#!/usr/bin/python -Wall # ================================================================ # John Kerl # kerl at math dot arizona dot edu # 2008-05-12 # ================================================================ from __future__ import division # 1/2 = 0.5, not 0. import random from math import * import copy import sys import re # ---------------------------------------------------------------- def usage(): print >> sys.stderr, "Usage: %s [options]" % (sys.argv[0]) print >> sys.stderr, "Options:" print >> sys.stderr, " T=[number]" print >> sys.stderr, " nt=[number]" print >> sys.stderr, " X0=[number]" print >> sys.stderr, " nX=[number]" sys.exit(1) # ---------------------------------------------------------------- # SDE: dX = -X dt + exp(-t) db # Solution: X(t) = (X(0) + b(t)) * exp(-t). T = 10 nt = 1000 X0 = 1 nX = 5 argc = len(sys.argv) for argi in range(1, argc): if re.match(r'^T=', sys.argv[argi]): T = float(sys.argv[argi][2:]) elif re.match(r'^nt=', sys.argv[argi]): nt = int (sys.argv[argi][3:]) elif re.match(r'^X0=', sys.argv[argi]): X0 = float(sys.argv[argi][3:]) elif re.match(r'^nX=', sys.argv[argi]): nX = int (sys.argv[argi][3:]) else: usage() dt = T/nt t = 0 approx = [X0] * nX exact = [X0] * nX Bt = [0.0] * nX sqrtdt = sqrt(dt) while (t <= T): for k in range(0, nX): exact[k] = (X0 + Bt[k]) * exp(-t) print "%11.7f" % (t), for k in range(0, nX): print "%11.7f %11.7f %9.3e" % \ (exact[k], approx[k], exact[k]-approx[k]), print "%11.7f" % (X0 * exp(-t)) for k in range(0, nX): dB = random.gauss(0, sqrtdt) approx[k] += -approx[k] * dt + exp(-t) * dB Bt[k] += dB t += dt