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final.py
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final.py
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import sys
NUMPAD_DIR = '/home/voila/Documents/2014GRAD/'
sys.path.append(NUMPAD_DIR)
from numpad import *
import numpy as np
import unittest
import nlopt
import matplotlib.pyplot as plt
from pdb import set_trace
import unittest
"Unit test"
class TestMain(unittest.TestCase):
def setUp(self):
self.xs = np.linspace(0,1,100)
self.uinit = np.sin(np.pi*self.xs)/2. + .5
self.tinit = 0.
self.tfinal = 1.
self.source = array([0.3, -0.3])
self.tgrid = linspace(self.tinit, self.tfinal, 100)
# primal parameters
self.A = 2.
# twin parameters
self.nsig = 10
self.rangesig = [-.1, 1.1]
@unittest.skipIf(True, '')
def test_primal(self):
primal = \
PrimalModel(self.uinit, self.xs, self.tinit, self.tfinal, self.A)
primal.set_source(self.source)
primal.integrate(self.tfinal)
plt.clf()
primal.plot_utx(self.tgrid)
@unittest.skipIf(True, '')
def test_twin(self):
twin = \
TwinModel(self.uinit, self.xs, self.tinit, self.tfinal, self.nsig, self.rangesig)
twin.set_source(self.source)
twin.flux.setcoef(np.loadtxt('xcoef'))
twin.integrate(self.tfinal)
plt.clf()
twin.plot_utx(self.tgrid)
@unittest.skipIf(True, '')
def test_mismatch(self):
coef = np.loadtxt('xcoef')
infertwin = \
InferTwinModel(self.xs, self.uinit, self.tinit, self.tfinal, self.source,
self.A, self.nsig, self.rangesig, coef)
lasso_reg = 1e-4
grad = np.zeros(coef.size)
val0 = infertwin.var_grad(coef, grad, lasso_reg, infertwin.primal.tfinal)
infertwin.clean()
dcoef = zeros(coef.shape)
dcoef[5] += 1e-4
infertwin.twin.flux.setcoef(coef+dcoef)
infertwin.twin.set_source(self.source)
val1 = infertwin.var_grad(coef+dcoef, grad, lasso_reg, infertwin.primal.tfinal)
print (val1-val0)/1e-4, grad[5]
@unittest.skipIf(True, '')
def test_infer(self):
coef = np.zeros(self.nsig)
infertwin = \
InferTwinModel(self.xs, self.uinit, self.tinit, self.tfinal, self.source,
self.A, self.nsig, self.rangesig, coef)
lasso_reg = 1e-4
trained_coef = infertwin.infer(coef, lasso_reg)
@unittest.skipIf(True, '')
def test_Matern(self):
mat = Matern(1., 1.)
cs = upgrade(np.random.rand(2,10))
c0,c1 = cs[0],cs[1]
K0 = mat.K0(c0, c1)
dc = np.random.rand(1,10)*1e-5
Kd0 = mat.K0(c0+dc, c1)
print np.dot(K0.diff(c0).todense().view(np.ndarray)[0], dc[0])
print Kd0-K0
dc = np.random.rand(1,10)*1e-5
Kd1 = mat.K0(c0, c1+dc)
print np.dot(mat.K1(c0,c1)._value, dc[0])
print Kd1-K0
dc0 = np.random.rand(1,10)*1e-5
print mat.K1(c0+dc0,c1) - mat.K1(c0,c1)
print dot(dc0, mat.K2(c0,c1))
set_trace()
@unittest.skipIf(True, '')
def test_mle(self):
dimc = 2
bayes = BayesOpt(dimc)
cx = np.linspace(-1.,1.,3)
cy = np.linspace(-1.,1.,3)
CX, CY = np.meshgrid(cx, cy)
obj = np.sin(CX+1.2*CY).ravel()
cs = np.array( zip(CX.ravel(), CY.ravel()) )
grad = np.array( zip(np.cos(CX+1.2*CY).ravel(), 1.2*np.cos(CX+1.2*CY).ravel()) )
