DOUBLE PRECISION FUNCTION PDLANSY( NORM, UPLO, 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, UPLO INTEGER IA, JA, N * .. * .. Array Arguments .. INTEGER DESCA( * ) DOUBLE PRECISION A( * ), WORK( * ) * .. * * Purpose * ======= * * PDLANSY returns the value of the one norm, or the Frobenius norm, * or the infinity norm, or the element of largest absolute value of a * real symmetric distributed matrix sub( A ) = A(IA:IA+N-1,JA:JA+N-1). * * PDLANSY 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 PDLANSY as described * above. * * UPLO (global input) CHARACTER * Specifies whether the upper or lower triangular part of the * symmetric matrix sub( A ) is to be referenced. * = 'U': Upper triangular part of sub( A ) is referenced, * = 'L': Lower triangular part of sub( A ) is referenced. * * 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, PDLANSY is set to zero. N >= 0. * * A (local input) DOUBLE PRECISION pointer into the local memory * to an array of dimension (LLD_A, LOCc(JA+N-1)) containing the * local pieces of the symmetric distributed matrix sub( A ). * If UPLO = 'U', the leading N-by-N upper triangular part of * sub( A ) contains the upper triangular matrix which norm is * to be computed, and the strictly lower triangular part of * this matrix is not referenced. If UPLO = 'L', the leading * N-by-N lower triangular part of sub( A ) contains the lower * triangular matrix which norm is to be computed, and the * strictly upper triangular part of sub( A ) is not referenced. * * 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), * 2*Nq0+Np0+LDW if NORM = '1', 'O', 'o', 'I' or 'i', * where LDW is given by: * IF( NPROW.NE.NPCOL ) THEN * LDW = MB_A*CEIL(CEIL(Np0/MB_A)/(LCM/NPROW)) * ELSE * LDW = 0 * END IF * 0 if NORM = 'F', 'f', 'E' or 'e' (not referenced), * * where LCM is the least common multiple of NPROW and NPCOL * LCM = ILCM( NPROW, NPCOL ) and CEIL denotes the ceiling * operation (ICEIL). * * 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 ), * * ICEIL, ILCM, 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 I, IAROW, IACOL, IB, ICOFF, ICTXT, ICURCOL, $ ICURROW, II, IIA, IN, IROFF, ICSR, ICSR0, $ IOFFA, IRSC, IRSC0, IRSR, IRSR0, JJ, JJA, K, $ LDA, LL, MYCOL, MYROW, NP, NPCOL, NPROW, NQ DOUBLE PRECISION SCALE, SUM, VALUE * .. * .. Local Arrays .. DOUBLE PRECISION RWORK( 2 ) * .. * .. External Subroutines .. EXTERNAL BLACS_GRIDINFO, DAXPY, DCOMBSSQ, $ DGAMX2D, DGSUM2D, DGEBR2D, $ DGEBS2D, DLASSQ, PDCOL2ROW, $ PDTREECOMB * .. * .. External Functions .. LOGICAL LSAME INTEGER ICEIL, IDAMAX, NUMROC EXTERNAL ICEIL, IDAMAX, LSAME, NUMROC * .. * .. Intrinsic Functions .. INTRINSIC ABS, MAX, MIN, MOD, SQRT * .. * .. Executable Statements .. * * Get grid parameters and local indexes. * 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 ) ICSR = 1 IRSR = ICSR + NQ IRSC = IRSR + NQ IF( MYROW.EQ.IAROW ) THEN IRSC0 = IRSC + IROFF NP = NP - IROFF ELSE IRSC0 = IRSC END IF IF( MYCOL.EQ.IACOL ) THEN ICSR0 = ICSR + ICOFF IRSR0 = IRSR + ICOFF NQ = NQ - ICOFF ELSE ICSR0 = ICSR IRSR0 = IRSR END IF IN = MIN( ICEIL( IA, DESCA( MB_ ) ) * DESCA( MB_ ), IA+N-1 ) LDA = DESCA( LLD_ ) * * If the matrix is symmetric, we address only a triangular portion * of the matrix. A sum of row (column) i of the complete matrix * can be obtained by adding along row i and column i of the the * triangular matrix, stopping/starting at the diagonal, which is * the point of reflection. The pictures below demonstrate this. * In the following code, the row sums created by --- rows below are * refered to as ROWSUMS, and the column sums shown by | are refered * to as COLSUMS. Infinity-norm = 1-norm = ROWSUMS+COLSUMS. * * UPLO = 'U' UPLO = 'L' * ____i______ ___________ * |\ | | |\ | * | \ | | | \ | * | \ | | | \ | * | \|------| i i|---\ | * | \ | | |\ | * | \ | | | \ | * | \ | | | \ | * | \ | | | \ | * | \ | | | \ | * | \ | | | \ | * |__________\| |___|______\| * i * * II, JJ : local indices into array A * ICURROW : process row containing diagonal block * ICURCOL : process column containing diagonal block * IRSC0 : pointer to part of work used to store the ROWSUMS while * they are stored along a process column * IRSR0 : pointer to part of work used to store the ROWSUMS after * they have been transposed to be along a process row * II = IIA JJ = JJA * IF( N.EQ.0 ) THEN * VALUE = ZERO * ELSE IF( LSAME( NORM, 'M' ) ) THEN * * Find max(abs(A(i,j))). * VALUE = ZERO * IF( LSAME( UPLO, 'U' ) ) THEN * * Handle first block separately * IB = IN-IA+1 * * Find COLMAXS * IF( MYCOL.EQ.IACOL ) THEN DO 20 K = (JJ-1)*LDA, (JJ+IB-2)*LDA, LDA IF( II.GT.IIA ) THEN DO 10 LL = IIA, II-1 VALUE = MAX( VALUE, ABS( A( LL+K ) ) ) 10 CONTINUE END IF IF( MYROW.EQ.IAROW ) $ II = II + 1 20 CONTINUE * * Reset local indices so we can find ROWMAXS * IF( MYROW.EQ.IAROW ) $ II = II - IB * END IF * * Find ROWMAXS * IF( MYROW.EQ.IAROW ) THEN DO 40 K = II, II+IB-1 IF( JJ.LE.JJA+NQ-1 ) THEN DO 30 LL = (JJ-1)*LDA, (JJA+NQ-2)*LDA, LDA VALUE = MAX( VALUE, ABS( A( K+LL ) ) ) 30 CONTINUE END IF IF( MYCOL.EQ.IACOL ) $ JJ = JJ + 1 40 CONTINUE II = II + IB ELSE IF( MYCOL.EQ.IACOL ) THEN JJ = JJ + IB END IF * ICURROW = MOD( IAROW+1, NPROW ) ICURCOL = MOD( IACOL+1, NPCOL ) * * Loop over the remaining rows/columns of the matrix. * DO 90 I = IN+1, IA+N-1, DESCA( MB_ ) IB = MIN( DESCA( MB_ ), IA+N-I ) * * Find COLMAXS * IF( MYCOL.EQ.ICURCOL ) THEN DO 60 K = (JJ-1)*LDA, (JJ+IB-2)*LDA, LDA IF( II.GT.IIA ) THEN DO 50 LL = IIA, II-1 VALUE = MAX( VALUE, ABS( A( LL+K ) ) ) 50 CONTINUE END IF IF( MYROW.EQ.ICURROW ) $ II = II + 1 60 CONTINUE * * Reset local indices so we can find ROWMAXS * IF( MYROW.EQ.ICURROW ) $ II = II - IB END IF * * Find ROWMAXS * IF( MYROW.EQ.ICURROW ) THEN DO 80 K = II, II+IB-1 IF( JJ.LE.JJA+NQ-1 ) THEN DO 70 LL = (JJ-1)*LDA, (JJA+NQ-2)*LDA, LDA VALUE = MAX( VALUE, ABS( A( K+LL ) ) ) 70 CONTINUE END IF IF( MYCOL.EQ.ICURCOL ) $ JJ = JJ + 1 80 CONTINUE II = II + IB ELSE IF( MYCOL.EQ.ICURCOL ) THEN JJ = JJ + IB END IF ICURROW = MOD( ICURROW+1, NPROW ) ICURCOL = MOD( ICURCOL+1, NPCOL ) 90 CONTINUE * ELSE * * Handle first block separately * IB = IN-IA+1 * * Find COLMAXS * IF( MYCOL.EQ.IACOL ) THEN DO 110 K = (JJ-1)*LDA, (JJ+IB-2)*LDA, LDA IF( II.LE.IIA+NP-1 ) THEN DO 100 LL = II, IIA+NP-1 VALUE = MAX( VALUE, ABS( A( LL+K ) ) ) 100 CONTINUE END IF IF( MYROW.EQ.IAROW ) $ II = II + 1 110 CONTINUE * * Reset local indices so we can find ROWMAXS * IF( MYROW.EQ.IAROW ) $ II = II - IB END IF * * Find ROWMAXS * IF( MYROW.EQ.IAROW ) THEN DO 130 K = 0, IB-1 IF( JJ.GT.JJA ) THEN DO 120 LL = (JJA-1)*LDA, (JJ-2)*LDA, LDA VALUE = MAX( VALUE, ABS( A( II+LL ) ) ) 120 CONTINUE END IF II = II + 1 IF( MYCOL.EQ.IACOL ) $ JJ = JJ + 1 130 CONTINUE ELSE IF( MYCOL.EQ.IACOL ) THEN JJ = JJ + IB END IF * ICURROW = MOD( IAROW+1, NPROW ) ICURCOL = MOD( IACOL+1, NPCOL ) * * Loop over rows/columns of global matrix. * DO 180 I = IN+1, IA+N-1, DESCA( MB_ ) IB = MIN( DESCA( MB_ ), IA+N-I ) * * Find COLMAXS * IF( MYCOL.EQ.ICURCOL ) THEN DO 150 K = (JJ-1)*LDA, (JJ+IB-2)*LDA, LDA IF( II.LE.IIA+NP-1 ) THEN DO 140 LL = II, IIA+NP-1 VALUE = MAX( VALUE, ABS( A( LL+K ) ) ) 140 CONTINUE END IF IF( MYROW.EQ.ICURROW ) $ II = II + 1 150 CONTINUE * * Reset local indices so we can find ROWMAXS * IF( MYROW.EQ.ICURROW ) $ II = II - IB END IF * * Find ROWMAXS * IF( MYROW.EQ.ICURROW ) THEN DO 170 K = 0, IB-1 IF( JJ.GT.JJA ) THEN DO 160 LL = (JJA-1)*LDA, (JJ-2)*LDA, LDA VALUE = MAX( VALUE, ABS( A( II+LL ) ) ) 160 CONTINUE END IF II = II + 1 IF( MYCOL.EQ.ICURCOL ) $ JJ = JJ + 1 170 CONTINUE ELSE IF( MYCOL.EQ.ICURCOL ) THEN JJ = JJ + IB END IF ICURROW = MOD( ICURROW+1, NPROW ) ICURCOL = MOD( ICURCOL+1, NPCOL ) * 180 CONTINUE * END IF * * Gather the result on process (IAROW,IACOL). * CALL DGAMX2D( ICTXT, 'All', ' ', 1, 1, VALUE, 1, I, K, -1, $ IAROW, IACOL ) * ELSE IF( LSAME( NORM, 'I' ) .OR. LSAME( NORM, 'O' ) .OR. $ NORM.EQ.'1' ) THEN * * Find normI( sub( A ) ) ( = norm1( sub( A ) ), since sub( A ) is * symmetric). * IF( LSAME( UPLO, 'U' ) ) THEN * * Handle first block separately * IB = IN-IA+1 * * Find COLSUMS * IF( MYCOL.EQ.IACOL ) THEN IOFFA = ( JJ - 1 ) * LDA DO 200 K = 0, IB-1 SUM = ZERO IF( II.GT.IIA ) THEN DO 190 LL = IIA, II-1 SUM = SUM + ABS( A( LL+IOFFA ) ) 190 CONTINUE END IF IOFFA = IOFFA + LDA WORK( JJ+K-JJA+ICSR0 ) = SUM IF( MYROW.EQ.IAROW ) $ II = II + 1 200 CONTINUE * * Reset local indices so we can find ROWSUMS * IF( MYROW.EQ.IAROW ) $ II = II - IB * END IF * * Find ROWSUMS * IF( MYROW.EQ.IAROW ) THEN DO 220 K = II, II+IB-1 SUM = ZERO IF( JJA+NQ.GT.JJ ) THEN DO 210 LL = (JJ-1)*LDA, (JJA+NQ-2)*LDA, LDA SUM = SUM + ABS( A( K+LL ) ) 210 CONTINUE END IF WORK( K-IIA+IRSC0 ) = SUM IF( MYCOL.EQ.IACOL ) $ JJ = JJ + 1 220 CONTINUE II = II + IB ELSE IF( MYCOL.EQ.IACOL ) THEN JJ = JJ + IB END IF * ICURROW = MOD( IAROW+1, NPROW ) ICURCOL = MOD( IACOL+1, NPCOL ) * * Loop over remaining rows/columns of global matrix. * DO 270 I = IN+1, IA+N-1, DESCA( MB_ ) IB = MIN( DESCA( MB_ ), IA+N-I ) * * Find COLSUMS * IF( MYCOL.EQ.ICURCOL ) THEN IOFFA = ( JJ - 1 ) * LDA DO 240 K = 0, IB-1 SUM = ZERO IF( II.GT.IIA ) THEN DO 230 LL = IIA, II-1 SUM = SUM + ABS( A( IOFFA+LL ) ) 230 CONTINUE END IF IOFFA = IOFFA + LDA WORK( JJ+K-JJA+ICSR0 ) = SUM IF( MYROW.EQ.ICURROW ) $ II = II + 1 240 CONTINUE * * Reset local indices so we can find ROWSUMS * IF( MYROW.EQ.ICURROW ) $ II = II - IB * END IF * * Find ROWSUMS * IF( MYROW.EQ.ICURROW ) THEN DO 260 K = II, II+IB-1 SUM = ZERO IF( JJA+NQ.GT.JJ ) THEN DO 250 LL = (JJ-1)*LDA, (JJA+NQ-2)*LDA, LDA SUM = SUM + ABS( A( K+LL ) ) 250 CONTINUE END IF WORK( K-IIA+IRSC0 ) = SUM IF( MYCOL.EQ.ICURCOL ) $ JJ = JJ + 1 260 CONTINUE II = II + IB ELSE IF( MYCOL.EQ.ICURCOL ) THEN JJ = JJ + IB END IF * ICURROW = MOD( ICURROW+1, NPROW ) ICURCOL = MOD( ICURCOL+1, NPCOL ) * 270 CONTINUE * ELSE * * Handle first block separately * IB = IN-IA+1 * * Find COLSUMS * IF( MYCOL.EQ.IACOL ) THEN IOFFA = (JJ-1)*LDA DO 290 K = 0, IB-1 SUM = ZERO IF( IIA+NP.GT.II ) THEN DO 280 LL = II, IIA+NP-1 SUM = SUM + ABS( A( IOFFA+LL ) ) 280 CONTINUE END IF IOFFA = IOFFA + LDA WORK( JJ+K-JJA+ICSR0 ) = SUM IF( MYROW.EQ.IAROW ) $ II = II + 1 290 CONTINUE * * Reset local indices so we can find ROWSUMS * IF( MYROW.EQ.IAROW ) $ II = II - IB * END IF * * Find ROWSUMS * IF( MYROW.EQ.IAROW ) THEN DO 310 K = II, II+IB-1 SUM = ZERO IF( JJ.GT.JJA ) THEN DO 300 LL = (JJA-1)*LDA, (JJ-2)*LDA, LDA SUM = SUM + ABS( A( K+LL ) ) 300 CONTINUE END IF WORK( K-IIA+IRSC0 ) = SUM IF( MYCOL.EQ.IACOL ) $ JJ = JJ + 1 310 CONTINUE II = II + IB ELSE IF( MYCOL.EQ.IACOL ) THEN JJ = JJ + IB END IF * ICURROW = MOD( IAROW+1, NPROW ) ICURCOL = MOD( IACOL+1, NPCOL ) * * Loop over rows/columns of global matrix. * DO 360 I = IN+1, IA+N-1, DESCA( MB_ ) IB = MIN( DESCA( MB_ ), IA+N-I ) * * Find COLSUMS * IF( MYCOL.EQ.ICURCOL ) THEN IOFFA = ( JJ - 1 ) * LDA DO 330 K = 0, IB-1 SUM = ZERO IF( IIA+NP.GT.II ) THEN DO 320 LL = II, IIA+NP-1 SUM = SUM + ABS( A( LL+IOFFA ) ) 320 CONTINUE END IF IOFFA = IOFFA + LDA WORK( JJ+K-JJA+ICSR0 ) = SUM IF( MYROW.EQ.ICURROW ) $ II = II + 1 330 CONTINUE * * Reset local indices so we can find ROWSUMS * IF( MYROW.EQ.ICURROW ) $ II = II - IB * END IF * * Find ROWSUMS * IF( MYROW.EQ.ICURROW ) THEN DO 350 K = II, II+IB-1 SUM = ZERO IF( JJ.GT.JJA ) THEN DO 340 LL = (JJA-1)*LDA, (JJ-2)*LDA, LDA SUM = SUM + ABS( A( K+LL ) ) 340 CONTINUE END IF WORK(K-IIA+IRSC0) = SUM IF( MYCOL.EQ.ICURCOL ) $ JJ = JJ + 1 350 CONTINUE II = II + IB ELSE IF( MYCOL.EQ.ICURCOL ) THEN JJ = JJ + IB END IF * ICURROW = MOD( ICURROW+1, NPROW ) ICURCOL = MOD( ICURCOL+1, NPCOL ) * 360 CONTINUE END IF * * After calls to DGSUM2D, process row 0 will have global * COLSUMS and process column 0 will have global ROWSUMS. * Transpose ROWSUMS and add to COLSUMS to get global row/column * sum, the max of which is the infinity or 1 norm. * IF( MYCOL.EQ.IACOL ) $ NQ = NQ + ICOFF CALL DGSUM2D( ICTXT, 'Columnwise', ' ', 1, NQ, WORK( ICSR ), 1, $ IAROW, MYCOL ) IF( MYROW.EQ.IAROW ) $ NP = NP + IROFF CALL DGSUM2D( ICTXT, 'Rowwise', ' ', NP, 1, WORK( IRSC ), $ MAX( 1, NP ), MYROW, IACOL ) * CALL PDCOL2ROW( ICTXT, N, 1, DESCA( MB_ ), WORK( IRSC ), $ MAX( 1, NP ), WORK( IRSR ), MAX( 1, NQ ), $ IAROW, IACOL, IAROW, IACOL, WORK( IRSC+NP ) ) * IF( MYROW.EQ.IAROW ) THEN IF( MYCOL.EQ.IACOL ) $ NQ = NQ - ICOFF CALL DAXPY( NQ, ONE, WORK( IRSR0 ), 1, WORK( ICSR0 ), 1 ) IF( NQ.LT.1 ) THEN VALUE = ZERO ELSE VALUE = WORK( IDAMAX( NQ, WORK( ICSR0 ), 1 ) ) END IF CALL DGAMX2D( ICTXT, 'Rowwise', ' ', 1, 1, VALUE, 