def K(self, logtheta, *args):
'''K(params,x1) - params = [factor,length-scale(s)]'''
# additional index: one index after dimension: derivative index!
x1 = args[0][:, 0:self.dimension]
#noise_diag comes from the last input dimension:
noise_diag = args[0][:, -1]
if (len(args) == 1):
x2 = x1
noise = diag(noise_diag) * (exp(2 * logtheta[-1]) + 1E-6)
else:
x2 = args[1][:, 0:self.dimension]
noise = 0
# 2. exponentiate params:
V0 = exp(2 * logtheta[0])
L = exp(logtheta[1:1 + self.dimension])
d1 = x1[:, -1::]
d2 = x2[:, -1::]
x1 = x1[:, 0:self.dimension] / L
x2 = x2[:, 0:self.dimension] / L
# calculate the distance betwen x1,x2 for each dimension separately.
dd = sqdist.dist(x1, x2)
# sq. distance is neede anyway:
sqd = dd * dd
sqd = sqd.sum(axis=2)
#3. calcualte withotu derivatives, need this anyway:
rv = V0 * exp(-0.5 * sqd) + noise
return rv
def K(self, logtheta, *args):
'''K(params,x1) - params = [factor,length-scale(s),noise(per class)]'''
# additional index: one index after dimension: derivative index!
x1 = args[0][:, 0:self.dimension]
#cluster index is in the next index, convert to int to allow indexing
cluster = array(args[0][:, self.dimension], dtype='int')
if (len(args) == 1):
x2 = x1
#noise depends on the cluster memebership:
noise = (exp(2 * logtheta[-self.clusters + cluster]) + 1E-2)
else:
x2 = args[1][:, 0:self.dimension]
noise = [0]
# 2. exponentiate params:
V0 = exp(2 * logtheta[0])
L = exp(logtheta[1:1 + self.dimension])
d1 = x1[:, -1::]
d2 = x2[:, -1::]
x1 = x1[:, 0:self.dimension] / L
x2 = x2[:, 0:self.dimension] / L
# calculate the distance betwen x1,x2 for each dimension separately.
dd = sqdist.dist(x1, x2)
# sq. distance is neede anyway:
sqd = dd * dd
sqd = sqd.sum(axis=2)
#3. calcualte withotu derivatives, need this anyway:
rv = V0 * exp(-0.5 * sqd) + diag(noise)
return rv
def K(self, logtheta, *args):
'''K(params,x1) - params = [factor,length-scale(s),noise(per class)]'''
# additional index: one index after dimension: derivative index!
x1 = args[0][:,0:self.dimension]
#cluster index is in the next index, convert to int to allow indexing
cluster = array(args[0][:,self.dimension],dtype='int')
if(len(args)==1):
x2 = x1
#noise depends on the cluster memebership:
noise=(exp(2*logtheta[-self.clusters+cluster])+1E-2)
else:
x2 = args[1][:,0:self.dimension]
noise = [0]
# 2. exponentiate params:
V0 = exp(2*logtheta[0])
L = exp(logtheta[1:1+self.dimension])
d1 = x1[:,-1::]
d2 = x2[:,-1::]
x1 = x1[:,0:self.dimension]/L
x2 = x2[:,0:self.dimension]/L
# calculate the distance betwen x1,x2 for each dimension separately.
dd = sqdist.dist(x1,x2)
# sq. distance is neede anyway:
sqd = dd*dd
sqd = sqd.sum(axis=2)
#3. calcualte withotu derivatives, need this anyway:
rv = V0*exp(-0.5*sqd) + diag(noise)
return rv
def K(self, logtheta, *args):
'''K(params,x1) - params = [factor,length-scale(s)]'''
# additional index: one index after dimension: derivative index!
x1 = args[0][:,0:self.dimension]
#noise_diag comes from the last input dimension:
noise_diag = args[0][:,-1]
if(len(args)==1):
x2 = x1
noise=diag(noise_diag)*(exp(2*logtheta[-1])+1E-6)
else:
x2 = args[1][:,0:self.dimension]
noise =0
# 2. exponentiate params:
V0 = exp(2*logtheta[0])
L = exp(logtheta[1:1+self.dimension])
d1 = x1[:,-1::]
d2 = x2[:,-1::]
x1 = x1[:,0:self.dimension]/L
x2 = x2[:,0:self.dimension]/L
# calculate the distance betwen x1,x2 for each dimension separately.
dd = sqdist.dist(x1,x2)
# sq. distance is neede anyway:
sqd = dd*dd
sqd = sqd.sum(axis=2)
#3. calcualte withotu derivatives, need this anyway:
rv = V0*exp(-0.5*sqd) + noise
return rv
def K(self, logtheta, *args):
'''K(params,x1) - params = [factor,length-scale(s)]'''
