# NAG CL Interfacef11zcc (real_​rect_​sort)

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## 1Purpose

f11zcc sorts the nonzero elements of a real sparse rectangular matrix, represented in coordinate storage or compressed column storage format.

## 2Specification

 #include
 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.

## 3Description

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 $m×n$ 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).

None.

## 5Arguments

1: $\mathbf{m}$Integer Input
On entry: $m$, the number of rows in the matrix $A$.
Constraint: ${\mathbf{m}}\ge 1$.
2: $\mathbf{n}$Integer Input
On entry: $n$, the number of columns in the matrix $A$.
Constraint: ${\mathbf{n}}\ge 1$.
3: $\mathbf{nnz}$Integer * Input/Output
On entry: the number of elements supplied in the array a.
Constraint: ${\mathbf{nnz}}\ge 0$.
On exit: the number of elements with unique row and column indices.
4: $\mathbf{a}\left[{\mathbf{nnz}}\right]$double Input/Output
On entry: the nonzero elements of the matrix $A$. If ${\mathbf{store}}=\mathrm{Nag_SparseNsym_StoreCS}$, the elements may be in any order. If ${\mathbf{store}}=\mathrm{Nag_SparseNsym_StoreCCS}$, 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: $\mathbf{irow}\left[{\mathbf{nnz}}\right]$Integer Input/Output
On entry: the row indices corresponding to the elements supplied in the array a.
Constraint: $1\le {\mathbf{irow}}\left[\mathit{i}\right]\le {\mathbf{m}}$, for $\mathit{i}=0,1,\dots ,{\mathbf{nnz}}-1$.
On exit: the first nnz elements contain the row indices corresponding to the elements returned in the array a.
6: $\mathbf{icol}\left[{\mathbf{nnz}}\right]$Integer Input/Output
On entry: if ${\mathbf{store}}=\mathrm{Nag_SparseNsym_StoreCS}$, the column indices corresponding to the elements supplied in the array a.
If ${\mathbf{store}}=\mathrm{Nag_SparseNsym_StoreCCS}$, icol need not be set.
Constraint: if ${\mathbf{store}}=\mathrm{Nag_SparseNsym_StoreCS}$, $1\le {\mathbf{icol}}\left[\mathit{i}\right]\le {\mathbf{n}}$, for $\mathit{i}=0,1,\dots ,{\mathbf{nnz}}-1$.
On exit: the first nnz elements contain the column indices corresponding to the elements returned in the array a.
7: $\mathbf{istc}\left[{\mathbf{n}}+1\right]$Integer Input/Output
On entry: if ${\mathbf{store}}=\mathrm{Nag_SparseNsym_StoreCCS}$, the starting address of each column, as supplied in the array a.
If ${\mathbf{store}}=\mathrm{Nag_SparseNsym_StoreCS}$, istc need not be set.
Constraints:
if ${\mathbf{store}}=\mathrm{Nag_SparseNsym_StoreCCS}$,
• ${\mathbf{istc}}\left[0\right]=1$;
• ${\mathbf{istc}}\left[{\mathbf{n}}\right]={\mathbf{nnz}}+1$;
• ${\mathbf{istc}}\left[\mathit{i}-1\right]\le {\mathbf{istc}}\left[\mathit{i}\right]$, for $\mathit{i}=1,2,\dots ,{\mathbf{n}}$.
On exit: the starting address of each column, as returned in the array a. ${\mathbf{istc}}\left[{\mathbf{n}}\right]-1$ is the address of the last element in a plus one.
8: $\mathbf{store}$Nag_SparseNsym_Store Input
On entry: indicates which storage format the matrix $A$ is represented with on entry.
${\mathbf{store}}=\mathrm{Nag_SparseNsym_StoreCS}$
$A$ is represented in coordinate storage (CS) format using a, irow and icol.
${\mathbf{store}}=\mathrm{Nag_SparseNsym_StoreCCS}$
$A$ is represented in compressed column storage (CCS) format using a, irow and istc.
Constraint: ${\mathbf{store}}=\mathrm{Nag_SparseNsym_StoreCS}$ or $\mathrm{Nag_SparseNsym_StoreCCS}$.
9: $\mathbf{dup}$Nag_SparseNsym_Dups Input
On entry: indicates how elements in a with duplicate row and column indices are to be treated.
${\mathbf{dup}}=\mathrm{Nag_SparseNsym_RemoveDups}$
Duplicate entries are removed, only the first entry is kept.
${\mathbf{dup}}=\mathrm{Nag_SparseNsym_SumDups}$
The relevant values in a are summed.
${\mathbf{dup}}=\mathrm{Nag_SparseNsym_FailDups}$
The function fails with ${\mathbf{fail}}\mathbf{.}\mathbf{code}=$ NE_NON_ZERO_DUP on detecting a duplicate.
Constraint: ${\mathbf{dup}}=\mathrm{Nag_SparseNsym_RemoveDups}$, $\mathrm{Nag_SparseNsym_SumDups}$ or $\mathrm{Nag_SparseNsym_FailDups}$.
10: $\mathbf{zero}$Nag_SparseNsym_Zeros Input
On entry: indicates how elements in a with zero values are to be treated.
${\mathbf{zero}}=\mathrm{Nag_SparseNsym_RemoveZeros}$
The entries are removed.
${\mathbf{zero}}=\mathrm{Nag_SparseNsym_KeepZeros}$
The entries are kept.
${\mathbf{zero}}=\mathrm{Nag_SparseNsym_FailZeros}$
The function fails with ${\mathbf{fail}}\mathbf{.}\mathbf{code}=$ NE_ZERO_COEFF on detecting a zero.
Constraint: ${\mathbf{zero}}=\mathrm{Nag_SparseNsym_RemoveZeros}$, $\mathrm{Nag_SparseNsym_KeepZeros}$ or $\mathrm{Nag_SparseNsym_FailZeros}$.
11: $\mathbf{fail}$NagError * Input/Output
The NAG error argument (see Section 7 in the Introduction to the NAG Library CL Interface).

