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import theano
from theano import tensor, function
import numpy as np
import cvxopt
def l1regls(M_val, w_val):
"""
Solves:
min - sum theta
s.t theta <= 0
|e^{M*theta} - (1 - w)|_2 <= 1
"""
m, n = M_val.shape
c = cvxopt.matrix(-1.0, (n,1))
theta = tensor.row().T
z = tensor.row().T
theta_ = theta.flatten()
z_ = z.flatten()
M = theano.shared(M_val.astype(theano.config.floatX))
w = theano.shared(w_val.astype(theano.config.floatX))
y = (tensor.exp(M.dot(theta_)) - (1 - w)).norm(2) - 1
y_diff = tensor.grad(y, theta_)
y_hess = z[0] * theano.gradient.hessian(y, theta_)
f_x = theano.function([theta], [y, y_diff], allow_input_downcast=True)
f_xz = theano.function([theta, z], [y, y_diff, y_hess])
def F(x=None, z=None):
if x is None:
return 1, cvxopt.matrix(1.0, (n,1))
elif z is None:
y, y_diff = f_x(x)
return cvxopt.matrix(float(y), (1, 1)), cvxopt.matrix(y_diff.astype("float64")).T
else:
y, y_diff, y_hess = f_xz(x, z)
return cvxopt.matrix(float(y), (1, 1)), \
cvxopt.matrix(y_diff.astype("float64")).T, \
cvxopt.matrix(y_hess.astype("float64"))
return cvxopt.solvers.cpl(c,F)['x']
if __name__=="__main__":
M_val = np.random.rand(100, 20)
w_val = np.random.rand(100)
l1regls(M_val, w_val)
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