NAME
PDLACON - estimate the 1-norm of a square, real distributed matrix A
SYNOPSIS
SUBROUTINE PDLACON( N, V, IV, JV, DESCV, X, IX, JX, DESCX, ISGN, EST,
KASE )
INTEGER IV, IX, JV, JX, KASE, N
DOUBLE PRECISION EST
INTEGER DESCV( * ), DESCX( * ), ISGN( * )
DOUBLE PRECISION V( * ), X( * )
PURPOSE
PDLACON estimates the 1-norm of a square, real 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
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
N (global input) INTEGER
The length of the distributed vectors V and X. N >= 0.
V (local workspace) DOUBLE PRECISION 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) DOUBLE PRECISION 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, PDLACON 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.
ISGN (local workspace) INTEGER array, dimension
LOCr(N+MOD(IX-1,MB_X)). ISGN is aligned with X and V.
EST (global output) DOUBLE PRECISION
An estimate (a lower bound) for norm(A).
KASE (local input/local output) INTEGER
On the initial call to PDLACON, KASE should be 0. On an
intermediate return, KASE will be 1 or 2, indicating whether X
should be overwritten by A * X or A’ * X. On the final return
from PDLACON, KASE will again be 0.
FURTHER DETAILS
The serial version DLACON has been contributed by Nick Higham,
University 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.