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added Category:Software using the Apache license using HotCat

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{{Multiple issues|
{{Notability|Product|date=January 2023}}
{{COI|date=January 2023}}
}}

{{Infobox software
| name =
| author = Peter Abeles
| operating system = [[Cross-platform]]
| latest_release_version = 0.41.1
| latest_release_date = {{Start date and age|2022|12|04}}
| genre = Library
| license = [[Apache License]]
| website = {{url|http://ejml.org/}}
}}

'''Efficient Java Matrix Library''' (EJML) is a linear algebra library for manipulating real/complex/dense/sparse matrices. Its design goals are; 1) to be as computationally and memory efficient as possible for both small and large matrices, and 2) to be accessible to both novices and experts. These goals are accomplished by dynamically selecting the best algorithms to use at runtime, clean API, and multiple interfaces. EJML is free, written in 100% Java and has been released under an Apache v2.0 license.

EJML has three distinct ways to interact with it: 1) Procedural, 2) SimpleMatrix, and 3) Equations. The procedural style provides all capabilities of EJML and almost complete control over matrix creation, speed, and specific algorithms. The SimpleMatrix style provides a simplified subset of the core capabilities in an easy to use flow-styled object-oriented API, inspired by [[JAMA (numerical linear algebra library)|JAMA]]. The Equations style provides a symbolic interface, similar in spirit to Matlab and other CAS, that provides a compact way of writing equations.<ref name="ProjectPage"/>

== Capabilities ==

EJML provides the following capabilities for dense matrices.

* Basic Operators (addition, multiplication, ... )
* Matrix Manipulation (extract, insert, combine, ... )
* Linear Solvers (linear, least squares, incremental, ... )
* Decompositions (LU, QR, Cholesky, SVD, Eigenvalue, ...)
* Matrix Features (rank, symmetric, definitiveness, ... )
* Random Matrices (covariance, orthogonal, symmetric, ... )
* Different Internal Formats (row-major, block)
* Unit Testing

== Usage examples ==
=== Equation style ===

Computing the [[Kalman gain]]:

<syntaxhighlight lang="java">
eq.process("K = P*H'*inv( H*P*H' + R )");
</syntaxhighlight>

=== Procedural style ===

Computing Kalman gain:

<syntaxhighlight lang="java">
mult(H, P, c);
multTransB(c, H, S);
addEquals(S, R);
if (!invert(S, S_inv))
throw new RuntimeException("Invert failed");
multTransA(H, S_inv, d);
mult(P, d, K);
</syntaxhighlight>

=== SimpleMatrix style ===

Example of [[singular value decomposition]] (SVD):
<syntaxhighlight lang="java">
SimpleSVD s = matA.svd();
SimpleMatrix U = s.getU();
SimpleMatrix W = s.getW();
SimpleMatrix V = s.getV();
</syntaxhighlight>

Example of matrix multiplication:
<syntaxhighlight lang="java">
SimpleMatrix result = matA.mult(matB);
</syntaxhighlight>

=== DecompositionFactory ===

Use of a DecompositionFactory to compute a Singular Value Decomposition with a Dense Double Row Major matrix (DDRM):<ref>{{cite web|access-date=2021-04-24|title=Matrix Decompositions - Efficient Java Matrix Library|url=http://ejml.org/wiki/index.php?title=Matrix_Decompositions|website=ejml.org}}</ref>

<syntaxhighlight lang="java">
SingularValueDecomposition_F64<DenseMatrix64F> svd =
DecompositionFactory_DDRM.svd(true, true, true);

if (!DecompositionFactory.decomposeSafe(svd, matA))
throw new DetectedException("Decomposition failed.");

DenseMatrix64F U = svd.getU(null, false);
DenseMatrix64F S = svd.getW(null);
DenseMatrix64F V = svd.getV(null, false);
</syntaxhighlight>

Example of matrix multiplication:
<syntaxhighlight lang="java">
CommonOps_DDRM.mult(matA, matB, result);
</syntaxhighlight>

==See also==
* [[List of numerical libraries]]

== References ==
{{reflist|refs=
<ref name=ProjectPage>{{cite web |url=http://ejml.org/ |title=EJML Project Page |work=EJML|publisher=Peter Abeles|access-date=Jan 21, 2019}}</ref>
}}

== External links ==
* [http://ejml.org/ Efficient Java Matrix Library (EJML) homepage]

[[Category:Numerical libraries]]
[[Category:Software using the Apache license]]

Efficient Java Matrix Library - Revision history

imported>Deltaspace42: added Category:Software using the Apache license using HotCat