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..
.. Array Arguments ..
..
Purpose
=======
PDPOSV computes the solution to a real system of linear equations
sub( A ) * X = sub( B ),
where sub( A ) denotes A(IA:IA+N-1,JA:JA+N-1) and is an N-by-N
symmetric distributed positive definite matrix and X and sub( B )
denoting B(IB:IB+N-1,JB:JB+NRHS-1) are N-by-NRHS distributed
matrices.
The Cholesky decomposition is used to factor sub( A ) as
sub( A ) = U**T * U, if UPLO = 'U', or
sub( A ) = L * L**T, if UPLO = 'L',
where U is an upper triangular matrix and L is a lower triangular
matrix. The factored form of sub( A ) is then used to solve the
system of equations.
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
This routine requires square block decomposition ( MB_A = NB_A ).
Arguments
=========
UPLO (global input) CHARACTER
= 'U': Upper triangle of sub( A ) is stored;
= 'L': Lower triangle of sub( A ) is stored.
N (global input) INTEGER
The number of rows and columns to be operated on, i.e. the
order of the distributed submatrix sub( A ). N >= 0.
NRHS (global input) INTEGER
The number of right hand sides, i.e., the number of columns
of the distributed submatrix sub( B ). NRHS >= 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, this array contains the local pieces of the
N-by-N symmetric distributed matrix sub( A ) to be factored.
If UPLO = 'U', the leading N-by-N upper triangular part of
sub( A ) contains the upper triangular part of the matrix,
and its strictly lower triangular part is not referenced.
If UPLO = 'L', the leading N-by-N lower triangular part of
sub( A ) contains the lower triangular part of the distribu-
ted matrix, and its strictly upper triangular part is not
referenced. On exit, if INFO = 0, this array contains the
local pieces of the factor U or L from the Cholesky factori-
zation sub( A ) = U**T*U or L*L**T.
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.
B (local input/local output) DOUBLE PRECISION pointer into the
local memory to an array of dimension (LLD_B,LOC(JB+NRHS-1)).
On entry, the local pieces of the right hand sides distribu-
ted matrix sub( B ). On exit, if INFO = 0, sub( B ) is over-
written with the solution distributed matrix X.
IB (global input) INTEGER
The row index in the global array B indicating the first
row of sub( B ).
JB (global input) INTEGER
The column index in the global array B indicating the
first column of sub( B ).
DESCB (global and local input) INTEGER array of dimension DLEN_.
The array descriptor for the distributed matrix B.
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.
> 0: If INFO = K, the leading minor of order K,
A(IA:IA+K-1,JA:JA+K-1) is not positive definite, and
the factorization could not be completed, and the
solution has not been computed.
=====================================================================
.. Parameters ..
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001 SUBROUTINE PDPOSV( UPLO , N , NRHS , A , IA , JA , DESCA , B , IB , JB ,
002 $DESCB , 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 1 , 1997
008
009 * .. Scalar Arguments ..
010 CHARACTER UPLO
011 INTEGER IA , IB , INFO , JA , JB , N , NRHS
012 INTEGER BLOCK_CYCLIC_2D , CSRC_ , CTXT_ , DLEN_ , DTYPE_ ,
013 $LLD_ , MB_ , M_ , NB_ , N_ , RSRC_
014 PARAMETER( BLOCK_CYCLIC_2D = 1 , DLEN_ = 9 , DTYPE_ = 1 ,
015 $CTXT_ = 2 , M_ = 3 , N_ = 4 , MB_ = 5 , NB_ = 6 ,
016 $RSRC_ = 7 , CSRC_ = 8 , LLD_ = 9 )
017 * ..
018 * .. Local Scalars ..
019 LOGICAL UPPER
020 INTEGER IAROW , IBROW , ICOFFA , ICTXT , IROFFA , IROFFB ,
021 $MYCOL , MYROW , NPCOL , NPROW
022 * ..
023 * .. Local Arrays ..
024 INTEGER IDUM1( 1 ) , IDUM2( 1 )
025 * ..
026 * .. External Subroutines ..
027 EXTERNAL BLACS_GRIDINFO , CHK1MAT , PCHK2MAT , PDPOTRF ,
028 $PDPOTRS , PXERBLA
029 * ..
030 * .. External Functions ..
031 LOGICAL LSAME
032 INTEGER INDXG2P
033 EXTERNAL INDXG2P , LSAME
034 * ..
035 * .. Intrinsic Functions ..
036 INTRINSIC ICHAR , MOD
037 * ..
038 * .. Executable Statements ..
