pzlacon.f

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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 )
.EQ.      IF( MYROWIMAXROW ) 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 )
.EQ..AND..EQ.      IF( DESCV( M_ )1  N1 ) THEN
.EQ.         IF( MYROWIVXROW ) 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
.LE.      IF( ESTESTOLD )
     $   GO TO 100
*
      DO 80 I = IOFFVX, IOFFVX+NP-1
.GT.         IF( ABS( X( I ) )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 )
.EQ..AND..EQ.      IF( DESCX( M_ )1  N1 ) THEN
.EQ.         IF( MYROWIVXROW ) 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 )
.NE..AND.      IF( ( DBLE( JLMAX )ABS( DBLE( XMAX ) ) )
.LT.     $    ( ITERITMAX                        ) ) 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
.EQ.         IF( MOD( K, 2 )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 )
.EQ..AND..EQ.      IF( DESCX( M_ )1  N1 ) THEN
.EQ.         IF( MYROWIVXROW ) 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 ) )
.GT.      IF( TEMPEST ) THEN
         CALL ZCOPY( NP, X( IOFFVX ), 1, V( IOFFVX ), 1 )
         EST = TEMP
      END IF
*
  130 CONTINUE
      KASE = 0
*
      RETURN
*
*     End of PZLACON
*
      END