NAG Library Routine Document

f11zbf (real_symm_sort)

1
Purpose

f11zbf sorts the nonzero elements of a real sparse symmetric matrix, represented in symmetric coordinate storage format.

2
Specification

Fortran Interface
Subroutine f11zbf ( n, nnz, a, irow, icol, dup, zer, istr, iwork, ifail)
Integer, Intent (In):: n
Integer, Intent (Inout):: nnz, irow(*), icol(*), ifail
Integer, Intent (Out):: istr(n+1), iwork(n)
Real (Kind=nag_wp), Intent (Inout):: a(*)
Character (1), Intent (In):: dup, zer
C Header Interface
#include <nagmk26.h>
void  f11zbf_ (const Integer *n, Integer *nnz, double a[], Integer irow[], Integer icol[], const char *dup, const char *zer, Integer istr[], Integer iwork[], Integer *ifail, const Charlen length_dup, const Charlen length_zer)

3
Description

f11zbf takes a symmetric coordinate storage (SCS) representation (see Section 2.1.2 in the F11 Chapter Introduction) of a real n by n sparse symmetric 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.
f11zbf also returns a pointer array istr to the starting address of each row in A.

4
References

None.

5
Arguments

1:     n – IntegerInput
On entry: n, the order of the matrix A.
Constraint: n1.
2:     nnz – IntegerInput/Output
On entry: the number of elements supplied in the array a.
Constraint: nnz0.
On exit: the number of elements with unique row and column indices.
3:     a* – Real (Kind=nag_wp) arrayInput/Output
Note: the dimension of the array a must be at least max1,nnz.
On entry: the nonzero elements of the lower triangular part of the real 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 lower triangular 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* – Integer arrayInput/Output
Note: the dimension of the array irow must be at least max1,nnz.
On entry: the row indices corresponding to the elements supplied in the array a.
Constraint: 1irowin, for i=1,2,,nnz.
On exit: the first nnz elements contain the row indices corresponding to the elements returned in the array a.
5:     icol* – Integer arrayInput/Output
Note: the dimension of the array icol must be at least max1,nnz.
On entry: the column indices corresponding to the elements supplied in the array a.
Constraint: 1icoliirowi, for i=1,2,,nnz.
On exit: the first nnz elements contain the column indices corresponding to the elements returned in the array a.
6:     dup – Character(1)Input
On entry: indicates how elements in a with duplicate row and column indices are to be treated.
dup='R'
Duplicate entries are removed, only the first entry is kept.
dup='S'
The relevant values in a are summed.
dup='F'
The routine fails with ifail=3 on detecting a duplicate.
Constraint: dup='R', 'S' or 'F'.
7:     zer – Character(1)Input
On entry: indicates how elements in a with zero values are to be treated.
zer='R'
The entries are removed.
zer='K'
The entries are kept.
zer='F'
The routine fails with ifail=4 on detecting a zero.
Constraint: zer='R', 'K' or 'F'.
8:     istrn+1 – Integer arrayOutput
On exit: istri, for i=1,2,,n, is the starting address in the arrays a, irow and icol of row i of the matrix A. istrn+1 is the address of the last element in a plus one.
9:     iworkn – Integer arrayWorkspace
10:   ifail – IntegerInput/Output
On entry: ifail must be set to 0, -1 or 1. If you are unfamiliar with this argument you should refer to Section 3.4 in How to Use the NAG Library and its Documentation for details.
For environments where it might be inappropriate to halt program execution when an error is detected, the value -1 or 1 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 -1 or 1 is used it is essential to test the value of ifail on exit.
On exit: ifail=0 unless the routine detects an error or a warning has been flagged (see Section 6).

6
Error Indicators and Warnings

If on entry 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:
ifail=1
On entry, dup=value.
Constraint: dup='R', 'S' or 'F'.
On entry, n=value.
Constraint: n1.
On entry, nnz=value.
Constraint: nnz0.
On entry, zer=value.
Constraint: zer='R', 'K' or 'F'.
ifail=2
On entry, i=value, icoli=value and n=value.
Constraint: icoli1 and icolin.
On entry, i=value, irowi=value and n=value.
Constraint: irowi1 and irowin.
ifail=3
On entry, a duplicate entry has been found in row I and column J: I=value, J=value.
ifail=4
On entry, a zero entry has been found in row I and column J: I=value, J=value.
ifail=-99
An unexpected error has been triggered by this routine. Please contact NAG.
See Section 3.9 in How to Use the NAG Library and its Documentation for further information.
ifail=-399
Your licence key may have expired or may not have been installed correctly.
See Section 3.8 in How to Use the NAG Library and its Documentation for further information.
ifail=-999
Dynamic memory allocation failed.
See Section 3.7 in How to Use the NAG Library and its Documentation for further information.

7
Accuracy

Not applicable.

8
Parallelism and Performance

f11zbf is not threaded in any implementation.

9
Further Comments

The time taken for a call to f11zbf 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 istri=istri+1.
Two sparse matrices can be added by concatenating the three pairs of SCS format arrays, representing the two matrices, and passing these new arrays to f11zbf, specifying that duplicates should be summed. This functionality is illustrated in Section 10 in f11zaf.

10
Example

This example reads the SCS representation of a real sparse symmetric matrix A, calls f11zbf to reorder the nonzero elements, and outputs the original and the reordered representations.

10.1
Program Text

Program Text (f11zbfe.f90)

10.2
Program Data

Program Data (f11zbfe.d)

10.3
Program Results

Program Results (f11zbfe.r)