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ScaLAPACK
2.0.2
ScaLAPACK: Scalable Linear Algebra PACKage
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ScaLAPACK
2.0.2
ScaLAPACK: Scalable Linear Algebra PACKage
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#include "pblas.h"#include "PBpblas.h"#include "PBtools.h"#include "PBblacs.h"#include "PBblas.h"Go to the source code of this file.
Functions/Subroutines | |
| void | pdznrm2_ (int *N, double *NORM2, double *X, int *IX, int *JX, int *DESCX, int *INCX) |
| void pdznrm2_ | ( | int * | N, |
| double * | NORM2, | ||
| double * | X, | ||
| int * | IX, | ||
| int * | JX, | ||
| int * | DESCX, | ||
| int * | INCX | ||
| ) |
Definition at line 23 of file pdznrm2_.c.
{
/*
* Purpose
* =======
*
* PDZNRM2 computes the 2-norm of a subvector sub( X ),
*
* where
*
* 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.
*
* 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
* =========
*
* N (global input) INTEGER
* On entry, N specifies the length of the subvector sub( X ).
* N must be at least zero.
*
* NORM2 (local output) DOUBLE PRECISION
* On exit, NORM2 specifies the 2-norm of the subvector sub( X )
* only in its scope (See below for further details).
*
* 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.
*
* Further Details
* ===============
*
* When the result of a vector-oriented PBLAS call is a scalar, this
* scalar is set only within the process scope which owns the vector(s)
* being operated on. Let sub( X ) be a generic term for the input vec-
* tor(s). Then, the processes owning the correct the answer is determi-
* ned as follows: if an operation involves more than one vector, the
* processes receiving the result will be the union of the following set
* of processes for each vector:
*
* If N = 1, M_X = 1 and INCX = 1, then one cannot determine if a pro-
* cess row or process column owns the vector operand, therefore only
* the process owning sub( X ) receives the correct result;
*
* If INCX = M_X, then sub( X ) is a vector distributed over a process
* row. Each process in this row receives the result;
*
* If INCX = 1, then sub( X ) is a vector distributed over a process
* column. Each process in this column receives the result;
*
* -- Written on April 1, 1998 by
* Antoine Petitet, University of Tennessee, Knoxville 37996, USA.
*
* ---------------------------------------------------------------------
*/
/*
* .. Local Scalars ..
*/
char * Xptr = NULL, top;
int Xcol, Xi, Xii, Xj, Xjj, Xld, Xnp, Xnq, Xrow, ctxt, dst, dist,
info, k, mycol, mydist, myrow, npcol, nprow, src, size;
double Xtmp, scale, ssq, temp1, temp2;
PBTYP_T * type;
/*
* .. Local Arrays ..
*/
int Xd[DLEN_];
double work[4];
/* ..
* .. Executable Statements ..
*
*/
PB_CargFtoC( *IX, *JX, DESCX, &Xi, &Xj, Xd );
#ifndef NO_ARGCHK
/*
* Test the input parameters
*/
Cblacs_gridinfo( ( ctxt = Xd[CTXT_] ), &nprow, &npcol, &myrow, &mycol );
if( !( info = ( ( nprow == -1 ) ? -( 601 + CTXT_ ) : 0 ) ) )
PB_Cchkvec( ctxt, "PDZNRM2", "X", *N, 1, Xi, Xj, Xd, *INCX, 6, &info );
if( info ) { PB_Cabort( ctxt, "PDZNRM2", info ); return; }
#endif
/*
* Initialize NORM2
*/
*NORM2 = ZERO;
/*
* Quick return if possible
*/
if( *N == 0 ) return;