# additional index: one index after dimension: derivative index!
x1 = args[0][:, 0:self.dimension + 1]
if (len(args) == 1):
x2 = x1
else:
x2 = args[1][:, 0:self.dimension + 1]
# 2. exponentiate params:
V0 = exp(2 * logtheta[0])
L = exp(logtheta[1:1 + self.dimension])
d1 = x1[:, -1::]
d2 = x2[:, -1::]
x1 = x1[:, 0:self.dimension] / L
x2 = x2[:, 0:self.dimension] / L
# calculate the distance betwen x1,x2 for each dimension separately.
dd = sqdist.dist(x1, x2)
# sq. distance is neede anyway:
sqd = dd * dd
sqd = sqd.sum(axis=2)
#3. calcualte withotu derivatives, need this anyway:
rv = V0 * exp(-0.5 * sqd)
#4. go through all other combinations and calc the corresponding terms:
def k_(d1):
rv = dd[:, :, d1] / L[d1]
return rv
def k__(d1, d2):
f1 = dd[:, :, d1] / L[d1]
f2 = dd[:, :, d2] / L[d2]
return ((d1 == d2) / (L[d1]**2) - f1 * f2)
for i in arange(-1, self.dimension):
for j in arange(-1, self.dimension):
if i == j == -1:
continue
index = Bdist(d1 == i, d2 == j)
if not any(index):
continue
if ((i == -1) & (j != -1)):
rv[index] *= -1 * k_(j)[index]
elif ((i != -1) & (j == -1)):
rv[index] *= k_(i)[index]
else:
rv[index] *= k__(i, j)[index]
if (len(args) == 1
): # add noise if we do not have two independen input data-sets
rv += eye(len(x1)) * exp(2 * logtheta[-1])
return rv
def K(self, logtheta, *args):
'''K(params,x1) - params = [factor,length-scale(s)]'''
# additional index: one index after dimension: derivative index!
x1 = args[0][:,0:self.dimension+1]
if(len(args)==1):
x2 = x1
else:
x2 = args[1][:,0:self.dimension+1]
# 2. exponentiate params:
V0 = exp(2*logtheta[0])
L = exp(logtheta[1:1+self.dimension])
d1 = x1[:,-1::]
d2 = x2[:,-1::]
x1 = x1[:,0:self.dimension]/L
x2 = x2[:,0:self.dimension]/L
# calculate the distance betwen x1,x2 for each dimension separately.
dd = sqdist.dist(x1,x2)
# sq. distance is neede anyway:
sqd = dd*dd
sqd = sqd.sum(axis=2)
#3. calcualte withotu derivatives, need this anyway:
rv = V0*exp(-0.5*sqd)
#4. go through all other combinations and calc the corresponding terms:
def k_(d1):
rv = dd[:,:,d1]/L[d1]
return rv
def k__(d1,d2):
f1 = dd[:,:,d1]/L[d1]
f2 = dd[:,:,d2]/L[d2]
return ((d1==d2)/(L[d1]**2) - f1*f2)
for i in arange(-1,self.dimension):
for j in arange(-1,self.dimension):
if i==j==-1:
continue
index = Bdist(d1==i,d2==j)
if not any(index):
continue
if((i==-1) & (j!=-1)):
rv[index] *= -1*k_(j)[index]
elif((i!=-1) &(j==-1)):
rv[index] *= k_(i)[index]
else:
rv[index] *= k__(i,j)[index]
if(len(args)==1): # add noise if we do not have two independen input data-sets
rv+=eye(len(x1))*exp(2*logtheta[-1])
return rv
def Kd(self, logtheta, *args):
'''Kd(params,x1) - params = [factor,length-scale(s)]'''
# additional index: one index after dimension: derivative index!
x1 = args[0][:,0:self.dimension]
cluster = array(args[0][:,self.dimension],dtype='int')
if(len(args)==1):
x2 = x1
noise=ones(len(x1))*exp(2*logtheta[-self.clusters+cluster]+1E-2)
else:
x2 = args[1][:,0:self.dimension]
noise =zeros(len(x1))
# 2. exponentiate params:
V0 = exp(2*logtheta[0])
L = exp(logtheta[1:1+self.dimension])
d1 = x1[:,-1::]
d2 = x2[:,-1::]
x1 = x1[:,0:self.dimension]/L
x2 = x2[:,0:self.dimension]/L
# calculate the distance betwen x1,x2 for each dimension separately.
dd = sqdist.dist(x1,x2)
# sq. distance is neede anyway:
sqd = dd*dd
sqdd = sqd.transpose(2,0,1)
sqd = sqd.sum(axis=2)
#3. calcualte withotu derivatives, need this anyway:
rv0 = V0*exp(-0.5*sqd)
rv = zeros((self.n_params,len(x1),len(x2)))
#3. calcualte without derivatives, need this anyway:
rv[:] = V0*exp(-0.5*sqd)
#amplitude:
rv[0] = rv[0]*2
#lengthscales:
rv[1:1+self.dimension] *= sqdd
#noise:
for ic in range(self.clusters):
Ic = (cluster==ic)
diagonal = zeros(x1.shape[0])
diagonal[Ic] = 2*noise[Ic]
rv[-self.clusters+ic][:,:] = diag(diagonal)
return rv
def Kd(self, logtheta, *args):
'''Kd(params,x1) - params = [factor,length-scale(s)]'''
