void	f11zac (Integer n, Integer nnz, double a[], Integer irow[], Integer icol[], Nag_SparseNsym_Dups dup, Nag_SparseNsym_Zeros zero, Integer istr[], NagError fail)

The function may be called by the names: f11zac, nag_sparse_real_gen_sort or nag_sparse_nsym_sort.

3 Description

f11zac takes a coordinate storage (CS) representation (see Section 2.1.1 in the F11 Chapter Introduction) of a real

n \times 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. Alternatively, duplicate entries may be summed, which facilitates spare matrix addition (see Section 9). Any entries with zero values may optionally be removed.

f11zac also returns a pointer array istr to the starting address 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: $n$ – Integer Input

On entry:

n

, the order of the matrix

A

Constraint:

n \geq 1

2: $nnz$ – Integer * Input/Output

On entry: the number of elements supplied in the array a.

Constraint:

nnz \geq 0

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

3: $a [\dim]$ – double Input/Output

Note: the dimension, dim, of the array a must be at least

\max (1, nnz)

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: $irow [\dim]$ – Integer Input/Output

Note: the dimension, dim, of the array irow must be at least

\max (1, nnz)

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

5: $icol [\dim]$ – Integer Input/Output

Note: the dimension, dim, of the array icol must be at least

\max (1, nnz)

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

6: $dup$ – Nag_SparseNsym_Dups Input

On entry: indicates how elements in a with duplicate row and column indices are to be treated.

$dup = Nag_SparseNsym_RemoveDups$: Duplicate entries are removed, only the first entry is kept.
$dup = Nag_SparseNsym_SumDups$: The relevant values in a are summed.
$dup = Nag_SparseNsym_FailDups$: The function fails with $fail . code =$ NE_NON_ZERO_DUP on detecting a duplicate.

Constraint:

dup = Nag_SparseNsym_RemoveDups

Nag_SparseNsym_SumDups

Nag_SparseNsym_FailDups

7: $zero$ – Nag_SparseNsym_Zeros Input

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

$zero = Nag_SparseNsym_RemoveZeros$: The entries are removed.
$zero = Nag_SparseNsym_KeepZeros$: The entries are kept.
$zero = Nag_SparseNsym_FailZeros$: The function fails with $fail . code =$ NE_ZERO_COEFF on detecting a zero.

Constraint:

zero = Nag_SparseNsym_RemoveZeros

Nag_SparseNsym_KeepZeros

Nag_SparseNsym_FailZeros

8: $istr [n + 1]$ – Integer Output

On exit:

istr [i - 1] - 1

, for

i = 1, 2, \dots, n

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

i

of the matrix

A

istr [n] - 1

is the address of the last element in a plus one.

9: $fail$ – NagError * Input/Output

The NAG error argument (see Section 7 in the Introduction to the NAG Library CL Interface).

6 Error Indicators and Warnings

NE_ALLOC_FAIL: Dynamic memory allocation failed.
See Section 3.1.2 in the Introduction to the NAG Library CL Interface for further information.
NE_BAD_PARAM: On entry, argument $⟨ value ⟩$ 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_INTERNAL_ERROR: An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.
See Section 7.5 in the Introduction to the NAG Library CL Interface for further information.
NE_NO_LICENCE: Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library CL Interface for further information.
NE_NON_ZERO_DUP: On entry, a duplicate entry has been found in row $i$ and column $j$ : $i = ⟨ value ⟩$ , $j = ⟨ value ⟩$ .
NE_NONSYMM_MATRIX: On entry, $i = ⟨ value ⟩$ , $icol [i - 1] = ⟨ value ⟩$ and $n = ⟨ value ⟩$ .
Constraint: $icol [i - 1] \geq 1$ and $icol [i - 1] \leq n$ .

On entry, $i = ⟨ value ⟩$ , $irow [i - 1] = ⟨ value ⟩$ and $n = ⟨ value ⟩$ .
Constraint: $irow [i - 1] \geq 1$ and $irow [i - 1] \leq n$ .
NE_ZERO_COEFF: On entry, a zero entry has been found in row $i$ and column $j$ : $i = ⟨ value ⟩$ , $j = ⟨ value ⟩$ .

7 Accuracy

Not applicable.

8 Parallelism and Performance

f11zac is not threaded in any implementation.

9 Further Comments

The time taken for a call to f11zac is the sum of two contributions, where one is proportional to nnz and the other is proportional to n.

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]

To transpose a matrix in CS format simply interchange irow and icol. If you need the elements to be sorted, then pass these interchanged arrays to f11zac.

Two sparse matrices can be added by concatenating the three pairs of CS format arrays, representing the two matrices, and passing these new arrays to f11zac, specifying that duplicates should be summed.

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 format array holding the row indices must be passed as icol and the array holding the column indices must be passed as irow in a call to f11zac. On exit from f11zac, the CCS representation of the matrix is given by the output arrays a, icol, and istr, where icol holds irowix and istr holds icolzp as described in Section 2.1.3 in the F11 Chapter Introduction.

10 Example

This example reads the CS representation of the real sparse matrices

B

and

C

, and finds their sum,

A

, displaying the ordered elements in CS format. The matrix

A

is then converted to CCS format and its

1

-norm found. The CCS format is converted back to CS format and checked to be identical to the original ordered CS representation. The transpose of

A

is also found and displayed in CS format.

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

f11za: FL CL CPP AD

NAG CL Interfacef11zac (real_​gen_​sort)

▸▿ 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 CL Interface
f11zac (real_gen_sort)