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![:= [ :x| x sin ].
:= 1/2.
iffForward := [:h| (((f value: (x+h)) - (f value: x)) / h)].
rror := [:h| ((diffForward value: h) - x cos) abs].
rror value: 0.1](https://image.slidesharecdn.com/3-polymath1-191104144754/85/Polymath-Version-1-0-and-Beyond-18-320.jpg)
![f := [ :x| (x*x) sin ].
pi := Float pi.
x := pi /2.
h := 0.001.
((f value: (h*1i +x )) imaginary) / h.
pi * ((pi*pi/4) cos)](https://image.slidesharecdn.com/3-polymath1-191104144754/85/Polymath-Version-1-0-and-Beyond-20-320.jpg)
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Polymath: Version 1.0 and Beyond
- 1. version 1.0 andbeyond Serge Stinckwich, Oleksandr Zaytsev HemalVarambhia, Konrad Hinsen Atharva Khare, Nikhil Pinnaparaju Werner Kassens le logotype : les différentes formes en couleur version verticale version compacte
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- 5. • A numericframework for Pharo (written in pure Pharo) • Ordinary differential equations, Random Number Generators, Linear Algebra, Matrices, Complex Numbers, FFT, Polynomials, Probability distributions, … • DataFrames, data analysis on tabular data • MIT Licence • PolyMath 1.0 release • https://github.com/PolyMathOrg/PolyMath
- 6. Contributors • Thank youall ! • All contributions are valuable (code&documentation) • Regular meeting on Discord (#polymath channel) Hemal Varambhia Konrad Hinsen Atharva Khare Oleksandr Zaytsev Nikhil Pinnaparaju
- 7. Since last year •Release 1.0 version + new logo • Clean the code (All PM prefix classes), add more unit tests • PCA and t-SNE, DataFrames (Atharva, Nikhil, Oleks) • Random Numbers cleaning (Hemal) • Automatic Differentiation package cleaning (Serge) • Data Transformer hierarchy (PMStandardizationScaler) like in scikit-learn • Trunk-based development since 1.0 (all code is committed to master branch + one release branch) • Add a contributing guide and code of conduct
- 8. Metrics • 300 classes,59 packages, 24K LOC • 806 green unit tests, 1034 commits, 100 stars on github (9th Pharo project on github)
- 13. designed by LusyDolia
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- 16. Derivatives • The derivativesf’(x) of a function of a single variable x is the rate at which the value of f changes at x. • How to compute derivatives numerically ?
- 17. Numerical differentiation by usingfinite difference • Theoretically, the smaller the h is, the better the derivative estimates • Practically very small value of h can result in numerical cancellation errors …
- 18. := [ :x|x sin ]. := 1/2. iffForward := [:h| (((f value: (x+h)) - (f value: x)) / h)]. rror := [:h| ((diffForward value: h) - x cos) abs]. rror value: 0.1
- 19. Numerical differentiation by theComplex Step Method • The Complex Step Method bypass the subtractive errors, by using only one single function evaluation (but on complex numbers). • Taylor expansion for an imaginary step is:
- 20. f := [:x| (x*x) sin ]. pi := Float pi. x := pi /2. h := 0.001. ((f value: (h*1i +x )) imaginary) / h. pi * ((pi*pi/4) cos)
- 22. Automatic Differentiation • Automatic Differentiationis a generalisation of derivatives on general programs.
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- 25. What is dimensionality reduction? • Process of reducing the number of variables under consideration by obtaining a set of principal variables
- 26. Principal Component Analysis (PCA) •Used in machine learning, statistics to solve the dimensionality curse. • Dimension reductionality approach that perform a linear mapping of the data to a lower-dimensional space, in such a way that the variance of the data in low- dimensional representation is maximised.
- 28. t-SNE • t-SNE shortstory: The goal is to take a set of points in a high-dimensional space and find a faithful representation of those points in a lower-dimensional space, typically the 2D plane. • Probabilistic non-linear algorithm • Demo of Atharva Kharve
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- 30. ActivePapers Pharo • Workof Konrad Hinsen • Pharo + GToolkit + ActivePapers + PolyMath = Scientific Workbench • Presented at IWST 2019 (Tuesday)
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- 32. Port of Domains toPharo • Work of Luciano Notarfrancesco • Computational algebra system in Smalltalk (Group, Morphism, Monoids, Elliptic curves, …) • Ongoing port to Pharo : https://github.com/PolyMathOrg/ Domains
- 34. Support PolyMath • Youcan contribute code and documentation. Pull requests are welcome • Please contribute fundings for PolyMath. • BountySource: https://www.bountysource.com/teams/ polymath • Ask to be funded by NumFocus (Numpy, Matplotlib, pandas …)