NAG Library Routine Document
F11MFF
1 Purpose
F11MFF solves a real sparse system of linear equations with multiple right-hand sides given an
factorization of the sparse matrix computed by
F11MEF.
2 Specification
SUBROUTINE F11MFF ( |
TRANS, N, IPRM, IL, LVAL, IU, UVAL, NRHS, B, LDB, IFAIL) |
INTEGER |
N, IPRM(7*N), IL(*), IU(*), NRHS, LDB, IFAIL |
REAL (KIND=nag_wp) |
LVAL(*), UVAL(*), B(LDB,*) |
CHARACTER(1) |
TRANS |
|
3 Description
F11MFF solves a real system of linear equations with multiple right-hand sides
or
, according to the value of the parameter
TRANS, where the matrix factorization
corresponds to an
decomposition of a sparse matrix stored in compressed column (Harwell–Boeing) format, as computed by
F11MEF.
In the above decomposition is a lower triangular sparse matrix with unit diagonal elements and is an upper triangular sparse matrix; and are permutation matrices.
4 References
None.
5 Parameters
- 1: – CHARACTER(1)Input
-
On entry: specifies whether
or
is solved.
- is solved.
- is solved.
Constraint:
or .
- 2: – INTEGERInput
-
On entry: , the order of the matrix .
Constraint:
.
- 3: – INTEGER arrayInput
-
On entry: the column permutation which defines
, the row permutation which defines
, plus associated data structures as computed by
F11MEF.
- 4: – INTEGER arrayInput
-
Note: the dimension of the array
IL
must be at least
as large as the dimension of the array of the same name in
F11MEF.
On entry: records the sparsity pattern of matrix
as computed by
F11MEF.
- 5: – REAL (KIND=nag_wp) arrayInput
-
Note: the dimension of the array
LVAL
must be at least
as large as the dimension of the array of the same name in
F11MEF.
On entry: records the nonzero values of matrix
and some nonzero values of matrix
as computed by
F11MEF.
- 6: – INTEGER arrayInput
-
Note: the dimension of the array
IU
must be at least
as large as the dimension of the array of the same name in
F11MEF.
On entry: records the sparsity pattern of matrix
as computed by
F11MEF.
- 7: – REAL (KIND=nag_wp) arrayInput
-
Note: the dimension of the array
UVAL
must be at least
as large as the dimension of the array of the same name in
F11MEF.
On entry: records some nonzero values of matrix
as computed by
F11MEF.
- 8: – INTEGERInput
-
On entry: , the number of right-hand sides in .
Constraint:
.
- 9: – REAL (KIND=nag_wp) arrayInput/Output
-
Note: the second dimension of the array
B
must be at least
.
On entry: the by right-hand side matrix .
On exit: the by solution matrix .
- 10: – INTEGERInput
-
On entry: the first dimension of the array
B as declared in the (sub)program from which F11MFF is called.
Constraint:
.
- 11: – 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).
6 Error Indicators and Warnings
If on entry
or
, 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 , |
or | , |
or | , |
or | . |
-
Ill-defined row permutation in array . Internal checks have revealed that the array is corrupted.
-
Ill-defined column permutations in array . Internal checks have revealed that the array is corrupted.
-
Unable to allocate required internal workspace.
An unexpected error has been triggered by this routine. Please
contact
NAG.
See
Section 3.8 in the Essential Introduction for further information.
Your licence key may have expired or may not have been installed correctly.
See
Section 3.7 in the Essential Introduction for further information.
Dynamic memory allocation failed.
See
Section 3.6 in the Essential Introduction for further information.
7 Accuracy
For each right-hand side vector
, the computed solution
is the exact solution of a perturbed system of equations
, where
is a modest linear function of
, and
is the
machine precision, when partial pivoting is used.
If
is the true solution, then the computed solution
satisfies a forward error bound of the form
where
.
Note that
can be much smaller than
, and
can be much larger (or smaller) than
.
Forward and backward error bounds can be computed by calling
F11MHF, and an estimate for
can be obtained by calling
F11MGF.
8 Parallelism and Performance
F11MFF is threaded by NAG for parallel execution in multithreaded implementations of the NAG Library.
F11MFF makes calls to BLAS and/or LAPACK routines, which may be threaded within the vendor library used by this implementation. Consult the documentation for the vendor library for further information.
Please consult the
X06 Chapter Introduction for information on how to control and interrogate the OpenMP environment used within this routine. Please also consult the
Users' Note for your implementation for any additional implementation-specific information.
F11MFF may be followed by a call to
F11MHF to refine the solution and return an error estimate.
10 Example
This example solves the system of equations
, where
Here
is nonsymmetric and must first be factorized by
F11MEF.
10.1 Program Text
Program Text (f11mffe.f90)
10.2 Program Data
Program Data (f11mffe.d)
10.3 Program Results
Program Results (f11mffe.r)