pzhengst.f

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      SUBROUTINE pzhengst( IBTYPE, UPLO, N, A, IA, JA, DESCA, B, IB, JB,
     $                     DESCB, SCALE, WORK, LWORK, INFO )
*
*  -- ScaLAPACK routine (version 1.7) --
*     University of Tennessee, Knoxville, Oak Ridge National Laboratory,
*     and University of California, Berkeley.
*     October 15, 1999
*
*     .. Scalar Arguments ..
      CHARACTER          UPLO
      INTEGER            IA, IB, IBTYPE, INFO, JA, JB, LWORK, N
      DOUBLE PRECISION   SCALE
*     ..
*     .. Array Arguments ..
      INTEGER            DESCA( * ), DESCB( * )
      COMPLEX*16         A( * ), B( * ), WORK( * )
*     ..
*
*  Purpose
*
*  =======
*
*  PZHENGST reduces a complex Hermitian-definite generalized
*  eigenproblem to standard form.
*
*  PZHENGST performs the same function as PZHEGST, but is based on
*  rank 2K updates, which are faster and more scalable than
*  triangular solves (the basis of PZHENGST).
*
*  PZHENGST calls PZHEGST when UPLO='U', hence PZHENGST provides
*  improved performance only when UPLO='L', IBTYPE=1.
*
*  PZHENGST also calls PZHEGST when insufficient workspace is
*  provided,  hence PZHENGST provides improved
*  performance only when LWORK >= 2 * NP0 * NB + NQ0 * NB + NB * NB
*
*  In the following sub( A ) denotes A( IA:IA+N-1, JA:JA+N-1 ) and
*  sub( B ) denotes B( IB:IB+N-1, JB:JB+N-1 ).
*
*  If IBTYPE = 1, the problem is sub( A )*x = lambda*sub( B )*x,
*  and sub( A ) is overwritten by inv(U**H)*sub( A )*inv(U) or
*  inv(L)*sub( A )*inv(L**H)
*
*  If IBTYPE = 2 or 3, the problem is sub( A )*sub( B )*x = lambda*x or
*  sub( B )*sub( A )*x = lambda*x, and sub( A ) is overwritten by
*  U*sub( A )*U**H or L**H*sub( A )*L.
*
*  sub( B ) must have been previously factorized as U**H*U or L*L**H by
*  PZPOTRF.
*
*  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
*  =========
*
*  IBTYPE   (global input) INTEGER
*          = 1: compute inv(U**H)*sub( A )*inv(U) or
*               inv(L)*sub( A )*inv(L**H);
*          = 2 or 3: compute U*sub( A )*U**H or L**H*sub( A )*L.
*
*  UPLO    (global input) CHARACTER
*          = 'U':  Upper triangle of sub( A ) is stored and sub( B ) is
*                  factored as U**H*U;
*          = 'L':  Lower triangle of sub( A ) is stored and sub( B ) is
*                  factored as L*L**H.
*
*  N       (global input) INTEGER
*          The order of the matrices sub( A ) and sub( B ).  N >= 0.
*
*  A       (local input/local output) COMPLEX*16 pointer into the
*          local memory to an array of dimension (LLD_A, LOCc(JA+N-1)).
*          On entry, this array contains the local pieces of the
*          N-by-N Hermitian distributed matrix sub( A ). If UPLO = 'U',
*          the leading N-by-N upper triangular part of sub( A ) contains
*          the upper triangular part of the matrix, and its strictly
*          lower triangular part is not referenced.  If UPLO = 'L', the
*          leading N-by-N lower triangular part of sub( A ) contains
*          the lower triangular part of the matrix, and its strictly
*          upper triangular part is not referenced.
*
*          On exit, if INFO = 0, the transformed matrix, stored in the
*          same format as sub( A ).
*
*  IA      (global input) INTEGER
*          A's global row index, which points to the beginning of the
*          submatrix which is to be operated on.
*
*  JA      (global input) INTEGER
*          A's global column index, which points to the beginning of
*          the submatrix which is to be operated on.
*
*  DESCA   (global and local input) INTEGER array of dimension DLEN_.
*          The array descriptor for the distributed matrix A.
*
*  B       (local input) COMPLEX*16 pointer into the local memory
*          to an array of dimension (LLD_B, LOCc(JB+N-1)). On entry,
*          this array contains the local pieces of the triangular factor
*          from the Cholesky factorization of sub( B ), as returned by
*          PZPOTRF.
