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test_script.py
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import numpy as np
import scipy
from time import time
import timeit
from tqdm import tqdm
from torch import optim
from qcqp import QPFn2, QCQPFn2
import torch
torch.set_default_dtype(torch.double)
import torch.nn as nn
from torch.autograd import Function, Variable
from torch.autograd.functional import jacobian
from torch.nn.parameter import Parameter
import torch.nn.functional as F
#from cvxpylayers.torch import CvxpyLayer
#import cvxpy as cp
#from qpth.qp import QPFunction
import matplotlib.pyplot as plt
#import osqp
plt.style.use('bmh')
from qcqp import QCQPFn2, QPFn2
n = 2
torch.manual_seed(5)
qp = QPFn2().apply
S = torch.rand(1, n, n) + 0.01
P = torch.bmm(S, S.transpose(1, 2)).requires_grad_(True)
q = -torch.rand((1, n, 1))-0.1
warm_start = torch.zeros(q.size())
lf = qp(P, q, warm_start, 1e-12, 10000)
lf[0, 1].backward()
print("Pgrad",P.grad)
P.grad.zero_()
with torch.no_grad():
grad_num = torch.zeros_like(P)
for i in range(P.size()[1]):
for j in range(P.size()[2]):
delt = torch.zeros(P.size())
delt[0, i, j] = 1e-8
lf_1 = qp(P+delt, q, warm_start, 1e-12,10000)
lf_2 = qp(P-delt, q, warm_start, 1e-12,10000)
grad_num[0, i, j] = (lf_1[0, 1]-lf_2[0, 1]).detach().item()/2e-8
print("grad_num",grad_num)
class QCQP_cvxpy(nn.Module):
def __init__(self,eps=1e-14, max_iter = 100):
'''
'''
super().__init__()
self.eps = eps
self.max_iter = max_iter
def forward(self,P,q,l_n,mu):
N = q.size()[1]
l_t = cp.Variable(N)
A = cp.Parameter((N, N),nonneg= True)
b = cp.Parameter(N)
c = cp.Parameter(N//2, nonneg=True)
#Gs = []
#for i in range(N//2):
constraints = [cp.SOC(c[i], l_t[2*i:2*(i+1)]) for i in range(N//2)]
#constraints = []
#objective = cp.Minimize(0.5 * cp.quad_form(l_t,A) + b.T@l_t )
objective = cp.Minimize(0.5 * cp.sum_squares(A@l_t) + b.T@l_t )
problem = cp.Problem(objective, constraints)
assert problem.is_dpp()
cvxpylayer = CvxpyLayer(problem, parameters=[A, b, c], variables=[l_t])
# solve the problem
k=1e-11 #regularization of P to get Cholesky's decomposition
k=0.
P_sqrt = scipy.linalg.sqrtm(P.detach().numpy().copy()[0,:,:])
P_sqrt = torch.tensor(P_sqrt).unsqueeze(0)
#L = torch.transpose(torch.cholesky(P+k*torch.eye(P.size()[1])),1,2)
solution, = cvxpylayer(P_sqrt,q.squeeze(2),(mu*l_n).squeeze(2),solver_args={'eps': self.eps,'max_iters':self.max_iter})
solution, = cvxpylayer(P,q.squeeze(2),(mu*l_n).squeeze(2),solver_args={'eps': self.eps,'max_iters':self.max_iter})
#print(solution)
return solution
cvxpy_time = {'forward': [], 'backward':[]}
qcqp_time = {'forward': [], 'backward':[]}
n_testqcqp= 0
for i in tqdm(range(n_testqcqp)):
#P = torch.rand((1,8,8),dtype = torch.double)
P = torch.rand(8)*20 -10
P = torch.diag(torch.exp(P)).unsqueeze(0)
#P = torch.diag(P).unsqueeze(0)
#P = torch.matmul(P, torch.transpose(P,1,2))
P = torch.nn.parameter.Parameter(P, requires_grad= True)
q = torch.rand((1,8,1),dtype = torch.double)*2-1
q = torch.nn.parameter.Parameter(q, requires_grad= True)
l_n = torch.rand((1,4,1),dtype = torch.double)
l_n = torch.nn.parameter.Parameter(l_n, requires_grad= True)
mu = torch.rand((1,4,1),dtype = torch.double)
mu = torch.nn.parameter.Parameter(mu, requires_grad= True)
lr = 0.1
optimizer2 = optim.Adam([P,q,l_n,mu], lr=lr)
loss = nn.MSELoss()
relu = torch.nn.ReLU()
threshold = nn.Threshold(threshold=1e-5, value =1e-5)
target = torch.ones(q.size())
qcqp = QCQPFn2().apply
#warm_start = torch.zeros(q.size())
warm_start = torch.rand(q.size())
t0 = time()
l1= qcqp(P,q,l_n,mu,warm_start,1e-10,1000000)
t1= time()
qcqp_time['forward']+= [timeit.timeit(lambda:qcqp(P,q,l_n,mu,warm_start,1e-10,1000000),number = 10)/10.]