grad += (np.random.rand(grad.size).reshape(grad.shape)-.5)
for i in range(obj.size):
bayes.add_data( cs[i], np.array([obj[i]]), grad[i] )
params = np.array([ 1., 1., 1., .1])
params = bayes.mle(params,maxiter=2000)
set_trace()
@unittest.skipIf(True, '')
def test_posterior_and_acquisition(self):
dimc = 1
bayes = BayesOpt(dimc)
c = np.linspace(-1., 1.1, 6)
obj = c**2
grad = 2*c+np.random.randn(c.size)*.1
for i in range(obj.size):
bayes.add_data( np.array([c[i]]), np.array([obj[i]]), np.array([grad[i]]))
params = np.array([1., .2, .5, .02])
print 'posterior test:'
nextc0 = array(0.2)
muc0, sigc0 = bayes.posterior(nextc0, params)
nextc1= array(0.2+1e-5)
muc1, sigc1 = bayes.posterior(nextc1, params)
print muc1-muc0
print muc0.diff(nextc0)[0,0] * 1e-5
print sigc1-sigc0
print sigc0.diff(nextc0)[0,0] * 1e-5
test_num = 101
muc = zeros(test_num)
sigc = zeros(test_num)
nextc = np.linspace(-1.1, 1.1, test_num)
for i in range(test_num):
c = array(nextc[i])
muc[i], sigc[i] = bayes.posterior(c, params)
muc[i].obliviate()
sigc[i].obliviate()
muc = degrade(muc)
sigc = degrade(sigc)
plt.figure()
plt.plot(nextc, nextc**2, color='black')
plt.plot(nextc, muc, linestyle='--', color='black')
plt.fill_between(nextc, muc+sigc, muc-sigc, alpha=.5, edgecolor='#FF9848',
facecolor='#FF9848')
print 'acquisition test:'
EI = np.zeros(test_num)
grads = np.zeros(test_num)
nextc = upgrade(nextc)
for i in range(test_num):
c = array(nextc[i])
gradi = np.zeros(dimc)
EI[i] = bayes.acquisition(c, gradi, params)
grads[i] = gradi
plt.fill_between(nextc, EI*10., np.zeros(test_num), alpha=.5, edgecolor='#0000FF',
facecolor='#0011FF')
plt.plot(nextc, grads, color='blue', linestyle='--')
plt.show()
set_trace()
@unittest.skipIf(True, '')
def test_next_design(self):
print 'DIM 1 TEST'
dimc = 1
bayes = BayesOpt(dimc)
c = np.linspace(-1., 1.1, 6)
obj = c**2
grad = 2*c+np.random.randn(c.size)*.1
for i in range(obj.size):
bayes.add_data( np.array([c[i]]), np.array([obj[i]]), np.array([grad[i]]))
params = np.array([1., .2, .5, .02])
nextc, maxEI = bayes.next_design(params)
print 'next design: ', nextc
print 'max EI: ', maxEI
print 'DIM 2 TEST'
dimc = 2
bayes = BayesOpt(dimc)
cx = np.linspace(-1.,1.,4)
cy = np.linspace(-1.,1.,4)
CX, CY = np.meshgrid(cx, cy)
obj = (CX**2+CY**2).ravel()
cs = np.array( zip(CX.ravel(), CY.ravel()) )
grad = np.array( zip(2.*CX.ravel(), 2.*CY.ravel()) )
grad += np.random.rand(grad.size).reshape(grad.shape) * .1
for i in range(obj.size):
bayes.add_data( cs[i], np.array([obj[i]]), grad[i] )
params = np.array([ 1., .2, 1., .2])
nextc, maxEI = bayes.next_design(params)
print 'next design: ', nextc
print 'max EI: ', maxEI
set_trace()
@unittest.skipIf(False, '')
def test_target_solution(self):
coef = np.loadtxt('xcoef')
self.source = array([0.4, 0.1, 0.3, -0.3, 0.2]) # target design
#self.source = zeros(10)
infertwin = \
InferTwinModel(self.xs, self.uinit, self.tinit, self.tfinal, self.source,
self.A, self.nsig, self.rangesig, coef)
set_trace()
