def bounds(Xs, Ys, ns=100):
#use a gp to infer mean and bounds on sets of x/y data that have diffent x
#f,a = plt.subplots(2)
#for i in xrange(len(Ys)):
# a[0].plot(Xs[i],Ys[i])
X = sp.hstack(Xs)
np = X.size
Y = sp.hstack(Ys)
X.resize([np, 1])
Y.resize([np, 1])
#a[1].plot(X,Y,'r.')
np = X.size
S = sp.zeros(np)
D = [[sp.NaN]] * np
ki = GPdc.MAT52CS
mprior = sp.array([1., 2., 1.])
sprior = sp.array([2., 2., 2.])
#MAPH = GPdc.searchMAPhyp(X,Y,S,D,mprior,sprior, ki,mx=500)
MAPH = sp.array([0.5, 5., 0.3])
g = GPdc.GPcore(X, Y, S, D, GPdc.kernel(ki, 1, MAPH))
sup = sp.linspace(min(X), max(X), ns)
[m, V] = g.infer_diag_post(sup, [[sp.NaN]] * ns)
std = sp.sqrt(V + MAPH[2])
#plt.fill_between(sup.flatten(),(m-std).flatten(),(m+std).flatten(),facecolor='lightblue',edgecolor='lightblue',alpha=0.5)
#a[1].plot(sup,m.flatten(),'b')
return [sup, m, std]
def EIMAPaq(optstate,persist,ev=None, ub = None, lb=None, nrandinit=None, mprior=None,sprior=None,kindex = None,directmaxiter=None):
para = copy.deepcopy(para)
if persist==None:
persist = {'n':0,'d':len(ub)}
n = persist['n']
d = persist['d']
if n<nrandinit:
persist['n']+=1
return randomaq(optstate,persist,ev=ev,lb=lb,ub=ub)
logger.info('EIMAPaq')
#logger.debug(sp.vstack([e[0] for e in optstate.ev]))
#raise
x=sp.vstack(optstate.x)
y=sp.vstack(optstate.y)
s= sp.vstack([e['s'] for e in optstate.ev])
dx=[e['d'] for e in optstate.ev]
MAP = GPdc.searchMAPhyp(x,y,s,dx,mprior,sprior, kindex)
logger.info('MAPHYP {}'.format(MAP))
G = GPdc.GPcore(x,y,s,dx,GPdc.kernel(kindex,d,MAP))
def directwrap(xq,y):
xq.resize([1,d])
a = G.infer_lEI(xq,[ev['d']])
return (-a[0,0],0)
[xmin,ymin,ierror] = DIRECT.solve(directwrap,lb,ub,user_data=[], algmethod=0, maxf = directmaxiter, logfilename='/dev/null')
#logger.debug([xmin,ymin,ierror])
persist['n']+=1
return [i for i in xmin],ev,persist,{'MAPHYP':MAP,'logEImin':ymin,'DIRECTmessage':ierror}
def gensquexpdraw(d, lb, ub, ignores=-1):
nt = 14
[X, Y, S, D] = ESutils.gen_dataset(nt, d, lb, ub, GPdc.SQUEXP,
sp.array([1.5] + [0.30] * d))
G = GPdc.GPcore(X, Y, S, D,
GPdc.kernel(GPdc.SQUEXP, d, sp.array([1.5] + [0.30] * d)))
def obj(x, s, d, override=False):
#print [x,s,d]
if ignores > 0:
s = ignores
if s == 0. or override:
noise = 0.
else:
noise = sp.random.normal(scale=sp.sqrt(s))
print "EVAL WITH NOISE: " + str(noise) + "FROM S= " + str(s)
return [G.infer_m(x, [d])[0, 0] + noise, 1.]
def dirwrap(x, y):
z = G.infer_m(x, [[sp.NaN]])[0, 0]
#z = obj(x,0.,[sp.NaN])
return (z, 0)
[xmin, ymin, ierror] = DIRECT.solve(dirwrap,
lb,
ub,
user_data=[],
algmethod=1,
maxf=89000,
logfilename='/dev/null')
return [obj, xmin, ymin]
def genmat52ojf(d, lb, ub):
from ESutils import gen_dataset
nt = 14
[X, Y, S, D] = gen_dataset(nt, d, lb, ub, GPdc.MAT52,
sp.array([1.5] + [0.55] * d))
G = GPdc.GPcore(X, Y, S, D,
GPdc.kernel(GPdc.MAT52, d, sp.array([1.5] + [0.55] * d)))
def ojf(x, **ev):
dx = ev['d']
s = ev['s']
if ev['s'] > 0:
noise = sp.random.normal(scale=sp.sqrt(ev['s']))
else:
noise = 0
return G.infer_m(sp.array(x), [dx])[0, 0] + noise, 1., dict()
def dirwrap(x, y):
z = G.infer_m(x, [[sp.NaN]])[0, 0]
#z = obj(x,0.,[sp.NaN])
return (z, 0)
[xmin, ymin, ierror] = DIRECT.solve(dirwrap,
lb,
ub,
user_data=[],
algmethod=1,
maxf=89000,
logfilename='/dev/null')
logger.info('generated function xmin {} ymin {} {}'.format(
xmin, ymin, ierror))
return ojf, xmin, ymin
def gpmapasrecc(optstate, **para):
if para["onlyafter"] > len(optstate.y) or not len(optstate.y) % para["everyn"] == 0:
return [sp.NaN for i in para["lb"]], {"didnotrun": True}
logger.info("gpmapas reccomender")
d = len(para["lb"])
x = sp.hstack([sp.vstack(optstate.x), sp.vstack([e["xa"] for e in optstate.ev])])
y = sp.vstack(optstate.y)
s = sp.vstack([e["s"] for e in optstate.ev])
dx = [e["d"] for e in optstate.ev]
MAP = GPdc.searchMAPhyp(x, y, s, dx, para["mprior"], para["sprior"], para["kindex"])
logger.info("MAPHYP {}".format(MAP))
G = GPdc.GPcore(x, y, s, dx, GPdc.kernel(para["kindex"], d + 1, MAP))
def directwrap(xq, y):
xq.resize([1, d])
xe = sp.hstack([xq, sp.array([[0.0]])])
# print xe
a = G.infer_m(xe, [[sp.NaN]])
return (a[0, 0], 0)
[xmin, ymin, ierror] = DIRECT.solve(
directwrap, para["lb"], para["ub"], user_data=[], algmethod=1, volper=para["volper"], logfilename="/dev/null"
)
logger.info("reccsearchresult: {}".format([xmin, ymin, ierror]))
return [i for i in xmin], {"MAPHYP": MAP, "ymin": ymin}
def gpmapasrecc(optstate, **para):
if para['onlyafter'] > len(
optstate.y) or not len(optstate.y) % para['everyn'] == 0:
return [sp.NaN for i in para['lb']], {'didnotrun': True}
logger.info('gpmapas reccomender')
d = len(para['lb'])
x = sp.hstack(
[sp.vstack(optstate.x),
sp.vstack([e['xa'] for e in optstate.ev])])
y = sp.vstack(optstate.y)
s = sp.vstack([e['s'] for e in optstate.ev])
dx = [e['d'] for e in optstate.ev]
MAP = GPdc.searchMAPhyp(x, y, s, dx, para['mprior'], para['sprior'],
para['kindex'])
logger.info('MAPHYP {}'.format(MAP))
G = GPdc.GPcore(x, y, s, dx, GPdc.kernel(para['kindex'], d + 1, MAP))
def directwrap(xq, y):
xq.resize([1, d])
xe = sp.hstack([xq, sp.array([[0.]])])