039
040 * Get grid parameters
041
042 ICTXT = DESCA( CTXT_ )
043 CALL BLACS_GRIDINFO( ICTXT , NPROW , NPCOL , MYROW , MYCOL )
044
045 * Test the input parameters
046
047 INFO = 0
048 IF( NPROW.EQ. - 1 ) THEN
048
049 INFO = - (700 + CTXT_)
050 ELSE
050
051 UPPER = LSAME( UPLO , 'U' )
052 CALL CHK1MAT( N , 2 , N , 2 , IA , JA , DESCA , 7 , INFO )
053 IF( INFO.EQ.0 ) THEN
053
054 IAROW = INDXG2P( IA , DESCA( MB_ ) , MYROW , DESCA( RSRC_ ) ,
055 $ NPROW )
056 IBROW = INDXG2P( IB , DESCB( MB_ ) , MYROW , DESCB( RSRC_ ) ,
057 $ NPROW )
058 IROFFA = MOD( IA - 1 , DESCA( MB_ ) )
059 IROFFB = MOD( IB - 1 , DESCB( MB_ ) )
060 ICOFFA = MOD( JA - 1 , DESCA( NB_ ) )
061 IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO , 'L' ) ) THEN
061
062 INFO = - 1
063 ELSE IF( IROFFA.NE.0 ) THEN
063
064 INFO = - 5
065 ELSE IF( ICOFFA.NE.0 ) THEN
065
066 INFO = - 6
067 ELSE IF( DESCA( MB_ ).NE.DESCA( NB_ ) ) THEN
067
068 INFO = - (700 + NB_)
069 ELSE IF( IROFFB.NE.0 .OR. IBROW.NE.IAROW ) THEN
069
070 INFO = - 9
071 ELSE IF( DESCB( MB_ ).NE.DESCA( NB_ ) ) THEN
071
072 INFO = - (1000 + NB_)
073 END IF
074 END IF
075 IF( UPPER ) THEN
075
076 IDUM1( 1 ) = ICHAR( 'U' )
077 ELSE
077
078 IDUM1( 1 ) = ICHAR( 'L' )
079 END IF
080 IDUM2( 1 ) = 1
081 CALL PCHK2MAT( N , 2 , N , 2 , IA , JA , DESCA , 7 , N , 2 , NRHS ,
082 $ 3 , IB , JB , DESCB , 11 , 1 , IDUM1 , IDUM2 , INFO )
083 END IF
084
085 IF( INFO.NE.0 ) THEN
085
086 CALL PXERBLA( ICTXT , 'PDPOSV' , - INFO )
087 RETURN
088 END IF
089
090 * Compute the Cholesky factorization sub( A ) = U'*U or L*L'.
091
092 CALL PDPOTRF ( UPLO , N , A , IA , JA , DESCA , INFO )
093
094 IF( INFO.EQ.0 ) THEN
095
096 * Solve the system sub( A ) * X = sub( B ) overwriting sub( B )
097 * with X.
098
098
099 CALL PDPOTRS ( UPLO , N , NRHS , A , IA , JA , DESCA , B , IB , JB ,
100 $ DESCB , INFO )
101
102 END IF
103
104 RETURN
105
106 * End of PDPOSV
107
108 END16
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Variables in Routine PDPOSV()
| Summary Report |
| Data Type | Quantity | Size(byte) |
| CHARACTER | 1 | 1 |
| INTEGER | 31 | 128 |
| LOGICAL | 2 | 2 |
| TOTAL | 34 | 131 |
List of Variables
CHARACTER
INTEGER
| BLOCK_CYCLIC_2D | CSRC_ | CTXT_ | DLEN_ | DTYPE_ |
| IA | IAROW | IB | IBROW | ICOFFA |
| ICTXT | IDUM1( 1 ) | IDUM2( 1 ) | INDXG2P | INFO |
| IROFFA | IROFFB | JA | JB | LLD_ |
| M_ | MB_ | MYCOL | MYROW | N |
| N_ | NB_ | NPCOL | NPROW | NRHS |
| RSRC_ | | | | |
LOGICAL
Variables Dependence Graph Put the mouse over a right hand side variable to display the corresponding line of the dependence | | - | | - | - | | IAROW | <--- | INDXG2PIAROW = INDXG2P( IA, DESCA( MB_ ), MYROW, DESCA( RSRC_ ),, MB_IAROW = INDXG2P( IA, DESCA( MB_ ), MYROW, DESCA( RSRC_ ),, MYROWIAROW = INDXG2P( IA, DESCA( MB_ ), MYROW, DESCA( RSRC_ ),, NPROWIAROW = INDXG2P( IA, DESCA( MB_ ), MYROW, DESCA( RSRC_ ),, RSRC_IAROW = INDXG2P( IA, DESCA( MB_ ), MYROW, DESCA( RSRC_ ),, IAIAROW = INDXG2P( IA, DESCA( MB_ ), MYROW, DESCA( RSRC_ ), |