@unittest.skipIf(True, '')
def test_optimize_control(self):
dimc = 5
lasso_reg = 1e-4
self.source = zeros(5)
coef = np.loadtxt('xcoef_final')
target = np.loadtxt('target')
bayes = BayesOpt(dimc)
for i in range(50):
infertwin = \
InferTwinModel(self.xs, self.uinit, self.tinit, self.tfinal, self.source,
self.A, self.nsig, self.rangesig, coef)
trained_coef = infertwin.infer(coef, lasso_reg)
infertwin.twin.integrate(self.tfinal)
utwin = infertwin.twin.interp_tgrid(self.tgrid)
twin_target = utwin[-1]
obj = linalg.norm(twin_target-target,2)
grads = obj.diff(infertwin.twin.source)
grad = np.zeros(self.source.size)
for j in range(len(infertwin.twin.profiles)):
grad[j] = np.dot( degrade( infertwin.twin.profiles[j] ),
np.asarray(degrade(grads))[0] )
params = np.array([ 5., .2, .3, .2])
bayes.add_data( degrade(self.source), np.array([obj._value]), grad )
nextc, maxEI = bayes.next_design(params)
self.source = array(nextc)
np.savetxt('50_obj'+str(i), array([obj._value]))
np.savetxt('50_source'+str(i), self.source._value)
"Utilities"
def degrade(_adarray_):
if isinstance(_adarray_, adarray):
return _adarray_._value
return _adarray_
def upgrade(_ndarray_):
if isinstance(_ndarray_, np.ndarray):
return array(_ndarray_)
return _ndarray_
'Buckley-Leverett flux'
class BLFlux:
def __init__(self, A):
self.A = A
def fluxfun(self, us):
A = self.A
fvar = us**2 / (1.+A*(1-us)**2)
return fvar
def fluxder(self, us):
A = self.A
fder = ( 2*us*(1+A*(1-us)**2) + us**2 * (2*A*(1-us)) ) \
/ (1+A*(1-us)**2)**2
return fder
def plotflux(self, cl='r', grad=False):
x = np.linspace(0.,1.,100)
if not grad:
y = self.fluxfun(x)
else:
y = self.fluxder(x)
handle, = plt.plot(x,y,color=cl)
return handle
'Sigmoid basis library for the flux'
class Flux:
def __init__(self, nsig, rangesig):
self.nsig = nsig
self.beta = 3./2 * nsig
self.uis = np.linspace(rangesig[0], rangesig[1], nsig)
self.coef = None
self.activelist = np.ones(self.uis.shape)
def activate(self, list_to_activate):
# activate a list of basis
list_to_activate = degrade(list_to_activate)
self.activelist = list_to_activate
def setcoef(self, coef):
# set sigmoids coefficients
assert(coef.size)
self.coef = upgrade(coef)
def fluxfun(self, us):
# evaluate flux function value
assert(self.coef is not None)
result = zeros(us.shape)
for basis in range(self.nsig):
if bool(self.activelist[basis]):
result += sigmoid(self.beta* (us - self.uis[basis])) \
* self.coef[basis]
return result
def fluxder(self, us):
# compute flux function derivative to u
assert(self.coef is not None)
result = zeros(array(us).shape)
for basis in range(self.nsig):
if bool(self.activelist[basis]):
result += sigmoid_der(self.beta * (us - self.uis[basis])) \
* self.coef[basis] * self.beta
return result
def plotflux(self, cl='b', grad=False):
distance = self.uis[-1] - self.uis[0]
lend = self.uis[0] - .1 * distance
rend = self.uis[-1] + .1 * distance
us = linspace(degrade(lend), degrade(rend), 1000)
if not grad:
