orths2 = pc.outer(orths, orths) print pc.E(orths2, dist) # [[ 1. 0. 0. 0. 0.] # [ 0. 1. 0. 0. 0.] # [ 0. 0. 2. 0. 0.] # [ 0. 0. 0. 6. 0.] # [ 0. 0. 0. 0. 24.]] #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]
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,
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)
# you mistype something
#end
from pylab import *
import current as pc
rc("figure", figsize=[8., 4.])
rc("figure.subplot", left=.08, top=.95, right=.95, bottom=.12)
seed(1000)
U1 = pc.Uniform(0, 1)
U2 = pc.Uniform(0, 1)
add = U1 + U2
Q = pc.J(U1, add)
#end
def cdf(self, q, G):
if "par1" in G.K:
num = G.K["par1"]
dist = G.D["par2"]
else:
num = G.K["par2"]
dist = G.D["par1"]
return G(q - num, dist)
#end
nodes, weights = pc.quadgen(1, [0,1], rule="E", composite=2)
print nodes
# [[ 0.10566243 0.39433757 0.60566243 0.89433757]]
print weights
# [ 0.25 0.25 0.25 0.25]
#end
nodes, weights = pc.quadgen(1, [0,1], rule="E", composite=[0.2])
print nodes
# [[ 0.04226497 0.15773503 0.36905989 0.83094011]]
print weights
# [ 0.1 0.1 0.4 0.4]
#end
dist = pc.Uniform(0,1)
print dist.mom([0,1,2])
# [ 1. 0.5 0.33333333]
#end
def mom(self, k):
return 1./(1+k)
dist.addattr(mom=mom)
#end
def pdf(self, x):
out = 9/16.*(x+1)*(x<1/3.)
out += 3/4.*(x>=1/3.)
return out
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)