L1 = loss(l1, target)
optimizer2.zero_grad()
qcqp_time['backward']+= [timeit.timeit(lambda:L1.backward(retain_graph=True),number = 10)/10.]
t2 = time()
L1.backward()
t3 = time()
qcqp_time['forward']+= [t1-t0]
qcqp_time['backward']+= [t3-t2]
qcqp2 = QCQP_cvxpy(eps=1e-10,max_iter = 1000000)
t4 = time()
l1 = qcqp2(P,q,l_n,mu)
t5= time()
L1 = loss(l1.unsqueeze(2), target)
optimizer2.zero_grad()
t6 = time()
L1.backward()
t7 = time()
cvxpy_time['forward']+= [t5-t4]
cvxpy_time['backward']+= [t7-t6]
optnet_time = {'forward': [], 'backward':[]}
qp_time = {'forward': [], 'backward':[]}
osqp_time = {'forward': []}
n_testqp= 1
for i in tqdm(range(n_testqp)):
#P = torch.rand((1,8,8),dtype = torch.double)
P = torch.rand(8)*20 -10
#P = P.unsqueeze(0)
#P = torch.rand(8)*10
#P = torch.diag(P).unsqueeze(0)
P = torch.diag(torch.exp(P)).unsqueeze(0)
P = torch.matmul(P, torch.transpose(P,1,2))
P = torch.matmul(P, torch.transpose(P,1,2))
P = torch.nn.parameter.Parameter(P, requires_grad= True)
q = torch.rand((1,8,1),dtype = torch.double)*2-1
q = torch.nn.parameter.Parameter(q, requires_grad= True)
#P = torch.tensor([[[0.4979, 0.3295],[0.3295, 0.2432]]], requires_grad= True)
#q = torch.tensor([[[-0.3661],[-0.9514]]], requires_grad = True)
lr = 0.1
optimizer2 = optim.Adam([P,q], lr=lr)
loss = nn.MSELoss()
target = torch.ones(q.size())
qp = QPFn2.apply
warm_start = torch.zeros(q.size())
t0 = time()
#qp_time['forward']+= [timeit.timeit(lambda:qp(P,q,warm_start,1e-10,1000000),number = 10)/10.]
l1= qp(P,q,warm_start,1e-10,1000000)
l1[0,1].backward()
#print(jacobian(lambda x,y: qp(x,y, warm_start,1e-10,1000000), (P,q))) #get jacobian of the solution wrt parameters of QP
t1= time()
L1 = loss(l1, target)
optimizer2.zero_grad()
#qp_time['backward']+= [timeit.timeit(lambda:L1.backward(retain_graph=True),number = 10)/10.]
t2 = time()
L1.backward()
qp_time['forward']+= [t1-t0]
qp_time['backward']+= [t3-t2]
e = Variable(torch.Tensor())
u = torch.zeros(q.size(), requires_grad = False, dtype = torch.double).squeeze(2)
B = -torch.eye(q.size()[1], requires_grad = False, dtype = torch.double).unsqueeze(0)
t4 = time()
l1 = QPFunction(eps = 1e-10, verbose=-1, maxIter=1000000)(P, q.squeeze(2), B, u, e, e)
optnet_time['forward']+= [timeit.timeit(lambda:QPFunction(eps = 1e-10, verbose=-1, maxIter=1000000)(P, q.squeeze(2), B, u, e, e),number = 10)/10.]
t5= time()
L1 = loss(l1.unsqueeze(2), target)
optimizer2.zero_grad()
t6 = time()
optnet_time['backward']+= [timeit.timeit(lambda:L1.backward(retain_graph=True),number = 10)/10.]
