Apache Commons Math 3.6.1 · org.apache.commons.math3.analysis.solvers.BaseAbstractUnivariateSolver

Modifier and Type	Field and Description
private final double	absoluteAccuracy Absolute accuracy.
private static final double	DEFAULT_FUNCTION_VALUE_ACCURACY Default function value accuracy.
private static final double	DEFAULT_RELATIVE_ACCURACY Default relative accuracy.
private IntegerSequence.Incrementor	evaluations Evaluations counter.
private FUNC	function Function to solve.
private final double	functionValueAccuracy Function value accuracy.
private final double	relativeAccuracy Relative accuracy.
private double	searchMax Higher end of search interval.
private double	searchMin Lower end of search interval.
private double	searchStart Initial guess.

Access	Constructor and Description
protected	BaseAbstractUnivariateSolver(final double Maximum absolute error. absoluteAccuracy) Construct a solver with given absolute accuracy.
protected	BaseAbstractUnivariateSolver(final double Maximum relative error. relativeAccuracy, final double Maximum absolute error. absoluteAccuracy) Construct a solver with given accuracies.
protected	BaseAbstractUnivariateSolver(final double Maximum relative error. relativeAccuracy, final double Maximum absolute error. absoluteAccuracy, final double Maximum function value error. functionValueAccuracy) Construct a solver with given accuracies.

Method Summary

Modifier and Type	Method and Description
protected double	Returns: the objective function value at specified point. computeObjectiveValue(double Point at which the objective function must be evaluated. point) Compute the objective function value.
protected abstract double	Returns: the root. doSolve() Method for implementing actual optimization algorithms in derived classes.
public double	getAbsoluteAccuracy() Implements org.apache.commons.math3.analysis.solvers.BaseUnivariateSolver.getAbsoluteAccuracy. Get the absolute accuracy of the solver.
public int	getEvaluations() Implements org.apache.commons.math3.analysis.solvers.BaseUnivariateSolver.getEvaluations. Get the number of evaluations of the objective function.
public double	getFunctionValueAccuracy() Implements org.apache.commons.math3.analysis.solvers.BaseUnivariateSolver.getFunctionValueAccuracy. Get the function value accuracy of the solver.
public double	Returns: the higher end of the search interval. getMax()
public int	getMaxEvaluations() Implements org.apache.commons.math3.analysis.solvers.BaseUnivariateSolver.getMaxEvaluations. Get the maximum number of function evaluations.
public double	Returns: the lower end of the search interval. getMin()
public double	getRelativeAccuracy() Implements org.apache.commons.math3.analysis.solvers.BaseUnivariateSolver.getRelativeAccuracy. Get the relative accuracy of the solver.
public double	Returns: the initial guess. getStartValue()
protected void	incrementEvaluationCount() Increment the evaluation count by one.
protected boolean	Returns: `true` if the function values have opposite signs at the given points. isBracketing(final double Lower endpoint. lower, final double Upper endpoint. upper) Check whether the function takes opposite signs at the endpoints.
protected boolean	Returns: `true` if the arguments form an increasing sequence. isSequence(final double First number. start, final double Second number. mid, final double Third number. end) Check whether the arguments form a (strictly) increasing sequence.
protected void	setup(int Maximum number of evaluations. maxEval, FUNC Function to solve. f, double Lower bound for the interval. min, double Upper bound for the interval. max, double Start value to use. startValue) Prepare for computation.
public double	solve(int Maximum number of evaluations. maxEval, FUNC Function to solve. f, double Lower bound for the interval. min, double Upper bound for the interval. max, double Start value to use. startValue) Implements org.apache.commons.math3.analysis.solvers.BaseUnivariateSolver.solve. Solve for a zero in the given interval, start at `startValue`.
public double	solve(int Maximum number of evaluations. maxEval, FUNC Function to solve. f, double Lower bound for the interval. min, double Upper bound for the interval. max) Implements org.apache.commons.math3.analysis.solvers.BaseUnivariateSolver.solve. Solve for a zero root in the given interval.
public double	solve(int Maximum number of evaluations. maxEval, FUNC Function to solve. f, double Start value to use. startValue) Implements org.apache.commons.math3.analysis.solvers.BaseUnivariateSolver.solve. Solve for a zero in the vicinity of `startValue`.
protected void	verifyBracketing(final double Lower endpoint. lower, final double Upper endpoint. upper) Check that the endpoints specify an interval and the function takes opposite signs at the endpoints.
protected void	verifyInterval(final double Lower endpoint. lower, final double Upper endpoint. upper) Check that the endpoints specify an interval.
protected void	verifySequence(final double Lower endpoint. lower, final double Initial value. initial, final double Upper endpoint. upper) Check that `lower < initial < upper`.

