UnivariateSolverUtils (patrius 4.5.1 API)

java.lang.Object
- fr.cnes.sirius.patrius.math.analysis.solver.UnivariateSolverUtils

```
public final class UnivariateSolverUtils
extends Object
```
Utility routines for UnivariateSolver objects.

Version:

$Id: UnivariateSolverUtils.java 18108 2017-10-04 06:45:27Z bignon $

Method Summary

All Methods Static Methods Concrete Methods
Modifier and Type	Method and Description
`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`	`verifyIntervalStrict(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`.
`static void`	`verifySequenceStrict(double lower, double initial, double upper)` Check that `lower <= initial <= upper & lower < upper`.

Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

- Method Detail
  - solve
```
public static double solve(UnivariateFunction function,
                           double x0,
                           double x1)
```
    Convenience method to find a zero of a univariate real function. A default solver is used.
    
    Parameters:
    
    function - Function.
    
    x0 - Lower bound for the interval.
    
    x1 - Upper bound for the interval.
    
    Returns:
    
    a value where the function is zero.
    
    Throws:
    
    NoBracketingException - if the function has the same sign at the endpoints.
    
    NullArgumentException - if function is null.
  - solve
```
public static double solve(UnivariateFunction function,
                           double x0,
                           double x1,
                           double absoluteAccuracy)
```
    Convenience method to find a zero of a univariate real function. A default solver is used.
    
    Parameters:
    
    function - Function.
    
    x0 - Lower bound for the interval.
    
    x1 - Upper bound for the interval.
    
    absoluteAccuracy - Accuracy to be used by the solver.
    
    Returns:
    
    a value where the function is zero.
    
    Throws:
    
    NoBracketingException - if the function has the same sign at the endpoints.
    
    NullArgumentException - if function is null.
  - forceSide
```
public 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.
    
    Parameters:
    
    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 solve
    
    bracketing - bracketing solver to use for shifting the root
    
    baseRoot - original root found by a previous non-bracketing solver
    
    min - minimal bound of the search interval
    
    max - maximal bound of the search interval
    
    allowedSolution - the kind of solutions that the root-finding algorithm may accept as solutions.
    
    Returns:
    
    a root approximation, on the specified side of the exact root
    
    Throws:
    
    NoBracketingException - if the function has the same sign at the endpoints.
  - bracket
```
public 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.
    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.
    Parameters:
    
    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).
    
    Returns:
    
    a two-element array holding a and b.
    
    Throws:
    
    NoBracketingException - if a root cannot be bracketted.
    
    NotStrictlyPositiveException - if maximumIterations <= 0.
    
    NullArgumentException - if function is null.
  - bracket
```
public 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.
    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
    Parameters:
    
    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
    
    Returns:
    
    a two element array holding a and b.
    
    Throws:
    
    NoBracketingException - if the algorithm fails to find a and b satisfying the desired conditions.
    
    NotStrictlyPositiveException - if maximumIterations <= 0.
    
    NullArgumentException - if function is null.
  - midpoint
```
public static double midpoint(double a,
                              double b)
```
    Compute the midpoint of two values.
    
    Parameters:
    
    a - first value.
    
    b - second value.
    
    Returns:
    
    the midpoint.
  - isBracketing
```
public static boolean isBracketing(UnivariateFunction function,
                                   double lower,
                                   double upper)
```
    Check whether the interval bounds bracket a root. That is, if the values at the endpoints are not equal to zero, then the function takes opposite signs at the endpoints.
    
    Parameters:
    
    function - Function.
    
    lower - Lower endpoint.
    
    upper - Upper endpoint.
    
    Returns:
    
    true if the function values have opposite signs at the given points.
    
    Throws:
    
    NullArgumentException - if function is null.
  - isSequence
```
public static boolean isSequence(double start,
                                 double mid,
                                 double end)
```
    Check whether the arguments form a (strictly) increasing sequence.
    
    Parameters:
    
    start - First number.
    
    mid - Second number.
    
    end - Third number.
    
    Returns:
    
    true if the arguments form an increasing sequence.
  - verifyInterval
```
public static void verifyInterval(double lower,
                                  double upper)
```
    Check that the endpoints specify an interval.
    
    Parameters:
    
    lower - Lower endpoint.
    
    upper - Upper endpoint.
    
    Throws:
    
    NumberIsTooLargeException - if lower >= upper.
  - verifyIntervalStrict
```
public static void verifyIntervalStrict(double lower,
                                        double upper)
```
    Check that the endpoints specify an interval.
    
    Parameters:
    
    lower - Lower endpoint.
    
    upper - Upper endpoint.
    
    Throws:
    
    NumberIsTooLargeException - if lower > upper.
  - verifySequence
```
public static void verifySequence(double lower,
                                  double initial,
                                  double upper)
```
    Check that lower < initial < upper.
    
    Parameters:
    
    lower - Lower endpoint.
    
    initial - Initial value.
    
    upper - Upper endpoint.
    
    Throws:
    
    NumberIsTooLargeException - if lower >= initial or initial >= upper.
  - verifySequenceStrict
```
public static void verifySequenceStrict(double lower,
                                        double initial,
                                        double upper)
```
    Check that lower <= initial <= upper & lower < upper.
    
    Parameters:
    
    lower - Lower endpoint.
    
    initial - Initial value.
    
    upper - Upper endpoint.
    
    Throws:
    
    NumberIsTooLargeException - if lower > initial or initial > upper or lower >= upper.
  - verifyBracketing
```
public static void verifyBracketing(UnivariateFunction function,
                                    double lower,
                                    double upper)
```
    Check that the endpoints specify an interval and the end points bracket a root.
    
    Parameters:
    
    function - Function.
    
    lower - Lower endpoint.
    
    upper - Upper endpoint.
    
    Throws:
    
    NoBracketingException - if the function has the same sign at the endpoints.
    
    NullArgumentException - if function is null.

Class UnivariateSolverUtils

Method Summary

Methods inherited from class java.lang.Object

Method Detail

solve

solve

forceSide

bracket

bracket

midpoint

isBracketing

isSequence

verifyInterval

verifyIntervalStrict

verifySequence

verifySequenceStrict

verifyBracketing