PCLACON(l) ) PCLACON(l)NAME
PCLACON - estimate the 1-norm of a square, complex distributed matrix A
SYNOPSIS
SUBROUTINE PCLACON( N, V, IV, JV, DESCV, X, IX, JX, DESCX, EST, KASE )
INTEGER IV, IX, JV, JX, KASE, N
REAL EST
INTEGER DESCV( * ), DESCX( * )
COMPLEX V( * ), X( * )
PURPOSE
PCLACON estimates the 1-norm of a square, complex distributed matrix A.
Reverse communication is used for evaluating matrix-vector products. X
and V are aligned with the distributed matrix A, this information is
implicitly contained within IV, IX, DESCV, and DESCX.
Notes
=====
Each global data object is described by an associated description vec‐
tor. This vector stores the information required to establish the map‐
ping 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 col‐
umn.
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
N (global input) INTEGER
The length of the distributed vectors V and X. N >= 0.
V (local workspace) COMPLEX pointer into the local
memory to an array of dimension LOCr(N+MOD(IV-1,MB_V)). On the
final return, V = A*W, where EST = norm(V)/norm(W) (W is not
returned).
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.
X (local input/local output) COMPLEX pointer into the
local memory to an array of dimension LOCr(N+MOD(IX-1,MB_X)).
On an intermediate return, X should be overwritten by A * X,
if KASE=1, A' * X, if KASE=2, where A' is the conjugate trans‐
pose of A, and PCLACON must be re-called with all the other
parameters unchanged.
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.
EST (global output) REAL
An estimate (a lower bound) for norm(A).
KASE (local input/local output) INTEGER
On the initial call to PCLACON, KASE should be 0. On an inter‐
mediate return, KASE will be 1 or 2, indicating whether X
should be overwritten by A * X or A' * X. On the final return
from PCLACON, KASE will again be 0.
FURTHER DETAILS
The serial version CLACON has been contributed by Nick Higham, Univer‐
sity of Manchester. It was originally named SONEST, dated March 16,
1988.
Reference: N.J. Higham, "FORTRAN codes for estimating the one-norm of a
real or complex matrix, with applications to condition estimation", ACM
Trans. Math. Soft., vol. 14, no. 4, pp. 381-396, December 1988.
ScaLAPACK version 1.7 13 August 2001 PCLACON(l)
