NAG FL Interfacef11zcf (real_​rect_​sort)

1Purpose

f11zcf sorts the nonzero elements of a real sparse rectangular matrix, represented in coordinate storage or compressed column storage format.

2Specification

Fortran Interface
 Subroutine f11zcf ( m, n, nnz, a, irow, icol, istc, dup, zer,
 Integer, Intent (In) :: m, n, store Integer, Intent (Inout) :: nnz, irow(nnz), icol(nnz), istc(n+1), ifail Real (Kind=nag_wp), Intent (Inout) :: a(nnz) Character (1), Intent (In) :: dup, zer
#include <nag.h>
 void f11zcf_ (const Integer *m, const Integer *n, Integer *nnz, double a[], Integer irow[], Integer icol[], Integer istc[], const Integer *store, const char *dup, const char *zer, Integer *ifail, const Charlen length_dup, const Charlen length_zer)
The routine may be called by the names f11zcf or nagf_sparse_real_rect_sort.

3Description

f11zcf 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 $m$ by $n$ 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 f11zcf 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: $\mathbf{a}\left({\mathbf{nnz}}\right)$Real (Kind=nag_wp) array Input/Output
On entry: the nonzero elements of the matrix $A$. If ${\mathbf{store}}=1$, the elements may be in any order. If ${\mathbf{store}}=2$, 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 array 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 $\mathit{i}=1,2,\dots ,{\mathbf{nnz}}$.
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 array Input/Output
On entry: if ${\mathbf{store}}=1$, the column indices corresponding to the elements supplied in the array a.
If ${\mathbf{store}}=2$, icol need not be set.
Constraint: if ${\mathbf{store}}=1$, $1\le {\mathbf{icol}}\left(\mathit{i}\right)\le {\mathbf{n}}$, for $\mathit{i}=1,2,\dots ,{\mathbf{nnz}}$.
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 array Input/Output
On entry: if ${\mathbf{store}}=2$, the starting address of each column, as supplied in the array a.
If ${\mathbf{store}}=1$, istc need not be set.
Constraints:
if ${\mathbf{store}}=2$,
• ${\mathbf{istc}}\left(1\right)=1$;
• ${\mathbf{istc}}\left({\mathbf{n}}+1\right)={\mathbf{nnz}}+1$;
• ${\mathbf{istc}}\left(\mathit{i}\right)\le {\mathbf{istc}}\left(\mathit{i}+1\right)$, for $\mathit{i}=1,2,\dots ,{\mathbf{n}}$.
On exit: the starting address of each column, as returned in the array a. ${\mathbf{istc}}\left({\mathbf{n}}+1\right)$ is the address of the last element in a plus one.
8: $\mathbf{store}$Integer Input
On entry: indicates which storage format the matrix $A$ is represented with on entry.
${\mathbf{store}}=1$
$A$ is represented in coordinate storage (CS) format using a, irow and icol.
${\mathbf{store}}=2$
$A$ is represented in compressed column storage (CCS) format using a, irow and istc.
Constraint: ${\mathbf{store}}=1$ or $2$.
9: $\mathbf{dup}$Character(1) Input
On entry: indicates how elements in a with duplicate row and column indices are to be treated.
${\mathbf{dup}}=\text{'R'}$
Duplicate entries are removed, only the first entry is kept.
${\mathbf{dup}}=\text{'S'}$
The relevant values in a are summed.
${\mathbf{dup}}=\text{'F'}$
The routine fails with ${\mathbf{ifail}}={\mathbf{12}}$ on detecting a duplicate.
Constraint: ${\mathbf{dup}}=\text{'R'}$, $\text{'S'}$ or $\text{'F'}$.
10: $\mathbf{zer}$Character(1) Input
On entry: indicates how elements in a with zero values are to be treated.
${\mathbf{zer}}=\text{'R'}$
The entries are removed.
${\mathbf{zer}}=\text{'K'}$
The entries are kept.
${\mathbf{zer}}=\text{'F'}$
The routine fails with ${\mathbf{ifail}}={\mathbf{13}}$ on detecting a zero.
Constraint: ${\mathbf{zer}}=\text{'R'}$, $\text{'K'}$ or $\text{'F'}$.
11: $\mathbf{ifail}$Integer Input/Output
On entry: ifail must be set to $0$, . If you are unfamiliar with this argument you should refer to Section 4 in the Introduction to the NAG Library FL Interface for details.
For environments where it might be inappropriate to halt program execution when an error is detected, the value is recommended. If the output of error messages is undesirable, then the value $1$ is recommended. Otherwise, if you are not familiar with this argument, the recommended value is $0$. When the value is used it is essential to test the value of ifail on exit.
On exit: ${\mathbf{ifail}}={\mathbf{0}}$ unless the routine detects an error or a warning has been flagged (see Section 6).

