integrators/tolerance.py

This example looks at the effect of the 'reltol' setting of casadi::Integrator.

View output (PDF) | source (python)

See also

casadi::integrator();

 



 
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()