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James Hensman 2015-04-01 09:15:39 +01:00
commit c3d20c744f
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32
GPy/core/parameterization/variational.py
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@ -50,31 +50,29 @@ class SpikeAndSlabPrior(VariationalPrior):
def KL_divergence(self, variational_posterior): def KL_divergence(self, variational_posterior):
mu = variational_posterior.mean mu = variational_posterior.mean
S = variational_posterior.variance S = variational_posterior.variance
gamma,gamma1 = variational_posterior.gamma_probabilities() gamma = variational_posterior.gamma.values
log_gamma,log_gamma1 = variational_posterior.gamma_log_prob()
if len(self.pi.shape)==2: if len(self.pi.shape)==2:
idx = np.unique(gamma._raveled_index()/gamma.shape[-1]) idx = np.unique(variational_posterior.gamma._raveled_index()/gamma.shape[-1])
pi = self.pi[idx] pi = self.pi[idx]
else: else:
pi = self.pi pi = self.pi
var_mean = np.square(mu)/self.variance var_mean = np.square(mu)/self.variance
var_S = (S/self.variance - np.log(S)) var_S = (S/self.variance - np.log(S))
var_gamma = (gamma*(log_gamma-np.log(pi))).sum()+(gamma1*(log_gamma1-np.log(1-pi))).sum() var_gamma = (gamma*np.log(gamma/pi)).sum()+((1-gamma)*np.log((1-gamma)/(1-pi))).sum()
return var_gamma+ (gamma* (np.log(self.variance)-1. +var_mean + var_S)).sum()/2. return var_gamma+ (gamma* (np.log(self.variance)-1. +var_mean + var_S)).sum()/2.
def update_gradients_KL(self, variational_posterior): def update_gradients_KL(self, variational_posterior):
mu = variational_posterior.mean mu = variational_posterior.mean
S = variational_posterior.variance S = variational_posterior.variance
gamma,gamma1 = variational_posterior.gamma_probabilities() gamma = variational_posterior.gamma.values
log_gamma,log_gamma1 = variational_posterior.gamma_log_prob()
if len(self.pi.shape)==2: if len(self.pi.shape)==2:
idx = np.unique(gamma._raveled_index()/gamma.shape[-1]) idx = np.unique(variational_posterior.gamma._raveled_index()/gamma.shape[-1])
pi = self.pi[idx] pi = self.pi[idx]
else: else:
pi = self.pi pi = self.pi
variational_posterior.binary_prob.gradient -= (np.log((1-pi)/pi)+log_gamma-log_gamma1+((np.square(mu)+S)/self.variance-np.log(S)+np.log(self.variance)-1.)/2.)*gamma*gamma1 variational_posterior.binary_prob.gradient -= np.log((1-pi)/pi*gamma/(1.-gamma))+((np.square(mu)+S)/self.variance-np.log(S)+np.log(self.variance)-1.)/2.
mu.gradient -= gamma*mu/self.variance mu.gradient -= gamma*mu/self.variance
S.gradient -= (1./self.variance - 1./S) * gamma /2. S.gradient -= (1./self.variance - 1./S) * gamma /2.
if self.learnPi: if self.learnPi:
@ -162,25 +160,9 @@ class SpikeAndSlabPosterior(VariationalPosterior):
binary_prob : the probability of the distribution on the slab part. binary_prob : the probability of the distribution on the slab part.
""" """
super(SpikeAndSlabPosterior, self).__init__(means, variances, name) super(SpikeAndSlabPosterior, self).__init__(means, variances, name)
self.gamma = Param("binary_prob",binary_prob) self.gamma = Param("binary_prob",binary_prob,Logistic(0.,1.))
self.link_parameter(self.gamma) self.link_parameter(self.gamma)
@Cache_this(limit=5)
def gamma_probabilities(self):
prob = np.zeros_like(param_to_array(self.gamma))
prob[self.gamma>-710] = 1./(1.+np.exp(-self.gamma[self.gamma>-710]))
prob1 = -np.zeros_like(param_to_array(self.gamma))
prob1[self.gamma<710] = 1./(1.+np.exp(self.gamma[self.gamma<710]))
return prob, prob1
@Cache_this(limit=5)
def gamma_log_prob(self):
loggamma = param_to_array(self.gamma).copy()
loggamma[loggamma>-40] = -np.log1p(np.exp(-loggamma[loggamma>-40]))
loggamma1 = -param_to_array(self.gamma).copy()
loggamma1[loggamma1>-40] = -np.log1p(np.exp(-loggamma1[loggamma1>-40]))
return loggamma,loggamma1
def set_gradients(self, grad): def set_gradients(self, grad):
self.mean.gradient, self.variance.gradient, self.gamma.gradient = grad self.mean.gradient, self.variance.gradient, self.gamma.gradient = grad

2
GPy/inference/latent_function_inference/__init__.py
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@ -62,7 +62,7 @@ class InferenceMethodList(LatentFunctionInference, list):
self.append(inf) self.append(inf)
from exact_gaussian_inference import ExactGaussianInference from exact_gaussian_inference import ExactGaussianInference
from laplace import Laplace from laplace import Laplace, LaplaceBlock
from GPy.inference.latent_function_inference.var_dtc import VarDTC from GPy.inference.latent_function_inference.var_dtc import VarDTC
from expectation_propagation import EP from expectation_propagation import EP
from expectation_propagation_dtc import EPDTC from expectation_propagation_dtc import EPDTC