#print xe
a = G.infer_m(xe, [[sp.NaN]])
return (a[0, 0], 0)
[xmin, ymin, ierror] = DIRECT.solve(directwrap,
para['lb'],
para['ub'],
user_data=[],
algmethod=1,
volper=para['volper'],
logfilename='/dev/null')
logger.info('reccsearchresult: {}'.format([xmin, ymin, ierror]))
return [i for i in xmin], {'MAPHYP': MAP, 'ymin': ymin}
def ojf(x, s, d, override=False):
#print "called ojf: "+str(x)
try:
x = x.flatten(0)
except:
pass
xlow = [-2., -2.]
xupp = [2., 2.]
xthis = [
xlow[i] + 0.5 * (xin + 1) * (xupp[i] - xlow[i])
for i, xin in enumerate(x)
]
hyp = [10**i for i in xthis]
print hyp
t0 = time.clock()
llk = sp.clip(
GPdc.GP_LKonly(X, Y, S, D, GPdc.kernel(GPdc.MAT52, 1,
sp.array(hyp))).plk(pm, ps),
-1e60, 1e60)
t1 = time.clock()
if llk < -1.:
out = sp.log(-llk) + 1.
else:
out = -llk
print "--->llk: {0} {1} t: {2}".format(llk, out, t1 - t0)
return [out, t1 - t0]
def run_search(self):
MAP = GPdc.searchMAPhyp(self.X, self.Y, self.S, self.D, self.mprior,
self.sprior, self.kindex)
try:
del (self.G)
except:
pass
self.G = GPdc.GPcore(self.X, self.Y, self.S, self.D,
GPdc.kernel(self.kindex, self.d, MAP))
def directwrap(x, y):
x.resize([1, self.d])
a = self.G.infer_lEI(x, [[sp.NaN]])
#print [x,a]
#print G.infer_diag_post(x,[[sp.NaN]])
return (-a[0, 0], 0)
[xmin, ymin, ierror] = DIRECT.solve(directwrap,
self.lb,
self.ub,
user_data=[],
algmethod=1,
volper=self.volper,
logfilename='/dev/null')
return [xmin, self.s, [sp.NaN]]
def makeG(X,Y,S,D,kindex,mprior,sprior,nh):
#draw hyps based on plk
#print "RRRRRRRRRRRRRR"+str([X,Y,S,D,kindex,mprior,sprior,nh])
H = ESutils.drawhyp_plk(X,Y,S,D,kindex,mprior,sprior,nh)
G = GPdc.GPcore(X,Y,S,D,[GPdc.kernel(kindex,X.shape[1],i) for i in H])
return G
def gen_dataset(nt, d, lb, ub, kindex, hyp, s=1e-9):
X = draw_support(d, lb, ub, nt, SUPPORT_UNIFORM)
D = [[sp.NaN]] * (nt)
kf = GPdc.kernel(kindex, d, hyp)
Kxx = GPdc.buildKsym_d(kf, X, D)
Y = spl.cholesky(Kxx, lower=True) * sp.matrix(sps.norm.rvs(
0, 1., nt)).T + sp.matrix(sps.norm.rvs(0, sp.sqrt(s), nt)).T
S = sp.matrix([s] * nt).T
return [X, Y, S, D]
def gen_dataset(nt, d, lb, ub, kindex, hyp, s=1e-9):
X = draw_support(d, lb, ub, nt, SUPPORT_UNIFORM)
D = [[sp.NaN]] * (nt)
kf = GPdc.kernel(kindex, d, hyp)
Kxx = GPdc.buildKsym_d(kf, X, D)
Y = (
spl.cholesky(Kxx, lower=True) * sp.matrix(sps.norm.rvs(0, 1.0, nt)).T
+ sp.matrix(sps.norm.rvs(0, sp.sqrt(s), nt)).T
)
S = sp.matrix([s] * nt).T
return [X, Y, S, D]
def train_costest(self):
print self.X[:,0]
X = self.X[:,0].copy().reshape([len(self.C),1])
C = sp.array(self.C)
D = [[sp.NaN]]*len(self.C)
S = sp.zeros([len(self.C),1])
lbc = sp.array([-3.,-2.,-6.])
ubc = sp.array([3.,2.,1.])
MLEC = GPdc.searchMLEhyp(X,sp.log(C),S,D,lbc,ubc,GPdc.SQUEXPCS,mx=10000)
print "MLEC "+str(MLEC)
self.ce = GPdc.GPcore(X.copy(),sp.log(C),S,D,GPdc.kernel(GPdc.SQUEXPCS,1,sp.array(MLEC)))
#self.ce = GPdc.GPcore(X,C,S,D,GPdc.kernel(GPdc.SQUEXPCS,1,sp.array([1.,0.3,1e-3])))
#self.ce.printc()
return
def EIMAPaq(optstate,
persist,
ev=None,
ub=None,
lb=None,
nrandinit=None,
mprior=None,
sprior=None,
kindex=None,
directmaxiter=None):
para = copy.deepcopy(para)
if persist == None:
persist = {'n': 0, 'd': len(ub)}
n = persist['n']
d = persist['d']
if n < nrandinit:
persist['n'] += 1
return randomaq(optstate, persist, ev=ev, lb=lb, ub=ub)
logger.info('EIMAPaq')
#logger.debug(sp.vstack([e[0] for e in optstate.ev]))
#raise
x = sp.vstack(optstate.x)
y = sp.vstack(optstate.y)
s = sp.vstack([e['s'] for e in optstate.ev])
dx = [e['d'] for e in optstate.ev]
MAP = GPdc.searchMAPhyp(x, y, s, dx, mprior, sprior, kindex)
logger.info('MAPHYP {}'.format(MAP))
G = GPdc.GPcore(x, y, s, dx, GPdc.kernel(kindex, d, MAP))
def directwrap(xq, y):
xq.resize([1, d])
a = G.infer_lEI(xq, [ev['d']])
return (-a[0, 0], 0)
[xmin, ymin, ierror] = DIRECT.solve(directwrap,
lb,
ub,
user_data=[],
algmethod=0,
maxf=directmaxiter,
logfilename='/dev/null')
#logger.debug([xmin,ymin,ierror])
persist['n'] += 1
return [i for i in xmin], ev, persist, {
'MAPHYP': MAP,
'logEImin': ymin,
'DIRECTmessage': ierror
}
def run_search(self):
MAP = GPdc.searchMAPhyp(self.X,self.Y,self.S,self.D,self.mprior,self.sprior, self.kindex)
try:
del(self.G)
except:
pass
self.G = GPdc.GPcore(self.X,self.Y,self.S,self.D,GPdc.kernel(self.kindex,self.d,MAP))
def directwrap(x,y):
x.resize([1,self.d])
a = self.G.infer_LCB(x,[[sp.NaN]],1.)[0,0]
return (a,0)
[xmin,ymin,ierror] = DIRECT.solve(directwrap,self.lb,self.ub,user_data=[], algmethod=1, volper=self.volper, logfilename='/dev/null')
return [xmin,self.s,[sp.NaN]]
def genmat52ojf(d, lb, ub):
from ESutils import gen_dataset
nt = 14
[X, Y, S, D] = gen_dataset(nt, d, lb, ub, GPdc.MAT52, sp.array([1.5] + [0.55] * d))
G = GPdc.GPcore(X, Y, S, D, GPdc.kernel(GPdc.MAT52, d, sp.array([1.5] + [0.55] * d)))
def ojf(x, **ev):
dx = ev["d"]
s = ev["s"]
if ev["s"] > 0:
noise = sp.random.normal(scale=sp.sqrt(ev["s"]))
else:
noise = 0
return G.infer_m(sp.array(x), [dx])[0, 0] + noise, 1.0, dict()
def dirwrap(x, y):
z = G.infer_m(x, [[sp.NaN]])[0, 0]
# z = obj(x,0.,[sp.NaN])
return (z, 0)
[xmin, ymin, ierror] = DIRECT.solve(dirwrap, lb, ub, user_data=[], algmethod=1, maxf=89000, logfilename="/dev/null")
logger.info("generated function xmin {} ymin {} {}".format(xmin, ymin, ierror))
return ojf, xmin, ymin
def genbiasedmat52ojf(d, lb, ub, sls):
# s normalised to 0 exact, 1
from ESutils import gen_dataset
nt = 20
[X, Y, S, D] = gen_dataset(nt, d + 1, [0.0] + lb, [1.0] + ub, GPdc.MAT52, sp.array([1.5] + [0.30] * d + [sls]))
G = GPdc.GPcore(X, Y, S, D, GPdc.kernel(GPdc.MAT52, d + 1, sp.array([1.5] + [0.30] * d + [sls])))
def ojf(x, **ev):
# print "\nojfinput: {} : {}".format(x,ev)
dx = ev["d"]
s = ev["s"]
if ev["s"] > 0:
noise = sp.random.normal(scale=sp.sqrt(ev["s"]))
else:
noise = 0
xa = ev["xa"]
x = sp.array(x)
xfull = sp.hstack([x, xa])
return G.infer_m(xfull, [dx])[0, 0] + noise, 1.0, dict()
def dirwrap(x, y):
z = G.infer_m(sp.hstack(sp.array(x) + [0.0]), [[sp.NaN]])[0, 0]
return (z, 0)
[xmin, ymin, ierror] = DIRECT.solve(dirwrap, lb, ub, user_data=[], algmethod=1, maxf=89000, logfilename="/dev/null")
logger.info("generated function xmin {} ymin {}".format(xmin, ymin))
return ojf, xmin, ymin
def gensquexpIPdraw(d,lb,ub,sl,su,sfn,sls,cfn):
#axis = 0 value = sl
#d dimensional objective +1 for s
nt=25
#print sp.hstack([sp.array([[sl]]),lb])
#print sp.hstack([sp.array([[su]]),ub])
[X,Y,S,D] = ESutils.gen_dataset(nt,d+1,sp.hstack([sp.array([[sl]]),lb]).flatten(),sp.hstack([sp.array([[su]]),ub]).flatten(),GPdc.SQUEXP,sp.array([1.5]+[sls]+[0.30]*d))
G = GPdc.GPcore(X,Y,S,D,GPdc.kernel(GPdc.SQUEXP,d+1,sp.array([1.5]+[sls]+[0.30]*d)))
def obj(x,s,d,override=False):
x = x.flatten()
if sfn(x)==0. or override:
noise = 0.
