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test_velocity_perturbation.py
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test_velocity_perturbation.py
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from Sjoe_m_func2 import *
from Sjoe_index import Index
from numpy import *
import IVP
import time
def Sjoe(args = None):
if args != None:
def rhs(t,y):
return oderhs(t,y, args)
else:
def rhs(t,y):
return oderhs(t,y)
rhs.name = 'rhs'
return rhs
#Sjoe.name = 'Sjoe'
## Initial position/motion of the rolling elements
n = 8
N = 5*n+4
u0 = array(zeros(N))
ind = Index(n)
for i in xrange(0,n):
u0[ind.r(i)] = (b0+c0)/2 # r
u0[ind.theta(i)] = -pi/2 + 2*pi*i/n# theta
u0[ind.rdot(i)] = 0 # rdot
u0[ind.thetadot(i)] = b0/(b0+c0)*w0 # thetadot
u0[ind.phidot(i)] = b0/2/a0*w0 # phidot - note that phi is not a state variable since it does not matter here
rhs = Sjoe()
cv=IVP.CVode(rhs,u0)
cv.set_method('BDF','Newton')
atol = array(zeros(N))
for i in range(0,N):
atol[i] = 1e-8
cv.set_tolerance(atol,rtol=1.e-8)
numsteps = 100
t0 = 0.005
ex_time0 = time.clock()
cv(t0,numsteps)
ex_time0 = time.clock() - ex_time0
stats=cv.stats(pr=1)
print stats
Y = cv.aus
t = cv.ts
state0 = Y[-1]
for i in range(0,n):
subplot(n+1,5,5*i+1) # r
plot(t, Y[:,ind.r(i)])
subplot(n+1,5,5*i+2) # th
plot(t, Y[:,ind.theta(i)])
subplot(n+1,5,5*i+3) # rdot
plot(t, Y[:,ind.rdot(i)])
subplot(n+1,5,5*i+4) # thetadot
plot(t, Y[:,ind.thetadot(i)])
subplot(n+1,5,5*i+5) # phidot
plot(t, Y[:,ind.phidot(i)])
subplot(n+1,5,5*n+1)
plot(t, Y[:,ind.x()])
subplot(n+1,5,5*n+2)
plot(t, Y[:,ind.xdot()])
subplot(n+1,5,5*n+3)
plot(t, Y[:,ind.y()])
subplot(n+1,5,5*n+4)
plot(t, Y[:,ind.ydot()])
show()
#
#len0 = len(cv.ts)
#
#t1 = 2*t0
#
#ex_time1 = time.clock()
#cv(t1,numsteps)
#ex_time1 = time.clock() - ex_time1
#
#Y = cv.aus[len0:]
#t = cv.ts[len0:]
#state0 = Y[-1]
#
#figure()
#for i in range(0,n):
# subplot(n+1,5,5*i+1) # r
# plot(t, Y[:,ind.r(i)])
#
# subplot(n+1,5,5*i+2) # th
# plot(t, Y[:,ind.theta(i)])
#
# subplot(n+1,5,5*i+3) # rdot
# plot(t, Y[:,ind.rdot(i)])
#
# subplot(n+1,5,5*i+4) # thetadot
# plot(t, Y[:,ind.thetadot(i)])
#
# subplot(n+1,5,5*i+5) # phidot
# plot(t, Y[:,ind.phidot(i)])
#
#subplot(n+1,5,5*n+1)
#plot(t, Y[:,ind.x()])
#subplot(n+1,5,5*n+2)
#plot(t, Y[:,ind.xdot()])
#subplot(n+1,5,5*n+3)
#plot(t, Y[:,ind.y()])
#subplot(n+1,5,5*n+4)
#plot(t, Y[:,ind.ydot()])
#
#show()
#
#
## Endstate at t=0.005:
# array([ -3.12389648e-07, 2.82812046e-05, 2.50096813e-02,
# 3.14817787e-01, 2.50262817e-02, 1.09934532e+00,
# 2.50282524e-02, 1.88060072e+00, 2.50144220e-02,
# 2.66663069e+00, 2.49960013e-02, 3.45423783e+00,
# 2.49875915e-02, 4.24115807e+00, 2.49866347e-02,
# 5.02732275e+00, 2.49936367e-02, 5.81286402e+00,
# -7.46800018e-03, -7.59069491e-04, 2.77472966e-03,
# 3.76622261e+02, 1.88670729e+03, 8.29568845e-04,
# 3.76254001e+02, 1.88824350e+03, -1.57856688e-03,
# 3.75725818e+02, 1.89094483e+03, -3.08763092e-03,
# 3.76585387e+02, 1.88703174e+03, -1.43424948e-03,
# 3.77056381e+02, 1.88573443e+03, -4.33668989e-04,
# 3.77137066e+02, 1.88709100e+03, 8.07733445e-04,
# 3.77137365e+02, 1.88720102e+03, 1.57545715e-03,
# 3.77056246e+02, 1.88600149e+03])
#
## Endstate at t=0.01:
#array([ -7.71179565e-07, 2.77200897e-05, 2.50241704e-02,
# 2.19440825e+00, 2.50064179e-02, 2.98048553e+00,
# 2.49923984e-02, 3.76239529e+00, 2.49864966e-02,
# 4.55196442e+00, 2.49887012e-02, 5.34042404e+00,
# 2.49977697e-02, 6.12728920e+00, 2.50169088e-02,
# 6.91226752e+00, 2.50284747e-02, 7.69513877e+00,
# 3.00859059e-04, -4.27336583e-04, -6.39188912e-03,
# 3.75812567e+02, 1.88934890e+03, -1.06498480e-02,
# 3.76828366e+02, 1.88567604e+03, -4.37114190e-03,
# 3.77172556e+02, 1.88672359e+03, -7.89437877e-04,
# 3.77293844e+02, 1.88799973e+03, 3.23063768e-03,
# 3.77240661e+02, 1.88748347e+03, 5.64121419e-03,
# 3.77047727e+02, 1.88549098e+03, 8.61246496e-03,
# 3.76267256e+02, 1.88751593e+03, 1.55778140e-03,
# 3.75710508e+02, 1.88946348e+03])
#
# Execution times:
# 0.005: 187.48000000000013
# 0.01 : 45.1400000000001
#
#u0old = copy(u0)
#u0 = array([ -3.12389648e-07, 2.82812046e-05, 2.50096813e-02,
# 3.14817787e-01, 2.50262817e-02, 1.09934532e+00,
# 2.50282524e-02, 1.88060072e+00, 2.50144220e-02,
# 2.66663069e+00, 2.49960013e-02, 3.45423783e+00,
# 2.49875915e-02, 4.24115807e+00, 2.49866347e-02,
# 5.02732275e+00, 2.49936367e-02, 5.81286402e+00,
# -7.46800018e-03, -7.59069491e-04, 2.77472966e-03,
# 3.76622261e+02, 1.88670729e+03, 8.29568845e-04,
# 3.76254001e+02, 1.88824350e+03, -1.57856688e-03,
# 3.75725818e+02, 1.89094483e+03, -3.08763092e-03,
# 3.76585387e+02, 1.88703174e+03, -1.43424948e-03,
# 3.77056381e+02, 1.88573443e+03, -4.33668989e-04,
# 3.77137066e+02, 1.88709100e+03, 8.07733445e-04,
# 3.77137365e+02, 1.88720102e+03, 1.57545715e-03,
# 3.77056246e+02, 1.88600149e+03])
#
##for i in range(0,n):
## u0[ind.thetadot(i)] = u0old[ind.thetadot(i)]
#
#cv=IVP.CVode(rhs,u0)
#cv.set_method('BDF','Newton')
#atol = array(zeros(N))
#for i in range(0,N):
# atol[i] = 1e-8
#cv.set_tolerance(atol,rtol=1.e-8)
#
#numsteps = 100
#
## Perturb the velocities:
#for i in range(0,n):
# u0[ind.thetadot(i)] *= (1 + rand()/10.)
#
#
#t1 = 0.005
#
#ex_time1 = time.clock()
#cv(t1,numsteps)
#ex_time1 = time.clock() - ex_time1
#
#Y = cv.aus
#t = cv.ts
#state0 = Y[-1]
#
#figure()
#for i in range(0,n):
# subplot(n+1,5,5*i+1) # r
# plot(t, Y[:,ind.r(i)])
#
# subplot(n+1,5,5*i+2) # th
# plot(t, Y[:,ind.theta(i)])
#
# subplot(n+1,5,5*i+3) # rdot
# plot(t, Y[:,ind.rdot(i)])
#
# subplot(n+1,5,5*i+4) # thetadot
# plot(t, Y[:,ind.thetadot(i)])
#
# subplot(n+1,5,5*i+5) # phidot
# plot(t, Y[:,ind.phidot(i)])
#
#subplot(n+1,5,5*n+1)
#plot(t, Y[:,ind.x()])
#subplot(n+1,5,5*n+2)
#plot(t, Y[:,ind.xdot()])
#subplot(n+1,5,5*n+3)
#plot(t, Y[:,ind.y()])
#subplot(n+1,5,5*n+4)
#plot(t, Y[:,ind.ydot()])
#
#show()
### Results:
###
### Initial 0.005 seconds : 205 seconds
###
### Restart with same values : 43 seconds
### Restart with original values : 57 seconds
### Restart with max 10% random diff: 64.62 sec
### 76.29 sec
### 69.85 sec
### 61.36 sec
### 75.63 sec
###
### Average: 69.55 sec