204
GPy/inference/latent_function_inference/laplace.py
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@ -51,21 +51,25 @@ class Laplace(LatentFunctionInference):
#Find mode #Find mode
if self.bad_fhat or self.first_run: if self.bad_fhat or self.first_run:
Ki_f_init = np.zeros_like(Y) Ki_f_init = np.zeros_like(Y)
first_run = False self.first_run = False
else: else:
Ki_f_init = self._previous_Ki_fhat Ki_f_init = self._previous_Ki_fhat
Ki_f_init = np.zeros_like(Y)# FIXME: take this out
f_hat, Ki_fhat = self.rasm_mode(K, Y, likelihood, Ki_f_init, Y_metadata=Y_metadata) f_hat, Ki_fhat = self.rasm_mode(K, Y, likelihood, Ki_f_init, Y_metadata=Y_metadata)
self.f_hat = f_hat self.f_hat = f_hat
self.Ki_fhat = Ki_fhat #self.Ki_fhat = Ki_fhat
self.K = K.copy() #self.K = K.copy()
#Compute hessian and other variables at mode #Compute hessian and other variables at mode
log_marginal, woodbury_inv, dL_dK, dL_dthetaL = self.mode_computations(f_hat, Ki_fhat, K, Y, likelihood, kern, Y_metadata) log_marginal, woodbury_inv, dL_dK, dL_dthetaL = self.mode_computations(f_hat, Ki_fhat, K, Y, likelihood, kern, Y_metadata)
self._previous_Ki_fhat = Ki_fhat.copy() self._previous_Ki_fhat = Ki_fhat.copy()
return Posterior(woodbury_vector=Ki_fhat, woodbury_inv=woodbury_inv, K=K), log_marginal, {'dL_dK':dL_dK, 'dL_dthetaL':dL_dthetaL} return Posterior(woodbury_vector=Ki_fhat, woodbury_inv=woodbury_inv, K=K), log_marginal, {'dL_dK':dL_dK, 'dL_dthetaL':dL_dthetaL}
def rasm_mode(self, K, Y, likelihood, Ki_f_init, Y_metadata=None): def rasm_mode(self, K, Y, likelihood, Ki_f_init, Y_metadata=None, *args, **kwargs):
""" """
Rasmussen's numerically stable mode finding Rasmussen's numerically stable mode finding
For nomenclature see Rasmussen & Williams 2006 For nomenclature see Rasmussen & Williams 2006
@ -90,7 +94,12 @@ class Laplace(LatentFunctionInference):
#define the objective function (to be maximised) #define the objective function (to be maximised)
def obj(Ki_f, f): def obj(Ki_f, f):
return -0.5*np.dot(Ki_f.flatten(), f.flatten()) + np.sum(likelihood.logpdf(f, Y, Y_metadata=Y_metadata)) ll = -0.5*np.sum(np.dot(Ki_f.T, f)) + np.sum(likelihood.logpdf(f, Y, Y_metadata=Y_metadata))
if np.isnan(ll):
return -np.inf
else:
return ll
difference = np.inf difference = np.inf
iteration = 0 iteration = 0
@ -105,7 +114,7 @@ class Laplace(LatentFunctionInference):
W_f = W*f W_f = W*f
b = W_f + grad # R+W p46 line 6. b = W_f + grad # R+W p46 line 6.
W12BiW12, _, _ = self._compute_B_statistics(K, W, likelihood.log_concave) W12BiW12, _, _, _ = self._compute_B_statistics(K, W, likelihood.log_concave, *args, **kwargs)
W12BiW12Kb = np.dot(W12BiW12, np.dot(K, b)) W12BiW12Kb = np.dot(W12BiW12, np.dot(K, b))
#Work out the DIRECTION that we want to move in, but don't choose the stepsize yet #Work out the DIRECTION that we want to move in, but don't choose the stepsize yet
@ -122,7 +131,9 @@ class Laplace(LatentFunctionInference):
step = optimize.brent(inner_obj, tol=1e-4, maxiter=12) step = optimize.brent(inner_obj, tol=1e-4, maxiter=12)
Ki_f_new = Ki_f + step*dKi_f Ki_f_new = Ki_f + step*dKi_f
f_new = np.dot(K, Ki_f_new) f_new = np.dot(K, Ki_f_new)
#print "new {} vs old {}".format(obj(Ki_f_new, f_new), obj(Ki_f, f))
if obj(Ki_f_new, f_new) < obj(Ki_f, f):
raise ValueError("Shouldn't happen, brent optimization failing")
difference = np.abs(np.sum(f_new - f)) + np.abs(np.sum(Ki_f_new - Ki_f)) difference = np.abs(np.sum(f_new - f)) + np.abs(np.sum(Ki_f_new - Ki_f))
Ki_f = Ki_f_new Ki_f = Ki_f_new
f = f_new f = f_new
@ -153,14 +164,10 @@ class Laplace(LatentFunctionInference):
if np.any(np.isnan(W)): if np.any(np.isnan(W)):
raise ValueError('One or more element(s) of W is NaN') raise ValueError('One or more element(s) of W is NaN')
K_Wi_i, L, LiW12 = self._compute_B_statistics(K, W, likelihood.log_concave) K_Wi_i, logdet_I_KW, I_KW_i, Ki_W_i = self._compute_B_statistics(K, W, likelihood.log_concave)
#compute vital matrices
C = np.dot(LiW12, K)
Ki_W_i = K - C.T.dot(C)
#compute the log marginal #compute the log marginal
log_marginal = -0.5*np.dot(Ki_f.flatten(), f_hat.flatten()) + np.sum(likelihood.logpdf(f_hat, Y, Y_metadata=Y_metadata)) - np.sum(np.log(np.diag(L))) log_marginal = -0.5*np.sum(np.dot(Ki_f.T, f_hat)) + np.sum(likelihood.logpdf(f_hat, Y, Y_metadata=Y_metadata)) - 0.5*logdet_I_KW
# Compute matrices for derivatives # Compute matrices for derivatives
dW_df = -likelihood.d3logpdf_df3(f_hat, Y, Y_metadata=Y_metadata) # -d3lik_d3fhat dW_df = -likelihood.d3logpdf_df3(f_hat, Y, Y_metadata=Y_metadata) # -d3lik_d3fhat
@ -197,23 +204,23 @@ class Laplace(LatentFunctionInference):
dL_dthetaL = np.zeros(num_params) dL_dthetaL = np.zeros(num_params)
for thetaL_i in range(num_params): for thetaL_i in range(num_params):
#Explicit #Explicit
dL_dthetaL_exp = ( np.sum(dlik_dthetaL[thetaL_i]) dL_dthetaL_exp = ( np.sum(dlik_dthetaL[thetaL_i,:, :])
# The + comes from the fact that dlik_hess_dthetaL == -dW_dthetaL # The + comes from the fact that dlik_hess_dthetaL == -dW_dthetaL
+ 0.5*np.sum(np.diag(Ki_W_i).flatten()*dlik_hess_dthetaL[:, thetaL_i].flatten()) + 0.5*np.sum(np.diag(Ki_W_i)*np.squeeze(dlik_hess_dthetaL[thetaL_i, :, :]))
) )
#Implicit #Implicit
dfhat_dthetaL = mdot(I_KW_i, K, dlik_grad_dthetaL[:, thetaL_i]) dfhat_dthetaL = mdot(I_KW_i, K, dlik_grad_dthetaL[thetaL_i, :, :])
#dfhat_dthetaL = mdot(Ki_W_i, dlik_grad_dthetaL[:, thetaL_i]) #dfhat_dthetaL = mdot(Ki_W_i, dlik_grad_dthetaL[thetaL_i, :, :])
dL_dthetaL_imp = np.dot(dL_dfhat.T, dfhat_dthetaL) dL_dthetaL_imp = np.dot(dL_dfhat.T, dfhat_dthetaL)
dL_dthetaL[thetaL_i] = dL_dthetaL_exp + dL_dthetaL_imp dL_dthetaL[thetaL_i] = np.sum(dL_dthetaL_exp + dL_dthetaL_imp)
else: else:
dL_dthetaL = np.zeros(likelihood.size) dL_dthetaL = np.zeros(likelihood.size)
return log_marginal, K_Wi_i, dL_dK, dL_dthetaL return log_marginal, K_Wi_i, dL_dK, dL_dthetaL
def _compute_B_statistics(self, K, W, log_concave): def _compute_B_statistics(self, K, W, log_concave, *args, **kwargs):
""" """
Rasmussen suggests the use of a numerically stable positive definite matrix B Rasmussen suggests the use of a numerically stable positive definite matrix B
Which has a positive diagonal elements and can be easily inverted Which has a positive diagonal elements and can be easily inverted
@ -226,7 +233,7 @@ class Laplace(LatentFunctionInference):
""" """
if not log_concave: if not log_concave:
#print "Under 1e-10: {}".format(np.sum(W < 1e-6)) #print "Under 1e-10: {}".format(np.sum(W < 1e-6))
W[W<1e-6] = 1e-6 W = np.clip(W, 1e-6, 1e+30)
# NOTE: when setting a parameter inside parameters_changed it will allways come to closed update circles!!! # NOTE: when setting a parameter inside parameters_changed it will allways come to closed update circles!!!
#W.__setitem__(W < 1e-6, 1e-6, update=False) # FIXME-HACK: This is a hack since GPy can't handle negative variances which can occur #W.__setitem__(W < 1e-6, 1e-6, update=False) # FIXME-HACK: This is a hack since GPy can't handle negative variances which can occur
# If the likelihood is non-log-concave. We wan't to say that there is a negative variance # If the likelihood is non-log-concave. We wan't to say that there is a negative variance
@ -248,5 +255,160 @@ class Laplace(LatentFunctionInference):
#K_Wi_i_2 , _= dpotri(L2) #K_Wi_i_2 , _= dpotri(L2)
#symmetrify(K_Wi_i_2) #symmetrify(K_Wi_i_2)
return K_Wi_i, L, LiW12 #compute vital matrices
C = np.dot(LiW12, K)
Ki_W_i = K - C.T.dot(C)
I_KW_i = np.eye(K.shape[0]) - np.dot(K, K_Wi_i)
logdet_I_KW = 2*np.sum(np.log(np.diag(L)))
return K_Wi_i, logdet_I_KW, I_KW_i, Ki_W_i
class LaplaceBlock(Laplace):
def rasm_mode(self, K, Y, likelihood, Ki_f_init, Y_metadata=None, *args, **kwargs):
Ki_f = Ki_f_init.copy()
f = np.dot(K, Ki_f)
#define the objective function (to be maximised)
def obj(Ki_f, f):
ll = -0.5*np.dot(Ki_f.T, f) + np.sum(likelihood.logpdf_sum(f, Y, Y_metadata=Y_metadata))
if np.isnan(ll):
return -np.inf
else:
return ll
difference = np.inf
iteration = 0
I = np.eye(K.shape[0])
while difference > self._mode_finding_tolerance and iteration < self._mode_finding_max_iter:
W = -likelihood.d2logpdf_df2(f, Y, Y_metadata=Y_metadata)
W[np.diag_indices_from(W)] = np.clip(np.diag(W), 1e-6, 1e+30)
W_f = np.dot(W, f)
grad = likelihood.dlogpdf_df(f, Y, Y_metadata=Y_metadata)
b = W_f + grad # R+W p46 line 6.
K_Wi_i, _, _, _ = self._compute_B_statistics(K, W, likelihood.log_concave, *args, **kwargs)
#Work out the DIRECTION that we want to move in, but don't choose the stepsize yet
#a = (I - (K+Wi)i*K)*b
full_step_Ki_f = np.dot(I - np.dot(K_Wi_i, K), b)
dKi_f = full_step_Ki_f - Ki_f
#define an objective for the line search (minimize this one)
def inner_obj(step_size):
Ki_f_trial = Ki_f + step_size*dKi_f
f_trial = np.dot(K, Ki_f_trial)
return -obj(Ki_f_trial, f_trial)
#use scipy for the line search, the compute new values of f, Ki_f
step = optimize.brent(inner_obj, tol=1e-4, maxiter=12)
Ki_f_new = Ki_f + step*dKi_f
f_new = np.dot(K, Ki_f_new)
difference = np.abs(np.sum(f_new - f)) + np.abs(np.sum(Ki_f_new - Ki_f))
Ki_f = Ki_f_new
f = f_new
iteration += 1
#Warn of bad fits
if difference > self._mode_finding_tolerance:
if not self.bad_fhat:
warnings.warn("Not perfect f_hat fit difference: {}".format(difference))
self._previous_Ki_fhat = np.zeros_like(Y)
self.bad_fhat = True
elif self.bad_fhat:
self.bad_fhat = False
warnings.warn("f_hat now fine again")
if iteration > self._mode_finding_max_iter:
warnings.warn("didn't find the best")
return f, Ki_f
def mode_computations(self, f_hat, Ki_f, K, Y, likelihood, kern, Y_metadata):
#At this point get the hessian matrix (or vector as W is diagonal)
W = -likelihood.d2logpdf_df2(f_hat, Y, Y_metadata=Y_metadata)
W[np.diag_indices_from(W)] = np.clip(np.diag(W), 1e-6, 1e+30)
K_Wi_i, log_B_det, I_KW_i, Ki_W_i = self._compute_B_statistics(K, W, likelihood.log_concave)
#compute the log marginal
#FIXME: The derterminant should be output_dim*0.5 I think, gradients may now no longer check
log_marginal = -0.5*np.dot(f_hat.T, Ki_f) + np.sum(likelihood.logpdf_sum(f_hat, Y, Y_metadata=Y_metadata)) - 0.5*log_B_det
#Compute vival matrices for derivatives
dW_df = -likelihood.d3logpdf_df3(f_hat, Y, Y_metadata=Y_metadata) # -d3lik_d3fhat
#dL_dfhat = np.zeros((f_hat.shape[0]))
#for i in range(f_hat.shape[0]):
#dL_dfhat[i] = -0.5*np.trace(np.dot(Ki_W_i, dW_df[:,:,i]))
dL_dfhat = -0.5*np.einsum('ij,ijk->k', Ki_W_i, dW_df)
woodbury_vector = likelihood.dlogpdf_df(f_hat, Y, Y_metadata=Y_metadata)
####################
#compute dL_dK#
####################
if kern.size > 0 and not kern.is_fixed:
#Explicit
explicit_part = 0.5*(np.dot(Ki_f, Ki_f.T) - K_Wi_i)
#Implicit
implicit_part = woodbury_vector.dot(dL_dfhat[None,:]).dot(I_KW_i)
#implicit_part = Ki_f.dot(dL_dfhat[None,:]).dot(I_KW_i)
dL_dK = explicit_part + implicit_part
else:
dL_dK = np.zeros_like(K)
####################
#compute dL_dthetaL#
####################
if likelihood.size > 0 and not likelihood.is_fixed:
raise NotImplementedError
else:
dL_dthetaL = np.zeros(likelihood.size)
#self.K_Wi_i = K_Wi_i
#self.Ki_W_i = Ki_W_i
#self.W = W
#self.K = K
#self.dL_dfhat = dL_dfhat
#self.explicit_part = explicit_part
#self.implicit_part = implicit_part
return log_marginal, K_Wi_i, dL_dK, dL_dthetaL
def _compute_B_statistics(self, K, W, log_concave, *args, **kwargs):
"""
Rasmussen suggests the use of a numerically stable positive definite matrix B
Which has a positive diagonal element and can be easyily inverted
:param K: Prior Covariance matrix evaluated at locations X
:type K: NxN matrix
:param W: Negative hessian at a point (diagonal matrix)
:type W: Vector of diagonal values of hessian (1xN)
:returns: (K_Wi_i, L_B, not_provided)
"""
#w = GPy.util.diag.view(W)
#W[:] = np.where(w<1e-6, 1e-6, w)
#B = I + KW
B = np.eye(K.shape[0]) + np.dot(K, W)
#Bi, L, Li, logdetB = pdinv(B)
Bi = np.linalg.inv(B)
#K_Wi_i = np.eye(K.shape[0]) - mdot(W, Bi, K)
K_Wi_i = np.dot(W, Bi)
#self.K_Wi_i_brute = np.linalg.inv(K + np.linalg.inv(W))
#self.B = B
#self.Bi = Bi
Ki_W_i = np.dot(Bi, K)
sign, logdetB = np.linalg.slogdet(B)
return K_Wi_i, sign*logdetB, Bi, Ki_W_i