else:
noise = sp.random.normal(scale=sp.sqrt(sfn(x)))
return [G.infer_m(x,[d])[0,0]+noise,cfn(x)]
def dirwrap(x,y):
z = obj(sp.array([[sl]+[i for i in x]]),sl,[sp.NaN],override=True)
return (z,0)
[xmin0,ymin0,ierror] = DIRECT.solve(dirwrap,lb,ub,user_data=[], algmethod=1, maxf=89000, logfilename='/dev/null')
lb2 = xmin0-sp.ones(d)*1e-4
ub2 = xmin0+sp.ones(d)*1e-4
[xmin,ymin,ierror] = DIRECT.solve(dirwrap,lb2,ub2,user_data=[], algmethod=1, maxf=89000, logfilename='/dev/null')
#print "RRRRR"+str([xmin0,xmin,ymin0,ymin,xmin0-xmin,ymin0-ymin])
return [obj,xmin,ymin]
def ojf(x,s,d,override=False):
#print "called ojf: "+str(x)
try:
x=x.flatten(0)
except:
pass
xlow = [-2.,-2.]
xupp = [2.,2.]
xthis = [xlow[i]+0.5*(xin+1)*(xupp[i]-xlow[i]) for i,xin in enumerate(x)]
hyp = [10**i for i in xthis]
print hyp
t0=time.clock()
llk = sp.clip(GPdc.GP_LKonly(X,Y,S,D,GPdc.kernel(GPdc.MAT52,1,sp.array(hyp))).plk(pm,ps),-1e60,1e60)
t1=time.clock()
if llk<-1.:
out = sp.log(-llk)+1.
else:
out = -llk
print "--->llk: {0} {1} t: {2}".format(llk,out,t1-t0)
return [out,t1-t0]
def bounds(Xs,Ys,ns=100):
#use a gp to infer mean and bounds on sets of x/y data that have diffent x
#f,a = plt.subplots(2)
#for i in xrange(len(Ys)):
# a[0].plot(Xs[i],Ys[i])
X = sp.hstack(Xs)
np = X.size
Y = sp.hstack(Ys)
X.resize([np,1])
Y.resize([np,1])
#a[1].plot(X,Y,'r.')
np = X.size
S = sp.zeros(np)
D = [[sp.NaN]]*np
ki = GPdc.MAT52CS
mprior = sp.array([1.,2.,1.])
sprior = sp.array([2.,2.,2.])
#MAPH = GPdc.searchMAPhyp(X,Y,S,D,mprior,sprior, ki,mx=500)
MAPH = sp.array([0.5,5.,0.3])
g = GPdc.GPcore(X,Y,S,D,GPdc.kernel(ki,1,MAPH))
sup = sp.linspace(min(X),max(X),ns)
[m,V] = g.infer_diag_post(sup,[[sp.NaN]]*ns)
std = sp.sqrt(V+MAPH[2])
#plt.fill_between(sup.flatten(),(m-std).flatten(),(m+std).flatten(),facecolor='lightblue',edgecolor='lightblue',alpha=0.5)
#a[1].plot(sup,m.flatten(),'b')
return [sup,m,std]
def gensquexpIPdraw(d, lb, ub, sl, su, sfn, sls, cfn):
#axis = 0 value = sl
#d dimensional objective +1 for s
nt = 25
#print sp.hstack([sp.array([[sl]]),lb])
#print sp.hstack([sp.array([[su]]),ub])
[X, Y,
S, D] = ESutils.gen_dataset(nt, d + 1,
sp.hstack([sp.array([[sl]]), lb]).flatten(),
sp.hstack([sp.array([[su]]), ub]).flatten(),
GPdc.SQUEXP,
sp.array([1.5] + [sls] + [0.30] * d))
G = GPdc.GPcore(
X, Y, S, D,
GPdc.kernel(GPdc.SQUEXP, d + 1, sp.array([1.5] + [sls] + [0.30] * d)))
def obj(x, s, d, override=False):
x = x.flatten()
if sfn(x) == 0. or override:
noise = 0.
else:
noise = sp.random.normal(scale=sp.sqrt(sfn(x)))
return [G.infer_m(x, [d])[0, 0] + noise, cfn(x)]
def dirwrap(x, y):
z = obj(sp.array([[sl] + [i for i in x]]), sl, [sp.NaN], override=True)
return (z, 0)
[xmin0, ymin0, ierror] = DIRECT.solve(dirwrap,
lb,
ub,
user_data=[],
algmethod=1,
maxf=89000,
logfilename='/dev/null')
lb2 = xmin0 - sp.ones(d) * 1e-4
ub2 = xmin0 + sp.ones(d) * 1e-4
[xmin, ymin, ierror] = DIRECT.solve(dirwrap,
lb2,
ub2,
user_data=[],
algmethod=1,
maxf=89000,
logfilename='/dev/null')
#print "RRRRR"+str([xmin0,xmin,ymin0,ymin,xmin0-xmin,ymin0-ymin])
return [obj, xmin, ymin]
def llks(self, hy, sub):
t0 = time.clock()
Xs = sp.empty([sub, self.d])
Ys = sp.empty([sub, 1])
Ss = sp.zeros([sub, 1])
Ds = []
ix = npr.choice(range(self.n), size=sub, replace=False)
for i, x in enumerate(ix):
Xs[i, :] = self.X[x, :]
Ys[i, :] = self.Y[x, :]
Ds.append(self.D[x])
t1 = time.clock()
r = GPdc.GP_LKonly(Xs, Ys, Ss, Ds, GPdc.kernel(self.ki, self.d,
hy)).llk()
t2 = time.clock()
#print [t1-t0,t2-t1]
return [r, t2 - t0]
def f(loghyp):
ub = hm + 1.8 * hs
lb = hm - 1.8 * hs
if all(loghyp < ub) and all(loghyp > lb):
r = GPdc.GP_LKonly(
X, Y, S, D, GPdc.kernel(ki, X.shape[1],
[10**i for i in loghyp])).plk(hm, hs)
if sp.isnan(r):
class MJMError(Exception):
pass
print 'nan from GPLKonly with input'
print[X, Y, S, D, ki, hm, hs, n, burn, subsam]
raise MJMError('nan from GPLKonly with input')
else:
r = -1e99
#print [loghyp, r]
return r
def ojfa(x, s, d, override=False):
#print "called ojf: "+str(x)
try:
x = x.flatten(0)
except:
pass
xlow = [-2., -2.]
xupp = [2., 2.]
xthis = [
xlow[i] + 0.5 * (xin + 1) * (xupp[i] - xlow[i])
for i, xin in enumerate(x[1:])
]
hyp = [10**i for i in xthis]
#hyp = [10**i for i in x.flatten()[1:]]
print hyp
t0 = time.clock()
sub = x.flatten()[0]
npts = int((1. - 0.9 * sub) * n)
if override:
npts = n
print "subsampling {0} of {1} at x[0]={2}".format(npts, n, x.flatten()[0])
ps = npr.choice(range(n), size=npts, replace=False)
Xd = sp.vstack([X[i] for i in ps])
Yd = sp.vstack([Y[i] for i in ps])
Sd = sp.vstack([S[i] for i in ps])
Dd = [[sp.NaN]] * npts
llk = GPdc.GP_LKonly(Xd, Yd, Sd, Dd,
GPdc.kernel(GPdc.MAT52, 1,
sp.array(hyp))).plk(pm, ps)
t1 = time.clock()
if llk < -1.:
out = sp.log(-llk) + 1.
else:
out = -llk
print "--->llk: {0} {1} t: {2}".format(llk, out, t1 - t0)
return [out, t1 - t0]
def train_costest(self):
print self.X[:, 0]
X = self.X[:, 0].copy().reshape([len(self.C), 1])
C = sp.array(self.C)
D = [[sp.NaN]] * len(self.C)
S = sp.zeros([len(self.C), 1])
lbc = sp.array([-3., -2., -6.])
ubc = sp.array([3., 2., 1.])
