void	f11zcc (Integer m, Integer n, Integer nnz, double a[], Integer irow[], Integer icol[], Integer istc[], Nag_SparseNsym_Store store, Nag_SparseNsym_Dups dup, Nag_SparseNsym_Zeros zero, NagError fail)

The function may be called by the names: f11zcc or nag_sparse_real_rect_sort.

3 Description

f11zcc takes a coordinate storage (CS) representation (see Section 2.1.1 in the F11 Chapter Introduction), or compressed column storage (CCS) representation (see Section 2.1.3 in the F11 Chapter Introduction) of a real

m \times n

sparse rectangular matrix

A

, and reorders the nonzero elements by increasing column index and increasing row index within each column.

Entries with duplicate row and column indices may be removed. Alternatively, duplicate entries may be summed, which facilitates sparse matrix addition (see Section 9). Any entries with zero values may optionally be removed.

Both CS and CCS representations of the resulting matrix are output, which allows f11zcc to be used to convert between the two formats (see Section 9).

4 References

None.

5 Arguments

1: $m$ – Integer Input

On entry:

m

, the number of rows in the matrix

A

Constraint:

m \geq 1

2: $n$ – Integer Input

On entry:

n

, the number of columns in the matrix

A

Constraint:

n \geq 1

3: $nnz$ – 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.

4: $a [nnz]$ – double Input/Output

On entry: the nonzero elements of the matrix

A

. If

store = Nag_SparseNsym_StoreCS

, the elements may be in any order. If

store = Nag_SparseNsym_StoreCCS

, the elements must be ordered by increasing column index. There may be multiple nonzero elements with the same row and column indices.

On exit: the nonzero elements ordered by increasing column index, and by increasing row index within each column. Each nonzero element has a unique row and column index.

5: $irow [nnz]$ – Integer Input/Output

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

Constraint:

1 \leq irow [i] \leq m

, 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.

6: $icol [nnz]$ – Integer Input/Output

On entry: if

store = Nag_SparseNsym_StoreCS

, the column indices corresponding to the elements supplied in the array a.

store = Nag_SparseNsym_StoreCCS

, icol need not be set.

Constraint: if

store = Nag_SparseNsym_StoreCS

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.

7: $istc [n + 1]$ – Integer Input/Output

On entry: if

store = Nag_SparseNsym_StoreCCS

, the starting address of each column, as supplied in the array a.

store = Nag_SparseNsym_StoreCS

, istc need not be set.

Constraints:

store = Nag_SparseNsym_StoreCCS

$istc [0] = 1$ ;
$istc [n] = nnz + 1$ ;
$istc [i - 1] \leq istc [i]$ , for $i = 1, 2, \dots, n$ .

On exit: the starting address of each column, as returned in the array a.

istc [n] - 1

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

8: $store$ – Nag_SparseNsym_Store Input

On entry: indicates which storage format the matrix

A

is represented with on entry.

$store = Nag_SparseNsym_StoreCS$: $A$ is represented in coordinate storage (CS) format using a, irow and icol.
$store = Nag_SparseNsym_StoreCCS$: $A$ is represented in compressed column storage (CCS) format using a, irow and istc.

Constraint:

store = Nag_SparseNsym_StoreCS

Nag_SparseNsym_StoreCCS

9: $dup$ – 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

10: $zero$ – 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

11: $fail$ – 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: On entry, $istc [0] = ⟨ value ⟩$ .
Constraint: $istc [0] = 1$ .

On entry, $m = ⟨ value ⟩$ .
Constraint: $m \geq 1$ .

On entry, $n = ⟨ value ⟩$ .
Constraint: $n \geq 1$ .

On entry, $nnz = ⟨ value ⟩$ .
Constraint: $nnz \geq 0$ .
NE_INT_3: On entry, $i = ⟨ value ⟩$ , $icol [i - 1] = ⟨ value ⟩$ and $n = ⟨ value ⟩$ .
Constraint: if $store = Nag_SparseNsym_StoreCS$ , then $1 \leq icol [i - 1] \leq n$ .

On entry, $i = ⟨ value ⟩$ , $irow [i - 1] = ⟨ value ⟩$ and $m = ⟨ value ⟩$ .
Constraint: $1 \leq irow [i - 1] \leq m$ .

On entry, $i = ⟨ value ⟩$ , $istc [i - 1] = ⟨ value ⟩$ and $istc [i] = ⟨ value ⟩$ .
Constraint: $istc [i - 1] \leq istc [i]$ , for $i = 1, 2, \dots, n$

On entry, $n = ⟨ value ⟩$ , $istc [n] = ⟨ value ⟩$ and $nnz = ⟨ value ⟩$ .
Constraint: $istc [n] = nnz + 1$ .
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 $⟨ value ⟩$ and column $⟨ value ⟩$ .
NE_ZERO_COEFF: On entry, a zero entry has been found in row $⟨ value ⟩$ and column $⟨ value ⟩$ .

7 Accuracy

Not applicable.

8 Parallelism and Performance

f11zcc is not threaded in any implementation.

9 Further Comments

Note that the resulting matrix may have either rows or columns with no entries. If column

i

has no entries then

istc [i - 1] = istc [i]

To transpose a matrix in CS format simply interchange irow and icol, and m and n. If you need the elements to be sorted, then pass these interchanged arrays to f11zcc.

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 f11zcc, specifying that duplicates should be summed.

This function can be used to convert between CS and CCS formats. Use either format to pass

A

into f11zcc, with the appropriate store set. The resulting matrix is output in both formats using a, irow, icol (for CS format) and istc (for CCS format).

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 both CS and CCS format. The order of rows within some columns of

A

are changed, and the matrix is input in CCS format to be re-sorted. The CS format is output to compare to the previous result. The matrix

A

is also sorted into row-major order by passing its transpose to f11zcc.

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

f11zc: FL CL CPP AD

NAG CL Interfacef11zcc (real_​rect_​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
f11zcc (real_rect_sort)