Routine PZGEQRF() Documented By Universal Report

Routine: PZGEQRF()

File: SRC\pzgeqrf.f

# lines:	313
# code:	313
# comment:	0
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# Variables:	44
# Callers:	3
# Callings:	3
# Words:	119
# Keywords:	68

..
     .. Array Arguments ..
     ..
  Purpose
  =======
  PZGEQRF 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 >= 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 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 PZGEQRF( 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 , PB_TOPGET ,
029       $PB_TOPSET , PXERBLA , PZGEQR2 , PZLARFB ,
030       $PZLARFT  
031  *     ..
032  *     .. External Functions ..
033        INTEGER ICEIL , INDXG2P , NUMROC
034        EXTERNAL ICEIL , INDXG2P , NUMROC
035  *     ..
036  *     .. Intrinsic Functions ..
037        INTRINSIC DBLE , DCMPLX , 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                ICOFF = MOD( JA - 1 , DESCA( NB_ ) )
055                IAROW = INDXG2P( IA , DESCA( MB_ ) , MYROW , DESCA( RSRC_ ) ,
056       $        NPROW )
057                IACOL = INDXG2P( JA , DESCA( NB_ ) , MYCOL , DESCA( CSRC_ ) ,
058       $        NPCOL )
059                MP0 = NUMROC( M + MOD( IA - 1 , DESCA( MB_ ) ) , DESCA( MB_ ) ,
060       $        MYROW , IAROW , NPROW )
061                NQ0 = NUMROC( N + ICOFF , DESCA( NB_ ) , MYCOL , IACOL , NPCOL )
062                LWMIN = DESCA( NB_ ) * ( MP0 + NQ0 + DESCA( NB_ ) )
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                IF( LWORK.EQ. - 1 ) THEN
069                       
070                    IDUM1( 1 ) = - 1
071                ELSE
071                       
072                    IDUM1( 1 ) = 1
073                END IF
074                IDUM2( 1 ) = 9
075                CALL PCHK1MAT( M , 1 , N , 2 , IA , JA , DESCA , 6 , 1 , IDUM1 , IDUM2 ,
076       $        INFO )
077            END IF
078  
079            IF( INFO.NE.0 ) THEN
079                   
080                CALL PXERBLA( ICTXT , 'PZGEQRF' , - INFO )
081                RETURN
082            ELSE IF( LQUERY ) THEN
082                   
083                RETURN
084            END IF
085  
086  *         Quick return if possible
087  
088            IF( M.EQ.0 .OR. N.EQ.0 )
088                   
089       $        RETURN
090  
091                K = MIN( M , N )
092                IPW = DESCA( NB_ ) * DESCA( NB_ ) + 1
093                CALL PB_TOPGET( ICTXT , 'Broadcast' , 'Rowwise' , ROWBTOP )
094                CALL PB_TOPGET( ICTXT , 'Broadcast' , 'Columnwise' , COLBTOP )
095                CALL PB_TOPSET( ICTXT , 'Broadcast' , 'Rowwise' , 'I - ring' )
096                CALL PB_TOPSET( ICTXT , 'Broadcast' , 'Columnwise' , ' ' )
097  
098  *             Handle the first block of columns separately
099  
100                JN = MIN( ICEIL( JA , DESCA( NB_ ) ) * DESCA( NB_ ) , JA + K - 1 )
101                JB = JN - JA + 1
102  
103  *             Compute the QR factorization of the first block A(ia : ia + m - 1 , ja : jn)
104  
105                CALL PZGEQR2 ( M , JB , A , IA , JA , DESCA , TAU , WORK , LWORK , IINFO )
106  
107                IF( JA + JB.LE.JA + N - 1 ) THEN
108  
109  *                 Form the triangular factor of the block reflector
110  *                 H = H(ja) H(ja + 1) . . . H(jn)
111  
111                       
112                    CALL PZLARFT ( 'Forward' , 'Columnwise' , M , JB , A , IA , JA , DESCA ,
113       $            TAU , WORK , WORK( IPW ) )
114  
115  *                 Apply H' to A(ia : ia + m - 1 , ja + jb : ja + n - 1) from the left
116  
117                    CALL PZLARFB ( 'Left' , 'Conjugate transpose' , 'Forward' ,
118       $            'Columnwise' , M , N - JB , JB , A , IA , JA , DESCA ,
119       $            WORK , A , IA , JA + JB , DESCA , WORK( IPW ) )
120                END IF
121  
122  *             Loop over the remaining blocks of columns
123  
124                DO 10 J = JN + 1 , JA + K - 1 , DESCA( NB_ )
124                       
125                    JB = MIN( K - J + JA , DESCA( NB_ ) )
126                    I = IA + J - JA
127  
128  *                 Compute the QR factorization of the current block
129  *                 A(i : ia + m - 1 , j : j + jb - 1)
130  
131                    CALL PZGEQR2 ( M - J + JA , JB , A , I , J , DESCA , TAU , WORK , LWORK ,
132       $            IINFO )
133  
134                    IF( J + JB.LE.JA + N - 1 ) THEN
135  
136  *                     Form the triangular factor of the block reflector
137  *                     H = H(j) H(j + 1) . . . H(j + jb - 1)
138  
138                           
139                        CALL PZLARFT ( 'Forward' , 'Columnwise' , M - J + JA , JB , A , I , J ,
140       $                DESCA , TAU , WORK , WORK( IPW ) )
141  
142  *                     Apply H' to A(i : ia + m - 1 , j + jb : ja + n - 1) from the left
143  
144                        CALL PZLARFB ( 'Left' , 'Conjugate transpose' , 'Forward' ,
145       $                'Columnwise' , M - J + JA , N - J - JB + JA , JB , A , I , J ,
146       $                DESCA , WORK , A , I , J + JB , DESCA , WORK( IPW ) )
147                    END IF
148  
149     10         CONTINUE
150  
150                   
151                CALL PB_TOPSET( ICTXT , 'Broadcast' , 'Rowwise' , ROWBTOP )
152                CALL PB_TOPSET( ICTXT , 'Broadcast' , 'Columnwise' , COLBTOP )
153  
154                WORK( 1 ) = DCMPLX( DBLE( LWMIN ) )
155  
156                RETURN
157  
158  *             End of PZGEQRF
159  
160            END3235

Variables in Routine PZGEQRF()

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