MLEC = GPdc.searchMLEhyp(X,
sp.log(C),
S,
D,
lbc,
ubc,
GPdc.SQUEXPCS,
mx=10000)
print "MLEC " + str(MLEC)
self.ce = GPdc.GPcore(X.copy(), sp.log(C), S, D,
GPdc.kernel(GPdc.SQUEXPCS, 1, sp.array(MLEC)))
#self.ce = GPdc.GPcore(X,C,S,D,GPdc.kernel(GPdc.SQUEXPCS,1,sp.array([1.,0.3,1e-3])))
#self.ce.printc()
return
def genbiasedmat52ojf(d, lb, ub, sls):
#s normalised to 0 exact, 1
from ESutils import gen_dataset
nt = 20
[X, Y, S, D] = gen_dataset(nt, d + 1, [0.] + lb, [1.] + ub, GPdc.MAT52,
sp.array([1.5] + [0.30] * d + [sls]))
G = GPdc.GPcore(
X, Y, S, D,
GPdc.kernel(GPdc.MAT52, d + 1, sp.array([1.5] + [0.30] * d + [sls])))
def ojf(x, **ev):
#print "\nojfinput: {} : {}".format(x,ev)
dx = ev['d']
s = ev['s']
if ev['s'] > 0:
noise = sp.random.normal(scale=sp.sqrt(ev['s']))
else:
noise = 0
xa = ev['xa']
x = sp.array(x)
xfull = sp.hstack([x, xa])
return G.infer_m(xfull, [dx])[0, 0] + noise, 1., dict()
def dirwrap(x, y):
z = G.infer_m(sp.hstack(sp.array(x) + [0.]), [[sp.NaN]])[0, 0]
return (z, 0)
[xmin, ymin, ierror] = DIRECT.solve(dirwrap,
lb,
ub,
user_data=[],
algmethod=1,
maxf=89000,
logfilename='/dev/null')
logger.info('generated function xmin {} ymin {}'.format(xmin, ymin))
return ojf, xmin, ymin
def llks(self,hy,sub):
t0 = time.clock()
Xs = sp.empty([sub,self.d])
Ys = sp.empty([sub,1])
Ss = sp.zeros([sub,1])
Ds = []
ix = npr.choice(range(self.n),size=sub, replace=False)
for i,x in enumerate(ix):
Xs[i,:] = self.X[x,:]
Ys[i,:] = self.Y[x,:]
Ds.append(self.D[x])
t1 = time.clock()
r = GPdc.GP_LKonly(Xs,Ys,Ss,Ds,GPdc.kernel(self.ki,self.d,hy)).llk()
t2=time.clock()
#print [t1-t0,t2-t1]
return [r,t2-t0]
def __init__(self,X,Y,S,D,lb,ub,kindex,mprior,sprior,DH_SAMPLES=8,DM_SAMPLES=8, DM_SUPPORT=400,DM_SLICELCBPARA=1.,mode=ESutils.SUPPORT_SLICELCB,noS=False):
print "PES init:"
self.lb=lb
self.ub=ub
self.noS=noS
if noS:
S=sp.zeros(S.shape)
self.G = makeG(X,Y,S,D,kindex,mprior,sprior,DH_SAMPLES)
HS = sp.vstack([k.hyp for k in self.G.kf])
print "\nhyp mean: "+str(sp.mean(HS,axis=0))
print "hyp std: "+str(sp.sqrt(sp.mean(HS,axis=0)))
self.Z = drawmins(self.G,DM_SAMPLES,lb,ub,SUPPORT=DM_SUPPORT,SLICELCB_PARA=DM_SLICELCBPARA,mode=mode)
print "mindraws: "+str(self.Z)
self.Ga = [GPdc.GPcore(*addmins(self.G,X,Y,S,D,self.Z[i,:])+[self.G.kf]) for i in xrange(DM_SAMPLES)]
def __init__(self,X,Y,S,D,lb,ub,kindex,mprior,sprior,axis,value,DH_SAMPLES=8,DM_SAMPLES=8, DM_SUPPORT=400,DM_SLICELCBPARA=1.,AM_POLICY=NOMIN,mode=ESutils.SUPPORT_SLICELCB,noS=False):
print "PES init:"
self.lb=lb
self.ub=ub
self.noS=noS
self.X=X
if noS:
S=sp.zeros(S.shape)
print [X.shape,Y.shape,mprior,sprior]
self.G = makeG(X,Y,S,D,kindex,mprior,sprior,DH_SAMPLES)
HS = sp.vstack([k.hyp for k in self.G.kf])
print "\nhyp mean: "+str(sp.mean(HS,axis=0))
print "hyp std: "+str(sp.sqrt(sp.mean(HS,axis=0)))
self.Z = drawmins_inplane(self.G,DM_SAMPLES,lb,ub,axis=axis,value=value,SUPPORT=DM_SUPPORT,SLICELCB_PARA=DM_SLICELCBPARA,mode=mode)
print "mindraws:\n"+str(self.Z)
self.Ga = [GPdc.GPcore(*addmins_inplane(self.G,X,Y,S,D,self.Z[i,:],axis=axis,value=value,MINPOLICY=AM_POLICY)+[self.G.kf]) for i in xrange(DM_SAMPLES)]
return
def f(loghyp):
ub = hm + 1.8 * hs
lb = hm - 1.8 * hs
if all(loghyp < ub) and all(loghyp > lb):
r = GPdc.GP_LKonly(X, Y, S, D, GPdc.kernel(ki, X.shape[1], [10 ** i for i in loghyp])).plk(hm, hs)
if sp.isnan(r):
class MJMError(Exception):
pass
print "nan from GPLKonly with input"
print [X, Y, S, D, ki, hm, hs, n, burn, subsam]
raise MJMError("nan from GPLKonly with input")
else:
r = -1e99
# print [loghyp, r]
return r
def gensquexpdraw(d,lb,ub,ignores=-1):
nt=14
[X,Y,S,D] = ESutils.gen_dataset(nt,d,lb,ub,GPdc.SQUEXP,sp.array([1.5]+[0.30]*d))
G = GPdc.GPcore(X,Y,S,D,GPdc.kernel(GPdc.SQUEXP,d,sp.array([1.5]+[0.30]*d)))
def obj(x,s,d,override=False):
#print [x,s,d]
if ignores>0:
s=ignores
if s==0. or override:
noise = 0.
else:
noise = sp.random.normal(scale=sp.sqrt(s))
print "EVAL WITH NOISE: "+str(noise) + "FROM S= "+str(s)
return [G.infer_m(x,[d])[0,0]+noise,1.]
def dirwrap(x,y):
z = G.infer_m(x,[[sp.NaN]])[0,0]
#z = obj(x,0.,[sp.NaN])
return (z,0)
[xmin,ymin,ierror] = DIRECT.solve(dirwrap,lb,ub,user_data=[], algmethod=1, maxf=89000, logfilename='/dev/null')
return [obj,xmin,ymin]
def ojfa(x,s,d,override=False):
#print "called ojf: "+str(x)
try:
x=x.flatten(0)
except:
pass
xlow = [-2.,-2.]
xupp = [2.,2.]
xthis = [xlow[i]+0.5*(xin+1)*(xupp[i]-xlow[i]) for i,xin in enumerate(x[1:])]
hyp = [10**i for i in xthis]
#hyp = [10**i for i in x.flatten()[1:]]
print hyp
t0=time.clock()
sub = x.flatten()[0]
npts = int((1.-0.9*sub)*n)
if override:
npts=n
print "subsampling {0} of {1} at x[0]={2}".format(npts,n,x.flatten()[0])
ps = npr.choice(range(n),size=npts, replace=False)
Xd = sp.vstack([X[i] for i in ps])
Yd = sp.vstack([Y[i] for i in ps])
Sd = sp.vstack([S[i] for i in ps])
Dd = [[sp.NaN]]*npts
llk = GPdc.GP_LKonly(Xd,Yd,Sd,Dd,GPdc.kernel(GPdc.MAT52,1,sp.array(hyp))).plk(pm,ps)
t1=time.clock()
if llk<-1.:
out = sp.log(-llk)+1.
else:
out = -llk
print "--->llk: {0} {1} t: {2}".format(llk,out,t1-t0)
return [out,t1-t0]
#!/usr/bin/env python2
#encoding: UTF-8
#test the 1d periodic matern5/2 kernel
import sys
sys.path.append("./..")
import scipy as sp
from matplotlib import pyplot as plt
import seaborn as sns
import GPdc
kp = GPdc.kernel(GPdc.MAT52, 1, sp.array([0.75, 0.1]))
kq = GPdc.kernel(GPdc.MAT52PER, 1, sp.array([0.75, 0.1, 4.5]))
kr = GPdc.kernel(GPdc.MAT52PPT, 1, sp.array([0.75, 0.1, 4.5, 15.]))
ks = GPdc.kernel(GPdc.DEV, 1, sp.array([0.75, 0.1, 4.5, 0.5, 0.4, 10.]))