y = degrade(self.fluxfun(us))
else:
y = degrade(self.fluxder(us))
handle, = plt.plot(degrade(us), y, color=cl)
return handle
'Model base class'
class Model:
def __init__(self, uinit, xs, tinit, tfinal):
assert( xs.size == uinit.size and isinstance(xs, np.ndarray) )
self.uinit = uinit
self.tinit = tinit
self.tfinal = tfinal
self.N = uinit.size
self.xs = xs
self.dx = self.xs[1] - self.xs[0]
self.source = None
self.profiles = None
self.flux = None
self.utx = uinit[np.newaxis,:]
self.ts = np.array(tinit)
def set_source(self, source):
# set space dependent design (source)
# source is constant in time, modelled by bubble profiles in space
if isinstance(source, np.ndarray):
source = upgrade(source)
dim = source.size
location = np.linspace(0,1,dim)
distance = location[1] - location[0]
profiles = \
[exp( -(self.xs-center)**2/ distance**2 ) for center in location]
self.profiles = profiles
self.source = sum( [profiles[ii] * source[ii] for ii in range(dim)], 0 )
def residual(self, un, u0, dt):
# one timestep residual
assert(self.flux is not None)
un_ext = hstack([un[-2:], un, un[:2]]) # N+4
fn = self.flux.fluxfun(un_ext) # N+4
lamn = sqrt( self.flux.fluxder(un_ext) ** 2 + 1e-14) # N+4
coefn = sigmoid( (lamn[:-1] - lamn[1:]) / 1e-6 ) # N+3
lamn = coefn*lamn[:-1] + (1-coefn)*lamn[1:] # N+3
Dn = un_ext[:-1] - un_ext[1:] # N+3
x1n = Dn[:-2] # N+1
x2n = Dn[2:] # N+1
L = zeros(array(x1n).shape)
index = (x1n._value * x2n._value > 0.)
L[ ~ index ] = zeros(np.sum(~index)._value)
L[ index ] = 2 * (x1n * x2n)[index] / (x1n + x2n)[index]
fluxn = (fn[1:-2] + fn[2:-1])/2. \
+ .5 * lamn[1:-1] * (Dn[1:-1] - L)
# -------------------------------------------
u0_ext = hstack([u0[-2:], u0, u0[:2]])
f0 = self.flux.fluxfun(u0_ext)
lam0 = sqrt( self.flux.fluxder(u0_ext) ** 2 + 1e-14)
coef0 = sigmoid( (lam0[:-1] - lam0[1:]) / 1e-6 )
lam0 = coef0*lam0[:-1] + (1-coef0)*lam0[1:]
D0 = u0_ext[:-1] - u0_ext[1:]
x10 = D0[:-2]
x20 = D0[2:]
L = zeros(array(x10).shape)
index = (x10._value * x20._value > 0.)
L[ ~ index ] = zeros(np.sum(~index)._value)
L[ index ] = 2 * (x10 * x20)[index] / (x10 + x20)[index]
flux0 = (f0[1:-2] + f0[2:-1])/2. \
+ .5 * lam0[1:-1] * (D0[1:-1] - L)
# -------------------------------------------
if self.source is None:
print 'warning: source unset'
res = (un - u0)/dt + (fluxn[1::]-fluxn[:-1:])/self.dx/2.\
+ (flux0[1::]-flux0[:-1:])/self.dx/2. - self.source
return res
def integrate(self, tcutoff):
self.ts = np.array([self.tinit])
tnow = self.tinit
dt = (np.min([self.tfinal, tcutoff]) - self.tinit)/50
mindt = dt/2e2
endt = np.min([self.tfinal, tcutoff])
print '-'*40
while tnow<endt:
print tnow
adsol = solve(self.residual, self.utx[-1], \
args = (self.utx[-1], dt), \
max_iter=100, verbose=False)
tnow += dt
self.utx = vstack([self.utx, adsol.reshape([1,adsol.size])])
self.ts = hstack([self.ts, np.array(tnow)])
if adsol._n_Newton < 4:
dt *= 2.
elif adsol._n_Newton < 12:
pass
elif adsol._n_Newton < 64 and dt>mindt:
dt /= 2.
