SUBROUTINE PDGEQPF( M, N, A, IA, JA, DESCA, IPIV, TAU, WORK, $ LWORK, INFO ) * * -- ScaLAPACK routine (version 1.7) -- * University of Tennessee, Knoxville, Oak Ridge National Laboratory, * and University of California, Berkeley. * March 14, 2000 * * .. Scalar Arguments .. INTEGER IA, JA, INFO, LWORK, M, N * .. * .. Array Arguments .. INTEGER DESCA( * ), IPIV( * ) DOUBLE PRECISION A( * ), TAU( * ), WORK( * ) * .. * * Purpose * ======= * * PDGEQPF computes a QR factorization with column pivoting of a * M-by-N distributed matrix sub( A ) = A(IA:IA+M-1,JA:JA+N-1): * * sub( A ) * P = Q * R. * * 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)). * On entry, the local pieces of the M-by-N distributed matrix * sub( A ) which is to be factored. On exit, the elements on * and above the diagonal of sub( A ) contain the min(M,N) by N * upper trapezoidal matrix R (R is upper triangular if M >= N); * the elements below the diagonal, with the array TAU, repre- * sent the orthogonal matrix Q as a product of elementary * reflectors (see Further Details). * * 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. * * IPIV (local output) INTEGER array, dimension LOCc(JA+N-1). * On exit, if IPIV(I) = K, the local i-th column of sub( A )*P * was the global K-th column of sub( A ). IPIV is tied to the * distributed matrix A. * * TAU (local output) DOUBLE PRECISION array, dimension * LOCc(JA+MIN(M,N)-1). This array contains the scalar factors * TAU of the elementary reflectors. TAU is tied to the * distributed matrix A. * * WORK (local workspace/local output) DOUBLE PRECISION array, * dimension (LWORK) * On exit, WORK(1) returns the minimal and optimal LWORK. * * LWORK (local or global input) INTEGER * The dimension of the array WORK. * LWORK is local input and must be at least * LWORK >= MAX(3,Mp0 + Nq0) + LOCc(JA+N-1)+Nq0. * * IROFF = MOD( IA-1, MB_A ), ICOFF = 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+IROFF, MB_A, MYROW, IAROW, NPROW ), * Nq0 = NUMROC( N+ICOFF, NB_A, MYCOL, IACOL, NPCOL ), * LOCc(JA+N-1) = NUMROC( JA+N-1, NB_A, MYCOL, CSRC_A, NPCOL ) * * and NUMROC, INDXG2P are ScaLAPACK tool functions; * MYROW, MYCOL, NPROW and NPCOL can be determined by calling * the subroutine BLACS_GRIDINFO. * * If LWORK = -1, then LWORK is global input and a workspace * query is assumed; the routine only calculates the minimum * and