#support
ns = 1201
xax = sp.array([sp.linspace(-15, 15, ns)]).T
d0 = [[sp.NaN]]
x0 = sp.array([[0.]])
p = sp.empty(ns)
q = sp.empty(ns)
r = sp.empty(ns)
s = sp.empty(ns)
for i in xrange(ns):
p[i] = kp(x0, xax[i, :], d0, d0)
q[i] = kq(x0, xax[i, :], d0, d0) + 1
r[i] = kr(x0, xax[i, :], d0, d0) + 2
s[i] = ks(x0, xax[i, :], d0, d0) + 3
import ctypes as ct
import scipy as sp
from scipy import stats as sps
from scipy import linalg as spl
from matplotlib import pyplot as plt
import os
libGP = ct.cdll.LoadLibrary(
os.path.join(os.path.dirname(os.path.realpath(__file__)),
'../../../dist/Release/GNU-Linux/libGPshared.so'))
ctpd = ct.POINTER(ct.c_double)
import GPdc
ni = 50
kf = GPdc.kernel(GPdc.SQUEXP, 1, sp.array([1.3, 0.3]))
X = sp.matrix(sp.linspace(-1, 1, ni)).T
D = [[sp.NaN]] * ni
Kxx = GPdc.buildKsym_d(kf, X, D)
tmp = spl.cholesky(Kxx, lower=True)
Ch = sp.vstack([tmp[i, :] for i in xrange(ni)]) #hack/force row major storage
z = 5
b = sp.empty([ni, z])
libGP.drawcov(Ch.ctypes.data_as(ctpd), ct.c_int(ni), b.ctypes.data_as(ctpd),
ct.c_int(z))
#print b
f,ax = plt.subplots(n,sharex=True)
ns=200
sup = sp.linspace(-6,6,ns)
for i in xrange(n):
ax[i].plot(sup,sps.norm.pdf(sup,loc=m[i],scale=sp.sqrt(v[i,i])),'b')
ax[i].plot(sup,sps.norm.pdf(sup,loc=mu[i],scale=sp.sqrt(vu[i,i])),'r')
ax[i].twinx().plot(sup,sps.norm.cdf(Z[i]*(sup-Y[i])/max(F[i],1e-20))*sps.norm.pdf(sup,loc=m[i],scale=sp.sqrt(v[i,i])),'g')
#est on a gp
import ESutils
import GPdc
nt=5
X = sp.matrix(sp.linspace(-1,1,nt)).T
D = [[sp.NaN]]*(nt)
hyp = sp.array([1.5,0.15])
kf = GPdc.kernel(GPdc.SQUEXP,1,hyp)
Kxx = GPdc.buildKsym_d(kf,X,D)
Y = spl.cholesky(Kxx,lower=True)*sp.matrix(sps.norm.rvs(0,1.,nt)).T+sp.matrix(sps.norm.rvs(0,1e-3,nt)).T
S = sp.matrix([1e-2]*nt).T
g = GPdc.GPcore(X,Y,S,D,kf)
f,a = plt.subplots(2)
Xe = sp.array([-0.25,0.25])
De = [[sp.NaN]]*2
[m0,V0] = g.infer_full(Xe,De)
Ye = sp.array([2.,-2.])
Ze = sp.array([1.,-1.])
Fe = sp.array([(1e-6)**2,(1e-6)**2])
mt,vt = eprop.expectation_prop(m0,V0,Ye,Ze,Fe,20)
print D+De
#!/usr/bin/env python2
# encoding: UTF-8
# test the 1d periodic matern5/2 kernel
import sys
sys.path.append("./..")
import scipy as sp
from matplotlib import pyplot as plt
import seaborn as sns
import GPdc
kp = GPdc.kernel(GPdc.MAT52, 1, sp.array([0.75, 0.1]))
kq = GPdc.kernel(GPdc.MAT52PER, 1, sp.array([0.75, 0.1, 4.5]))
kr = GPdc.kernel(GPdc.MAT52PPT, 1, sp.array([0.75, 0.1, 4.5, 15.0]))
ks = GPdc.kernel(GPdc.DEV, 1, sp.array([0.75, 0.1, 4.5, 0.5, 0.4, 10.0]))
# support
ns = 1201
xax = sp.array([sp.linspace(-15, 15, ns)]).T
d0 = [[sp.NaN]]
x0 = sp.array([[0.0]])
p = sp.empty(ns)
q = sp.empty(ns)
r = sp.empty(ns)
s = sp.empty(ns)
for i in xrange(ns):
p[i] = kp(x0, xax[i, :], d0, d0)
q[i] = kq(x0, xax[i, :], d0, d0) + 1
# To change this template file, choose Tools | Templates # and open the template in the editor. from scipy import stats as sps from scipy import linalg as spl import scipy as sp from matplotlib import pyplot as plt import GPdc nt=12 X = sp.matrix(sp.linspace(-1,1,nt)).T D = [[sp.NaN]]*(nt) hyp = sp.array([1.5,0.15]) kf = GPdc.gen_sqexp_k_d(hyp) print "X" print kf(sp.array([0.1]),sp.array([0.2]),[[sp.NaN]],[[sp.NaN]]) Kxx = GPdc.buildKsym_d(kf,X,D) print "X" Y = spl.cholesky(Kxx,lower=True)*sp.matrix(sps.norm.rvs(0,1.,nt)).T+sp.matrix(sps.norm.rvs(0,1e-3,nt)).T S = sp.matrix([1e-6]*nt).T f0,a0 = plt.subplots(1) a0.plot(sp.array(X[:,0]).flatten(),Y,'g.') lb = sp.array([-2.,-2.]) ub = sp.array([2.,2.]) MLEH = GPdc.searchMLEhyp(X,Y,S,D,lb,ub,GPdc.SQUEXP,mx=10000) print "X" print MLEH
def traincfn(x, c):
n = x.size
g = GPdc.GPcore(x, c, sp.array([1e-1] * n), [[sp.NaN]] * n, GPdc.kernel(GPdc.MAT52, 1, [1.0, 0.2]))
return cfnobj(g)
from scipy import stats as sps
from scipy import linalg as spl
import scipy as sp
from matplotlib import pyplot as plt
import ESutils
import GPdc
nt = 82
X = sp.matrix(sp.linspace(-1, 1, nt)).T
D = [[sp.NaN]] * (nt)
hyp0 = sp.array([1.5, 0.15])
hyp1 = sp.array([1.5, 0.05])
hyp2 = sp.array([1.5, 0.20])
kf = GPdc.kernel(GPdc.SQUEXP, 1, hyp0)
Kxx = GPdc.buildKsym_d(kf, X, D)
Y = spl.cholesky(Kxx, lower=True) * sp.matrix(sps.norm.rvs(
0, 1., nt)).T + sp.matrix(sps.norm.rvs(0, 1e-3, nt)).T
S = sp.matrix([1e-6] * nt).T
G = GPdc.GPcore(X, Y, S, D, [
GPdc.kernel(GPdc.SQUEXP, 1, hyp0),
GPdc.kernel(GPdc.SQUEXP, 1, hyp1),
GPdc.kernel(GPdc.SQUEXP, 1, hyp2),
GPdc.kernel(GPdc.SQUEXP, 1, hyp0)
])
#G.printc()
np = 200
X = sp.array([sp.linspace(0,nf,np)]).T
H = sp.empty([np,1])
T = sp.empty([np,1])
for i in xrange(np):
[H[i,0],T[i,0]] = L.llks(sp.array([1.3,0.13,0.2,1e-2]),int(X[i,0]))
#lb = sp.array([0.,0.,-4.,-0.5*float(nf),float(nf)])
#ub = sp.array([4.,3.,3.,0.,1.5*float(nf)])
#MLEH = GPdc.searchMLEhyp(X,H,sp.zeros([np,1]),[[sp.NaN]]*(np),lb,ub,GPdc.SQUEXPPS,mx=10000)
#G = GPdc.GPcore(X.copy(),H,sp.zeros([np,1]),[[sp.NaN]]*(np),GPdc.kernel(GPdc.SQUEXPPS,1,sp.array(MLEH)))
lb = sp.array([0.,0.,-4.,-1.,-3.])
ub = sp.array([4.,3.,3.,0.5,3.])
