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..
.. Array Arguments ..
..
Purpose
=======
PSLARZT forms the triangular factor T of a real block reflector
H of order > n, which is defined as a product of k elementary
reflectors as returned by PSTZRZF.
If DIRECT = 'F', H = H(1) H(2) . . . H(k) and T is upper triangular;
If DIRECT = 'B', H = H(k) . . . H(2) H(1) and T is lower triangular.
If STOREV = 'C', the vector which defines the elementary reflector
H(i) is stored in the i-th column of the array V, and
H = I - V * T * V'
If STOREV = 'R', the vector which defines the elementary reflector
H(i) is stored in the i-th row of the array V, and
H = I - V' * T * V
Currently, only STOREV = 'R' and DIRECT = 'B' are supported.
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
=========
DIRECT (global input) CHARACTER
Specifies the order in which the elementary reflectors are
multiplied to form the block reflector:
= 'F': H = H(1) H(2) . . . H(k) (Forward, not supported yet)
= 'B': H = H(k) . . . H(2) H(1) (Backward)
STOREV (global input) CHARACTER
Specifies how the vectors which define the elementary
reflectors are stored (see also Further Details):
= 'C': columnwise (not supported yet)
= 'R': rowwise
N (global input) INTEGER
The number of meaningful entries of the block reflector H.
N >= 0.
K (global input) INTEGER
The order of the triangular factor T (= the number of
elementary reflectors). 1 <= K <= MB_V (= NB_V).
V (input/output) REAL pointer into the local memory
to an array of local dimension (LOCr(IV+K-1),LOCc(JV+N-1)).
The distributed matrix V contains the Householder vectors.
See further details.
IV (global input) INTEGER
The row index in the global array V indicating the first
row of sub( V ).
JV (global input) INTEGER
The column index in the global array V indicating the
first column of sub( V ).
DESCV (global and local input) INTEGER array of dimension DLEN_.
The array descriptor for the distributed matrix V.
TAU (local input) REAL, array, dimension LOCr(IV+K-1)
if INCV = M_V, and LOCc(JV+K-1) otherwise. This array
contains the Householder scalars related to the Householder
vectors. TAU is tied to the distributed matrix V.
T (local output) REAL array, dimension (MB_V,MB_V)
It contains the k-by-k triangular factor of the block
reflector associated with V. T is lower triangular.
WORK (local workspace) REAL array,
dimension (K*(K-1)/2)
Further Details
===============
The shape of the matrix V and the storage of the vectors which define
the H(i) is best illustrated by the following example with n = 5 and
k = 3. The elements equal to 1 are not stored; the corresponding
array elements are modified but restored on exit. The rest of the
array is not used.
DIRECT = 'F' and STOREV = 'C': DIRECT = 'F' and STOREV = 'R':
______V_____
( v1 v2 v3 ) / \
( v1 v2 v3 ) ( v1 v1 v1 v1 v1 . . . . 1 )
V = ( v1 v2 v3 ) ( v2 v2 v2 v2 v2 . . . 1 )
( v1 v2 v3 ) ( v3 v3 v3 v3 v3 . . 1 )
( v1 v2 v3 )
. . .
. . .
1 . .
1 .
1
DIRECT = 'B' and STOREV = 'C': DIRECT = 'B' and STOREV = 'R':
______V_____
1 / \
. 1 ( 1 . . . . v1 v1 v1 v1 v1 )
. . 1 ( . 1 . . . v2 v2 v2 v2 v2 )
. . . ( . . 1 . . v3 v3 v3 v3 v3 )
. . .
( v1 v2 v3 )
( v1 v2 v3 )
V = ( v1 v2 v3 )
( v1 v2 v3 )
( v1 v2 v3 )
=====================================================================
.. Parameters ..
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001 SUBROUTINE PSLARZT( DIRECT , STOREV , N , K , V , IV , JV , DESCV , TAU ,
002 $T , WORK )
003
004 * -- ScaLAPACK auxiliary 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 DIRECT , STOREV
011 INTEGER IV , JV , K , N
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 REAL ZERO
018 PARAMETER( ZERO = 0.0E + 0 )
019 * ..
020 * .. Local Scalars ..
021 INTEGER ICOFF , ICTXT , II , IIV , INFO , IVCOL , IVROW ,
022 $ITMP0 , ITMP1 , IW , JJV , LDV , MYCOL , MYROW ,
023 $NPCOL , NPROW , NQ
024 * ..
025 * .. External Subroutines ..
026 EXTERNAL BLACS_ABORT , BLACS_GRIDINFO , INFOG2L , PXERBLA ,
027 $SCOPY , SGEMV , SGSUM2D , SLASET ,
028 $STRMV
029 * ..
030 * .. External Functions ..
031 LOGICAL LSAME
032 INTEGER NUMROC
033 EXTERNAL LSAME , NUMROC
034 * ..
035 * .. Intrinsic Functions ..
036 INTRINSIC MOD
037 * ..
038 * .. Executable Statements ..
039
040 * Get grid parameters
041
042 ICTXT = DESCV( CTXT_ )
043 CALL BLACS_GRIDINFO( ICTXT , NPROW , NPCOL , MYROW , MYCOL )
044
045 * Check for currently supported options
046
047 INFO = 0
048 IF( .NOT.LSAME( DIRECT , 'B' ) ) THEN
048
049 INFO = - 1
050 ELSE IF( .NOT.LSAME( STOREV , 'R' ) ) THEN
050
051 INFO = - 2
052 END IF
053 IF( INFO.NE.0 ) THEN
053
054 CALL PXERBLA( ICTXT , 'PSLARZT' , - INFO )
055 CALL BLACS_ABORT( ICTXT , 1 )
056 RETURN
057 END IF
058
059 CALL INFOG2L( IV , JV , DESCV , NPROW , NPCOL , MYROW , MYCOL ,
060 $IIV , JJV , IVROW , IVCOL )
061
062 IF( MYROW.EQ.IVROW ) THEN
062
063 IW = 1
064 ITMP0 = 0
065 LDV = DESCV( LLD_ )
066 ICOFF = MOD( JV - 1 , DESCV( NB_ ) )
067 NQ = NUMROC( N + ICOFF , DESCV( NB_ ) , MYCOL , IVCOL , NPCOL )
068 IF( MYCOL.EQ.IVCOL )
068
069 $ NQ = NQ - ICOFF
070
071 DO 10 II = IIV + K - 2 , IIV , - 1
072
073 * T(i + 1 : k , i) = - tau( iv + i - 1 ) *
074 * V(iv + i : iv + k - 1 , jv : jv + n - 1) * V(iv + i - 1 , jv : jv + n - 1)'
075
075
076 ITMP0 = ITMP0 + 1
077 IF( NQ.GT.0 ) THEN
077
078 CALL SGEMV( 'No transpose' , ITMP0 , NQ , - TAU( II ) ,
079 $ V( II + 1 + (JJV - 1)*LDV ) , LDV ,
080 $ V( II + (JJV - 1)*LDV ) , LDV , ZERO , WORK( IW ) ,
081 $ 1 )
082 ELSE
082
083 CALL SLASET( 'All' , ITMP0 , 1 , ZERO , ZERO , WORK( IW ) ,
084 $ ITMP0 )
085 END IF
086 IW = IW + ITMP0
087
088 10 CONTINUE
089
089
090 CALL SGSUM2D( ICTXT , 'Rowwise' , ' ' , IW - 1 , 1 , WORK , IW - 1 ,
091 $ MYROW , IVCOL )
092
093 IF( MYCOL.EQ.IVCOL ) THEN
