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|
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
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