def Task11a(mode):
'''time evolution'''
if mode == 0: #simple oscillation
a = [0, 0, np.pi / 2, 0]
figtitle = 'Simple oscillation time evolution'
elif mode == 1: #full rotation
a = [0, 0, 0, 2]
figtitle = 'Full rotation time evolution'
cart.setState(a)
cart.performAction()
cart.sysvar[2] = [remap_angle(value) for value in cart.sysvar[2]]
v = np.asarray(cart.sysvar)
titles = ['Cart location', 'Cart velocity', 'Pole angle', 'Pole velocity']
fig, axes = plt.subplots(2, 2)
plt.subplots_adjust(hspace=0.3, wspace=0.4, bottom=0.15)
for ax, var, title in zip(axes.flatten(), v, titles):
ax.plot(var)
ax.set_xlabel('Time (s)')
ax.set_xticks(np.linspace(0, cart.sim_steps, 5))
ax.set_xticklabels(np.linspace(0, cart.delta_time, 5))
ax.set_ylabel(title)
fig.tight_layout()
fig.suptitle(figtitle)
fig.subplots_adjust(top=0.9)
def LFunc(p, v0, nsteps=10):
l, n = 0, 0
state, a = v0[:4], v0[4]
while n < nsteps:
a = np.dot(p, state.T)
cart.setState(state)
cart.performAction(action=a)
cart.sysvar[2] = np.array([remap_angle(s) for s in cart.sysvar[2]])
state = cart.sysvar[:, -1]
l += np.mean([loss(s) for s in cart.sysvar.T])
n += 1
return l / nsteps
def check_error(model, n=1, remap=False, force=False, nv=10):
VL = np.array([getv0(force=force) for i in range(nv)])
error = 0
for v in VL:
cart.setState(v[:4])
cart.performAction(action=v[4])
sysvar = np.asarray(cart.sysvar)[:, -1]
if remap:
sysvar[2] = remap_angle(sysvar[2])
actual = sysvar
pred = sim2(v, model, nsteps=n)[-1]
error += np.mean((actual - pred)**2)
return error
def Task21a(n=2000,
m=160,
l=0.1,
dt=0.2,
specific=True,
v=np.array([0, 0, np.pi, 0, 0]),
remap=False,
force=False):
'''one step ok'''
cm = plt.cm.tab20(np.arange(20))
fig1, axes1 = plt.subplots(2, 2)
ax1 = axes1.flatten()
plt.subplots_adjust(hspace=0.3, wspace=0.4, bottom=0.15)
fig2, axes2 = plt.subplots(2, 2)
ax2 = axes2.flatten()
plt.subplots_adjust(hspace=0.3, wspace=0.4, bottom=0.15)
model = NLModel(n=n, m=m, l=l, force=force, dt=dt)
var, xlabels = getvar(force=True)
v0 = getv0(force) if specific == False else np.array(v)
title = v0.copy()
for i in range(4):
actual, pred = [], []
for w in var[i]:
v0[i] = w
cart.setState(v0[:4])
cart.performAction(action=v0[4])
sysvar = np.asarray(cart.sysvar)[:, -1]
if remap:
sysvar[2] = remap_angle(sysvar[2])
actual.append(sysvar)
pred.append(sim2(v0, model)[-1])
actual = np.asarray(actual)
pred = np.asarray(pred).reshape((41, 4))
ax1[i].set_xlabel(titles[i] + ' input')
ax1[i].set_xticks([i * 5 for i in np.arange(9)])
ax1[i].set_xticklabels(xlabels[i])
ax1[i].set_ylabel('Next step')
for j in range(4):
ax1[i].plot(actual[:, j], color=cm[j * 2])
ax1[i].plot(pred[:, j], color=cm[1 + j * 2])
ax2[i].plot(actual[:, i], pred[:, i], color=cm[i * 2])
ax2[i].set_xlabel('Actual ' + titles[i])
ax2[i].set_ylabel('Predicted ' + titles[i])
custom_lines = [Line2D([0], [0], color=cm[c * 2]) for c in range(4)]
fig1.legend(custom_lines, titles, loc='lower center', ncol=4)
fig1.suptitle(["%.2f" % title[t] for t in range(5)])
def sim(v0, model, nsteps=1, remap=True):
state = np.asarray(v0[:4]).reshape((1, 4))
force = np.asarray(v0[4])
oldstate = state
n = 0
while n < nsteps:
vector = np.append(oldstate, force)
newstate = oldstate + np.matmul(vector, model)
if remap:
newstate[:, 2] = remap_angle(newstate[:, 2])
state = np.append(state, newstate, axis=0)
oldstate = newstate
n += 1
return state
def sim2(v0, model, nsteps=1, remap=False):
sigma, xprime, am = model['sigma'], model['xprime'], model['am']
state = v0[:4]
force = v0[4]
pred = [state]
n = 0
while n < nsteps:
curr = np.append(state, force)
Knm = np.asarray([calc_K(curr, value, sigma) for value in xprime])
y = np.matmul(Knm, am)
state = state + y
if remap:
state[2] = remap_angle(state[2])
pred.append(state)
n += 1
return np.asarray(pred)
def Task21b(n=2000,
m=160,
