pzher2_()

void pzher2_	(	F_CHAR_T	UPLO,
		Int *	N,
		double *	ALPHA,
		double *	X,
		Int *	IX,
		Int *	JX,
		Int *	DESCX,
		Int *	INCX,
		double *	Y,
		Int *	IY,
		Int *	JY,
		Int *	DESCY,
		Int *	INCY,
		double *	A,
		Int *	IA,
		Int *	JA,
		Int *	DESCA
	)

Definition at line 25 of file pzher2_.c.

{
/*
*  Purpose
*  =======
*
*  PZHER2  performs the Hermitian rank 2 operation
*
*     sub( A ) := alpha*sub( X )*conjg( sub( Y )' ) +
*                 conjg( alpha )*sub( Y )*conjg( sub( X )' ) + sub( A ),
*
*  where
*
*     sub( A ) denotes A(IA:IA+N-1,JA:JA+N-1),
*
*     sub( X ) denotes X(IX,JX:JX+N-1) if INCX = M_X,
*                      X(IX:IX+N-1,JX) if INCX = 1 and INCX <> M_X, and,
*
*     sub( Y ) denotes Y(IY,JY:JY+N-1) if INCY = M_Y,
*                      Y(IY:IY+N-1,JY) if INCY = 1 and INCY <> M_Y.
*
*  Alpha is a scalar, sub( X ) and sub( Y ) are n element subvectors and
*  sub( A ) is an n by n Hermitian submatrix.
*
*  Notes
*  =====
*
*  A description  vector  is associated with each 2D block-cyclicly dis-
*  tributed matrix.  This  vector  stores  the  information  required to
*  establish the  mapping  between a  matrix entry and its corresponding
*  process and memory location.
*
*  In  the  following  comments,   the character _  should  be  read  as
*  "of  the  distributed  matrix".  Let  A  be a generic term for any 2D
*  block cyclicly distributed matrix.  Its description vector is DESC_A:
*
*  NOTATION         STORED IN       EXPLANATION
*  ---------------- --------------- ------------------------------------
*  DTYPE_A (global) DESCA[ DTYPE_ ] The descriptor type.
*  CTXT_A  (global) DESCA[ CTXT_  ] The BLACS context handle, indicating
*                                   the NPROW x NPCOL BLACS process grid
*                                   A  is  distributed over. The context
*                                   itself  is  global,  but  the handle
*                                   (the integer value) may vary.
*  M_A     (global) DESCA[ M_     ] The  number of rows in the distribu-
*                                   ted matrix A, M_A >= 0.
*  N_A     (global) DESCA[ N_     ] The number of columns in the distri-
*                                   buted matrix A, N_A >= 0.
*  IMB_A   (global) DESCA[ IMB_   ] The number of rows of the upper left
*                                   block of the matrix A, IMB_A > 0.
*  INB_A   (global) DESCA[ INB_   ] The  number  of columns of the upper
*                                   left   block   of   the  matrix   A,
*                                   INB_A > 0.
*  MB_A    (global) DESCA[ MB_    ] The blocking factor used to  distri-
*                                   bute the last  M_A-IMB_A  rows of A,
*                                   MB_A > 0.
*  NB_A    (global) DESCA[ NB_    ] The blocking factor used to  distri-
*                                   bute the last  N_A-INB_A  columns of
*                                   A, NB_A > 0.
*  RSRC_A  (global) DESCA[ RSRC_  ] The process row over which the first
*                                   row of the matrix  A is distributed,
*                                   NPROW > RSRC_A >= 0.
*  CSRC_A  (global) DESCA[ CSRC_  ] The  process column  over  which the
*                                   first column of  A  is  distributed.
*                                   NPCOL > CSRC_A >= 0.
*  LLD_A   (local)  DESCA[ LLD_   ] The  leading dimension  of the local
*                                   array  storing  the  local blocks of
*                                   the distributed matrix A,
*                                   IF( Lc( 1, N_A ) > 0 )
*                                      LLD_A >= MAX( 1, Lr( 1, M_A ) )
*                                   ELSE
*                                      LLD_A >= 1.
