Routine PDGERQF() Documented By Universal Report

Routine: PDGERQF()

File: SRC\pdgerqf.f

# lines:	309
# code:	309
# comment:	0
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# Variables:	45
# Callers:	2
# Callings:	3
# Words:	118
# Keywords:	65

..
     .. Array Arguments ..
     ..
  Purpose
  =======
  PDGERQF computes a RQ factorization of a real distributed M-by-N
  matrix sub( A ) = A(IA:IA+M-1,JA:JA+N-1) = R * Q.
  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, if M <= N, the
          upper triangle of A( IA:IA+M-1, JA+N-M:JA+N-1 ) contains the
          M by M upper triangular matrix R; if M >= N, the elements on
          and above the (M-N)-th subdiagonal contain the M by N upper
          trapezoidal matrix R; the remaining elements, with the array
          TAU, represent 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.
  TAU     (local output) DOUBLE PRECISION array, dimension LOCr(IA+M-1)
          This array contains the scalar factors 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 >= MB_A * ( Mp0 + Nq0 + MB_A ), where
          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 ),
          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(ia) H(ia+1) . . . H(ia+k-1), where k = min(m,n).
  Each H(i) has the form
     H(i) = I - tau * v * v'
  where tau is a real scalar, and v is a real vector with
  v(n-k+i+1:n) = 0 and v(n-k+i) = 1; v(1:n-k+i-1) is stored on exit in
  A(ia+m-k+i-1,ja:ja+n-k+i-2), and tau in TAU(ia+m-k+i-1).
  =====================================================================
     .. Parameters ..

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001        SUBROUTINE PDGERQF( M , N , 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 , 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  *     ..
017  *     .. Local Scalars ..
018        LOGICAL LQUERY
019        CHARACTER COLBTOP , ROWBTOP
020        INTEGER I , IACOL , IAROW , IB , ICTXT , IINFO , IL , IN , IPW ,
021       $K , LWMIN , MP0 , MU , MYCOL , MYROW , NPCOL , NPROW ,
022       $NQ0 , NU
023  *     ..
024  *     .. Local Arrays ..
025        INTEGER IDUM1( 1 ) , IDUM2( 1 )
026  *     ..
027  *     .. External Subroutines ..
028        EXTERNAL BLACS_GRIDINFO , CHK1MAT , PCHK1MAT , PDGERQ2 ,
029       $PDLARFB , PDLARFT , PB_TOPGET , PB_TOPSET , PXERBLA
030  *     ..
031  *     .. External Functions ..
032        INTEGER ICEIL , INDXG2P , NUMROC
033        EXTERNAL ICEIL , 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
048               
049            INFO = - (600 + CTXT_)
050        ELSE
050               
051            CALL CHK1MAT( M , 1 , N , 2 , IA , JA , DESCA , 6 , INFO )
052            IF( INFO.EQ.0 ) THEN
052                   
053                IAROW = INDXG2P( IA , DESCA( MB_ ) , MYROW , DESCA( RSRC_ ) ,
054       $        NPROW )
055                IACOL = INDXG2P( JA , DESCA( NB_ ) , MYCOL , DESCA( CSRC_ ) ,
056       $        NPCOL )
057                MP0 = NUMROC( M + MOD( IA - 1 , DESCA( MB_ ) ) , DESCA( MB_ ) ,
058       $        MYROW , IAROW , NPROW )
059                NQ0 = NUMROC( N + MOD( JA - 1 , DESCA( NB_ ) ) , DESCA( NB_ ) ,
060       $        MYCOL , IACOL , NPCOL )
061                LWMIN = DESCA( MB_ ) * ( MP0 + NQ0 + DESCA( MB_ ) )
062  
063                WORK( 1 ) = DBLE( LWMIN )
064                LQUERY =( LWORK.EQ. - 1 )
065                IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY )
065                       
066       $            INFO = - 9
067                END IF
068                IF( LQUERY ) THEN
068                       
069                    IDUM1( 1 ) = - 1
070                ELSE
070                       
071                    IDUM1( 1 ) = 1
072                END IF
073                IDUM2( 1 ) = 9
074                CALL PCHK1MAT( M , 1 , N , 2 , IA , JA , DESCA , 6 , 1 , IDUM1 , IDUM2 ,
075       $        INFO )
076            END IF
077  
078            IF( INFO.NE.0 ) THEN
078                   
079                CALL PXERBLA( ICTXT , 'PDGERQF' , - INFO )
080                RETURN
081            ELSE IF( LQUERY ) THEN
081                   
082                RETURN
083            END IF
084  
085  *         Quick return if possible
086  
087            IF( M.EQ.0 .OR. N.EQ.0 )
087                   
088       $        RETURN
089  
090                K = MIN( M , N )
091                IPW = DESCA( MB_ ) * DESCA( MB_ ) + 1
092                IN = MIN( ICEIL( IA + M - K , DESCA( MB_ ) ) * DESCA( MB_ ) , IA + M - 1 )
093                IL = MAX(((IA + M - 2) / DESCA( MB_ ) ) * DESCA( MB_ ) + 1 , IA )
094                CALL PB_TOPGET( ICTXT , 'Broadcast' , 'Rowwise' , ROWBTOP )
095                CALL PB_TOPGET( ICTXT , 'Broadcast' , 'Columnwise' , COLBTOP )
096                CALL PB_TOPSET( ICTXT , 'Broadcast' , 'Rowwise' , ' ' )
097                CALL PB_TOPSET( ICTXT , 'Broadcast' , 'Columnwise' , 'D - ring' )
098  
099                IF( IL.GE.IN + 1 ) THEN
100  
101  *                 Use blocked code initially
102  
102                       
103                    DO 10 I = IL , IN + 1 , - DESCA( MB_ )
103                           
104                        IB = MIN( IA + M - I , DESCA( MB_ ) )
105  
106  *                     Compute the RQ factorization of the current block
107  *                     A(i : i + ib - 1 , ja : ja + n - m + i + ib - ia - 1)
108  
109                        CALL PDGERQ2 ( IB , N - M + I + IB - IA , A , I , JA , DESCA , TAU , WORK ,
110       $                LWORK , IINFO )
111  
112                        IF( I.GT.IA ) THEN
113  
114  *                         Form the triangular factor of the block reflector
115  *                         H = H(i + ib - 1) . . . H(i + 1) H(i)
116  
116                               
117                            CALL PDLARFT ( 'Backward' , 'Rowwise' , N - M + I + IB - IA , IB , A ,
118       $                    I , JA , DESCA , TAU , WORK , WORK( IPW ) )
119  
120  *                         Apply H to A(ia : i - 1 , ja : ja + n - m + i + ib - ia - 1) from the
121  *                         right
122  
123                            CALL PDLARFB ( 'Right' , 'No transpose' , 'Backward' ,
124       $                    'Rowwise' , I - IA , N - M + I + IB - IA , IB , A , I , JA ,
125       $                    DESCA , WORK , A , IA , JA , DESCA ,
126       $                    WORK( IPW ) )
127                        END IF
128  
129     10             CONTINUE
130  
130                       
131                    MU = IN - IA + 1
132                    NU = N - M + IN - IA + 1
133  
134                ELSE
135  
135                       
136                    MU = M
137                    NU = N
138  
139                END IF
140  
141  *             Use unblocked code to factor the last or only block
142  
143                IF( MU.GT.0 .AND. NU.GT.0 )
143                       
144       $            CALL PDGERQ2 ( MU , NU , A , IA , JA , DESCA , TAU , WORK , LWORK ,
145       $            IINFO )
146  
147                    CALL PB_TOPSET( ICTXT , 'Broadcast' , 'Rowwise' , ROWBTOP )
148                    CALL PB_TOPSET( ICTXT , 'Broadcast' , 'Columnwise' , COLBTOP )
149  
150                    WORK( 1 ) = DBLE( LWMIN )
151  
152                    RETURN
153  
154  *                 End of PDGERQF
155  
156                END2933

