DOUBLE PRECISION FUNCTION PZLANHS( NORM, N, A, IA, JA, DESCA, $ WORK ) * * -- ScaLAPACK auxiliary routine (version 1.5) -- * University of Tennessee, Knoxville, Oak Ridge National Laboratory, * and University of California, Berkeley. * May 1, 1997 * * .. Scalar Arguments .. CHARACTER NORM INTEGER IA, JA, N * .. * .. Array Arguments .. INTEGER DESCA( * ) DOUBLE PRECISION WORK( * ) COMPLEX*16 A( * ) * .. * * Purpose * ======= * * PZLANHS returns the value of the one norm, or the Frobenius norm, * or the infinity norm, or the element of largest absolute value of a * Hessenberg distributed matrix sub( A ) = A(IA:IA+N-1,JA:JA+N-1). * * PZLANHS returns the value * * ( max(abs(A(i,j))), NORM = 'M' or 'm' with IA <= i <= IA+N-1, * ( and JA <= j <= JA+N-1, * ( * ( norm1( sub( A ) ), NORM = '1', 'O' or 'o' * ( * ( normI( sub( A ) ), NORM = 'I' or 'i' * ( * ( normF( sub( A ) ), NORM = 'F', 'f', 'E' or 'e' * * where norm1 denotes the one norm of a matrix (maximum column sum), * normI denotes the infinity norm of a matrix (maximum row sum) and * normF denotes the Frobenius norm of a matrix (square root of sum of * squares). Note that max(abs(A(i,j))) is not a matrix norm. * * Notes * ===== * * Each global data object is described by an associated description * vector. This vector stores the information required to establish * the mapping between an object element and its corresponding process * and memory location. * * Let A be a generic term for any 2D block cyclicly distributed array. * Such a global array has an associated description vector DESCA. * In the following comments, the character _ should be read as * "of the global array". * * NOTATION STORED IN EXPLANATION * --------------- -------------- -------------------------------------- * DTYPE_A(global) DESCA( DTYPE_ )The descriptor type. In this case, * DTYPE_A = 1. * CTXT_A (global) DESCA( CTXT_ ) The BLACS context handle, indicating * the BLACS process grid A is distribu- * ted over. The context itself is glo- * bal, but the handle (the integer * value) may vary. * M_A (global) DESCA( M_ ) The number of rows in the global * array A. * N_A (global) DESCA( N_ ) The number of columns in the global * array A. * MB_A (global) DESCA( MB_ ) The blocking factor used to distribute * the rows of the array. * NB_A (global) DESCA( NB_ ) The blocking factor used to distribute * the columns of the array. * RSRC_A (global) DESCA( RSRC_ ) The process row over which the first * row of the array A is