SciPy (pronounced "Sigh Pie") is open-source software for mathematics, science, and engineering. The SciPy library is built to work with NumPy arrays, and provides many user-friendly and efficient numerical routines such as routines for numerical integration and optimization. SciPy provides modules for Statistics, Optimization, Numerical integration, Linear algebra, Fourier transforms, Signal processing, Image processing, ODE solvers. 
 Sourceforge location: <A HREF="http://sourceforge.net/projects/scipy/" target="_blank">http://sourceforge.net/projects/scipy/</A>

SciPy (pronounced "Sigh Pie") is open-source software for mathematics, science, and engineering. The SciPy library is built to work with NumPy arrays, and provides many user-friendly and efficient numerical routines such as routines for numerical integration and optimization.

SciPy - software for Mathematics, Science, and Engineering

GNU Octave is a high-level interpreted language, primarily intended for numerical computations. It provides capabilities for the numerical solution of linear and nonlinear problems, and for performing other numerical experiments. It also provides extensive graphics capabilities for data visualization and manipulation. Octave Forge is a place for development of its packages; from bioinformatics and fuzzy logic to mechanics and instrument control.

GNU Octave - Language for Numerical Computations

Colt distribution consists of several free Java libraries bundled under one single uniform umbrella. Namely the Colt library, the Jet library, the CoreJava library, and the Concurrent library. 

 The Colt library provides fundamental general-purpose data structures optimized for numerical data, such as resizable arrays, dense and sparse matrices (multi-dimensional arrays), linear algebra, associative containers and buffer management. The Jet library contains mathematical and statistical tools for data analysis, powerful histogramming functionality, Random Number Generators and Distributions useful for (event) simulations, and more. The CoreJava library contains C-like print formatting. The Concurrent library contains standardized, efficient utility classes commonly encountered in parallel & concurrent programming.

Colt distribution consists of several free Java libraries bundled under one single uniform umbrella. Namely the Colt library, the Jet library, the CoreJava library, and the Concurrent library. It provides support for resizable arrays, dense, sparse matrices, histogramming functionality, Random Number Generators etc.

Colt - Scientific and Technical Computing in Java

NumPy is the fundamental package needed for scientific computing with Python. Numerical Python adds a fast and sophisticated N-dimensional array facility to the Python language. NumPy can also be used as an efficient multi-dimensional container of generic data. Arbitrary data-types can be defined. This allows NumPy to seamlessly and speedily integrate with a wide variety of databases.

NumPy - fundamental package for scientific computing with Python

FreeMat is a free environment for rapid engineering and scientific prototyping and data processing. It is similar to commercial systems such as MATLAB and IDL. It has built in arithmetic for manipulation of all supported data types, N-dimensional array manipulation, 2D and 3D plotting and image display, Visualization, Image manipulation, and as well as parallel programming. Google hosting: <A HREF="http://code.google.com/p/freemat" target="_blank">http://code.google.com/p/freemat</A>
 
 <img src="/AppImages/Article/freemat-img1.png" alt="" class="float-center">

FreeMat is a free environment for rapid engineering and scientific prototyping and data processing. It is similar to commercial systems such as MATLAB and IDL. It has built in arithmetic for manipulation of all supported data types, N-dimensional array manipulation, 2D and 3D plotting and image display, Visualization, Image manipulation, and as well as parallel programming.

Freemat - A Matlab alternative

Spyder is a Python development environment with advanced editing, interactive testing, debugging and introspection features. It is especially recommended for scientific computing thanks to NumPy (linear algebra), SciPy (signal and image processing), matplotlib (interactive 2D/3D plotting) and MayaVi’s mlab (interactive 3D visualization) support. Spyder may also be used as an extension library providing powerful console-related PyQt4 widgets. Spyder is part of spyderlib, a Python module based on PyQt4 and QScintilla2.

Spyder is a Python development environment with advanced editing, interactive testing, debugging and introspection features. It is especially recommended for scientific computing thanks to NumPy (linear algebra), SciPy (signal and image processing), matplotlib (interactive 2D/3D plotting) and MayaVi’s mlab (interactive 3D visualization) support.

Spyder

The GNU Scientific Library (GSL) is a numerical library for C and C++ programmers. The library provides a wide range of mathematical routines such as random number generators, special functions and least-squares fitting. There are over 1000 functions in total with an extensive test suite.
 
The complete range of subject areas covered by the library includes:
	<ul>
 <li>Complex Numbers</li>
 <li>Roots of Polynomials</li>
 <li>Special Functions</li>
 <li>Vectors and Matrices</li>
 <li>Permutations</li>
 <li>Sorting</li>
 <li>BLAS Support</li>
 <li>Linear Algebra</li>
 <li>Eigensystems</li>
 <li>Fast Fourier Transforms</li>
 <li>Quadrature</li>
 <li>Random Numbers</li>
 <li>Quasi-Random Sequences</li>
 <li>Random Distributions</li>
 <li>Statistics</li>
 <li>Histograms</li>
 <li>N-Tuples</li>
 <li>Monte Carlo Integration</li>
 <li>Simulated Annealing</li>
 <li>Differential Equations</li>
 <li>Interpolation</li>
 <li>Numerical Differentiation</li>
 <li>Chebyshev Approximation</li>
 <li>Series Acceleration</li>
 <li>Discrete Hankel Transforms</li>
 <li>Root-Finding</li>
 <li>Minimization</li>
 <li>Least-Squares Fitting</li>
 <li>Physical Constants</li>
 <li>IEEE Floating-Point</li>
 <li>Discrete Wavelet Transforms</li>
 <li>Basis splines</li>
 <li>Running Statistics</li>
 <li>Sparse Matrices and Linear Algebra</li>
 </ul>

The GNU Scientific Library (GSL) is a numerical library for C and C++ programmers. The library provides a wide range of mathematical routines such as random number generators, special functions and least-squares fitting. There are over 1000 functions in total with an extensive test suite.

GSL - GNU Scientific Library

Deeplearning4J is an open source, distributed neural net library written in Java and Scala. It integrates with Hadoop and Spark and runs on several backends that enable use of CPUs and GPUs. It provides versatile n-dimensional array class for Java and Scala. 
 
It is best suited for Face/image recognition, Voice search, Speech-to-text (transcription), Spam filtering (anomaly detection), Fraud detection, Recommender Systems (CRM, adtech, churn prevention), Regression.

Deeplearning4J is an open source, distributed neural net library written in Java and Scala. It integrates with Hadoop and Spark and runs on several backends that enable use of CPUs and GPUs. It provides versatile n-dimensional array class for Java and Scala. 

Deeplearning4J - Neural Net Platform in Java and Scala

SciRust is a Scientific computing library written in Rust programming language. The objective is to design a generic library which can be used as a backbone for scientific computing. Its current areas of focus includes Matrices, Linear algebra, Statistics, 
and Signal processing.

Scirust - Scientific Computing Library in Rust

ND4J is an open-sourced scientific computing library for the JVM. Its features include Versatile n-dimensional array object, Multiplatform functionality including GPUs Linear algebra and signal processing functions and lot more.


ND4j - Scientific Computing for the JVM (NDArrays)

Pathomx is a workflow-based tool for the analysis of metabolic pathways and visualisation of associated experimental data. 

Pathomx - Rapid workflow-based multi-omics analysis

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