PCLARFC - applie a complex elementary reflector Q**H to a complex M-by-N
distributed matrix sub( C ) = C(IC:IC+M-1,JC:JC+N-1),
- SUBROUTINE PCLARFC(
- SIDE, M, N, V, IV, JV, DESCV, INCV, TAU, C, IC, JC, DESCC, WORK )
CHARACTER SIDE INTEGER IC, INCV, IV, JC, JV, M, N INTEGER DESCC( * ), DESCV( * )
COMPLEX C( * ), TAU( * ), V( * ), WORK( * )
PCLARFC applies a complex elementary reflector Q**H to a complex M-by-N
distributed matrix sub( C ) = C(IC:IC+M-1,JC:JC+N-1), from either the left or
the right. Q is represented in the form
Q = I - tau * v * v'
where tau is a complex scalar and v is a complex vector.
If tau = 0, then Q is taken to be the unit matrix.
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
Because vectors may be viewed as a subclass of matrices, a distributed vector is
considered to be a distributed matrix.
Restrictions
============
If SIDE = 'Left' and INCV = 1, then the row process having the first entry
V(IV,JV) must also have the first row of sub( C ). Moreover, MOD(IV-1,MB_V)
must be equal to MOD(IC-1,MB_C), if INCV=M_V, only the last equality must be
satisfied.
If SIDE = 'Right' and INCV = M_V then the column process having the first entry
V(IV,JV) must also have the first column of sub( C ) and MOD(JV-1,NB_V) must
be equal to MOD(JC-1,NB_C), if INCV = 1 only the last equality must be
satisfied.
- SIDE (global input) CHARACTER
- = 'L': form Q**H * sub( C ),
= 'R': form sub( C ) * Q**H.
- M (global input) INTEGER
- The number of rows to be operated on i.e the number of rows of the
distributed submatrix sub( C ). M >= 0.
- N (global input) INTEGER
- The number of columns to be operated on i.e the number of columns of the
distributed submatrix sub( C ). N >= 0.
- V (local input) COMPLEX pointer into the local memory
- to an array of dimension (LLD_V,*) containing the local pieces of the
distributed vectors V representing the Householder transformation Q,
V(IV:IV+M-1,JV) if SIDE = 'L' and INCV = 1,
V(IV,JV:JV+M-1) if SIDE = 'L' and INCV = M_V,
V(IV:IV+N-1,JV) if SIDE = 'R' and INCV = 1,
V(IV,JV:JV+N-1) if SIDE = 'R' and INCV = M_V,
The vector v in the representation of Q. V is not used if TAU = 0.
- 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.
- INCV (global input) INTEGER
- The global increment for the elements of V. Only two values of INCV are
supported in this version, namely 1 and M_V. INCV must not be zero.
- TAU (local input) COMPLEX, array, dimension LOCc(JV) if
- INCV = 1, and LOCr(IV) otherwise. This array contains the Householder
scalars related to the Householder vectors. TAU is tied to the distributed
matrix V.
- C (local input/local output) COMPLEX pointer into the
- local memory to an array of dimension (LLD_C, LOCc(JC+N-1) ), containing
the local pieces of sub( C ). On exit, sub( C ) is overwritten by the Q**H
* sub( C ) if SIDE = 'L', or sub( C ) * Q**H if SIDE = 'R'.
- IC (global input) INTEGER
- The row index in the global array C indicating the first row of sub( C
).
- JC (global input) INTEGER
- The column index in the global array C indicating the first column of sub(
C ).
- DESCC (global and local input) INTEGER array of dimension DLEN_.
- The array descriptor for the distributed matrix C.
- WORK (local workspace) COMPLEX array, dimension (LWORK)
- If INCV = 1, if SIDE = 'L', if IVCOL = ICCOL, LWORK >= NqC0 else LWORK
>= MpC0 + MAX( 1, NqC0 ) end if else if SIDE = 'R', LWORK >= NqC0 +
MAX( MAX( 1, MpC0 ), NUMROC( NUMROC( N+ICOFFC,NB_V,0,0,NPCOL
),NB_V,0,0,LCMQ ) ) end if else if INCV = M_V, if SIDE = 'L', LWORK >=
MpC0 + MAX( MAX( 1, NqC0 ), NUMROC( NUMROC( M+IROFFC,MB_V,0,0,NPROW
),MB_V,0,0,LCMP ) ) else if SIDE = 'R', if IVROW = ICROW, LWORK >= MpC0
else LWORK >= NqC0 + MAX( 1, MpC0 ) end if end if end if
where LCM is the least common multiple of NPROW and NPCOL and LCM = ILCM(
NPROW, NPCOL ), LCMP = LCM / NPROW, LCMQ = LCM / NPCOL,
IROFFC = MOD( IC-1, MB_C ), ICOFFC = MOD( JC-1, NB_C ), ICROW = INDXG2P( IC,
MB_C, MYROW, RSRC_C, NPROW ), ICCOL = INDXG2P( JC, NB_C, MYCOL, CSRC_C,
NPCOL ), MpC0 = NUMROC( M+IROFFC, MB_C, MYROW, ICROW, NPROW ), NqC0 =
NUMROC( N+ICOFFC, NB_C, MYCOL, ICCOL, NPCOL ),
ILCM, INDXG2P and NUMROC are ScaLAPACK tool functions; MYROW, MYCOL, NPROW
and NPCOL can be determined by calling the subroutine BLACS_GRIDINFO.
Alignment requirements ======================
The distributed submatrices V(IV:*, JV:*) and C(IC:IC+M-1,JC:JC+N-1) must
verify some alignment properties, namely the following expressions should
be true:
MB_V = NB_V,
If INCV = 1, If SIDE = 'Left', ( MB_V.EQ.MB_C .AND. IROFFV.EQ.IROFFC .AND.
IVROW.EQ.ICROW ) If SIDE = 'Right', ( MB_V.EQ.NB_A .AND. MB_V.EQ.NB_C
.AND. IROFFV.EQ.ICOFFC ) else if INCV = M_V, If SIDE = 'Left', (
MB_V.EQ.NB_V .AND. MB_V.EQ.MB_C .AND. ICOFFV.EQ.IROFFC ) If SIDE =
'Right', ( NB_V.EQ.NB_C .AND. ICOFFV.EQ.ICOFFC .AND. IVCOL.EQ.ICCOL ) end
if