distributed. * CSRC_A (global) DESCA( CSRC_ ) The process column over which the * first column of the array A is * distributed. * LLD_A (local) DESCA( LLD_ ) The leading dimension of the local * array. LLD_A >= MAX(1,LOCr(M_A)). * * Let K be the number of rows or columns of a distributed matrix, * and assume that its process grid has dimension p x q. * LOCr( K ) denotes the number of elements of K that a process * would receive if K were distributed over the p processes of its * process column. * Similarly, LOCc( K ) denotes the number of elements of K that a * process would receive if K were distributed over the q processes of * its process row. * The values of LOCr() and LOCc() may be determined via a call to the * ScaLAPACK tool function, NUMROC: * LOCr( M ) = NUMROC( M, MB_A, MYROW, RSRC_A, NPROW ), * LOCc( N ) = NUMROC( N, NB_A, MYCOL, CSRC_A, NPCOL ). * An upper bound for these quantities may be computed by: * LOCr( M ) <= ceil( ceil(M/MB_A)/NPROW )*MB_A * LOCc( N ) <= ceil( ceil(N/NB_A)/NPCOL )*NB_A * * Arguments * ========= * * NORM (global input) CHARACTER * Specifies the value to be returned in PZLANHS as described * above. * * N (global input) INTEGER * The number of rows and columns to be operated on i.e the * number of rows and columns of the distributed submatrix * sub( A ). When N = 0, PZLANHS is set to zero. N >= 0. * * A (local input) COMPLEX*16 pointer into the local memory * to an array of dimension (LLD_A, LOCc(JA+N-1) ) containing * the local pieces of sub( A ). * * IA (global input) INTEGER * The row index in the global array A indicating the first * row of sub( A ). * * JA (global input) INTEGER * The column index in the global array A indicating the * first column of sub( A ). * * DESCA (global and local input) INTEGER array of dimension DLEN_. * The array descriptor for the distributed matrix A. * * WORK (local workspace) DOUBLE PRECISION array dimension (LWORK) * LWORK >= 0 if NORM = 'M' or 'm' (not referenced), * Nq0 if NORM = '1', 'O' or 'o', * Mp0 if NORM = 'I' or 'i', * 0 if NORM = 'F', 'f', 'E' or 'e' (not referenced), * where * * IROFFA = MOD( IA-1, MB_A ), ICOFFA = MOD( JA-1, NB_A ), * IAROW = INDXG2P( IA, MB_A, MYROW, RSRC_A, NPROW ), * IACOL = INDXG2P( JA, NB_A, MYCOL, CSRC_A, NPCOL ), * Np0 = NUMROC( N+IROFFA, MB_A, MYROW, IAROW, NPROW ), * Nq0 = NUMROC( N+ICOFFA, NB_A, MYCOL, IACOL, NPCOL ), * * INDXG2P and NUMROC are ScaLAPACK tool functions; MYROW, * MYCOL, NPROW and NPCOL can be determined by calling the * subroutine BLACS_GRIDINFO. * * ===================================================================== * * .. Parameters .. INTEGER BLOCK_CYCLIC_2D, CSRC_, CTXT_, DLEN_, DTYPE_, $ LLD_, MB_, M_, NB_, N_, RSRC_ PARAMETER ( BLOCK_CYCLIC_2D = 1, DLEN_ = 9, DTYPE_ = 1, $ CTXT_ = 2, M_ = 3, N_ = 4, MB_ = 5, NB_ = 6, $ RSRC_ = 7, CSRC_ = 8, LLD_ = 9 ) DOUBLE PRECISION ONE, ZERO PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) * .. * .. Local Scalars .. INTEGER IACOL, IAROW, ICTXT, II, IIA, ICOFF, INXTROW, $ IOFFA, IROFF, J, JB, JJ, JJA, JN, KK, LDA, LL, $ MYCOL, MYROW, NP, NPCOL, NPROW, NQ DOUBLE PRECISION SCALE, SUM, VALUE * .. * .. Local Arrays .. DOUBLE PRECISION RWORK( 2 ) * .. * .. External Subroutines .. EXTERNAL BLACS_GRIDINFO, DCOMBSSQ, DGEBR2D, $ DGEBS2D, DGAMX2D, DGSUM2D, $ INFOG2L, PDTREECOMB, ZLASSQ * .. * .. External Functions .. LOGICAL LSAME INTEGER ICEIL, IDAMAX, NUMROC EXTERNAL LSAME, ICEIL, IDAMAX, NUMROC * .. * .. Intrinsic Functions .. INTRINSIC ABS, MAX, MIN, MOD, SQRT * .. * .. Executable Statements .. * * Get grid parameters. * ICTXT = DESCA( CTXT_ ) CALL BLACS_GRIDINFO( ICTXT, NPROW, NPCOL, MYROW, MYCOL ) * CALL INFOG2L( IA, JA, DESCA, NPROW, NPCOL, MYROW, MYCOL, IIA, JJA, $ IAROW, IACOL ) IROFF = MOD( IA-1, DESCA( MB_ ) ) ICOFF = MOD( JA-1, DESCA( NB_ ) ) NP = NUMROC( N+IROFF, DESCA( MB_ ), MYROW, IAROW, NPROW ) NQ = NUMROC( N+ICOFF, DESCA( NB_ ), MYCOL, IACOL, NPCOL ) IF( MYROW.EQ.IAROW ) $ NP = NP - IROFF IF( MYCOL.EQ.IACOL ) $ NQ = NQ - ICOFF LDA = DESCA( LLD_ ) IOFFA = ( JJA - 1 ) * LDA * IF( N.EQ.0 ) THEN * VALUE = ZERO * ELSE IF( LSAME( NORM, 'M' ) ) THEN * VALUE = ZERO * * Find max(abs(A(i,j))). * II = IIA JJ = JJA JN = MIN( ICEIL( JA, DESCA( NB_ ) ) * DESCA( NB_ ), JA+N-1 ) JB = JN-JA+1 * * Only one process row * IF( NPROW.EQ.1 ) THEN * * Handle first block of columns separately * IF( MYCOL.EQ.IACOL ) THEN DO 20 LL = JJ, JJ+JB-1 DO 10 KK = IIA, MIN( II+LL-JJ+1, IIA+NP-1 ) VALUE = MAX( VALUE, ABS( A( IOFFA+KK ) ) ) 10 CONTINUE IOFFA = IOFFA + LDA 20 CONTINUE JJ = JJ + JB END IF * IACOL = MOD( IACOL+1, NPCOL ) * * Loop over remaining block of columns * DO 50 J = JN+1, JA+N-1, DESCA( NB_ ) JB = MIN( JA+N-J, DESCA( NB_ ) ) * IF( MYCOL.EQ.IACOL ) THEN DO 40 LL = JJ, JJ+JB-1 DO 30 KK = IIA, MIN( II+LL-JJ+1, IIA+NP-1 ) VALUE = MAX( VALUE, ABS( A( IOFFA+KK ) ) ) 30 CONTINUE IOFFA = IOFFA + LDA 40 CONTINUE JJ = JJ + JB END IF * II = II + JB IACOL = MOD( IACOL+1, NPCOL ) * 50 CONTINUE * ELSE * * Handle first block