Routine: PDLAUU2()  File: SRC\pdlauu2.f

 
 
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..
     .. Array Arguments ..
     ..
  Purpose
  =======
  PDLAUU2 computes the product U * U' or L' * L, where the triangular
  factor U or L is stored in the upper or lower triangular part of
  the matrix sub( A ) = A(IA:IA+N-1,JA:JA+N-1).
  If UPLO = 'U' or 'u' then the upper triangle of the result is stored,
  overwriting the factor U in sub( A ).
  If UPLO = 'L' or 'l' then the lower triangle of the result is stored,
  overwriting the factor L in sub( A ).
  This is the unblocked form of the algorithm, calling Level 2 BLAS.
  No communication is performed by this routine, the matrix to operate
  on should be strictly local to one process.
  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
  =========
  UPLO    (global input) CHARACTER*1
          Specifies whether the triangular factor stored in the matrix
          sub( A ) is upper or lower triangular:
          = 'U':  Upper triangular,
          = 'L':  Lower triangular.
  N       (global input) INTEGER
          The number of rows and columns to be operated on, i.e. the
          order of the order of the triangular factor U or L.  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 triangular factor L or U.
          On exit, if UPLO = 'U', the upper triangle of the distributed
          matrix sub( A ) is overwritten with the upper triangle of the
          product U * U'; if UPLO = 'L', the lower triangle of sub( A )
          is overwritten with the lower triangle of the product L' * L.
  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.
  =====================================================================
     .. Parameters ..

 
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01        SUBROUTINE PDLAUU2( UPLO , N , A , IA , JA , DESCA )
02  
03  *     -- ScaLAPACK auxiliary routine(version 1.7) --
04  *     University of Tennessee , Knoxville , Oak Ridge National Laboratory ,
05  *     and University of California , Berkeley.
06  *     May 1 , 1997
07  
08  *     .. Scalar Arguments ..
09        CHARACTER UPLO
10        INTEGER IA , JA , N
11        INTEGER BLOCK_CYCLIC_2D , CSRC_ , CTXT_ , DLEN_ , DTYPE_ ,
12       $LLD_ , MB_ , M_ , NB_ , N_ , RSRC_
13        PARAMETER( BLOCK_CYCLIC_2D = 1 , DLEN_ = 9 , DTYPE_ = 1 ,
14       $CTXT_ = 2 , M_ = 3 , N_ = 4 , MB_ = 5 , NB_ = 6 ,
15       $RSRC_ = 7 , CSRC_ = 8 , LLD_ = 9 )
16        DOUBLE PRECISION ONE
17        PARAMETER( ONE = 1.0D + 0 )
18  *     ..
19  *     .. Local Scalars ..
20        INTEGER IACOL , IAROW , ICURR , IDIAG , IIA , IOFFA , JJA ,
21       $LDA , MYCOL , MYROW , NA , NPCOL , NPROW
22        DOUBLE PRECISION AII
23  *     ..
24  *     .. External Subroutines ..
25        EXTERNAL BLACS_GRIDINFO , INFOG2L , DGEMV , DSCAL
26  *     ..
27  *     .. External Functions ..
28        LOGICAL LSAME
29        DOUBLE PRECISION DDOT
30        EXTERNAL DDOT , LSAME
31  *     ..
32  *     .. Executable Statements ..
33  
34  *     Quick return if possible
35  
36        IF( N.EQ.0 )
37       $    RETURN
38  
39  *         Get grid parameters and compute local indexes
40  
41            CALL BLACS_GRIDINFO( DESCA( CTXT_ ) , NPROW , NPCOL , MYROW , MYCOL )
42            CALL INFOG2L( IA , JA , DESCA , NPROW , NPCOL , MYROW , MYCOL , IIA , JJA ,
43       $    IAROW , IACOL )
44  
45            IF( MYROW.EQ.IAROW .AND. MYCOL.EQ.IACOL ) THEN
46  
47                LDA = DESCA( LLD_ )
48                IDIAG = IIA + ( JJA - 1 ) * LDA
49                IOFFA = IDIAG
50  
51                IF( LSAME( UPLO , 'U' ) ) THEN
52  
53  *                 Compute the product U * U'.
54  
55                    DO 10 NA = N - 1 , 1 , - 1
56                        AII = A( IDIAG )
57                        ICURR = IDIAG + LDA
58                        A( IDIAG ) = AII*AII + DDOT( NA , A( ICURR ) , LDA ,
59       $                A( ICURR ) , LDA )
60                        CALL DGEMV( 'No transpose' , N - NA - 1 , NA , ONE ,
61       $                A( IOFFA + LDA ) , LDA , A( ICURR ) , LDA , AII ,
62       $                A( IOFFA ) , 1 )
63                        IDIAG = IDIAG + LDA + 1
64                        IOFFA = IOFFA + LDA
65     10             CONTINUE
66                    AII = A( IDIAG )
67                    CALL DSCAL( N , AII , A( IOFFA ) , 1 )
68  
69                ELSE
70  
71  *                 Compute the product L' * L.
72  
73                    DO 20 NA = 1 , N - 1
74                        AII = A( IDIAG )
75                        ICURR = IDIAG + 1
76                        A(IDIAG) = AII*AII + DDOT( N - NA , A( ICURR ) , 1 ,
77       $                A( ICURR ) , 1 )
78                        CALL DGEMV( 'Transpose' , N - NA , NA - 1 , ONE , A( IOFFA + 1 ) ,
79       $                LDA , A( ICURR ) , 1 , AII , A( IOFFA ) , LDA )
80                        IDIAG = IDIAG + LDA + 1
81                        IOFFA = IOFFA + 1
82     20             CONTINUE
83                    AII = A( IDIAG )
84                    CALL DSCAL( N , AII , A( IOFFA ) , LDA )
85  
86                END IF
87  
88            END IF
89  
90            RETURN
91  
92  *         End of PDLAUU2
93  
94        END