Routine: PDORGL2()  File: SRC\pdorgl2.f

 
 
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..
     .. Array Arguments ..
     ..
  Purpose
  =======
  PDORGL2 generates an M-by-N real distributed matrix Q denoting
  A(IA:IA+M-1,JA:JA+N-1) with orthonormal rows, which is defined as
  the first M rows of a product of K elementary reflectors of order N
        Q  =  H(k) . . . H(2) H(1)
  as returned by PDGELQF.
  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 Q. M >= 0.
  N       (global input) INTEGER
          The number of columns to be operated on i.e the number of
          columns of the distributed submatrix Q. N >= M >= 0.
  K       (global input) INTEGER
          The number of elementary reflectors whose product defines the
          matrix Q. M >= K >= 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 i-th row must contain the vector which defines
          the elementary reflector H(i), IA <= i <= IA+K-1, as
          returned by PDGELQF in the K rows of its distributed matrix
          argument A(IA:IA+K-1,JA:*). On exit, this array contains the
          local pieces of the M-by-N distributed matrix Q.
  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.
  TAU     (local input) DOUBLE PRECISION array, dimension LOCr(IA+K-1).
          This array contains the scalar factors TAU(i) of the
          elementary reflectors H(i) as returned by PDGELQF.
          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 >= NqA0 + MAX( 1, MpA0 ), where
          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 ),
          MpA0 = NUMROC( M+IROFFA, MB_A, MYROW, IAROW, NPROW ),
          NqA0 = 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.
          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    (local 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.
  =====================================================================
     .. Parameters ..

