Apache Commons logo Commons Math


Creating and maintaining a mathematical and statistical library that is accurate requires a greater degree of communication than might be the case for other components. It is important that developers follow guidelines laid down by the community to ensure that the code they create can be successfully maintained by others.


Developers are asked to comply with the following development guidelines. Code that does not comply with the guidelines including the word must will not be committed. Our aim will be to fix all of the exceptions to the "should" guidelines prior to a release.


Getting Started

  1. Start by reviewing the overall objectives stated in the proposal upon which the project is founded.
  2. Download the Commons Math source code. Follow the instructions under the heading "Repository Checkout" on the Git at the ASF page. The git url for the current development sources of Commons Math is
    for anonymous read-only access and
    (where apacheid should be replaced by each committer Apache ID) for committers read-write access.
  3. Like most commons components, Commons Math uses Apache Maven as our build tool. The sources can also be built using Ant (a working Ant build.xml is included in the top level project directory). To build Commons Math using Maven, you can follow the instructions for Building a project with Maven. Launch Maven from the top-level directory in the checkout of Commons Math trunk. No special setup is required, except that currently to build the site (i.e. to execute Maven's "site" goal), you may need to increase the default memory allocation (e.g. export MAVEN_OPTS=-Xmx512m) before launching Maven.
  4. Have a look at the new features that users and developers have requested on the Math Wish List Wiki Page.
  5. Be sure to join the commons-dev and commons-user email lists and use them appropriately (make sure the string "[math]" starts the Subject line of all your postings). Make any proposals here where the group can comment on them.
  6. Setup an account on JIRA and use it to submit patches and identify bugs. Read the directions for submitting bugs and search the database to determine if an issue exists or has already been dealt with.

    See the Commons Math Issue Tracking Page for more information on how to search for or submit bugs or enhancement requests.

  7. Generating patches: The requested format for generating patches is the Unified Diff format, which can be easily generated using the git client or various IDEs.
    git diff -p > patch 
    Run this command from the top-level project directory (where pom.xml resides).

Contributing ideas and code

Follow the steps below when making suggestions for additions or enhancements to Commons Math. This will make it easier for the community to comment on your ideas and for the committers to keep track of them. Thanks in advance!

  1. Start with a post to the commons-dev mailing list, with [math] at the beginning of the subject line, followed by a good, short title describing the new feature or enhancement. For example, "[math] Principal Components Analysis." The body of the post should include each of the following items (but be as brief as possible):
    • A concise description of the new feature / enhancement
    • References to definitions and algorithms. Using standard definitions and algorithms makes communication much easier and will greatly increase the chances that we will accept the code / idea
    • Some indication of why the addition / enhancement is practically useful
  2. Assuming a generally favorable response to the idea on commons-dev, the next step is to add an entry to the Math Wish List corresponding to the idea. Include a reference to the discussion thread.
  3. Create a JIRA ticket using the the feature title as the short description. Incorporate feedback from the initial posting in the description. Add a reference to the JIRA ticket to the WishList entry.
  4. Submit code as attachments to the JIRA ticket. Please use one ticket for each feature, adding multiple patches to the ticket as necessary. Use the git diff command to generate your patches as diffs. Please do not submit modified copies of existing java files. Be patient (but not too patient) with committers reviewing patches. Post a *nudge* message to commons-dev with a reference to the ticket if a patch goes more than a few days with no comment or commit.

Coding Style

Commons Math follows Code Conventions for the Java Programming Language. As part of the maven build process, style checking is performed using the Checkstyle plugin, using the properties specified in checkstyle.xml. Committed code should generate no Checkstyle errors. One thing that Checkstyle will complain about is tabs included in the source code. Please make sure to set your IDE or editor to use spaces instead of tabs.

Committers should configure the

and git repository (or global) settings with
git config
. They define the identity and mail of the committer. See Customizing Git - Git Configuration in the git book for explanation about how to configure these settings and more.


