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| # Variables: | 33 |
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| # Words: | 69 |
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..
.. Array Arguments ..
..
Purpose
=======
PZLAUU2 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) 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 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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001 SUBROUTINE PZLAUU2( UPLO , N , A , IA , JA , DESCA )
002
003 * -- ScaLAPACK auxiliary routine(version 1.7) --
004 * University of Tennessee , Knoxville , Oak Ridge National Laboratory ,
005 * and University of California , Berkeley.
006 * May 1 , 1997
007
008 * .. Scalar Arguments ..
009 CHARACTER UPLO
010 INTEGER IA , JA , 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 INTEGER IACOL , IAROW , ICURR , IDIAG , IIA , IOFFA , JJA ,
021 $LDA , MYCOL , MYROW , NA , NPCOL , NPROW
022 DOUBLE PRECISION AII
023 * ..
024 * .. External Subroutines ..
025 EXTERNAL BLACS_GRIDINFO , INFOG2L , ZDSCAL , ZGEMV ,
026 $ZLACGV
027 * ..
028 * .. External Functions ..
029 LOGICAL LSAME
030 COMPLEX*16 ZDOTC
031 EXTERNAL LSAME , ZDOTC
032 * ..
033 * .. Intrinsic Functions ..
034 INTRINSIC DCMPLX , DBLE
035 * ..
036 * .. Executable Statements ..
037
038 * Quick return if possible
039
040 IF( N.EQ.0 )
040
041 $ RETURN
042
043 * Get grid parameters and compute local indexes
044
045 CALL BLACS_GRIDINFO( DESCA( CTXT_ ) , NPROW , NPCOL , MYROW , MYCOL )
046 CALL INFOG2L( IA , JA , DESCA , NPROW , NPCOL , MYROW , MYCOL , IIA , JJA ,
047 $ IAROW , IACOL )
048
049 IF( MYROW.EQ.IAROW .AND. MYCOL.EQ.IACOL ) THEN
050
050
051 LDA = DESCA( LLD_ )
052 IDIAG = IIA + ( JJA - 1 ) * LDA
053 IOFFA = IDIAG
054
055 IF( LSAME( UPLO , 'U' ) ) THEN
056
057 * Compute the product U * U'.
058
058
059 DO 10 NA = N - 1 , 1 , - 1
059
060 AII = A( IDIAG )
061 ICURR = IDIAG + LDA
062 A( IDIAG ) = AII*AII + DBLE( ZDOTC( NA , A( ICURR ) , LDA ,
063 $ A( ICURR ) , LDA ) )
064 CALL ZLACGV( NA , A( ICURR ) , LDA )
065 CALL ZGEMV( 'No transpose' , N - NA - 1 , NA , ONE ,
066 $ A( IOFFA + LDA ) , LDA , A( ICURR ) , LDA ,
067 $ DCMPLX( AII ) , A( IOFFA ) , 1 )
068 CALL ZLACGV( NA , A( ICURR ) , LDA )
069 IDIAG = IDIAG + LDA + 1
070 IOFFA = IOFFA + LDA
071 10 CONTINUE
071
072 AII = A( IDIAG )
073 CALL ZDSCAL( N , AII , A( IOFFA ) , 1 )
074
075 ELSE
076
077 * Compute the product L' * L.
078
078
079 DO 20 NA = 1 , N - 1
079
080 AII = A( IDIAG )
081 ICURR = IDIAG + 1
082 A( IDIAG ) = AII*AII + DBLE( ZDOTC( N - NA , A( ICURR ) , 1 ,
083 $ A( ICURR ) , 1 ) )
084 CALL ZLACGV( NA - 1 , A( IOFFA ) , LDA )
085 CALL ZGEMV( 'Conjugate transpose' , N - NA , NA - 1 , ONE ,
086 $ A( IOFFA + 1 ) , LDA , A( ICURR ) , 1 ,
087 $ DCMPLX( AII ) , A( IOFFA ) , LDA )
088 CALL ZLACGV( NA - 1 , A( IOFFA ) , LDA )
089 IDIAG = IDIAG + LDA + 1
090 IOFFA = IOFFA + 1
091 20 CONTINUE
091
092 AII = A( IDIAG )
093 CALL ZDSCAL( N , AII , A( IOFFA ) , LDA )
094
095 END IF
096
097 END IF
098
099 RETURN
100
101 * End of PZLAUU2
102
103 END19
8
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Variables in Routine PZLAUU2()
| Summary Report |
| Data Type | Quantity | Size(byte) |
| CHARACTER | 1 | 1 |
| COMPLEX*16 | 2 | ? |
| DOUBLE PRECISION | 1 | 4 |
| INTEGER | 27 | 108 |
| LOGICAL | 1 | 1 |
| REAL | 1 | 4 |
| TOTAL | 33 | 118 |
List of Variables
CHARACTER
COMPLEX*16
DOUBLE PRECISION
INTEGER
| BLOCK_CYCLIC_2D | CSRC_ | CTXT_ | DLEN_ | DTYPE_ |
| IA | IACOL | IAROW | ICURR | IDIAG |
