* 468 ELSE IF( LSAME( NORM, 'I' ) .OR. LSAME( NORM, 'O' ) .OR. 469 $ NORM.EQ.'1' ) THEN 470* 471* Find normI( sub( A ) ) ( = norm1( sub( A ) ), since sub( A ) is 472* symmetric). 473* 474 IF( LSAME( UPLO, 'U' ) ) THEN 475* 476* Handle first block separately 477* 478 IB = IN-IA+1 479* 480* Find COLSUMS 481* 482 IF( MYCOL.EQ.IACOL ) THEN 483 IOFFA = ( JJ - 1 ) * LDA 484 DO 200 K = 0, IB-1 485 SUM = ZERO 486 IF( II.GT.IIA ) THEN 487 DO 190 LL = IIA, II-1 488 SUM = SUM + ABS( A( LL+IOFFA ) ) 489 190 CONTINUE 490 END IF 491 IOFFA = IOFFA + LDA 492 WORK( JJ+K-JJA+ICSR0 ) = SUM 493 IF( MYROW.EQ.IAROW ) 494 $ II = II + 1 495 200 CONTINUE 496* 497* Reset local indices so we can find ROWSUMS 498* 499 IF( MYROW.EQ.IAROW ) 500 $ II = II - IB 501* 502 END IF 503* 504* Find ROWSUMS 505* 506 IF( MYROW.EQ.IAROW ) THEN 507 DO 220 K = II, II+IB-1 508 SUM = ZERO 509 IF( JJA+NQ.GT.JJ ) THEN 510 DO 210 LL = (JJ-1)*LDA, (JJA+NQ-2)*LDA, LDA 511 SUM = SUM + ABS( A( K+LL ) ) 512 210 CONTINUE 513 END IF 514 WORK( K-IIA+IRSC0 ) = SUM 515 IF( MYCOL.EQ.IACOL ) 516 $ JJ = JJ + 1 517 220 CONTINUE 518 II = II + IB 519 ELSE IF( MYCOL.EQ.IACOL ) THEN 520 JJ = JJ + IB 521 END IF 522* 523 ICURROW = MOD( IAROW+1, NPROW ) 524 ICURCOL = MOD( IACOL+1, NPCOL ) 525* 526* Loop over remaining rows/columns of global matrix. 527* 528 DO 270 I = IN+1, IA+N-1, DESCA( MB_ ) 529 IB = MIN( DESCA( MB_ ), IA+N-I ) 530* 531* Find COLSUMS 532* 533 IF( MYCOL.EQ.ICURCOL ) THEN 534 IOFFA = ( JJ - 1 ) * LDA 535 DO 240 K = 0, IB-1 536 SUM = ZERO 537 IF( II.GT.IIA ) THEN 538 DO 230 LL = IIA, II-1 539 SUM = SUM + ABS( A( IOFFA+LL ) ) 540 230 CONTINUE 541 END IF 542 IOFFA = IOFFA + LDA 543 WORK( JJ+K-JJA+ICSR0 ) = SUM 544 IF( MYROW.EQ.ICURROW ) 545 $ II = II + 1 546 240 CONTINUE 547* 548* Reset local indices so we can find ROWSUMS 549* 550 IF( MYROW.EQ.ICURROW ) 551 $ II = II - IB 552* 553 END IF 554* 555* Find ROWSUMS 556* 557 IF( MYROW.EQ.ICURROW ) THEN 558 DO 260 K = II, II+IB-1 559 SUM = ZERO 560 IF( JJA+NQ.GT.JJ ) THEN 561 DO 250 LL = (JJ-1)*LDA, (JJA+NQ-2)*LDA, LDA 562 SUM = SUM + ABS( A( K+LL ) ) 563 250 CONTINUE 564 END IF 565 WORK( K-IIA+IRSC0 ) = SUM 566 IF( MYCOL.EQ.ICURCOL ) 567 $ JJ = JJ + 1 568 260 CONTINUE 569 II = II + IB 570 ELSE IF( MYCOL.EQ.ICURCOL ) THEN 571 JJ = JJ + IB 572 END IF 573* 574 ICURROW = MOD( ICURROW+1, NPROW ) 575 ICURCOL = MOD( ICURCOL+1, NPCOL ) 576* 577 270 CONTINUE 578* 579 ELSE 580* 581* Handle first block separately 582* 583 IB = IN-IA+1 584* 585* Find COLSUMS 586* 587 IF( MYCOL.EQ.IACOL ) THEN 588 IOFFA = (JJ-1)*LDA 589 DO 290 K = 0, IB-1 590 SUM = ZERO 591 IF( IIA+NP.GT.II ) THEN 592 DO 280 LL = II, IIA+NP-1 593 SUM = SUM + ABS( A( IOFFA+LL ) ) 594 280 CONTINUE 595 END IF 596 IOFFA = IOFFA + LDA 597 WORK( JJ+K-JJA+ICSR0 ) = SUM 598 IF( MYROW.EQ.IAROW ) 599 $ II = II + 1 600 290 CONTINUE 601* 602* Reset local indices so we can find ROWSUMS 603* 604 IF( MYROW.EQ.IAROW ) 605 $ II = II - IB 606* 607 END IF 608* 609* Find ROWSUMS 610* 611 IF( MYROW.EQ.IAROW ) THEN 612 DO 310 K = II, II+IB-1 613 SUM = ZERO 614 IF( JJ.GT.JJA ) THEN 615 DO 300 LL = (JJA-1)*LDA, (JJ-2)*LDA, LDA 616 SUM = SUM + ABS( A( K+LL ) ) 617 300 CONTINUE 618 END IF 619 WORK( K-IIA+IRSC0 ) = SUM 620 IF( MYCOL.EQ.IACOL ) 621 $ JJ = JJ + 1 622 310 CONTINUE 623 II = II + IB 624 ELSE IF( MYCOL.EQ.IACOL ) THEN 625 JJ = JJ + IB 626 END IF 627* 628 ICURROW = MOD( IAROW+1, NPROW ) 629 ICURCOL = MOD( IACOL+1, NPCOL ) 630* 631* Loop over rows/columns of global matrix. 632* 633 DO 360 I = IN+1, IA+N-1, DESCA( MB_ ) 634 IB = MIN( DESCA( MB_ ), IA+N-I ) 635* 636* Find COLSUMS 637* 638 IF( MYCOL.EQ.ICURCOL ) THEN 639 IOFFA = ( JJ - 1 ) * LDA 640 DO 330 K = 0, IB-1 641 SUM = ZERO 642 IF( IIA+NP.GT.II ) THEN 643 DO 320 LL = II, IIA+NP-1 644 SUM = SUM + ABS( A( LL+IOFFA ) ) 645 320 CONTINUE 646 END IF 647 IOFFA = IOFFA + LDA 648 WORK( JJ+K-JJA+ICSR0 ) = SUM 649 IF( MYROW.EQ.ICURROW ) 650 $ II = II + 1 651 330 CONTINUE 652* 653* Reset local indices so we can find ROWSUMS 654* 655 IF( MYROW.EQ.ICURROW ) 656 $ II = II - IB 657* 658 END IF 659* 660* Find ROWSUMS 661* 662 IF( MYROW.EQ.ICURROW ) THEN 663 DO 350 K = II, II+IB-1 664 SUM = ZERO 665 IF( JJ.GT.JJA ) THEN 666 DO 340 LL = (JJA-1)*LDA, (JJ-2)*LDA, LDA 667 SUM = SUM + ABS( A( K+LL ) ) 668 340 CONTINUE 669 END IF 670 WORK(K-IIA+IRSC0) = SUM 671 IF( MYCOL.EQ.ICURCOL ) 672 $ JJ = JJ + 1 673 350 CONTINUE 674 II = II + IB 675 ELSE IF( MYCOL.EQ.ICURCOL ) THEN 676 JJ = JJ + IB 677 END IF 678* 679 ICURROW = MOD( ICURROW+1, NPROW ) 680 ICURCOL = MOD( ICURCOL+1, NPCOL ) 681* 682 360 CONTINUE 683 END IF 684* 685* After calls to DGSUM2D, process row 0 will have global 686* COLSUMS and process column 0 will have global ROWSUMS. 