/*
* Retrieve process grid information
*/
#ifdef NO_ARGCHK
Cblacs_gridinfo( ( ctxt = Xd[CTXT_] ), &nprow, &npcol, &myrow, &mycol );
#endif
/*
* Retrieve sub( X )'s local information: Xii, Xjj, Xrow, Xcol
*/
PB_Cinfog2l( Xi, Xj, Xd, nprow, npcol, myrow, mycol, &Xii, &Xjj,
&Xrow, &Xcol );
/*
* Handle degenerate case separately, sub( X )'s scope is just one process
*/
if( ( *N == 1 ) && ( *INCX == 1 ) && ( Xd[M_] == 1 ) )
{
/*
* Make sure I own some data and compute NORM2
*/
if( ( ( myrow == Xrow ) || ( Xrow < 0 ) ) &&
( ( mycol == Xcol ) || ( Xcol < 0 ) ) )
{
scale = ZERO;
ssq = ONE;
type = PB_Cztypeset();
Xptr = Mptr( ((char *) X), Xii, Xjj, Xd[LLD_], type->size );
Xtmp = ((double *) Xptr)[REAL_PART];
if( Xtmp != ZERO )
{
temp1 = ABS( Xtmp );
if( scale < temp1 )
{
temp2 = scale / temp1;
ssq = ONE + ssq * ( temp2 * temp2 );
scale = temp1;
}
else
{
temp2 = temp1 / scale;
ssq = ssq + ( temp2 * temp2 );
}
}
Xtmp = ((double *) Xptr)[IMAG_PART];
if( Xtmp != ZERO )
{
temp1 = ABS( Xtmp );
if( scale < temp1 )
{
temp2 = scale / temp1;
ssq = ONE + ssq * ( temp2 * temp2 );
scale = temp1;
}
else
{
temp2 = temp1 / scale;
ssq = ssq + ( temp2 * temp2 );
}
}
/*
* Compute NORM2 = SCALE * SQRT( SSQ )
*/
dasqrtb_( &scale, &ssq, NORM2 );
}
return;
}
else if( *INCX == Xd[M_] )
{
/*
* sub( X ) resides in (a) process row(s)
*/
if( ( myrow == Xrow ) || ( Xrow < 0 ) )
{
/*
* Initialize SCALE and SSQ
*/
scale = ZERO;
ssq = ONE;
/*
* Make sure I own some data and compute local sum of squares
*/
Xnq = PB_Cnumroc( *N, Xj, Xd[INB_], Xd[NB_], mycol, Xd[CSRC_], npcol );
if( Xnq > 0 )
{
Xld = Xd[LLD_];
type = PB_Cztypeset(); size = type->size;
Xptr = Mptr( ((char *) X), Xii, Xjj, Xld, size );
for( k = 0; k < Xnq; k++ )
{
Xtmp = ((double *) Xptr)[REAL_PART];
if( Xtmp != ZERO )
{
temp1 = ABS( Xtmp );
if( scale < temp1 )
{
temp2 = scale / temp1;
ssq = ONE + ssq * ( temp2 * temp2 );
scale = temp1;
}
else
{
temp2 = temp1 / scale;
ssq = ssq + ( temp2 * temp2 );
}
}
Xtmp = ((double *) Xptr)[IMAG_PART];
if( Xtmp != ZERO )
{
temp1 = ABS( Xtmp );
if( scale < temp1 )
{
temp2 = scale / temp1;
ssq = ONE + ssq * ( temp2 * temp2 );
scale = temp1;
}
else
{
temp2 = temp1 / scale;
ssq = ssq + ( temp2 * temp2 );
}
}
Xptr += Xld * size;
}
}
/*
* If Xnq <= 0, SCALE is zero and SSQ is one (see initialization above)
*/
if( ( npcol >= 2 ) && ( Xcol >= 0 ) )
{
/*
* Combine the local sum of squares using a 1-tree topology within process row
* 0 if npcol > 1 and Xcol >= 0, i.e sub( X ) is distributed.
*/
work[0] = scale;
work[1] = ssq;
mydist = mycol;
k = 1;
l_10:
if( mydist & 1 )
{
dist = k * ( mydist - 1 );
dst = MPosMod( dist, npcol );
Cdgesd2d( ctxt, 2, 1, ((char*) work), 2, myrow, dst );
goto l_20;
}
else
{
dist = mycol + k;
src = MPosMod( dist, npcol );
if( mycol < src )
{
Cdgerv2d( ctxt, 2, 1, ((char*)&work[2]), 2, myrow, src );
if( work[0] >= work[2] )
{
if( work[0] != ZERO )
{
temp1 = work[2] / work[0];
work[1] = work[1] + ( temp1 * temp1 ) * work[3];
}
}
else
{
temp1 = work[0] / work[2];
work[1] = work[3] + ( temp1 * temp1 ) * work[1];
work[0] = work[2];
}
}
mydist >>= 1;
}
k <<= 1;
if( k < npcol ) goto l_10;
l_20:
/*
* Process column 0 broadcasts the combined values of SCALE and SSQ within their
* process row.
