Routine PSGEQRF() Documented By Universal Report

Routine: PSGEQRF()

File: SRC\psgeqrf.f

# lines:	312
# code:	312
# comment:	0
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# Variables:	44
# Callers:	3
# Callings:	3
# Words:	116
# Keywords:	69

..
     .. Array Arguments ..
     ..
  Purpose
  =======
  PSGEQRF computes a QR factorization of a real distributed M-by-N
  matrix sub( A ) = A(IA:IA+M-1,JA:JA+N-1) = 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) REAL 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,
          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) REAL, 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) REAL 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 >= NB_A * ( Mp0 + Nq0 + NB_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(ja) H(ja+1) . . . H(ja+k-1), where k = min(m,n).
  Each H(i) has the form
     H(j) = 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:ia+m-1,ja+i-1),
  and tau in TAU(ja+i-1).
  =====================================================================
     .. Parameters ..

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001        SUBROUTINE PSGEQRF( 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 , ICOFF , ICTXT , IINFO , IPW , J ,
021       $JB , JN , K , LWMIN , MP0 , MYCOL , MYROW , NPCOL ,
022       $NPROW , NQ0
023  *     ..
024  *     .. Local Arrays ..
025        INTEGER IDUM1( 1 ) , IDUM2( 1 )
026  *     ..
027  *     .. External Subroutines ..
028        EXTERNAL BLACS_GRIDINFO , CHK1MAT , PCHK1MAT , PSGEQR2 ,
029       $PSLARFB , PSLARFT , 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 MIN , MOD , REAL
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                ICOFF = MOD( JA - 1 , DESCA( NB_ ) )
054                IAROW = INDXG2P( IA , DESCA( MB_ ) , MYROW , DESCA( RSRC_ ) ,
055       $        NPROW )
056                IACOL = INDXG2P( JA , DESCA( NB_ ) , MYCOL , DESCA( CSRC_ ) ,
057       $        NPCOL )
058                MP0 = NUMROC( M + MOD( IA - 1 , DESCA( MB_ ) ) , DESCA( MB_ ) ,
059       $        MYROW , IAROW , NPROW )
060                NQ0 = NUMROC( N + ICOFF , DESCA( NB_ ) , MYCOL , IACOL , NPCOL )
061                LWMIN = DESCA( NB_ ) * ( MP0 + NQ0 + DESCA( NB_ ) )
062  
063                WORK( 1 ) = REAL( LWMIN )
064                LQUERY =( LWORK.EQ. - 1 )
065                IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY )
065                       
066       $            INFO = - 9
067                END IF
068                IF( LWORK.EQ. - 1 ) 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 , 'PSGEQRF' , - 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( NB_ ) * DESCA( NB_ ) + 1
092                CALL PB_TOPGET( ICTXT , 'Broadcast' , 'Rowwise' , ROWBTOP )
093                CALL PB_TOPGET( ICTXT , 'Broadcast' , 'Columnwise' , COLBTOP )
094                CALL PB_TOPSET( ICTXT , 'Broadcast' , 'Rowwise' , 'I - ring' )
095                CALL PB_TOPSET( ICTXT , 'Broadcast' , 'Columnwise' , ' ' )
096  
097  *             Handle the first block of columns separately
098  
099                JN = MIN( ICEIL( JA , DESCA( NB_ ) ) * DESCA( NB_ ) , JA + K - 1 )
100                JB = JN - JA + 1
101  
102  *             Compute the QR factorization of the first block A(ia : ia + m - 1 , ja : jn)
103  
104                CALL PSGEQR2 ( M , JB , A , IA , JA , DESCA , TAU , WORK , LWORK , IINFO )
105  
106                IF( JA + JB.LE.JA + N - 1 ) THEN
107  
108  *                 Form the triangular factor of the block reflector
109  *                 H = H(ja) H(ja + 1) . . . H(jn)
110  
110                       
111                    CALL PSLARFT ( 'Forward' , 'Columnwise' , M , JB , A , IA , JA , DESCA ,
112       $            TAU , WORK , WORK( IPW ) )
113  
114  *                 Apply H' to A(ia : ia + m - 1 , ja + jb : ja + n - 1) from the left
115  
116                    CALL PSLARFB ( 'Left' , 'Transpose' , 'Forward' , 'Columnwise' , M ,
117       $            N - JB , JB , A , IA , JA , DESCA , WORK , A , IA , JA + JB ,
118       $            DESCA , WORK( IPW ) )
119                END IF
120  
121  *             Loop over the remaining blocks of columns
122  
123                DO 10 J = JN + 1 , JA + K - 1 , DESCA( NB_ )
123                       
124                    JB = MIN( K - J + JA , DESCA( NB_ ) )
125                    I = IA + J - JA
126  
127  *                 Compute the QR factorization of the current block
128  *                 A(i : ia + m - 1 , j : j + jb - 1)
129  
130                    CALL PSGEQR2 ( M - J + JA , JB , A , I , J , DESCA , TAU , WORK , LWORK ,
131       $            IINFO )
132  
133                    IF( J + JB.LE.JA + N - 1 ) THEN
134  
135  *                     Form the triangular factor of the block reflector
136  *                     H = H(j) H(j + 1) . . . H(j + jb - 1)
137  
137                           
138                        CALL PSLARFT ( 'Forward' , 'Columnwise' , M - J + JA , JB , A , I , J ,
139       $                DESCA , TAU , WORK , WORK( IPW ) )
140  
141  *                     Apply H' to A(i : ia + m - 1 , j + jb : ja + n - 1) from the left
142  
143                        CALL PSLARFB ( 'Left' , 'Transpose' , 'Forward' , 'Columnwise' ,
144       $                M - J + JA , N - J - JB + JA , JB , A , I , J , DESCA , WORK ,
145       $                A , I , J + JB , DESCA , WORK( IPW ) )
146                    END IF
147  
148     10         CONTINUE
149  
149                   
150                CALL PB_TOPSET( ICTXT , 'Broadcast' , 'Rowwise' , ROWBTOP )
151                CALL PB_TOPSET( ICTXT , 'Broadcast' , 'Columnwise' , COLBTOP )
152  
153                WORK( 1 ) = REAL( LWMIN )
154  
155                RETURN
156  
157  *             End of PSGEQRF
158  
159            END3235