delta_time=0.2,
step_size=50,
v=np.array([0, 0, 0.3, 0, 0]),
l=0.1,
nsteps=10,
remap=True,
specific=False,
force=True):
'''time evolution ok'''
v0 = getv0(force) if not specific else v
cart.sim_steps = step_size * nsteps
cart.delta_time = delta_time * nsteps
cart.setState(v0[:4])
cart.performAction(action=v0[4])
actual = np.asarray(cart.sysvar)
model = NLModel(n=n, m=m, l=l, force=force, dt=delta_time)
pred = np.asarray(sim2(v0, model, nsteps=nsteps, remap=remap))
if remap:
actual[2] = np.asarray([remap_angle(value) for value in actual[2]])
aindex = len(actual[0])
pindex = [
index * step_size for index in range(int(np.ceil(aindex / step_size)))
]
cm = plt.cm.tab20(np.arange(20))
fig, axes = plt.subplots(2, 2)
ax = axes.flatten()
plt.subplots_adjust(hspace=0.3, wspace=0.4, bottom=0.15)
xspace = int(nsteps / 5)
for i in range(4):
ax[i].plot(actual[i])
ax[i].plot(pindex, pred[:, i])
ax[i].set_xticks(
[n * step_size * xspace for n in np.arange(int(nsteps / xspace))])
ax[i].set_xticklabels(
[n * xspace for n in np.arange(int((nsteps + 1) / xspace))])
ax[i].set_xlabel('Number of steps')
ax[i].set_ylabel(titles[i])
fig.legend(['Actual', 'Predicted'], loc='lower center', ncol=2)
fig.suptitle('Actual vs predicted Time Evolution')
print(v0)
return model
def Task14(model,
delta_time=0.2,
step_size=50,
nsteps=10,
remap=True,
specific=None,
force=False):
'''time evolution'''
cart.sim_steps = step_size * nsteps
cart.delta_time = delta_time * nsteps
fig, axes = plt.subplots(2, 2)
ax = axes.flatten()
plt.subplots_adjust(hspace=0.3, wspace=0.4, bottom=0.15)
xspace = int(nsteps / 5)
if specific == None:
v0 = getv0(force)
else:
v0 = specific
cart.setState(v0[:4])
cart.performAction(action=v0[4])
actual = np.asarray(cart.sysvar)
if remap:
actual[2] = np.asarray([remap_angle(value) for value in actual[2]])
pred = sim(v0, model, nsteps=nsteps, remap=remap)
nindex = len(actual[0])
rindex = [
index * step_size for index in range(int(np.ceil(nindex / step_size)))
]
for i in range(4):
ax[i].plot(actual[i])
ax[i].plot(rindex, pred[:, i])
ax[i].set_xticks(
[n * step_size * xspace for n in np.arange(int(nsteps / xspace))])
ax[i].set_xticklabels(
[n * xspace for n in np.arange(int((nsteps + 1) / xspace))])
ax[i].set_xlabel('Number of steps')
ax[i].set_ylabel(titles[i])
fig.legend(['Actual', 'Predicted'], loc='lower center', ncol=2)
fig.suptitle('Actual vs predicted Time Evolution')
print(v0)
def Task13(model, nsteps=1, remap=True, force=False):
'''(one step) change in state var against var'''
cm = plt.cm.tab20(np.arange(20))
fig1, axes1 = plt.subplots(2, 2)
ax1 = axes1.flatten()
plt.subplots_adjust(hspace=0.3, wspace=0.4, bottom=0.15)
fig2, axes2 = plt.subplots(2, 2)
ax2 = axes2.flatten()
plt.subplots_adjust(hspace=0.3, wspace=0.4, bottom=0.15)
var, xlabels = getvar()
v0 = getv0(force)
title = v0.copy()
for i in range(4):
actual, pred = [], []
for w in var[i]:
v0[i] = w
cart.setState(v0[:4])
cart.performAction(action=v0[4])
if remap:
cart.sysvar[2] = [
remap_angle(value) for value in cart.sysvar[2]
]
actual.append(np.asarray(cart.sysvar)[:, -1])
pred.append(sim(v0, model, nsteps=nsteps, remap=remap)[-1])
actual = np.asarray(actual).reshape((41, 4))
pred = np.asarray(pred).reshape((41, 4))
ax1[i].set_xlabel(titles[i] + ' input')
ax1[i].set_xticks([i * 5 for i in np.arange(9)])
ax1[i].set_xticklabels(xlabels[i])
ax1[i].set_ylabel('Next step')
for v in range(4):
ax1[i].plot(actual[:, v], color=cm[v * 2])
ax1[i].plot(pred[:, v], color=cm[1 + v * 2])
ax2[i].plot(actual[:, i], pred[:, i], color=cm[i * 2])
ax2[i].set_xlabel('Actual ' + titles[i])
ax2[i].set_ylabel('Predicted ' + titles[i])
custom_lines = [Line2D([0], [0], color=cm[c * 2]) for c in range(4)]
fig1.legend(custom_lines, titles, loc='lower center', ncol=4)
fig1.suptitle(["%.2f" % title[t] for t in range(5)])