6Error Indicators and Warnings

If on entry ${\mathbf{ifail}}=0$ or $-1$, explanatory error messages are output on the current error message unit (as defined by x04aaf).
Errors or warnings detected by the routine:
${\mathbf{ifail}}=1$
On entry, ${\mathbf{m}}=〈\mathit{\text{value}}〉$.
Constraint: ${\mathbf{m}}\ge 1$.
${\mathbf{ifail}}=2$
On entry, ${\mathbf{n}}=〈\mathit{\text{value}}〉$.
Constraint: ${\mathbf{n}}\ge 1$.
${\mathbf{ifail}}=3$
On entry, ${\mathbf{nnz}}=〈\mathit{\text{value}}〉$.
Constraint: ${\mathbf{nnz}}\ge 0$.
${\mathbf{ifail}}=4$
On entry, ${\mathbf{store}}=〈\mathit{\text{value}}〉$.
Constraint: ${\mathbf{store}}=1$ or $2$.
${\mathbf{ifail}}=5$
On entry, ${\mathbf{dup}}=〈\mathit{\text{value}}〉$.
Constraint: ${\mathbf{dup}}=\text{'R'}$, $\text{'S'}$ or $\text{'F'}$.
${\mathbf{ifail}}=6$
On entry, ${\mathbf{zer}}=〈\mathit{\text{value}}〉$.
Constraint: ${\mathbf{zer}}=\text{'R'}$, $\text{'K'}$ or $\text{'F'}$.
${\mathbf{ifail}}=7$
On entry, $i=〈\mathit{\text{value}}〉$, ${\mathbf{irow}}\left(i\right)=〈\mathit{\text{value}}〉$ and ${\mathbf{m}}=〈\mathit{\text{value}}〉$.
Constraint: $1\le {\mathbf{irow}}\left(i\right)\le {\mathbf{m}}$.
${\mathbf{ifail}}=8$
On entry, $i=〈\mathit{\text{value}}〉$, ${\mathbf{icol}}\left(i\right)=〈\mathit{\text{value}}〉$ and ${\mathbf{n}}=〈\mathit{\text{value}}〉$.
Constraint: if ${\mathbf{store}}=1$, then $1\le {\mathbf{icol}}\left(i\right)\le {\mathbf{n}}$.
${\mathbf{ifail}}=9$
On entry, ${\mathbf{istc}}\left(1\right)=〈\mathit{\text{value}}〉$.
Constraint: ${\mathbf{istc}}\left(1\right)=1$.
${\mathbf{ifail}}=10$
On entry, $i=〈\mathit{\text{value}}〉$, ${\mathbf{istc}}\left(\mathit{i}\right)=〈\mathit{\text{value}}〉$ and ${\mathbf{istc}}\left(\mathit{i}+1\right)=〈\mathit{\text{value}}〉$.
Constraint: ${\mathbf{istc}}\left(\mathit{i}\right)\le {\mathbf{istc}}\left(\mathit{i}+1\right)$, for $\mathit{i}=1,2,\dots ,{\mathbf{n}}$
${\mathbf{ifail}}=11$
On entry, ${\mathbf{n}}=〈\mathit{\text{value}}〉$, ${\mathbf{istc}}\left({\mathbf{n}}+1\right)=〈\mathit{\text{value}}〉$ and ${\mathbf{nnz}}=〈\mathit{\text{value}}〉$.
Constraint: ${\mathbf{istc}}\left({\mathbf{n}}+1\right)={\mathbf{nnz}}+1$.
${\mathbf{ifail}}=12$
On entry, a duplicate entry has been found in row $〈\mathit{\text{value}}〉$ and column $〈\mathit{\text{value}}〉$.
${\mathbf{ifail}}=13$
On entry, a zero entry has been found in row $〈\mathit{\text{value}}〉$ and column $〈\mathit{\text{value}}〉$.
${\mathbf{ifail}}=-99$
See Section 7 in the Introduction to the NAG Library FL Interface for further information.
${\mathbf{ifail}}=-399$
Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library FL Interface for further information.
${\mathbf{ifail}}=-999$
Dynamic memory allocation failed.
See Section 9 in the Introduction to the NAG Library FL Interface for further information.

Not applicable.

8Parallelism and Performance

f11zcf 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 ${\mathbf{istc}}\left(i\right)={\mathbf{istc}}\left(i+1\right)$.
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 f11zcf.
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 f11zcf, specifying that duplicates should be summed. This functionality is illustrated in Section 10.
This routine can be used to convert between CS and CCS formats. Use either format to pass $A$ into f11zcf, 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). This is illustrated in Section 10.

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 f11zcf.
 $B= 2.00 1.00 0 0 0 0 1.00 -1.00 4.00 0 1.00 0 and C= 4.00 0 2.00 0 0 -1.00 0 1.00 0 0 0 2.00 .$

10.1Program Text

Program Text (f11zcfe.f90)

10.2Program Data

Program Data (f11zcfe.d)

10.3Program Results

Program Results (f11zcfe.r)