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|
DOUBLE PRECISION FUNCTION PZLANSY( NORM, UPLO, 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 NORM, UPLO
INTEGER IA, JA, N
* ..
* .. Array Arguments ..
INTEGER DESCA( * )
DOUBLE PRECISION WORK( * )
COMPLEX*16 A( * )
* ..
*
* Purpose
* =======
*
* PZLANSY 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).
*
* PZLANSY 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 PZLANSY 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, PZLANSY 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 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 SUM, VALUE
* ..
* .. Local Arrays ..
DOUBLE PRECISION SSQ( 2 ), COLSSQ( 2 )
* ..
* .. External Subroutines ..
EXTERNAL BLACS_GRIDINFO, DAXPY, DCOMBSSQ,
$ DGAMX2D, DGSUM2D, DGEBR2D,
$ DGEBS2D, PDCOL2ROW, PDTREECOMB,
$ ZLASSQ
* ..
* .. 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
*
************************************************************************
* max norm
*
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 )
*
************************************************************************
* one or inf norm
*
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
*
************************************************************************
* Frobenius norm
* SSQ(1) is scale
* SSQ(2) is sum-of-squares
*
ELSE IF( LSAME( NORM, 'F' ) .OR. LSAME( NORM, 'E' ) ) THEN
*
* Find normF( sub( A ) ).
*
SSQ(1) = ZERO
SSQ(2) = 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
COLSSQ(1) = ZERO
COLSSQ(2) = ONE
CALL ZLASSQ( II-IIA, A( IIA+K ), 1,
$ COLSSQ(1), COLSSQ(2) )
IF( MYROW.EQ.IAROW )
$ II = II + 1
CALL ZLASSQ( II-IIA, A( IIA+K ), 1,
$ COLSSQ(1), COLSSQ(2) )
CALL DCOMBSSQ( SSQ, COLSSQ )
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
COLSSQ(1) = ZERO
COLSSQ(2) = ONE
CALL ZLASSQ( II-IIA, A( IIA+K ), 1,
$ COLSSQ(1), COLSSQ(2) )
IF( MYROW.EQ.ICURROW )
$ II = II + 1
CALL ZLASSQ( II-IIA, A (IIA+K ), 1,
$ COLSSQ(1), COLSSQ(2) )
CALL DCOMBSSQ( SSQ, COLSSQ )
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
COLSSQ(1) = ZERO
COLSSQ(2) = ONE
CALL ZLASSQ( IIA+NP-II, A( II+K ), 1,
$ COLSSQ(1), COLSSQ(2) )
IF( MYROW.EQ.IAROW )
$ II = II + 1
CALL ZLASSQ( IIA+NP-II, A( II+K ), 1,
$ COLSSQ(1), COLSSQ(2) )
CALL DCOMBSSQ( SSQ, COLSSQ )
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
COLSSQ(1) = ZERO
COLSSQ(2) = ONE
CALL ZLASSQ( IIA+NP-II, A( II+K ), 1,
$ COLSSQ(1), COLSSQ(2) )
IF( MYROW.EQ.ICURROW )
$ II = II + 1
CALL ZLASSQ( IIA+NP-II, A( II+K ), 1,
$ COLSSQ(1), COLSSQ(2) )
CALL DCOMBSSQ( SSQ, COLSSQ )
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
*
CALL PDTREECOMB( ICTXT, 'All', 2, SSQ, IAROW, IACOL,
$ DCOMBSSQ )
VALUE = SSQ( 1 ) * SQRT( SSQ( 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
*
PZLANSY = VALUE
*
RETURN
*
* End of PZLANSY
*
END
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