The routine PARALLEL_NONNEGATIVE_LSQ
is used to solve dense least-squares systems. These are represented by
where A is an
coefficient data
matrix,
is a given right-hand side
-vector, and
is the solution
-vector being computed. Further, there is a constraint
requirement,
. The routine PARALLEL_BOUNDED_LSQ
is used when the problem has lower and upper bounds for the solution,
. By making the bounds large, individual constraints can
be eliminated. There are no restrictions on the relative sizes
of
and
. When
is large, these codes can substantially reduce
computer time and storage requirements, compared with using a routine for
solving a constrained system and a single processor.
The user provides the matrix partitioned by blocks of columns:
.
An individual block of the partitioned matrix, say , is located entirely on the processor with rank
, where MP_RANK
is packaged in the module MPI_SETUP_INT.
This module, and the function MP_SETUP(),define
the Fortran Library MPI communicator, MP_LIBRARY_WORLD.
See Chapter 10, Dense Matrix
Parallelism Using MPI.
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