4
GPy/inference/latent_function_inference/svgp.py
View file

@ -72,7 +72,7 @@ class SVGP(LatentFunctionInference):
#rescale the F term if working on a batch #rescale the F term if working on a batch
F, dF_dmu, dF_dv = F*batch_scale, dF_dmu*batch_scale, dF_dv*batch_scale F, dF_dmu, dF_dv = F*batch_scale, dF_dmu*batch_scale, dF_dv*batch_scale
if dF_dthetaL is not None: if dF_dthetaL is not None:
dF_dthetaL = dF_dthetaL.sum(1)*batch_scale dF_dthetaL = dF_dthetaL.sum(1).sum(1)*batch_scale
#derivatives of expected likelihood, assuming zero mean function #derivatives of expected likelihood, assuming zero mean function
Adv = A.T[:,:,None]*dF_dv[None,:,:] # As if dF_Dv is diagonal Adv = A.T[:,:,None]*dF_dv[None,:,:] # As if dF_Dv is diagonal
@ -101,7 +101,7 @@ class SVGP(LatentFunctionInference):
dL_dchol = np.dstack([2.*np.dot(dL_dS[:,:,i], L[:,:,i]) for i in range(num_outputs)]) dL_dchol = np.dstack([2.*np.dot(dL_dS[:,:,i], L[:,:,i]) for i in range(num_outputs)])
dL_dchol = choleskies.triang_to_flat(dL_dchol) dL_dchol = choleskies.triang_to_flat(dL_dchol)
grad_dict = {'dL_dKmm':dL_dKmm, 'dL_dKmn':dL_dKmn, 'dL_dKdiag': dF_dv, 'dL_dm':dL_dm, 'dL_dchol':dL_dchol, 'dL_dthetaL':dF_dthetaL} grad_dict = {'dL_dKmm':dL_dKmm, 'dL_dKmn':dL_dKmn, 'dL_dKdiag': dF_dv.sum(1), 'dL_dm':dL_dm, 'dL_dchol':dL_dchol, 'dL_dthetaL':dF_dthetaL}
if mean_function is not None: if mean_function is not None:
grad_dict['dL_dmfZ'] = dF_dmfZ - dKL_dmfZ grad_dict['dL_dmfZ'] = dF_dmfZ - dKL_dmfZ
grad_dict['dL_dmfX'] = dF_dmfX grad_dict['dL_dmfX'] = dF_dmfX

