'''Cantilever beam optimization with CSDL'''
import numpy as np
import scipy.sparse as sp
from modopt import CSDLAlphaProblem, SLSQP
import time
import csdl_alpha as csdl
E0, L0, b0, vol0, F0 = 1., 1., 0.1, 0.01, -1.
def get_problem(n_el): # 23 statements excluding comments, returns, name assignment,
# and an extra line for concatenating u with [0., 0.].
rec = csdl.Recorder()
rec.start()
# add design variables
x = csdl.Variable(name = 'x', shape=(n_el,), value=1.0)
x.set_as_design_variable(lower = 1e-2)
# add objective
E, L, b, vol = E0, L0, b0, vol0
L_el = L / n_el
n_nodes = n_el + 1
# Moment of inertia
I = b * x**3 / 12
# Force vector
F = np.zeros((n_nodes*2,))
F[-2] = F0
# Stiffness matrix
c_el = E / L_el**3 * np.array([[12, 6*L_el, -12, 6*L_el],
[6*L_el, 4*L_el**2, -6*L_el, 2*L_el**2],
[-12, -6*L_el, 12, -6*L_el],
[6*L_el, 2*L_el**2, -6*L_el, 4*L_el**2]])
K = csdl.Variable(name='K', value=np.zeros((n_nodes*2, n_nodes*2)))
for i in range(n_el):
K = K.set(csdl.slice[2*i:2*i+4, 2*i:2*i+4], K[2*i:2*i+4, 2*i:2*i+4] + c_el * I[i])
# K[2*i:2*i+4, 2*i:2*i+4] += c_el * I[i]
u = csdl.solve_linear(K[2:,2:], F[2:])
# Missing statement for concatenating u with [0., 0.]. Add 1 extra line.
c = csdl.vdot(F[2:], u)
c.add_name('compliance')
c.set_as_objective()
# add constraints
v = L_el * b * csdl.sum(x)
v.add_name('volume')
v.set_as_constraint(lower=vol0, upper=vol0)
rec.stop()
# Create a Simulator object from the Recorder object
# sim = csdl.experimental.PySimulator(rec)
sim = csdl.experimental.JaxSimulator(rec, gpu=False)
# Instantiate your problem using the csdl Simulator object and name your problem
prob = CSDLAlphaProblem(problem_name=f'cantilever_{n_el}_csdl', simulator=sim)
return prob
if __name__ == '__main__':
# # Test to see if the problem is correctly defined
# prob = get_problem(50)
# print(prob._compute_objective(np.ones(50))) # 39.99999999905752
# print(prob._compute_constraints(np.ones(50))) # [0.09]
# exit()
# SLSQP
print('\tSLSQP \n\t-----')
n_el = 50
optimizer = SLSQP(get_problem(n_el), solver_options={'maxiter': 200, 'ftol': 1e-9})
start_time = time.time()
optimizer.solve()
opt_time = time.time() - start_time
success = optimizer.results['success']
print('\tTime:', opt_time)
print('\tSuccess:', success)
print('\tOptimized vars:', optimizer.results['x'])
print('\tOptimized obj:', optimizer.results['fun'])
optimizer.print_results()
import matplotlib.pyplot as plt
plt.figure()
plt.plot(optimizer.results['x'])
plt.xlabel('Lengthwise location')
plt.ylabel('Optimized thickness')
plt.show()
assert np.allclose(optimizer.results['x'],
[0.14915754, 0.14764328, 0.14611321, 0.14456715, 0.14300421, 0.14142417,
0.13982611, 0.13820976, 0.13657406, 0.13491866, 0.13324268, 0.13154528,
0.12982575, 0.12808305, 0.12631658, 0.12452477, 0.12270701, 0.12086183,
0.11898809, 0.11708424, 0.11514904, 0.11318072, 0.11117762, 0.10913764,
0.10705891, 0.10493903, 0.10277539, 0.10056526, 0.09830546, 0.09599246,
0.09362243, 0.09119084, 0.08869265, 0.08612198, 0.08347229, 0.08073573,
0.07790323, 0.07496382, 0.07190453, 0.06870925, 0.0653583, 0.06182632,
0.05808044, 0.05407658, 0.04975295, 0.0450185, 0.03972912, 0.03363155,
0.02620192, 0.01610863], rtol=0, atol=1e-5)