of columns separately * INXTROW = MOD( IAROW+1, NPROW ) IF( MYCOL.EQ.IACOL ) THEN IF( MYROW.EQ.IAROW ) THEN DO 70 LL = JJ, JJ + JB -1 DO 60 KK = IIA, MIN( II+LL-JJ+1, IIA+NP-1 ) VALUE = MAX( VALUE, ABS( A( IOFFA+KK ) ) ) 60 CONTINUE IOFFA = IOFFA + LDA 70 CONTINUE ELSE DO 90 LL = JJ, JJ+JB-1 DO 80 KK = IIA, MIN( II-1, IIA+NP-1 ) VALUE = MAX( VALUE, ABS( A( IOFFA+KK ) ) ) 80 CONTINUE IOFFA = IOFFA + LDA 90 CONTINUE IF( MYROW.EQ.INXTROW .AND. II.LE.IIA+NP-1 ) $ VALUE = MAX( VALUE, ABS( A( II+(JJ+JB-2)*LDA ) ) ) END IF JJ = JJ + JB END IF * IF( MYROW.EQ.IAROW ) $ II = II + JB IAROW = INXTROW IAROW = MOD( IAROW+1, NPROW ) IACOL = MOD( IACOL+1, NPCOL ) * * Loop over remaining block of columns * DO 140 J = JN+1, JA+N-1, DESCA( NB_ ) JB = MIN( JA+N-J, DESCA( NB_ ) ) * IF( MYCOL.EQ.IACOL ) THEN IF( MYROW.EQ.IAROW ) THEN DO 110 LL = JJ, JJ + JB -1 DO 100 KK = IIA, MIN( II+LL-JJ+1, IIA+NP-1 ) VALUE = MAX( VALUE, ABS( A( IOFFA+KK ) ) ) 100 CONTINUE IOFFA = IOFFA + LDA 110 CONTINUE ELSE DO 130 LL = JJ, JJ + JB -1 DO 120 KK = IIA, MIN( II-1, IIA+NP-1 ) VALUE = MAX( VALUE, ABS( A( IOFFA+KK ) ) ) 120 CONTINUE IOFFA = IOFFA + LDA 130 CONTINUE IF( MYROW.EQ.INXTROW .AND. II.LE.IIA+NP-1 ) $ VALUE = MAX( VALUE, $ ABS( A( II+(JJ+JB-2)*LDA ) ) ) END IF JJ = JJ + JB END IF * IF( MYROW.EQ.IAROW ) $ II = II + JB IAROW = INXTROW IAROW = MOD( IAROW+1, NPROW ) IACOL = MOD( IACOL+1, NPCOL ) * 140 CONTINUE * END IF * * Gather the intermediate results to process (0,0). * CALL DGAMX2D( ICTXT, 'All', ' ', 1, 1, VALUE, 1, KK, LL, -1, $ 0, 0 ) * ELSE IF( LSAME( NORM, 'O' ) .OR. NORM.EQ.'1' ) THEN * VALUE = ZERO II = IIA JJ = JJA JN = MIN( ICEIL( JA, DESCA( NB_ ) ) * DESCA( NB_ ), JA+N-1 ) JB = JN-JA+1 * * Only one process row * IF( NPROW.EQ.1 ) THEN * * Handle first block of columns separately * IF( MYCOL.EQ.IACOL ) THEN DO 160 LL = JJ, JJ+JB-1 SUM = ZERO DO 150 KK = IIA, MIN( II+LL-JJ+1, IIA+NP-1 ) SUM = SUM + ABS( A( IOFFA+KK ) ) 150 CONTINUE IOFFA = IOFFA + LDA WORK( LL-JJA+1 ) = SUM 160 CONTINUE JJ = JJ + JB END IF * IACOL = MOD( IACOL+1, NPCOL ) * * Loop over remaining block of columns * DO 190 J = JN+1, JA+N-1, DESCA( NB_ ) JB = MIN( JA+N-J, DESCA( NB_ ) ) * IF( MYCOL.EQ.IACOL ) THEN DO 180 LL = JJ, JJ+JB-1 SUM = ZERO DO 170 KK = IIA, MIN( II+LL-JJ+1, IIA+NP-1 ) SUM = SUM + ABS( A( IOFFA+KK ) ) 170 CONTINUE IOFFA = IOFFA + LDA WORK( LL-JJA+1 ) = SUM 180 CONTINUE JJ = JJ + JB END IF * II = II + JB IACOL = MOD( IACOL+1, NPCOL ) * 190 CONTINUE * ELSE * * Handle first