094
094
095 IW = 1
096 ITMP0 = 0
097 ITMP1 = K + 1 + (K - 1) * DESCV( MB_ )
098
099 T( ITMP1 - 1 ) = TAU( IIV + K - 1 )
100
101 DO 20 II = IIV + K - 2 , IIV , - 1
102
103 * T(i + 1 : k , i) = T(i + 1 : k , i + 1 : k) * T(i + 1 : k , i)
104
104
105 ITMP0 = ITMP0 + 1
106 ITMP1 = ITMP1 - DESCV( MB_ ) - 1
107 CALL SCOPY( ITMP0 , WORK( IW ) , 1 , T( ITMP1 ) , 1 )
108 IW = IW + ITMP0
109
110 CALL STRMV( 'Lower' , 'No transpose' , 'Non - unit' , ITMP0 ,
111 $ T( ITMP1 + DESCV( MB_ ) ) , DESCV( MB_ ) ,
112 $ T( ITMP1 ) , 1 )
113 T( ITMP1 - 1 ) = TAU( II )
114
115 20 CONTINUE
116
116
117 END IF
118
119 END IF
120
121 RETURN
122
123 * End of PSLARZT
124
125 END26
12
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Variables in Routine PSLARZT()
| Summary Report |
| Data Type | Quantity | Size(byte) |
| CHARACTER | 2 | 2 |
| INTEGER | 33 | 132 |
| LOGICAL | 1 | 1 |
| REAL | 2 | 8 |
| TOTAL | 38 | 143 |
List of Variables
CHARACTER
INTEGER
| BLOCK_CYCLIC_2D | CSRC_ | CTXT_ | DLEN_ | DTYPE_ |
| ICOFF | ICTXT | II | IIV | INFO |
| ITMP0 | ITMP1 | IV | IVCOL | IVROW |
| IW | JJV | JV | K | LDV |
| LLD_ | M_ | MB_ | MYCOL | MYROW |
| N | N_ | NB_ | NPCOL | NPROW |
| NQ | NUMROC | RSRC_ | | |
LOGICAL
REAL
Variables Dependence Graph Put the mouse over a right hand side variable to display the corresponding line of the dependence | | - | | - | - | | ICOFF | <--- | JVICOFF = MOD( JV-1, DESCV( NB_ ) ), NB_ICOFF = MOD( JV-1, DESCV( NB_ ) ) |
| ICTXT | <--- | CTXT_ICTXT = DESCV( CTXT_ ) |
| II | <--- | IIVDO 20 II = IIV+K-2, IIV, -1{2DO 10 II = IIV+K-2, IIV, -1}, KDO 20 II = IIV+K-2, IIV, -1{2DO 10 II = IIV+K-2, IIV, -1} |
| ITMP0 | <--- | ITMP0ITMP0 = ITMP0 + 1{2ITMP0 = ITMP0 + 1} |
| ITMP1 | <--- | ITMP1ITMP1 = ITMP1 - DESCV( MB_ ) - 1, KITMP1 = K + 1 + (K-1) * DESCV( MB_ ), MB_ITMP1 = ITMP1 - DESCV( MB_ ) - 1{2ITMP1 = K + 1 + (K-1) * DESCV( MB_ )} |
| IW | <--- | ITMP0IW = IW + ITMP0{2IW = IW + ITMP0}, IWIW = IW + ITMP0{2IW = IW + ITMP0} |
| LDV | <--- | LLD_LDV = DESCV( LLD_ ) |
| NQ | <--- | IVCOLNQ = NUMROC( N+ICOFF, DESCV( NB_ ), MYCOL, IVCOL, NPCOL ), MYCOLNQ = NUMROC( N+ICOFF, DESCV( NB_ ), MYCOL, IVCOL, NPCOL ), NNQ = NUMROC( N+ICOFF, DESCV( NB_ ), MYCOL, IVCOL, NPCOL ), NB_NQ = NUMROC( N+ICOFF, DESCV( NB_ ), MYCOL, IVCOL, NPCOL ), NPCOLNQ = NUMROC( N+ICOFF, DESCV( NB_ ), MYCOL, IVCOL, NPCOL ), NUMROCNQ = NUMROC( N+ICOFF, DESCV( NB_ ), MYCOL, IVCOL, NPCOL ), ICOFFNQ = NUMROC( N+ICOFF, DESCV( NB_ ), MYCOL, IVCOL, NPCOL ) |
