## Uses of Interface
org.apache.commons.math3.analysis.UnivariateFunction

- Packages that use UnivariateFunction
  Package | Description
  --- | ---
  org.apache.commons.math3.analysis | Parent package for common numerical analysis procedures, including root finding, function interpolation and integration.
  org.apache.commons.math3.analysis.function | The `function` package contains function objects that wrap the methods contained in `Math`, as well as common mathematical functions such as the gaussian and sinc functions.
  org.apache.commons.math3.analysis.integration | Numerical integration (quadrature) algorithms for univariate real functions.
  org.apache.commons.math3.analysis.interpolation | Univariate real functions interpolation algorithms.
  org.apache.commons.math3.analysis.polynomials | Univariate real polynomials implementations, seen as differentiable univariate real functions.
  org.apache.commons.math3.analysis.solvers | Root finding algorithms, for univariate real functions.
  org.apache.commons.math3.linear | Linear algebra support.
  org.apache.commons.math3.optimization.univariate | Univariate real functions minimum finding algorithms.
  org.apache.commons.math3.transform | Implementations of transform methods, including Fast Fourier transforms.

- - ### Uses of UnivariateFunction in org.apache.commons.math3.analysis

    Subinterfaces of UnivariateFunction in org.apache.commons.math3.analysis
    Modifier and Type | Interface and Description
    --- | ---
    `interface` | `DifferentiableUnivariateFunction` Extension of `UnivariateFunction` representing a differentiable univariate real function.

    Methods in org.apache.commons.math3.analysis that return UnivariateFunction
    Modifier and Type | Method and Description
    --- | ---
    `static UnivariateFunction` | FunctionUtils.`add(UnivariateFunction... f)` Add functions.
    `static UnivariateFunction` | FunctionUtils.`combine(BivariateFunction combiner, UnivariateFunction f, UnivariateFunction g)` Returns the univariate function `h(x) = combiner(f(x), g(x))`.
    `static UnivariateFunction` | FunctionUtils.`compose(UnivariateFunction... f)` Compose functions.
    `UnivariateFunction` | DifferentiableUnivariateFunction.`derivative()` Returns the derivative of the function
    `static UnivariateFunction` | FunctionUtils.`fix1stArgument(BivariateFunction f, double fixed)` Create a unary function by fixing the first argument of a binary function.
    `static UnivariateFunction` | FunctionUtils.`fix2ndArgument(BivariateFunction f, double fixed)` Create a unary function by fixing the second argument of a binary function.
    `static UnivariateFunction` | FunctionUtils.`multiply(UnivariateFunction... f)` Multiply functions.

    Methods in org.apache.commons.math3.analysis with parameters of type UnivariateFunction
    Modifier and Type | Method and Description
    --- | ---
    `static UnivariateFunction` | FunctionUtils.`add(UnivariateFunction... f)` Add functions.
    `static MultivariateFunction` | FunctionUtils.`collector(BivariateFunction combiner, UnivariateFunction f, double initialValue)` Returns a MultivariateFunction h(x[]) defined by
    `static UnivariateFunction` | FunctionUtils.`combine(BivariateFunction combiner, UnivariateFunction f, UnivariateFunction g)` Returns the univariate function `h(x) = combiner(f(x), g(x))`.
    `static UnivariateFunction` | FunctionUtils.`compose(UnivariateFunction... f)` Compose functions.
    `static UnivariateFunction` | FunctionUtils.`multiply(UnivariateFunction... f)` Multiply functions.
    `static double[]` | FunctionUtils.`sample(UnivariateFunction f, double min, double max, int n)` Samples the specified univariate real function on the specified interval.