MLEH = GPdc.searchMLEhyp(1./float(nf)*X,H,sp.zeros([np,1]),[[sp.NaN]]*(np),lb,ub,GPdc.SQUEXPBS,mx=10000)
G = GPdc.GPcore(1./float(nf)*X.copy(),H,sp.zeros([np,1]),[[sp.NaN]]*(np),GPdc.kernel(GPdc.SQUEXPBS,1,sp.array(MLEH)))
[m,v] = G.infer_diag(1./float(nf)*X,[[sp.NaN]]*(np))
S = sp.empty([np,1])
for i in xrange(np):
S[i,0] = MLEH[2]*((1./float(nf)*X[i,0])**(MLEH[3]*MLEH[4]))* ((1.-1./float(nf)*X[i,0])**(MLEH[3]*(1.-MLEH[4])))
lbc = sp.array([-4.,0.,-6.])
ubc = sp.array([2.,3.,0.])
MLEC = GPdc.searchMLEhyp(X,sp.log(T),sp.zeros([np,1]),[[sp.NaN]]*(np),lbc,ubc,GPdc.SQUEXPCS,mx=10000)
C = GPdc.GPcore(X.copy(),sp.log(T),sp.zeros([np,1]),[[sp.NaN]]*(np),GPdc.kernel(GPdc.SQUEXPCS,1,sp.array(MLEC)))
f,a = plt.subplots(2)
a[0].plot(X.flatten(),H.flatten(),'g.')
from scipy import linalg as spl
from matplotlib import pyplot as plt
import GPdc
import OPTutils
import ESutils
import DIRECT
#base dimension
d = 2
kindex = GPdc.MAT52
nt = 34
lb = sp.array([0.]+[-1.]*d)
ub = sp.array([5.]+[1.]*d)
Htrue = sp.array([1.4,4.]+[0.25]*d)
[X,Y,S,D] = ESutils.gen_dataset(nt,d+1,lb,ub,kindex,Htrue, s=1e-8)
G = GPdc.GPcore(X,Y,S,D,GPdc.kernel(kindex,d+1,Htrue))
def ojfaugnn(x):
return G.infer_m(x,[[sp.NaN]])[0,0]
def opt_ip(s):
def dwrap(x,y):
X = sp.hstack([[s],x])
return (ojfaugnn(X),0)
[xm,ym,ierror] = DIRECT.solve(dwrap,lb[1:],ub[1:], user_data=[], algmethod=1, maxf=12000, logfilename='/dev/null')
print "DIRECT found: " +str([xm,ym,ierror])
return xm
mintrue = opt_ip(0.)
minaug = sp.hstack([[0.],mintrue])
#Draw 200 hyperparameters from the posterior, plot the draws on a countour plot, first for very few points, then a large number
import ESutils
import scipy as sp
from scipy import linalg as spl
from scipy import stats as sps
from matplotlib import pyplot as plt
import GPdc
#test on a single point
nt = 3
X = ESutils.draw_support(1, sp.array([-1.]), sp.array([1.]), nt,
ESutils.SUPPORT_UNIFORM)
D = [[sp.NaN]] * (nt)
hyp = sp.array([1.5, 0.15])
kf = GPdc.gen_sqexp_k_d(hyp)
Kxx = GPdc.buildKsym_d(kf, X, D)
Y = spl.cholesky(Kxx, lower=True) * sp.matrix(sps.norm.rvs(
0, 1., nt)).T + sp.matrix(sps.norm.rvs(0, 1e-3, nt)).T
S = sp.matrix([1e-6] * nt).T
G = GPdc.GPcore(X, Y, S, D, GPdc.kernel(GPdc.SQUEXP, 2, hyp))
ng = 40
A = sp.empty([ng, ng])
print 'startimage1'
sup = sp.logspace(-3, 2, ng)
for i, hi in enumerate(sup):
for j, hj in enumerate(sup):
A[i,
j] = GPdc.GP_LKonly(X, Y, S, D,
from scipy import linalg as spl
from matplotlib import pyplot as plt
import GPdc
import OPTutils
import ESutils
import DIRECT
#base dimension
d = 2
kindex = GPdc.MAT52
nt = 34
lb = sp.array([0.] + [-1.] * d)
ub = sp.array([5.] + [1.] * d)
Htrue = sp.array([1.4, 4.] + [0.25] * d)
[X, Y, S, D] = ESutils.gen_dataset(nt, d + 1, lb, ub, kindex, Htrue, s=1e-8)
G = GPdc.GPcore(X, Y, S, D, GPdc.kernel(kindex, d + 1, Htrue))
def ojfaugnn(x):
return G.infer_m(x, [[sp.NaN]])[0, 0]
def opt_ip(s):
def dwrap(x, y):
X = sp.hstack([[s], x])
return (ojfaugnn(X), 0)
[xm, ym, ierror] = DIRECT.solve(dwrap,
lb[1:],
ub[1:],
user_data=[],
from scipy import stats as sps from scipy import linalg as spl import scipy as sp from matplotlib import pyplot as plt import ESutils import GPdc nt=82 X = sp.matrix(sp.linspace(-1,1,nt)).T D = [[sp.NaN]]*(nt) hyp0 = sp.array([1.5,0.15]) hyp1 = sp.array([1.5,0.05]) hyp2 = sp.array([1.5,0.20]) kf = GPdc.kernel(GPdc.SQUEXP,1,hyp0) Kxx = GPdc.buildKsym_d(kf,X,D) Y = spl.cholesky(Kxx,lower=True)*sp.matrix(sps.norm.rvs(0,1.,nt)).T+sp.matrix(sps.norm.rvs(0,1e-3,nt)).T S = sp.matrix([1e-6]*nt).T G = GPdc.GPcore(X,Y,S,D,[GPdc.kernel(GPdc.SQUEXP,1,hyp0),GPdc.kernel(GPdc.SQUEXP,1,hyp1),GPdc.kernel(GPdc.SQUEXP,1,hyp2),GPdc.kernel(GPdc.SQUEXP,1,hyp0)]) #G.printc() np=100 sup = sp.linspace(-1,1,np) Dp = [[sp.NaN]]*np Xp = sp.vstack([sp.array([i]) for i in sup]) m = G.infer_m(Xp,Dp)
X = sp.vstack([sp.array([i,0.]) for i in x]) Y = sp.matrix(y).T #X = sp.matrix([[0.,-9.],[0.2,5.],[0.4,12.],[0.6,3.],[0.8,9.]]) #Y = sp.matrix([0.2,0.1,0.,-0.15,-0.3]).T D = [[sp.NaN]]*(X.shape[0]) S = sp.matrix([0.005**2]*X.shape[0]).T f0 = plt.figure() a0 = plt.subplot(111) a0.plot(sp.array(X[:,0]).flatten(),Y,'g.') lb = sp.array([-2.,-1.,-2.]) ub = sp.array([2.,1.,2.]) MLEH = GPdc.searchMLEhyp(X,Y,S,D,lb,ub,GPdc.LIN1,mx=10000) print MLEH G = GPdc.GPcore(X,Y,S,D,GPdc.kernel(GPdc.LIN1,2,MLEH)) print G.llk() np=180 sup = sp.linspace(-1,1,np) Dp = [[sp.NaN]]*np Xp = sp.vstack([sp.array([i,1.]) for i in sup]) [m,v] = G.infer_diag(Xp,Dp) a0.plot(sup,m.flatten()) sq = sp.sqrt(v)
ax[i].plot(sup, sps.norm.pdf(sup, loc=mu[i], scale=sp.sqrt(vu[i, i])), "r")
ax[i].twinx().plot(
sup,
sps.norm.cdf(Z[i] * (sup - Y[i]) / max(F[i], 1e-20)) * sps.norm.pdf(sup, loc=m[i], scale=sp.sqrt(v[i, i])),
"g",
)
# est on a gp
import ESutils
import GPdc
nt = 5
X = sp.matrix(sp.linspace(-1, 1, nt)).T
D = [[sp.NaN]] * (nt)
hyp = sp.array([1.5, 0.15])
kf = GPdc.kernel(GPdc.SQUEXP, 1, hyp)
Kxx = GPdc.buildKsym_d(kf, X, D)
Y = spl.cholesky(Kxx, lower=True) * sp.matrix(sps.norm.rvs(0, 1.0, nt)).T + sp.matrix(sps.norm.rvs(0, 1e-3, nt)).T
S = sp.matrix([1e-2] * nt).T
g = GPdc.GPcore(X, Y, S, D, kf)
f, a = plt.subplots(2)
Xe = sp.array([-0.25, 0.25])
De = [[sp.NaN]] * 2
[m0, V0] = g.infer_full(Xe, De)
Ye = sp.array([2.0, -2.0])
Ze = sp.array([1.0, -1.0])
Fe = sp.array([(1e-6) ** 2, (1e-6) ** 2])
mt, vt = eprop.expectation_prop(m0, V0, Ye, Ze, Fe, 20)
print D + De
# To change this license header, choose License Headers in Project Properties.
# To change this template file, choose Tools | Templates
# and open the template in the editor.
import sys
sys.path.append("./..")