*
*  Let K be the number of  rows of a matrix A starting at the global in-
*  dex IA,i.e, A( IA:IA+K-1, : ). Lr( IA, K ) denotes the number of rows
*  that the process of row coordinate MYROW ( 0 <= MYROW < NPROW ) would
*  receive if these K rows were distributed over NPROW processes.  If  K
*  is the number of columns of a matrix  A  starting at the global index
*  JA, i.e, A( :, JA:JA+K-1, : ), Lc( JA, K ) denotes the number  of co-
*  lumns that the process MYCOL ( 0 <= MYCOL < NPCOL ) would  receive if
*  these K columns were distributed over NPCOL processes.
*
*  The values of Lr() and Lc() may be determined via a call to the func-
*  tion PB_Cnumroc:
*  Lr( IA, K ) = PB_Cnumroc( K, IA, IMB_A, MB_A, MYROW, RSRC_A, NPROW )
*  Lc( JA, K ) = PB_Cnumroc( K, JA, INB_A, NB_A, MYCOL, CSRC_A, NPCOL )
*
*  Arguments
*  =========
*
*  UPLO    (global input) CHARACTER*1
*          On  entry,   UPLO  specifies  whether  the  local  pieces  of
*          the array  A  containing the  upper or lower triangular  part
*          of the Hermitian submatrix  sub( A )  are to be referenced as
*          follows:
*
*             UPLO = 'U' or 'u'   Only the local pieces corresponding to
*                                 the   upper  triangular  part  of  the
*                                 Hermitian submatrix sub( A ) are to be
*                                 referenced,
*
*             UPLO = 'L' or 'l'   Only the local pieces corresponding to
*                                 the   lower  triangular  part  of  the
*                                 Hermitian submatrix sub( A ) are to be
*                                 referenced.
*
*  N       (global input) INTEGER
*          On entry,  N specifies the order of the  submatrix  sub( A ).
*          N must be at least zero.
*
*  ALPHA   (global input) COMPLEX*16
*          On entry, ALPHA specifies the scalar alpha.   When  ALPHA  is
*          supplied  as  zero  then  the  local entries of the arrays  X
*          and Y corresponding to the entries of the subvectors sub( X )
*          and sub( Y ) respectively need not be set on input.
*
*  X       (local input) COMPLEX*16 array
*          On entry, X is an array of dimension (LLD_X, Kx), where LLD_X
*          is   at  least  MAX( 1, Lr( 1, IX ) )  when  INCX = M_X   and
*          MAX( 1, Lr( 1, IX+N-1 ) )  otherwise,  and,  Kx  is  at least
*          Lc( 1, JX+N-1 )  when  INCX = M_X  and Lc( 1, JX ) otherwise.
*          Before  entry,  this array  contains the local entries of the
*          matrix X.
*
*  IX      (global input) INTEGER
*          On entry, IX  specifies X's global row index, which points to
*          the beginning of the submatrix sub( X ).
*
*  JX      (global input) INTEGER
*          On entry, JX  specifies X's global column index, which points
*          to the beginning of the submatrix sub( X ).
*
*  DESCX   (global and local input) INTEGER array
*          On entry, DESCX  is an integer array of dimension DLEN_. This
*          is the array descriptor for the matrix X.
*
*  INCX    (global input) INTEGER
*          On entry,  INCX   specifies  the  global  increment  for  the
*          elements of  X.  Only two values of  INCX   are  supported in
*          this version, namely 1 and M_X. INCX  must not be zero.
*
*  Y       (local input) COMPLEX*16 array
*          On entry, Y is an array of dimension (LLD_Y, Ky), where LLD_Y
*          is   at  least  MAX( 1, Lr( 1, IY ) )  when  INCY = M_Y   and
*          MAX( 1, Lr( 1, IY+N-1 ) )  otherwise,  and,  Ky  is  at least
*          Lc( 1, JY+N-1 )  when  INCY = M_Y  and Lc( 1, JY ) otherwise.
*          Before  entry,  this array  contains the local entries of the
*          matrix Y.
*
*  IY      (global input) INTEGER
*          On entry, IY  specifies Y's global row index, which points to
*          the beginning of the submatrix sub( Y ).