block of columns separately * INXTROW = MOD( IAROW+1, NPROW ) IF( MYCOL.EQ.IACOL ) THEN IF( MYROW.EQ.IAROW ) THEN DO 210 LL = JJ, JJ + JB -1 SUM = ZERO DO 200 KK = IIA, MIN( II+LL-JJ+1, IIA+NP-1 ) SUM = SUM + ABS( A( IOFFA+KK ) ) 200 CONTINUE IOFFA = IOFFA + LDA WORK( LL-JJA+1 ) = SUM 210 CONTINUE ELSE DO 230 LL = JJ, JJ + JB -1 SUM = ZERO DO 220 KK = IIA, MIN( II-1, IIA+NP-1 ) SUM = SUM + ABS( A( IOFFA+KK ) ) 220 CONTINUE IOFFA = IOFFA + LDA WORK( LL-JJA+1 ) = SUM 230 CONTINUE IF( MYROW.EQ.INXTROW .AND. II.LE.IIA+NP-1 ) $ WORK( JJ+JB-JJA ) = WORK( JJ+JB-JJA ) + $ ABS( A( II+(JJ+JB-2)*LDA ) ) END IF JJ = JJ + JB END IF * IF( MYROW.EQ.IAROW ) $ II = II + JB IAROW = INXTROW IAROW = MOD( IAROW+1, NPROW ) IACOL = MOD( IACOL+1, NPCOL ) * * Loop over remaining block of columns * DO 280 J = JN+1, JA+N-1, DESCA( NB_ ) JB = MIN( JA+N-J, DESCA( NB_ ) ) * IF( MYCOL.EQ.IACOL ) THEN IF( MYROW.EQ.IAROW ) THEN DO 250 LL = JJ, JJ + JB -1 SUM = ZERO DO 240 KK = IIA, MIN( II+LL-JJ+1, IIA+NP-1 ) SUM = SUM + ABS( A( IOFFA+KK ) ) 240 CONTINUE IOFFA = IOFFA + LDA WORK( LL-JJA+1 ) = SUM 250 CONTINUE ELSE DO 270 LL = JJ, JJ + JB -1 SUM = ZERO DO 260 KK = IIA, MIN( II-1, IIA+NP-1 ) SUM = SUM + ABS( A( IOFFA+KK ) ) 260 CONTINUE IOFFA = IOFFA + LDA WORK( LL-JJA+1 ) = SUM 270 CONTINUE IF( MYROW.EQ.INXTROW .AND. II.LE.IIA+NP-1 ) $ WORK( JJ+JB-JJA ) = WORK( JJ+JB-JJA ) + $ ABS( A( II+(JJ+JB-2)*LDA ) ) END IF JJ = JJ + JB END IF * IF( MYROW.EQ.IAROW ) $ II = II + JB IAROW = INXTROW IAROW = MOD( IAROW+1, NPROW ) IACOL = MOD( IACOL+1, NPCOL ) * 280 CONTINUE * END IF * * Find sum of global matrix columns and store on row 0 of * process grid * CALL DGSUM2D( ICTXT, 'Columnwise', ' ', 1, NQ, WORK, 1, $ 0, MYCOL ) * * Find maximum sum of columns for 1-norm * IF( MYROW.EQ.0 ) THEN IF( NQ.GT.0 ) THEN VALUE = WORK( IDAMAX( NQ, WORK, 1 ) ) ELSE VALUE = ZERO END IF CALL DGAMX2D( ICTXT, 'Rowwise', ' ', 1, 1, VALUE, 1, KK, LL, $ -1, 0, 0 ) END IF * ELSE IF( LSAME( NORM, 'I' ) ) THEN * DO 290 KK = IIA, IIA+NP-1 WORK( KK ) = ZERO 290 CONTINUE * II = IIA JJ = JJA JN = MIN( ICEIL( JA, DESCA( NB_ ) ) * DESCA( NB_ ), JA+N-1 ) JB = JN-JA+1 * * Only one process row * IF( NPROW.EQ.1 ) THEN * * Handle first block of columns separately * IF( MYCOL.EQ.IACOL ) THEN DO 310 LL = JJ, JJ+JB-1 DO 300 KK = IIA, MIN( II+LL-JJ+1, IIA+NP-1 ) WORK( KK-IIA+1 ) = WORK( KK-IIA+1 ) + $ ABS( A( IOFFA+KK ) ) 300 CONTINUE IOFFA = IOFFA + LDA 310 CONTINUE JJ = JJ + JB END IF * IACOL = MOD( IACOL+1, NPCOL ) * * Loop