SUBROUTINE PCLASSQ( N, X, IX, JX, DESCX, INCX, SCALE, SUMSQ ) * * -- ScaLAPACK auxiliary routine (version 1.5) -- * University of Tennessee, Knoxville, Oak Ridge National Laboratory, * and University of California, Berkeley. * May 1, 1997 * * .. Scalar Arguments .. INTEGER IX, INCX, JX, N REAL SCALE, SUMSQ * .. * .. Array Arguments .. INTEGER DESCX( * ) COMPLEX X( * ) * .. * * Purpose * ======= * * PCLASSQ returns the values scl and smsq such that * * ( scl**2 )*smsq = x( 1 )**2 +...+ x( n )**2 + ( scale**2 )*sumsq, * * where x( i ) = sub( X ) = abs( X( IX+(JX-1)*DESCX(M_)+(i-1)*INCX ) ). * The value of sumsq is assumed to be at least unity and the value of * ssq will then satisfy * * 1.0 .le. ssq .le. ( sumsq + 2*n ). * * scale is assumed to be non-negative and scl returns the value * * scl = max( scale, abs( real( x( i ) ) ), abs( aimag( x( i ) ) ) ), * i * * scale and sumsq must be supplied in SCALE and SUMSQ respectively. * SCALE and SUMSQ are overwritten by scl and ssq respectively. * * The routine makes only one pass through the vector sub( X ). * * 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 * * Because vectors may be viewed as a subclass of matrices, a * distributed vector is considered to be a distributed matrix. * * The result are only available in the scope of sub( X ), i.e if * sub( X ) is distributed along a process row, the correct results are * only available in this process row of the grid. Similarly if sub( X ) * is distributed along a process column, the correct results are only * available in this process column of the grid. * * Arguments * ========= * * N (global input) INTEGER * The length of the distributed vector sub( X ). * * X (input) COMPLEX * The vector for which a scaled sum of squares is computed. * x( i ) = X(IX+(JX-1)*M_X +(i-1)*INCX ), 1 <= i <= n. * * 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. * * INCX (global input) INTEGER * 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. * * SCALE (local input/local output) REAL * On entry, the value scale in the equation above. * On exit, SCALE is overwritten with scl , the scaling factor * for the sum of squares. * * SUMSQ (local input/local output) REAL * On entry, the value sumsq in the equation above. * On exit, SUMSQ is overwritten with smsq , the basic sum of * squares from which scl has been factored out. * * ===================================================================== * * .. 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 ) REAL ZERO PARAMETER ( ZERO = 0.0E+0 ) * .. * .. Local Scalars .. INTEGER I, ICOFF, ICTXT, IIX, IOFF, IROFF, IXCOL, $ IXROW, JJX, LDX, MYCOL, MYROW, NP, NPCOL, $ NPROW, NQ REAL TEMP1 * .. * .. Local Arrays .. REAL WORK( 2 ) * .. * .. External Subroutines .. EXTERNAL BLACS_GRIDINFO, INFOG2L, PSTREECOMB, SCOMBSSQ * .. * .. External Functions .. INTEGER NUMROC EXTERNAL NUMROC * .. * .. Intrinsic Functions .. INTRINSIC ABS, AIMAG, MOD, REAL * .. * .. Executable Statements .. * * Get grid parameters. * ICTXT = DESCX( CTXT_ ) CALL BLACS_GRIDINFO( ICTXT, NPROW, NPCOL, MYROW, MYCOL ) * * Figure local indexes * CALL INFOG2L( IX, JX, DESCX, NPROW, NPCOL, MYROW, MYCOL, IIX, JJX, $ IXROW, IXCOL ) * LDX = DESCX( LLD_ ) IF( INCX.EQ.DESCX( M_ ) ) THEN * * X is rowwise distributed. * IF( MYROW.NE.IXROW ) $ RETURN ICOFF = MOD( JX, DESCX( NB_ ) ) NQ = NUMROC( N+ICOFF, DESCX( NB_ ), MYCOL, IXCOL, NPCOL ) IF( MYCOL.EQ.IXCOL ) $ NQ = NQ - ICOFF * * Code direct from LAPACK's CLASSQ, (save subroutine call) * IF( NQ.GT.0 ) THEN IOFF = IIX + ( JJX - 1 ) * LDX DO 10 I = 1, NQ IF( REAL( X( IOFF ) ).NE.ZERO ) THEN TEMP1 = ABS( REAL( X( IOFF ) ) ) IF( SCALE.LT.TEMP1 ) THEN SUMSQ = 1 + SUMSQ * ( SCALE / TEMP1 )**2 SCALE = TEMP1 ELSE SUMSQ = SUMSQ + ( TEMP1 / SCALE )**2 END IF END IF IF( AIMAG( X( IOFF ) ).NE.ZERO ) THEN TEMP1 = ABS( AIMAG( X( IOFF ) ) ) IF( SCALE.LT.TEMP1 ) THEN SUMSQ = 1 + SUMSQ*( SCALE / TEMP1 )**2 SCALE = TEMP1 ELSE SUMSQ = SUMSQ + ( TEMP1 / SCALE )**2 END IF END IF IOFF = IOFF + LDX 10 CONTINUE END IF * * Take local result and find global * WORK( 1 ) = SCALE WORK( 2 ) = SUMSQ * CALL PSTREECOMB( ICTXT, 'Rowwise', 2, WORK, -1, IXCOL, $ SCOMBSSQ ) * SCALE = WORK( 1 ) SUMSQ = WORK( 2 ) * ELSE IF( INCX.EQ.1 ) THEN * * X is columnwise distributed. * IF( MYCOL.NE.IXCOL ) $ RETURN IROFF = MOD( IX, DESCX( MB_ ) ) NP = NUMROC( N+IROFF, DESCX( MB_ ), MYROW, IXROW, NPROW ) IF( MYROW.EQ.IXROW ) $ NP = NP - IROFF * * Code direct from LAPACK's CLASSQ, (save subroutine call) * IF( NP.GT.0 ) THEN IOFF = IIX + ( JJX - 1 ) * LDX DO 20 I = 1, NP IF( REAL( X( IOFF ) ).NE.ZERO ) THEN TEMP1 = ABS( REAL( X( IOFF ) ) ) IF( SCALE.LT.TEMP1 ) THEN SUMSQ = 1 + SUMSQ*( SCALE / TEMP1 )**2 SCALE = TEMP1 ELSE SUMSQ = SUMSQ + ( TEMP1 / SCALE )**2 END IF END IF IF( AIMAG( X( IOFF ) ).NE.ZERO ) THEN TEMP1 = ABS( AIMAG( X( IOFF ) ) ) IF( SCALE.LT.TEMP1 ) THEN SUMSQ = 1 + SUMSQ*( SCALE / TEMP1 )**2 SCALE = TEMP1 ELSE SUMSQ = SUMSQ + ( TEMP1 / SCALE )**2 END IF END IF IOFF = IOFF + 1 20 CONTINUE END IF * * Take local result and find global * WORK( 1 ) = SCALE WORK( 2 ) = SUMSQ * CALL PSTREECOMB( ICTXT, 'Columnwise', 2, WORK, -1, IXCOL, $ SCOMBSSQ ) * SCALE = WORK( 1 ) SUMSQ = WORK( 2 ) * END IF * RETURN * * End of PCLASSQ * END