687* Transpose ROWSUMS and add to COLSUMS to get global row/column 688* sum, the max of which is the infinity or 1 norm. 689* 690 IF( MYCOL.EQ.IACOL ) 691 $ NQ = NQ + ICOFF 692 CALL DGSUM2D( ICTXT, 'Columnwise', ' ', 1, NQ, WORK( ICSR ), 1, 693 $ IAROW, MYCOL ) 694 IF( MYROW.EQ.IAROW ) 695 $ NP = NP + IROFF 696 CALL DGSUM2D( ICTXT, 'Rowwise', ' ', NP, 1, WORK( IRSC ), 697 $ MAX( 1, NP ), MYROW, IACOL ) 698* 699 CALL PDCOL2ROW( ICTXT, N, 1, DESCA( MB_ ), WORK( IRSC ), 700 $ MAX( 1, NP ), WORK( IRSR ), MAX( 1, NQ ), 701 $ IAROW, IACOL, IAROW, IACOL, WORK( IRSC+NP ) ) 702* 703 IF( MYROW.EQ.IAROW ) THEN 704 IF( MYCOL.EQ.IACOL ) 705 $ NQ = NQ - ICOFF 706 CALL DAXPY( NQ, ONE, WORK( IRSR0 ), 1, WORK( ICSR0 ), 1 ) 707 IF( NQ.LT.1 ) THEN 708 VALUE = ZERO 709 ELSE 710 VALUE = WORK( IDAMAX( NQ, WORK( ICSR0 ), 1 ) ) 711 END IF 712 CALL DGAMX2D( ICTXT, 'Rowwise', ' ', 1, 1, VALUE, 1, I, K, 713 $ -1, IAROW, IACOL ) 714 END IF 715* 716************************************************************************ 717* Frobenius norm 718* SSQ(1) is scale 719* SSQ(2) is sum-of-squares 720* 721 ELSE IF( LSAME( NORM, 'F' ) .OR. LSAME( NORM, 'E' ) ) THEN 722* 723* Find normF( sub( A ) ). 724* 725 SSQ(1) = ZERO 726 SSQ(2) = ONE 727* 728* Add off-diagonal entries, first 729* 730 IF( LSAME( UPLO, 'U' ) ) THEN 731* 732* Handle first block separately 733* 734 IB = IN-IA+1 735* 736 IF( MYCOL.EQ.IACOL ) THEN 737 DO 370 K = (JJ-1)*LDA, (JJ+IB-2)*LDA, LDA 738 COLSSQ(1) = ZERO 739 COLSSQ(2) = ONE 740 CALL ZLASSQ( II-IIA, A( IIA+K ), 1, 741 $ COLSSQ(1), COLSSQ(2) ) 742 IF( MYROW.EQ.IAROW ) 743 $ II = II + 1 744 CALL ZLASSQ( II-IIA, A( IIA+K ), 1, 745 $ COLSSQ(1), COLSSQ(2) ) 746 CALL DCOMBSSQ( SSQ, COLSSQ ) 747 370 CONTINUE 748* 749 JJ = JJ + IB 750 ELSE IF( MYROW.EQ.IAROW ) THEN 751 II = II + IB 752 END IF 753* 754 ICURROW = MOD( IAROW+1, NPROW ) 755 ICURCOL = MOD( IACOL+1, NPCOL ) 756* 757* Loop over rows/columns of global matrix. 