PZLACON - estimate the 1-norm of a square, complex distributed matrix A
- SUBROUTINE PZLACON(
- N, V, IV, JV, DESCV, X, IX, JX, DESCX, EST, KASE )
INTEGER IV, IX, JV, JX, KASE, N DOUBLE PRECISION EST INTEGER DESCV( * ), DESCX(
* ) COMPLEX*16 V( * ), X( * )
PZLACON 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 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) COMPLEX*16 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*16 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 transpose of A, and PZLACON 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) DOUBLE PRECISION
- An estimate (a lower bound) for norm(A).
- KASE (local input/local output) INTEGER
- On the initial call to PZLACON, 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 PZLACON, KASE will again be
0.
The serial version ZLACON 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.