*
*  IB      (global input) INTEGER
*          B's global row index, which points to the beginning of the
*          submatrix which is to be operated on.
*
*  JB      (global input) INTEGER
*          B's global column index, which points to the beginning of
*          the submatrix which is to be operated on.
*
*  DESCB   (global and local input) INTEGER array of dimension DLEN_.
*          The array descriptor for the distributed matrix B.
*
*  SCALE   (global output) DOUBLE PRECISION
*          Amount by which the eigenvalues should be scaled to
*          compensate for the scaling performed in this routine.
*          At present, SCALE is always returned as 1.0, it is
*          returned here to allow for future enhancement.
*
*  WORK    (local workspace/local output) COMPLEX*16 array,
*                                                  dimension (LWORK)
*          On exit, WORK( 1 ) returns the minimal and optimal LWORK.
*
*  LWORK   (local or global input) INTEGER
*          The dimension of the array WORK.
*          LWORK is local input and must be at least
*          LWORK >= MAX( NB * ( NP0 +1 ), 3 * NB )
*
*          When IBTYPE = 1 and UPLO = 'L', PZHENGST provides improved
*          performance when LWORK >= 2 * NP0 * NB + NQ0 * NB + NB * NB
*
*          where NB = MB_A = NB_A,
*          NP0 = NUMROC( N, NB, 0, 0, NPROW ),
*          NQ0 = NUMROC( N, NB, 0, 0, NPROW ),
*
*          NUMROC ia a ScaLAPACK tool functions
*          MYROW, MYCOL, NPROW and NPCOL can be determined by calling
*          the subroutine BLACS_GRIDINFO.
*
*          If LWORK = -1, then LWORK is global input and a workspace
*          query is assumed; the routine only calculates the
*          optimal size for all work arrays. Each of these
*          values is returned in the first entry of the corresponding
*          work array, and no error message is issued by PXERBLA.
*
*  INFO    (global output) INTEGER
*          = 0:  successful exit
*          < 0:  If the i-th argument is an array and the j-entry had
*                an illegal value, then INFO = -(i*100+j), if the i-th
*                argument is a scalar and had an illegal value, then
*                INFO = -i.
*
*  =====================================================================
*
*
*
*     .. Parameters ..
      COMPLEX*16         ONEHALF, ONE, MONE
      DOUBLE PRECISION   RONE
      parameter( onehalf = ( 0.5d0, 0.0d0 ),
     $                   one = ( 1.0d0, 0.0d0 ),
     $                   mone = ( -1.0d0, 0.0d0 ), rone = 1.0d0 )
      INTEGER            DLEN_, CTXT_, MB_, NB_, RSRC_, CSRC_, LLD_
      parameter( dlen_ = 9, ctxt_ = 2, mb_ = 5, nb_ = 6,
     $                   rsrc_ = 7, csrc_ = 8, lld_ = 9 )
*     ..
*     .. Local Scalars ..
      LOGICAL            LQUERY, UPPER
      INTEGER            I, IACOL, IAROW, IBCOL, IBROW, ICOFFA, ICOFFB,
     $                   ictxt, indaa, indg, indr, indrt, iroffa,
     $                   iroffb, j, k, kb, lwmin, lwopt, mycol, myrow,
     $                   nb, np0, npcol, npk, nprow, nq0, postk
*     ..
*     .. Local Arrays ..
      INTEGER            DESCAA( DLEN_ ), DESCG( DLEN_ ),
     $                   descr( dlen_ ), descrt( dlen_ ), idum1( 2 ),
     $                   idum2( 2 )
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      INTEGER            INDXG2P, NUMROC
      EXTERNAL           lsame, indxg2p, numroc
*     ..
*     .. External Subroutines ..
      EXTERNAL           blacs_gridinfo, chk1mat, descset, pchk2mat,
     $                   pxerbla, pzgemm, pzhegst, pzhemm, pzher2k,
     $                   pzlacpy, pztrsm
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          dble, dcmplx, dconjg, ichar, max, min, mod
*     ..
