FContin
Solve F(u, λ) = 0 over λ with just F!
This repository contains natural and pseudo-arclength/Euler-Newton continuation library using JAX for automatic differentiation, numdifftools for numerical differentiation using real or complex derivatives, and Pacopy
This enables automatic/numerical differentiation to obtain the Jacobian and derivative with respect to the parameter. GPU/TPU support is packaged as part of JAX.
How to install and execute?
Just run
pip install fcontin
The following program illustrates a basic example
from fcontin.ContProblem import ContProblem
###
# Define problem
###
def f(u, lmbda):
"""The evaluation of the function to be solved
"""
return [
u[0] + u[1] - (lmbda + 1.), u[0] - u[1] - lmbda
]
###
# Solving and Plotting
###
# Initial guess
u0 = [0., 0.]
# Initial parameter value
lmbda0 = 1.0
# Creating the problem
# Natural or Euler-Newton for cont_method
# Forward, Reverse, Numerical, Complex for jac_mode
problem = ContProblem(f, u0, lmbda0,
cont_method='Euler-Newton',
jac_mode='Complex',
max_steps=10,
newton_tol=1e-10,
callback=callback
)
problem.solve()Whom to contact?
Please direct your queries to gpavanb1 for any questions.
