Class ConjugateGradient
This is an implementation of the conjugate gradient method for
RealLinearOperator
. It follows closely the template by Barrett et al. (1994) (figure 2.5). The linear system at
hand is A · x = b, and the residual is r = b - A · x.
Default stopping criterion
A default stopping criterion is implemented. The iterations stop when || r || ≤ δ || b ||, where b is the right-hand side vector, r the current estimate of the residual, and δ a user-specified tolerance. It should be noted that r is the so-called updated residual, which might differ from the true residual due to rounding-off errors (see e.g. Strakos and Tichy, 2002).
Iteration count
In the present context, an iteration should be understood as one evaluation of the matrix-vector product A · x. The initialization phase therefore counts as one iteration.
Besides standard MathIllegalArgumentException
, this class might throw
MathIllegalArgumentException
if the linear operator or
the preconditioner are not positive definite.
- key
"operator"
points to the offending linear operator, say L, - key
"vector"
points to the offending vector, say x, such that xT · L · x < 0.
References
- Barret et al. (1994)
- R. Barrett, M. Berry, T. F. Chan, J. Demmel, J. M. Donato, J. Dongarra, V. Eijkhout, R. Pozo, C. Romine and H. Van der Vorst, Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods, SIAM
- Strakos and Tichy (2002)
- Z. Strakos and P. Tichy, On error estimation in the conjugate gradient method and why it works in finite precision computations, Electronic Transactions on Numerical Analysis 13: 56-80, 2002
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Field Summary
Modifier and TypeFieldDescriptionstatic final String
Key for the exception context.static final String
Key for the exception context. -
Constructor Summary
ConstructorDescriptionConjugateGradient
(int maxIterations, double delta, boolean check) Creates a new instance of this class, with default stopping criterion.ConjugateGradient
(IterationManager manager, double delta, boolean check) Creates a new instance of this class, with default stopping criterion and custom iteration manager. -
Method Summary
Modifier and TypeMethodDescriptionfinal boolean
Returnstrue
if positive-definiteness should be checked for both matrix and preconditioner.solveInPlace
(RealLinearOperator a, RealLinearOperator m, RealVector b, RealVector x0) Returns an estimate of the solution to the linear system A · x = b.Methods inherited from class org.hipparchus.linear.PreconditionedIterativeLinearSolver
checkParameters, solve, solve, solve, solve, solveInPlace
Methods inherited from class org.hipparchus.linear.IterativeLinearSolver
checkParameters, getIterationManager
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Field Details
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OPERATOR
Key for the exception context.- See Also:
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VECTOR
Key for the exception context.- See Also:
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Constructor Details
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ConjugateGradient
public ConjugateGradient(int maxIterations, double delta, boolean check) Creates a new instance of this class, with default stopping criterion.- Parameters:
maxIterations
- the maximum number of iterationsdelta
- the δ parameter for the default stopping criterioncheck
-true
if positive definiteness of both matrix and preconditioner should be checked
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ConjugateGradient
public ConjugateGradient(IterationManager manager, double delta, boolean check) throws NullArgumentException Creates a new instance of this class, with default stopping criterion and custom iteration manager.- Parameters:
manager
- the custom iteration managerdelta
- the δ parameter for the default stopping criterioncheck
-true
if positive definiteness of both matrix and preconditioner should be checked- Throws:
NullArgumentException
- ifmanager
isnull
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Method Details
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shouldCheck
public final boolean shouldCheck()Returnstrue
if positive-definiteness should be checked for both matrix and preconditioner.- Returns:
true
if the tests are to be performed- Since:
- 1.4
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solveInPlace
public RealVector solveInPlace(RealLinearOperator a, RealLinearOperator m, RealVector b, RealVector x0) throws MathIllegalArgumentException, NullArgumentException, MathIllegalStateException Returns an estimate of the solution to the linear system A · x = b. The solution is computed in-place (initial guess is modified).- Specified by:
solveInPlace
in classPreconditionedIterativeLinearSolver
- Parameters:
a
- the linear operator A of the systemm
- the preconditioner, M (can benull
)b
- the right-hand side vectorx0
- the initial guess of the solution- Returns:
- a reference to
x0
(shallow copy) updated with the solution - Throws:
MathIllegalArgumentException
- ifa
orm
is not positive definiteNullArgumentException
- if one of the parameters isnull
MathIllegalStateException
- at exhaustion of the iteration count, unless a customcallback
has been set at construction of theIterationManager
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