1, I, K, $ -1, IAROW, IACOL ) END IF * ELSE IF( LSAME( NORM, 'F' ) .OR. LSAME( NORM, 'E' ) ) THEN * * Find normF( sub( A ) ). * SCALE = ZERO SUM = ONE * * Add off-diagonal entries, first * IF( LSAME( UPLO, 'U' ) ) THEN * * Handle first block separately * IB = IN-IA+1 * IF( MYCOL.EQ.IACOL ) THEN DO 370 K = (JJ-1)*LDA, (JJ+IB-2)*LDA, LDA CALL DLASSQ( II-IIA, A( IIA+K ), 1, SCALE, SUM ) IF( MYROW.EQ.IAROW ) $ II = II + 1 CALL DLASSQ( II-IIA, A( IIA+K ), 1, SCALE, SUM ) 370 CONTINUE * JJ = JJ + IB ELSE IF( MYROW.EQ.IAROW ) THEN II = II + IB END IF * ICURROW = MOD( IAROW+1, NPROW ) ICURCOL = MOD( IACOL+1, NPCOL ) * * Loop over rows/columns of global matrix. * DO 390 I = IN+1, IA+N-1, DESCA( MB_ ) IB = MIN( DESCA( MB_ ), IA+N-I ) * IF( MYCOL.EQ.ICURCOL ) THEN DO 380 K = (JJ-1)*LDA, (JJ+IB-2)*LDA, LDA CALL DLASSQ( II-IIA, A( IIA+K ), 1, SCALE, SUM ) IF( MYROW.EQ.ICURROW ) $ II = II + 1 CALL DLASSQ( II-IIA, A( IIA+K ), 1, SCALE, SUM ) 380 CONTINUE * JJ = JJ + IB ELSE IF( MYROW.EQ.ICURROW ) THEN II = II + IB END IF * ICURROW = MOD( ICURROW+1, NPROW ) ICURCOL = MOD( ICURCOL+1, NPCOL ) * 390 CONTINUE * ELSE * * Handle first block separately * IB = IN-IA+1 * IF( MYCOL.EQ.IACOL ) THEN DO 400 K = (JJ-1)*LDA, (JJ+IB-2)*LDA, LDA CALL DLASSQ( IIA+NP-II, A( II+K ), 1, SCALE, SUM ) IF( MYROW.EQ.IAROW ) $ II = II + 1 CALL DLASSQ( IIA+NP-II, A( II+K ), 1, SCALE, SUM ) 400 CONTINUE * JJ = JJ + IB ELSE IF( MYROW.EQ.IAROW ) THEN II = II + IB END IF * ICURROW = MOD( IAROW+1, NPROW ) ICURCOL = MOD( IACOL+1, NPCOL ) * * Loop over rows/columns of global matrix. * DO 420 I = IN+1, IA+N-1, DESCA( MB_ ) IB = MIN( DESCA( MB_ ), IA+N-I ) * IF( MYCOL.EQ.ICURCOL ) THEN DO 410 K = (JJ-1)*LDA, (JJ+IB-2)*LDA, LDA CALL DLASSQ( IIA+NP-II, A( II+K ), 1, SCALE, SUM ) IF( MYROW.EQ.ICURROW ) $ II = II + 1 CALL DLASSQ( IIA+NP-II, A( II+K ), 1, SCALE, SUM ) 410 CONTINUE * JJ = JJ + IB ELSE IF( MYROW.EQ.ICURROW ) THEN II = II + IB END IF * ICURROW = MOD( ICURROW+1, NPROW ) ICURCOL = MOD( ICURCOL+1, NPCOL ) * 420 CONTINUE * END IF * * Perform the global scaled sum * RWORK( 1 ) = SCALE RWORK( 2 ) = SUM * CALL PDTREECOMB( ICTXT, 'All', 2, RWORK, IAROW, IACOL, $ DCOMBSSQ ) VALUE = RWORK( 1 ) * SQRT( RWORK( 2 ) ) * END IF * * Broadcast the result to the other processes * IF( MYROW.EQ.IAROW .AND. MYCOL.EQ.IACOL ) THEN CALL DGEBS2D( ICTXT, 'All', ' ', 1, 1, VALUE, 1 ) ELSE CALL DGEBR2D( ICTXT, 'All', ' ', 1, 1, VALUE, 1, IAROW, $ IACOL ) END IF * PDLANSY = VALUE * RETURN * * End of PDLANSY * END