else:
return False
return True
def interp_tgrid(self, tgrid):
# interp utx from ts to tgrid
utx_grid = zeros([tgrid.size, self.N])
for ix in range(self.N):
interp_base = interp(self.ts, self.utx[:,ix])
utx_grid[:,ix] = interp_base(tgrid)
return utx_grid
def plot_utx(self, tgrid):
utx_grid = self.interp_tgrid(tgrid)
T,X = np.meshgrid(degrade(tgrid), degrade(self.xs))
plt.contourf(T,X,degrade(utx_grid))
'Primal model'
class PrimalModel(Model):
def __init__(self, uinit, xs, tinit, tfinal, A):
Model.__init__(self, uinit, xs, tinit, tfinal)
self.flux = BLFlux(A)
'Twin model'
class TwinModel(Model):
def __init__(self, uinit, xs, tinit, tfinal, nsig, rangesig):
Model.__init__(self, uinit, xs, tinit, tfinal)
self.flux = Flux(nsig, rangesig)
'Infer twin model'
class InferTwinModel:
# infer design/source dependent twin model
def __init__(self, xs, uinit, tinit, tfinal, source,
A, nsig, rangesig, coef=None):
# solve primal model for reference solution on tgrid
self.primal = PrimalModel(uinit, xs, tinit, tfinal, A)
self.primal.set_source(source)
self.primal.integrate(tfinal)
# initialize twin model
self.twin = TwinModel(uinit, xs, tinit, tfinal, nsig, rangesig)
self.twin.set_source(source)
if coef is None:
coef = np.loadtxt('xcoef')
self.twin.flux.setcoef(coef.copy())
self.last_working_coef = coef.copy()
self.u_target = None
def clean(self):
self.twin.utx.obliviate()
self.twin.source.obliviate()
self.twin.flux.coef.obliviate()
if self.twin.utx.shape[0]>1:
self.twin.utx = self.twin.utx[0][np.newaxis,:].copy()
def mismatch(self, lasso_reg, tcutoff):
# solution mismatch in [0,tcutoff], with Lasso basis selection
# map twin model solution to primal model's time grid
if not self.twin.integrate(tcutoff):
return False
tgrid = linspace(self.primal.tinit, np.min([self.primal.tfinal, tcutoff]),
1+np.ceil(50.*tcutoff/self.primal.tfinal))
uprimal = self.primal.interp_tgrid(tgrid)
utwin = self.twin.interp_tgrid(tgrid)
self.u_target = utwin[-1]
sol_mismatch = linalg.norm(uprimal-utwin,2)**2
reg = linalg.norm(self.twin.flux.coef, 1)
self.last_working_coef = degrade(self.twin.flux.coef).copy()
return sol_mismatch + lasso_reg * reg
def var_grad(self, coef, grad, lasso_reg, tcutoff):
# solution mismatch value and gradient
self.twin.flux.setcoef(coef.copy())
val = self.mismatch(lasso_reg, tcutoff)
if isinstance(val, bool):
val = 1e10
grads = .1/(coef-self.last_working_coef)[np.newaxis,:]
else:
grads = val.diff(self.twin.flux.coef)
val.obliviate()
for i in range(self.twin.flux.coef.size):
grad[i] = grads[0,i]
print tcutoff, 'val: ', degrade(val)
self.clean()
return float(degrade(val))
def infer(self, coef, lasso_reg):
# optimize selected basis coefficients
for tcutoff in np.logspace(-3,0,5)*self.primal.tfinal:
opt = nlopt.opt(nlopt.LD_LBFGS, coef.size)
opt.set_min_objective(lambda coef, grad:
self.var_grad(coef, grad, lasso_reg, tcutoff))
opt.set_stopval(1e-1)
opt.set_ftol_rel(1e-2)
opt.set_maxeval(100)
if tcutoff == self.primal.tfinal:
opt.set_stopval(0.)
