void	nag_sparse_nsym_sort (Integer n, Integer nnz, double a[], Integer irow[], Integer icol[], Nag_SparseNsym_Dups dup, Nag_SparseNsym_Zeros zero, Integer istr[], NagError fail)

3 Description

nag_sparse_nsym_sort (f11zac) takes a coordinate storage (CS) representation (see the f11 Chapter Introduction) of a real

n

n

sparse nonsymmetric matrix

A

, 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

A

. This can be used to construct a compressed column storage (CCS) representation of the matrix (see Section 9).

4 References

None.

5 Arguments

1: $n$ – IntegerInput

On entry: the order of the matrix

A

Constraint:

n \geq 1

2: $nnz$ – Integer *Input/Output

On entry: the number of nonzero elements in the matrix

A

Constraint:

nnz \geq 0

On exit: the number of nonzero elements with unique row and column indices.

3: $a [\max (1, nnz)]$ – doubleInput/Output

On entry: the nonzero elements of the matrix

A

. 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: $irow [\max (1, nnz)]$ – IntegerInput/Output

On entry: the row indices of the elements supplied in array a.

Constraint:

1 \leq irow [i] \leq n

, for

i = 0, 1, \dots, nnz - 1

On exit: the first nnz elements contain the row indices corresponding to the elements returned in array a.

5: $icol [\max (1, nnz)]$ – IntegerInput/Output

On entry: the column indices of the elements supplied in array a.

Constraint:

1 \leq icol [i] \leq n

, for

i = 0, 1, \dots, nnz - 1

On exit: the first nnz elements contain the column indices corresponding to the elements returned in array a.

6: $dup$ – Nag_SparseNsym_DupsInput

On entry: indicates how any nonzero elements with duplicate row and column indices are to be treated:

if $dup = Nag_SparseNsym_RemoveDups$ then duplicate elements are removed;
if $dup = Nag_SparseNsym_SumDups$ then the relevant values in array a are summed;
if $dup = Nag_SparseNsym_FailDups$ then the function fails on detecting a duplicate.

Constraint:

dup = Nag_SparseNsym_RemoveDups

Nag_SparseNsym_SumDups

Nag_SparseNsym_FailDups

7: $zero$ – Nag_SparseNsym_ZerosInput

On entry: indicates how any elements with zero values in a are to be treated:

if $zero = Nag_SparseNsym_RemoveZeros$ then the entries are removed;
if $zero = Nag_SparseNsym_KeepZeros$ then the entries are kept;
if $zero = Nag_SparseNsym_FailZeros$ then the function fails on detecting a zero.

Constraint:

zero = Nag_SparseNsym_RemoveZeros

Nag_SparseNsym_KeepZeros

Nag_SparseNsym_FailZeros

8: $istr [n + 1]$ – IntegerOutput

On exit:

istr [i - 1] - 1

, for

i = 1, 2, \dots, n

, is the starting index in the arrays a, irow and icol of each row

i

of the matrix

A

istr [n]

contains the number of nonzero elements in

A

plus one.

9: $fail$ – NagError *Input/Output

The NAG error argument (see Section 2.7 in How to Use the NAG Library and its Documentation).

6 Error Indicators and Warnings

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, $n = 〈value〉$ .
Constraint: $n \geq 1$ .

On entry, $nnz = 〈value〉$ .
Constraint: $nnz \geq 0$ .
NE_NON_ZERO_DUP: Nonzero elements have been supplied which have duplicate row and column indices, when $dup = Nag_SparseNsym_FailDups$ .
NE_NONSYMM_MATRIX: A nonzero element has been supplied which does not lie within the matrix $A$ ,
i.e., one or more of the following constraints has been violated:
$1 \leq irow [i] \leq n$ , $1 \leq icol [i] \leq n$ , for $i = 0, 1, \dots, nnz - 1$ .
NE_ZERO_COEFF: At least one matrix element has been supplied with a zero coefficient value, when $zero = Nag_SparseNsym_FailZeros$ .

7 Accuracy

Not applicable.

8 Parallelism and Performance

nag_sparse_nsym_sort (f11zac) is not threaded in any implementation.

9 Further Comments

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

i

has no entries then

istr [i - 1] = istr [i]

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.

10 Example

This example program reads the CS representation of a real sparse matrix

A

, 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.

A = (\begin{matrix} 2.00 & 1.00 & 0 & 0 & 0 \\ 0 & 0 & 1.00 & - 1.00 & 0 \\ 4.00 & 0 & 1.00 & 0 & 1.00 \\ 0 & 0 & 0 & 1.00 & 2.00 \\ 0 & - 2.00 & 0 & 0 & 3.00 \end{matrix}) .

NAG Library Function Documentnag_sparse_nsym_sort (f11zac)

▸▿ Contents

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

6 Error Indicators and Warnings

7 Accuracy

8 Parallelism and Performance

9 Further Comments

10 Example

10.1 Program Text

10.2 Program Data

10.3 Program Results

NAG Library Function Document

nag_sparse_nsym_sort (f11zac)