## 6Error 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.
On entry, argument $⟨\mathit{\text{value}}⟩$ had an illegal value.
NE_INT
On entry, ${\mathbf{istc}}\left[0\right]=⟨\mathit{\text{value}}⟩$.
Constraint: ${\mathbf{istc}}\left[0\right]=1$.
On entry, ${\mathbf{m}}=⟨\mathit{\text{value}}⟩$.
Constraint: ${\mathbf{m}}\ge 1$.
On entry, ${\mathbf{n}}=⟨\mathit{\text{value}}⟩$.
Constraint: ${\mathbf{n}}\ge 1$.
On entry, ${\mathbf{nnz}}=⟨\mathit{\text{value}}⟩$.
Constraint: ${\mathbf{nnz}}\ge 0$.
NE_INT_3
On entry, $i=⟨\mathit{\text{value}}⟩$, ${\mathbf{icol}}\left[i-1\right]=⟨\mathit{\text{value}}⟩$ and ${\mathbf{n}}=⟨\mathit{\text{value}}⟩$.
Constraint: if ${\mathbf{store}}=\mathrm{Nag_SparseNsym_StoreCS}$, then $1\le {\mathbf{icol}}\left[i-1\right]\le {\mathbf{n}}$.
On entry, $i=⟨\mathit{\text{value}}⟩$, ${\mathbf{irow}}\left[i-1\right]=⟨\mathit{\text{value}}⟩$ and ${\mathbf{m}}=⟨\mathit{\text{value}}⟩$.
Constraint: $1\le {\mathbf{irow}}\left[i-1\right]\le {\mathbf{m}}$.
On entry, $i=⟨\mathit{\text{value}}⟩$, ${\mathbf{istc}}\left[\mathit{i}-1\right]=⟨\mathit{\text{value}}⟩$ and ${\mathbf{istc}}\left[\mathit{i}\right]=⟨\mathit{\text{value}}⟩$.
Constraint: ${\mathbf{istc}}\left[\mathit{i}-1\right]\le {\mathbf{istc}}\left[\mathit{i}\right]$, for $\mathit{i}=1,2,\dots ,{\mathbf{n}}$
On entry, ${\mathbf{n}}=⟨\mathit{\text{value}}⟩$, ${\mathbf{istc}}\left[{\mathbf{n}}\right]=⟨\mathit{\text{value}}⟩$ and ${\mathbf{nnz}}=⟨\mathit{\text{value}}⟩$.
Constraint: ${\mathbf{istc}}\left[{\mathbf{n}}\right]={\mathbf{nnz}}+1$.
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 $⟨\mathit{\text{value}}⟩$ and column $⟨\mathit{\text{value}}⟩$.
NE_ZERO_COEFF
On entry, a zero entry has been found in row $⟨\mathit{\text{value}}⟩$ and column $⟨\mathit{\text{value}}⟩$.

Not applicable.

## 8Parallelism and Performance

f11zcc is not threaded in any implementation.

Note that the resulting matrix may have either rows or columns with no entries. If column $i$ has no entries then ${\mathbf{istc}}\left[i-1\right]={\mathbf{istc}}\left[i\right]$.
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).

## 10Example

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.
 $B=( 2.00 1.00 0 0 0 0 1.00 -1.00 4.00 0 1.00 0 ) and C=( 4.00 0 2.00 0 0 -1.00 0 1.00 0 0 0 2.00 ) .$

### 10.1Program Text

Program Text (f11zcce.c)

### 10.2Program Data

Program Data (f11zcce.d)

### 10.3Program Results

Program Results (f11zcce.r)