Inherited from java.lang.Object:: clone equals finalize getClass hashCode notify notifyAll toString wait wait wait

absoluteAccuracy	back to summary
private final double absoluteAccuracy Absolute accuracy.

DEFAULT_FUNCTION_VALUE_ACCURACY	back to summary
private static final double DEFAULT_FUNCTION_VALUE_ACCURACY Default function value accuracy.

DEFAULT_RELATIVE_ACCURACY	back to summary
private static final double DEFAULT_RELATIVE_ACCURACY Default relative accuracy.

evaluations	back to summary
private IntegerSequence.Incrementor evaluations Evaluations counter.

function	back to summary
private FUNC function Function to solve.

functionValueAccuracy	back to summary
private final double functionValueAccuracy Function value accuracy.

relativeAccuracy	back to summary
private final double relativeAccuracy Relative accuracy.

searchMax	back to summary
private double searchMax Higher end of search interval.

searchMin	back to summary
private double searchMin Lower end of search interval.

searchStart	back to summary
private double searchStart Initial guess.

BaseAbstractUnivariateSolver	back to summary
protected BaseAbstractUnivariateSolver(final double absoluteAccuracy) Construct a solver with given absolute accuracy. Parameters absoluteAccuracy:double Maximum absolute error.

BaseAbstractUnivariateSolver	back to summary
protected BaseAbstractUnivariateSolver(final double relativeAccuracy, final double absoluteAccuracy) Construct a solver with given accuracies. Parameters relativeAccuracy:double Maximum relative error. absoluteAccuracy:double Maximum absolute error.

BaseAbstractUnivariateSolver	back to summary
protected BaseAbstractUnivariateSolver(final double relativeAccuracy, final double absoluteAccuracy, final double functionValueAccuracy) Construct a solver with given accuracies. Parameters relativeAccuracy:double Maximum relative error. absoluteAccuracy:double Maximum absolute error. functionValueAccuracy:double Maximum function value error.

Method Detail

computeObjectiveValue	back to summary
protected double computeObjectiveValue(double point) throws TooManyEvaluationsException Compute the objective function value. Parameters point:double Point at which the objective function must be evaluated. Returns:double the objective function value at specified point. Exceptions TooManyEvaluationsException: if the maximal number of evaluations is exceeded.

computeObjectiveValue

back to summary

protected double computeObjectiveValue(double point) throws TooManyEvaluationsException

Compute the objective function value.

Parameters

point:double: Point at which the objective function must be evaluated.

Returns:double

the objective function value at specified point.

Exceptions

TooManyEvaluationsException:: if the maximal number of evaluations is exceeded.

doSolve	back to summary
protected abstract double doSolve() throws TooManyEvaluationsException, NoBracketingException Method for implementing actual optimization algorithms in derived classes. Returns:double the root. Exceptions TooManyEvaluationsException: if the maximal number of evaluations is exceeded. NoBracketingException: if the initial search interval does not bracket a root and the solver requires it.

doSolve

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protected abstract double doSolve() throws TooManyEvaluationsException, NoBracketingException

Method for implementing actual optimization algorithms in derived classes.

Returns:double

the root.

Exceptions

TooManyEvaluationsException:: if the maximal number of evaluations is exceeded.
NoBracketingException:: if the initial search interval does not bracket a root and the solver requires it.

getAbsoluteAccuracy back to summary

getAbsoluteAccuracy	back to summary
public double getAbsoluteAccuracy() Implements org.apache.commons.math3.analysis.solvers.BaseUnivariateSolver.getAbsoluteAccuracy. Doc from org.apache.commons.math3.analysis.solvers.BaseUnivariateSolver.getAbsoluteAccuracy. Get the absolute accuracy of the solver. Solutions returned by the solver should be accurate to this tolerance, i.e., if ε is the absolute accuracy of the solver and `v` is a value returned by one of the `solve` methods, then a root of the function should exist somewhere in the interval (`v` - ε, `v` + ε). Returns:double the absolute accuracy.

public double getAbsoluteAccuracy()

Implements org.apache.commons.math3.analysis.solvers.BaseUnivariateSolver.getAbsoluteAccuracy.

Doc from org.apache.commons.math3.analysis.solvers.BaseUnivariateSolver.getAbsoluteAccuracy.

