# [ 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] #end q = pc.variable() dist = pc.Normal() print pc.E(q, dist) # 0.0 #end
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)
print pc.around(approx, 14)
# [q0q1, -1.58058656357q0q1+1.63819248006q0+1.0]
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,
# -0.0289986479139q1-0.0289986479139q0+0.481038906386]
#end
print pc.E(approx, Q)
# [ 0. 0.19270877 0.38541753]
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
# [ 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] #end q = pc.variable() dist = pc.Normal() print pc.E(q, dist) # 0.0 #end
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,
# -0.0289986479139q1-0.0289986479139q0+0.481038906386]
#end
print pc.E(approx, Q)
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
