PZLARFG - generate a complex elementary reflector H of order n, such that H *
sub( X ) = H * ( x(iax,jax) ) = ( alpha ), H' * H = I
- SUBROUTINE PZLARFG(
- N, ALPHA, IAX, JAX, X, IX, JX, DESCX, INCX, TAU )
INTEGER IAX, INCX, IX, JAX, JX, N COMPLEX*16 ALPHA INTEGER DESCX( * ) COMPLEX*16
TAU( * ), X( * )
PZLARFG generates a complex elementary reflector H of order n, such that H *
sub( X ) = H * ( x(iax,jax) ) = ( alpha ), H' * H = I. ( x ) ( 0 )
where alpha is a real scalar, and sub( X ) is an (N-1)-element complex
distributed vector X(IX:IX+N-2,JX) if INCX = 1 and X(IX,JX:JX+N-2) if INCX =
DESCX(M_). H is represented in the form
H = I - tau * ( 1 ) * ( 1 v' ) ,
( v )
where tau is a complex scalar and v is a complex (N-1)-element vector. Note that
H is not Hermitian.
If the elements of sub( X ) are all zero and X(IAX,JAX) is real, then tau = 0
and H is taken to be the unit matrix.
Otherwise 1 <= real(tau) <= 2 and abs(tau-1) <= 1.
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.
- N (global input) INTEGER
- The global order of the elementary reflector. N >= 0.
- ALPHA (local output) COMPLEX*16
- On exit, alpha is computed in the process scope having the vector sub( X
).
- IAX (global input) INTEGER
- The global row index in X of X(IAX,JAX).
- JAX (global input) INTEGER
- The global column index in X of X(IAX,JAX).
- X (local input/local output) COMPLEX*16, pointer into the
- local memory to an array of dimension (LLD_X,*). This array contains the
local pieces of the distributed vector sub( X ). Before entry, the
incremented array sub( X ) must contain the vector x. On exit, it is
overwritten with the vector v.
- IX (global input) INTEGER
- The row index in the global array X indicating the first row of sub( X
).
- JX (global input) INTEGER
- The column index in the global array X indicating the first column of sub(
X ).
- DESCX (global and local input) INTEGER array of dimension DLEN_.
- The array descriptor for the distributed matrix X.
- INCX (global input) INTEGER
- The global increment for the elements of X. Only two values of INCX are
supported in this version, namely 1 and M_X. INCX must not be zero.
- TAU (local output) COMPLEX*16, array, dimension LOCc(JX)
- if INCX = 1, and LOCr(IX) otherwise. This array contains the Householder
scalars related to the Householder vectors. TAU is tied to the distributed
matrix X.