Get the absolute accuracy of the solver. Solutions returned by the solver should be accurate to this tolerance, i.e., if ε is the absolute accuracy of the solver and v is a value returned by one of the solve methods, then a root of the function should exist somewhere in the interval (v - ε, v + ε).

Returns:double: the absolute accuracy.

getEvaluations back to summary

getEvaluations	back to summary
public int getEvaluations() Implements org.apache.commons.math3.analysis.solvers.BaseUnivariateSolver.getEvaluations. Doc from org.apache.commons.math3.analysis.solvers.BaseUnivariateSolver.getEvaluations. Get the number of evaluations of the objective function. The number of evaluations corresponds to the last call to the `optimize` method. It is 0 if the method has not been called yet. Returns:int the number of evaluations of the objective function.

public int getEvaluations()

Implements org.apache.commons.math3.analysis.solvers.BaseUnivariateSolver.getEvaluations.

Doc from org.apache.commons.math3.analysis.solvers.BaseUnivariateSolver.getEvaluations.

Get the number of evaluations of the objective function. The number of evaluations corresponds to the last call to the optimize method. It is 0 if the method has not been called yet.

Returns:int: the number of evaluations of the objective function.

getFunctionValueAccuracy back to summary

getFunctionValueAccuracy	back to summary
public double getFunctionValueAccuracy() Implements org.apache.commons.math3.analysis.solvers.BaseUnivariateSolver.getFunctionValueAccuracy. Doc from org.apache.commons.math3.analysis.solvers.BaseUnivariateSolver.getFunctionValueAccuracy. Get the function value accuracy of the solver. If `v` is a value returned by the solver for a function `f`, then by contract, `\|f(v)\|` should be less than or equal to the function value accuracy configured for the solver. Returns:double the function value accuracy.

public double getFunctionValueAccuracy()

Implements org.apache.commons.math3.analysis.solvers.BaseUnivariateSolver.getFunctionValueAccuracy.

Doc from org.apache.commons.math3.analysis.solvers.BaseUnivariateSolver.getFunctionValueAccuracy.

Get the function value accuracy of the solver. If v is a value returned by the solver for a function f, then by contract, |f(v)| should be less than or equal to the function value accuracy configured for the solver.

Returns:double: the function value accuracy.

getMax	back to summary
public double getMax() Returns:double the higher end of the search interval.

getMaxEvaluations	back to summary
public int getMaxEvaluations() Implements org.apache.commons.math3.analysis.solvers.BaseUnivariateSolver.getMaxEvaluations. Doc from org.apache.commons.math3.analysis.solvers.BaseUnivariateSolver.getMaxEvaluations. Get the maximum number of function evaluations. Returns:int the maximum number of function evaluations.

getMaxEvaluations

back to summary

public int getMaxEvaluations()

Implements org.apache.commons.math3.analysis.solvers.BaseUnivariateSolver.getMaxEvaluations.

Doc from org.apache.commons.math3.analysis.solvers.BaseUnivariateSolver.getMaxEvaluations.

Get the maximum number of function evaluations.

Returns:int: the maximum number of function evaluations.

getMin	back to summary
public double getMin() Returns:double the lower end of the search interval.

getRelativeAccuracy back to summary

getRelativeAccuracy	back to summary
public double getRelativeAccuracy() Implements org.apache.commons.math3.analysis.solvers.BaseUnivariateSolver.getRelativeAccuracy. Doc from org.apache.commons.math3.analysis.solvers.BaseUnivariateSolver.getRelativeAccuracy. Get the relative accuracy of the solver. The contract for relative accuracy is the same as `getAbsoluteAccuracy()`, but using relative, rather than absolute error. If ρ is the relative accuracy configured for a solver and `v` is a value returned, then a root of the function should exist somewhere in the interval (`v` - ρ `v`, `v` + ρ `v`). Returns:double the relative accuracy.

public double getRelativeAccuracy()

Implements org.apache.commons.math3.analysis.solvers.BaseUnivariateSolver.getRelativeAccuracy.

Doc from org.apache.commons.math3.analysis.solvers.BaseUnivariateSolver.getRelativeAccuracy.

Get the relative accuracy of the solver. The contract for relative accuracy is the same as getAbsoluteAccuracy(), but using relative, rather than absolute error. If ρ is the relative accuracy configured for a solver and v is a value returned, then a root of the function should exist somewhere in the interval (v - ρ v, v + ρ v).