*/
top = *PB_Ctop( &ctxt, BCAST, ROW, TOP_GET );
if( mycol == 0 )
{
Cdgebs2d( ctxt, ROW, &top, 2, 1, ((char*)work), 2 );
}
else
{
Cdgebr2d( ctxt, ROW, &top, 2, 1, ((char*)work), 2,
myrow, 0 );
}
/*
* Compute NORM2 redundantly NORM2 = WORK( 1 ) * SQRT( WORK( 2 ) )
*/
dasqrtb_( &work[0], &work[1], NORM2 );
}
else
{
/*
* Compute NORM2 redundantly ( sub( X ) is not distributed )
*/
dasqrtb_( &scale, &ssq, NORM2 );
}
}
return;
}
else
{
/*
* sub( X ) resides in (a) process column(s)
*/
if( ( mycol == Xcol ) || ( Xcol < 0 ) )
{
/*
* Initialize SCALE and SSQ
*/
scale = ZERO;
ssq = ONE;
/*
* Make sure I own some data and compute local sum of squares
*/
Xnp = PB_Cnumroc( *N, Xi, Xd[IMB_], Xd[MB_], myrow, Xd[RSRC_], nprow );
if( Xnp > 0 )
{
type = PB_Cztypeset(); size = type->size;
Xptr = Mptr( ((char *) X), Xii, Xjj, Xd[LLD_], size );
for( k = 0; k < Xnp; k++ )
{
Xtmp = ((double *) Xptr)[REAL_PART];
if( Xtmp != ZERO )
{
temp1 = ABS( Xtmp );
if( scale < temp1 )
{
temp2 = scale / temp1;
ssq = ONE + ssq * ( temp2 * temp2 );
scale = temp1;
}
else
{
temp2 = temp1 / scale;
ssq = ssq + ( temp2 * temp2 );
}
}
Xtmp = ((double *) Xptr)[IMAG_PART];
if( Xtmp != ZERO )
{
temp1 = ABS( Xtmp );
if( scale < temp1 )
{
temp2 = scale / temp1;
ssq = ONE + ssq * ( temp2 * temp2 );
scale = temp1;
}
else
{
temp2 = temp1 / scale;
ssq = ssq + ( temp2 * temp2 );
}
}
Xptr += size;
}
}
/*
* If Xnp <= 0, SCALE is zero and SSQ is one (see initialization above)
*/
if( ( nprow >= 2 ) && ( Xrow >= 0 ) )
{
/*
* Combine the local sum of squares using a 1-tree topology within process
* column 0 if nprow > 1 and Xrow >= 0, i.e sub( X ) is distributed.
*/
work[0] = scale;
work[1] = ssq;
mydist = myrow;
k = 1;
l_30:
if( mydist & 1 )
{
dist = k * ( mydist - 1 );
dst = MPosMod( dist, nprow );
Cdgesd2d( ctxt, 2, 1, ((char*)work), 2, dst, mycol );
goto l_40;
}
else
{
dist = myrow + k;
src = MPosMod( dist, nprow );
if( myrow < src )
{
Cdgerv2d( ctxt, 2, 1, ((char*)&work[2]), 2, src, mycol );
if( work[0] >= work[2] )
{
if( work[0] != ZERO )
{
temp1 = work[2] / work[0];
work[1] = work[1] + ( temp1 * temp1 ) * work[3];
}
}
else
{
temp1 = work[0] / work[2];
work[1] = work[3] + ( temp1 * temp1 ) * work[1];
work[0] = work[2];
}
}
mydist >>= 1;
}
k <<= 1;
if( k < nprow ) goto l_30;
l_40:
/*
* Process column 0 broadcasts the combined values of SCALE and SSQ within their
* process column
*/
top = *PB_Ctop( &ctxt, BCAST, COLUMN, TOP_GET );
if( myrow == 0 )
{
Cdgebs2d( ctxt, COLUMN, &top, 2, 1, ((char*)work), 2 );
}
else
{
Cdgebr2d( ctxt, COLUMN, &top, 2, 1, ((char*)work), 2,
0, mycol );
}
/*
* Compute NORM2 redundantly NORM2 = WORK[0] * SQRT( WORK[1] )
*/
dasqrtb_( &work[0], &work[1], NORM2 );
}
else
{
/*
* Compute NORM2 redundantly ( sub( X ) is not distributed )
*/
dasqrtb_( &scale, &ssq, NORM2 );
}
}
return;
}
/*
* End of PDZNRM2
*/
}