over remaining block of columns * DO 340 J = JN+1, JA+N-1, DESCA( NB_ ) JB = MIN( JA+N-J, DESCA( NB_ ) ) * IF( MYCOL.EQ.IACOL ) THEN DO 330 LL = JJ, JJ+JB-1 DO 320 KK = IIA, MIN( II+LL-JJ+1, IIA+NP-1 ) WORK( KK-IIA+1 ) = WORK( KK-IIA+1 ) + $ ABS( A( IOFFA+KK ) ) 320 CONTINUE IOFFA = IOFFA + LDA 330 CONTINUE JJ = JJ + JB END IF * II = II + JB IACOL = MOD( IACOL+1, NPCOL ) * 340 CONTINUE * ELSE * * Handle first block of columns separately * INXTROW = MOD( IAROW+1, NPROW ) IF( MYCOL.EQ.IACOL ) THEN IF( MYROW.EQ.IAROW ) THEN DO 360 LL = JJ, JJ + JB -1 DO 350 KK = IIA, MIN( II+LL-JJ+1, IIA+NP-1 ) WORK( KK-IIA+1 ) = WORK( KK-IIA+1 ) + $ ABS( A( IOFFA+KK ) ) 350 CONTINUE IOFFA = IOFFA + LDA 360 CONTINUE ELSE DO 380 LL = JJ, JJ + JB -1 DO 370 KK = IIA, MIN( II-1, IIA+NP-1 ) WORK( KK-IIA+1 ) = WORK( KK-IIA+1 ) + $ ABS( A( IOFFA+KK ) ) 370 CONTINUE IOFFA = IOFFA + LDA 380 CONTINUE IF( MYROW.EQ.INXTROW .AND. II.LE.IIA+NP-1 ) $ WORK( II-IIA+1 ) = WORK( II-IIA+1 ) + $ ABS( A( II+(JJ+JB-2)*LDA ) ) END IF JJ = JJ + JB END IF * IF( MYROW.EQ.IAROW ) $ II = II + JB IAROW = INXTROW IAROW = MOD( IAROW+1, NPROW ) IACOL = MOD( IACOL+1, NPCOL ) * * Loop over remaining block of columns * DO 430 J = JN+1, JA+N-1, DESCA( NB_ ) JB = MIN( JA+N-J, DESCA( NB_ ) ) * IF( MYCOL.EQ.IACOL ) THEN IF( MYROW.EQ.IAROW ) THEN DO 400 LL = JJ, JJ + JB -1 DO 390 KK = IIA, MIN( II+LL-JJ+1, IIA+NP-1 ) WORK( KK-IIA+1 ) = WORK( KK-IIA+1 ) + $ ABS( A( IOFFA+KK ) ) 390 CONTINUE IOFFA = IOFFA + LDA 400 CONTINUE ELSE DO 420 LL = JJ, JJ + JB -1 DO 410 KK = IIA, MIN( II-1, IIA+NP-1 ) WORK( KK-IIA+1 ) = WORK( KK-IIA+1 ) + $ ABS(A(IOFFA+KK)) 410 CONTINUE IOFFA = IOFFA + LDA 420 CONTINUE IF( MYROW.EQ.INXTROW .AND. II.LE.IIA+NP-1 ) $ WORK( II-IIA+1 ) = WORK( II-IIA+1 ) + $ ABS( A( II+(JJ+JB-2)*LDA ) ) END IF JJ = JJ + JB END IF * IF( MYROW.EQ.IAROW ) $ II = II + JB IAROW = INXTROW IAROW = MOD( IAROW+1, NPROW ) IACOL = MOD( IACOL+1, NPCOL ) * 430 CONTINUE * END IF * * Find sum of global matrix rows and store on column 0 of * process grid * CALL DGSUM2D( ICTXT, 'Rowwise', ' ', NP, 1, WORK, MAX( 1, NP ), $ MYROW, 0 ) * * Find maximum sum of rows for Infinity-norm * IF( MYCOL.EQ.0 ) THEN IF( NP.GT.0 ) THEN VALUE = WORK( IDAMAX( NP, WORK, 1 ) ) ELSE VALUE = ZERO END IF CALL DGAMX2D( ICTXT, 'Columnwise', ' ', 1, 1, VALUE, 1, KK, $ LL, -1, 0, 0 ) END IF * ELSE IF( LSAME( NORM, 'F' ) .OR. LSAME( NORM, 'E' ) ) THEN * SCALE = ZERO SUM = ONE II = IIA JJ = JJA JN = MIN( ICEIL( JA, DESCA( NB_ ) ) * DESCA( NB_ ), JA+N-1 ) JB = JN-JA+1 * * Only one process row * IF( NPROW.EQ.1 ) THEN * * Handle first block of columns separately * IF( MYCOL.EQ.IACOL ) THEN DO 440 LL = JJ, JJ+JB-1 CALL ZLASSQ( MIN( II+LL-JJ+1, IIA+NP-1 )-IIA+1, $ A( IIA+IOFFA ), 1, SCALE, SUM ) IOFFA = IOFFA + LDA 440 CONTINUE JJ = JJ + JB END IF * IACOL = MOD( IACOL+1, NPCOL ) * * Loop over remaining block of columns * DO 460 J = JN+1, JA+N-1, DESCA( NB_ ) JB = MIN( JA+N-J, DESCA( NB_ ) ) * IF( MYCOL.EQ.IACOL ) THEN DO 450 LL = JJ, JJ+JB-1 CALL ZLASSQ( MIN( II+LL-JJ+1, IIA+NP-1 )-IIA+1, $ A( IIA+IOFFA ), 1, SCALE, SUM ) IOFFA = IOFFA + LDA 450 CONTINUE JJ = JJ + JB END IF * II = II + JB IACOL = MOD( IACOL+1, NPCOL ) * 460 CONTINUE * ELSE * * Handle first block of columns separately * INXTROW = MOD( IAROW+1, NPROW ) IF( MYCOL.EQ.IACOL ) THEN IF( MYROW.EQ.IAROW ) THEN DO 470 LL = JJ, JJ + JB -1 CALL ZLASSQ( MIN( II+LL-JJ+1, IIA+NP-1 )-IIA+1, $ A( IIA+IOFFA ), 1, SCALE, SUM ) IOFFA = IOFFA + LDA 470 CONTINUE ELSE DO 480 LL = JJ, JJ + JB -1 CALL ZLASSQ( MIN( II-1, IIA+NP-1 )-IIA+1, $ A( IIA+IOFFA ), 1, SCALE, SUM ) IOFFA = IOFFA + LDA 480 CONTINUE IF( MYROW.EQ.INXTROW .AND. II.LE.IIA+NP-1 ) $ CALL ZLASSQ( 1, A( II+(JJ+JB-2)*LDA ), 1, $ SCALE, SUM ) END IF JJ = JJ + JB END IF * IF( MYROW.EQ.IAROW ) $ II = II + JB IAROW = INXTROW IAROW = MOD( IAROW+1, NPROW ) IACOL = MOD( IACOL+1, NPCOL ) * * Loop over remaining block of columns * DO 510 J = JN+1, JA+N-1, DESCA( NB_ ) JB = MIN( JA+N-J, DESCA( NB_ ) ) * IF( MYCOL.EQ.IACOL ) THEN IF( MYROW.EQ.IAROW ) THEN DO 490 LL = JJ, JJ + JB -1 CALL ZLASSQ( MIN( II+LL-JJ+1, IIA+NP-1 )-IIA+1, $ A( IIA+IOFFA ), 1, SCALE, SUM ) IOFFA = IOFFA + LDA 490 CONTINUE ELSE DO 500 LL = JJ, JJ + JB -1 CALL ZLASSQ( MIN( II-1, IIA+NP-1 )-IIA+1, $ A( IIA+IOFFA ), 1, SCALE, SUM ) IOFFA = IOFFA + LDA 500 CONTINUE IF( MYROW.EQ.INXTROW .AND. II.LE.IIA+NP-1 ) $ CALL ZLASSQ( 1, A( II+(JJ+JB-2)*LDA ), 1, $ SCALE, SUM ) END IF JJ = JJ + JB END IF * IF( MYROW.EQ.IAROW ) $ II = II + JB IAROW = INXTROW IAROW = MOD( IAROW+1, NPROW ) IACOL = MOD( IACOL+1, NPCOL ) * 510 CONTINUE * END IF * * Perform the global scaled sum * RWORK( 1 ) = SCALE RWORK( 2 ) = SUM CALL PDTREECOMB( ICTXT, 'All', 2, RWORK, 0, 0, DCOMBSSQ ) VALUE = RWORK( 1 ) * SQRT( RWORK( 2 ) ) * END IF * IF( MYROW.EQ.0 .AND. MYCOL.EQ.0 ) THEN CALL DGEBS2D( ICTXT, 'All', ' ', 1, 1, VALUE, 1 ) ELSE CALL DGEBR2D( ICTXT, 'All', ' ', 1, 1, VALUE, 1, 0, 0 ) END IF * PZLANHS = VALUE * RETURN * * End of PZLANHS * END