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),
#end dist = pc.Gamma(2) print pc.orth_bert(2, dist) # [1.0, q0-2.0, q0^2-6.0q0+6.0] #end dist = pc.Uniform(-1, 1) print dist.ttr([0, 1, 2, 3]) # [[ 0. 0. 0. 0. ] # [-0. 0.33333333 0.26666667 0.25714286]] #end dist = pc.Lognormal(0.01) orths = pc.orth_ttr(2, dist) print orths # [1.0, q0-1.00501252086, q0^2-2.04042818514q0+0.842739860094] #end dist = pc.Iid(pc.Gamma(1), 2) orths = pc.orth_ttr(2, dist) print orths # [1.0, q1-1.0, q0-1.0, q1^2-4.0q1+2.0, q0q1-q1-q0+1.0, q0^2-4.0q0+2.0] #end q = pc.variable() dist = pc.Normal() print pc.E(q, dist) # 0.0 #end
plot(z, q05, "k:")
plot(z, q95, "k:")
xlabel(r"Spacial location \verb;x;")
ylabel(r"Flow velocity")
axis([0, 1, 0, 1])
legend(loc="upper left")
savefig("intro3.pdf")
clf()
mu = [0.001, 0.01, 0.1]
Sigma = [[1, .5, .5], [.5, 1, .5], [.5, .5, 1]]
#end
N = pc.Iid(pc.Normal(0, 1), 3)
L = linalg.cholesky(Sigma)
Q = e**(N0 * L + mu)
#end
orth_poly = pc.orth_ttr(2, N)
#end
approx = pc.pcm(model_wrapper, 2, Q, proxy_dist=N)
fail
print len(w)
# 9
print approx
# [0.0, -0.014499323957q1-0.014499323957q0+0.240519453193,
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.Iid(pc.Uniform(), 5)
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)
from numpy import * import current as pc function = lambda q: q[0] * e**q[1] + 1 dist = pc.Iid(pc.Normal(), 2) approx = pc.pcm(function, 2, dist, rule="G") print pc.around(approx, 14) # 1.64234906518q0q1+1.64796896005q0+1.0 print pc.E(approx, dist) # 1.0 print pc.Var(approx, dist) # 5.41311214518 #end
from pylab import *
import current as pc
rc("figure", figsize=[8.,4.])
rc("figure.subplot", left=.08, top=.95, right=.95, bottom=.12)
pc.seed(1000)
Q = pc.Iid(pc.Uniform(0,4), 2)
C = pc.Frank(Q, 1.5)
#end
subplot(121)
R = C.sample(1000)
scatter(R[0], R[1], marker="s", color="k", alpha=.7)
xlabel(r"$Q_0$")
ylabel(r"$Q_1$")
xticks(range(5))
yticks(range(5))
axis([0,4,0,4])
title("Scatter")
subplot(122)
s,t = meshgrid(linspace(0,4,100), linspace(0,4,100))
contourf(s,t,C.pdf([s,t]), 30)
xlabel(r"$q_0$")
ylabel(r"$q_1$")
xticks(range(5))
yticks(range(5))
title("Probability Density")
subplots_adjust(bottom=0.12, right=0.85, top=0.9)
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