opt.set_ftol_rel(1e-4)
coef = opt.optimize(degrade(coef).copy())
return coef
'Matern kernel'
class Matern:
def __init__(self, sig, rho):
self.sig = upgrade(sig)
self.rho = upgrade(rho)
def update_param(self, sig, rho):
self.sig = upgrade(sig)
self.rho = upgrade(rho)
def K0(self, c0, c1):
# scalar return
d = linalg.norm(c0-c1,2)
return \
self.sig**2 * (1+np.sqrt(5.)*d/self.rho+5./3*d**2/self.rho**2) \
* exp(-np.sqrt(5)*d/self.rho)
def K1(self, c0, c1):
# vector return
d = linalg.norm(c0-c1,2)
return \
self.sig**2 * exp(-np.sqrt(5.)*d/self.rho) \
* (5./3/self.rho**2 + 5*np.sqrt(5.)/3*d/self.rho**3) \
* (c0-c1)
def K2(self, c0, c1):
# matrix return
diffc = upgrade(c0-c1)
d = linalg.norm(diffc,2)
matrix = dot(diffc[np.newaxis,:].transpose() , diffc[np.newaxis,:])
return \
self.sig**2 * exp(-np.sqrt(5.)*d/self.rho) * \
( (5./3/self.rho**2 + 5.*np.sqrt(5.)/3*d/self.rho**3) * eye(diffc.size)
- 25./3/self.rho**4*matrix
)
'Bayesian optimization'
class BayesOpt:
def __init__(self, dimc):
self.c_list = [] # design list
self.obj_list = [] # objective function evaluation list
self.grad_list = [] # estimated gradient evaluation list
self.best_index = None # current best design index in list
self.dimc = dimc
self.obj_kernel = None
self.err_kernel = None
self.like_matrix = None # ndarray
self.mu = None # ndarray
def add_data(self, c, obj, grad):
self.c_list.append(degrade(c))
self.obj_list.append(degrade(obj))
self.grad_list.append(degrade(grad))
self.best_index = np.argmin(np.hstack(self.obj_list))
def update_kernel(self, sig, sige, rho, rhoe):
self.obj_kernel = Matern(sig, rho.copy())
self.err_kernel = Matern(sige, rhoe.copy())
def likelihood(self, params, grad, verbose=False):
# construct data likelihood matrix and mean, evaluate data -1*likelihood
# ndarray output
sig, sige, rho, rhoe = params[0], params[1], params[2], params[3]
self.update_kernel(sig, sige, rho, rhoe)
like_matrix = np.zeros([len(self.obj_list)*(self.dimc+1),
len(self.obj_list)*(self.dimc+1)])
for i in range(len(self.c_list)):
ci = self.c_list[i]
istart = len(self.c_list)+i*self.dimc
iend = istart + self.dimc
for j in range(len(self.c_list)):
cj = self.c_list[j]
jstart = len(self.c_list)+j*self.dimc
jend = jstart + self.dimc
# fill K0
like_matrix[i,j] = degrade( self.obj_kernel.K0(ci, cj) )
# fill K1
like_matrix[i,jstart:jend] = degrade( self.obj_kernel.K1(ci,cj) )
# fill K2 obj
like_matrix[istart:iend, jstart:jend] = degrade( self.obj_kernel.K2(ci, cj) )
# fill K2 err
like_matrix[istart:iend, jstart:jend] += \
degrade( self.err_kernel.K0(ci, cj) * np.eye(self.dimc) )
like_matrix = np.triu(like_matrix,1).transpose() + np.triu(like_matrix)
obj_list = np.hstack(self.obj_list)
grad_list = np.hstack(self.grad_list)
datavec = np.hstack([obj_list, grad_list])
# posterior mean of objective
matrix = like_matrix[:len(self.obj_list),:len(self.obj_list)]
data = datavec[:len(self.obj_list)]
try:
mu_obj = np.sum( np.linalg.solve( matrix, data ) ) / \
np.sum( np.linalg.solve( matrix, np.ones(len(obj_list)) ) )
except:
return 1e5