*     .. Executable Statements ..
      ictxt = desca( ctxt_ )
      CALL blacs_gridinfo( ictxt, nprow, npcol, myrow, mycol )
      scale = 1.0d0
*
      nb = desca( mb_ )
*
*
*     Test the input parameters
*
      info = 0
      IF( nprow.EQ.-1 ) THEN
         info = -( 700+ctxt_ )
      ELSE
         upper = lsame( uplo, 'U' )
         CALL chk1mat( n, 3, n, 3, ia, ja, desca, 7, info )
         CALL chk1mat( n, 3, n, 3, ib, jb, descb, 11, info )
         IF( info.EQ.0 ) THEN
            iarow = indxg2p( ia, desca( mb_ ), myrow, desca( rsrc_ ),
     $              nprow )
            ibrow = indxg2p( ib, descb( mb_ ), myrow, descb( rsrc_ ),
     $              nprow )
            iacol = indxg2p( ja, desca( nb_ ), mycol, desca( csrc_ ),
     $              npcol )
            ibcol = indxg2p( jb, descb( nb_ ), mycol, descb( csrc_ ),
     $              npcol )
            iroffa = mod( ia-1, desca( mb_ ) )
            icoffa = mod( ja-1, desca( nb_ ) )
            iroffb = mod( ib-1, descb( mb_ ) )
            icoffb = mod( jb-1, descb( nb_ ) )
            np0 = numroc( n, nb, 0, 0, nprow )
            nq0 = numroc( n, nb, 0, 0, npcol )
            lwmin = max( nb*( np0+1 ), 3*nb )
            IF( ibtype.EQ.1 .AND. .NOT.upper ) THEN
               lwopt = 2*np0*nb + nq0*nb + nb*nb
            ELSE
               lwopt = lwmin
            END IF
            work( 1 ) = dcmplx( dble( lwopt ) )
            lquery = ( lwork.EQ.-1 )
            IF( ibtype.LT.1 .OR. ibtype.GT.3 ) THEN
               info = -1
            ELSE IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
               info = -2
            ELSE IF( n.LT.0 ) THEN
               info = -3
            ELSE IF( iroffa.NE.0 ) THEN
               info = -5
            ELSE IF( icoffa.NE.0 ) THEN
               info = -6
            ELSE IF( desca( mb_ ).NE.desca( nb_ ) ) THEN
               info = -( 700+nb_ )
            ELSE IF( iroffb.NE.0 .OR. ibrow.NE.iarow ) THEN
               info = -9
            ELSE IF( icoffb.NE.0 .OR. ibcol.NE.iacol ) THEN
               info = -10
            ELSE IF( descb( mb_ ).NE.desca( mb_ ) ) THEN
               info = -( 1100+mb_ )
            ELSE IF( descb( nb_ ).NE.desca( nb_ ) ) THEN
               info = -( 1100+nb_ )
            ELSE IF( ictxt.NE.descb( ctxt_ ) ) THEN
               info = -( 1100+ctxt_ )
            ELSE IF( lwork.LT.lwmin .AND. .NOT.lquery ) THEN
               info = -13
            END IF
         END IF
         idum1( 1 ) = ibtype
         idum2( 1 ) = 1
         IF( upper ) THEN
            idum1( 2 ) = ichar( 'U' )
         ELSE
            idum1( 2 ) = ichar( 'L' )
         END IF
         idum2( 2 ) = 2
         CALL pchk2mat( n, 3, n, 3, ia, ja, desca, 7, n, 3, n, 3, ib,
     $                  jb, descb, 11, 2, idum1, idum2, info )
      END IF
*
      IF( info.NE.0 ) THEN
         CALL pxerbla( ictxt, 'PZHENGST', -info )
         RETURN
      ELSE IF( lquery ) THEN
         RETURN
      END IF
*
*     Quick return if possible
*
      IF( n.EQ.0 )
     $   RETURN
*
*
      IF( ibtype.NE.1 .OR. upper .OR. lwork.LT.lwopt ) THEN
         CALL pzhegst( ibtype, uplo, n, a, ia, ja, desca, b, ib, jb,
     $                 descb, scale, info )
         RETURN
      END IF
*
      CALL descset( descg, n, nb, nb, nb, iarow, iacol, ictxt, np0 )
      CALL descset( descr, n, nb, nb, nb, iarow, iacol, ictxt, np0 )
      CALL descset( descrt, nb, n, nb, nb, iarow, iacol, ictxt, nb )
