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java.lang.Objectorg.apache.commons.math3.analysis.solvers.UnivariateSolverUtils
public class UnivariateSolverUtils
Utility routines for UnivariateSolver objects.
| Method Summary | |
|---|---|
static double[] |
bracket(UnivariateFunction function,
double initial,
double lowerBound,
double upperBound)
This method attempts to find two values a and b satisfying lowerBound <= a < initial < b <= upperBound
f(a) * f(b) < 0
If f is continuous on [a,b], this means that a
and b bracket a root of f. |
static double[] |
bracket(UnivariateFunction function,
double initial,
double lowerBound,
double upperBound,
int maximumIterations)
This method attempts to find two values a and b satisfying lowerBound <= a < initial < b <= upperBound
f(a) * f(b) <= 0
If f is continuous on [a,b], this means that a
and b bracket a root of f. |
static double |
forceSide(int maxEval,
UnivariateFunction f,
BracketedUnivariateSolver<UnivariateFunction> bracketing,
double baseRoot,
double min,
double max,
AllowedSolution allowedSolution)
Force a root found by a non-bracketing solver to lie on a specified side, as if the solver was a bracketing one. |
static boolean |
isBracketing(UnivariateFunction function,
double lower,
double upper)
Check whether the interval bounds bracket a root. |
static boolean |
isSequence(double start,
double mid,
double end)
Check whether the arguments form a (strictly) increasing sequence. |
static double |
midpoint(double a,
double b)
Compute the midpoint of two values. |
static double |
solve(UnivariateFunction function,
double x0,
double x1)
Convenience method to find a zero of a univariate real function. |
static double |
solve(UnivariateFunction function,
double x0,
double x1,
double absoluteAccuracy)
Convenience method to find a zero of a univariate real function. |
static void |
verifyBracketing(UnivariateFunction function,
double lower,
double upper)
Check that the endpoints specify an interval and the end points bracket a root. |
static void |
verifyInterval(double lower,
double upper)
Check that the endpoints specify an interval. |
static void |
verifySequence(double lower,
double initial,
double upper)
Check that lower < initial < upper. |
| Methods inherited from class java.lang.Object |
|---|
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait |
| Method Detail |
|---|
public static double solve(UnivariateFunction function,
double x0,
double x1)
throws NullArgumentException,
NoBracketingException
function - Function.x0 - Lower bound for the interval.x1 - Upper bound for the interval.
NoBracketingException - if the function has the same sign at the
endpoints.
NullArgumentException - if function is null.
public static double solve(UnivariateFunction function,
double x0,
double x1,
double absoluteAccuracy)
throws NullArgumentException,
NoBracketingException
function - Function.x0 - Lower bound for the interval.x1 - Upper bound for the interval.absoluteAccuracy - Accuracy to be used by the solver.
NoBracketingException - if the function has the same sign at the
endpoints.
NullArgumentException - if function is null.
public static double forceSide(int maxEval,
UnivariateFunction f,
BracketedUnivariateSolver<UnivariateFunction> bracketing,
double baseRoot,
double min,
double max,
AllowedSolution allowedSolution)
throws NoBracketingException
maxEval - maximal number of new evaluations of the function
(evaluations already done for finding the root should have already been subtracted
from this number)f - function to solvebracketing - bracketing solver to use for shifting the rootbaseRoot - original root found by a previous non-bracketing solvermin - minimal bound of the search intervalmax - maximal bound of the search intervalallowedSolution - the kind of solutions that the root-finding algorithm may
accept as solutions.
NoBracketingException - if the function has the same sign at the
endpoints.
public static double[] bracket(UnivariateFunction function,
double initial,
double lowerBound,
double upperBound)
throws NullArgumentException,
NotStrictlyPositiveException,
NoBracketingException
lowerBound <= a < initial < b <= upperBound f(a) * f(b) < 0 [a,b], this means that a
and b bracket a root of f.
The algorithm starts by setting
a := initial -1; b := initial +1, examines the value of the
function at a and b and keeps moving
the endpoints out by one unit each time through a loop that terminates
when one of the following happens:
f(a) * f(b) < 0 -- success! a = lower and b = upper
-- NoBracketingException Integer.MAX_VALUE iterations elapse
-- NoBracketingException
Note: this method can take
Integer.MAX_VALUE iterations to throw a
ConvergenceException. Unless you are confident that there
is a root between lowerBound and upperBound
near initial, it is better to use
bracket(UnivariateFunction, double, double, double, int),
explicitly specifying the maximum number of iterations.
function - Function.initial - Initial midpoint of interval being expanded to
bracket a root.lowerBound - Lower bound (a is never lower than this value)upperBound - Upper bound (b never is greater than this
value).
NoBracketingException - if a root cannot be bracketted.
NotStrictlyPositiveException - if maximumIterations <= 0.
NullArgumentException - if function is null.
public static double[] bracket(UnivariateFunction function,
double initial,
double lowerBound,
double upperBound,
int maximumIterations)
throws NullArgumentException,
NotStrictlyPositiveException,
NoBracketingException
lowerBound <= a < initial < b <= upperBound f(a) * f(b) <= 0 [a,b], this means that a
and b bracket a root of f.
The algorithm starts by setting
a := initial -1; b := initial +1, examines the value of the
function at a and b and keeps moving
the endpoints out by one unit each time through a loop that terminates
when one of the following happens:
f(a) * f(b) <= 0 -- success! a = lower and b = upper
-- NoBracketingException maximumIterations iterations elapse
-- NoBracketingException
function - Function.initial - Initial midpoint of interval being expanded to
bracket a root.lowerBound - Lower bound (a is never lower than this value).upperBound - Upper bound (b never is greater than this
value).maximumIterations - Maximum number of iterations to perform
NoBracketingException - if the algorithm fails to find a and b
satisfying the desired conditions.
NotStrictlyPositiveException - if maximumIterations <= 0.
NullArgumentException - if function is null.
public static double midpoint(double a,
double b)
a - first value.b - second value.
public static boolean isBracketing(UnivariateFunction function,
double lower,
double upper)
throws NullArgumentException
function - Function.lower - Lower endpoint.upper - Upper endpoint.
true if the function values have opposite signs at the
given points.
NullArgumentException - if function is null.
public static boolean isSequence(double start,
double mid,
double end)
start - First number.mid - Second number.end - Third number.
true if the arguments form an increasing sequence.
public static void verifyInterval(double lower,
double upper)
throws NumberIsTooLargeException
lower - Lower endpoint.upper - Upper endpoint.
NumberIsTooLargeException - if lower >= upper.
public static void verifySequence(double lower,
double initial,
double upper)
throws NumberIsTooLargeException
lower < initial < upper.
lower - Lower endpoint.initial - Initial value.upper - Upper endpoint.
NumberIsTooLargeException - if lower >= initial or
initial >= upper.
public static void verifyBracketing(UnivariateFunction function,
double lower,
double upper)
throws NullArgumentException,
NoBracketingException
function - Function.lower - Lower endpoint.upper - Upper endpoint.
NoBracketingException - if the function has the same sign at the
endpoints.
NullArgumentException - if function is null.
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