nag_sparse_sym_matvec (f11xec) computes the matrix-vector product
where
is an
by
symmetric sparse matrix, of arbitrary sparsity pattern, stored in symmetric coordinate storage (SCS) format (see
Section 2.1.2 in the f11 Chapter Introduction). The array
a stores all nonzero elements in the lower triangular part of
, while arrays
irow and
icol store the corresponding row and column indices respectively.
It is envisaged that a common use of
nag_sparse_sym_matvec (f11xec) will be to compute the matrix-vector product required in the application of
nag_sparse_sym_basic_solver (f11gec) to sparse symmetric linear systems. An illustration of this usage appears in
nag_sparse_sym_precon_ssor_solve (f11jdc).
None.
The computed vector
satisfies the error bound
where
is a modest linear function of
, and
is the
machine precision.
Please consult the
x06 Chapter Introduction for information on how to control and interrogate the OpenMP environment used within this function. Please also consult the
Users' Note for your implementation for any additional implementation-specific information.
The time taken for a call to
nag_sparse_sym_matvec (f11xec) is proportional to
nnz.
It is expected that a common use of
nag_sparse_sym_matvec (f11xec) will be to compute the matrix-vector product required in the application of
nag_sparse_sym_basic_solver (f11gec) to sparse symmetric linear systems. In this situation
nag_sparse_sym_matvec (f11xec) 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.