6
GPy/inference/latent_function_inference/var_dtc_parallel.py
View file

@ -169,11 +169,13 @@ class VarDTC_minibatch(LatentFunctionInference):
Kmm = kern.K(Z).copy() Kmm = kern.K(Z).copy()
diag.add(Kmm, self.const_jitter) diag.add(Kmm, self.const_jitter)
Lm = jitchol(Kmm, maxtries=100) if not np.isfinite(Kmm).all():
print Kmm
Lm = jitchol(Kmm)
LmInvPsi2LmInvT = backsub_both_sides(Lm,psi2_full,transpose='right') LmInvPsi2LmInvT = backsub_both_sides(Lm,psi2_full,transpose='right')
Lambda = np.eye(Kmm.shape[0])+LmInvPsi2LmInvT Lambda = np.eye(Kmm.shape[0])+LmInvPsi2LmInvT
LL = jitchol(Lambda, maxtries=100) LL = jitchol(Lambda)
logdet_L = 2.*np.sum(np.log(np.diag(LL))) logdet_L = 2.*np.sum(np.log(np.diag(LL)))
b = dtrtrs(LL,dtrtrs(Lm,psi1Y_full.T)[0])[0] b = dtrtrs(LL,dtrtrs(Lm,psi1Y_full.T)[0])[0]
bbt = np.square(b).sum() bbt = np.square(b).sum()

3
GPy/kern/__init__.py
View file

@ -16,5 +16,6 @@ from _src.poly import Poly
from _src.eq_ode2 import EQ_ODE2 from _src.eq_ode2 import EQ_ODE2
from _src.trunclinear import TruncLinear,TruncLinear_inf from _src.trunclinear import TruncLinear,TruncLinear_inf
from _src.splitKern import SplitKern,DiffGenomeKern from _src.splitKern import SplitKern,DEtime
from _src.splitKern import DEtime as DiffGenomeKern

40
GPy/kern/_src/psi_comp/sslinear_psi_comp.py
View file

@ -37,11 +37,11 @@ def psiDerivativecomputations(dL_dpsi0, dL_dpsi1, dL_dpsi2, variance, Z, variati
# Compute for psi0 and psi1 # Compute for psi0 and psi1
mu2S = np.square(mu)+S mu2S = np.square(mu)+S
dL_dvar += np.einsum('n,nq,nq->q',dL_dpsi0,gamma,mu2S) + np.einsum('nm,nq,mq,nq->q',dL_dpsi1,gamma,Z,mu) dL_dvar += (dL_dpsi0[:,None]*gamma*mu2S).sum(axis=0) + (dL_dpsi1.T.dot(gamma*mu)*Z).sum(axis=0)
dL_dgamma += np.einsum('n,q,nq->nq',dL_dpsi0,variance,mu2S) + np.einsum('nm,q,mq,nq->nq',dL_dpsi1,variance,Z,mu) dL_dgamma += dL_dpsi0[:,None]*variance*mu2S+ dL_dpsi1.dot(Z)*mu*variance
dL_dmu += np.einsum('n,nq,q,nq->nq',dL_dpsi0,gamma,2.*variance,mu) + np.einsum('nm,nq,q,mq->nq',dL_dpsi1,gamma,variance,Z) dL_dmu += dL_dpsi0[:,None]*2.*variance*gamma*mu + dL_dpsi1.dot(Z)*gamma*variance
dL_dS += np.einsum('n,nq,q->nq',dL_dpsi0,gamma,variance) dL_dS += dL_dpsi0[:,None]*variance*gamma
dL_dZ += np.einsum('nm,nq,q,nq->mq',dL_dpsi1,gamma, variance,mu) dL_dZ += dL_dpsi1.T.dot(gamma*mu)*variance
return dL_dvar, dL_dZ, dL_dmu, dL_dS, dL_dgamma return dL_dvar, dL_dZ, dL_dmu, dL_dS, dL_dgamma
@ -64,29 +64,23 @@ def _psi2computations(dL_dpsi2, variance, Z, mu, S, gamma):
gamma2 = np.square(gamma) gamma2 = np.square(gamma)
variance2 = np.square(variance) variance2 = np.square(variance)
mu2S = mu2+S # NxQ mu2S = mu2+S # NxQ
gvm = np.einsum('nq,nq,q->nq',gamma,mu,variance) gvm = gamma*mu*variance
common_sum = np.einsum('nq,mq->nm',gvm,Z) common_sum = gvm.dot(Z.T)
# common_sum = np.einsum('nq,q,mq,nq->nm',gamma,variance,Z,mu) # NxM Z_expect = (np.dot(dL_dpsi2,Z)*Z).sum(axis=0)
Z_expect = np.einsum('mo,mq,oq->q',dL_dpsi2,Z,Z) Z_expect_var2 = Z_expect*variance2
dL_dpsi2T = dL_dpsi2+dL_dpsi2.T dL_dpsi2T = dL_dpsi2+dL_dpsi2.T
tmp = np.einsum('mo,oq->mq',dL_dpsi2T,Z) common_expect = common_sum.dot(dL_dpsi2T).dot(Z)
common_expect = np.einsum('mq,nm->nq',tmp,common_sum) Z2_expect = common_sum.dot(dL_dpsi2T)
# common_expect = np.einsum('mo,mq,no->nq',dL_dpsi2+dL_dpsi2.T,Z,common_sum) Z1_expect = dL_dpsi2T.dot(Z)
Z2_expect = np.einsum('om,nm->no',dL_dpsi2T,common_sum)
Z1_expect = np.einsum('om,mq->oq',dL_dpsi2T,Z)
dL_dvar = np.einsum('nq,q,q->q',2.*(gamma*mu2S-gamma2*mu2),variance,Z_expect)+\ dL_dvar = variance*Z_expect*2.*(gamma*mu2S-gamma2*mu2).sum(axis=0)+(common_expect*gamma*mu).sum(axis=0)
np.einsum('nq,nq,nq->q',common_expect,gamma,mu)
dL_dgamma = np.einsum('q,q,nq->nq',Z_expect,variance2,(mu2S-2.*gamma*mu2))+\ dL_dgamma = Z_expect_var2*(mu2S-2.*gamma*mu2)+common_expect*mu*variance
np.einsum('nq,q,nq->nq',common_expect,variance,mu)
dL_dmu = np.einsum('q,q,nq,nq->nq',Z_expect,variance2,mu,2.*(gamma-gamma2))+\ dL_dmu = Z_expect_var2*mu*2.*(gamma-gamma2) + common_expect*gamma*variance
np.einsum('nq,nq,q->nq',common_expect,gamma,variance)
dL_dS = np.einsum('q,nq,q->nq',Z_expect,gamma,variance2) dL_dS = gamma*Z_expect_var2
# dL_dZ = 2.*(np.einsum('om,nq,q,mq,nq->oq',dL_dpsi2,gamma,variance2,Z,(mu2S-gamma*mu2))+np.einsum('om,nq,q,nq,nm->oq',dL_dpsi2,gamma,variance,mu,common_sum)) dL_dZ = (gamma*(mu2S-gamma*mu2)).sum(axis=0)*variance2*Z1_expect+ Z2_expect.T.dot(gamma*mu)*variance
dL_dZ = Z1_expect*np.einsum('nq,q,nq->q',gamma,variance2,(mu2S-gamma*mu2))+np.einsum('nq,q,nq,nm->mq',gamma,variance,mu,Z2_expect)
return dL_dvar, dL_dgamma, dL_dmu, dL_dS, dL_dZ return dL_dvar, dL_dgamma, dL_dmu, dL_dS, dL_dZ