# posterior mean of grads
mu_grad = np.zeros(self.dimc)
for i in range(self.dimc):
matrix = like_matrix[len(self.obj_list)+i::self.dimc, len(self.obj_list)+i::self.dimc]
data = datavec[len(self.obj_list)+i::self.dimc]
mu_grad[i] = np.sum( np.linalg.solve( matrix, data ) ) / \
np.sum( np.linalg.solve( matrix, np.ones(len(obj_list)) ) )
mu = np.hstack([mu_obj, mu_grad])
self.mu = mu
self.like_matrix = like_matrix
mu = np.tile(mu,[len(obj_list),1])
mu = np.ravel(mu.transpose())
like_det = np.linalg.det(like_matrix)
neg_like_eval = \
np.dot(datavec-mu, np.linalg.solve(like_matrix, datavec-mu)) + np.log(like_det)
if verbose:
print 'LK: ',neg_like_eval
print 'param ', params
return neg_like_eval
def mle(self, params, maxiter=100):
opt = nlopt.opt(nlopt.LN_COBYLA, params.size)
opt.set_min_objective(self.likelihood)
opt.set_maxeval(maxiter)
opt.set_lower_bounds(np.zeros( params.size) )
opt.set_initial_step(np.linalg.norm(params))
opt.set_ftol_rel(1e-3)
params = opt.optimize( params )
return params
def posterior(self, c, params):
# posterior evaluation, adarray output
self.likelihood(params, None)
vec = []
for i in range(len(self.c_list)):
ci = self.c_list[i]
vec.append( self.obj_kernel.K0(c,ci) )
for i in range(len(self.c_list)):
ci = self.c_list[i]
istart = len(self.c_list)+i*self.dimc
iend = istart+self.dimc
vec.append( self.obj_kernel.K1(c, ci) )
vec = hstack(vec)
mu_data = np.tile(self.mu,[len(self.obj_list),1])
mu_data = np.ravel(mu_data.transpose())
datavec = hstack([hstack(self.obj_list), hstack(self.grad_list)])
muc = self.mu[0] + \
dot( vec,
linalg.solve(self.like_matrix, datavec-mu_data)
)
sigc = params[0] - dot(vec, linalg.solve(self.like_matrix, vec))
return muc, sigc
def acquisition(self, cnd, grad, params, scheme='EI'):
# evaluate EI acquisition function and its gradient to c
if self.best_index is None:
print 'posterior initialization required'
exit(1)
c = upgrade(cnd)
muc, sigc = self.posterior(c, params)
if scheme=='EI':
if sigc._value>1e-10:
zc = (self.obj_list[self.best_index] - muc) / sigc
EI = sigc * ( zc/2 * (1+erf(zc/np.sqrt(2))) +
1./np.sqrt(2*np.pi)*exp(-zc**2/2) )
else:
EI = self.obj_list[self.best_index] - muc
elif scheme=='UCB':
EI = - muc + 3.*sigc
else:
print 'scheme not recognized'
exit(1)
print 'EI: ', EI._value
EI_grad = EI.diff(c)
EI.obliviate()
for i in range(self.dimc):
grad[i] = degrade(EI_grad[0,i])
return float(degrade(EI))
def next_design(self, params):
# next candidate design
opt = nlopt.opt(nlopt.LD_TNEWTON_PRECOND_RESTART, self.dimc)
opt.set_max_objective( lambda c, grad:
self.acquisition(c, grad, params) )
opt.set_stopval(1e5)
opt.set_maxeval(50)
agent_num = 30
agent_best_c = None
agent_best_val = -1.
for i in range(agent_num):
print 'agent', i
agent_init = np.array(self.c_list[self.best_index]) \
+ np.random.randn(self.dimc)*.2
try:
nextc = opt.optimize(agent_init.copy())
if opt.last_optimum_value() > agent_best_val:
agent_best_c = nextc
agent_best_val = opt.last_optimum_value()
except:
pass
return agent_best_c, agent_best_val
if __name__ == '__main__':
unittest.main()