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SUBROUTINE PZLACON( N, V, IV, JV, DESCV, X, IX, JX, DESCX, EST,
$ KASE )
*
* -- ScaLAPACK auxiliary routine (version 1.7) --
* University of Tennessee, Knoxville, Oak Ridge National Laboratory,
* and University of California, Berkeley.
* May 1, 1997
*
* .. Scalar Arguments ..
INTEGER IV, IX, JV, JX, KASE, N
DOUBLE PRECISION EST
* ..
* .. Array Arguments ..
INTEGER DESCV( * ), DESCX( * )
COMPLEX*16 V( * ), X( * )
* ..
*
* Purpose
* =======
*
* PZLACON estimates the 1-norm of a square, complex distributed matrix
* A. Reverse communication is used for evaluating matrix-vector
* products. X and V are aligned with the distributed matrix A, this
* information is implicitly contained within IV, IX, DESCV, and DESCX.
*
* 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
* =========
*
* N (global input) INTEGER
* The length of the distributed vectors V and X. N >= 0.
*
* V (local workspace) COMPLEX*16 pointer into the local
* memory to an array of dimension LOCr(N+MOD(IV-1,MB_V)). On
* the final return, V = A*W, where EST = norm(V)/norm(W)
* (W is not returned).
*
* IV (global input) INTEGER
* The row index in the global array V indicating the first
* row of sub( V ).
*
* JV (global input) INTEGER
* The column index in the global array V indicating the
* first column of sub( V ).
*
* DESCV (global and local input) INTEGER array of dimension DLEN_.
* The array descriptor for the distributed matrix V.
*
* X (local input/local output) COMPLEX*16 pointer into the
* local memory to an array of dimension
* LOCr(N+MOD(IX-1,MB_X)). On an intermediate return, X
* should be overwritten by
* A * X, if KASE=1,
* A' * X, if KASE=2,
* where A' is the conjugate transpose of A, and PZLACON must
* be re-called with all the other parameters unchanged.
*
* IX (global input) INTEGER
* The row index in the global array X indicating the first
* row of sub( X ).
*
* JX (global input) INTEGER
* The column index in the global array X indicating the
* first column of sub( X ).
*
* DESCX (global and local input) INTEGER array of dimension DLEN_.
* The array descriptor for the distributed matrix X.
*
*
* EST (global output) DOUBLE PRECISION
* An estimate (a lower bound) for norm(A).
*
* KASE (local input/local output) INTEGER
* On the initial call to PZLACON, KASE should be 0.
* On an intermediate return, KASE will be 1 or 2, indicating
* whether X should be overwritten by A * X or A' * X.
* On the final return from PZLACON, KASE will again be 0.
*
* Further Details
* ===============
*
* The serial version ZLACON has been contributed by Nick Higham,
* University of Manchester. It was originally named SONEST, dated
* March 16, 1988.
*
* Reference: N.J. Higham, "FORTRAN codes for estimating the one-norm of
* a real or complex matrix, with applications to condition estimation",
* ACM Trans. Math. Soft., vol. 14, no. 4, pp. 381-396, December 1988.
*
* =====================================================================
*
* .. 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 )
INTEGER ITMAX
PARAMETER ( ITMAX = 5 )
DOUBLE PRECISION ONE, TWO
PARAMETER ( ONE = 1.0D+0, TWO = 2.0D+0 )
COMPLEX*16 CZERO, CONE
PARAMETER ( CZERO = ( 0.0D+0, 0.0D+0 ),
$ CONE = ( 1.0D+0, 0.0D+0 ) )
* ..
* .. Local Scalars ..
INTEGER I, ICTXT, IIVX, IMAXROW, IOFFVX, IROFF, ITER,
$ IVXCOL, IVXROW, J, JLAST, JJVX, JUMP, K,
$ MYCOL, MYROW, NP, NPCOL, NPROW
DOUBLE PRECISION ALTSGN, ESTOLD, SAFMIN, TEMP
COMPLEX*16 JLMAX, XMAX
* ..
* .. Local Arrays ..
COMPLEX*16 WORK( 2 )
* ..
* .. External Subroutines ..
EXTERNAL BLACS_GRIDINFO, INFOG2L, DGEBR2D,
$ DGEBS2D, PDZSUM1, PZELGET,
$ PZMAX1, ZCOPY, ZGEBR2D, ZGEBS2D
* ..
* .. External Functions ..