      CALL descset( descaa, nb, nb, nb, nb, iarow, iacol, ictxt, nb )
*
      indg = 1
      indr = indg + descg( lld_ )*nb
      indaa = indr + descr( lld_ )*nb
      indrt = indaa + descaa( lld_ )*nb
*
      DO 30 k = 1, n, nb
*
         kb = min( n-k+1, nb )
         postk = k + kb
         npk = n - postk + 1
*
*
         CALL pzlacpy( 'A', n-postk+1, kb, b, postk+ib-1, k+jb-1, descb,
     $                 work( indg ), postk, 1, descg )
         CALL pzlacpy( 'A', n-postk+1, kb, a, postk+ia-1, k+ja-1, desca,
     $                 work( indr ), postk, 1, descr )
         CALL pzlacpy( 'A', kb, k-1, a, k+ia-1, ja, desca,
     $                 work( indrt ), 1, 1, descrt )
*
         CALL pzlacpy( 'L', kb, kb, a, k+ia-1, k+ja-1, desca,
     $                 work( indr ), k, 1, descr )
         CALL pztrsm( 'Right', 'L', 'N', 'N', npk, kb, mone, b, k+ib-1,
     $                k+jb-1, descb, work( indg ), postk, 1, descg )
*
         CALL pzhemm( 'Right', 'L', npk, kb, onehalf, a, k+ia-1, k+ja-1,
     $                desca, work( indg ), postk, 1, descg, one,
     $                work( indr ), postk, 1, descr )
*
         CALL pzher2k( 'Lower', 'No T', npk, kb, one, work( indg ),
     $                 postk, 1, descg, work( indr ), postk, 1, descr,
     $                 rone, a, postk+ia-1, postk+ja-1, desca )
*
         CALL pzgemm( 'No T', 'No Conj', npk, k-1, kb, one,
     $                work( indg ), postk, 1, descg, work( indrt ), 1,
     $                1, descrt, one, a, postk+ia-1, ja, desca )
*
         CALL pzhemm( 'Right', 'L', npk, kb, one, work( indr ), k, 1,
     $                descr, work( indg ), postk, 1, descg, one, a,
     $                postk+ia-1, k+ja-1, desca )
*
         CALL pztrsm( 'Left', 'Lower', 'No Conj', 'Non-unit', kb, k-1,
     $                one, b, k+ib-1, k+jb-1, descb, a, k+ia-1, ja,
     $                desca )
*
         CALL pzlacpy( 'L', kb, kb, a, k+ia-1, k+ja-1, desca,
     $                 work( indaa ), 1, 1, descaa )
*
         IF( myrow.EQ.descaa( rsrc_ ) .AND. mycol.EQ.descaa( csrc_ ) )
     $        THEN
            DO 20 i = 1, kb
               DO 10 j = 1, i
                  work( indaa+j-1+( i-1 )*descaa( lld_ ) )
     $               = dconjg( work( indaa+i-1+( j-1 )*
     $               descaa( lld_ ) ) )
   10          CONTINUE
   20       CONTINUE
         END IF
*
         CALL pztrsm( 'Left', 'Lower', 'No Conj', 'Non-unit', kb, kb,
     $                one, b, k+ib-1, k+jb-1, descb, work( indaa ), 1,
     $                1, descaa )
*
         CALL pztrsm( 'Right', 'Lower', 'Conj', 'Non-unit', kb, kb, one,
     $                b, k+ib-1, k+jb-1, descb, work( indaa ), 1, 1,
     $                descaa )
*
         CALL pzlacpy( 'L', kb, kb, work( indaa ), 1, 1, descaa, a,
     $                 k+ia-1, k+ja-1, desca )
*
         CALL pztrsm( 'Right', 'Lower', 'Conj', 'Non-unit', npk, kb,
     $                one, b, k+ib-1, k+jb-1, descb, a, postk+ia-1,
     $                k+ja-1, desca )
*
         descr( csrc_ ) = mod( descr( csrc_ )+1, npcol )
         descg( csrc_ ) = mod( descg( csrc_ )+1, npcol )
         descrt( rsrc_ ) = mod( descrt( rsrc_ )+1, nprow )
         descaa( rsrc_ ) = mod( descaa( rsrc_ )+1, nprow )
         descaa( csrc_ ) = mod( descaa( csrc_ )+1, npcol )
   30 CONTINUE
*
      work( 1 ) = dcmplx( dble( lwopt ) )
*
      RETURN
      END