DOUBLE PRECISION FUNCTION PZLANTR( NORM, UPLO, DIAG, M, N, A, $ IA, JA, DESCA, WORK ) IMPLICIT NONE * * -- ScaLAPACK auxiliary routine (version 1.7) -- * University of Tennessee, Knoxville, Oak Ridge National Laboratory, * and University of California, Berkeley. * May 1, 1997 * * .. Scalar Arguments .. CHARACTER DIAG, NORM, UPLO INTEGER IA, JA, M, N * .. * .. Array Arguments .. INTEGER DESCA( * ) DOUBLE PRECISION WORK( * ) COMPLEX*16 A( * ) * .. * * Purpose * ======= * * PZLANTR returns the value of the one norm, or the Frobenius norm, * or the infinity norm, or the element of largest absolute value of a * trapezoidal or triangular distributed matrix sub( A ) denoting * A(IA:IA+M-1, JA:JA+N-1). * * PZLANTR returns the value * * ( max(abs(A(i,j))), NORM = 'M' or 'm' with ia <= i <= ia+m-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 PZLANTR as described * above. * * UPLO (global input) CHARACTER * Specifies whether the matrix sub( A ) is upper or lower * trapezoidal. * = 'U': Upper trapezoidal * = 'L': Lower trapezoidal * Note that sub( A ) is triangular instead of trapezoidal * if M = N. * * DIAG (global input) CHARACTER * Specifies whether or not the distributed matrix sub( A ) has * unit diagonal. * = 'N': Non-unit diagonal * = 'U': Unit diagonal * * M (global input) INTEGER * The number of rows to be operated on i.e the number of rows * of the distributed submatrix sub( A ). When M = 0, PZLANTR is * set to zero. M >= 0. * * N (global input) INTEGER * The number of columns to be operated on i.e the number of * columns of the distributed submatrix sub( A ). When N = 0, * PZLANTR 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 ), * Mp0 = NUMROC( M+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 .. LOGICAL UDIAG INTEGER IACOL, IAROW, ICTXT, II, IIA, ICOFF, IOFFA, $ IROFF, J, JB, JJ, JJA, JN, KK, LDA, LL, MP, $ MYCOL, MYROW, NP, NPCOL, NPROW, NQ DOUBLE PRECISION SUM, VALUE * .. * .. Local Arrays .. DOUBLE PRECISION SSQ( 2 ), COLSSQ( 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, DBLE, MAX, MIN, MOD, SQRT * .. * .. Executable Statements .. * * Get grid parameters * ICTXT = DESCA( CTXT_ ) CALL BLACS_GRIDINFO( ICTXT, NPROW, NPCOL, MYROW, MYCOL ) * UDIAG = LSAME( DIAG, 'U' ) 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_ ) ) MP = NUMROC( M+IROFF, DESCA( MB_ ), MYROW, IAROW, NPROW ) NQ = NUMROC( N+ICOFF, DESCA( NB_ ), MYCOL, IACOL, NPCOL ) IF( MYROW.EQ.IAROW ) $ MP = MP - IROFF IF( MYCOL.EQ.IACOL ) $ NQ = NQ - ICOFF LDA = DESCA( LLD_ ) IOFFA = ( JJA - 1 ) * LDA * IF( MIN( M, N ).EQ.0 ) THEN * VALUE = ZERO * ************************************************************************ * max norm * ELSE IF( LSAME( NORM, 'M' ) ) THEN * * Find max(abs(A(i,j))). * IF( UDIAG ) THEN VALUE = ONE ELSE VALUE = ZERO END IF * IF( LSAME( UPLO, 'U' ) ) THEN * * Upper triangular matrix * II = IIA JJ = JJA JN = MIN( ICEIL( JA, DESCA( NB_ ) ) * DESCA( NB_ ), JA+N-1 ) JB = JN-JA+1 * IF( MYCOL.EQ.IACOL ) THEN IF( MYROW.EQ.IAROW ) THEN IF( UDIAG ) THEN DO 20 LL = JJ, JJ + JB -1 DO 10 KK = IIA, MIN(II+LL-JJ-1,IIA+MP-1) VALUE = MAX( VALUE, ABS( A( IOFFA+KK ) ) ) 10 CONTINUE IOFFA = IOFFA + LDA 20 CONTINUE ELSE DO 40 LL = JJ, JJ + JB -1 DO 30 KK = IIA, MIN( II+LL-JJ, IIA+MP-1 ) VALUE = MAX( VALUE, ABS( A( IOFFA+KK ) ) ) 30 CONTINUE IOFFA = IOFFA + LDA 40 CONTINUE END IF ELSE DO 60 LL = JJ, JJ + JB -1 DO 50 KK = IIA, MIN( II-1, IIA+MP-1 ) VALUE = MAX( VALUE, ABS( A( IOFFA+KK ) ) ) 50 CONTINUE IOFFA = IOFFA + LDA 60 CONTINUE END IF JJ = JJ + JB END IF * IF( MYROW.EQ.IAROW ) $ II = II + JB IAROW = MOD( IAROW+1, NPROW ) IACOL = MOD( IACOL+1, NPCOL ) * * Loop over remaining block of columns * DO 130 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 IF( UDIAG ) THEN DO 80 LL = JJ, JJ + JB -1 DO 70 KK = IIA, MIN( II+LL-JJ-1, IIA+MP-1 ) VALUE = MAX( VALUE, ABS( A( IOFFA+KK ) ) ) 70 CONTINUE IOFFA = IOFFA + LDA 80 CONTINUE ELSE DO 100 LL = JJ, JJ + JB -1 DO 90 KK = IIA, MIN( II+LL-JJ, IIA+MP-1 ) VALUE = MAX( VALUE, ABS( A( IOFFA+KK ) ) ) 90 CONTINUE IOFFA = IOFFA + LDA 100 CONTINUE END IF ELSE DO 120 LL = JJ, JJ + JB -1 DO 110 KK = IIA, MIN( II-1, IIA+MP-1 ) VALUE = MAX( VALUE, ABS( A( IOFFA+KK ) ) ) 110 CONTINUE IOFFA = IOFFA + LDA 120 CONTINUE END IF JJ = JJ + JB END IF * IF( MYROW.EQ.IAROW ) $ II = II + JB IAROW = MOD( IAROW+1, NPROW ) IACOL = MOD( IACOL+1, NPCOL ) * 130 CONTINUE * ELSE * * Lower triangular matrix * II = IIA JJ = JJA JN = MIN( ICEIL( JA, DESCA( NB_ ) ) * DESCA( NB_ ), JA+N-1 ) JB = JN-JA+1 * IF( MYCOL.EQ.IACOL ) THEN IF( MYROW.EQ.IAROW ) THEN IF( UDIAG ) THEN DO 150 LL = JJ, JJ + JB -1 DO 140 KK = II+LL-JJ+1, IIA+MP-1 VALUE = MAX( VALUE, ABS( A( IOFFA+KK ) ) ) 140 CONTINUE IOFFA = IOFFA + LDA 150 CONTINUE ELSE DO 170 LL = JJ, JJ + JB -1 DO 160 KK = II+LL-JJ, IIA+MP-1 VALUE = MAX( VALUE, ABS( A( IOFFA+KK ) ) ) 160 CONTINUE IOFFA = IOFFA + LDA 170 CONTINUE END IF ELSE DO 190 LL = JJ, JJ + JB -1 DO 180 KK = II, IIA+MP-1 VALUE = MAX( VALUE, ABS( A( IOFFA+KK ) ) ) 180 CONTINUE IOFFA = IOFFA + LDA 190 CONTINUE END IF JJ = JJ + JB END IF * IF( MYROW.EQ.IAROW ) $ II = II + JB IAROW = MOD( IAROW+1, NPROW ) IACOL = MOD( IACOL+1, NPCOL ) * * Loop over remaining block of columns * DO 260 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 IF( UDIAG ) THEN DO 210 LL = JJ, JJ + JB -1 DO 200 KK = II+LL-JJ+1, IIA+MP-1 VALUE = MAX( VALUE, ABS( A( IOFFA+KK ) ) ) 200 CONTINUE IOFFA = IOFFA + LDA 210 CONTINUE ELSE DO 230 LL = JJ, JJ + JB -1 DO 220 KK = II+LL-JJ, IIA+MP-1 VALUE = MAX( VALUE, ABS( A( IOFFA+KK ) ) ) 220 CONTINUE IOFFA = IOFFA + LDA 230 CONTINUE END IF ELSE DO 250 LL = JJ, JJ + JB -1 DO 240 KK = II, IIA+MP-1 VALUE = MAX( VALUE, ABS( A( IOFFA+KK ) ) ) 240 CONTINUE IOFFA = IOFFA + LDA 250 CONTINUE END IF JJ = JJ + JB END IF * IF( MYROW.EQ.IAROW ) $ II = II + JB IAROW = MOD( IAROW+1, NPROW ) IACOL = MOD( IACOL+1, NPCOL ) * 260 CONTINUE * END IF * * Gather the intermediate results to process (0,0). * CALL DGAMX2D( ICTXT, 'All', ' ', 1, 1, VALUE, 1, KK, LL, -1, $ 0, 0 ) * ************************************************************************ * one norm * ELSE IF( LSAME( NORM, 'O' ) .OR. NORM.EQ.'1' ) THEN * VALUE = ZERO * IF( LSAME( UPLO, 'U' ) ) THEN * * Upper triangular matrix * II = IIA JJ = JJA JN = MIN( ICEIL( JA, DESCA( NB_ ) ) * DESCA( NB_ ), JA+N-1 ) JB = JN-JA+1 * IF( MYCOL.EQ.IACOL ) THEN IF( MYROW.EQ.IAROW ) THEN IF( UDIAG ) THEN DO 280 LL = JJ, JJ + JB -1 SUM = ZERO DO 270 KK = IIA, MIN( II+LL-JJ-1, IIA+MP-1 ) SUM = SUM + ABS( A( IOFFA+KK ) ) 270 CONTINUE * Unit diagonal entry KK = II+LL-JJ IF (KK <= IIA+MP-1) THEN SUM = SUM + ONE ENDIF IOFFA = IOFFA + LDA WORK( LL-JJA+1 ) = SUM 280 CONTINUE ELSE DO 300 LL = JJ, JJ + JB -1 SUM = ZERO DO 290 KK = IIA, MIN( II+LL-JJ, IIA+MP-1 ) SUM = SUM + ABS( A( IOFFA+KK ) ) 290 CONTINUE IOFFA = IOFFA + LDA WORK( LL-JJA+1 ) = SUM 300 CONTINUE END IF ELSE DO 320 LL = JJ, JJ + JB -1 SUM = ZERO DO 310 KK = IIA, MIN( II-1, IIA+MP-1 ) SUM = SUM + ABS( A( IOFFA+KK ) ) 310 CONTINUE IOFFA = IOFFA + LDA WORK( LL-JJA+1 ) = SUM 320 CONTINUE END IF JJ = JJ + JB END IF * IF( MYROW.EQ.IAROW ) $ II = II + JB IAROW = MOD( IAROW+1, NPROW ) IACOL = MOD( IACOL+1, NPCOL ) * * Loop over remaining block of columns * DO 390 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 IF( UDIAG ) THEN DO 340 LL = JJ, JJ + JB -1 SUM = ZERO DO 330 KK = IIA, MIN( II+LL-JJ-1, IIA+MP-1 ) SUM = SUM + ABS( A( IOFFA+KK ) ) 330 CONTINUE * Unit diagonal entry KK = II+LL-JJ IF (KK <= IIA+MP-1) THEN SUM = SUM + ONE ENDIF IOFFA = IOFFA + LDA WORK( LL-JJA+1 ) = SUM 340 CONTINUE ELSE DO 360 LL = JJ, JJ + JB -1 SUM = ZERO DO 350 KK = IIA, MIN( II+LL-JJ, IIA+MP-1 ) SUM = SUM + ABS( A( IOFFA+KK ) ) 350 CONTINUE IOFFA = IOFFA + LDA WORK( LL-JJA+1 ) = SUM 360 CONTINUE END IF ELSE DO 380 LL = JJ, JJ + JB -1 SUM = ZERO DO 370 KK = IIA, MIN( II-1, IIA+MP-1 ) SUM = SUM + ABS( A( IOFFA+KK ) ) 370 CONTINUE IOFFA = IOFFA + LDA WORK( LL-JJA+1 ) = SUM 380 CONTINUE END IF JJ = JJ + JB END IF * IF( MYROW.EQ.IAROW ) $ II = II + JB IAROW = MOD( IAROW+1, NPROW ) IACOL = MOD( IACOL+1, NPCOL ) * 390 CONTINUE * ELSE * * Lower triangular matrix * II = IIA JJ = JJA JN = MIN( ICEIL( JA, DESCA( NB_ ) ) * DESCA( NB_ ), JA+N-1 ) JB = JN-JA+1 * IF( MYCOL.EQ.IACOL ) THEN IF( MYROW.EQ.IAROW ) THEN IF( UDIAG ) THEN DO 410 LL = JJ, JJ + JB -1 SUM = ONE DO 400 KK = II+LL-JJ+1, IIA+MP-1 SUM = SUM + ABS( A( IOFFA+KK ) ) 400 CONTINUE IOFFA = IOFFA + LDA WORK( LL-JJA+1 ) = SUM 410 CONTINUE ELSE DO 430 LL = JJ, JJ + JB -1 SUM = ZERO DO 420 KK = II+LL-JJ, IIA+MP-1 SUM = SUM + ABS( A( IOFFA+KK ) ) 420 CONTINUE IOFFA = IOFFA + LDA WORK( LL-JJA+1 ) = SUM 430 CONTINUE END IF ELSE DO 450 LL = JJ, JJ + JB -1 SUM = ZERO DO 440 KK = II, IIA+MP-1 SUM = SUM + ABS( A( IOFFA+KK ) ) 440 CONTINUE IOFFA = IOFFA + LDA WORK( LL-JJA+1 ) = SUM 450 CONTINUE END IF JJ = JJ + JB END IF * IF( MYROW.EQ.IAROW ) $ II = II + JB IAROW = MOD( IAROW+1, NPROW ) IACOL = MOD( IACOL+1, NPCOL ) * * Loop over remaining block of columns * DO 520 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 IF( UDIAG ) THEN DO 470 LL = JJ, JJ + JB -1 SUM = ONE DO 460 KK = II+LL-JJ+1, IIA+MP-1 SUM = SUM + ABS( A( IOFFA+KK ) ) 460 CONTINUE IOFFA = IOFFA + LDA WORK( LL-JJA+1 ) = SUM 470 CONTINUE ELSE DO 490 LL = JJ, JJ + JB -1 SUM = ZERO DO 480 KK = II+LL-JJ, IIA+MP-1 SUM = SUM + ABS( A( IOFFA+KK ) ) 480 CONTINUE IOFFA = IOFFA + LDA WORK( LL-JJA+1 ) = SUM 490 CONTINUE END IF ELSE DO 510 LL = JJ, JJ + JB -1 SUM = ZERO DO 500 KK = II, IIA+MP-1 SUM = SUM + ABS( A( IOFFA+KK ) ) 500 CONTINUE IOFFA = IOFFA + LDA WORK( LL-JJA+1 ) = SUM 510 CONTINUE END IF JJ = JJ + JB END IF * IF( MYROW.EQ.IAROW ) $ II = II + JB IAROW = MOD( IAROW+1, NPROW ) IACOL = MOD( IACOL+1, NPCOL ) * 520 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 * ************************************************************************ * infinity norm * ELSE IF( LSAME( NORM, 'I' ) ) THEN * IF( LSAME( UPLO, 'U' ) ) THEN DO 540 KK = IIA, IIA+MP-1 WORK( KK ) = ZERO 540 CONTINUE ELSE DO 570 KK = IIA, IIA+MP-1 WORK( KK ) = ZERO 570 CONTINUE END IF * IF( LSAME( UPLO, 'U' ) ) THEN * * Upper triangular matrix * II = IIA JJ = JJA JN = MIN( ICEIL( JA, DESCA( NB_ ) ) * DESCA( NB_ ), JA+N-1 ) JB = JN-JA+1 * IF( MYCOL.EQ.IACOL ) THEN IF( MYROW.EQ.IAROW ) THEN IF( UDIAG ) THEN DO 590 LL = JJ, JJ + JB -1 DO 580 KK = IIA, MIN( II+LL-JJ-1, IIA+MP-1 ) WORK( KK-IIA+1 ) = WORK( KK-IIA+1 ) + $ ABS( A( IOFFA+KK ) ) 580 CONTINUE * Unit diagonal entry KK = II+LL-JJ IF (KK <= IIA+MP-1) THEN WORK( KK-IIA+1 ) = WORK( KK-IIA+1 ) + ONE ENDIF IOFFA = IOFFA + LDA 590 CONTINUE ELSE DO 610 LL = JJ, JJ + JB -1 DO 600 KK = IIA, MIN( II+LL-JJ, IIA+MP-1 ) WORK( KK-IIA+1 ) = WORK( KK-IIA+1 ) + $ ABS( A( IOFFA+KK ) ) 600 CONTINUE IOFFA = IOFFA + LDA 610 CONTINUE END IF ELSE DO 630 LL = JJ, JJ + JB -1 DO 620 KK = IIA, MIN( II-1, IIA+MP-1 ) WORK( KK-IIA+1 ) = WORK( KK-IIA+1 ) + $ ABS( A( IOFFA+KK ) ) 620 CONTINUE IOFFA = IOFFA + LDA 630 CONTINUE END IF JJ = JJ + JB END IF * IF( MYROW.EQ.IAROW ) $ II = II + JB IAROW = MOD( IAROW+1, NPROW ) IACOL = MOD( IACOL+1, NPCOL ) * * Loop over remaining block of columns * DO 700 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 IF( UDIAG ) THEN DO 650 LL = JJ, JJ + JB -1 DO 640 KK = IIA, MIN( II+LL-JJ-1, IIA+MP-1 ) WORK( KK-IIA+1 ) = WORK( KK-IIA+1 ) + $ ABS( A( IOFFA+KK ) ) 640 CONTINUE * Unit diagonal entry KK = II+LL-JJ IF (KK <= IIA+MP-1) THEN WORK( KK-IIA+1 ) = WORK( KK-IIA+1 ) + ONE ENDIF IOFFA = IOFFA + LDA 650 CONTINUE ELSE DO 670 LL = JJ, JJ + JB -1 DO 660 KK = IIA, MIN( II+LL-JJ, IIA+MP-1 ) WORK( KK-IIA+1 ) = WORK( KK-IIA+1 ) + $ ABS( A( IOFFA+KK ) ) 660 CONTINUE IOFFA = IOFFA + LDA 670 CONTINUE END IF ELSE DO 690 LL = JJ, JJ + JB -1 DO 680 KK = IIA, MIN( II-1, IIA+MP-1 ) WORK( KK-IIA+1 ) = WORK( KK-IIA+1 ) + $ ABS( A( IOFFA+KK ) ) 680 CONTINUE IOFFA = IOFFA + LDA 690 CONTINUE END IF JJ = JJ + JB