compute_fp.py

"""
Origin: QE by John Stachurski and Thomas J. Sargent
Filename: compute_fp.py
Authors: John Stachurski and Thomas Sargent
LastModified: 11/08/2013

Compute the fixed point of a given operator T, starting from 
specified initial condition v.
"""

import numpy as np

def compute_fixed_point(T, specs, v, error_tol=1e-3, max_iter=50, verbose=1):
    """
    Computes and returns T^k v, where T is an operator, v is an initial
    condition and k is the number of iterates. Provided that T is a
    contraction mapping or similar, T^k v will be an approximation to the
    fixed point.

    The convention for using this function is that T can be called as 
    
        new_v = T(specs, v).

    """
    iterate = 0 
    error = error_tol + 1
    while iterate < max_iter and error > error_tol:
        new_v = T(specs, v)
        iterate += 1
        error = np.max(np.abs(new_v - v))
        if verbose:
            print "Computed iterate %d with error %f" % (iterate, error)
        v = new_v
    return v