from pylab import *
import current as pc
rc("figure", figsize=[8., 4.])
rc("figure.subplot", left=.08, top=.93, right=.98)
seed(1000)
dist = pc.Iid(pc.Normal(), 2)
nodes, weights = pc.quadgen(1, dist, rule="G")
print nodes
# [[-1. -1. 1. 1.]
# [-1. 1. -1. 1.]]
print weights
# [ 0.25 0.25 0.25 0.25]
#end
dist = pc.Iid(pc.Uniform(), 2)
nodes1, weights1 = pc.quadgen([3, 5], dist, rule="C", sparse=True)
print len(weights1)
# 105
nodes2, weights2 = pc.quadgen([3, 5], dist, rule="C", growth=True)
print len(weights2)
# 297
#end
subplot(122)
scatter(nodes2[0],
nodes2[1],
marker="s",
s=50 * sqrt(weights2),
from pylab import *
import current as pc
rc("figure", figsize=[8.,4.])
rc("figure.subplot", left=.08, top=.95, right=.98)
seed(1000)
dist = pc.Laplace(pi, .5)
f = pc.lazy_eval(dist.pdf)
#end
q0, w0 = pc.quadgen(2, [-10,10])
print q0
# [[-10. 0. 10.]]
#end
comp = [-10, 0, 10]
q, w = pc.quadgen(2, [-10,10], composite=comp)
print q
# [[-10. -5. 0. 5. 10.]]
#end
def eval_errors(q, f):
errors = [0.]
for i in xrange(1, len(q[0])-1):
a,b,c = q[0,i-1:i+2]
f_approx = ((f(c)-f(a))*b + f(a)*c-f(c)*a)/(c-a)
f_diff = abs(f(q[0,i]) - f_approx)
from pylab import *
import current as pc
dist = pc.Iid(pc.Normal(), 2)
# end
nodes, weights = pc.quadgen(2, dist, rule="G")
print nodes
# [[-1.73205081 -1.73205081 -1.73205081 0. 0.
# 0. 1.73205081 1.73205081 1.73205081]
# [-1.73205081 0. 1.73205081 -1.73205081 0.
# 1.73205081 -1.73205081 0. 1.73205081]]
print weights
# [ 0.02777778 0.11111111 0.02777778 0.11111111 0.44444444
# 0.11111111 0.02777778 0.11111111 0.02777778]
# 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)
# [ 0.14367935 0.22228764]
# [ 0.28735869 0.44457529]]
#end
mu = [-1.0, -2.0, -1.0, -2.0]
Cov = [[1.0, 0.5, 0.5, 0.5], [0.5, 1.0, 0.5, 0.5], [0.5, 0.5, 1.0, 0.5],
[0.5, 0.5, 0.5, 1.0]]
Q = pc.MvLognormal(mu, Cov)
#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)
from pylab import *
import current as pc
rc("figure", figsize=[8.,4.])
rc("figure.subplot", left=.08, top=.93, right=.98)
seed(1000)
dist = pc.Iid(pc.Normal(), 2)
nodes, weights = pc.quadgen(1, dist, rule="G")
print nodes
# [[-1. -1. 1. 1.]
# [-1. 1. -1. 1.]]
print weights
# [ 0.25 0.25 0.25 0.25]
#end
dist = pc.Iid(pc.Uniform(), 2)
nodes1, weights1 = pc.quadgen([3,5], dist, rule="C", sparse=True)
print len(weights1)
# 105
nodes2, weights2 = pc.quadgen([3,5], dist, rule="C", growth=True)
print len(weights2)
# 297
#end
subplot(122)
scatter(nodes2[0], nodes2[1], marker="s",
s=50*sqrt(weights2),
alpha=.7, color="k")
xlabel(r"$q_0$")
model_solver = pc.lazy_eval(model_solver)
#end
current = array([1, 1, 1, 1, 1])
current_error = inf
#end
for step in range(10):
for direction in eye(len(dist), dtype=int):
#end
orth = pc.orth_ttr(current + direction, dist)
nodes, weights = pc.quadgen(current + direction,
dist,
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
from pylab import *
import current as pc
rc("figure", figsize=[8.,4.])
rc("figure.subplot", left=.08, top=.95, right=.98)
seed(1000)
nodes, weights = pc.quadgen(2, [0,1])
print nodes
# [[ 0. 0.5 1. ]]
print weights
# [ 0.16666667 0.66666667 0.16666667]
#end
dist = pc.Beta(2,2)
nodes, weights = pc.quadgen(3, dist)
print nodes
# [[ 0.14644661 0.5 0.85355339]]
print weights
# [ 0.2 0.6 0.2]
#end
nodes, weights = pc.quadgen(2, dist, rule="G")
print nodes
# [[ 0.17267316 0.5 0.82732684]]
print weights
# [ 0.23333333 0.53333333 0.23333333]
#end
nodes, weights = pc.quadgen(1, [0,1], rule="E", composite=2)
#end
mu = [-1.0, -2.0, -1.0, -2.0]
Cov = [[1.0, 0.5, 0.5, 0.5],
[0.5, 1.0, 0.5, 0.5],
[0.5, 0.5, 1.0, 0.5],
[0.5, 0.5, 0.5, 1.0]]
Q = pc.MvLognormal(mu, Cov)
#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)
from pylab import *
import current as pc
rc("figure", figsize=[8., 4.])
rc("figure.subplot", left=.08, top=.95, right=.98)
seed(1000)
dist = pc.Laplace(pi, .5)
f = pc.lazy_eval(dist.pdf)
#end
q0, w0 = pc.quadgen(2, [-10, 10])
print q0
# [[-10. 0. 10.]]
#end
comp = [-10, 0, 10]
q, w = pc.quadgen(2, [-10, 10], composite=comp)
print q
# [[-10. -5. 0. 5. 10.]]
#end
def eval_errors(q, f):
errors = [0.]
for i in xrange(1, len(q[0]) - 1):
a, b, c = q[0, i - 1:i + 2]
f_approx = ((f(c) - f(a)) * b + f(a) * c - f(c) * a) / (c - a)
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
def model_solver(q):
return q[0]*e**-q[1]/(q[2]+1) + sin(q[3])
model_solver = pc.lazy_eval(model_solver)
#end
current = array([1,1,1,1,1])
current_error = inf
#end
for step in range(10):
for direction in eye(len(dist), dtype=int):
#end
orth = pc.orth_ttr(current+direction, dist)
nodes, weights = pc.quadgen(current+direction, dist,
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
