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The Python and Julia Programming Languages Scientific, Numerical and Signal Processing Numerical Signal Processing Numerical Programming Languages Python Julia The Python and Julia Programming Languages scientific, numerical and signal processing Jos´eJasnau Caeiro [email protected] Lab SEPSI Instituto Polit´ecnicode Beja Beja, 15th May 2014 1 de 26 Caeiro The Python and Julia Programming Languages Numerical Signal Processing Numerical Programming Languages Python Julia 1 Numerical Signal Processing 2 Numerical Programming Languages 3 Python 4 Julia 2 de 26 Caeiro The Python and Julia Programming Languages Numerical Signal Processing Numerical Programming Languages Python Julia Signals and Signal Processing An informal definition of signal is, Definition A signal is a function of independent variables such as time, distance, position, temperature, and pressure (S. K. Mitra, 2002) another signal processing is, according to Wikipedia (2014), Definition Signal processing is an area of Systems Engineering, Electrical Engineering and Applied Mathematics that deals with operations on or analysis of analog as well as digitized signals, representing time-varying or spatially varying physical quantities. 3 de 26 Caeiro The Python and Julia Programming Languages Numerical Signal Processing Numerical Programming Languages Python Julia Examples of Signals Some examples of signals are: sound air pressure as a function of time at a certain point in 3D space; electromagnetic radiation ECG electrocardiography signal, a function representing the electrical activity; images photographs or video frames; sensor generated signals temperature, pressure, etc. 4 de 26 Caeiro The Python and Julia Programming Languages Numerical Signal Processing Numerical Programming Languages Python Julia Typical Signal Processing Data structures and operations: matrix operations; discrete vector based processing; Fast Fourier Transform; Discrete Transforms; filtering; 1D and 2D discrete convolution (a multiply and add operation); N-dimensional statistical signal processing; image point and local based operators. And most of the time several data formats must be supported and also scientific plotting. 5 de 26 Caeiro The Python and Julia Programming Languages Numerical Signal Processing Numerical Programming Languages Python Julia Some historical landmarks Fortran a general purpose imperative programming language (late 1950's) high performance compiler; huge set of numerical and scientific libraries; static memory allocation; C another general purpose imperative programming language (1973) maps efficiently to typical machine instructions; available for the majority of computer architectures and operating systems, namely microcontroler and digital signal processors (DSPs); 6 de 26 Caeiro The Python and Julia Programming Languages Numerical Signal Processing Numerical Programming Languages Python Julia MATLAB The golden standard programming language used for signal processing research and development developed in the late 1970s to give easy access to students to LINPACK and EISPACK Fortran algebraic libraries; popular in applied mathematics, control engineering, image processing, numerical analysis and signal processing; simple syntax with dynamic programming languages properties; can call functions and subroutines written in C or Fortran; large set of functions and toolkits (a set of functions and libraries dedicated to a specific field). 7 de 26 Caeiro The Python and Julia Programming Languages Numerical Signal Processing Numerical Programming Languages Python Julia MATLAB MATLAB is a proprietary product of MathWorks; very expensive with toolboxes sold separately using a license model; last release is MATLAB 8.3; offers some support for parallel processing; poor syntax for advanced programming and data structures, namely object oriented programming, lists, dictionaries, etc. offers support to symbolic processing through MuPAD; Java, Perl or .NET libraries can be directly called from MATLAB; 8 de 26 Caeiro The Python and Julia Programming Languages Numerical Signal Processing Numerical Programming Languages Python Julia MATLAB and alternatives Some open source alternatives have appeared offering a large extent of compatibility: GNU Octave appeared around 1988 and is mostly compatible with MATLAB adopting a GNU General Public License; Scilab appeared around 1990 within INRIA, it is the most compatible language with MATLAB, and although free presents a commercial support through scilab enterprises; FreeMat another free alternative under GPL and with 95% compatibility with MATLAB; ScalaLab provides an efficient MATLAB like working style for the Java Virtual Machine and is programmed in Scala. 