| IIA | IOFFA | JA | JJA | LDA |
| LLD_ | M_ | MB_ | MYCOL | MYROW |
| N | N_ | NA | NB_ | NPCOL |
| NPROW | RSRC_ | | | |
LOGICAL
REAL
Variables Dependence Graph Put the mouse over a right hand side variable to display the corresponding line of the dependence | | - | | - | - | | A | <--- | AA( IDIAG ) = AII*AII + DBLE( ZDOTC( NA, A( ICURR ), LDA,{2A( IDIAG ) = AII*AII + DBLE( ZDOTC( N-NA, A( ICURR ), 1,}, ICURRA( IDIAG ) = AII*AII + DBLE( ZDOTC( NA, A( ICURR ), LDA,{2A( IDIAG ) = AII*AII + DBLE( ZDOTC( N-NA, A( ICURR ), 1,}, LDAA( IDIAG ) = AII*AII + DBLE( ZDOTC( NA, A( ICURR ), LDA,, AIIA( IDIAG ) = AII*AII + DBLE( ZDOTC( NA, A( ICURR ), LDA,{2A( IDIAG ) = AII*AII + DBLE( ZDOTC( N-NA, A( ICURR ), 1,}, NA( IDIAG ) = AII*AII + DBLE( ZDOTC( N-NA, A( ICURR ), 1,, NAA( IDIAG ) = AII*AII + DBLE( ZDOTC( NA, A( ICURR ), LDA,{2A( IDIAG ) = AII*AII + DBLE( ZDOTC( N-NA, A( ICURR ), 1,}, ZDOTCA( IDIAG ) = AII*AII + DBLE( ZDOTC( NA, A( ICURR ), LDA,{2A( IDIAG ) = AII*AII + DBLE( ZDOTC( N-NA, A( ICURR ), 1,} |
| AII | <--- | AAII = A( IDIAG ){2AII = A( IDIAG ), 3AII = A( IDIAG ), 4AII = A( IDIAG )}, IDIAGAII = A( IDIAG ){2AII = A( IDIAG ), 3AII = A( IDIAG ), 4AII = A( IDIAG )} |
| ICURR | <--- | IDIAGICURR = IDIAG + LDA{2ICURR = IDIAG + 1}, LDAICURR = IDIAG + LDA |
| IDIAG | <--- | IDIAGIDIAG = IDIAG + LDA + 1{2IDIAG = IDIAG + LDA + 1}, IIAIDIAG = IIA + ( JJA - 1 ) * LDA, JJAIDIAG = IIA + ( JJA - 1 ) * LDA, LDAIDIAG = IIA + ( JJA - 1 ) * LDA{2IDIAG = IDIAG + LDA + 1, 3IDIAG = IDIAG + LDA + 1} |
| IOFFA | <--- | IDIAGIOFFA = IDIAG, IOFFAIOFFA = IOFFA + LDA{2IOFFA = IOFFA + 1}, LDAIOFFA = IOFFA + LDA |
| LDA | <--- | LLD_LDA = DESCA( LLD_ ) |
| NA | <--- | NDO 10 NA = N-1, 1, -1{2DO 20 NA = 1, N-1} |
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Analysis elements of the routine PZLAUU2() Put the mouse over each element to display detailed matching information
Assigned variables |
| | | AII , BLOCK_CYCLIC_2D , CSRC_ , CTXT_ , DLEN_ , DTYPE_ , ICURR , IDIAG , IOFFA , LDA , LLD_ , M_ , MB_ , N_ , NA , NB_ , ONE , RSRC_ |
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Active variables |
| | | A , AII , BLOCK_CYCLIC_2D , CSRC_ , CTXT_ , DESCA , DLEN_ , DTYPE_ , IA , IACOL , IAROW , ICURR , IDIAG , IIA , IOFFA , JA , JJA , LDA , LLD_ , LSAME , M_ , MB_ , MYCOL , MYROW , N , N_ , NA , NB_ , NPCOL , NPROW , ONE , RSRC_ , UPLO , ZDOTC |
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Accessed arrays [ array name : associated index ] |
| | A | : ICURR , ICURR , ICURR , ICURR , ICURR , ICURR , ICURR , ICURR , IDIAG , IDIAG , IDIAG , IDIAG , IDIAG , IDIAG , IOFFA , IOFFA , IOFFA , IOFFA , IOFFA , IOFFA , IOFFA+1 , IOFFA+LDA |
| | DESCA | : CTXT_ , LLD_ |
| | LSAME | : UPLO, 'U' |
|
Conditional statements [ statement : associated predicate ] |
| | do | : ( 10 NA = N - 1 , 1 , - 1 ) , ( 20 NA = 1 , N - 1 ) |
| | if | : ( possible ) , ( N.EQ.0 ) , ( MYROW.EQ.IAROW .AND. MYCOL.EQ.IACOL ) , ( (LSAME( UPLO , 'U' ) ) ) |
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| List of variables | A AII BLOCK_CYCLIC_2D CSRC_ CTXT_ DLEN_ DTYPE_
| IA IACOL IAROW ICURR IDIAG IIA IOFFA JA
| JJA LDA LLD_ LSAME M_ MB_ MYCOL MYROW
| N N_ NA NB_ NPCOL NPROW ONE RSRC_
| UPLO ZDOTC | | close
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A
AII
BLOCK_CYCLIC_2D
CSRC_
CTXT_
DLEN_
DTYPE_
IA
IACOL
IAROW
ICURR
IDIAG
IIA
IOFFA
JA
JJA
LDA
LLD_
LSAME
M_
MB_
MYCOL
MYROW
N
N_
NA
NB_
NPCOL
NPROW
ONE
RSRC_
UPLO
ZDOTC
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