optimal size for all work arrays. Each of these * values is returned in the first entry of the corresponding * work array, and no error message is issued by PXERBLA. * * * INFO (global output) INTEGER * = 0: successful exit * < 0: If the i-th argument is an array and the j-entry had * an illegal value, then INFO = -(i*100+j), if the i-th * argument is a scalar and had an illegal value, then * INFO = -i. * * Further Details * =============== * * The matrix Q is represented as a product of elementary reflectors * * Q = H(1) H(2) . . . H(n) * * Each H(i) has the form * * H = I - tau * v * v' * * where tau is a real scalar, and v is a real vector with v(1:i-1) = 0 * and v(i) = 1; v(i+1:m) is stored on exit in A(ia+i-1:ia+m-1,ja+i-1). * * The matrix P is represented in jpvt as follows: If * jpvt(j) = i * then the jth column of P is the ith canonical unit vector. * * ===================================================================== * * .. 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 ( ONE = 1.0D+0, ZERO = 0.0D+0 ) * .. * .. Local Scalars .. LOGICAL LQUERY INTEGER I, IACOL, IAROW, ICOFF, ICTXT, ICURROW, $ ICURCOL, II, IIA, IOFFA, IPN, IPCOL, IPW, $ IROFF, ITEMP, J, JB, JJ, JJA, JJPVT, JN, KB, $ K, KK, KSTART, KSTEP, LDA, LL, LWMIN, MN, MP, $ MYCOL, MYROW, NPCOL, NPROW, NQ, NQ0, PVT DOUBLE PRECISION AJJ, ALPHA, TEMP, TEMP2 * .. * .. Local Arrays .. INTEGER DESCN( DLEN_ ), IDUM1( 1 ), IDUM2( 1 ) * .. * .. External Subroutines .. EXTERNAL BLACS_GRIDINFO, CHK1MAT, DCOPY, DESCSET, $ DGEBR2D, DGEBS2D, DGERV2D, $ DGESD2D, DLARFG, DSWAP, IGERV2D, $ IGESD2D, INFOG1L, INFOG2L, PCHK1MAT, PDAMAX, $ PDELSET, PDLARF, PDLARFG, PDNRM2, $ PXERBLA * .. * .. External Functions .. INTEGER ICEIL, INDXG2P, NUMROC EXTERNAL ICEIL, INDXG2P, NUMROC * .. * .. Intrinsic Functions .. INTRINSIC ABS, DBLE, IDINT, MAX, MIN, MOD, SQRT * .. * .. Executable Statements .. * * Get grid parameters * ICTXT = DESCA( CTXT_ ) CALL BLACS_GRIDINFO( ICTXT, NPROW, NPCOL, MYROW, MYCOL ) * * Test the input parameters * INFO = 0 IF( NPROW.EQ.-1 ) THEN INFO = -(600+CTXT_) ELSE CALL CHK1MAT( M, 1, N, 2, IA, JA, DESCA, 6, INFO ) IF( INFO.EQ.0 ) THEN IROFF = MOD( IA-1, DESCA( MB_ ) ) ICOFF = MOD( JA-1, DESCA( NB_ ) ) IAROW = INDXG2P( IA, DESCA( MB_ ), MYROW, DESCA( RSRC_ ), $ NPROW ) IACOL = INDXG2P( JA, DESCA( NB_ ), MYCOL, DESCA( CSRC_ ), $ NPCOL ) MP = NUMROC( M+IROFF, DESCA( MB_ ), MYROW, IAROW, NPROW ) NQ = NUMROC( N+ICOFF, DESCA( NB_ ), MYCOL, IACOL, NPCOL ) NQ0 = NUMROC( JA+N-1, DESCA( NB_ ), MYCOL, DESCA( CSRC_ ), $ NPCOL ) LWMIN = MAX( 3, MP + NQ ) + NQ0 + NQ * WORK( 1 ) = DBLE( LWMIN ) LQUERY = ( LWORK.EQ.