| T | <--- | IIVT( ITMP1-1 ) = TAU( IIV+K-1 ), KT( ITMP1-1 ) = TAU( IIV+K-1 ), IIT( ITMP1-1 ) = TAU( II ) |
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Analysis elements of the routine PSLARZT() Put the mouse over each element to display detailed matching information
Assigned variables |
| | | BLOCK_CYCLIC_2D , CSRC_ , CTXT_ , DLEN_ , DTYPE_ , ICOFF , ICTXT , II , INFO , ITMP0 , ITMP1 , IW , LDV , LLD_ , M_ , MB_ , N_ , NB_ , NQ , RSRC_ , ZERO |
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Active variables |
| | | BLOCK_CYCLIC_2D , CSRC_ , CTXT_ , DESCV , DIRECT , DLEN_ , DTYPE_ , ICOFF , ICTXT , II , IIV , INFO , ITMP0 , ITMP1 , IV , IVCOL , IVROW , IW , JJV , JV , K , LDV , LLD_ , LSAME , M_ , MB_ , MYCOL , MYROW , N , N_ , NB_ , NPCOL , NPROW , NQ , NUMROC , RSRC_ , STOREV , T , TAU , V , WORK , ZERO |
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Accessed arrays [ array name : associated index ] |
| | DESCV | : CTXT_ , LLD_ , MB_ , MB_ , MB_ , NB_ , NB_ |
| | LSAME | : DIRECT, 'B' , STOREV, 'R' |
| | NUMROC | : N+ICOFF, DESCV( NB_ ), MYCOL, IVCOL, NPCOL |
| | T | : i+1:k,i , i+1:k,i , i+1:k,i+1:k , ITMP1 , ITMP1 , ITMP1+DESCV( MB_ ) , ITMP1-1 , ITMP1-1 |
| | TAU | : II , II , IIV+K-1 , iv+i-1 |
| | V | : II+(JJV-1)*LDV , II+1+(JJV-1)*LDV , iv+i:iv+k-1,jv:jv+n-1 , iv+i-1,jv:jv+n-1 |
| | WORK | : IW , IW , IW |
|
Conditional statements [ statement : associated predicate ] |
| | do | : ( 10 II = IIV + K - 2 , IIV , - 1 ) , ( 20 II = IIV + K - 2 , IIV , - 1 ) |
| | for | : ( currently supported options ) |
| | if | : ( (.NOT.LSAME( DIRECT , 'B' ) ) ) , ( (.NOT.LSAME( STOREV , 'R' ) ) ) , ( INFO.NE.0 ) , ( MYROW.EQ.IVROW ) , ( MYCOL.EQ.IVCOL ) , ( NQ.GT.0 ) , ( MYCOL.EQ.IVCOL ) |
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| List of variables | BLOCK_CYCLIC_2D CSRC_ CTXT_ DIRECT DLEN_ DTYPE_ ICOFF
| ICTXT II IIV INFO ITMP0 ITMP1 IV IVCOL
| IVROW IW JJV JV K LDV LLD_ LSAME
| M_ MB_ MYCOL MYROW N N_ NB_ NPCOL
| NPROW NQ NUMROC RSRC_ STOREV T ZERO | | close
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BLOCK_CYCLIC_2D
CSRC_
CTXT_
DIRECT
DLEN_
DTYPE_
ICOFF
ICTXT
II
IIV
INFO
ITMP0
ITMP1
IV
IVCOL
IVROW
IW
JJV
JV
K
LDV
LLD_
LSAME
M_
MB_
MYCOL
MYROW
N
N_
NB_
NPCOL
NPROW
NQ
NUMROC
RSRC_
STOREV
T
ZERO
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