DOUBLE PRECISION FUNCTION PDQRT14( TRANS, M, N, NRHS, A, IA, JA, $ DESCA, X, IX, JX, DESCX, WORK ) * * -- ScaLAPACK routine (version 1.7) -- * University of Tennessee, Knoxville, Oak Ridge National Laboratory, * and University of California, Berkeley. * May 1, 1997 * * .. Scalar Arguments .. CHARACTER TRANS INTEGER IA, IX, JA, JX, M, N, NRHS * .. * .. Array Arguments .. INTEGER DESCA( * ), DESCX( * ) DOUBLE PRECISION A( * ), WORK( * ), X( * ) * .. * * Purpose * ======= * * PDQRT14 checks whether sub( X ) is in the row space of sub( A ) or * sub( A )', where sub( A ) denotes A( IA:IA+M-1, JA:JA+N-1 ) and * sub( X ) denotes X( IX:IX+N-1, JX:JX+NRHS-1 ) if TRANS = 'N', and * X( IX:IX+N-1, JX:JX+NRHS-1 ) otherwise. It does so by scaling both * sub( X ) and sub( A ) such that their norms are in the range * [sqrt(eps), 1/sqrt(eps)], then computing an LQ factorization of * [sub( A )',sub( X )]' (if TRANS = 'N') or a QR factorization of * [sub( A ),sub( X )] otherwise, and returning the norm of the trailing * triangle, scaled by MAX(M,N,NRHS)*eps. * * 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 * ========= * * TRANS (global input) CHARACTER*1 * = 'N': No transpose, check for sub( X ) in the row space of * sub( A ), * = 'T': Transpose, check for sub( X ) in row space of * sub( A )'. * * 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. * * NRHS (global input) INTEGER * The number of right hand sides, i.e., the number of columns * of the distributed submatrix sub( X ). NRHS >= 0. * * A (local input) DOUBLE PRECISION pointer into the local memory * to an array of dimension (LLD_A, LOCc(JA+N-1)). This array * contains the local pieces of the M-by-N distributed matrix * sub( A ). * * 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. * * X (local input) DOUBLE PRECISION pointer into the local * memory to an array of dimension (LLD_X,LOCc(JX+NRHS-1)). * On entry, this array contains the local pieces of the * N-by-NRHS distributed submatrix sub( X ) if TRANS = 'N', * and the M-by-NRHS distributed submatrix sub( X ) otherwise. * * 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. * * WORK (local workspace) DOUBLE PRECISION array dimension (LWORK) * If TRANS='N', LWORK >= MNRHSP * NQ + LTAU + LWF and * LWORK >= MP * NNRHSQ + LTAU + LWF otherwise, where * * IF TRANS='N', (LQ fact) * MNRHSP = NUMROC( M+NRHS+IROFFA, MB_A, MYROW, IAROW, * NPROW ) * LTAU = NUMROC( IA+MIN( M+NRHS, N )-1, MB_A, MYROW, * RSRC_A, NPROW ) * LWF = MB_A * ( MB_A + MNRHSP + NQ0 ) * ELSE (QR fact) * NNRHSQ = NUMROC( N+NRHS+ICOFFA, NB_A, MYCOL, IACOL, * NPCOL ) * LTAU = NUMROC( JA+MIN( M, N+NRHS )-1, NB_A, MYCOL, * CSRC_A, NPCOL ) * LWF = NB_A * ( NB_A + MP0 + NNRHSQ ) * END IF * * and, * * IROFFA = MOD( IA-1, MB_A ), ICOFFA = MOD( JA-1, NB_A ), * IAROW = INDXG2P( IA, MB_A, MYROW, RSRC_A, NPROW ), * IACOL = INDXG2P( JA, NB_A, MYCOL, CSRC_A, NPCOL ), * MP0 = NUMROC( M+IROFFA, MB_A, MYROW, IAROW, NPROW ), * NQ0 = NUMROC( N+ICOFFA, NB_A, MYCOL, IACOL, NPCOL ). * * INDXG2P and NUMROC are ScaLAPACK tool functions; * MYROW, MYCOL, NPROW and NPCOL can be determined by calling * the subroutine BLACS_GRIDINFO. * * * ===================================================================== * * .. 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, ZERO PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) * .. * .. Local Scalars .. LOGICAL TPSD INTEGER IACOL, IAROW, ICOFFA, ICTXT, IDUM, IIA, INFO, $ IPTAU, IPW, IPWA, IROFFA, IWA, IWX, J, JJA, $ JWA, JWX, LDW, LWORK, MPWA, MPW, MQW, MYCOL, $ MYROW, NPCOL, NPROW, NPW, NQWA, NQW DOUBLE PRECISION AMAX, ANRM, ERR, XNRM * .. * .. Local Arrays .. INTEGER DESCW( DLEN_ ), IDUM1( 1 ), IDUM2( 1 ) DOUBLE PRECISION RWORK( 1 ) * .. * .. External Functions .. LOGICAL LSAME INTEGER NUMROC DOUBLE PRECISION PDLANGE, PDLAMCH EXTERNAL LSAME, NUMROC, PDLANGE, PDLAMCH * .. * .. External Subroutines .. EXTERNAL BLACS_GRIDINFO, DESCSET, DGAMX2D, INFOG2L, $ PDAMAX, PDCOPY, PDGELQF, PDGEQRF, $ PDLACPY, PDLASCL, PXERBLA * .. * .. Intrinsic Functions .. INTRINSIC ABS, DBLE, MAX, MIN, MOD * .. * .. Executable Statements .. * * Get grid parameters * ICTXT = DESCA( CTXT_ ) CALL BLACS_GRIDINFO( ICTXT, NPROW, NPCOL, MYROW, MYCOL ) * PDQRT14 = ZERO * IPWA = 1 IROFFA = MOD( IA-1, DESCA( MB_ ) ) ICOFFA = MOD( JA-1, DESCA( NB_ ) ) IWA = IROFFA + 1 JWA = ICOFFA + 1 CALL INFOG2L( IA, JA, DESCA, NPROW, NPCOL, MYROW, MYCOL, IIA, $ JJA, IAROW, IACOL ) MPWA = NUMROC( M+IROFFA, DESCA( MB_ ), MYROW, IAROW, NPROW ) NQWA = NUMROC( N+ICOFFA, DESCA( NB_ ), MYCOL, IACOL, NPCOL ) * INFO = 0 IF( LSAME( TRANS, 'N' ) ) THEN IF( N.LE.0 .OR. NRHS.LE.0 ) $ RETURN TPSD = .FALSE. MPW = NUMROC( M+NRHS+IROFFA, DESCA( MB_ ), MYROW, IAROW, $ NPROW ) NQW = NQWA * * Assign descriptor DESCW for workspace WORK and pointers to * matrices sub( A ) and sub( X ) in workspace * IWX = IWA + M JWX = JWA LDW = MAX( 1, MPW ) CALL DESCSET( DESCW, M+NRHS+IROFFA, N+ICOFFA, DESCA( MB_ ), $ DESCA( NB_ ), IAROW, IACOL, ICTXT, LDW ) * ELSE IF( LSAME( TRANS, 'T' ) ) THEN IF( M.LE.0 .OR. NRHS.LE.0 ) $ RETURN TPSD = .TRUE. MPW = MPWA NQW = NUMROC( N+NRHS+ICOFFA, DESCA( NB_ ), MYCOL, IACOL, $ NPCOL ) * * Assign descriptor DESCW for workspace WORK and pointers to * matrices sub( A ) and sub( X ) in workspace * IWX = IWA JWX = JWA + N LDW = MAX( 1, MPW ) CALL DESCSET( DESCW, M+IROFFA, N+NRHS+ICOFFA, DESCA( MB_ ), $ DESCA( NB_ ), IAROW, IACOL, ICTXT, LDW ) ELSE CALL PXERBLA( ICTXT, 'PDQRT14', -1 ) RETURN END IF * * Copy and scale sub( A ) * IPTAU = IPWA + MPW*NQW CALL PDLACPY( 'All', M, N, A, IA, JA, DESCA, WORK( IPWA ), IWA, $ JWA, DESCW ) RWORK( 1 ) = ZERO ANRM = PDLANGE( 'M', M, N, WORK( IPWA ), IWA, JWA, DESCW, RWORK ) IF( ANRM.NE.ZERO ) $ CALL PDLASCL( 'G', ANRM, ONE, M, N, WORK( IPWA ), IWA, $ JWA, DESCW, INFO ) * * Copy sub( X ) or sub( X )' into the right place and scale it * IF( TPSD ) THEN * * Copy sub( X ) into columns jwa+n:jwa+n+nrhs-1 of work * DO 10 J = 1, NRHS CALL PDCOPY( M, X, IX, JX+J-1, DESCX, 1, WORK( IPWA ), IWX, $ JWX+J-1, DESCW, 1 ) 10 CONTINUE XNRM = PDLANGE( 'M', M, NRHS, WORK( IPWA ), IWX, JWX, DESCW, $ RWORK ) IF( XNRM.NE.ZERO ) $ CALL PDLASCL( 'G', XNRM, ONE, M, NRHS, WORK( IPWA ), IWX, $ JWX, DESCW, INFO ) * * Compute QR factorization of work(iwa:iwa+m-1,jwa:jwa+n+nrhs-1) * MQW = NUMROC( M+ICOFFA, DESCA( NB_ ), MYCOL, IACOL, NPCOL ) IPW = IPTAU + MIN( MQW, NQW ) LWORK = DESCW( NB_ ) * ( MPW + NQW + DESCW( NB_ ) ) CALL PDGEQRF( M, N+NRHS, WORK( IPWA ), IWA, JWA, DESCW, $ WORK( IPTAU ), WORK( IPW ), LWORK, INFO ) * * Compute largest entry in upper triangle of * work(iwa+n:iwa+m-1,jwa+n:jwa+n+nrhs-1) * ERR = ZERO IF( N.LT.M ) THEN DO 20 J = JWX, JWA+N+NRHS-1 CALL PDAMAX( MIN(M-N,J-JWX+1), AMAX, IDUM, WORK( IPWA ), $ IWA+N, J, DESCW, 1 ) ERR = MAX( ERR, ABS( AMAX ) ) 20 CONTINUE END IF CALL DGAMX2D( ICTXT, 'All', ' ', 1, 1, ERR, 1, IDUM1, IDUM2, $ -1, -1, 0 ) * ELSE * * Copy sub( X )' into rows iwa+m:iwa+m+nrhs-1 of work * DO 30 J = 1, NRHS CALL PDCOPY( N, X, IX, JX+J-1, DESCX, 1, WORK( IPWA ), $ IWX+J-1, JWX, DESCW, DESCW( M_ ) ) 30 CONTINUE * XNRM = PDLANGE( 'M', NRHS, N, WORK( IPWA ), IWX, JWX, DESCW, $ RWORK ) IF( XNRM.NE.ZERO ) $ CALL PDLASCL( 'G', XNRM, ONE, NRHS, N, WORK( IPWA ), IWX, $ JWX, DESCW, INFO ) * * Compute LQ factorization of work(iwa:iwa+m+nrhs-1,jwa:jwa+n-1) * NPW = NUMROC( N+IROFFA, DESCA( MB_ ), MYROW, IAROW, NPROW ) IPW = IPTAU + MIN( MPW, NPW ) LWORK = DESCW( MB_ ) * ( MPW + NQW + DESCW( MB_ ) ) CALL PDGELQF( M+NRHS, N, WORK( IPWA ), IWA, JWA, DESCW, $ WORK( IPTAU ), WORK( IPW ), LWORK, INFO ) * * Compute largest entry in lower triangle in * work(iwa+m:iwa+m+nrhs-1,jwa+m:jwa+n-1) * ERR = ZERO DO 40 J = JWA+M, MIN( JWA+N-1, JWA+M+NRHS-1 ) CALL PDAMAX( JWA+M+NRHS-J, AMAX, IDUM, WORK( IPWA ), $ IWX+J-JWA-M, J, DESCW, 1 ) ERR = MAX( ERR, ABS( AMAX ) ) 40 CONTINUE CALL DGAMX2D( ICTXT, 'All', ' ', 1, 1, ERR, 1, IDUM1, IDUM2, $ -1, -1, 0 ) * END IF * PDQRT14 = ERR / ( DBLE( MAX( M, N, NRHS ) ) * $ PDLAMCH( ICTXT, 'Epsilon' ) ) * RETURN * * End of PDQRT14 * END