SUBROUTINE PDLAQGE( M, N, A, IA, JA, DESCA, R, C, ROWCND, COLCND, $ AMAX, EQUED ) * * -- ScaLAPACK auxiliary routine (version 1.7) -- * University of Tennessee, Knoxville, Oak Ridge National Laboratory, * and University of California, Berkeley. * May 1, 1997 * * .. Scalar Arguments .. CHARACTER EQUED INTEGER IA, JA, M, N DOUBLE PRECISION AMAX, COLCND, ROWCND * .. * .. Array Arguments .. INTEGER DESCA( * ) DOUBLE PRECISION A( * ), C( * ), R( * ) * .. * * Purpose * ======= * * PDLAQGE equilibrates a general M-by-N distributed matrix * sub( A ) = A(IA:IA+M-1,JA:JA+N-1) using the row and scaling * factors in the vectors R and C. * * 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 * ========= * * M (global input) INTEGER * The number of rows to be operated on i.e the number of rows * of the distributed submatrix sub( A ). M >= 0. * * N (global input) INTEGER * The number of columns to be operated on i.e the number of * columns of the distributed submatrix sub( A ). N >= 0. * * A (local input/local output) DOUBLE PRECISION pointer into the * local memory to an array of dimension (LLD_A,LOCc(JA+N-1)) * containing on entry the M-by-N matrix sub( A ). On exit, * the equilibrated distributed matrix. See EQUED for the * form of the equilibrated distributed submatrix. * * IA (global input) INTEGER * The row index in the global array A indicating the first * row of sub( A ). * * JA (global input) INTEGER * The column index in the global array A indicating the * first column of sub( A ). * * DESCA (global and local input) INTEGER array of dimension DLEN_. * The array descriptor for the distributed matrix A. * * R (local input) DOUBLE PRECISION array, dimension LOCr(M_A) * The row scale factors for sub( A ). R is aligned with the * distributed matrix A, and replicated across every process * column. R is tied to the distributed matrix A. * * C (local input) DOUBLE PRECISION array, dimension LOCc(N_A) * The column scale factors of sub( A ). C is aligned with the * distributed matrix A, and replicated down every process * row. C is tied to the distributed matrix A. * * ROWCND (global input) DOUBLE PRECISION * The global ratio of the smallest R(i) to the largest R(i), * IA <= i <= IA+M-1. * * COLCND (global input) DOUBLE PRECISION * The global ratio of the smallest C(i) to the largest C(i), * JA <= j <= JA+N-1. * * AMAX (global input) DOUBLE PRECISION * Absolute value of largest distributed submatrix entry. * * EQUED (global output) CHARACTER * Specifies the form of equilibration that was done. * = 'N': No equilibration * = 'R': Row equilibration, i.e., sub( A ) has been pre- * multiplied by diag(R(IA:IA+M-1)), * = 'C': Column equilibration, i.e., sub( A ) has been post- * multiplied by diag(C(JA:JA+N-1)), * = 'B': Both row and column equilibration, i.e., sub( A ) * has been replaced by * diag(R(IA:IA+M-1)) * sub( A ) * diag(C(JA:JA+N-1)). * * Internal Parameters * =================== * * THRESH is a threshold value used to decide if row or column scaling * should be done based on the ratio of the row or column scaling * factors. If ROWCND < THRESH, row scaling is done, and if * COLCND < THRESH, column scaling is done. * * LARGE and SMALL are threshold values used to decide if row scaling * should be done based on the absolute size of the largest matrix * element. If AMAX > LARGE or AMAX < SMALL, row scaling is done. * * ===================================================================== * * .. 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 ) DOUBLE PRECISION ONE, THRESH PARAMETER ( ONE = 1.0D+0, THRESH = 0.1D+0 ) * .. * .. Local Scalars .. INTEGER I, IACOL, IAROW, ICOFF, ICTXT, IIA, IOFFA, $ IROFF, J, JJA, LDA, MP, MYCOL, MYROW, NPCOL, $ NPROW, NQ DOUBLE PRECISION CJ, LARGE, SMALL * .. * .. External Subroutines .. EXTERNAL BLACS_GRIDINFO, INFOG2L * .. * .. External Functions .. INTEGER NUMROC DOUBLE PRECISION PDLAMCH EXTERNAL NUMROC, PDLAMCH * .. * .. Intrinsic Functions .. INTRINSIC MOD * .. * .. Executable Statements .. * * Quick return if possible * IF( M.LE.0 .OR. N.LE.0 ) THEN EQUED = 'N' RETURN END IF * * Get grid parameters and compute local indexes * ICTXT = DESCA( CTXT_ ) CALL BLACS_GRIDINFO( ICTXT, NPROW, NPCOL, MYROW, MYCOL ) CALL INFOG2L( IA, JA, DESCA, NPROW, NPCOL, MYROW, MYCOL, IIA, JJA, $ IAROW, IACOL ) IROFF = MOD( IA-1, DESCA( MB_ ) ) ICOFF = MOD( JA-1, DESCA( NB_ ) ) MP = NUMROC( M+IROFF, DESCA( MB_ ), MYROW, IAROW, NPROW ) NQ = NUMROC( N+ICOFF, DESCA( NB_ ), MYCOL, IACOL, NPCOL ) IF( MYROW.EQ.IAROW ) $ MP = MP - IROFF IF( MYCOL.EQ.IACOL ) $ NQ = NQ - ICOFF LDA = DESCA( LLD_ ) * * Initialize LARGE and SMALL. * SMALL = PDLAMCH( ICTXT, 'Safe minimum' ) / $ PDLAMCH( ICTXT, 'Precision' ) LARGE = ONE / SMALL * IF( ROWCND.GE.THRESH .AND. AMAX.GE.SMALL .AND. AMAX.LE.LARGE ) $ THEN * * No row scaling * IF( COLCND.GE.THRESH ) THEN * * No column scaling * EQUED = 'N' * ELSE * * Column scaling * IOFFA = (JJA-1)*LDA DO 20 J = JJA, JJA+NQ-1 CJ = C( J ) DO 10 I = IIA, IIA+MP-1 A( IOFFA + I ) = CJ*A( IOFFA + I ) 10 CONTINUE IOFFA = IOFFA + LDA 20 CONTINUE EQUED = 'C' END IF * ELSE IF( COLCND.GE.THRESH ) THEN * * Row scaling, no column scaling * IOFFA = (JJA-1)*LDA DO 40 J = JJA, JJA+NQ-1 DO 30 I = IIA, IIA+MP-1 A( IOFFA + I ) = R( I )*A( IOFFA + I ) 30 CONTINUE IOFFA = IOFFA + LDA 40 CONTINUE EQUED = 'R' * ELSE * * Row and column scaling * IOFFA = (JJA-1)*LDA DO 60 J = JJA, JJA+NQ-1 CJ = C( J ) DO 50 I = IIA, IIA+MP-1 A( IOFFA + I ) = CJ*R( I )*A( IOFFA + I ) 50 CONTINUE IOFFA = IOFFA + LDA 60 CONTINUE EQUED = 'B' * END IF * RETURN * * End of PDLAQGE * END