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| # Variables: | 31 |
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| # Callings: | 2 |
| # Words: | 87 |
| # Keywords: | 57 |
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..
.. Array Arguments ..
..
Purpose
=======
PDGESV computes the solution to a real system of linear equations
sub( A ) * X = sub( B ),
where sub( A ) = A(IA:IA+N-1,JA:JA+N-1) is an N-by-N distributed
matrix and X and sub( B ) = B(IB:IB+N-1,JB:JB+NRHS-1) are N-by-NRHS
distributed matrices.
The LU decomposition with partial pivoting and row interchanges is
used to factor sub( A ) as sub( A ) = P * L * U, where P is a permu-
tation matrix, L is unit lower triangular, and U is upper triangular.
L and U are stored in sub( A ). The factored form of sub( A ) is then
used to solve the system of equations sub( A ) * X = sub( B ).
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
=========
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, the local pieces of the N-by-N distributed matrix
sub( A ) to be factored. On exit, this array contains the
local pieces of the factors L and U from the factorization
sub( A ) = P*L*U; the unit diagonal elements of L are not
stored.
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.
IPIV (local output) INTEGER array, dimension ( LOCr(M_A)+MB_A )
This array contains the pivoting information.
IPIV(i) -> The global row local row i was swapped with.
This array is tied to the distributed matrix A.
B (local input/local output) DOUBLE PRECISION pointer into the
local memory to an array of dimension
(LLD_B,LOCc(JB+NRHS-1)). On entry, the right hand side
distributed matrix sub( B ). On exit, if INFO = 0, sub( B )
is overwritten by 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, U(IA+K-1,JA+K-1) is exactly zero.
The factorization has been completed, but the factor U
is exactly singular, so the solution could not be
computed.
=====================================================================
.. Parameters ..
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01 SUBROUTINE PDGESV( N , NRHS , A , IA , JA , DESCA , IPIV , B , IB , JB ,
02 $DESCB , INFO )
03
04 * -- ScaLAPACK routine(version 1.7) --
05 * University of Tennessee , Knoxville , Oak Ridge National Laboratory ,
06 * and University of California , Berkeley.
07 * Jan 30 , 2006
08
09 * .. Scalar Arguments ..
10 INTEGER IA , IB , INFO , JA , JB , N , NRHS
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 * ..
17 * .. Local Scalars ..
18 INTEGER IAROW , IBROW , ICOFFA , ICTXT , IROFFA , IROFFB ,
19 $MYCOL , MYROW , NPCOL , NPROW
20 * ..
21 * .. Local Arrays ..
22 INTEGER IDUM1( 1 ) , IDUM2( 1 )
23 * ..
24 * .. External Subroutines ..
25 EXTERNAL BLACS_GRIDINFO , CHK1MAT , PCHK2MAT , PDGETRF ,
26 $PDGETRS , PXERBLA
27 * ..
28 * .. External Functions ..
29 INTEGER INDXG2P
30 EXTERNAL INDXG2P
31 * ..
32 * .. Intrinsic Functions ..
33 INTRINSIC MOD
34 * ..
35 * .. Executable Statements ..