  - ### Uses of UnivariateFunction in org.apache.commons.math3.analysis.function

    Classes in org.apache.commons.math3.analysis.function that implement UnivariateFunction
    Modifier and Type | Class and Description
    --- | ---
    `class` | `Abs` Absolute value function.
    `class` | `Acos` Arc-cosine function.
    `class` | `Acosh` Hyperbolic arc-cosine function.
    `class` | `Asin` Arc-sine function.
    `class` | `Asinh` Hyperbolic arc-sine function.
    `class` | `Atan` Arc-tangent function.
    `class` | `Atanh` Hyperbolic arc-tangent function.
    `class` | `Cbrt` Cube root function.
    `class` | `Ceil` `ceil` function.
    `class` | `Constant` Constant function.
    `class` | `Cos` Cosine function.
    `class` | `Cosh` Hyperbolic cosine function.
    `class` | `Exp` Exponential function.
    `class` | `Expm1` `ex-1` function.
    `class` | `Floor` `floor` function.
    `class` | `Gaussian` Gaussian function.
    `class` | `HarmonicOscillator` simple harmonic oscillator function.
    `class` | `Identity` Identity function.
    `class` | `Inverse` Inverse function.
    `class` | `Log` Natural logarithm function.
    `class` | `Log10` Base 10 logarithm function.
    `class` | `Log1p` `log(1 + p)` function.
    `class` | `Logistic` Generalised logistic function.
    `class` | `Logit` Logit function.
    `class` | `Minus` Minus function.
    `class` | `Power` Power function.
    `class` | `Rint` `rint` function.
    `class` | `Sigmoid` Sigmoid function.
    `class` | `Signum` `signum` function.
    `class` | `Sin` Sine function.
    `class` | `Sinc` Sinc function, defined by
    `class` | `Sinh` Hyperbolic sine function.
    `class` | `Sqrt` Square-root function.
    `class` | `StepFunction` Step function.
    `class` | `Tan` Tangent function.
    `class` | `Tanh` Hyperbolic tangent function.
    `class` | `Ulp` `ulp` function.

    Methods in org.apache.commons.math3.analysis.function that return UnivariateFunction
    Modifier and Type | Method and Description
    --- | ---
    `UnivariateFunction` | Asinh.`derivative()` Returns the derivative of the function
    `UnivariateFunction` | Expm1.`derivative()` Returns the derivative of the function
    `UnivariateFunction` | Sinc.`derivative()` Returns the derivative of the function
    `UnivariateFunction` | Log10.`derivative()` Returns the derivative of the function
    `UnivariateFunction` | Sqrt.`derivative()` Returns the derivative of the function
    `UnivariateFunction` | Logit.`derivative()` Returns the derivative of the function
    `UnivariateFunction` | Asin.`derivative()` Returns the derivative of the function
    `UnivariateFunction` | Exp.`derivative()` Returns the derivative of the function
    `UnivariateFunction` | HarmonicOscillator.`derivative()` Returns the derivative of the function
    `UnivariateFunction` | Gaussian.`derivative()` Returns the derivative of the function
    `UnivariateFunction` | Cos.`derivative()` Returns the derivative of the function
    `UnivariateFunction` | Acosh.`derivative()` Returns the derivative of the function
    `UnivariateFunction` | Tanh.`derivative()` Returns the derivative of the function
    `UnivariateFunction` | Log.`derivative()` Returns the derivative of the function
    `UnivariateFunction` | Cbrt.`derivative()` Returns the derivative of the function
    `UnivariateFunction` | Tan.`derivative()` Returns the derivative of the function
    `UnivariateFunction` | Sigmoid.`derivative()` Returns the derivative of the function
    `UnivariateFunction` | Inverse.`derivative()` Returns the derivative of the function
    `UnivariateFunction` | Logistic.`derivative()` Returns the derivative of the function
    `UnivariateFunction` | Power.`derivative()` Returns the derivative of the function
    `UnivariateFunction` | Acos.`derivative()` Returns the derivative of the function
    `UnivariateFunction` | Atan.`derivative()` Returns the derivative of the function
    `UnivariateFunction` | Atanh.`derivative()` Returns the derivative of the function
    `UnivariateFunction` | Log1p.`derivative()` Returns the derivative of the function

  - ### Uses of UnivariateFunction in org.apache.commons.math3.analysis.integration

    Methods in org.apache.commons.math3.analysis.integration with parameters of type UnivariateFunction
    Modifier and Type | Method and Description
    --- | ---
    `double` | UnivariateIntegrator.`integrate(int maxEval, UnivariateFunction f, double min, double max)` Integrate the function in the given interval.
    `double` | BaseAbstractUnivariateIntegrator.`integrate(int maxEval, UnivariateFunction f, double lower, double upper)` Integrate the function in the given interval.
    `protected void` | BaseAbstractUnivariateIntegrator.`setup(int maxEval, UnivariateFunction f, double lower, double upper)` Prepare for computation.

