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)
#end
z = linspace(0, 1, 1000)
def model_wrapper(q):
layers = [0.001, 1., 0.001, 1.]
bounds = [0, q[0], q[1], q[2], 1]
U_0, U_L = 0, 1
sl = SerialLayers(layers, bounds, U_0, U_L)
return sl(z)
#end
model_wrapper = pc.lazy_eval(model_wrapper, load="model_data.d")
#end
model_wrapper.save("model_data.d")
#end
samples = Q.sample(5)
U = [model_wrapper(q) for q in samples.T]
#end
plot(z, array(U).T, "k")
xlabel(r"Spacial location \verb;x;")
ylabel(r"Flow velocity \verb;U;")
savefig("intro1.pdf")
clf()
approx = pc.pcm(model_wrapper, 2, Q)
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)
q0 = pc.Triangle(0/6., 1/6., 2/6.)
q1 = pc.Triangle(2/6., 3/6., 4/6.)
q2 = pc.Triangle(4/6., 5/6., 6/6.)
Q = pc.J(q0,q1,q2)
#end
z = linspace(0,1,1000)
def model_wrapper(q):
layers = [0.001, 1., 0.001, 1.]
bounds = [0, q[0], q[1], q[2], 1]
U_0, U_L = 0, 1
sl = SerialLayers(layers, bounds, U_0, U_L)
return sl(z)
#end
model_wrapper = pc.lazy_eval(model_wrapper, load="model_data.d")
#end
model_wrapper.save("model_data.d")
#end
samples = Q.sample(5)
U = [model_wrapper(q) for q in samples.T]
#end
plot(z, array(U).T, "k")
xlabel(r"Spacial location \verb;x;")
ylabel(r"Flow velocity \verb;U;")
savefig("intro1.pdf"); clf()
approx = pc.pcm(model_wrapper, 2, Q)
#end
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
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)
vals = [model_solver(q) for q in nodes.T]
#end
residuals = pc.cross_validate(orth, nodes, vals, folds=5)
error = sum(residuals**2)
