F11XAF computes a matrix-vector or transposed matrix-vector product involving a real sparse nonsymmetric matrix stored in coordinate storage format.
F11XAF computes either the matrix-vector product
, or the transposed matrix-vector product
, according to the value of the argument
TRANS, where
is an
by
sparse nonsymmetric matrix, of arbitrary sparsity pattern. The matrix
is stored in coordinate storage (CS) format (see
Section 2.1.1 in the F11 Chapter Introduction). The array
A stores all nonzero elements of
, while arrays
IROW and
ICOL store the corresponding row and column indices respectively.
It is envisaged that a common use of F11XAF will be to compute the matrix-vector product required in the application of
F11BEF to sparse linear systems. An illustration of this usage appears in
Section 10 in F11DDF.
None.
If on entry
or
, explanatory error messages are output on the current error message unit (as defined by
X04AAF).
The computed vector
satisfies the error bound:
- , if , or
- ,
if ,
where
is a modest linear function of
, and
is the
machine precision.
F11XAF is threaded by NAG for parallel execution in multithreaded implementations of the NAG Library.
F11XAF makes calls to BLAS and/or LAPACK routines, which may be threaded within the vendor library used by this implementation. Consult the documentation for the vendor library for further information.
Please consult the
X06 Chapter Introduction for information on how to control and interrogate the OpenMP environment used within this routine. Please also consult the
Users' Note for your implementation for any additional implementation-specific information.
The time taken for a call to F11XAF is proportional to
NNZ.
It is expected that a common use of F11XAF will be to compute the matrix-vector product required in the application of
F11BEF to sparse linear systems. In this situation F11XAF is likely to be called many times with the same matrix
. In the interests of both reliability and efficiency you are recommended to set
for the first of such calls, and to set
for all subsequent calls.