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|
REAL FUNCTION PSLANHS( NORM, N, A, IA, JA, DESCA,
$ WORK )
*
* -- 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
INTEGER IA, JA, N
* ..
* .. Array Arguments ..
INTEGER DESCA( * )
REAL A( * ), WORK( * )
* ..
*
* Purpose
* =======
*
* PSLANHS 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).
*
* PSLANHS 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 PSLANHS 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, PSLANHS is set to zero. N >= 0.
*
* A (local input) REAL 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) REAL 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 )
REAL ONE, ZERO
PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+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
REAL SCALE, SUM, VALUE
* ..
* .. Local Arrays ..
REAL RWORK( 2 )
* ..
* .. External Subroutines ..
EXTERNAL BLACS_GRIDINFO, INFOG2L, PSTREECOMB,
$ SCOMBSSQ, SGEBR2D, SGEBS2D,
$ SGAMX2D, SGSUM2D, SLASSQ
* ..
* .. External Functions ..
LOGICAL LSAME
INTEGER ICEIL, ISAMAX, NUMROC
EXTERNAL LSAME, ICEIL, ISAMAX, 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 SGAMX2D( 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 SGSUM2D( 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( ISAMAX( NQ, WORK, 1 ) )
ELSE
VALUE = ZERO
END IF
CALL SGAMX2D( 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 SGSUM2D( 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( ISAMAX( NP, WORK, 1 ) )
ELSE
VALUE = ZERO
END IF
CALL SGAMX2D( 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 SLASSQ( 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 SLASSQ( 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 SLASSQ( 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 SLASSQ( 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 SLASSQ( 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 SLASSQ( 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 SLASSQ( 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 SLASSQ( 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 PSTREECOMB( ICTXT, 'All', 2, RWORK, 0, 0, SCOMBSSQ )
VALUE = RWORK( 1 ) * SQRT( RWORK( 2 ) )
*
END IF
*
IF( MYROW.EQ.0 .AND. MYCOL.EQ.0 ) THEN
CALL SGEBS2D( ICTXT, 'All', ' ', 1, 1, VALUE, 1 )
ELSE
CALL SGEBR2D( ICTXT, 'All', ' ', 1, 1, VALUE, 1, 0, 0 )
END IF
*
PSLANHS = VALUE
*
RETURN
*
* End of PSLANHS
*
END
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