def __init__(self, f, x, test = 'f'):
self.f = f
self.x = x.copy()
# sA = FuncDesigner.oovar('A',shape=(len(x),len(x)))
sx = FuncDesigner.oovar('x', size = len(x))
sy = 0.5*FuncDesigner.dot(sx*sx,FuncDesigner.dot(f.A,sx))
print 'sy=',sy
# self.sA = sA
self.sx = sx
self.sy = sy
def __init__(self, f, x, test = 'f'):
self.f = f
self.x = x.copy()
# sA = FuncDesigner.oovar('A',shape=(len(x),len(x)))
sx = FuncDesigner.oovar('x', size = len(x))
sy = 0.5*FuncDesigner.dot(sx*sx,FuncDesigner.dot(f.A,sx))
print('sy=',sy)
# self.sA = sA
self.sx = sx
self.sy = sy
def fit_kernel_model(kernel, loss, X, y, gamma, weights=None):
n_samples = X.shape[0]
gamma = float(gamma)
if weights is not None:
weights = weights / np.sum(weights) * weights.size
# --- optimize bias term ---
bias = fd.oovar('bias', size=1)
if weights is None:
obj_fun = fd.sum(loss(y, bias))
else:
obj_fun = fd.sum(fd.dot(weights, loss(y, bias)))
optimizer = NLP(obj_fun, {bias: 0.}, ftol=1e-6, iprint=-1)
result = optimizer.solve('ralg')
bias = result(bias)
# --- optimize betas ---
beta = fd.oovar('beta', size=n_samples)
# gram matrix
K = kernel(X, X)
assert K.shape == (n_samples, n_samples)
K_dot_beta = fd.dot(K, beta)
penalization_term = gamma * fd.dot(beta, K_dot_beta)
if weights is None:
loss_term = fd.sum(loss(y - bias, K_dot_beta))
else:
loss_term = fd.sum(fd.dot(weights, loss(y - bias, K_dot_beta)))
obj_fun = penalization_term + loss_term
beta0 = np.zeros((n_samples, ))
optimizer = NLP(obj_fun, {beta: beta0}, ftol=1e-4, iprint=-1)
result = optimizer.solve('ralg')
beta = result(beta)
return KernelModel(X, kernel, beta, bias)
def compressed_sensing2(x1, trans):
"""L1 compressed sensing
:Parameters:
x1 : array-like, shape=(n_outputs,)
input sparse vector
trans : array-like, shape=(n_outputs, n_inputs)
transformation matrix
:Returns:
decoded vector, shape=(n_inpus,)
:RType:
array-like
"""
# obrain sizes of inputs and outputs
(n_outputs, n_inputs) = trans.shape
# define variable
t = fd.oovar('t', size=n_inputs)
x = fd.oovar('x', size=n_inputs)
# objective to minimize: f x^T -> min
objective = fd.sum(t)
# init constraints
constraints = []
# equality constraint: a_eq x^T = b_eq
constraints.append(fd.dot(trans, x) == x1)
# inequality constraint: -t < x < t
constraints.append(-t <= x)
constraints.append(x <= t)
# start_point
start_point = {x:np.zeros(n_inputs), t:np.zeros(n_inputs)}
# solve linear programming
prob = LP(objective, start_point, constraints=constraints)
result = prob.minimize('pclp') # glpk, lpSolve... if available
# print result
# print "x =", result.xf # arguments at mimimum
# print "objective =", result.ff # value of objective
return result.xf[x]
def automaticdiffertest():
#from FuncDesigner import *
a, b, c = fd.oovars('a', 'b', 'c')
f1, f2 = fd.sin(a) + fd.cos(b) - fd.log2(c) + fd.sqrt(b), fd.sum(c) + c * fd.cosh(b) / fd.arctan(a) + c[0] * c[1] + c[-1] / (a * c.size)
f3 = f1*f2 + 2*a + fd.sin(b) * (1+2*c.size + 3*f2.size)
f = 2*a*b*c + f1*f2 + f3 + fd.dot(a+c, b+c)
point = {a:1, b:2, c:[3, 4, 5]} # however, you'd better use numpy arrays instead of Python lists
print(f(point))
print(f.D(point))
print(f.D(point, a))
print(f.D(point, [b]))
print(f.D(point, fixedVars = [a, c]))
h = []
for i in range(n):
if i == j:
h.append(12+n/(i+1.0))
elif i == j + 1:
h.append(0)
elif j == i + 2:
h.append(0)
else:
h.append(15/((i+1)+0.1*(j+1)))
H.append(h)
#print H
#H = [[15,0,4.83871],
# [12.5,13.5,0],
# [0,6.52174,13]]
#print H
x = fd.oovars(n)
f = fd.dot(fd.dot(x, H), x)
startPoint = {x: np.zeros(n)}
constraints = []
constraints.append(x > np.zeros(n))
constraints.append(fd.sum(x) == 1)
p = QP(f, startPoint, constraints=constraints)
r = p.solve("qlcp")
x_opt = r(x)
print(math.sqrt(r.ff))
# problem
# http://abel.ee.ucla.edu/cvxopt/examples/tutorial/qp.html