# Main Page

 Efficient Java Matrix Library (EJML) is a linear algebra library for manipulating dense 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. Procedure provides all capabilities of EJML and almost complete control over memory creation, speed, and specific algorithms. SimpleMatrix provides a simplified subset of the core capabilities in an easy to use flow styled object-oriented API, inspired by Jama. Equations is a symbolic interface, similar in spirit to Matlab and other CAS, that provides a compact way of writing equations.
 Version: v0.30 Date: November 9, 2016 Change Log
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## Code Examples

Demonstrations on how to compute the Kalman gain "K" using each interface in EJML.

 Procedural ```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); ``` SimpleMatrix ```SimpleMatrix S = H.mult(P).mult(H.transpose()).plus(R); SimpleMatrix K = P.mult(H.transpose().mult(S.invert())); ``` Equations ```eq.process("K = P*H'*inv( H*P*H' + R )"); ```

## Functionality

Data Structures Operations
• Fixed Sized
• Dense Real
• Row-major
• Block
• Dense Complex
• Row-major
• 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, ... )
• Unit Testing
.

Decomposition Dense Real Dense Complex Sparse Real Sparse Complex
LU X X
Cholesky LL X X
Cholesky LDL X
QR X X
QRP X
SVD X
Eigen-Symmetric X
Eigen-General X

Support is provided for doubles only. Next release (v0.31) will provide support for floats.

EJML is currently a single threaded library only. Multi threaded work will start once block implementations of SVD and Eigenvalue are finished.