END IF * IF( MYROW.EQ.IAROW ) $ II = II + JB IAROW = MOD( IAROW+1, NPROW ) IACOL = MOD( IACOL+1, NPCOL ) * 700 CONTINUE * ELSE * * Lower triangular matrix * II = IIA JJ = JJA JN = MIN( ICEIL( JA, DESCA( NB_ ) ) * DESCA( NB_ ), JA+N-1 ) JB = JN-JA+1 * IF( MYCOL.EQ.IACOL ) THEN IF( MYROW.EQ.IAROW ) THEN IF( UDIAG ) THEN DO 720 LL = JJ, JJ + JB -1 * Unit diagonal entry KK = II+LL-JJ WORK( KK-IIA+1 ) = WORK( KK-IIA+1 ) + ONE DO 710 KK = II+LL-JJ+1, IIA+MP-1 WORK( KK-IIA+1 ) = WORK( KK-IIA+1 ) + $ ABS( A( IOFFA+KK ) ) 710 CONTINUE IOFFA = IOFFA + LDA 720 CONTINUE ELSE DO 740 LL = JJ, JJ + JB -1 DO 730 KK = II+LL-JJ, IIA+MP-1 WORK( KK-IIA+1 ) = WORK( KK-IIA+1 ) + $ ABS( A( IOFFA+KK ) ) 730 CONTINUE IOFFA = IOFFA + LDA 740 CONTINUE END IF ELSE DO 760 LL = JJ, JJ + JB -1 DO 750 KK = II, IIA+MP-1 WORK( KK-IIA+1 ) = WORK( KK-IIA+1 ) + $ ABS( A( IOFFA+KK ) ) 750 CONTINUE IOFFA = IOFFA + LDA 760 CONTINUE END IF JJ = JJ + JB END IF * IF( MYROW.EQ.IAROW ) $ II = II + JB IAROW = MOD( IAROW+1, NPROW ) IACOL = MOD( IACOL+1, NPCOL ) * * Loop over remaining block of columns * DO 830 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 IF( UDIAG ) THEN DO 780 LL = JJ, JJ + JB -1 * Unit diagonal entry KK = II+LL-JJ WORK( KK-IIA+1 ) = WORK( KK-IIA+1 ) + ONE DO 770 KK = II+LL-JJ+1, IIA+MP-1 WORK( KK-IIA+1 ) = WORK( KK-IIA+1 ) + $ ABS( A( IOFFA+KK ) ) 770 CONTINUE IOFFA = IOFFA + LDA 780 CONTINUE ELSE DO 800 LL = JJ, JJ + JB -1 DO 790 KK = II+LL-JJ, IIA+MP-1 WORK( KK-IIA+1 ) = WORK( KK-IIA+1 ) + $ ABS( A( IOFFA+KK ) ) 790 CONTINUE IOFFA = IOFFA + LDA 800 CONTINUE END IF ELSE DO 820 LL = JJ, JJ + JB -1 DO 810 KK = II, IIA+MP-1 WORK( KK-IIA+1 ) = WORK( KK-IIA+1 ) + $ ABS( A( IOFFA+KK ) ) 810 CONTINUE IOFFA = IOFFA + LDA 820 CONTINUE END IF JJ = JJ + JB END IF * IF( MYROW.EQ.IAROW ) $ II = II + JB IAROW = MOD( IAROW+1, NPROW ) IACOL = MOD( IACOL+1, NPCOL ) * 830 CONTINUE * END IF * * Find sum of global matrix rows and store on column 0 of * process grid * CALL DGSUM2D( ICTXT, 'Rowwise', ' ', MP, 1, WORK, MAX( 1, MP ), $ MYROW, 0 ) * * Find maximum sum of rows for Infinity-norm * IF( MYCOL.EQ.0 ) THEN IF( MP.GT.0 ) THEN VALUE = WORK( IDAMAX( MP, WORK, 1 ) ) ELSE VALUE = ZERO END IF CALL DGAMX2D( ICTXT, 'Columnwise', ' ', 1, 1, VALUE, 1, KK, $ LL, -1, 0, 0 ) END IF * ************************************************************************ * Frobenius