Returns:double: the relative accuracy.

getStartValue	back to summary
public double getStartValue() Returns:double the initial guess.

incrementEvaluationCount back to summary

incrementEvaluationCount	back to summary
protected void incrementEvaluationCount() throws TooManyEvaluationsException Increment the evaluation count by one. Method `computeObjectiveValue(double)` calls this method internally. It is provided for subclasses that do not exclusively use `computeObjectiveValue` to solve the function. See e.g. `AbstractUnivariateDifferentiableSolver`. Exceptions TooManyEvaluationsException: when the allowed number of function evaluations has been exhausted.

protected void incrementEvaluationCount() throws TooManyEvaluationsException

Increment the evaluation count by one. Method computeObjectiveValue(double) calls this method internally. It is provided for subclasses that do not exclusively use computeObjectiveValue to solve the function. See e.g. AbstractUnivariateDifferentiableSolver.

Exceptions

TooManyEvaluationsException:: when the allowed number of function evaluations has been exhausted.

isBracketing back to summary

isBracketing	back to summary
protected boolean isBracketing(final double lower, final double upper) Check whether the function takes opposite signs at the endpoints. Parameters lower:double Lower endpoint. upper:double Upper endpoint. Returns:boolean `true` if the function values have opposite signs at the given points.

protected boolean isBracketing(final double lower, final double upper)

Check whether the function takes opposite signs at the endpoints.

Parameters

lower:double: Lower endpoint.
upper:double: Upper endpoint.

Returns:boolean

true if the function values have opposite signs at the given points.

isSequence back to summary

isSequence	back to summary
protected boolean isSequence(final double start, final double mid, final double end) Check whether the arguments form a (strictly) increasing sequence. Parameters start:double First number. mid:double Second number. end:double Third number. Returns:boolean `true` if the arguments form an increasing sequence.

protected boolean isSequence(final double start, final double mid, final double end)

Check whether the arguments form a (strictly) increasing sequence.

Parameters

start:double: First number.
mid:double: Second number.
end:double: Third number.

Returns:boolean

true if the arguments form an increasing sequence.

setup back to summary

setup	back to summary
protected void setup(int maxEval, FUNC f, double min, double max, double startValue) throws NullArgumentException Prepare for computation. Subclasses must call this method if they override any of the `solve` methods. Parameters maxEval:int Maximum number of evaluations. f:FUNC Function to solve. min:double Lower bound for the interval. max:double Upper bound for the interval. startValue:double Start value to use. Exceptions NullArgumentException: if f is null

protected void setup(int maxEval, FUNC f, double min, double max, double startValue) throws NullArgumentException

Prepare for computation. Subclasses must call this method if they override any of the solve methods.

Parameters

maxEval:int: Maximum number of evaluations.
f:FUNC: Function to solve.
min:double: Lower bound for the interval.
max:double: Upper bound for the interval.
startValue:double: Start value to use.

Exceptions

NullArgumentException:: if f is null

solve back to summary

solve	back to summary
public double solve(int maxEval, FUNC f, double min, double max, double startValue) throws TooManyEvaluationsException, NoBracketingException Implements org.apache.commons.math3.analysis.solvers.BaseUnivariateSolver.solve. Doc from org.apache.commons.math3.analysis.solvers.BaseUnivariateSolver.solve. Solve for a zero in the given interval, start at `startValue`. A solver may require that the interval brackets a single zero root. Solvers that do require bracketing should be able to handle the case where one of the endpoints is itself a root. Parameters maxEval:int Maximum number of evaluations. f:FUNC Function to solve. min:double Lower bound for the interval. max:double Upper bound for the interval. startValue:double Start value to use. Returns:double a value where the function is zero. Exceptions TooManyEvaluationsException: if the allowed number of evaluations is exceeded.

public double solve(int maxEval, FUNC f, double min, double max, double startValue) throws TooManyEvaluationsException, NoBracketingException

Implements org.apache.commons.math3.analysis.solvers.BaseUnivariateSolver.solve.

Doc from org.apache.commons.math3.analysis.solvers.BaseUnivariateSolver.solve.

Solve for a zero in the given interval, start at startValue. A solver may require that the interval brackets a single zero root. Solvers that do require bracketing should be able to handle the case where one of the endpoints is itself a root.

Parameters

maxEval:int: Maximum number of evaluations.
f:FUNC: Function to solve.
min:double: Lower bound for the interval.
max:double: Upper bound for the interval.
startValue:double: Start value to use.

Returns:double

a value where the function is zero.