-1 ) IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) $ INFO = -10 END IF IF( LWORK.EQ.-1 ) THEN IDUM1( 1 ) = -1 ELSE IDUM1( 1 ) = 1 END IF IDUM2( 1 ) = 10 CALL PCHK1MAT( M, 1, N, 2, IA, JA, DESCA, 6, 1, IDUM1, IDUM2, $ INFO ) END IF * IF( INFO.NE.0 ) THEN CALL PXERBLA( ICTXT, 'PDGEQPF', -INFO ) RETURN ELSE IF( LQUERY ) THEN RETURN END IF * * Quick return if possible * IF( M.EQ.0 .OR. N.EQ.0 ) $ RETURN * CALL INFOG2L( IA, JA, DESCA, NPROW, NPCOL, MYROW, MYCOL, IIA, JJA, $ IAROW, IACOL ) IF( MYROW.EQ.IAROW ) $ MP = MP - IROFF IF( MYCOL.EQ.IACOL ) $ NQ = NQ - ICOFF MN = MIN( M, N ) * * Initialize the array of pivots * LDA = DESCA( LLD_ ) JN = MIN( ICEIL( JA, DESCA( NB_ ) ) * DESCA( NB_ ), JA+N-1 ) KSTEP = NPCOL * DESCA( NB_ ) * IF( MYCOL.EQ.IACOL ) THEN * * Handle first block separately * JB = JN - JA + 1 DO 10 LL = JJA, JJA+JB-1 IPIV( LL ) = JA + LL - JJA 10 CONTINUE KSTART = JN + KSTEP - DESCA( NB_ ) * * Loop over remaining block of columns * DO 30 KK = JJA+JB, JJA+NQ-1, DESCA( NB_ ) KB = MIN( JJA+NQ-KK, DESCA( NB_ ) ) DO 20 LL = KK, KK+KB-1 IPIV( LL ) = KSTART+LL-KK+1 20 CONTINUE KSTART = KSTART + KSTEP 30 CONTINUE ELSE KSTART = JN + ( MOD( MYCOL-IACOL+NPCOL, NPCOL )-1 )* $ DESCA( NB_ ) DO 50 KK = JJA, JJA+NQ-1, DESCA( NB_ ) KB = MIN( JJA+NQ-KK, DESCA( NB_ ) ) DO 40 LL = KK, KK+KB-1 IPIV( LL ) = KSTART+LL-KK+1 40 CONTINUE KSTART = KSTART + KSTEP 50 CONTINUE END IF * * Initialize partial column norms, handle first block separately * CALL DESCSET( DESCN, 1, DESCA( N_ ), 1, DESCA( NB_ ), MYROW, $ DESCA( CSRC_ ), ICTXT, 1 ) * IPN = 1 IPW = IPN + NQ0 + NQ JJ = IPN + JJA - 1 IF( MYCOL.EQ.IACOL ) THEN DO 60 KK = 0, JB-1 CALL PDNRM2( M, WORK( JJ+KK ), A, IA, JA+KK, DESCA, 1 ) WORK( NQ+JJ+KK ) = WORK( JJ+KK ) 60 CONTINUE JJ = JJ + JB END IF ICURCOL = MOD( IACOL+1, NPCOL ) * * Loop over the remaining blocks of columns * DO 80 J = JN+1, JA+N-1, DESCA( NB_ ) JB = MIN( JA+N-J, DESCA( NB_ ) ) * IF( MYCOL.EQ.ICURCOL ) THEN DO 70 KK = 0, JB-1 CALL PDNRM2( M, WORK( JJ+KK ), A, IA, J+KK, DESCA, 1 ) WORK( NQ+JJ+KK ) = WORK( JJ+KK ) 70 CONTINUE JJ = JJ + JB END IF ICURCOL = MOD( ICURCOL+1, NPCOL ) 80 CONTINUE * * Compute factorization * DO 120 J = JA, JA+MN-1 I = IA + J - JA * CALL INFOG1L( J, DESCA( NB_ ), NPCOL, MYCOL, DESCA( CSRC_ ), $ JJ, ICURCOL ) K = JA + N - J IF( K.GT.1 ) THEN CALL PDAMAX( K, TEMP, PVT, WORK( IPN ), 1, J, DESCN, $ DESCN( M_ ) ) ELSE PVT = J END IF IF( J.NE.PVT ) THEN CALL INFOG1L( PVT, DESCA( NB_ ), NPCOL, MYCOL, $ DESCA( CSRC_ ), JJPVT, IPCOL ) IF( ICURCOL.EQ.IPCOL ) THEN IF( MYCOL.EQ.ICURCOL ) THEN CALL DSWAP( MP, A( IIA+(JJ-1)*LDA ), 1, $ A( IIA+(JJPVT-1)*LDA ), 1 ) ITEMP = IPIV( JJPVT ) IPIV( JJPVT ) = IPIV( JJ ) IPIV( JJ ) = ITEMP WORK( IPN+JJPVT-1 ) = WORK( IPN+JJ-1 ) WORK( IPN+NQ+JJPVT-1 ) = WORK( IPN+NQ+JJ-1 ) END IF ELSE IF( MYCOL.EQ.ICURCOL ) THEN * CALL DGESD2D( ICTXT, MP, 1, A( IIA+(JJ-1)*LDA ), LDA, $ MYROW, IPCOL ) WORK( IPW ) = DBLE( IPIV( JJ ) ) WORK( IPW+1 ) = WORK( IPN + JJ - 1 ) WORK( IPW+2 ) = WORK( IPN + NQ + JJ - 1 ) CALL DGESD2D( ICTXT, 3, 1, WORK( IPW ), 3, MYROW, $ IPCOL ) * CALL DGERV2D( ICTXT, MP, 1, A( IIA+(JJ-1)*LDA ), LDA, $ MYROW, IPCOL ) CALL IGERV2D( ICTXT, 1, 1, IPIV( JJ ), 1, MYROW, $ IPCOL ) * ELSE IF( MYCOL.EQ.IPCOL ) THEN * CALL DGESD2D( ICTXT, MP, 1, A( IIA+(JJPVT-1)*LDA ), $ LDA, MYROW, ICURCOL ) CALL IGESD2D( ICTXT, 1, 1, IPIV( JJPVT ), 1, MYROW, $ ICURCOL ) * CALL DGERV2D( ICTXT, MP, 1, A( IIA+(JJPVT-1)*LDA ), $ LDA, MYROW, ICURCOL ) CALL DGERV2D( ICTXT, 3, 1, WORK( IPW ), 3, MYROW, $ ICURCOL ) IPIV( JJPVT ) = IDINT( WORK( IPW ) ) WORK( IPN+JJPVT-1 ) = WORK( IPW+1 ) WORK( IPN+NQ+JJPVT-1 ) = WORK( IPW+2 ) * END IF * END IF * END IF * * Generate elementary reflector H(i) * CALL INFOG1L( I, DESCA( MB_ ), NPROW, MYROW, DESCA( RSRC_ ), $ II, ICURROW ) IF( DESCA( M_ ).EQ.1 ) THEN IF( MYROW.EQ.ICURROW ) THEN IF( MYCOL.EQ.ICURCOL ) THEN IOFFA = II+(JJ-1)*DESCA( LLD_ ) AJJ = A( IOFFA ) CALL DLARFG( 1, AJJ, A( IOFFA ), 1, TAU( JJ ) ) IF( N.GT.1 ) THEN ALPHA = ONE - TAU( JJ ) CALL DGEBS2D( ICTXT, 'Rowwise', ' ', 1, 1, ALPHA, $ 1 ) CALL DSCAL( NQ-JJ, ALPHA, A( IOFFA+DESCA( LLD_ ) ), $ DESCA( LLD_ ) ) END IF CALL DGEBS2D( ICTXT, 'Columnwise', ' ', 1, 1, $ TAU( JJ ), 1 ) A( IOFFA ) = AJJ ELSE IF( N.GT.1 ) THEN CALL DGEBR2D( ICTXT, 'Rowwise', ' ', 1, 1, ALPHA, $ 1, ICURROW, ICURCOL ) CALL DSCAL( NQ-JJ+1, ALPHA, A( I ), DESCA( LLD_ ) ) END IF END IF ELSE IF( MYCOL.EQ.ICURCOL ) THEN CALL DGEBR2D( ICTXT, 'Columnwise', ' ', 1, 1, TAU( JJ ), $ 