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#
# This file is part of CasADi.
#
# CasADi -- A symbolic framework for dynamic optimization.
# Copyright (C) 2010-2023 Joel Andersson, Joris Gillis, Moritz Diehl,
# KU Leuven. All rights reserved.
# Copyright (C) 2011-2014 Greg Horn
#
# CasADi is free software; you can redistribute it and/or
# modify it under the terms of the GNU Lesser General Public
# License as published by the Free Software Foundation; either
# version 3 of the License, or (at your option) any later version.
#
# CasADi is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
# Lesser General Public License for more details.
#
# You should have received a copy of the GNU Lesser General Public
# License along with CasADi; if not, write to the Free Software
# Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
#
# Integrator tolerances
# =====================
from casadi import *
from numpy import *
from pylab import *
x=SX.sym('x')
dx=SX.sym('dx')
states = vertcat(x,dx)
dae={'x':states, 'ode':vertcat(dx,-x)}
tend = 2*pi*3
ts = linspace(0,tend,1000)
tolerances = [-10,-5,-4,-3,-2,-1]
figure()
for tol in tolerances:
opts = {'reltol':10.0**tol, 'abstol':10.0**tol, 'grid':ts, 'output_t0':True}
F = integrator('F', 'cvodes', dae, opts)
res = F(x0=[1,0])
plot(ts,array(res['xf'])[0,:].T,label='tol = 1e%d' % tol)
legend( loc='upper left')
xlabel('Time [s]')
ylabel('State x [-]')
show()
tolerances = logspace(-15,1,500)
endresult=[]
for tol in tolerances:
opts = {}
opts['reltol'] = tol
opts['abstol'] = tol
opts['tf'] = tend
F = integrator('F', 'cvodes', dae, opts)
res = F(x0=[1,0])
endresult.append(res['xf'][0])
endresult = vcat(endresult)
figure()
loglog(tolerances,(array(endresult)-1),'b',label='Positive error')
loglog(tolerances,-(array(endresult)-1),'r',label='Negative error')
xlabel('Integrator relative tolerance')
ylabel('Error at the end of integration time')
legend(loc='upper left')
show()
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