Coder Social home page Coder Social logo

tensor_calc's Introduction

tensor_calc

A tool for symbolically differentiating tensor expressions, created for my bachelor's thesis at FSU Jena in the summer semester of 2022.

Usage

View demo.py to get an idea of how the tool can be used to differentiate a tensor expression and how the resulting derivative can be checked numerically for correctness.

Language

The tool takes a string consisting of three parts as input:

  • the declaration part specifies the tensor variables used in the expression, along with how many axes they each have
  • the expression part specifies the tensor expression to be differentiated
  • the argument part specifies with respect to which tensor variable the expression is to be differentiated

The concrete language is specified by the following grammar in extended Backus-Naur form:

input = declaration expressionpart argument

declaration = 'declare' (tensordeclaration)*
tensordeclaration = tensorname (digit)*
tensorname = alpha { alpha | digit }
alpha = smallalpha | largealpha
smallalpha = [a-z]
largealpha = [A-Z]

expressionpart = 'expression' expr
expr = term (( '+' | '-' ) term)*
term = factor (( '*(' productindices ')') factor | '/' factor)*
productindices = tensorindices ',' tensorindices '->' tensorindices
tensorindices = (smallalpha)*
factor = {'-'} atom ('^' ('(' expr ')' | atom))*
atom = number | function '(' expr ')' | tensorname | '(' expr ')' | delta
number = ['-'] digit* '.' digit* [( 'e' | 'E' ) ['+' | '-'] (digit)*]
digit = [0-9]
function = 'sin' | 'cos' | 'tan' | 'arcsin' | 'arccos' | 'arctan' | 'tanh' | 'exp' 
         | 'log' | 'sign' | 'relu' | 'abs' | 'det' | 'inv' | 'adj'
delta = 'delta(' {digit}+ ')' 

argument = 'derivative wrt' tensorname

tensor_calc's People

Contributors

toucanmeister avatar

Watchers

James Cloos avatar  avatar

Recommend Projects

  • React photo React

    A declarative, efficient, and flexible JavaScript library for building user interfaces.

  • Vue.js photo Vue.js

    ๐Ÿ–– Vue.js is a progressive, incrementally-adoptable JavaScript framework for building UI on the web.

  • Typescript photo Typescript

    TypeScript is a superset of JavaScript that compiles to clean JavaScript output.

  • TensorFlow photo TensorFlow

    An Open Source Machine Learning Framework for Everyone

  • Django photo Django

    The Web framework for perfectionists with deadlines.

  • D3 photo D3

    Bring data to life with SVG, Canvas and HTML. ๐Ÿ“Š๐Ÿ“ˆ๐ŸŽ‰

Recommend Topics

  • javascript

    JavaScript (JS) is a lightweight interpreted programming language with first-class functions.

  • web

    Some thing interesting about web. New door for the world.

  • server

    A server is a program made to process requests and deliver data to clients.

  • Machine learning

    Machine learning is a way of modeling and interpreting data that allows a piece of software to respond intelligently.

  • Game

    Some thing interesting about game, make everyone happy.

Recommend Org

  • Facebook photo Facebook

    We are working to build community through open source technology. NB: members must have two-factor auth.

  • Microsoft photo Microsoft

    Open source projects and samples from Microsoft.

  • Google photo Google

    Google โค๏ธ Open Source for everyone.

  • D3 photo D3

    Data-Driven Documents codes.