*
*  JY      (global input) INTEGER
*          On entry, JY  specifies Y's global column index, which points
*          to the beginning of the submatrix sub( Y ).
*
*  DESCY   (global and local input) INTEGER array
*          On entry, DESCY  is an integer array of dimension DLEN_. This
*          is the array descriptor for the matrix Y.
*
*  INCY    (global input) INTEGER
*          On entry,  INCY   specifies  the  global  increment  for  the
*          elements of  Y.  Only two values of  INCY   are  supported in
*          this version, namely 1 and M_Y. INCY  must not be zero.
*
*  A       (local input/local output) COMPLEX*16 array
*          On entry, A is an array of dimension (LLD_A, Ka), where Ka is
*          at least Lc( 1, JA+N-1 ).  Before  entry, this array contains
*          the local entries of the matrix A.
*          Before  entry  with  UPLO = 'U' or 'u', this  array  contains
*          the local entries corresponding to the upper triangular  part
*          of  the  Hermitian submatrix  sub( A ), and the local entries
*          corresponding to the  strictly lower triangular  of  sub( A )
*          are not referenced.  On exit,  the upper  triangular  part of
*          sub( A ) is overwritten by the  upper triangular part  of the
*          updated submatrix.
*          Before  entry  with  UPLO = 'L' or 'l', this  array  contains
*          the local entries corresponding to the lower triangular  part
*          of  the  Hermitian submatrix  sub( A ), and the local entries
*          corresponding to the  strictly upper triangular  of  sub( A )
*          are not referenced.  On exit,  the lower  triangular  part of
*          sub( A ) is overwritten by the  lower triangular part  of the
*          updated submatrix.
*          Note that the  imaginary parts  of the local entries  corres-
*          ponding to the  diagonal elements  of  sub( A )  need not  be
*          set,  they are assumed to be zero,  and on exit they are  set
*          to zero.
*
*  IA      (global input) INTEGER
*          On entry, IA  specifies A's global row index, which points to
*          the beginning of the submatrix sub( A ).
*
*  JA      (global input) INTEGER
*          On entry, JA  specifies A's global column index, which points
*          to the beginning of the submatrix sub( A ).
*
*  DESCA   (global and local input) INTEGER array
*          On entry, DESCA  is an integer array of dimension DLEN_. This
*          is the array descriptor for the matrix A.
*
*  -- Written on April 1, 1998 by
*     Antoine Petitet, University of Tennessee, Knoxville 37996, USA.
*
*  ---------------------------------------------------------------------
*/
/*
*  .. Local Scalars ..
*/
   char           UploA;
   Int            Acol, Ai, Aii, Aimb1, Ainb1, Aj, Ajj, Akp, Akq, Ald, Amb,
                  Amp, Amp0, Anb, Anq, Anq0, Arow, XCfr, XCld, XRfr, XRld,
                  Xi, Xj, YCfr, YCld, YRfr, YRld, Yi, Yj, ctxt, info, ione=1,
                  k, kb, ktmp, mycol, myrow, nb, npcol, nprow, size, upper;
   cmplx16        Calpha;
   PBTYP_T        * type;
/*
*  .. Local Arrays ..
*/
   Int            Ad  [DLEN_], Ad0 [DLEN_], XCd0[DLEN_], XRd0[DLEN_], Xd[DLEN_],
                  YCd0[DLEN_], YRd0[DLEN_], Yd  [DLEN_];
   char           * Aptr = NULL, * XC = NULL, * XR = NULL, * YC = NULL,
                  * YR   = NULL;
/* ..
*  .. Executable Statements ..
