Routine PZGEQR2() Documented By Universal Report

Routine: PZGEQR2()

File: SRC\pzgeqr2.f

# lines:	308
# code:	308
# comment:	0
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# Variables:	42
# Callers:	1
# Callings:	2
# Words:	161
# Keywords:	88

..
     .. Array Arguments ..
     ..
  Purpose
  =======
  PZGEQR2 computes a QR factorization of a complex 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) COMPLEX*16 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 unitary 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) COMPLEX*16, 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) COMPLEX*16 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 >= Mp0 + MAX( 1, Nq0 ), 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    (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.
  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 complex scalar, and v is a complex 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 PZGEQR2( 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        COMPLEX*16 ONE
017        PARAMETER( ONE =( 1.0D + 0 , 0.0D + 0 ) )
018  *     ..
019  *     .. Local Scalars ..
020        LOGICAL LQUERY
021        CHARACTER COLBTOP , ROWBTOP
022        INTEGER I , II , IACOL , IAROW , ICTXT , J , JJ , K , LWMIN ,
023       $MP , MYCOL , MYROW , NPCOL , NPROW , NQ
024        COMPLEX*16 AJJ , ALPHA
025  *     ..
026  *     .. External Subroutines ..
027        EXTERNAL BLACS_ABORT , BLACS_GRIDINFO , CHK1MAT , INFOG2L ,
028       $PB_TOPGET , PB_TOPSET , PXERBLA , PZELSET ,
029       $PZLARFC , PZLARFG , ZGEBR2D , ZGEBS2D ,
030       $ZLARFG , ZSCAL
031  *     ..
032  *     .. External Functions ..
033        INTEGER INDXG2P , NUMROC
034        EXTERNAL INDXG2P , NUMROC
035  *     ..
036  *     .. Intrinsic Functions ..
037        INTRINSIC DBLE , DCMPLX , DCONJG , MAX , MIN , MOD
038  *     ..
039  *     .. Executable Statements ..
040  
041  *     Get grid parameters
042  
043        ICTXT = DESCA( CTXT_ )
044        CALL BLACS_GRIDINFO( ICTXT , NPROW , NPCOL , MYROW , MYCOL )
045  
046  *     Test the input parameters
047  
048        INFO = 0
049        IF( NPROW.EQ. - 1 ) THEN
049               
050            INFO = - (600 + CTXT_)
051        ELSE
051               
052            CALL CHK1MAT( M , 1 , N , 2 , IA , JA , DESCA , 6 , INFO )
053            IF( INFO.EQ.0 ) THEN
053                   
054                IAROW = INDXG2P( IA , DESCA( MB_ ) , MYROW , DESCA( RSRC_ ) ,
055       $        NPROW )
056                IACOL = INDXG2P( JA , DESCA( NB_ ) , MYCOL , DESCA( CSRC_ ) ,
057       $        NPCOL )
058                MP = NUMROC( M + MOD( IA - 1 , DESCA( MB_ ) ) , DESCA( MB_ ) ,
059       $        MYROW , IAROW , NPROW )
060                NQ = NUMROC( N + MOD( JA - 1 , DESCA( NB_ ) ) , DESCA( NB_ ) ,
061       $        MYCOL , IACOL , NPCOL )
062                LWMIN = MP + MAX( 1 , NQ )
063  
064                WORK( 1 ) = DCMPLX( DBLE( LWMIN ) )
065                LQUERY =( LWORK.EQ. - 1 )
066                IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY )
066                       
067       $            INFO = - 9
068                END IF
069            END IF
070  
071            IF( INFO.NE.0 ) THEN
071                   
072                CALL PXERBLA( ICTXT , 'PZGEQR2' , - INFO )
073                CALL BLACS_ABORT( ICTXT , 1 )
074                RETURN
075            ELSE IF( LQUERY ) THEN
075                   
076                RETURN
077            END IF
078  
079  *         Quick return if possible
080  
081            IF( M.EQ.0 .OR. N.EQ.0 )
081                   
082       $        RETURN
083  
084                CALL PB_TOPGET( ICTXT , 'Broadcast' , 'Rowwise' , ROWBTOP )
085                CALL PB_TOPGET( ICTXT , 'Broadcast' , 'Columnwise' , COLBTOP )
086                CALL PB_TOPSET( ICTXT , 'Broadcast' , 'Rowwise' , 'I - ring' )
087                CALL PB_TOPSET( ICTXT , 'Broadcast' , 'Columnwise' , ' ' )
088  
089                IF( DESCA( M_ ).EQ.1 ) THEN
089                       
090                    CALL INFOG2L( IA , JA , DESCA , NPROW , NPCOL , MYROW , MYCOL , II ,
091       $            JJ , IAROW , IACOL )
092                    IF( MYROW.EQ.IAROW ) THEN
092                           
093                        NQ = NUMROC( JA + N - 1 , DESCA( NB_ ) , MYCOL , DESCA( CSRC_ ) ,
094       $                NPCOL )
095                        I = II + (JJ - 1)*DESCA( LLD_ )
096                        IF( MYCOL.EQ.IACOL ) THEN
096                               
097                            AJJ = A( I )
098                            CALL ZLARFG( 1 , AJJ , A( I ) , 1 , TAU( JJ ) )
099                            IF( N.GT.1 ) THEN
099                                   
100                                ALPHA = ONE - DCONJG( TAU( JJ ) )
101                                CALL ZGEBS2D( ICTXT , 'Rowwise' , ' ' , 1 , 1 , ALPHA , 1 )
102                                CALL ZSCAL( NQ - JJ , ALPHA , A( I + DESCA( LLD_ ) ) ,
103       $                        DESCA( LLD_ ) )
104                            END IF
105                            CALL ZGEBS2D( ICTXT , 'Columnwise' , ' ' , 1 , 1 , TAU( JJ ) ,
106       $                    1 )
107                            A( I ) = AJJ
108                        ELSE
108                               
109                            IF( N.GT.1 ) THEN
109                                   
110                                CALL ZGEBR2D( ICTXT , 'Rowwise' , ' ' , 1 , 1 , ALPHA ,
111       $                        1 , IAROW , IACOL )
112                                CALL ZSCAL( NQ - JJ + 1 , ALPHA , A( I ) , DESCA( LLD_ ) )
113                            END IF
114                        END IF
115                    ELSE IF( MYCOL.EQ.IACOL ) THEN
115                           
116                        CALL ZGEBR2D( ICTXT , 'Columnwise' , ' ' , 1 , 1 , TAU( JJ ) , 1 ,
117       $                IAROW , IACOL )
118                    END IF
119  
120                ELSE
121  
121                       
122                    K = MIN( M , N )
123                    DO 10 J = JA , JA + K - 1
123                           
124                        I = IA + J - JA
125  
126  *                     Generate elementary reflector H(j) to annihilate
127  *                     A(i + 1 : ia + m - 1 , j)
128  
129                        CALL PZLARFG ( M - J + JA , AJJ , I , J , A , MIN( I + 1 , IA + M - 1 ) , J ,
130       $                DESCA , 1 , TAU )
131                        IF( J.LT.JA + N - 1 ) THEN
132  
133  *                         Apply H(j)' to A(i : ia + m - 1 , j + 1 : ja + n - 1) from the left
134  
134                               
135                            CALL PZELSET( A , I , J , DESCA , ONE )
136  
137                            CALL PZLARFC ( 'Left' , M - J + JA , N - J + JA - 1 , A , I , J , DESCA ,
138       $                    1 , TAU , A , I , J + 1 , DESCA , WORK )
139                        END IF
140                        CALL PZELSET( A , I , J , DESCA , AJJ )
141  
142     10             CONTINUE
143  
143                   
144                END IF
145  
146                CALL PB_TOPSET( ICTXT , 'Broadcast' , 'Rowwise' , ROWBTOP )
147                CALL PB_TOPSET( ICTXT , 'Broadcast' , 'Columnwise' , COLBTOP )
148  
149                WORK( 1 ) = DCMPLX( DBLE( LWMIN ) )
150  
151                RETURN
152  
153  *             End of PZGEQR2
154  
155            END2226