758* 759 DO 390 I = IN+1, IA+N-1, DESCA( MB_ ) 760 IB = MIN( DESCA( MB_ ), IA+N-I ) 761* 762 IF( MYCOL.EQ.ICURCOL ) THEN 763 DO 380 K = (JJ-1)*LDA, (JJ+IB-2)*LDA, LDA 764 COLSSQ(1) = ZERO 765 COLSSQ(2) = ONE 766 CALL ZLASSQ( II-IIA, A( IIA+K ), 1, 767 $ COLSSQ(1), COLSSQ(2) ) 768 IF( MYROW.EQ.ICURROW ) 769 $ II = II + 1 770 CALL ZLASSQ( II-IIA, A (IIA+K ), 1, 771 $ COLSSQ(1), COLSSQ(2) ) 772 CALL DCOMBSSQ( SSQ, COLSSQ ) 773 380 CONTINUE 774* 775 JJ = JJ + IB 776 ELSE IF( MYROW.EQ.ICURROW ) THEN 777 II = II + IB 778 END IF 779* 780 ICURROW = MOD( ICURROW+1, NPROW ) 781 ICURCOL = MOD( ICURCOL+1, NPCOL ) 782* 783 390 CONTINUE 784* 785 ELSE 786* 787* Handle first block separately 788* 789 IB = IN-IA+1 790* 791 IF( MYCOL.EQ.IACOL ) THEN 792 DO 400 K = (JJ-1)*LDA, (JJ+IB-2)*LDA, LDA 793 COLSSQ(1) = ZERO 794 COLSSQ(2) = ONE 795 CALL ZLASSQ( IIA+NP-II, A( II+K ), 1, 796 $ COLSSQ(1), COLSSQ(2) ) 797 IF( MYROW.EQ.IAROW ) 798 $ II = II + 1 799 CALL ZLASSQ( IIA+NP-II, A( II+K ), 1, 800 $ COLSSQ(1), COLSSQ(2) ) 801 CALL DCOMBSSQ( SSQ, COLSSQ ) 802 400 CONTINUE 803* 804 JJ = JJ + IB 805 ELSE IF( MYROW.EQ.IAROW ) THEN 806 II = II + IB 807 END IF 808* 809 ICURROW = MOD( IAROW+1, NPROW ) 810 ICURCOL = MOD( IACOL+1, NPCOL ) 811* 812* Loop over rows/columns of global matrix. 813* 814 DO 420 I = IN+1, IA+N-1, DESCA( MB_ ) 815 IB = MIN( DESCA( MB_ ), IA+N-I ) 816* 817 IF( MYCOL.EQ.ICURCOL ) THEN 818 DO 410 K = (JJ-1)*LDA, (JJ+IB-2)*LDA, LDA 819 COLSSQ(1) = ZERO 820 COLSSQ(2) = ONE 821 CALL ZLASSQ( IIA+NP-II, A( II+K ), 1, 822 $ COLSSQ(1), COLSSQ(2) ) 823 IF( MYROW.EQ.ICURROW ) 824 $ II = II + 1 825 CALL ZLASSQ( IIA+NP-II, A( II+K ), 1, 826 $ COLSSQ(1), COLSSQ(2) ) 827 CALL DCOMBSSQ( SSQ, COLSSQ ) 828 410 CONTINUE 829* 830 JJ = JJ + IB 831 ELSE IF( MYROW.EQ.ICURROW ) THEN 832 II = II + IB 833 END IF 834* 835 ICURROW = MOD( ICURROW+1, NPROW ) 836 ICURCOL = MOD( ICURCOL+1, NPCOL ) 837* 838 420 CONTINUE 839* 840 END IF 841* 842* Perform the global scaled sum 843* 844 CALL PDTREECOMB( ICTXT, 'All', 2, SSQ, IAROW, IACOL, 845 $ DCOMBSSQ ) 846 VALUE = SSQ( 1 ) * SQRT( SSQ( 2 ) ) 847* 848 END IF 849* 850* Broadcast the result to the other processes 851* 852 IF( MYROW.EQ.IAROW .AND. MYCOL.EQ.IACOL ) THEN 853 CALL DGEBS2D( ICTXT, 'All', ' ', 1, 1, VALUE, 1 ) 854 ELSE 855 CALL DGEBR2D( ICTXT, 'All', ' ', 1, 1, VALUE, 1, IAROW, 856 $ IACOL ) 857 END IF 858* 859 PZLANSY = VALUE 860* 861 RETURN 862* 863* End of PZLANSY 864* 865 END 866