# additional index: one index after dimension: derivative index!
x1 = args[0][:, 0:self.dimension]
cluster = array(args[0][:, self.dimension], dtype='int')
if (len(args) == 1):
x2 = x1
noise = ones(
len(x1)) * exp(2 * logtheta[-self.clusters + cluster] + 1E-2)
else:
x2 = args[1][:, 0:self.dimension]
noise = zeros(len(x1))
# 2. exponentiate params:
V0 = exp(2 * logtheta[0])
L = exp(logtheta[1:1 + self.dimension])
d1 = x1[:, -1::]
d2 = x2[:, -1::]
x1 = x1[:, 0:self.dimension] / L
x2 = x2[:, 0:self.dimension] / L
# calculate the distance betwen x1,x2 for each dimension separately.
dd = sqdist.dist(x1, x2)
# sq. distance is neede anyway:
sqd = dd * dd
sqdd = sqd.transpose(2, 0, 1)
sqd = sqd.sum(axis=2)
#3. calcualte withotu derivatives, need this anyway:
rv0 = V0 * exp(-0.5 * sqd)
rv = zeros((self.n_params, len(x1), len(x2)))
#3. calcualte without derivatives, need this anyway:
rv[:] = V0 * exp(-0.5 * sqd)
#amplitude:
rv[0] = rv[0] * 2
#lengthscales:
rv[1:1 + self.dimension] *= sqdd
#noise:
for ic in range(self.clusters):
Ic = (cluster == ic)
diagonal = zeros(x1.shape[0])
diagonal[Ic] = 2 * noise[Ic]
rv[-self.clusters + ic][:, :] = diag(diagonal)
return rv
def Kd(self, logtheta, *args):
'''Kd(params,x1) - params = [factor,length-scale(s)]'''
# additional index: one index after dimension: derivative index!
x1 = args[0][:,0:self.dimension]
noise_diag = args[0][:,-1]
if(len(args)==1):
x2 = x1
noise=diag(noise_diag)*exp(2*logtheta[-1])
else:
x2 = args[1][:,0:self.dimension]
noise =eye(len(x1))*0
# 2. exponentiate params:
V0 = exp(2*logtheta[0])
L = exp(logtheta[1:1+self.dimension])
d1 = x1[:,-1::]
d2 = x2[:,-1::]
x1 = x1[:,0:self.dimension]/L
x2 = x2[:,0:self.dimension]/L
# calculate the distance betwen x1,x2 for each dimension separately.
dd = sqdist.dist(x1,x2)
# sq. distance is neede anyway:
sqd = dd*dd
sqdd = sqd.transpose(2,0,1)
sqd = sqd.sum(axis=2)
#3. calcualte withotu derivatives, need this anyway:
rv0 = V0*exp(-0.5*sqd)
rv = zeros((self.n_params,len(x1),len(x2)))
#3. calcualte without derivatives, need this anyway:
rv[:] = V0*exp(-0.5*sqd)
#amplitude:
rv[0] = rv[0]*2
#lengthscales:
rv[1:1+self.dimension] *= sqdd
#noise:
rv[-1] = 2*noise
return rv
def Kd(self, logtheta, *args):
'''Kd(params,x1) - params = [factor,length-scale(s)]'''
# additional index: one index after dimension: derivative index!
x1 = args[0][:, 0:self.dimension]
noise_diag = args[0][:, -1]
if (len(args) == 1):
x2 = x1
noise = diag(noise_diag) * exp(2 * logtheta[-1])
else:
x2 = args[1][:, 0:self.dimension]
noise = eye(len(x1)) * 0
# 2. exponentiate params:
V0 = exp(2 * logtheta[0])
L = exp(logtheta[1:1 + self.dimension])
d1 = x1[:, -1::]
d2 = x2[:, -1::]
x1 = x1[:, 0:self.dimension] / L
x2 = x2[:, 0:self.dimension] / L
# calculate the distance betwen x1,x2 for each dimension separately.
dd = sqdist.dist(x1, x2)
# sq. distance is neede anyway:
sqd = dd * dd
sqdd = sqd.transpose(2, 0, 1)
sqd = sqd.sum(axis=2)
#3. calcualte withotu derivatives, need this anyway:
rv0 = V0 * exp(-0.5 * sqd)
rv = zeros((self.n_params, len(x1), len(x2)))
#3. calcualte without derivatives, need this anyway:
rv[:] = V0 * exp(-0.5 * sqd)
#amplitude:
rv[0] = rv[0] * 2
#lengthscales:
rv[1:1 + self.dimension] *= sqdd
#noise:
rv[-1] = 2 * noise
return rv
def dist(self, x1, x2, L):
"""Distance function"""
x1 = array(x1, dtype='float64') / L
x2 = array(x2, dtype='float64') / L
return sqdist.dist(x1, x2)
def dist(self,x1,x2,L):
"""Distance function"""
x1 = array(x1,dtype='float64')/L
x2 = array(x2,dtype='float64')/L
return sqdist.dist(x1,x2)