Variables in Routine PZGEQR2()

Summary Report
Data Type	Quantity	Size(byte)
CHARACTER	2	2
*COMPLEX16**	3	?
INTEGER	34	136
LOGICAL	1	1
REAL	2	8
TOTAL	42	147

List of Variables

CHARACTER

COLBTOP ROWBTOP

COMPLEX*16

AJJ ALPHA ONE

INTEGER

BLOCK_CYCLIC_2D CSRC_ CTXT_ DLEN_ DTYPE_
I IA IACOL IAROW ICTXT
II INDXG2P INFO J JA
JJ K LLD_ LWMIN LWORK
M M_ MB_ MP MYCOL
MYROW N N_ NB_ NPCOL
NPROW NQ NUMROC RSRC_

LOGICAL

LQUERY

REAL

A WORK

Variables Dependence Graph
Put the mouse over a right hand side variable to display the corresponding line of the dependence
-
- -
A <--- AJJA( I ) = AJJ

AJJ <--- AAJJ = A( I ), IAJJ = A( I )

ALPHA <--- JJALPHA = ONE - DCONJG( TAU( JJ ) ), ONEALPHA = ONE - DCONJG( TAU( JJ ) )

I <--- IAI = IA + J - JA, III = II+(JJ-1)*DESCA( LLD_ ), JI = IA + J - JA, JAI = IA + J - JA, JJI = II+(JJ-1)*DESCA( LLD_ ), LLD_I = II+(JJ-1)*DESCA( LLD_ )

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

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

ICTXT <--- CTXT_ICTXT = DESCA( CTXT_ )

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

J <--- JADO 10 J = JA, JA+K-1, KDO 10 J = JA, JA+K-1

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

LWMIN <--- MPLWMIN = MP + MAX( 1, NQ ), NQLWMIN = MP + MAX( 1, NQ )

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

NQ <--- IACOL, JA{2}, MYCOL{2}, N{2}, NB_{2}, NPCOL{2}, NUMROC{2}, CSRC_

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