Variables in Routine PDGERQF()

Summary Report
Data Type	Quantity	Size(byte)
CHARACTER	2	2
INTEGER	41	168
LOGICAL	1	1
REAL	1	4
TOTAL	45	175

List of Variables

CHARACTER

COLBTOP ROWBTOP

INTEGER

BLOCK_CYCLIC_2D CSRC_ CTXT_ DLEN_ DTYPE_
I IA IACOL IAROW IB
ICEIL ICTXT IDUM1( 1 ) IDUM2( 1 ) IINFO
IL IN INDXG2P INFO IPW
JA K LLD_ LWMIN LWORK
M M_ MB_ MP0 MU
MYCOL MYROW N N_ NB_
NPCOL NPROW NQ0 NU NUMROC
RSRC_

LOGICAL

LQUERY

REAL

WORK

Variables Dependence Graph
Put the mouse over a right hand side variable to display the corresponding line of the dependence
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- -
I <--- ILDO 10 I = IL, IN+1, -DESCA( MB_ ), INDO 10 I = IL, IN+1, -DESCA( MB_ ), MB_DO 10 I = IL, IN+1, -DESCA( MB_ )

IACOL <--- INDXG2P, JA, CSRC_, MYCOL, NB_, NPCOL

IAROW <--- INDXG2P, MB_, MYROW, NPROW, RSRC_, IA

IB <--- MIB = MIN( IA+M-I, DESCA( MB_ ) ), MB_IB = MIN( IA+M-I, DESCA( MB_ ) ), IIB = MIN( IA+M-I, DESCA( MB_ ) ), IAIB = MIN( IA+M-I, DESCA( MB_ ) )

ICTXT <--- CTXT_ICTXT = DESCA( CTXT_ )

IL <--- M, MB_, IA

IN <--- ICEIL, K, M, MB_, IA

INFO <--- CTXT_INFO = -(600+CTXT_)

IPW <--- MB_IPW = DESCA( MB_ ) * DESCA( MB_ ) + 1

K <--- MK = MIN( M, N ), NK = MIN( M, N )

LWMIN <--- MB_, MP0, NQ0

MP0 <--- IAROW, M, MB_, MYROW, NPROW, NUMROC, IA

MU <--- INMU = IN - IA + 1, MMU = M, IAMU = IN - IA + 1

NQ0 <--- JA, MYCOL, N, NB_, NPCOL, NUMROC, IACOL

NU <--- INNU = N - M + IN - IA + 1, MNU = N - M + IN - IA + 1, NNU = N - M + IN - IA + 1{2NU = N}, IANU = N - M + IN - IA + 1

WORK <--- LWMINWORK( 1 ) = DBLE( LWMIN ){2WORK( 1 ) = DBLE( LWMIN )}