nag_sparse_nsym_sort (f11zac) takes a coordinate storage (CS) representation (see the
f11 Chapter Introduction) of a real
by
sparse nonsymmetric matrix
, and reorders the nonzero elements by increasing row index and increasing column index within each row. Entries with duplicate row and column indices may be removed, or the values may be summed. Any entries with zero values may optionally be removed.
nag_sparse_nsym_sort (f11zac) also returns
istr which contains the starting indices of each row in
. This can be used to construct a compressed column storage (CCS) representation of the matrix (see
Section 9).
None.
- 1:
– IntegerInput
-
On entry: the order of the matrix .
Constraint:
.
- 2:
– Integer *Input/Output
-
On entry: the number of nonzero elements in the matrix .
Constraint:
.
On exit: the number of nonzero elements with unique row and column indices.
- 3:
– doubleInput/Output
-
On entry: the nonzero elements of the matrix . These may be in any order and there may be multiple nonzero elements with the same row and column indices.
On exit: the nonzero elements ordered by increasing row index, and by increasing column index within each row. Each nonzero element has a unique row and column index.
- 4:
– IntegerInput/Output
-
On entry: the row indices of the elements supplied in array
a.
Constraint:
, for .
On exit: the first
nnz elements contain the row indices corresponding to the elements returned in array
a.
- 5:
– IntegerInput/Output
-
On entry: the column indices of the elements supplied in array
a.
Constraint:
, for .
On exit: the first
nnz elements contain the column indices corresponding to the elements returned in array
a.
- 6:
– Nag_SparseNsym_DupsInput
-
On entry: indicates how any nonzero elements with duplicate row and column indices are to be treated:
- if then duplicate elements are removed;
- if then the relevant values in array a are summed;
- if then the function fails on detecting a duplicate.
Constraint:
, or .
- 7:
– Nag_SparseNsym_ZerosInput
-
On entry: indicates how any elements with zero values in
a are to be treated:
- if then the entries are removed;
- if then the entries are kept;
- if then the function fails on detecting a zero.
Constraint:
, or .
- 8:
– IntegerOutput
-
On exit:
, for
, is the starting index in the arrays
a,
irow and
icol of each row
of the matrix
.
contains the number of nonzero elements in
plus one.
- 9:
– NagError *Input/Output
-
The NAG error argument (see
Section 3.7 in How to Use the NAG Library and its Documentation).
- NE_ALLOC_FAIL
-
Dynamic memory allocation failed.
- NE_BAD_PARAM
-
On entry, argument
dup had an illegal value.
On entry, argument
zero had an illegal value.
- NE_INT_ARG_LT
-
On entry, .
Constraint: .
On entry, .
Constraint: .
- NE_NON_ZERO_DUP
-
Nonzero elements have been supplied which have duplicate row and column indices, when .
- NE_NONSYMM_MATRIX
-
A nonzero element has been supplied which does not lie within the matrix ,
i.e., one or more of the following constraints has been violated:
, , for .
- NE_ZERO_COEFF
-
At least one matrix element has been supplied with a zero coefficient value, when .
Not applicable.
The time taken for a call to
nag_sparse_nsym_sort (f11zac) is proportional to
nnz.
Note that the resulting matrix may have either rows or columns with no entries. If row has no entries then .
It is also possible to use this function to convert between coordinate storage (CS) and compressed column storage (CCS) formats. To achieve this the CS storage format arrays
irow and
icol must be interchanged in the call to
nag_sparse_nsym_sort (f11zac). On exit from
nag_sparse_nsym_sort (f11zac), the CCS representation of the matrix is then defined by arrays
a,
irow and
istr. This is illustrated in
Section 10.
This example program reads the CS representation of a real sparse matrix
, calls
nag_sparse_nsym_sort (f11zac) to reorder the nonzero elements, and outputs the original and the reordered representations.It then calls
nag_sparse_nsym_sort (f11zac) again with the alternative ordering, creating a CCS representation which is then passed to a function that computes a matrix norm for that representation.