INTEGER INDXG2L, INDXG2P, INDXL2G, NUMROC
DOUBLE PRECISION PDLAMCH
EXTERNAL INDXG2L, INDXG2P, INDXL2G, NUMROC, PDLAMCH
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS, DBLE, DCMPLX
* ..
* .. Save statement ..
SAVE
* ..
* .. Executable Statements ..
*
* Get grid parameters.
*
ICTXT = DESCX( CTXT_ )
CALL BLACS_GRIDINFO( ICTXT, NPROW, NPCOL, MYROW, MYCOL )
*
CALL INFOG2L( IX, JX, DESCX, NPROW, NPCOL, MYROW, MYCOL,
$ IIVX, JJVX, IVXROW, IVXCOL )
IF( MYCOL.NE.IVXCOL )
$ RETURN
IROFF = MOD( IX-1, DESCX( MB_ ) )
NP = NUMROC( N+IROFF, DESCX( MB_ ), MYROW, IVXROW, NPROW )
IF( MYROW.EQ.IVXROW )
$ NP = NP - IROFF
IOFFVX = IIVX + (JJVX-1)*DESCX( LLD_ )
*
SAFMIN = PDLAMCH( ICTXT, 'Safe minimum' )
IF( KASE.EQ.0 ) THEN
DO 10 I = IOFFVX, IOFFVX+NP-1
X( I ) = DCMPLX( ONE / DBLE( N ) )
10 CONTINUE
KASE = 1
JUMP = 1
RETURN
END IF
*
GO TO ( 20, 40, 70, 90, 120 )JUMP
*
* ................ ENTRY (JUMP = 1)
* FIRST ITERATION. X HAS BEEN OVERWRITTEN BY A*X
*
20 CONTINUE
IF( N.EQ.1 ) THEN
IF( MYROW.EQ.IVXROW ) THEN
V( IOFFVX ) = X( IOFFVX )
EST = ABS( V( IOFFVX ) )
CALL DGEBS2D( ICTXT, 'Columnwise', ' ', 1, 1, EST, 1 )
ELSE
CALL DGEBR2D( ICTXT, 'Columnwise', ' ', 1, 1, EST, 1,
$ IVXROW, MYCOL )
END IF
* ... QUIT
GO TO 130
END IF
CALL PDZSUM1( N, EST, X, IX, JX, DESCX, 1 )
IF( DESCX( M_ ).EQ.1 .AND. N.EQ.1 ) THEN
IF( MYROW.EQ.IVXROW ) THEN
CALL DGEBS2D( ICTXT, 'Columnwise', ' ', 1, 1, EST, 1 )
ELSE
CALL DGEBR2D( ICTXT, 'Columnwise', ' ', 1, 1, EST, 1,
$ IVXROW, MYCOL )
END IF
END IF
*
DO 30 I = IOFFVX, IOFFVX+NP-1
IF( ABS( X( I ) ).GT.SAFMIN ) THEN
X( I ) = X( I ) / DCMPLX( ABS( X( I ) ) )
ELSE
X( I ) = CONE
END IF
30 CONTINUE
KASE = 2
JUMP = 2
RETURN
*
* ................ ENTRY (JUMP = 2)
* FIRST ITERATION. X HAS BEEN OVERWRITTEN BY CTRANS(A)*X
*
40 CONTINUE
CALL PZMAX1( N, XMAX, J, X, IX, JX, DESCX, 1 )
IF( DESCX( M_ ).EQ.1 .AND. N.EQ.1 ) THEN
IF( MYROW.EQ.IVXROW ) THEN
WORK( 1 ) = XMAX
WORK( 2 ) = DCMPLX( DBLE( J ) )
CALL ZGEBS2D( ICTXT, 'Columnwise', ' ', 2, 1, WORK, 2 )
ELSE
CALL ZGEBR2D( ICTXT, 'Columnwise', ' ', 2, 1, WORK, 2,
$ IVXROW, MYCOL )
XMAX = WORK( 1 )
J = NINT( DBLE( WORK( 2 ) ) )
END IF
END IF
ITER = 2
*
* MAIN LOOP - ITERATIONS 2, 3,...,ITMAX
*
50 CONTINUE
DO 60 I = IOFFVX, IOFFVX+NP-1
X( I ) = CZERO
60 CONTINUE
IMAXROW = INDXG2P( J, DESCX( MB_ ), MYROW, DESCX( RSRC_ ), NPROW )