| IBROW | <--- | INDXG2PIBROW = INDXG2P( IB, DESCB( MB_ ), MYROW, DESCB( RSRC_ ),, MB_IBROW = INDXG2P( IB, DESCB( MB_ ), MYROW, DESCB( RSRC_ ),, MYROWIBROW = INDXG2P( IB, DESCB( MB_ ), MYROW, DESCB( RSRC_ ),, NPROWIBROW = INDXG2P( IB, DESCB( MB_ ), MYROW, DESCB( RSRC_ ),, RSRC_IBROW = INDXG2P( IB, DESCB( MB_ ), MYROW, DESCB( RSRC_ ),, IBIBROW = INDXG2P( IB, DESCB( MB_ ), MYROW, DESCB( RSRC_ ), |
| ICOFFA | <--- | JAICOFFA = MOD( JA-1, DESCA( NB_ ) ), NB_ICOFFA = MOD( JA-1, DESCA( NB_ ) ) |
| ICTXT | <--- | CTXT_ICTXT = DESCA( CTXT_ ) |
| INFO | <--- | NB_INFO = -(700+NB_){2INFO = -(1000+NB_)}, CTXT_INFO = -(700+CTXT_) |
| IROFFA | <--- | MB_IROFFA = MOD( IA-1, DESCA( MB_ ) ), IAIROFFA = MOD( IA-1, DESCA( MB_ ) ) |
| IROFFB | <--- | MB_IROFFB = MOD( IB-1, DESCB( MB_ ) ), IBIROFFB = MOD( IB-1, DESCB( MB_ ) ) |
| UPPER | <--- | LSAMEUPPER = LSAME( UPLO, 'U' ), UPLOUPPER = LSAME( UPLO, 'U' ) |
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Analysis elements of the routine PDPOSV() Put the mouse over each element to display detailed matching information
Assigned variables |
| | | A , BLOCK_CYCLIC_2D , CSRC_ , CTXT_ , DLEN_ , DTYPE_ , IAROW , IBROW , ICOFFA , ICTXT , IDUM1 , IDUM2 , INFO , IROFFA , IROFFB , LLD_ , M_ , MB_ , N_ , NB_ , RSRC_ , UPPER |
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Active variables |
| | | A , B , BLOCK_CYCLIC_2D , CSRC_ , CTXT_ , DESCA , DESCB , DLEN_ , DTYPE_ , IA , IAROW , IB , IBROW , ICOFFA , ICTXT , IDUM1 , IDUM2 , INDXG2P , INFO , IROFFA , IROFFB , JA , JB , LLD_ , LSAME , M_ , MB_ , MYCOL , MYROW , N , N_ , NB_ , NPCOL , NPROW , NRHS , RSRC_ , UPLO , UPPER |
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Accessed arrays [ array name : associated index ] |
| | DESCA | : CTXT_ , MB_ , MB_ , MB_ , NB_ , NB_ , NB_ , RSRC_ |
| | DESCB | : MB_ , MB_ , MB_ , RSRC_ |
| | IDUM1 | : 1 , 1 , 1 |
| | IDUM2 | : 1 , 1 |
| | LSAME | : UPLO, 'L' , UPLO, 'U' |
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Conditional statements [ statement : associated predicate ] |
| | if | : ( NPROW.EQ. - 1 ) , ( INFO.EQ.0 ) , ( (.NOT.UPPER .AND. .NOT.LSAME( UPLO , 'L' ) ) ) , ( IROFFA.NE.0 ) , ( ICOFFA.NE.0 ) , ( (DESCA( MB_ ).NE.DESCA( NB_ ) ) ) , ( IROFFB.NE.0 .OR. IBROW.NE.IAROW ) , ( (DESCB( MB_ ).NE.DESCA( NB_ ) ) ) , ( UPPER ) , ( INFO.NE.0 ) , ( INFO.EQ.0 ) |
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| List of variables | BLOCK_CYCLIC_2D CSRC_ CTXT_ DLEN_ DTYPE_ IA IAROW
| IB IBROW ICOFFA ICTXT IDUM1( 1 ) IDUM2( 1 ) INDXG2P INFO
| IROFFA IROFFB JA JB LLD_ LSAME M_ MB_
| MYCOL MYROW N N_ NB_ NPCOL NPROW NRHS
| RSRC_ UPLO UPPER | | close
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BLOCK_CYCLIC_2D
CSRC_
CTXT_
DLEN_
DTYPE_
IA
IAROW
IB
IBROW
ICOFFA
ICTXT
IDUM1( 1 )
IDUM2( 1 )
INDXG2P
INFO
IROFFA
IROFFB
JA
JB
LLD_
LSAME
M_
MB_
MYCOL
MYROW
N
N_
NB_
NPCOL
NPROW
NRHS
RSRC_
UPLO
UPPER
284#286
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