*
*/
   upper = ( ( UploA  = Mupcase( F2C_CHAR( UPLO )[0] ) ) == CUPPER );
   PB_CargFtoC( *IA, *JA, DESCA, &Ai, &Aj, Ad );
   PB_CargFtoC( *IX, *JX, DESCX, &Xi, &Xj, Xd );
   PB_CargFtoC( *IY, *JY, DESCY, &Yi, &Yj, Yd );
#ifndef NO_ARGCHK
/*
*  Test the input parameters
*/
   Cblacs_gridinfo( ( ctxt = Xd[CTXT_] ), &nprow, &npcol, &myrow, &mycol );
   if( !( info = ( ( nprow == -1 ) ? -( 701 + CTXT_ ) : 0 ) ) )
   {
      if( ( !upper ) && ( UploA != CLOWER ) )
      {
         PB_Cwarn( ctxt, __LINE__, "PZHER2", "Illegal UPLO = %c\n", UploA );
         info = -1;
      }
      PB_Cchkvec( ctxt, "PZHER2", "X", *N, 2, Xi, Xj, Xd, *INCX,  7, &info );
      PB_Cchkvec( ctxt, "PZHER2", "Y", *N, 2, Yi, Yj, Yd, *INCY, 12, &info );
      PB_Cchkmat( ctxt, "PZHER2", "A", *N, 2, *N, 2, Ai, Aj, Ad, 17, &info );
   }
   if( info ) { PB_Cabort( ctxt, "PZHER2", info ); return; }
#endif
/*
*  Quick return if possible
*/
   if( ( *N == 0 ) ||
       ( ( ALPHA[REAL_PART] == ZERO ) && ( ALPHA[IMAG_PART] == ZERO ) ) )
      return;
/*
*  Retrieve process grid information
*/
#ifdef NO_ARGCHK
   Cblacs_gridinfo( ( ctxt = Ad[CTXT_] ), &nprow, &npcol, &myrow, &mycol );
#endif
/*
*  Get type structure
*/
   type = PB_Cztypeset();
/*
*  Compute descriptor Ad0 for sub( A )
*/
   PB_Cdescribe( *N, *N, Ai, Aj, Ad, nprow, npcol, myrow, mycol, &Aii, &Ajj,
                 &Ald, &Aimb1, &Ainb1, &Amb, &Anb, &Arow, &Acol, Ad0 );
/*
*  Replicate sub( X ) in process rows (XR) and process columns (XC) spanned by
*  sub( A )
*/
   if( *INCX == Xd[M_] )
   {
      PB_CInV( type, NOCONJG, ROW,    *N, *N, Ad0, 1, ((char *) X), Xi, Xj,
               Xd,   ROW,    &XR, XRd0, &XRfr );
      PB_CInV( type, NOCONJG, COLUMN, *N, *N, Ad0, 1, XR,            0,  0,
               XRd0, ROW,    &XC, XCd0, &XCfr );
   }
   else
   {
      PB_CInV( type, NOCONJG, COLUMN, *N, *N, Ad0, 1, ((char *) X), Xi, Xj,
               Xd,   COLUMN, &XC, XCd0, &XCfr );
      PB_CInV( type, NOCONJG, ROW,    *N, *N, Ad0, 1, XC,            0,  0,
               XCd0, COLUMN, &XR, XRd0, &XRfr );
   }
/*
*  Replicate sub( Y ) in process rows (YR) and process columns (YC) spanned by
*  sub( A )
*/
   if( *INCY == Yd[M_] )
   {
      PB_CInV( type, NOCONJG, ROW,    *N, *N, Ad0, 1, ((char *) Y), Yi, Yj,
               Yd,   ROW,    &YR, YRd0, &YRfr );
      PB_CInV( type, NOCONJG, COLUMN, *N, *N, Ad0, 1, YR,            0,  0,
               YRd0, ROW,    &YC, YCd0, &YCfr );
   }
   else
   {
      PB_CInV( type, NOCONJG, COLUMN, *N, *N, Ad0, 1, ((char *) Y), Yi, Yj,
               Yd,   COLUMN, &YC, YCd0, &YCfr );
      PB_CInV( type, NOCONJG, ROW,    *N, *N, Ad0, 1, YC,            0,  0,
               YCd0, COLUMN, &YR, YRd0, &YRfr );
   }
/*
*  Local rank-2 update if I own some data
*/
   Amp = PB_Cnumroc( *N, 0, Aimb1, Amb, myrow, Arow, nprow );
   Anq = PB_Cnumroc( *N, 0, Ainb1, Anb, mycol, Acol, npcol );
 
   if( ( Amp > 0 ) && ( Anq > 0 ) )
   {
      size = type->size;
      Aptr = Mptr( ((char *) A), Aii, Ajj, Ald, size );
 
      XCld = XCd0[LLD_]; YCld = YCd0[LLD_];
      XRld = XRd0[LLD_]; YRld = YRd0[LLD_];
      Calpha[REAL_PART] =  ALPHA[REAL_PART];
      Calpha[IMAG_PART] = -ALPHA[IMAG_PART];
/*
*  Computational partitioning size is computed as the product of the logical
*  value returned by pilaenv_ and 2 * lcm( nprow, npcol ).