L1.backward()
t7 = time()
m = osqp.OSQP()
m.setup(P=scipy.sparse.csc_matrix(P[0,:,:].detach().numpy()), q=q[0,:,0].detach().numpy(), A=scipy.sparse.csc_matrix(np.eye(q.size()[1])), l=np.zeros(q.size()[1]), u=np.inf*np.ones(q.size()[1]), verbose = False, eps_abs = 1e-10,eps_rel = 1e-20,max_iter = 1000000)
osqp_time['forward']+= [timeit.timeit(lambda:m.solve(), number=1)/1.]
optnet_time['forward']+= [t5-t4]
optnet_time['backward']+= [t7-t6]
optnet_time['mean forward'] = sum(optnet_time['forward'])/n_testqp
optnet_time['mean backward'] = sum(optnet_time['backward'])/n_testqp
qp_time['mean forward'] = sum(qp_time['forward'])/n_testqp
qp_time['mean backward'] = sum(qp_time['backward'])/n_testqp
osqp_time['mean forward'] = sum(osqp_time['forward'])/n_testqp
optnet_time['error forward'] = np.std(optnet_time['forward'])
optnet_time['error backward'] = np.std(optnet_time['backward'])
print(optnet_time['error forward'],np.max(optnet_time['forward']), np.min(optnet_time['forward']))
qp_time['error forward'] = np.std(qp_time['forward'])
print(qp_time['error forward'], np.max(qp_time['forward']), np.min(qp_time['forward']))
qp_time['error backward'] = np.std(qp_time['backward'])
osqp_time['error forward'] = np.std(osqp_time['forward'])
print("osqp", osqp_time)
cvxpy_time['mean forward'] = sum(cvxpy_time['forward'])/n_testqcqp
cvxpy_time['mean backward'] = sum(cvxpy_time['backward'])/n_testqcqp
qcqp_time['mean forward'] = sum(qcqp_time['forward'])/n_testqcqp
qcqp_time['mean backward'] = sum(qcqp_time['backward'])/n_testqcqp
cvxpy_time['error forward'] = np.std(cvxpy_time['forward'])
cvxpy_time['error backward'] = np.std(cvxpy_time['backward'])
print(cvxpy_time['error forward'],np.max(cvxpy_time['forward']), np.min(cvxpy_time['forward']))
qcqp_time['error forward'] = np.std(qcqp_time['forward'])
print(qcqp_time['error forward'], np.max(qcqp_time['forward']), np.min(qcqp_time['forward']))
qcqp_time['error backward'] = np.std(qcqp_time['backward'])
barWidth = 0.35
y1 = [optnet_time['mean forward'],qp_time['mean forward']]
y2 = [optnet_time['mean backward'], qp_time['mean backward'] ]
er1 = [optnet_time['error forward'],qp_time['error forward']]
er2 = [optnet_time['error backward'],qp_time['error backward']]
r1 = range(len(y1))
r2 = [x + barWidth for x in r1]
plt.figure()
plt.bar(r1, y1, width = barWidth, color = ['cornflowerblue' for i in y1], linewidth = 2,log = True, label="forward", yerr = er1)
plt.bar(r2, y2, width = barWidth, color = ['coral' for i in y2], linewidth = 4,log = True,label="backward", yerr = er2)
plt.xticks([r + barWidth / 2 for r in range(len(y1))], ['OptNet', 'Ours'])
plt.ylabel('Runtime (s)')
plt.title('QP solvers')
plt.ylim(bottom = 1e-5, top= 1e-1)
plt.legend()
plt.show()
y1 = [cvxpy_time['mean forward'],qcqp_time['mean forward']]
y2 = [cvxpy_time['mean backward'], qcqp_time['mean backward'] ]
er1 = [cvxpy_time['error forward'],qcqp_time['error forward']]
er2 = [cvxpy_time['error backward'],qcqp_time['error backward']]
r1 = range(len(y1))
r2 = [x + barWidth for x in r1]
plt.figure()
plt.bar(r1, y1, width = barWidth, color = ['cornflowerblue' for i in y1], linewidth = 2,log = True, label="forward", yerr = er1)
plt.bar(r2, y2, width = barWidth, color = ['coral' for i in y1], linewidth = 4,log = True,label="backward", yerr = er2)
plt.xticks([r + barWidth / 2 for r in range(len(y1))], ['cvxpylayers', 'Ours'])
plt.ylabel('Runtime (s)')
plt.title('QCQP solvers')
plt.ylim(bottom = 1e-5, top= 1e-1)
plt.legend()
plt.show()