norm * SSQ(1) is scale * SSQ(2) is sum-of-squares * ELSE IF( LSAME( NORM, 'F' ) .OR. LSAME( NORM, 'E' ) ) THEN * IF( UDIAG ) THEN SSQ(1) = ONE SSQ(2) = DBLE( MIN( M, N ) ) / DBLE( NPROW*NPCOL ) ELSE SSQ(1) = ZERO SSQ(2) = ONE END IF * IF( LSAME( UPLO, 'U' ) ) THEN * * *********************** * Upper triangular matrix * II = IIA JJ = JJA JN = MIN( ICEIL( JA, DESCA( NB_ ) ) * DESCA( NB_ ), JA+N-1 ) JB = JN-JA+1 * * First block column of sub-matrix. * IF( MYCOL.EQ.IACOL ) THEN IF( MYROW.EQ.IAROW ) THEN * This process has part of current block column, * including diagonal block. IF( UDIAG ) THEN DO 840 LL = JJ, JJ + JB -1 COLSSQ(1) = ZERO COLSSQ(2) = ONE CALL ZLASSQ( MIN( II+LL-JJ-1, IIA+MP-1 )-IIA+1, $ A( IIA+IOFFA ), 1, $ COLSSQ(1), COLSSQ(2) ) CALL DCOMBSSQ( SSQ, COLSSQ ) IOFFA = IOFFA + LDA 840 CONTINUE ELSE DO 850 LL = JJ, JJ + JB -1 COLSSQ(1) = ZERO COLSSQ(2) = ONE CALL ZLASSQ( MIN( II+LL-JJ, IIA+MP-1 )-IIA+1, $ A( IIA+IOFFA ), 1, $ COLSSQ(1), COLSSQ(2) ) CALL DCOMBSSQ( SSQ, COLSSQ ) IOFFA = IOFFA + LDA 850 CONTINUE END IF ELSE * This rank has part of current block column, * but not diagonal block. * It seems this lassq will be length 0, since ii = iia. DO 860 LL = JJ, JJ + JB -1 COLSSQ(1) = ZERO COLSSQ(2) = ONE CALL ZLASSQ( MIN( II-1, IIA+MP-1 )-IIA+1, $ A( IIA+IOFFA ), 1, $ COLSSQ(1), COLSSQ(2) ) CALL DCOMBSSQ( SSQ, COLSSQ ) IOFFA = IOFFA + LDA 860 CONTINUE END IF JJ = JJ + JB END IF * * If this process has part of current block row, advance ii, * then advance iarow, iacol to next diagonal block. * IF( MYROW.EQ.IAROW ) $ II = II + JB IAROW = MOD( IAROW+1, NPROW ) IACOL = MOD( IACOL+1, NPCOL ) * * Loop over remaining block columns * DO 900 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 IF( UDIAG ) THEN DO 870 LL = JJ, JJ + JB -1 COLSSQ(1) = ZERO COLSSQ(2) = ONE CALL ZLASSQ( MIN(II+LL-JJ-1, IIA+MP-1)-IIA+1, $ A( IIA+IOFFA ), 1, $ COLSSQ(1), COLSSQ(2) ) CALL DCOMBSSQ( SSQ, COLSSQ ) IOFFA = IOFFA + LDA 870 CONTINUE ELSE DO 880 LL = JJ, JJ + JB -1 COLSSQ(1) = ZERO COLSSQ(2) = ONE CALL ZLASSQ( MIN( II+LL-JJ, IIA+MP-1 )-IIA+1, $ A( IIA+IOFFA ), 1, $ COLSSQ(1), COLSSQ(2) ) CALL DCOMBSSQ( SSQ, COLSSQ ) IOFFA = IOFFA + LDA 880 CONTINUE END IF ELSE DO 890 LL = JJ, JJ + JB -1 COLSSQ(1) = ZERO COLSSQ(2) = ONE CALL ZLASSQ( MIN( II-1, IIA+MP-1 )-IIA+1, $ A( IIA+IOFFA ), 1, $ COLSSQ(1), COLSSQ(2) ) CALL DCOMBSSQ( SSQ, COLSSQ ) IOFFA = IOFFA + LDA 890 CONTINUE END IF JJ = JJ + JB END IF * IF( MYROW.EQ.IAROW ) $ II = II + JB IAROW = MOD( IAROW+1, NPROW ) IACOL = MOD( IACOL+1, NPCOL ) * 900 CONTINUE * ELSE * * *********************** * Lower triangular matrix * II = IIA JJ = JJA JN = MIN( ICEIL( JA, DESCA( NB_ ) ) * DESCA( NB_ ), JA+N-1 ) JB = JN-JA+1 * IF( MYCOL.EQ.IACOL ) THEN IF( MYROW.EQ.IAROW ) THEN IF( UDIAG ) THEN DO 910 LL = JJ, JJ + JB -1 COLSSQ(1) = ZERO COLSSQ(2) = ONE CALL ZLASSQ( IIA+MP-(II+LL-JJ+1), $ A( II+LL-JJ+1+IOFFA ), 1, $ COLSSQ(1), COLSSQ(2) ) CALL DCOMBSSQ( SSQ, COLSSQ ) IOFFA = IOFFA + LDA 910 CONTINUE ELSE DO 920 LL = JJ, JJ + JB -1 COLSSQ(1) = ZERO COLSSQ(2) = ONE CALL ZLASSQ( IIA+MP-(II+LL-JJ), $ A( II+LL-JJ+IOFFA ), 1, $ COLSSQ(1), COLSSQ(2) ) CALL DCOMBSSQ( SSQ, COLSSQ ) IOFFA = IOFFA + LDA 920 CONTINUE END IF ELSE DO 930 LL = JJ, JJ + JB -1 COLSSQ(1) = ZERO COLSSQ(2) = ONE CALL ZLASSQ( IIA+MP-II, A( II+IOFFA ), 1, $ COLSSQ(1), COLSSQ(2) ) CALL DCOMBSSQ( SSQ, COLSSQ ) IOFFA = IOFFA + LDA 930 CONTINUE END IF JJ = JJ + JB END IF * IF( MYROW.EQ.IAROW ) $ II = II + JB IAROW = MOD( IAROW+1, NPROW ) IACOL = MOD( IACOL+1, NPCOL ) * * Loop over remaining block of columns * DO 970 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 IF( UDIAG ) THEN DO 940 LL = JJ, JJ + JB -1 COLSSQ(1) = ZERO COLSSQ(2) = ONE CALL ZLASSQ( IIA+MP-(II+LL-JJ+1), $ A( II+LL-JJ+1+IOFFA ), 1, $ COLSSQ(1), COLSSQ(2) ) CALL DCOMBSSQ( SSQ, COLSSQ ) IOFFA = IOFFA + LDA 940 CONTINUE ELSE DO 950 LL = JJ, JJ + JB -1 COLSSQ(1) = ZERO COLSSQ(2) = ONE CALL ZLASSQ( IIA+MP-(II+LL-JJ), $ A( II+LL-JJ+IOFFA ), 1, $ COLSSQ(1), COLSSQ(2) ) CALL DCOMBSSQ( SSQ, COLSSQ ) IOFFA = IOFFA + LDA 950 CONTINUE END IF ELSE DO 960 LL = JJ, JJ + JB -1 COLSSQ(1) = ZERO COLSSQ(2) = ONE CALL ZLASSQ( IIA+MP-II, A( II+IOFFA ), 1, $ COLSSQ(1), COLSSQ(2) ) CALL DCOMBSSQ( SSQ, COLSSQ ) IOFFA = IOFFA + LDA 960 CONTINUE END IF JJ = JJ + JB END IF * IF( MYROW.EQ.IAROW ) $ II = II + JB IAROW = MOD( IAROW+1, NPROW ) IACOL = MOD( IACOL+1, NPCOL ) * 970 CONTINUE * END IF * * *********************** * Perform the global scaled sum * CALL PDTREECOMB( ICTXT, 'All', 2, SSQ, 0, 0, DCOMBSSQ ) VALUE = SSQ( 1 ) * SQRT( SSQ( 2 ) ) * END IF * * Broadcast the result to every process in the grid. * 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 * PZLANTR = VALUE * RETURN * * End of PZLANTR * END