PSLACON(l)

NAME
PSLACON - estimate the 1-norm of a square, real distributed matrix A

SYNOPSIS

SUBROUTINE PSLACON(
    N, V, IV, JV, DESCV, X, IX, JX, DESCX, ISGN, EST, KASE )

INTEGER
    IV, IX, JV, JX, KASE, N

REAL
    EST

INTEGER
    DESCV( * ), DESCX( * ), ISGN( * )

REAL
    V( * ), X( * )

PURPOSE
PSLACON 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) REAL 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) REAL 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, PSLACON 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) REAL
    An estimate (a lower bound) for norm(A).

KASE    (local input/local output) INTEGER
    On the initial call to PSLACON, 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 PSLACON, KASE will again be 0.

FURTHER DETAILS
The serial version SLACON 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.