36
37 * Get grid parameters
38
39 ICTXT = DESCA( CTXT_ )
40 CALL BLACS_GRIDINFO( ICTXT , NPROW , NPCOL , MYROW , MYCOL )
41
42 * Test the input parameters
43
44 INFO = 0
45 IF( NPROW.EQ. - 1 ) THEN
45
46 INFO = - (600 + CTXT_)
47 ELSE
47
48 CALL CHK1MAT( N , 1 , N , 1 , IA , JA , DESCA , 6 , INFO )
49 CALL CHK1MAT( N , 1 , NRHS , 2 , IB , JB , DESCB , 11 , INFO )
50 IF( INFO.EQ.0 ) THEN
50
51 IAROW = INDXG2P( IA , DESCA( MB_ ) , MYROW , DESCA( RSRC_ ) ,
52 $ NPROW )
53 IBROW = INDXG2P( IB , DESCB( MB_ ) , MYROW , DESCB( RSRC_ ) ,
54 $ NPROW )
55 IROFFA = MOD( IA - 1 , DESCA( MB_ ) )
56 ICOFFA = MOD( JA - 1 , DESCA( NB_ ) )
57 IROFFB = MOD( IB - 1 , DESCB( MB_ ) )
58 IF( IROFFA.NE.0 ) THEN
58
59 INFO = - 4
60 ELSE IF( ICOFFA.NE.0 ) THEN
60
61 INFO = - 5
62 ELSE IF( DESCA( MB_ ).NE.DESCA( NB_ ) ) THEN
62
63 INFO = - (600 + NB_)
64 ELSE IF( IBROW.NE.IAROW .OR. ICOFFA.NE.IROFFB ) THEN
64
65 INFO = - 9
66 ELSE IF( DESCB( MB_ ).NE.DESCA( NB_ ) ) THEN
66
67 INFO = - (1100 + NB_)
68 ELSE IF( ICTXT.NE.DESCB( CTXT_ ) ) THEN
68
69 INFO = - (1100 + CTXT_)
70 END IF
71 END IF
72 CALL PCHK2MAT( N , 1 , N , 1 , IA , JA , DESCA , 6 , N , 1 , NRHS , 2 ,
73 $ IB , JB , DESCB , 11 , 0 , IDUM1 , IDUM2 , INFO )
74 END IF
75
76 IF( INFO.NE.0 ) THEN
76
77 CALL PXERBLA( ICTXT , 'PDGESV' , - INFO )
78 RETURN
79 END IF
80
81 * Compute the LU factorization of sub( A ).
82
83 CALL PDGETRF ( N , N , A , IA , JA , DESCA , IPIV , INFO )
84
85 IF( INFO.EQ.0 ) THEN
86
87 * Solve the system sub( A ) * X = sub( B ) , overwriting sub( B )
88 * with X.
89
89
90 CALL PDGETRS ( 'No transpose' , N , NRHS , A , IA , JA , DESCA , IPIV ,
91 $ B , IB , JB , DESCB , INFO )
92
93 END IF
94
95 RETURN
96
97 * End of PDGESV
98
99 END16
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Variables in Routine PDGESV()
| Summary Report |
| Data Type | Quantity | Size(byte) |
| INTEGER | 31 | 128 |
| TOTAL | 31 | 128 |
List of Variables
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_ | | | | |
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 = -(600+NB_){2INFO = -(1100+NB_)}, CTXT_INFO = -(600+CTXT_){2INFO = -(1100+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_ ) ) |
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Analysis elements of the routine PDGESV() Put the mouse over each element to display detailed matching information
Assigned variables |
| | | BLOCK_CYCLIC_2D , CSRC_ , CTXT_ , DLEN_ , DTYPE_ , IAROW , IBROW , ICOFFA , ICTXT , INFO , IROFFA , IROFFB , LLD_ , M_ , MB_ , N_ , NB_ , RSRC_ |
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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 , IPIV , IROFFA , IROFFB , JA , JB , LLD_ , M_ , MB_ , MYCOL , MYROW , N , N_ , NB_ , NPCOL , NPROW , NRHS , RSRC_ |
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Accessed arrays [ array name : associated index ] |
| | DESCA | : CTXT_ , MB_ , MB_ , MB_ , NB_ , NB_ , NB_ , RSRC_ |
| | DESCB | : CTXT_ , MB_ , MB_ , MB_ , RSRC_ |
| | IDUM1 | : 1 |
| | IDUM2 | : 1 |
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Conditional statements [ statement : associated predicate ] |
| | if | : ( NPROW.EQ. - 1 ) , ( INFO.EQ.0 ) , ( IROFFA.NE.0 ) , ( ICOFFA.NE.0 ) , ( (DESCA( MB_ ).NE.DESCA( NB_ ) ) ) , ( IBROW.NE.IAROW .OR. ICOFFA.NE.IROFFB ) , ( (DESCB( MB_ ).NE.DESCA( NB_ ) ) ) , ( (ICTXT.NE.DESCB( CTXT_ ) ) ) , ( 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_ M_ MB_ MYCOL MYROW
| N N_ NB_ NPCOL NPROW NRHS RSRC_ | | 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_
M_
MB_
MYCOL
MYROW
N
N_
NB_
NPCOL
NPROW
NRHS
RSRC_
197#199
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