20
GPy/kern/_src/psi_comp/ssrbf_psi_comp.py
View file

@ -22,12 +22,14 @@ try:
# _psi1 NxM # _psi1 NxM
mu = variational_posterior.mean mu = variational_posterior.mean
S = variational_posterior.variance S = variational_posterior.variance
gamma = variational_posterior.binary_prob
N,M,Q = mu.shape[0],Z.shape[0],mu.shape[1] N,M,Q = mu.shape[0],Z.shape[0],mu.shape[1]
l2 = np.square(lengthscale) l2 = np.square(lengthscale)
log_denom1 = np.log(S/l2+1) log_denom1 = np.log(S/l2+1)
log_denom2 = np.log(2*S/l2+1) log_denom2 = np.log(2*S/l2+1)
log_gamma,log_gamma1 = variational_posterior.gamma_log_prob() log_gamma = np.log(gamma)
log_gamma1 = np.log(1.-gamma)
variance = float(variance) variance = float(variance)
psi0 = np.empty(N) psi0 = np.empty(N)
psi0[:] = variance psi0[:] = variance
@ -37,6 +39,7 @@ try:
from ....util.misc import param_to_array from ....util.misc import param_to_array
S = param_to_array(S) S = param_to_array(S)
mu = param_to_array(mu) mu = param_to_array(mu)
gamma = param_to_array(gamma)
Z = param_to_array(Z) Z = param_to_array(Z)
support_code = """ support_code = """
@ -79,7 +82,7 @@ try:
} }
} }
""" """
weave.inline(code, support_code=support_code, arg_names=['psi1','psi2n','N','M','Q','variance','l2','Z','mu','S','log_denom1','log_denom2','log_gamma','log_gamma1'], type_converters=weave.converters.blitz) weave.inline(code, support_code=support_code, arg_names=['psi1','psi2n','N','M','Q','variance','l2','Z','mu','S','gamma','log_denom1','log_denom2','log_gamma','log_gamma1'], type_converters=weave.converters.blitz)
psi2 = psi2n.sum(axis=0) psi2 = psi2n.sum(axis=0)
return psi0,psi1,psi2,psi2n return psi0,psi1,psi2,psi2n
@ -94,12 +97,13 @@ try:
mu = variational_posterior.mean mu = variational_posterior.mean
S = variational_posterior.variance S = variational_posterior.variance
gamma = variational_posterior.binary_prob
N,M,Q = mu.shape[0],Z.shape[0],mu.shape[1] N,M,Q = mu.shape[0],Z.shape[0],mu.shape[1]
l2 = np.square(lengthscale) l2 = np.square(lengthscale)
log_denom1 = np.log(S/l2+1) log_denom1 = np.log(S/l2+1)
log_denom2 = np.log(2*S/l2+1) log_denom2 = np.log(2*S/l2+1)
log_gamma,log_gamma1 = variational_posterior.gamma_log_prob() log_gamma = np.log(gamma)
gamma, gamma1 = variational_posterior.gamma_probabilities() log_gamma1 = np.log(1.-gamma)
variance = float(variance) variance = float(variance)
dvar = np.zeros(1) dvar = np.zeros(1)
@ -113,6 +117,7 @@ try:
from ....util.misc import param_to_array from ....util.misc import param_to_array
S = param_to_array(S) S = param_to_array(S)
mu = param_to_array(mu) mu = param_to_array(mu)
gamma = param_to_array(gamma)
Z = param_to_array(Z) Z = param_to_array(Z)
support_code = """ support_code = """
@ -130,7 +135,6 @@ try:
double Zm1q = Z(m1,q); double Zm1q = Z(m1,q);
double Zm2q = Z(m2,q); double Zm2q = Z(m2,q);
double gnq = gamma(n,q); double gnq = gamma(n,q);
double g1nq = gamma1(n,q);
double mu_nq = mu(n,q); double mu_nq = mu(n,q);
if(m2==0) { if(m2==0) {
@ -156,7 +160,7 @@ try:
dmu(n,q) += lpsi1*Zmu*d_exp1/(denom*exp_sum); dmu(n,q) += lpsi1*Zmu*d_exp1/(denom*exp_sum);
dS(n,q) += lpsi1*(Zmu2_denom-1.)*d_exp1/(denom*exp_sum)/2.; dS(n,q) += lpsi1*(Zmu2_denom-1.)*d_exp1/(denom*exp_sum)/2.;
dgamma(n,q) += lpsi1*(d_exp1*g1nq-d_exp2*gnq)/exp_sum; dgamma(n,q) += lpsi1*(d_exp1/gnq-d_exp2/(1.-gnq))/exp_sum;
dl(q) += lpsi1*((Zmu2_denom+Snq/lq)/denom*d_exp1+Zm1q*Zm1q/(lq*lq)*d_exp2)/(2.*exp_sum); dl(q) += lpsi1*((Zmu2_denom+Snq/lq)/denom*d_exp1+Zm1q*Zm1q/(lq*lq)*d_exp2)/(2.*exp_sum);
dZ(m1,q) += lpsi1*(-Zmu/denom*d_exp1-Zm1q/lq*d_exp2)/exp_sum; dZ(m1,q) += lpsi1*(-Zmu/denom*d_exp1-Zm1q/lq*d_exp2)/exp_sum;
} }
@ -184,7 +188,7 @@ try:
dmu(n,q) += -2.*lpsi2*muZhat/denom*d_exp1/exp_sum; dmu(n,q) += -2.*lpsi2*muZhat/denom*d_exp1/exp_sum;
dS(n,q) += lpsi2*(2.*muZhat2_denom-1.)/denom*d_exp1/exp_sum; dS(n,q) += lpsi2*(2.*muZhat2_denom-1.)/denom*d_exp1/exp_sum;
dgamma(n,q) += lpsi2*(d_exp1*g1nq-d_exp2*gnq)/exp_sum; dgamma(n,q) += lpsi2*(d_exp1/gnq-d_exp2/(1.-gnq))/exp_sum;
dl(q) += lpsi2*(((Snq/lq+muZhat2_denom)/denom+dZm1m2*dZm1m2/(4.*lq*lq))*d_exp1+Z2/(2.*lq*lq)*d_exp2)/exp_sum; dl(q) += lpsi2*(((Snq/lq+muZhat2_denom)/denom+dZm1m2*dZm1m2/(4.*lq*lq))*d_exp1+Z2/(2.*lq*lq)*d_exp2)/exp_sum;
dZ(m1,q) += 2.*lpsi2*((muZhat/denom-dZm1m2/(2*lq))*d_exp1-Zm1q/lq*d_exp2)/exp_sum; dZ(m1,q) += 2.*lpsi2*((muZhat/denom-dZm1m2/(2*lq))*d_exp1-Zm1q/lq*d_exp2)/exp_sum;
} }
@ -192,7 +196,7 @@ try:
} }
} }
""" """
weave.inline(code, support_code=support_code, arg_names=['dL_dpsi1','dL_dpsi2','psi1','psi2n','N','M','Q','variance','l2','Z','mu','S','gamma','gamma1','log_denom1','log_denom2','log_gamma','log_gamma1','dvar','dl','dmu','dS','dgamma','dZ'], type_converters=weave.converters.blitz) weave.inline(code, support_code=support_code, arg_names=['dL_dpsi1','dL_dpsi2','psi1','psi2n','N','M','Q','variance','l2','Z','mu','S','gamma','log_denom1','log_denom2','log_gamma','log_gamma1','dvar','dl','dmu','dS','dgamma','dZ'], type_converters=weave.converters.blitz)
dl *= 2.*lengthscale dl *= 2.*lengthscale
if not ARD: if not ARD:

2
GPy/kern/_src/splitKern.py
View file

@ -7,7 +7,7 @@ from kern import Kern,CombinationKernel
from .independent_outputs import index_to_slices from .independent_outputs import index_to_slices
import itertools import itertools
class DiffGenomeKern(Kern): class DEtime(Kern):
def __init__(self, kernel, idx_p, Xp, index_dim=-1, name='DiffGenomeKern'): def __init__(self, kernel, idx_p, Xp, index_dim=-1, name='DiffGenomeKern'):
self.idx_p = idx_p self.idx_p = idx_p

28
GPy/likelihoods/gaussian.py
View file

@ -34,7 +34,9 @@ class Gaussian(Likelihood):
if gp_link is None: if gp_link is None:
gp_link = link_functions.Identity() gp_link = link_functions.Identity()
assert isinstance(gp_link, link_functions.Identity), "the likelihood only implemented for the identity link" if not isinstance(gp_link, link_functions.Identity):
print "Warning, Exact inference is not implemeted for non-identity link functions,\
if you are not already, ensure Laplace inference_method is used"
super(Gaussian, self).__init__(gp_link, name=name) super(Gaussian, self).__init__(gp_link, name=name)
@ -263,16 +265,19 @@ class Gaussian(Likelihood):
return d2logpdf_dlink2_dvar return d2logpdf_dlink2_dvar
def dlogpdf_link_dtheta(self, f, y, Y_metadata=None): def dlogpdf_link_dtheta(self, f, y, Y_metadata=None):
dlogpdf_dvar = self.dlogpdf_link_dvar(f, y, Y_metadata=Y_metadata) dlogpdf_dtheta = np.zeros((self.size, f.shape[0], f.shape[1]))
return dlogpdf_dvar dlogpdf_dtheta[0,:,:] = self.dlogpdf_link_dvar(f, y, Y_metadata=Y_metadata)
return dlogpdf_dtheta
def dlogpdf_dlink_dtheta(self, f, y, Y_metadata=None): def dlogpdf_dlink_dtheta(self, f, y, Y_metadata=None):
dlogpdf_dlink_dvar = self.dlogpdf_dlink_dvar(f, y, Y_metadata=Y_metadata) dlogpdf_dlink_dtheta = np.zeros((self.size, f.shape[0], f.shape[1]))
return dlogpdf_dlink_dvar dlogpdf_dlink_dtheta[0, :, :]= self.dlogpdf_dlink_dvar(f, y, Y_metadata=Y_metadata)
return dlogpdf_dlink_dtheta
def d2logpdf_dlink2_dtheta(self, f, y, Y_metadata=None): def d2logpdf_dlink2_dtheta(self, f, y, Y_metadata=None):
d2logpdf_dlink2_dvar = self.d2logpdf_dlink2_dvar(f, y, Y_metadata=Y_metadata) d2logpdf_dlink2_dtheta = np.zeros((self.size, f.shape[0], f.shape[1]))
return d2logpdf_dlink2_dvar d2logpdf_dlink2_dtheta[0, :, :] = self.d2logpdf_dlink2_dvar(f, y, Y_metadata=Y_metadata)
return d2logpdf_dlink2_dtheta
def _mean(self, gp): def _mean(self, gp):
""" """
@ -305,18 +310,17 @@ class Gaussian(Likelihood):
Ysim = np.array([np.random.normal(self.gp_link.transf(gpj), scale=np.sqrt(self.variance), size=1) for gpj in gp]) Ysim = np.array([np.random.normal(self.gp_link.transf(gpj), scale=np.sqrt(self.variance), size=1) for gpj in gp])
return Ysim.reshape(orig_shape) return Ysim.reshape(orig_shape)
def log_predictive_density(self, y_test, mu_star, var_star): def log_predictive_density(self, y_test, mu_star, var_star, Y_metadata=None):
""" """
assumes independence assumes independence
""" """
v = var_star + self.variance v = var_star + self.variance
return -0.5*np.log(2*np.pi) -0.5*np.log(v) - 0.5*np.square(y_test - mu_star)/v return -0.5*np.log(2*np.pi) -0.5*np.log(v) - 0.5*np.square(y_test - mu_star)/v
def variational_expectations(self, Y, m, v, gh_points=None): def variational_expectations(self, Y, m, v, gh_points=None, Y_metadata=None):
lik_var = float(self.variance) lik_var = float(self.variance)
F = -0.5*np.log(2*np.pi) -0.5*np.log(lik_var) - 0.5*(np.square(Y) + np.square(m) + v - 2*m*Y)/lik_var F = -0.5*np.log(2*np.pi) -0.5*np.log(lik_var) - 0.5*(np.square(Y) + np.square(m) + v - 2*m*Y)/lik_var
dF_dmu = (Y - m)/lik_var dF_dmu = (Y - m)/lik_var
dF_dv = np.ones_like(v)*(-0.5/lik_var) dF_dv = np.ones_like(v)*(-0.5/lik_var)
dF_dlik_var = np.sum(-0.5/lik_var + 0.5*(np.square(Y) + np.square(m) + v - 2*m*Y)/(lik_var**2)) dF_dtheta = -0.5/lik_var + 0.5*(np.square(Y) + np.square(m) + v - 2*m*Y)/(lik_var**2)
dF_dtheta = [dF_dlik_var] return F, dF_dmu, dF_dv, dF_dtheta.reshape(1, Y.shape[0], Y.shape[1])
return F, dF_dmu, dF_dv, dF_dtheta