  - ### Uses of UnivariateFunction in org.apache.commons.math3.analysis.interpolation

    Methods in org.apache.commons.math3.analysis.interpolation that return UnivariateFunction
    Modifier and Type | Method and Description
    --- | ---
    `UnivariateFunction` | UnivariateInterpolator.`interpolate(double[] xval, double[] yval)` Compute an interpolating function for the dataset.
    `UnivariateFunction` | UnivariatePeriodicInterpolator.`interpolate(double[] xval, double[] yval)` Compute an interpolating function for the dataset.

  - ### Uses of UnivariateFunction in org.apache.commons.math3.analysis.polynomials

    Classes in org.apache.commons.math3.analysis.polynomials that implement UnivariateFunction
    Modifier and Type | Class and Description
    --- | ---
    `class` | `PolynomialFunction` Immutable representation of a real polynomial function with real coefficients.
    `class` | `PolynomialFunctionLagrangeForm` Implements the representation of a real polynomial function in Lagrange Form.
    `class` | `PolynomialFunctionNewtonForm` Implements the representation of a real polynomial function in Newton Form.
    `class` | `PolynomialSplineFunction` Represents a polynomial spline function.

    Methods in org.apache.commons.math3.analysis.polynomials that return UnivariateFunction
    Modifier and Type | Method and Description
    --- | ---
    `UnivariateFunction` | PolynomialSplineFunction.`derivative()` Get the derivative of the polynomial spline function.
    `UnivariateFunction` | PolynomialFunction.`derivative()` Returns the derivative as a `UnivariateFunction`.

  - ### Uses of UnivariateFunction in org.apache.commons.math3.analysis.solvers

    Classes in org.apache.commons.math3.analysis.solvers with type parameters of type UnivariateFunction
    Modifier and Type | Class and Description
    --- | ---
    `class` | `BaseAbstractUnivariateSolver<FUNC extends UnivariateFunction>` Provide a default implementation for several functions useful to generic solvers.
    `interface` | `BaseUnivariateSolver<FUNC extends UnivariateFunction>` Interface for (univariate real) rootfinding algorithms.
    `interface` | `BracketedUnivariateSolver<FUNC extends UnivariateFunction>` Interface for `(univariate real) root-finding algorithms` that maintain a bracketed solution.

    Methods in org.apache.commons.math3.analysis.solvers with parameters of type UnivariateFunction
    Modifier and Type | Method and Description
    --- | ---
    `static double[]` | UnivariateSolverUtils.`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[]` | UnivariateSolverUtils.`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` | UnivariateSolverUtils.`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` | UnivariateSolverUtils.`isBracketing(UnivariateFunction function, double lower, double upper)` Check whether the interval bounds bracket a root.
    `double` | BaseSecantSolver.`solve(int maxEval, UnivariateFunction f, double min, double max, AllowedSolution allowedSolution)` Solve for a zero in the given interval.
    `double` | BracketingNthOrderBrentSolver.`solve(int maxEval, UnivariateFunction f, double min, double max, AllowedSolution allowedSolution)` Solve for a zero in the given interval.
    `double` | BaseSecantSolver.`solve(int maxEval, UnivariateFunction f, double min, double max, double startValue)` Solve for a zero in the given interval, start at `startValue`.
    `double` | BaseSecantSolver.`solve(int maxEval, UnivariateFunction f, double min, double max, double startValue, AllowedSolution allowedSolution)` Solve for a zero in the given interval, start at `startValue`.
    `double` | BracketingNthOrderBrentSolver.`solve(int maxEval, UnivariateFunction f, double min, double max, double startValue, AllowedSolution allowedSolution)` Solve for a zero in the given interval, start at `startValue`.
    `static double` | UnivariateSolverUtils.`solve(UnivariateFunction function, double x0, double x1)` Convenience method to find a zero of a univariate real function.
    `static double` | UnivariateSolverUtils.`solve(UnivariateFunction function, double x0, double x1, double absoluteAccuracy)` Convenience method to find a zero of a univariate real function.
    `static void` | UnivariateSolverUtils.`verifyBracketing(UnivariateFunction function, double lower, double upper)` Check that the endpoints specify an interval and the end points bracket a root.