9 de 26 Caeiro The Python and Julia Programming Languages Numerical Signal Processing Numerical Programming Languages Python Julia General Properties Python appeared in 1991 and is one of the most successful dynamic programming languages; supports a large set of programming paradigms; programmers productivity is high due to the language and the large set of libraries available; easy to interface to C; good support for high level data structures. 10 de 26 Caeiro The Python and Julia Programming Languages Numerical Signal Processing Numerical Programming Languages Python Julia numpy, scipy and matplotlib In 2005 a stable numerical package proposal was created by Travis Oliphant, based on previous ancestor packages: NumPy provides functionality comparable to MATLAB; easily interfaces with C; SciPy extends this functionality; Matplotlib is an advanced plotting package; A scientific programming framework joining several packages was created using Python: sage. It is very large (several GB and hundreds of packages) and is currently under version 6.2. 11 de 26 Caeiro The Python and Julia Programming Languages Numerical Signal Processing Numerical Programming Languages Python Julia Criticism of MATLAB MATLAB is proprietary and costly; MATLAB is used by only 0:711% of the general programming community; MATLAB data structures are cumbersome and does not support generic programming; MATLAB is slow when cycles and selections are involved. 12 de 26 Caeiro The Python and Julia Programming Languages Numerical Signal Processing Numerical Programming Languages Python Julia Criticism of Python not compatible with MATLAB; due to design there are some multi core programming limitations; slow when cycles and selections are involved. 13 de 26 Caeiro The Python and Julia Programming Languages Numerical Signal Processing Numerical Programming Languages Python Julia The Julia programming language The creators of Julia are based on the Massasuchets Institute of Technology and are: Alan Edelman, professor of Applied Mathematics at MIT; Stefan Karpinski, a programmer;Jeff Bezanson, another programmer; Viral Shah, a Bangalore programmer that works on Julia from India. 14 de 26 Caeiro The Python and Julia Programming Languages Numerical Signal Processing Numerical Programming Languages Python Julia And is being used at Julia is used at: Stanford University, Spring 2014, AA222, Introduction to Multidisciplinary Design Optimization (Prof. Mykel J. Kochenderfer) Pennsylvania State University, Spring 2014, ASTRO 585, High-Performance Scientific Computing for Astrophysics (Prof. Eric B. Ford) Cornell University, Spring 2014, CS 5220, Applications of Parallel Computers (Prof. David Bindel) MIT, Spring 2014 18.330, Introduction to Numerical Analysis (Dr. Homer Reid), 15.S60, Software Tools for Operations Research (Iain Dunning), 15.083, Integer Programming and Combinatorial Optimization (Prof. Juan Pablo Vielma) 15 de 26 Caeiro The Python and Julia Programming Languages Numerical Signal Processing Numerical Programming Languages Python Julia Why Julia? The authors wanted a programming language with the speed of C and the dynamic programming features of Python and Ruby; with a familiar syntax as MATLAB; usable for general programming as Python; supportive of Hadoop, an open source software framework for storage and large-scale processing of data-sets on clusters of commodity hardware (Wikipedia quote); easy to learn to people coming from the signal processing and machine learnig community. 16 de 26 Caeiro The Python and Julia Programming Languages Numerical Signal Processing Numerical Programming Languages Python Julia Julia Some characteristics of the Julia programming language: modern dynamic programming language (development started in 2009); designed for technical and scientific computing; syntax familiar for MATLAB programmers; calls Python and C functions directly; designed for parallel and distributed computation; MIT licensed: free and open source; developed at MIT. 17 de 26 Caeiro The Python and Julia Programming Languages Numerical Signal Processing Numerical Programming Languages Python Julia A larger set of features Multiple dispatch: providing the ability to define function behavior across many combinations of argument types; Dynamic type system: types for documentation, optimization, and dispatch; Lisp-like macros and other metaprogramming facilities; multiprocessing environment based on message passing; parallel processing with GPUs based on OpenCL with bindings based on PyOpenCL (a Python based package), https://github.com/JuliaGPU/OpenCL.jl; Coroutines: lightweight \green" threading; LLVM-based just in time compiler. 18 de 26 Caeiro The Python and Julia Programming Languages Numerical Signal Processing Numerical Programming Languages Python Julia Syntax example MATLAB 1 lena = imread('lena512. pgm'); lena = double(lena);channel = size(lena, 3); 3 h e i g h t = size(lena, 1);width = size(lena, 2); lenaOutput
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