Variables in Routine PSGEQRF()

Summary Report
Data Type	Quantity	Size(byte)
CHARACTER	2	2
INTEGER	40	164
LOGICAL	1	1
REAL	1	4
TOTAL	44	171

List of Variables

CHARACTER

COLBTOP ROWBTOP

INTEGER

BLOCK_CYCLIC_2D CSRC_ CTXT_ DLEN_ DTYPE_
I IA IACOL IAROW ICEIL
ICOFF ICTXT IDUM1( 1 ) IDUM2( 1 ) IINFO
INDXG2P INFO IPW J JA
JB JN K LLD_ LWMIN
LWORK M M_ MB_ MP0
MYCOL MYROW N N_ NB_
NPCOL NPROW NQ0 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
-
- -
I <--- JI = IA + J - JA, JAI = IA + J - JA, IAI = IA + J - JA

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

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

ICOFF <--- JAICOFF = MOD( JA-1, DESCA( NB_ ) ), NB_ICOFF = MOD( JA-1, DESCA( NB_ ) )

ICTXT <--- CTXT_ICTXT = DESCA( CTXT_ )

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

IPW <--- NB_IPW = DESCA( NB_ ) * DESCA( NB_ ) + 1

J <--- JADO 10 J = JN+1, JA+K-1, DESCA( NB_ ), JNDO 10 J = JN+1, JA+K-1, DESCA( NB_ ), KDO 10 J = JN+1, JA+K-1, DESCA( NB_ ), NB_DO 10 J = JN+1, JA+K-1, DESCA( NB_ )

JB <--- JJB = MIN( K-J+JA, DESCA( NB_ ) ), JAJB = JN - JA + 1{2JB = MIN( K-J+JA, DESCA( NB_ ) )}, JNJB = JN - JA + 1, KJB = MIN( K-J+JA, DESCA( NB_ ) ), NB_JB = MIN( K-J+JA, DESCA( NB_ ) )

JN <--- ICEIL, JA, K, NB_

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

LWMIN <--- MP0, NB_, NQ0

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

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

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