    Method parameters in org.apache.commons.math3.analysis.solvers with type arguments of type UnivariateFunction
    Modifier and Type | Method and Description
    --- | ---
    `static double` | UnivariateSolverUtils.`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.

  - ### Uses of UnivariateFunction in org.apache.commons.math3.linear

    Methods in org.apache.commons.math3.linear with parameters of type UnivariateFunction
    Modifier and Type | Method and Description
    --- | ---
    `RealVector` | RealVector.`map(UnivariateFunction function)` Acts as if implemented as:
    `ArrayRealVector` | ArrayRealVector.`map(UnivariateFunction function)` Acts as if implemented as:
    `RealVector` | RealVector.`mapToSelf(UnivariateFunction function)` Acts as if it is implemented as:
    `ArrayRealVector` | ArrayRealVector.`mapToSelf(UnivariateFunction function)` Acts as if it is implemented as:

  - ### Uses of UnivariateFunction in org.apache.commons.math3.optimization.univariate

    Classes in org.apache.commons.math3.optimization.univariate with type parameters of type UnivariateFunction
    Modifier and Type | Interface and Description
    --- | ---
    `interface` | `BaseUnivariateOptimizer<FUNC extends UnivariateFunction>` This interface is mainly intended to enforce the internal coherence of Commons-Math.
    `class` | `UnivariateMultiStartOptimizer<FUNC extends UnivariateFunction>` Special implementation of the `UnivariateOptimizer` interface adding multi-start features to an existing optimizer.

    Methods in org.apache.commons.math3.optimization.univariate with parameters of type UnivariateFunction
    Modifier and Type | Method and Description
    --- | ---
    `UnivariatePointValuePair` | BaseAbstractUnivariateOptimizer.`optimize(int maxEval, UnivariateFunction f, GoalType goalType, double min, double max)` Find an optimum in the given interval.
    `UnivariatePointValuePair` | BaseAbstractUnivariateOptimizer.`optimize(int maxEval, UnivariateFunction f, GoalType goalType, double min, double max, double startValue)` Find an optimum in the given interval, start at startValue.
    `void` | BracketFinder.`search(UnivariateFunction func, GoalType goal, double xA, double xB)` Search new points that bracket a local optimum of the function.

  - ### Uses of UnivariateFunction in org.apache.commons.math3.transform

    Methods in org.apache.commons.math3.transform with parameters of type UnivariateFunction
    Modifier and Type | Method and Description
    --- | ---
    `double[]` | FastSineTransformer.`transform(UnivariateFunction f, double min, double max, int n, TransformType type)` Returns the (forward, inverse) transform of the specified real function, sampled on the specified interval.
    `double[]` | FastCosineTransformer.`transform(UnivariateFunction f, double min, double max, int n, TransformType type)` Returns the (forward, inverse) transform of the specified real function, sampled on the specified interval.
    `Complex[]` | FastFourierTransformer.`transform(UnivariateFunction f, double min, double max, int n, TransformType type)` Returns the (forward, inverse) transform of the specified real function, sampled on the specified interval.
    `double[]` | FastHadamardTransformer.`transform(UnivariateFunction f, double min, double max, int n, TransformType type)` Returns the (forward, inverse) transform of the specified real function, sampled on the specified interval.
    `double[]` | RealTransformer.`transform(UnivariateFunction f, double min, double max, int n, TransformType type)` Returns the (forward, inverse) transform of the specified real function, sampled on the specified interval.

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