- 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( * )

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

- 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.

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.

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- SYNOPSIS
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Time: 21:52:13 GMT, April 16, 2011