*/
      nb = 2 * pilaenv_( &ctxt, C2F_CHAR( &type->type ) ) *
           PB_Clcm( ( Arow >= 0 ? nprow : 1 ), ( Acol >= 0 ? npcol : 1 ) );
      if( upper )
      {
         for( k = 0; k < *N; k += nb )
         {
            kb   = *N - k; kb = MIN( kb, nb );
            Akp  = PB_Cnumroc( k,  0, Aimb1, Amb, myrow, Arow, nprow );
            Akq  = PB_Cnumroc( k,  0, Ainb1, Anb, mycol, Acol, npcol );
            Anq0 = PB_Cnumroc( kb, k, Ainb1, Anb, mycol, Acol, npcol );
            if( Akp > 0 && Anq0 > 0 )
            {
               zgerc_( &Akp, &Anq0, ((char *) ALPHA), XC, &ione,
                       Mptr( YR,   0, Akq, YRld, size ), &YRld,
                       Mptr( Aptr, 0, Akq,  Ald, size ), &Ald );
               zgerc_( &Akp, &Anq0, ((char *) Calpha), YC, &ione,
                       Mptr( XR,   0, Akq, XRld, size ), &XRld,
                       Mptr( Aptr, 0, Akq,  Ald, size ), &Ald );
            }
            PB_Cpsyr2( type, UPPER, kb, 1, ((char *) ALPHA),
                       Mptr( XC, Akp,   0, XCld, size ), XCld,
                       Mptr( XR,   0, Akq, XRld, size ), XRld,
                       Mptr( YC, Akp,   0, YCld, size ), YCld,
                       Mptr( YR,   0, Akq, YRld, size ), YRld,
                       Aptr, k, k, Ad0, PB_Ctzher2 );
         }
      }
      else
      {
         for( k = 0; k < *N; k += nb )
         {
            kb  = *N - k; ktmp = k + ( kb = MIN( kb, nb ) );
            Akp = PB_Cnumroc( k, 0, Aimb1, Amb, myrow, Arow, nprow );
            Akq = PB_Cnumroc( k, 0, Ainb1, Anb, mycol, Acol, npcol );
            PB_Cpsyr2( type, LOWER, kb, 1, ((char *) ALPHA),
                       Mptr( XC, Akp,   0, XCld, size ), XCld,
                       Mptr( XR,   0, Akq, XRld, size ), XRld,
                       Mptr( YC, Akp,   0, YCld, size ), YCld,
                       Mptr( YR,   0, Akq, YRld, size ), YRld,
                       Aptr, k, k, Ad0, PB_Ctzher2 );
            Akp  = PB_Cnumroc( ktmp, 0, Aimb1, Amb, myrow, Arow, nprow );
            Amp0 = Amp - Akp;
            Anq0 = PB_Cnumroc( kb,   k, Ainb1, Anb, mycol, Acol, npcol );
            if( Amp0 > 0 && Anq0 > 0 )
            {
               zgerc_( &Amp0, &Anq0, ((char *) ALPHA),
                       Mptr( XC,   Akp,   0, XCld, size ), &ione,
                       Mptr( YR,     0, Akq, YRld, size ), &YRld,
                       Mptr( Aptr, Akp, Akq,  Ald, size ), &Ald );
               zgerc_( &Amp0, &Anq0, ((char *) Calpha),
                       Mptr( YC,   Akp,   0, YCld, size ), &ione,
                       Mptr( XR,     0, Akq, XRld, size ), &XRld,
                       Mptr( Aptr, Akp, Akq,  Ald, size ), &Ald );
            }
         }
      }
   }
   if( XRfr ) free( XR );
   if( XCfr ) free( XC );
   if( YRfr ) free( YR );
   if( YCfr ) free( YC );
/*
*  End of PZHER2
*/
}

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