256
GPy/likelihoods/likelihood.py
View file

@ -5,7 +5,7 @@ import numpy as np
from scipy import stats,special from scipy import stats,special
import scipy as sp import scipy as sp
import link_functions import link_functions
from ..util.misc import chain_1, chain_2, chain_3 from ..util.misc import chain_1, chain_2, chain_3, blockify_dhess_dtheta, blockify_third, blockify_hessian, safe_exp
from scipy.integrate import quad from scipy.integrate import quad
import warnings import warnings
from ..core.parameterization import Parameterized from ..core.parameterization import Parameterized
@ -39,6 +39,7 @@ class Likelihood(Parameterized):
assert isinstance(gp_link,link_functions.GPTransformation), "gp_link is not a valid GPTransformation." assert isinstance(gp_link,link_functions.GPTransformation), "gp_link is not a valid GPTransformation."
self.gp_link = gp_link self.gp_link = gp_link
self.log_concave = False self.log_concave = False
self.not_block_really = False
def _gradients(self,partial): def _gradients(self,partial):
return np.zeros(0) return np.zeros(0)
@ -180,6 +181,7 @@ class Likelihood(Parameterized):
if self.size: if self.size:
dF_dtheta = self.dlogpdf_dtheta(X, Y[:,None]) # Ntheta x (orig size) x N_{quad_points} dF_dtheta = self.dlogpdf_dtheta(X, Y[:,None]) # Ntheta x (orig size) x N_{quad_points}
dF_dtheta = np.dot(dF_dtheta, gh_w) dF_dtheta = np.dot(dF_dtheta, gh_w)
dF_dtheta = dF_dtheta.reshape(self.size, shape[0], shape[1])
else: else:
dF_dtheta = None # Not yet implemented dF_dtheta = None # Not yet implemented
return F.reshape(*shape), dF_dm.reshape(*shape), dF_dv.reshape(*shape), dF_dtheta return F.reshape(*shape), dF_dm.reshape(*shape), dF_dv.reshape(*shape), dF_dtheta
@ -193,20 +195,27 @@ class Likelihood(Parameterized):
""" """
#conditional_mean: the edpected value of y given some f, under this likelihood #conditional_mean: the edpected value of y given some f, under this likelihood
fmin = -np.inf
fmax = np.inf
def int_mean(f,m,v): def int_mean(f,m,v):
p = np.exp(-(0.5/v)*np.square(f - m)) exponent = -(0.5/v)*np.square(f - m)
#If exponent is under -30 then exp(exponent) will be very small, so don't exp it!)
#If p is zero then conditional_mean will overflow #If p is zero then conditional_mean will overflow
assert v.all() > 0
p = safe_exp(exponent)
#If p is zero then conditional_variance will overflow
if p < 1e-10: if p < 1e-10:
return 0. return 0.
else: else:
return self.conditional_mean(f)*p return self.conditional_mean(f)*p
scaled_mean = [quad(int_mean, -np.inf, np.inf,args=(mj,s2j))[0] for mj,s2j in zip(mu,variance)] scaled_mean = [quad(int_mean, fmin, fmax,args=(mj,s2j))[0] for mj,s2j in zip(mu,variance)]
mean = np.array(scaled_mean)[:,None] / np.sqrt(2*np.pi*(variance)) mean = np.array(scaled_mean)[:,None] / np.sqrt(2*np.pi*(variance))
return mean return mean
def _conditional_mean(self, f): def _conditional_mean(self, f):
"""Quadrature calculation of the conditional mean: E(Y_star|f)""" """Quadrature calculation of the conditional mean: E(Y_star|f_star)"""
raise NotImplementedError, "implement this function to make predictions" raise NotImplementedError, "implement this function to make predictions"
def predictive_variance(self, mu,variance, predictive_mean=None, Y_metadata=None): def predictive_variance(self, mu,variance, predictive_mean=None, Y_metadata=None):
@ -214,7 +223,7 @@ class Likelihood(Parameterized):
Approximation to the predictive variance: V(Y_star) Approximation to the predictive variance: V(Y_star)
The following variance decomposition is used: The following variance decomposition is used:
V(Y_star) = E( V(Y_star|f_star) ) + V( E(Y_star|f_star) ) V(Y_star) = E( V(Y_star|f_star)**2 ) + V( E(Y_star|f_star) )**2
:param mu: mean of posterior :param mu: mean of posterior
:param sigma: standard deviation of posterior :param sigma: standard deviation of posterior
@ -224,15 +233,22 @@ class Likelihood(Parameterized):
#sigma2 = sigma**2 #sigma2 = sigma**2
normalizer = np.sqrt(2*np.pi*variance) normalizer = np.sqrt(2*np.pi*variance)
fmin_v = -np.inf
fmin_m = np.inf
fmin = -np.inf
fmax = np.inf
from ..util.misc import safe_exp
# E( V(Y_star|f_star) ) # E( V(Y_star|f_star) )
def int_var(f,m,v): def int_var(f,m,v):
p = np.exp(-(0.5/v)*np.square(f - m)) exponent = -(0.5/v)*np.square(f - m)
p = safe_exp(exponent)
#If p is zero then conditional_variance will overflow #If p is zero then conditional_variance will overflow
if p < 1e-10: if p < 1e-10:
return 0. return 0.
else: else:
return self.conditional_variance(f)*p return self.conditional_variance(f)*p
scaled_exp_variance = [quad(int_var, -np.inf, np.inf,args=(mj,s2j))[0] for mj,s2j in zip(mu,variance)] scaled_exp_variance = [quad(int_var, fmin_v, fmax,args=(mj,s2j))[0] for mj,s2j in zip(mu,variance)]
exp_var = np.array(scaled_exp_variance)[:,None] / normalizer exp_var = np.array(scaled_exp_variance)[:,None] / normalizer
#V( E(Y_star|f_star) ) = E( E(Y_star|f_star)**2 ) - E( E(Y_star|f_star) )**2 #V( E(Y_star|f_star) ) = E( E(Y_star|f_star)**2 ) - E( E(Y_star|f_star) )**2
@ -244,14 +260,15 @@ class Likelihood(Parameterized):
#E( E(Y_star|f_star)**2 ) #E( E(Y_star|f_star)**2 )
def int_pred_mean_sq(f,m,v,predictive_mean_sq): def int_pred_mean_sq(f,m,v,predictive_mean_sq):
p = np.exp(-(0.5/v)*np.square(f - m)) exponent = -(0.5/v)*np.square(f - m)
p = np.exp(exponent)
#If p is zero then conditional_mean**2 will overflow #If p is zero then conditional_mean**2 will overflow
if p < 1e-10: if p < 1e-10:
return 0. return 0.
else: else:
return self.conditional_mean(f)**2*p return self.conditional_mean(f)**2*p
scaled_exp_exp2 = [quad(int_pred_mean_sq, -np.inf, np.inf,args=(mj,s2j,pm2j))[0] for mj,s2j,pm2j in zip(mu,variance,predictive_mean_sq)] scaled_exp_exp2 = [quad(int_pred_mean_sq, fmin_m, fmax,args=(mj,s2j,pm2j))[0] for mj,s2j,pm2j in zip(mu,variance,predictive_mean_sq)]
exp_exp2 = np.array(scaled_exp_exp2)[:,None] / normalizer exp_exp2 = np.array(scaled_exp_exp2)[:,None] / normalizer
var_exp = exp_exp2 - predictive_mean_sq var_exp = exp_exp2 - predictive_mean_sq
@ -299,8 +316,18 @@ class Likelihood(Parameterized):
:returns: likelihood evaluated for this point :returns: likelihood evaluated for this point
:rtype: float :rtype: float
""" """
inv_link_f = self.gp_link.transf(f) if isinstance(self.gp_link, link_functions.Identity):
return self.pdf_link(inv_link_f, y, Y_metadata=Y_metadata) return self.pdf_link(f, y, Y_metadata=Y_metadata)
else:
inv_link_f = self.gp_link.transf(f)
return self.pdf_link(inv_link_f, y, Y_metadata=Y_metadata)
def logpdf_sum(self, f, y, Y_metadata=None):
"""
Convenience function that can overridden for functions where this could
be computed more efficiently
"""
return np.sum(self.logpdf(f, y, Y_metadata=Y_metadata))