import scipy as sp
from matplotlib import pyplot as plt
import seaborn as sns
import GPdc
D = 4
ke = GPdc.kernel(GPdc.SQUEXP, D, sp.array([0.75, 0.1, 0.2, 0.25, 0.1]))
km = GPdc.kernel(GPdc.MAT52, D, sp.array([0.75, 0.1, 0.2, 0.25, 0.1]))
# support
ns = 1201
xax = sp.linspace(-1, 1, ns)
Xo = sp.vstack([0.0, 0.0, 0.0, 0.0] * ns)
X0 = sp.vstack([[i, 0.0, 0.0, 0.0] for i in xax])
X1 = sp.vstack([[0.0, i, 0.0, 0.0] for i in xax])
X2 = sp.vstack([[0.0, 0.0, i, 0.0] for i in xax])
X3 = sp.vstack([[0.0, 0.0, 0.0, i] for i in xax])
C0 = sp.vstack([[-i, i, -i, i] for i in xax])
C1 = sp.vstack([[i, -i, i, -i] for i in xax])
C2 = sp.vstack([[i, -i, -i, i] for i in xax])
C3 = sp.vstack([[-i, i, i, -i] for i in xax])
Xax = [X0, X1, X2, X3]
Cax = [C0, C1, C2, C3]
#Draw 200 hyperparameters from the posterior, plot the draws on a countour plot, first for very few points, then a large number
import ESutils
import scipy as sp
from scipy import linalg as spl
from scipy import stats as sps
from matplotlib import pyplot as plt
import GPdc
#test on a single point
nt=3
X = ESutils.draw_support(1, sp.array([-1.]),sp.array([1.]),nt,ESutils.SUPPORT_UNIFORM)
D = [[sp.NaN]]*(nt)
hyp = sp.array([1.5,0.15])
kf = GPdc.gen_sqexp_k_d(hyp)
Kxx = GPdc.buildKsym_d(kf,X,D)
Y = spl.cholesky(Kxx,lower=True)*sp.matrix(sps.norm.rvs(0,1.,nt)).T+sp.matrix(sps.norm.rvs(0,1e-3,nt)).T
S = sp.matrix([1e-6]*nt).T
G = GPdc.GPcore(X,Y,S,D,GPdc.kernel(GPdc.SQUEXP,2,hyp))
ng = 40
A = sp.empty([ng,ng])
print 'startimage1'
sup = sp.logspace(-3,2,ng)
for i,hi in enumerate(sup):
for j,hj in enumerate(sup):
A[i,j] = GPdc.GP_LKonly(X,Y,S,D,GPdc.kernel(GPdc.SQUEXP,2,sp.array([hi,hj]))).plk(sp.array([0.,-1.]),sp.array([1.,1.]))
A = -sp.log10(-A+sp.amax(A)+1.)
# To change this license header, choose License Headers in Project Properties. # To change this template file, choose Tools | Templates # and open the template in the editor. from scipy import stats as sps from scipy import linalg as spl import scipy as sp from matplotlib import pyplot as plt import GPdc ni = 100 kf = GPdc.kernel(GPdc.SQUEXP,2,sp.array([1.3,0.3,0.2])) X = sp.random.uniform(-1,1,size=[ni,2]) D = [[sp.NaN]]*ni Kxx = GPdc.buildKsym_d(kf,X,D) s = 1e-2 Y = spl.cholesky(Kxx,lower=True)*sp.matrix(sps.norm.rvs(0,1.,ni)).T+sp.matrix(sps.norm.rvs(0,s,ni)).T S = sp.ones(ni)*s print Y MLEHYP = GPdc.searchMLEhyp(X,Y,S,D,sp.array([2.,2.,2.]),sp.array([-2.,-2.,-2.]), GPdc.SQUEXP) print MLEHYP MAPHYP = GPdc.searchMAPhyp(X,Y,S,D,sp.array([0.,0.,0.]),sp.array([1.,1.,1.]), GPdc.SQUEXP) print MAPHYP
lb = sp.array([-1.]*d)
ub = sp.array([1.]*d)
[X,Y,S,D] = ESutils.gen_dataset(nt,d,lb,ub,GPdc.SQUEXP,sp.array([0.9,0.25]),s=0.)
S*=0.
for i in xrange(nt):
x = X[i,0]
s = -(1e-2)*(x-1.)*(x+1.1)
Y[i,0]+= sps.norm.rvs(0,sp.sqrt(s))
f0 = plt.figure()
a0 = plt.subplot(111)
a0.plot(sp.array(X[:,0]).flatten(),Y,'g.')
lb = sp.array([-2.,-2.,-9,-2.,-2.])
ub = sp.array([2.,2.,-1,2.,2.])
MLEH = GPdc.searchMLEhyp(X,Y,S,D,lb,ub,GPdc.SQUEXPPS,mx=20000)
mprior = sp.array([0.,-1.,-5.,-0.5,0.5])
sprior = sp.array([1.,1.,3.,1.,1.])
MAPH = GPdc.searchMAPhyp(X,Y,S,D,mprior,sprior,GPdc.SQUEXPPS,mx=20000)
print "MLEH: "+str(MLEH)
print "MAPH: "+str(MAPH)
G = GPdc.GPcore(X,Y,S,D,GPdc.kernel(GPdc.SQUEXPPS,1,sp.array(MAPH)))
print G.llk()
np=180
sup = sp.linspace(-1,1,np)
X = ESutils.draw_support(2, sp.array([-2,-1]),sp.array([0,3]),500,ESutils.SUPPORT_UNIFORM)
for i in xrange(X.shape[0]):
plt.plot(X[i,0],X[i,1],'r.')
plt.axis([-5,5,-5,5])
#2d gp test
nt=34
X = ESutils.draw_support(2, sp.array([-1.,-1.]),sp.array([1.,1.]),nt,ESutils.SUPPORT_UNIFORM)
D = [[sp.NaN]]*(nt)
hyp = sp.array([1.5,0.25,0.25])
kf = GPdc.gen_sqexp_k_d(hyp)
Kxx = GPdc.buildKsym_d(kf,X,D)
Y = spl.cholesky(Kxx,lower=True)*sp.matrix(sps.norm.rvs(0,1.,nt)).T+sp.matrix(sps.norm.rvs(0,1e-3,nt)).T
S = sp.matrix([1e-6]*nt).T
lb = sp.array([-2.,-2.,-2.])
ub = sp.array([2.,2.,2.])
#MLEH = GPdc.searchMLEhyp(X,Y,S,D,lb,ub,GPdc.SQUEXP,mx=10000)
G = GPdc.GPcore(X,Y,S,D,GPdc.kernel(GPdc.SQUEXP,2,sp.array([1.5,0.15,0.15])))
#np=180
#sup = sp.linspace(-1,1,np)
#Dp = [[sp.NaN]]*np
#Xp = sp.vstack([sp.array([i]) for i in sup])
#[m,v] = G.infer_diag(Xp,Dp)
#a0.plot(sup,m)
#sq = sp.sqrt(v)
ns = 200
sup = sp.linspace(-1, 1, 200)
#points are a high noise obs, a low noise obs, a derivative obs and a second derivative obs
X = sp.array([[-0.8], [-0.25], [0.25], [0.8]])
Y = sp.array([[0.3], [-0.2], [2.5], [50.]])
