JAMA : A Java Matrix Package |

[ Background ] ..... [ The Package ] ..... [ Request for Comments ] ..... [ Authors ] ..... [ Related Links ]

JAMA is a basic linear algebra package for Java. It provides user-level
classes for constructing and manipulating real, dense matrices. It is
meant to provide sufficient functionality for routine problems, packaged in a
way that is natural and understandable to non-experts. It is intended to
serve as *the* standard matrix class for Java, and will be proposed as
such to the Java
Grande Forum and then to Sun.
A straightforward public-domain reference implementation has been developed by
the MathWorks and NIST as a strawman for such a class. We
are releasing this version in order to obtain public comment. There is no
guarantee that future versions of JAMA will be compatible with this one.

A sibling matrix package, Jampack, has also been developed at NIST and the University of Maryland. The two packages arose from the need to evaluate alternate designs for the implementation of matrices in Java. JAMA is based on a single matrix class within a strictly object-oriented framework. Jampack uses a more open approach that lends itself to extension by the user. As it turns out, for the casual user the packages differ principally in the syntax of the matrix operations. We hope you will take the time to look at Jampack along with JAMA. There is much to be learned from both packages.

**Capabilities. **JAMA is comprised of six Java classes: Matrix,
CholeskyDecomposition, LUDecomposition, QRDecomposition, SingularValueDecomposition
and EigenvalueDecomposition.

The Matrix class provides the fundamental operations of numerical inear
algebra. Various constructors create Matrices from two dimensional
arrays of double precision floating point numbers. Various *gets
*and *sets* provide access to submatrices and matrix elements.
The basic arithmetic operations include matrix addition and multiplication,
matrix norms and selected element-by-element array operations. A
convenient matrix print method is also included.

Five fundamental matrix decompositions, which consist of pairs or triples of matrices, permutation vectors, and the like, produce results in five decomposition classes. These decompositions are accessed by the Matrix class to compute solutions of simultaneous linear equations, determinants, inverses and other matrix functions. The five decompositions are

- Cholesky Decomposition of symmetric, positive definite matrices
- LU Decomposition (Gaussian elimination) of rectangular matrices
- QR Decomposition of rectangular matrices
- Eigenvalue Decomposition of both symmetric and nonsymmetric square matrices
- Singular Value Decomposition of rectangular matrices

The design of JAMA represents a compromise between the need for pure and elegant object-oriented design and the need to enable high performance implementations.

Object Manipulation |
constructors
set elements get elements copy clone |

Elementary Operations |
addition
subtraction multiplication scalar multiplication element-wise multiplication element-wise division unary minus transpose norm |

Decompositions |
Cholesky
LU QR SVD symmetric eigenvalue nonsymmetric eigenvalue |

Equation Solution |
nonsingular systems
least squares |

Derived Quantities |
condition number
determinant rank inverse pseudoinverse |

**Example of Use.** The following simple example solves a 3x3
linear system Ax=b and computes the

norm of the residual.

double[][] array = {{1.,2.,3},{4.,5.,6.},{7.,8.,10.}};

Matrix
A = new Matrix(array);

Matrix
b = Matrix.random(3,1);

Matrix
x = A.solve(b);

Matrix
Residual = A.times(x).minus(b);

double
rnorm = Residual.normInf();

**Reference Implementation. **The implementation of JAMA downloadable
from this site is meant to be a reference implementation only.
As such, it is pedagogical in nature. The algorithms employed are
similar to those of the classic Wilkinson and Reinsch Handbook, i.e. the
same algorithms used in EISPACK,
LINPACK and MATLAB.
Matrices are stored internally as native Java arrays (i.e., double[][]).
The coding style is straightforward and readable. While the reference
implementation itself should provide reasonable execution speed for small
to moderate size applications, we fully expect software vendors and Java
VMs to provide versions which are optimized for particular environments.

**Not Covered. ** JAMA is by no means a complete linear algebra
environment. For example, there are no provisions for matrices with
particular structure (e.g., banded, sparse) or for more specialized decompositions
(e.g. Shur, generalized eigenvalue). Complex matrices are not included.
It is not our intention to ignore these important problems. We expect
that some of these (e.g. complex) will be addressed in future versions.
It is our intent that the design of JAMA not preclude extension to some
of these additional areas.

Finally, JAMA is not a general-purpose array class. Instead, it
focuses on the principle mathematical functionality required to do numerical
linear algebra. As a result, there are no methods for array operations
such as reshaping or applying elementary functions (e.g. sine, exp, log)
elementwise. Such operations, while quite useful in many applications,
are best collected into a separate *array* class.

- Documentation
- Example
- Source [ zip archive, 113Kb ] [ gzipped tar file, 81Kb ]
- Jar file [ Jama-1.0.1.jar ]
- ChangeLog

**Discussion Group**. A discussion group has been established for
such comments. Comments and suggestions sent to jama@nist.gov
will automatically be sent to the JAMA authors, as well as to all subscribers.
To subscribe, send email to listproc@nist.gov
containing the text ** subscribe jama your-name** in the message
body. A public archive
of the discussion can be browsed.

[Note: NIST will not use the email addresses provided for any
purpose other than the maintenance of this discussion list. Participants may
remove themselves at any time by sending an email message to listproc@nist.gov containing the text
** unsubscribe jama** in the message body. See the NIST Privacy
Policy.]

Joe Hicklin
Cleve Moler Peter Webb ...
from The MathWorks |
Ronald F. Boisvert
Bruce Miller Roldan Pozo Karin Remington ...
from NIST |

**Copyright Notice**
*This software is a cooperative product of The MathWorks and the National
Institute of Standards and Technology (NIST) which has been released to the
public domain. Neither The MathWorks nor NIST assumes any responsibility
whatsoever for its use by other parties, and makes no guarantees, expressed
or implied, about its quality, reliability, or any other characteristic.*

- Java for Computational Science and Engineering
- Java Numerics Working Group
- NIST Mathematical and Computational Sciences Division

Identification of commercial products on this page is for information only, and does not imply recommendation or endorsement by the National Institute of Standards and Technology.