Judi.jl

Just a differentiation library

Symbolic differentiation of vector/matrix/tensor expressions in Julia

This package is still under development - there be dragons. Issues are welcome.

Example

Create a matrix and a vector:

using Judi

@matrix A
@vector x

Create an expression:

expr = x' * A * x

The variable expr now contains an internal representation of the expression x' * A * x.

Compute the gradient and the Hessian with respect to the vector x.

g = gradient(expr, x)
H = hessian(expr, x)

Convert the gradient and the Hessian into standard notation using to_std_string:

to_std_string(g) # "Aᵀx + Ax"
to_std_string(H) # "Aᵀ + A"

Jacobians can be computed with jacobian:

to_std_string(jacobian(A * x, x)) # "A"

The method derivative can be used to compute arbitrary derivatives.

to_std_string(derivative(tr(A), A)) # "I"

The method to_std_string will throw an exception when given an expression that that cannot be converted to standard notation.

Supported operators

tr, sin, cos, +, -, *, ', .*

Installation

This library is not yet published in the general registry. To install it directly from Github:

using Pkg; Pkg.add("https://github.com/asterycs/Judi.jl.git")

Acknowledgements

The implementation is based on the ideas presented in

S. Laue, M. Mitterreiter, and J. Giesen. Computing Higher Order Derivatives of Matrix and Tensor Expressions, NeurIPS 2018.