S = sp.array([[1e-1], [1e-6], [1e-6], [1e-6]])
D = [[sp.NaN], [sp.NaN], [0], [0, 0]]
a[0].plot([-0.8, -0.8], [0.3 - sp.sqrt(1e-1), 0.3 + sp.sqrt(1e-1)], 'r')
a[0].plot([-0.8], [0.3], 'ro')
a[0].plot([-0.25], [-0.2], 'ro')
a[1].plot([0.25], [2.5], 'ro')
a[2].plot([0.8], [50], 'ro')
k = GPdc.kernel(GPdc.SQUEXP, 1, sp.array([0.5, 0.2]))
K = sp.empty([4, 4])
for i in xrange(4):
for j in xrange(i, 4):
K[i, j] = K[j, i] = k(X[i, :], X[j, :], D[i], D[j])
K[i, i] += 1e-6
g = GPdc.GPcore(X, Y, S, D, GPdc.kernel(GPdc.SQUEXP, 1, sp.array([0.5, 0.2])))
#g.printc()
C = g.get_cho()
print C
print spl.cho_solve((C, True), sp.eye(4)).dot(K)
for i, d in enumerate([[sp.NaN], [0], [0, 0]]):
m, v = g.infer_diag(sup, [d] * ns)
vl = (m - sp.sqrt(v)).flatten()
X = sp.vstack([X, [sp.array([i, -0.3]) for i in x]]) Y = sp.matrix(y).T #X = sp.matrix([[0.,-9.],[0.2,5.],[0.4,12.],[0.6,3.],[0.8,9.]]) #Y = sp.matrix([0.2,0.1,0.,-0.15,-0.3]).T D = [[sp.NaN]] * (X.shape[0]) S = sp.matrix([0.005**2] * X.shape[0]).T f0 = plt.figure() a0 = plt.subplot(111) a0.plot(sp.array(X[:, 0]).flatten(), Y, 'g.') lb = sp.array([-2., -1., -2., -2., -2.]) ub = sp.array([2., 1., 2., 2., 2.]) MLEH = GPdc.searchMLEhyp(X, Y, S, D, lb, ub, GPdc.LINXSQUEXP, mx=10000) print "xxx" GPdc.kernel(GPdc.LINXSQUEXP, 2, MLEH) print "yyyy" print MLEH G = GPdc.GPcore(X, Y, S, D, GPdc.kernel(GPdc.LINXSQUEXP, 2, MLEH)) print G.llk() np = 180 sup = sp.linspace(-1, 1, np) Dp = [[sp.NaN]] * np Xp = sp.vstack([sp.array([i, -0.3]) for i in sup]) [m, v] = G.infer_diag(Xp, Dp) a0.plot(sup, m) sq = sp.sqrt(v)
H = sp.empty([np, 1])
T = sp.empty([np, 1])
for i in xrange(np):
[H[i, 0], T[i, 0]] = L.llks(sp.array([1.3, 0.13, 0.2, 1e-2]), int(X[i, 0]))
#lb = sp.array([0.,0.,-4.,-0.5*float(nf),float(nf)])
#ub = sp.array([4.,3.,3.,0.,1.5*float(nf)])
#MLEH = GPdc.searchMLEhyp(X,H,sp.zeros([np,1]),[[sp.NaN]]*(np),lb,ub,GPdc.SQUEXPPS,mx=10000)
#G = GPdc.GPcore(X.copy(),H,sp.zeros([np,1]),[[sp.NaN]]*(np),GPdc.kernel(GPdc.SQUEXPPS,1,sp.array(MLEH)))
lb = sp.array([0., 0., -4., -1., -3.])
ub = sp.array([4., 3., 3., 0.5, 3.])
MLEH = GPdc.searchMLEhyp(1. / float(nf) * X,
H,
sp.zeros([np, 1]), [[sp.NaN]] * (np),
lb,
ub,
GPdc.SQUEXPBS,
mx=10000)
G = GPdc.GPcore(1. / float(nf) * X.copy(), H, sp.zeros([np,
1]), [[sp.NaN]] * (np),
GPdc.kernel(GPdc.SQUEXPBS, 1, sp.array(MLEH)))
[m, v] = G.infer_diag(1. / float(nf) * X, [[sp.NaN]] * (np))
S = sp.empty([np, 1])
for i in xrange(np):
S[i, 0] = MLEH[2] * ((1. / float(nf) * X[i, 0])**(MLEH[3] * MLEH[4])) * (
(1. - 1. / float(nf) * X[i, 0])**(MLEH[3] * (1. - MLEH[4])))
lbc = sp.array([-4., 0., -6.])
ub = sp.array([1.] * d)
[X, Y, S, D] = ESutils.gen_dataset(nt,
d,
lb,
ub,
GPdc.SQUEXP,
sp.array([0.9, 0.25]),
s=1e-8)
S *= 0.
f0 = plt.figure()
a0 = plt.subplot(111)
a0.plot(sp.array(X[:, 0]).flatten(), Y, 'g.')
lb = sp.array([-2., -2., -9])
ub = sp.array([2., 2., -1])
MLEH = GPdc.searchMLEhyp(X, Y, S, D, lb, ub, GPdc.SQUEXPCS, mx=10000)
mprior = sp.array([0., -1., -5.])
sprior = sp.array([1., 1., 3.])
MAPH = GPdc.searchMAPhyp(X, Y, S, D, mprior, sprior, GPdc.SQUEXPCS, mx=10000)
print "MLEH: " + str(MLEH)
print "MAPH: " + str(MAPH)
G = GPdc.GPcore(X, Y, S, D, GPdc.kernel(GPdc.SQUEXPCS, 1, sp.array(MLEH)))
print G.llk()
np = 180
sup = sp.linspace(-1, 1, np)
Dp = [[sp.NaN]] * np
Xp = sp.vstack([sp.array([i]) for i in sup])
ns = 200
sup = sp.linspace(-1,1,200)
#points are a high noise obs, a low noise obs, a derivative obs and a second derivative obs
X = sp.array([[-0.8],[-0.25],[0.25],[0.8]])
Y = sp.array([[0.3],[-0.2],[2.5],[50.]])
S = sp.array([[1e-1],[1e-6],[1e-6],[1e-6]])
D = [[sp.NaN],[sp.NaN],[0],[0,0]]
a[0].plot([-0.8,-0.8],[0.3-sp.sqrt(1e-1),0.3+sp.sqrt(1e-1)],'r')
a[0].plot([-0.8],[0.3],'ro')
a[0].plot([-0.25],[-0.2],'ro')
a[1].plot([0.25],[2.5],'ro')
a[2].plot([0.8],[50],'ro')
k= GPdc.kernel(GPdc.SQUEXP,1,sp.array([0.5,0.2]))
K = sp.empty([4,4])
for i in xrange(4):
for j in xrange(i,4):
K[i,j] =K[j,i] = k(X[i,:],X[j,:],D[i],D[j])
K[i,i]+=1e-6
g = GPdc.GPcore(X,Y,S,D,GPdc.kernel(GPdc.SQUEXP,1,sp.array([0.5,0.2])))
#g.printc()
C= g.get_cho()
print C
print spl.cho_solve((C,True),sp.eye(4)).dot(K)
for i,d in enumerate([[sp.NaN],[0],[0,0]]):
m,v = g.infer_diag(sup,[d]*ns)
# To change this license header, choose License Headers in Project Properties. # To change this template file, choose Tools | Templates # and open the template in the editor. from scipy import stats as sps from scipy import linalg as spl import scipy as sp from matplotlib import pyplot as plt import GPdc hyp = sp.array([1.5,0.25]) kf = GPdc.gen_sqexp_k_d(hyp) nt=18 x = sp.linspace(-1,1,nt) Dtmp = [[sp.NaN]]*nt Kxx = GPdc.buildKsym_d(kf,sp.matrix(x).T,Dtmp) Z = spl.cholesky(Kxx,lower=True)*sp.matrix(sps.norm.rvs(0,1.,nt)).T Z = sp.vstack([Z,spl.cholesky(Kxx,lower=True)*sp.matrix(sps.norm.rvs(0,1.,nt)).T]) Z = sp.vstack([Z,spl.cholesky(Kxx,lower=True)*sp.matrix(sps.norm.rvs(0,1.,nt)).T]) y = [-0.4*(i-0.2)+sps.norm.rvs(scale=0.005) for i in x] y+=[-0.6*(i+0.2)+sps.norm.rvs(scale=0.005) for i in x] y+=[0.1*(i+0.8)+sps.norm.rvs(scale=0.005) for i in x] X = sp.vstack([sp.array([i,0.]) for i in x]) X = sp.vstack([X,[sp.array([i,0.4]) for i in x]]) X = sp.vstack([X,[sp.array([i,-0.3]) for i in x]]) Y = sp.matrix(y).T+Z
def traincfn(x, c):
n = x.size
g = GPdc.GPcore(x, c, sp.array([1e-1] * n), [[sp.NaN]] * n,
GPdc.kernel(GPdc.MAT52, 1, [1., 0.2]))
return cfnobj(g)
