Automatsko deriviranje

undergraduate thesis

• Title (english): Automatic differentiation
• Author: Gustav Matula
• Mentor: Ante Đerek (mentor)
• Committee member: Ante Đerek (predsjednik povjerenstva)
• Committee member: Ivan Budiselić (član povjerenstva)
• Committee member: Klemo Vladimir (član povjerenstva)
• Granter: University of Zagreb; Faculty of Electrical Engineering and Computing; Zagreb
• Defense date and country: 2014-07-14, Croatia
• Scientific / art field, discipline and subdiscipline: TECHNICAL SCIENCES; Computing

Abstract

Derivacije funkcija se na računalima tipično računaju numerički (metodom konačnih
razlika), simbolički (korištenjem CAS (engl. Computer Algebra System)
alata, ili (nažalost, još uvijek) ručno. U ovome radu analiziramo osnove jednog alternativnog pristupa:
automatskog, ili algoritamskog deriviranja. Za razliku od numeričkog ili
simboličkog, automatsko deriviranje pretpostavlja poznavanje izvornog koda koji
implementira funkciju koju želimo derivirati, i temeljem tog znanja stvara kod
koji implementira njezinu derivaciju. Prednost pred numeričkim deriviranjem je
preciznost (nema zaokruživanja), pred simboličkim mogućnost deriviranja algoritama za razliku od
jednostavnih izraza, a pred ručnim odsutstvo ljudske pogreške. U radu
obrađujemo dva osnovna tipa automatskog deriviranja: deriviranje prema
naprijed, i deriviranje prema natrag. Uz teoretska razmatranja bavimo se i
jednostavnom implementacijom u programskom jeziku Python.

Abstract (english)

Calculation of function derivatives are tipically done numerically (the method
of finite differences), symbolically (using a CAS (Computer Algebra
System), or (unfortunatelly, still) by hand. In this thesis we analyze the
basics of an alternative approach: automatic, or algorithmic differentiation.
Unlike numeric or symbolic, automatic differentiation assumes knowledge of
source code that implements the function we wish to differentiate, and based on
that builds the code that implements its derivative. The advantage with respect
to numerical differentiation is precision (no round-off errors), with respect
to symbolical differentiation the ability to differentiate algorithms in
contrast to simple expressions, and with respect to manual differentiation
simply the absence of human error. In the thesis we go through the two main
types of automatic differentiation: the forward and backward modes. In addition
to theory, we also deal with a simple implementation in Python.

• Keywords: automatsko deriviranje; algoritamsko deriviranje
• Keywords (english): automatic differentiation; algorithmic differentiation
• Language: croatian
• URN:NBN: urn:nbn:hr:168:145735
• Study programme: Title: Computing; Study programme type: university; Study level: undergraduate; Academic / professional title: sveučilišni/a prvostupnik/ prvostupnica (baccalaureus/baccalaurea) inženjer/inženjerka računarstva (sveučilišni/a prvostupnik/ prvostupnica (baccalaureus/baccalaurea) inženjer/inženjerka računarstva)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Closed access
• Created on: 2018-02-05 17:44:41