1, ICURROW, ICURCOL ) END IF * ELSE * CALL PDLARFG( M-J+JA, AJJ, I, J, A, MIN( I+1, IA+M-1 ), J, $ DESCA, 1, TAU ) IF( J.LT.JA+N-1 ) THEN * * Apply H(i) to A(ia+j-ja:ia+m-1,j+1:ja+n-1) from the left * CALL PDELSET( A, I, J, DESCA, ONE ) CALL PDLARF( 'Left', M-J+JA, JA+N-1-J, A, I, J, DESCA, $ 1, TAU, A, I, J+1, DESCA, WORK( IPW ) ) END IF CALL PDELSET( A, I, J, DESCA, AJJ ) * END IF * * Update partial columns norms * IF( MYCOL.EQ.ICURCOL ) $ JJ = JJ + 1 IF( MOD( J, DESCA( NB_ ) ).EQ.0 ) $ ICURCOL = MOD( ICURCOL+1, NPCOL ) IF( (JJA+NQ-JJ).GT.0 ) THEN IF( MYROW.EQ.ICURROW ) THEN CALL DGEBS2D( ICTXT, 'Columnwise', ' ', 1, JJA+NQ-JJ, $ A( II+( MIN( JJA+NQ-1, JJ )-1 )*LDA ), $ LDA ) CALL DCOPY( JJA+NQ-JJ, A( II+( MIN( JJA+NQ-1, JJ ) $ -1)*LDA ), LDA, WORK( IPW+MIN( JJA+NQ-1, $ JJ )-1 ), 1 ) ELSE CALL DGEBR2D( ICTXT, 'Columnwise', ' ', JJA+NQ-JJ, 1, $ WORK( IPW+MIN( JJA+NQ-1, JJ )-1 ), $ MAX( 1, NQ ), ICURROW, MYCOL ) END IF END IF * JN = MIN( ICEIL( J+1, DESCA( NB_ ) ) * DESCA( NB_ ), $ JA + N - 1 ) IF( MYCOL.EQ.ICURCOL ) THEN DO 90 LL = JJ-1, JJ + JN - J - 2 IF( WORK( IPN+LL ).NE.ZERO ) THEN TEMP = ONE-( ABS( WORK( IPW+LL ) ) / $ WORK( IPN+LL ) )**2 TEMP = MAX( TEMP, ZERO ) TEMP2 = ONE + 0.05D+0*TEMP* $ ( WORK( IPN+LL ) / WORK( IPN+NQ+LL ) )**2 IF( TEMP2.EQ.ONE ) THEN IF( IA+M-1.GT.I ) THEN CALL PDNRM2( IA+M-I-1, WORK( IPN+LL ), A, I+1, $ J+LL-JJ+2, DESCA, 1 ) WORK( IPN+NQ+LL ) = WORK( IPN+LL ) ELSE WORK( IPN+LL ) = ZERO WORK( IPN+NQ+LL ) = ZERO END IF ELSE WORK( IPN+LL ) = WORK( IPN+LL ) * SQRT( TEMP ) END IF END IF 90 CONTINUE JJ = JJ + JN - J END IF ICURCOL = MOD( ICURCOL+1, NPCOL ) * DO 110 K = JN+1, JA+N-1, DESCA( NB_ ) KB = MIN( JA+N-K, DESCA( NB_ ) ) * IF( MYCOL.EQ.ICURCOL ) THEN DO 100 LL = JJ-1, JJ+KB-2 IF( WORK( IPN+LL ).NE.ZERO ) THEN TEMP = ONE-( ABS( WORK( IPW+LL ) ) / $ WORK( IPN+LL ) )**2 TEMP = MAX( TEMP, ZERO ) TEMP2 = ONE + 0.05D+0*TEMP* $ ( WORK( IPN+LL ) / WORK( IPN+NQ+LL ) )**2 IF( TEMP2.EQ.ONE ) THEN IF( IA+M-1.GT.I ) THEN CALL PDNRM2( IA+M-I-1, WORK( IPN+LL ), A, $ I+1, K+LL-JJ+1, DESCA, 1 ) WORK( IPN+NQ+LL ) = WORK( IPN+LL ) ELSE WORK( IPN+LL ) = ZERO WORK( IPN+NQ+LL ) = ZERO END IF ELSE WORK( IPN+LL ) = WORK( IPN+LL ) * SQRT( TEMP ) END IF END IF 100 CONTINUE JJ = JJ + KB END IF ICURCOL = MOD( ICURCOL+1, NPCOL ) * 110 CONTINUE * 120 CONTINUE * WORK( 1 ) = DBLE( LWMIN ) * RETURN * * End of PDGEQPF * END