IF( MYROW.EQ.IMAXROW ) THEN
I = INDXG2L( J, DESCX( MB_ ), MYROW, DESCX( RSRC_ ), NPROW )
X( I ) = CONE
END IF
KASE = 1
JUMP = 3
RETURN
*
* ................ ENTRY (JUMP = 3)
* X HAS BEEN OVERWRITTEN BY A*X
*
70 CONTINUE
CALL ZCOPY( NP, X( IOFFVX ), 1, V( IOFFVX ), 1 )
ESTOLD = EST
CALL PDZSUM1( N, EST, V, IV, JV, DESCV, 1 )
IF( DESCV( M_ ).EQ.1 .AND. N.EQ.1 ) THEN
IF( MYROW.EQ.IVXROW ) THEN
CALL DGEBS2D( ICTXT, 'Columnwise', ' ', 1, 1, EST, 1 )
ELSE
CALL DGEBR2D( ICTXT, 'Columnwise', ' ', 1, 1, EST, 1,
$ IVXROW, MYCOL )
END IF
END IF
*
* TEST FOR CYCLING
IF( EST.LE.ESTOLD )
$ GO TO 100
*
DO 80 I = IOFFVX, IOFFVX+NP-1
IF( ABS( X( I ) ).GT.SAFMIN ) THEN
X( I ) = X( I ) / DCMPLX( ABS( X( I ) ) )
ELSE
X( I ) = CONE
END IF
80 CONTINUE
KASE = 2
JUMP = 4
RETURN
*
* ................ ENTRY (JUMP = 4)
* X HAS BEEN OVERWRITTEN BY CTRANS(A)*X
*
90 CONTINUE
JLAST = J
CALL PZMAX1( N, XMAX, J, X, IX, JX, DESCX, 1 )
IF( DESCX( M_ ).EQ.1 .AND. N.EQ.1 ) THEN
IF( MYROW.EQ.IVXROW ) THEN
WORK( 1 ) = XMAX
WORK( 2 ) = DCMPLX( DBLE( J ) )
CALL ZGEBS2D( ICTXT, 'Columnwise', ' ', 2, 1, WORK, 2 )
ELSE
CALL ZGEBR2D( ICTXT, 'Columnwise', ' ', 2, 1, WORK, 2,
$ IVXROW, MYCOL )
XMAX = WORK( 1 )
J = NINT( DBLE( WORK( 2 ) ) )
END IF
END IF
CALL PZELGET( 'Columnwise', ' ', JLMAX, X, JLAST, JX, DESCX )
IF( ( DBLE( JLMAX ).NE.ABS( DBLE( XMAX ) ) ).AND.
$ ( ITER.LT.ITMAX ) ) THEN
ITER = ITER + 1
GO TO 50
END IF
*
* ITERATION COMPLETE. FINAL STAGE.
*
100 CONTINUE
DO 110 I = IOFFVX, IOFFVX+NP-1
K = INDXL2G( I-IOFFVX+IIVX, DESCX( MB_ ), MYROW,
$ DESCX( RSRC_ ), NPROW )-IX+1
IF( MOD( K, 2 ).EQ.0 ) THEN
ALTSGN = -ONE
ELSE
ALTSGN = ONE
END IF
X( I ) = DCMPLX( ALTSGN*( ONE+DBLE( K-1 ) / DBLE( N-1 ) ) )
110 CONTINUE
KASE = 1
JUMP = 5
RETURN
*
* ................ ENTRY (JUMP = 5)
* X HAS BEEN OVERWRITTEN BY A*X
*
120 CONTINUE
CALL PDZSUM1( N, TEMP, X, IX, JX, DESCX, 1 )
IF( DESCX( M_ ).EQ.1 .AND. N.EQ.1 ) THEN
IF( MYROW.EQ.IVXROW ) THEN
CALL DGEBS2D( ICTXT, 'Columnwise', ' ', 1, 1, TEMP, 1 )
ELSE
CALL DGEBR2D( ICTXT, 'Columnwise', ' ', 1, 1, TEMP, 1,
$ IVXROW, MYCOL )
END IF
END IF
TEMP = TWO*( TEMP / DBLE( 3*N ) )
IF( TEMP.GT.EST ) THEN
CALL ZCOPY( NP, X( IOFFVX ), 1, V( IOFFVX ), 1 )
EST = TEMP
END IF
*
130 CONTINUE
KASE = 0
*
RETURN
*
* End of PZLACON
*
END
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