Routine PCGEQLF() Documented By Universal Report

Routine: PCGEQLF()

# lines:	311
# code:	311
# comment:	0
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# Variables:	45
# Callers:	0
# Callings:	3
# Words:	121
# Keywords:	67

..
     .. Array Arguments ..
     ..
  Purpose
  =======
  PCGEQLF computes a QL factorization of a complex distributed M-by-N
  matrix sub( A ) = A(IA:IA+M-1,JA:JA+N-1) = Q * L.
  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 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
          lower triangle of the distributed submatrix
          A( IA+M-N:IA+M-1, JA:JA+N-1 ) contains the N-by-N lower
          triangular matrix L; if M <= N, the elements on and below
          the (N-M)-th superdiagonal contain the M by N lower
          trapezoidal matrix L; the remaining elements, 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, array, dimension LOCc(JA+N-1)
          This array contains the scalar factors of the elementary
          reflectors. TAU is tied to the distributed matrix A.
  WORK    (local workspace/local output) COMPLEX 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+k-1) . . . H(ja+1) H(ja), where k = min(m,n).
  Each H(i) has the form
     H(i) = I - tau * v * v'
  where tau is a complex scalar, and v is a complex vector with
  v(m-k+i+1:m) = 0 and v(m-k+i) = 1; v(1:m-k+i-1) is stored on exit in
  A(ia:ia+m-k+i-2,ja+n-k+i-1), and tau in TAU(ja+n-k+i-1).
  =====================================================================
     .. Parameters ..

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001        SUBROUTINE PCGEQLF( 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 IACOL , IAROW , IINFO , ICTXT , IPW , J , JB , JL , JN ,
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 , PCGEQL2 ,
029       $PCLARFB , PCLARFT , PB_TOPGET , PB_TOPSET ,
030       $PXERBLA
031  *     ..
032  *     .. External Functions ..
033        INTEGER ICEIL , INDXG2P , NUMROC
034        EXTERNAL ICEIL , INDXG2P , NUMROC
035  *     ..
036  *     .. Intrinsic Functions ..
037        INTRINSIC CMPLX , MIN , MOD , REAL
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                MP0 = NUMROC( M + MOD( IA - 1 , DESCA( MB_ ) ) , DESCA( MB_ ) ,
059       $        MYROW , IAROW , NPROW )
060                NQ0 = NUMROC( N + MOD( JA - 1 , DESCA( NB_ ) ) , DESCA( NB_ ) ,
061       $        MYCOL , IACOL , NPCOL )
062                LWMIN = DESCA( NB_ ) * ( MP0 + NQ0 + DESCA( NB_ ) )
063  
064                WORK( 1 ) = CMPLX( REAL( 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 , 'PCGEQLF' , - 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                JN = MIN( ICEIL( JA + N - K , DESCA( NB_ ) ) * DESCA( NB_ ) , JA + N - 1 )
094                JL = MAX(((JA + N - 2) / DESCA( NB_ ) ) * DESCA( NB_ ) + 1 , JA )
095                CALL PB_TOPGET( ICTXT , 'Broadcast' , 'Rowwise' , ROWBTOP )
096                CALL PB_TOPGET( ICTXT , 'Broadcast' , 'Columnwise' , COLBTOP )
097                CALL PB_TOPSET( ICTXT , 'Broadcast' , 'Rowwise' , 'D - ring' )
098                CALL PB_TOPSET( ICTXT , 'Broadcast' , 'Columnwise' , ' ' )
099  
100                IF( JL.GE.JN + 1 ) THEN
101  
102  *                 Use blocked code initially
103  
103                       
104                    DO 10 J = JL , JN + 1 , - DESCA( NB_ )
104                           
105                        JB = MIN( JA + N - J , DESCA( NB_ ) )
106  
107  *                     Compute the QL factorization of the current block
108  *                     A(ia : ia + m - n + j + jb - ja - 1 , j : j + jb - 1)
109  
110                        CALL PCGEQL2 ( M - N + J + JB - JA , JB , A , IA , J , DESCA , TAU , WORK ,
111       $                LWORK , IINFO )
112  
113                        IF( J.GT.JA ) THEN
114  
115  *                         Form the triangular factor of the block reflector
116  *                         H = H(j + jb - 1) . . . H(j + 1) H(j)
117  
117                               
118                            CALL PCLARFT ( 'Backward' , 'Columnwise' , M - N + J + JB - JA , JB ,
119       $                    A , IA , J , DESCA , TAU , WORK , WORK( IPW ) )
120  
121  *                         Apply H' to A(ia : ia + m - n + j + jb - ja - 1 , ja : j - 1) from the
122  *                         left
123  
124                            CALL PCLARFB ( 'Left' , 'Conjugate transpose' , 'Backward' ,
125       $                    'Columnwise' , M - N + J + JB - JA , J - JA , JB , A , IA ,
126       $                    J , DESCA , WORK , A , IA , JA , DESCA ,
127       $                    WORK( IPW ) )
128                        END IF
129  
130     10             CONTINUE
131  
131                       
132                    MU = M - N + JN - JA + 1
133                    NU = JN - JA + 1
134  
135                ELSE
136  
136                       
137                    MU = M
138                    NU = N
139  
140                END IF
141  
142  *             Use unblocked code to factor the last or only block
143  
144                IF( MU.GT.0 .AND. NU.GT.0 )
144                       
145       $            CALL PCGEQL2 ( MU , NU , A , IA , JA , DESCA , TAU , WORK , LWORK ,
146       $            IINFO )
147  
148                    CALL PB_TOPSET( ICTXT , 'Broadcast' , 'Rowwise' , ROWBTOP )
149                    CALL PB_TOPSET( ICTXT , 'Broadcast' , 'Columnwise' , COLBTOP )
150  
151                    WORK( 1 ) = CMPLX( REAL( LWMIN ) )
152  
153                    RETURN
154  
155  *                 End of PCGEQLF
156  
157                END2933

Variables in Routine PCGEQLF()

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_
IA IACOL IAROW ICEIL ICTXT
IDUM1( 1 ) IDUM2( 1 ) IINFO INDXG2P INFO
IPW J JA JB JL
JN 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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IACOL <--- INDXG2P, JA, CSRC_, MYCOL, NB_, NPCOL

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

ICTXT <--- CTXT_ICTXT = DESCA( CTXT_ )

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

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

J <--- JLDO 10 J = JL, JN+1, -DESCA( NB_ ), JNDO 10 J = JL, JN+1, -DESCA( NB_ ), NB_DO 10 J = JL, JN+1, -DESCA( NB_ )

JB <--- JJB = MIN( JA+N-J, DESCA( NB_ ) ), JAJB = MIN( JA+N-J, DESCA( NB_ ) ), NJB = MIN( JA+N-J, DESCA( NB_ ) ), NB_JB = MIN( JA+N-J, DESCA( NB_ ) )

JL <--- JA, N, NB_

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

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

LWMIN <--- MP0, NB_, NQ0

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

MU <--- JAMU = M - N + JN - JA + 1, JNMU = M - N + JN - JA + 1, MMU = M - N + JN - JA + 1{2MU = M}, NMU = M - N + JN - JA + 1

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

NU <--- JANU = JN - JA + 1, JNNU = JN - JA + 1, NNU = N

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