| Package | Description | 
|---|---|
| org.apache.commons.math4.core.jdkmath | Alternative to  MathandStrictMath. | 
| org.apache.commons.math4.legacy.analysis | 
      Parent package for common numerical analysis procedures, including root finding,
      function interpolation and integration. | 
| org.apache.commons.math4.legacy.analysis.differentiation | 
   This package holds the main interfaces and basic building block classes
   dealing with differentiation. | 
| org.apache.commons.math4.legacy.analysis.function | 
      The  functionpackage contains function objects that wrap the
      methods contained inMath, as well as common
      mathematical functions such as the gaussian and sinc functions. | 
| org.apache.commons.math4.legacy.analysis.integration | Numerical integration (quadrature) algorithms for univariate real functions. | 
| org.apache.commons.math4.legacy.analysis.integration.gauss | Gauss family of quadrature schemes. | 
| org.apache.commons.math4.legacy.analysis.interpolation | Univariate real functions interpolation algorithms. | 
| org.apache.commons.math4.legacy.analysis.polynomials | Univariate real polynomials implementations, seen as differentiable
     univariate real functions. | 
| org.apache.commons.math4.legacy.analysis.solvers | Root finding algorithms, for univariate real functions. | 
| org.apache.commons.math4.legacy.core | Core math utilities. | 
| org.apache.commons.math4.legacy.core.dfp | Decimal floating point library for Java | 
| org.apache.commons.math4.legacy.distribution | Implementations of common discrete and continuous distributions. | 
| org.apache.commons.math4.legacy.distribution.fitting | Fitting of parameters against distributions. | 
| org.apache.commons.math4.legacy.exception | Specialized exceptions for algorithms errors. | 
| org.apache.commons.math4.legacy.exception.util | Classes supporting exception localization. | 
| org.apache.commons.math4.legacy.field | Utilities based on the  Fieldfunctionality defined in 
 Commons Numbers. | 
| org.apache.commons.math4.legacy.field.linalg | Linear algebra defined in term of matrices whose entries are elements
 of a  field. | 
| org.apache.commons.math4.legacy.filter | Implementations of common discrete-time linear filters. | 
| org.apache.commons.math4.legacy.fitting | Classes to perform curve fitting. | 
| org.apache.commons.math4.legacy.fitting.leastsquares | This package provides algorithms that minimize the residuals
 between observations and model values. | 
| org.apache.commons.math4.legacy.genetics | This package provides Genetic Algorithms components and implementations. | 
| org.apache.commons.math4.legacy.linear | Linear algebra support. | 
| org.apache.commons.math4.legacy.ml | Base package for machine learning algorithms. | 
| org.apache.commons.math4.legacy.ml.clustering | Clustering algorithms. | 
| org.apache.commons.math4.legacy.ml.clustering.evaluation | Cluster evaluation methods. | 
| org.apache.commons.math4.legacy.ml.distance | Common distance measures. | 
| org.apache.commons.math4.legacy.ode | 
 This package provides classes to solve Ordinary Differential Equations problems. | 
| org.apache.commons.math4.legacy.ode.events | 
 This package provides classes to handle discrete events occurring during
 Ordinary Differential Equations integration. | 
| org.apache.commons.math4.legacy.ode.nonstiff | 
 This package provides classes to solve non-stiff Ordinary Differential Equations problems. | 
| org.apache.commons.math4.legacy.ode.sampling | 
 This package provides classes to handle sampling steps during
 Ordinary Differential Equations integration. | 
| org.apache.commons.math4.legacy.optim | 
  Generally, optimizers are algorithms that will either
   minimizeormaximizea scalar function, called theobjective
  function. | 
| org.apache.commons.math4.legacy.optim.linear | Optimization algorithms for linear constrained problems. | 
| org.apache.commons.math4.legacy.optim.nonlinear.scalar | Algorithms for optimizing a scalar function. | 
| org.apache.commons.math4.legacy.optim.nonlinear.scalar.gradient | This package provides optimization algorithms that require derivatives. | 
| org.apache.commons.math4.legacy.optim.nonlinear.scalar.noderiv | This package provides optimization algorithms that do not require derivatives. | 
| org.apache.commons.math4.legacy.optim.univariate | One-dimensional optimization algorithms. | 
| org.apache.commons.math4.legacy.random | This package contains functionality related to random numbers. | 
| org.apache.commons.math4.legacy.special | Implementations of special functions such as Beta and Gamma. | 
| org.apache.commons.math4.legacy.stat | Data storage, manipulation and summary routines. | 
| org.apache.commons.math4.legacy.stat.correlation | Correlations/Covariance computations. | 
| org.apache.commons.math4.legacy.stat.descriptive | Generic univariate summary statistic objects. | 
| org.apache.commons.math4.legacy.stat.descriptive.moment | Summary statistics based on moments. | 
| org.apache.commons.math4.legacy.stat.descriptive.rank | Summary statistics based on ranks. | 
| org.apache.commons.math4.legacy.stat.descriptive.summary | Other summary statistics. | 
| org.apache.commons.math4.legacy.stat.inference | Classes providing hypothesis testing. | 
| org.apache.commons.math4.legacy.stat.interval | Classes providing binomial proportion confidence interval construction. | 
| org.apache.commons.math4.legacy.stat.ranking | Classes providing rank transformations. | 
| org.apache.commons.math4.legacy.stat.regression | Statistical routines involving multivariate data. | 
| org.apache.commons.math4.legacy.util | Convenience routines and common data structures used throughout the commons-math library. | 
| org.apache.commons.math4.neuralnet | Neural networks. | 
| org.apache.commons.math4.neuralnet.internal | Internal utility classes. | 
| org.apache.commons.math4.neuralnet.oned | One-dimensional neural networks. | 
| org.apache.commons.math4.neuralnet.sofm | Self Organizing Feature Map. | 
| org.apache.commons.math4.neuralnet.sofm.util | Miscellaneous utilities. | 
| org.apache.commons.math4.neuralnet.twod | Two-dimensional neural networks. | 
| org.apache.commons.math4.neuralnet.twod.util | Utilities to visualize two-dimensional neural networks. | 
| org.apache.commons.math4.transform | Implementations of transform methods. |