Z = pc.Iid(pc.Normal(), 4)
orth_poly = pc.orth_ttr(2, Z)
#end
nodes, weights = pc.quadgen(3, Z, gaussian=True, sparse=True)
print len(weights)
# 137
#end
mapped_nodes = Q.inv(Z.fwd(nodes))
t = linspace(0, 10, 100)
evaluations = [model_solver(t, q) for q in mapped_nodes.T]
#end
model_approx = pc.fitter_quad(orth_poly, nodes, weights, evaluations)
#end
samples_Z = Z.sample(100)
samples_Y = model_approx(*samples_Z)
E = pc.E(model_approx, Z)
#end
t = linspace(0, 10, 100)
plot(t, samples_Y, "k")
plot(t, E, "w-", lw=3)
plot(t, E, "k--", lw=3)
axis([0, 10, 0, 4])
xticks(range(11))
xlabel("time $t$")
# end
orth = pc.orth_ttr(2, dist)
print orth
# [1.0, q1, q0, q1^2-1.0, q0q1, q0^2-1.0]
# end
def model_solver(q):
return [q[0] * q[1], q[0] * e ** -q[1] + 1]
solves = [model_solver(q) for q in nodes.T]
# end
approx = pc.fitter_quad(orth, nodes, weights, solves)
print pc.around(approx, 14)
# [q0q1, -1.58058656357q0q1+1.63819248006q0+1.0]
# end
orth, norms = pc.orth_ttr(2, dist, retall=True)
approx2 = pc.fitter_quad(orth, nodes, weights, solves, norms=norms)
# end
print np.max(abs(approx - approx2).coeffs(), -1)
# [ 2.44249065e-15 3.77475828e-15]
# end
nodes = dist.sample(12, "M")
print nodes
growth=True)
vals = [model_solver(q) for q in nodes.T]
#end
residuals = pc.cross_validate(orth, nodes, vals, folds=5)
error = sum(residuals**2)
#end
if error < current_error:
current_error = error
proposed_dir = current + direction
#end
current = proposed_dir
#end
print current
# [ 1 3 4 6 1]
#end
orth, norms = pc.orth_ttr(current, dist, retall=True)
nodes, weights = pc.quadgen(current, dist, rule="C", growth=True)
vals = [model_solver(q) for q in nodes.T]
approx = pc.fitter_quad(orth, nodes, weights, vals, norms=norms)
print pc.E(approx, dist)
# 0.678773985695
print pc.Var(approx, dist)
# 0.0854146399504
#end
Z = pc.Iid(pc.Normal(), 4)
orth_poly = pc.orth_ttr(2, Z)
#end
nodes, weights = pc.quadgen(3, Z, gaussian=True, sparse=True)
print len(weights)
# 137
#end
mapped_nodes = Q.inv(Z.fwd(nodes))
t = linspace(0,10,100)
evaluations = [model_solver(t, q) for q in mapped_nodes.T]
#end
model_approx = pc.fitter_quad(orth_poly, nodes, weights, evaluations)
#end
samples_Z = Z.sample(100)
samples_Y = model_approx(*samples_Z)
E = pc.E(model_approx, Z)
#end
t = linspace(0,10,100)
plot(t, samples_Y, "k")
plot(t, E, "w-", lw=3)
plot(t, E, "k--", lw=3)
axis([0,10,0,4])
xticks(range(11))
xlabel("time $t$")
from pylab import * import current as pc dist_main = pc.MvNormal([0, 0], [[1, .5], [.5, 1]]) #end dist_aux = pc.Iid(pc.Normal(), 2) #end orth, norms = pc.orth_ttr(2, dist_aux, retall=True) print orth # [1.0, q1, q0, q1^2-1.0, q0q1, q0^2-1.0] #end nodes_aux, weights = pc.quadgen(3, dist_aux, rule="G") #end function = lambda q: q[0] * e**-q[1] + 1 #end nodes_main = dist_main.inv(dist_aux.fwd(nodes_aux)) solves = [function(q) for q in nodes_main.T] #end approx = pc.fitter_quad(orth, nodes_aux, weights, solves, norms=norms) print pc.E(approx, dist_aux) # 0.175824752014 #end
rule="C", growth=True)
vals = [model_solver(q) for q in nodes.T]
#end
residuals = pc.cross_validate(orth, nodes, vals, folds=5)
error = sum(residuals**2)
#end
if error < current_error:
current_error = error
proposed_dir = current+direction
#end
current = proposed_dir
#end
print current
# [ 1 3 4 6 1]
#end
orth, norms = pc.orth_ttr(current, dist, retall=True)
nodes, weights = pc.quadgen(current, dist, rule="C", growth=True)
vals = [model_solver(q) for q in nodes.T]
approx = pc.fitter_quad(orth, nodes, weights, vals, norms=norms)
print pc.E(approx, dist)
# 0.678773985695
print pc.Var(approx, dist)
# 0.0854146399504
#end
