def make2dPlot(expr, numticks=10, show_plot=False):
mc_ccVals = [None] * (numticks + 1)
mc_cvVals = [None] * (numticks + 1)
aff_cc = [None] * (numticks + 1)
aff_cv = [None] * (numticks + 1)
fvals = [None] * (numticks + 1)
mc_expr = mc(expr)
x = next(identify_variables(expr)) # get the first variable
tick_length = (x.ub - x.lb) / numticks
xaxis = [x.lb + tick_length * n for n in range(numticks + 1)]
x_val = value(x) # initial value of x
cc = mc_expr.subcc() # Concave overestimator subgradient at x_val
cv = mc_expr.subcv() # Convex underestimator subgradient at x_val
f_cc = mc_expr.concave() # Concave overestimator value at x_val
f_cv = mc_expr.convex() # Convex underestimator value at x_val
for i, x_tick in enumerate(xaxis):
aff_cc[i] = cc[x] * (x_tick - x_val) + f_cc
aff_cv[i] = cv[x] * (x_tick - x_val) + f_cv
mc_expr.changePoint(x, x_tick)
mc_ccVals[i] = mc_expr.concave()
mc_cvVals[i] = mc_expr.convex()
fvals[i] = value(expr)
if show_plot:
plt.plot(xaxis, fvals, 'r', xaxis, mc_ccVals, 'b--', xaxis,
mc_cvVals, 'b--', xaxis, aff_cc, 'k|', xaxis, aff_cv, 'k|')
plt.show()
return mc_ccVals, mc_cvVals, aff_cc, aff_cv
def plot_optimal_solution(m):
SolverFactory('ipopt').solve(m, tee=True)
x = []
u = []
F = []
for ii in m.t:
x.append(value(m.x[ii]))
u.append(value(m.u[ii]))
F.append(value(m.F[ii]))
plt.subplot(131)
plt.plot(m.t.value, x, 'ro', label='x')
plt.title('State Soln')
plt.xlabel('time')
plt.subplot(132)
plt.plot(m.t.value, u, 'ro', label='u')
plt.title('Control Soln')
plt.xlabel('time')
plt.subplot(133)
plt.plot(m.t.value, F, 'ro', label='Cost Integrand')
plt.title('Anti-derivative of \n Cost Integrand')
plt.xlabel('time')
#plt.show()
return plt