F11ZAF sorts the nonzero elements of a real sparse nonsymmetric matrix, represented in coordinate storage format.
F11ZAF takes a coordinate storage (CS) representation (see
Section 2.1.1 in the F11 Chapter Introduction) of a real
by
sparse nonsymmetric matrix
, 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, or the values may be summed. Any entries with zero values may optionally be removed.
F11ZAF also returns a pointer
ISTR to the starting address of each row in
. This can be used to construct a compressed column storage (CCS) representation of the matrix (see
Section 9).
None.
- 1: – INTEGERInput
-
On entry: , the order of the matrix .
Constraint:
.
- 2: – INTEGERInput/Output
-
On entry: the number of nonzero elements in the matrix .
Constraint:
.
On exit: the number of nonzero elements with unique row and column indices.
- 3: – REAL (KIND=nag_wp) arrayInput/Output
-
Note: the dimension of the array
A
must be at least
.
On entry: the nonzero elements of the matrix . 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: – INTEGER arrayInput/Output
-
Note: the dimension of the array
IROW
must be at least
.
On entry: the row indices corresponding to the nonzero elements supplied in the array
A.
Constraint:
, for .
On exit: the first
NNZ elements contain the row indices corresponding to the nonzero elements returned in the array
A.
- 5: – INTEGER arrayInput/Output
-
Note: the dimension of the array
ICOL
must be at least
.
On entry: the column indices corresponding to the nonzero elements supplied in the array
A.
Constraint:
, for .
On exit: the first
NNZ elements contain the row indices corresponding to the nonzero elements returned in the array
A.
- 6: – CHARACTER(1)Input
-
On entry: indicates how any nonzero elements with duplicate row and column indices are to be treated.
- The entries are removed.
- The relevant values in A are summed.
- The routine fails on detecting a duplicate, with .
Constraint:
, or .
- 7: – CHARACTER(1)Input
-
On entry: indicates how any elements with zero values in
A are to be treated.
- The entries are removed.
- The entries are kept.
- The routine fails on detecting a zero, with .
Constraint:
, or .
- 8: – INTEGER arrayOutput
-
On exit:
, for
, is the starting address in the arrays
A,
IROW and
ICOL of row
of the matrix
.
is the address of the last nonzero element in
plus one.
- 9: – INTEGER arrayWorkspace
-
- 10: – INTEGERInput/Output
-
On entry:
IFAIL must be set to
,
. If you are unfamiliar with this parameter you should refer to
Section 3.3 in the Essential Introduction 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
is recommended. Otherwise, if you are not familiar with this parameter, the recommended value is
.
When the value is used it is essential to test the value of IFAIL on exit.
On exit:
unless the routine detects an error or a warning has been flagged (see
Section 6).
If on entry
or
, explanatory error messages are output on the current error message unit (as defined by
X04AAF).
Not applicable.
Not applicable.
The time taken for a call to F11ZAF is proportional to
NNZ.
Note that the resulting matrix may have either rows or columns with no entries. If row has no entries then .
It is also possible to use this routine to convert between coordinate storage (CS) and compressed column storage (CCS) formats. To achieve this the CS storage format arrays
IROW and
ICOL must be interchanged in the call to F11ZAF. On exit from F11ZAF, the CCS representation of the matrix is then defined by arrays
A,
IROW and
ISTR. This is illustrated in
Section 10.
This example reads the CS representation of a real sparse matrix
, calls F11ZAF to reorder the nonzero elements, and outputs the original and the reordered representations. It then calls F11ZAF again with the alternative ordering, creating a CCS representation which is then passed to a routine that computes a matrix norm for that representation.