NAG Library Routine Document
F11XEF computes a matrix-vector product involving a real sparse symmetric matrix stored in symmetric coordinate storage format.
||N, NNZ, IROW(NNZ), ICOL(NNZ), IFAIL
||A(NNZ), X(N), Y(N)
F11XEF computes the matrix-vector product
symmetric sparse matrix, of arbitrary sparsity pattern, stored in symmetric coordinate storage (SCS) format (see Section 2.1.2
in the F11 Chapter Introduction). The array A
stores all nonzero elements in the lower triangular part of
, while arrays IROW
store the corresponding row and column indices respectively.
It is envisaged that a common use of F11XEF will be to compute the matrix-vector product required in the application of F11GEF
to sparse symmetric linear systems. An illustration of this usage appears in F11JDF
- 1: N – INTEGERInput
On entry: , the order of the matrix .
- 2: NNZ – INTEGERInput
On entry: the number of nonzero elements in the lower triangular part of .
- 3: A(NNZ) – REAL (KIND=nag_wp) arrayInput
: the nonzero elements in the lower triangular part of the matrix
, ordered by increasing row index, and by increasing column index within each row. Multiple entries for the same row and column indices are not permitted. The routine F11ZBF
may be used to order the elements in this way.
- 4: IROW(NNZ) – INTEGER arrayInput
- 5: ICOL(NNZ) – INTEGER arrayInput
: the row and column indices of the nonzero elements supplied in array A
must satisfy these constraints (which may be imposed by a call to F11ZBF
- and , for ;
- or and , for .
- 6: CHECK – CHARACTER(1)Input
: specifies whether or not the SCS representation of the matrix
, values of N
should be checked.
- Checks are carried out on the values of N, NNZ, IROW and ICOL.
- None of these checks are carried out.
- 7: X(N) – REAL (KIND=nag_wp) arrayInput
On entry: the vector .
- 8: Y(N) – REAL (KIND=nag_wp) arrayOutput
On exit: the vector .
- 9: IFAIL – INTEGERInput/Output
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.
unless the routine detects an error or a warning has been flagged (see Section 6
6 Error Indicators and Warnings
If on entry
, explanatory error messages are output on the current error message unit (as defined by X04AAF
Errors or warnings detected by the routine:
|On entry,|| or .|
On entry, the arrays IROW
fail to satisfy the following constraints:
- and , for ;
- or and , for .
Therefore a nonzero element has been supplied which does not lie in the lower triangular part of
, is out of order, or has duplicate row and column indices. Call F11ZBF
to reorder and sum or remove duplicates.
The computed vector
satisfies the error bound
is a modest linear function of
is the machine precision
The time taken for a call to F11XEF is proportional to NNZ
It is expected that a common use of F11XEF will be to compute the matrix-vector product required in the application of F11GEF
to sparse symmetric linear systems. In this situation F11XEF is likely to be called many times with the same matrix
. In the interests of both reliability and efficiency you are recommended to set
for the first of such calls, and to set
for all subsequent calls.
This example reads in a symmetric positive definite sparse matrix and a vector . It then calls F11XEF to compute the matrix-vector product .
9.1 Program Text
Program Text (f11xefe.f90)
9.2 Program Data
Program Data (f11xefe.d)
9.3 Program Results
Program Results (f11xefe.r)