 
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001        SUBROUTINE PDORGL2( M , N , K , A , IA , JA , DESCA , TAU , WORK , LWORK ,
002       $INFO )
003  
004  *     -- ScaLAPACK routine(version 1.7) --
005  *     University of Tennessee , Knoxville , Oak Ridge National Laboratory ,
006  *     and University of California , Berkeley.
007  *     May 25 , 2001
008  
009  *     .. Scalar Arguments ..
010        INTEGER IA , INFO , JA , K , LWORK , M , N
011        INTEGER BLOCK_CYCLIC_2D , CSRC_ , CTXT_ , DLEN_ , DTYPE_ ,
012       $LLD_ , MB_ , M_ , NB_ , N_ , RSRC_
013        PARAMETER( BLOCK_CYCLIC_2D = 1 , DLEN_ = 9 , DTYPE_ = 1 ,
014       $CTXT_ = 2 , M_ = 3 , N_ = 4 , MB_ = 5 , NB_ = 6 ,
015       $RSRC_ = 7 , CSRC_ = 8 , LLD_ = 9 )
016        DOUBLE PRECISION ONE , ZERO
017        PARAMETER( ONE = 1.0D + 0 , ZERO = 0.0D + 0 )
018  *     ..
019  *     .. Local Scalars ..
020        LOGICAL LQUERY
021        CHARACTER COLBTOP , ROWBTOP
022        INTEGER IACOL , IAROW , I , ICTXT , II , J , KP , LWMIN , MPA0 ,
023       $MYCOL , MYROW , NPCOL , NPROW , NQA0
024        DOUBLE PRECISION TAUI
025  *     ..
026  *     .. External Subroutines ..
027        EXTERNAL BLACS_ABORT , BLACS_GRIDINFO , CHK1MAT , PDELSET ,
028       $PDLARF , PDLASET , PDSCAL , PB_TOPGET ,
029       $PB_TOPSET , PXERBLA
030  *     ..
031  *     .. External Functions ..
032        INTEGER INDXG2L , INDXG2P , NUMROC
033        EXTERNAL INDXG2L , INDXG2P , NUMROC
034  *     ..
035  *     .. Intrinsic Functions ..
036        INTRINSIC DBLE , MAX , MIN , MOD
037  *     ..
038  *     .. Executable Statements ..
039  
040  *     Get grid parameters
041  
042        ICTXT = DESCA( CTXT_ )
043        CALL BLACS_GRIDINFO( ICTXT , NPROW , NPCOL , MYROW , MYCOL )
044  
045  *     Test the input parameters
046  
047        INFO = 0
048        IF( NPROW.EQ. - 1 ) THEN
049            INFO = - (700 + CTXT_)
050        ELSE
051            CALL CHK1MAT( M , 1 , N , 2 , IA , JA , DESCA , 7 , INFO )
052            IF( INFO.EQ.0 ) THEN
053                IAROW = INDXG2P( IA , DESCA( MB_ ) , MYROW , DESCA( RSRC_ ) ,
054       $        NPROW )
055                IACOL = INDXG2P( JA , DESCA( NB_ ) , MYCOL , DESCA( CSRC_ ) ,
056       $        NPCOL )
057                MPA0 = NUMROC( M + MOD( IA - 1 , DESCA( MB_ ) ) , DESCA( MB_ ) ,
058       $        MYROW , IAROW , NPROW )
059                NQA0 = NUMROC( N + MOD( JA - 1 , DESCA( NB_ ) ) , DESCA( NB_ ) ,
060       $        MYCOL , IACOL , NPCOL )
061                LWMIN = NQA0 + MAX( 1 , MPA0 )
062  
063                WORK( 1 ) = DBLE( LWMIN )
064                LQUERY =( LWORK.EQ. - 1 )
065                IF( N.LT.M ) THEN
066                    INFO = - 2
067                ELSE IF( K.LT.0 .OR. K.GT.M ) THEN
068                    INFO = - 3
069                ELSE IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN
070                    INFO = - 10
071                END IF
072            END IF
073        END IF
074        IF( INFO.NE.0 ) THEN
075            CALL PXERBLA( ICTXT , 'PDORGL2' , - INFO )
076            CALL BLACS_ABORT( ICTXT , 1 )
077            RETURN
078        ELSE IF( LQUERY ) THEN
079            RETURN
080        END IF
081  
082  *     Quick return if possible
083  
084        IF( M.LE.0 )
085       $    RETURN
086  
087            CALL PB_TOPGET( ICTXT , 'Broadcast' , 'Rowwise' , ROWBTOP )
088            CALL PB_TOPGET( ICTXT , 'Broadcast' , 'Columnwise' , COLBTOP )
089            CALL PB_TOPSET( ICTXT , 'Broadcast' , 'Rowwise' , ' ' )
090            CALL PB_TOPSET( ICTXT , 'Broadcast' , 'Columnwise' , 'D - ring' )
091  
092            IF( K.LT.M ) THEN
093  
094  *             Initialise rows ia + k : ia + m - 1 to rows of the unit matrix
095  
096                CALL PDLASET ( 'All' , M - K , K , ZERO , ZERO , A , IA + K , JA , DESCA )
097                CALL PDLASET ( 'All' , M - K , N - K , ZERO , ONE , A , IA + K , JA + K ,
098       $        DESCA )
099  
100            END IF
101  
102            TAUI = ZERO
103            KP = NUMROC( IA + K - 1 , DESCA( MB_ ) , MYROW , DESCA( RSRC_ ) , NPROW )
104  
105            DO 10 I = IA + K - 1 , IA , - 1
106  
107  *             Apply H(i) to A(i : ia + m - 1 , ja + i - ia : ja + n - 1) from the right
108  
109                J = JA + I - IA
110                II = INDXG2L( I , DESCA( MB_ ) , MYROW , DESCA( RSRC_ ) , NPROW )
111                IAROW = INDXG2P( I , DESCA( MB_ ) , MYROW , DESCA( RSRC_ ) ,
112       $        NPROW )
113                IF( MYROW.EQ.IAROW )
114       $            TAUI = TAU( MIN( II , KP ) )
115                    IF( J.LT.JA + N - 1 ) THEN
116                        IF( I.LT.IA + M - 1 ) THEN
117                            CALL PDELSET( A , I , J , DESCA , ONE )
118                            CALL PDLARF ( 'Right' , M - I + IA - 1 , N - J + JA , A , I , J , DESCA ,
119       $                    DESCA( M_ ) , TAU , A , I + 1 , J , DESCA , WORK )
120                        END IF
121                        CALL PDSCAL( N - J + JA - 1 , - TAUI , A , I , J + 1 , DESCA ,
122       $                DESCA( M_ ) )
123                    END IF
124                    CALL PDELSET( A , I , J , DESCA , ONE - TAUI )
125  
126  *                 Set A(i , ja : j - 1) to zero
127  
128                    CALL PDLASET ( 'All' , 1 , J - JA , ZERO , ZERO , A , I , JA , DESCA )
129  
130     10     CONTINUE
131  
132            CALL PB_TOPSET( ICTXT , 'Broadcast' , 'Rowwise' , ROWBTOP )
133            CALL PB_TOPSET( ICTXT , 'Broadcast' , 'Columnwise' , COLBTOP )
134  
135            WORK( 1 ) = DBLE( LWMIN )
136  
137            RETURN
138  
139  *         End of PDORGL2
140  
141        END