def test_zero_sulotion():
"""
Testing that Theta=epsilon=0 gives constant zero
solutions when inserted in simulate function
"""
#test for diffrent beta and time steps per period
N=[50,100,1000]
#it only makes phissical sence if beta is in (0,1)
B=[0.1,0.4,0.7,0.9]
#loop through the different test values
for n in N:
for beta in B:
#use simulate function we have made with arguments
#given in exercise. Also useing number_of_periods=1
x,y,tet,t=simulate(beta,0,0,1,n,False)
#find maximal values in x and y solution
x_max = abs(amax(x))
y_max = abs(amax(y))
#check that x_max and y_max is 0, with a possabillety
#for rounding errors.
assert ((x_max<10**(-16)) and (y_max<10**(-16)))
def test_zero_sulotion():
"""
Testing that Theta=epsilon=0 gives constant zero
solutions when inserted in simulate function
"""
#test for diffrent beta and time steps per period
N = [50, 100, 1000]
#it only makes phissical sence if beta is in (0,1)
B = [0.1, 0.4, 0.7, 0.9]
#loop through the different test values
for n in N:
for beta in B:
#use simulate function we have made with arguments
#given in exercise. Also useing number_of_periods=1
x, y, tet, t = simulate(beta, 0, 0, 1, n, False)
#find maximal values in x and y solution
x_max = abs(amax(x))
y_max = abs(amax(y))
#check that x_max and y_max is 0, with a possabillety
#for rounding errors.
assert ((x_max < 10**(-16)) and (y_max < 10**(-16)))
def test_vertical_motion(dt=2*pi*0.0001,tol=10**(-5)):
"""
Testing that vertical motion corrosponds with exact solution.
when Theta=0, epsilon in (0,1), we get pure vertical motion
satisfying y'' = -(beta/(1 - beta)y, which has exact solution
y(t)=Icos(wt), I = -epsilon, and w = sqrt(beta/(1 - beta)). This
is used to show that simulate is good.
I set tollerance for my test case to be 10**(-5), this depends
on size of dt.
"""
#test for diffrent epsilons and betas.
Beta_and_eps=[0.1,0.4,0.7,0.9]
#find timsteps_per_period with dt
n= int(round(2*pi/dt))
#loop throgh diffrent testing values.
for eps in Beta_and_eps:
for beta in Beta_and_eps:
#solve the equation
x,y,tet,t = simulate(beta,0,eps,1,n,False)
#create exact solution
w = sqrt(beta/(1 - beta))
I = -eps
y_exact = I*cos(w*t)
#calculate l2 error of exact solution minus
#numerical solution.
l2_error= sqrt(dt*sum((y-y_exact)**2))
#check if l2 norm is less then tolerence.
assert l2_error<tol
def test_vertical_motion(dt=2 * pi * 0.0001, tol=10**(-5)):
"""
Testing that vertical motion corrosponds with exact solution.
when Theta=0, epsilon in (0,1), we get pure vertical motion
satisfying y'' = -(beta/(1 - beta)y, which has exact solution
y(t)=Icos(wt), I = -epsilon, and w = sqrt(beta/(1 - beta)). This
is used to show that simulate is good.
I set tollerance for my test case to be 10**(-5), this depends
on size of dt.
"""
#test for diffrent epsilons and betas.
Beta_and_eps = [0.1, 0.4, 0.7, 0.9]
#find timsteps_per_period with dt
n = int(round(2 * pi / dt))
#loop throgh diffrent testing values.
for eps in Beta_and_eps:
for beta in Beta_and_eps:
#solve the equation
x, y, tet, t = simulate(beta, 0, eps, 1, n, False)
#create exact solution
w = sqrt(beta / (1 - beta))
I = -eps
y_exact = I * cos(w * t)
#calculate l2 error of exact solution minus
#numerical solution.
l2_error = sqrt(dt * sum((y - y_exact)**2))
#check if l2 norm is less then tolerence.
assert l2_error < tol