Exceptions

TooManyEvaluationsException:: if the allowed number of evaluations is exceeded.

solve	back to summary
public double solve(int maxEval, FUNC f, double min, double max) Implements org.apache.commons.math3.analysis.solvers.BaseUnivariateSolver.solve. Doc from org.apache.commons.math3.analysis.solvers.BaseUnivariateSolver.solve. Solve for a zero root in the given interval. A solver may require that the interval brackets a single zero root. Solvers that do require bracketing should be able to handle the case where one of the endpoints is itself a root. Parameters maxEval:int Maximum number of evaluations. f:FUNC Function to solve. min:double Lower bound for the interval. max:double Upper bound for the interval. Returns:double a value where the function is zero.

solve

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public double solve(int maxEval, FUNC f, double min, double max)

Implements org.apache.commons.math3.analysis.solvers.BaseUnivariateSolver.solve.

Doc from org.apache.commons.math3.analysis.solvers.BaseUnivariateSolver.solve.

Solve for a zero root in the given interval. A solver may require that the interval brackets a single zero root. Solvers that do require bracketing should be able to handle the case where one of the endpoints is itself a root.

Parameters

maxEval:int: Maximum number of evaluations.
f:FUNC: Function to solve.
min:double: Lower bound for the interval.
max:double: Upper bound for the interval.

Returns:double

a value where the function is zero.

solve back to summary

solve	back to summary
public double solve(int maxEval, FUNC f, double startValue) throws TooManyEvaluationsException, NoBracketingException Implements org.apache.commons.math3.analysis.solvers.BaseUnivariateSolver.solve. Doc from org.apache.commons.math3.analysis.solvers.BaseUnivariateSolver.solve. Solve for a zero in the vicinity of `startValue`. Parameters maxEval:int Maximum number of evaluations. f:FUNC Function to solve. startValue:double Start value to use. Returns:double a value where the function is zero. Exceptions TooManyEvaluationsException: if the allowed number of evaluations is exceeded.

public double solve(int maxEval, FUNC f, double startValue) throws TooManyEvaluationsException, NoBracketingException

Implements org.apache.commons.math3.analysis.solvers.BaseUnivariateSolver.solve.

Doc from org.apache.commons.math3.analysis.solvers.BaseUnivariateSolver.solve.

Solve for a zero in the vicinity of startValue.

Parameters

maxEval:int: Maximum number of evaluations.
f:FUNC: Function to solve.
startValue:double: Start value to use.

Returns:double

a value where the function is zero.

Exceptions

TooManyEvaluationsException:: if the allowed number of evaluations is exceeded.

verifyBracketing	back to summary
protected void verifyBracketing(final double lower, final double upper) throws NullArgumentException, NoBracketingException Check that the endpoints specify an interval and the function takes opposite signs at the endpoints. Parameters lower:double Lower endpoint. upper:double Upper endpoint. Exceptions NullArgumentException: if the function has not been set. NoBracketingException: if the function has the same sign at the endpoints.

verifyBracketing

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protected void verifyBracketing(final double lower, final double upper) throws NullArgumentException, NoBracketingException

Check that the endpoints specify an interval and the function takes opposite signs at the endpoints.

Parameters

lower:double: Lower endpoint.
upper:double: Upper endpoint.

Exceptions

NullArgumentException:: if the function has not been set.
NoBracketingException:: if the function has the same sign at the endpoints.

verifyInterval back to summary

verifyInterval	back to summary
protected void verifyInterval(final double lower, final double upper) throws NumberIsTooLargeException Check that the endpoints specify an interval. Parameters lower:double Lower endpoint. upper:double Upper endpoint. Exceptions NumberIsTooLargeException: if `lower >= upper`.

protected void verifyInterval(final double lower, final double upper) throws NumberIsTooLargeException

Check that the endpoints specify an interval.

Parameters

lower:double: Lower endpoint.
upper:double: Upper endpoint.

Exceptions

NumberIsTooLargeException:: if lower >= upper.

verifySequence back to summary

verifySequence	back to summary
protected void verifySequence(final double lower, final double initial, final double upper) throws NumberIsTooLargeException Check that `lower < initial < upper`. Parameters lower:double Lower endpoint. initial:double Initial value. upper:double Upper endpoint. Exceptions NumberIsTooLargeException: if `lower >= initial` or `initial >= upper`.

protected void verifySequence(final double lower, final double initial, final double upper) throws NumberIsTooLargeException

Check that lower < initial < upper.

Parameters

lower:double: Lower endpoint.
initial:double: Initial value.
upper:double: Upper endpoint.

Exceptions

NumberIsTooLargeException:: if lower >= initial or initial >= upper.

public abstract Class BaseAbstractUnivariateSolver<FUNC extends UnivariateFunction>

Field Summary

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Field Detail

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