# Difference between revisions of "Main Page"

 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 small and large, dense and sparse, real and complex 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: v0.43.1 Date: September 23, 2023 v0.31 Upgrade Script Change Log
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## News 2023

 - SimpleMatrix is going through bit of a rejuvenation SimpleMatrix has much improved support for complex matrices Introduced ConstMatrix for when you want to restrict access to read only

## 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
• Matrix 2x2 to 6x6
• Vector 2 to 6
• Dense Real
• Row-major
• Block
• Dense Complex
• Row-major
• Sparse Real
• Compressed Column
• Full support for floats and doubles
• 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 X
Cholesky LL X X X
Cholesky LDL X
QR X X X
QRP X
SVD X
Eigen-Symmetric X
Eigen-General X

Support for floats (32-bit) and doubles (64-bit) is available. Sparse matrix support is only available for basic operations at this time.