  • Committed code must include full javadoc.
  • All component contracts must be fully specified in the javadoc class, interface or method comments, including specification of acceptable ranges of values, exceptions or special return values.
  • External references or full statements of definitions for all mathematical terms used in component documentation must be provided.
  • Commons math javadoc generation now supports embedded LaTeX formulas via the MathJax javascript display engine. To embed mathematical expressions formatted in LaTeX in javadoc, simply surround the expression to be formatted with either
    \( ... \)
    for inline formulas, or
    \[ ... \]
    to have the formula appear on a separate line. For example,
    \(a^2 + b^2 = c^2\)
    will render an inline formula saying that (a, b, c) is Pythagorean triplet: \( a^2 + b^2 = c^2 \). See the MathJax and LaTex documentation for details on how to represent formulas and escape special characters.
  • Implementations should use standard algorithms and references or full descriptions of all algorithms should be provided.
  • Additions and enhancements should include updates to the User Guide.


  • Exceptions generated by Commons Math are all unchecked.
  • All public methods advertise all exceptions that they can generate. Exceptions must be documented in both javadoc and method signatures and the documentation in the javadoc must include full description of the conditions under which exceptions are thrown.
  • Methods should fully specify parameter preconditions required for successful activation. When preconditions are violated, a MathIllegalArgumentException should be thrown. Subclasses of MathIllegalArgumentException may be used to represent common parameter contract violations (for example, NoBracketingException). Exception messages must contain sufficient information on parameter values to determine the exact precondition failure.
  • Exceptions generated by Commons Math make sense without knowing implementation details other than those stated in the public API. For example, a NoBracketingException makes sense thrown by a solver that has a precondition requiring that initial points bracket a root. This exception does not make sense, however, thrown by an inverse cumulative probability estimator.
  • MathIllegalArgumentException should only be thrown in situations where preconditions can be exhaustively provided so that what arguments are "illegal" can be specified fully to the caller. Domain-specific exceptions need to be defined for cases where failures cannot be attributed to parameter precondition violation. For example, the exact domain of successful activation of a solver or quadrature method may be impossible to specify because of numerical properties of the method. If a solver fails to find a root or a quadrature method fails to converge for a given set of parameters, unless those parameters violate the advertised preconditions it is not appropriate to throw MathIllegalArgumentException.
  • State information included in exception messages must be available in exception properties - i.e., successful handling or reporting of Commons Math exceptions must not require parsing exception messages.

Unit Tests

  • Committed code must include unit tests.
  • Unit tests should provide full path coverage.
  • Unit tests should verify all boundary conditions specified in interface contracts, including verification that exceptions are thrown or special values (e.g. Double.NaN, Double.Infinity) are returned as expected.

Licensing and copyright

  • All new source file submissions must include the Apache Software License in a comment that begins the file
  • All contributions must comply with the terms of the Apache Contributor License Agreement (CLA)
  • Patches must be accompanied by a clear reference to a "source" - if code has been "ported" from another language, clearly state the source of the original implementation. If the "expression" of a given algorithm is derivative, please note the original source (textbook, paper, etc.).
  • References to source materials covered by restrictive proprietary licenses should be avoided. In particular, contributions should not implement or include references to algorithms in Numerical Recipes (NR). Any questions about copyright or patent issues should be raised on the commons-dev mailing list before contributing or committing code.

Recommended Readings

Here is a list of relevant materials. Much of the discussion surrounding the development of this component will refer to the various sources listed below, and frequently the Javadoc for a particular class or interface will link to a definition contained in these documents.

Recommended Readings

Concerning floating point arithmetic.
Numerical analysis
Scientific Computing FAQ @ Mathcom
Bibliography of accuracy and stability of numerical algorithms
SUNY Stony Brook numerical methods page
SIAM Journal of Numerical Analysis Online
Probability and statistics
Statlib at CMU
NIST Engineering Statistics Handbook
Online Introductory Statistics (David W. Stockburger)
Online Journal of Statistical Software

Javadoc comment resources

References for mathematical definitions.
Chan, T. F. and J. G. Lewis 1979, Communications of the ACM, vol. 22 no. 9, pp. 526-531.


XML related resources.