def logpdf(self, f, y, Y_metadata=None): def logpdf(self, f, y, Y_metadata=None):
""" """
@ -317,8 +344,11 @@ class Likelihood(Parameterized):
:returns: log likelihood evaluated for this point :returns: log likelihood evaluated for this point
:rtype: float :rtype: float
""" """
inv_link_f = self.gp_link.transf(f) if isinstance(self.gp_link, link_functions.Identity):
return self.logpdf_link(inv_link_f, y, Y_metadata=Y_metadata) return self.logpdf_link(f, y, Y_metadata=Y_metadata)
else:
inv_link_f = self.gp_link.transf(f)
return self.logpdf_link(inv_link_f, y, Y_metadata=Y_metadata)
def dlogpdf_df(self, f, y, Y_metadata=None): def dlogpdf_df(self, f, y, Y_metadata=None):
""" """
@ -336,11 +366,15 @@ class Likelihood(Parameterized):
:returns: derivative of log likelihood evaluated for this point :returns: derivative of log likelihood evaluated for this point
:rtype: 1xN array :rtype: 1xN array
""" """
inv_link_f = self.gp_link.transf(f) if isinstance(self.gp_link, link_functions.Identity):
dlogpdf_dlink = self.dlogpdf_dlink(inv_link_f, y, Y_metadata=Y_metadata) return self.dlogpdf_dlink(f, y, Y_metadata=Y_metadata)
dlink_df = self.gp_link.dtransf_df(f) else:
return chain_1(dlogpdf_dlink, dlink_df) inv_link_f = self.gp_link.transf(f)
dlogpdf_dlink = self.dlogpdf_dlink(inv_link_f, y, Y_metadata=Y_metadata)
dlink_df = self.gp_link.dtransf_df(f)
return chain_1(dlogpdf_dlink, dlink_df)
@blockify_hessian
def d2logpdf_df2(self, f, y, Y_metadata=None): def d2logpdf_df2(self, f, y, Y_metadata=None):
""" """
Evaluates the link function link(f) then computes the second derivative of log likelihood using it Evaluates the link function link(f) then computes the second derivative of log likelihood using it
@ -357,13 +391,18 @@ class Likelihood(Parameterized):
:returns: second derivative of log likelihood evaluated for this point (diagonal only) :returns: second derivative of log likelihood evaluated for this point (diagonal only)
:rtype: 1xN array :rtype: 1xN array
""" """
inv_link_f = self.gp_link.transf(f) if isinstance(self.gp_link, link_functions.Identity):
d2logpdf_dlink2 = self.d2logpdf_dlink2(inv_link_f, y, Y_metadata=Y_metadata) d2logpdf_df2 = self.d2logpdf_dlink2(f, y, Y_metadata=Y_metadata)
dlink_df = self.gp_link.dtransf_df(f) else:
dlogpdf_dlink = self.dlogpdf_dlink(inv_link_f, y, Y_metadata=Y_metadata) inv_link_f = self.gp_link.transf(f)
d2link_df2 = self.gp_link.d2transf_df2(f) d2logpdf_dlink2 = self.d2logpdf_dlink2(inv_link_f, y, Y_metadata=Y_metadata)
return chain_2(d2logpdf_dlink2, dlink_df, dlogpdf_dlink, d2link_df2) dlink_df = self.gp_link.dtransf_df(f)
dlogpdf_dlink = self.dlogpdf_dlink(inv_link_f, y, Y_metadata=Y_metadata)
d2link_df2 = self.gp_link.d2transf_df2(f)
d2logpdf_df2 = chain_2(d2logpdf_dlink2, dlink_df, dlogpdf_dlink, d2link_df2)
return d2logpdf_df2
@blockify_third
def d3logpdf_df3(self, f, y, Y_metadata=None): def d3logpdf_df3(self, f, y, Y_metadata=None):
""" """
Evaluates the link function link(f) then computes the third derivative of log likelihood using it Evaluates the link function link(f) then computes the third derivative of log likelihood using it
@ -380,64 +419,96 @@ class Likelihood(Parameterized):
:returns: third derivative of log likelihood evaluated for this point :returns: third derivative of log likelihood evaluated for this point
:rtype: float :rtype: float
""" """
inv_link_f = self.gp_link.transf(f) if isinstance(self.gp_link, link_functions.Identity):
d3logpdf_dlink3 = self.d3logpdf_dlink3(inv_link_f, y, Y_metadata=Y_metadata) d3logpdf_df3 = self.d3logpdf_dlink3(f, y, Y_metadata=Y_metadata)
dlink_df = self.gp_link.dtransf_df(f) else:
d2logpdf_dlink2 = self.d2logpdf_dlink2(inv_link_f, y, Y_metadata=Y_metadata) inv_link_f = self.gp_link.transf(f)
d2link_df2 = self.gp_link.d2transf_df2(f) d3logpdf_dlink3 = self.d3logpdf_dlink3(inv_link_f, y, Y_metadata=Y_metadata)
dlogpdf_dlink = self.dlogpdf_dlink(inv_link_f, y, Y_metadata=Y_metadata) dlink_df = self.gp_link.dtransf_df(f)
d3link_df3 = self.gp_link.d3transf_df3(f) d2logpdf_dlink2 = self.d2logpdf_dlink2(inv_link_f, y, Y_metadata=Y_metadata)
return chain_3(d3logpdf_dlink3, dlink_df, d2logpdf_dlink2, d2link_df2, dlogpdf_dlink, d3link_df3) d2link_df2 = self.gp_link.d2transf_df2(f)
dlogpdf_dlink = self.dlogpdf_dlink(inv_link_f, y, Y_metadata=Y_metadata)
d3link_df3 = self.gp_link.d3transf_df3(f)
d3logpdf_df3 = chain_3(d3logpdf_dlink3, dlink_df, d2logpdf_dlink2, d2link_df2, dlogpdf_dlink, d3link_df3)
return d3logpdf_df3
def dlogpdf_dtheta(self, f, y, Y_metadata=None): def dlogpdf_dtheta(self, f, y, Y_metadata=None):
""" """
TODO: Doc strings TODO: Doc strings
""" """
if self.size > 0: if self.size > 0:
inv_link_f = self.gp_link.transf(f) if self.not_block_really:
return self.dlogpdf_link_dtheta(inv_link_f, y, Y_metadata=Y_metadata) raise NotImplementedError("Need to make a decorator for this!")
if isinstance(self.gp_link, link_functions.Identity):
return self.dlogpdf_link_dtheta(f, y, Y_metadata=Y_metadata)
else:
inv_link_f = self.gp_link.transf(f)
return self.dlogpdf_link_dtheta(inv_link_f, y, Y_metadata=Y_metadata)
else: else:
# There are no parameters so return an empty array for derivatives # There are no parameters so return an empty array for derivatives
return np.zeros([1, 0]) return np.zeros((0, f.shape[0], f.shape[1]))
def dlogpdf_df_dtheta(self, f, y, Y_metadata=None): def dlogpdf_df_dtheta(self, f, y, Y_metadata=None):
""" """
TODO: Doc strings TODO: Doc strings
""" """
if self.size > 0: if self.size > 0:
inv_link_f = self.gp_link.transf(f) if self.not_block_really:
dlink_df = self.gp_link.dtransf_df(f) raise NotImplementedError("Need to make a decorator for this!")
dlogpdf_dlink_dtheta = self.dlogpdf_dlink_dtheta(inv_link_f, y, Y_metadata=Y_metadata) if isinstance(self.gp_link, link_functions.Identity):
return chain_1(dlogpdf_dlink_dtheta, dlink_df) return self.dlogpdf_dlink_dtheta(f, y, Y_metadata=Y_metadata)
else:
inv_link_f = self.gp_link.transf(f)
dlink_df = self.gp_link.dtransf_df(f)
dlogpdf_dlink_dtheta = self.dlogpdf_dlink_dtheta(inv_link_f, y, Y_metadata=Y_metadata)
dlogpdf_df_dtheta = np.zeros((self.size, f.shape[0], f.shape[1]))
#Chain each parameter of hte likelihood seperately
for p in range(self.size):
dlogpdf_df_dtheta[p, :, :] = chain_1(dlogpdf_dlink_dtheta[p,:,:], dlink_df)
return dlogpdf_df_dtheta
#return chain_1(dlogpdf_dlink_dtheta, dlink_df)
else: else:
# There are no parameters so return an empty array for derivatives # There are no parameters so return an empty array for derivatives
return np.zeros([f.shape[0], 0]) return np.zeros((0, f.shape[0], f.shape[1]))
def d2logpdf_df2_dtheta(self, f, y, Y_metadata=None): def d2logpdf_df2_dtheta(self, f, y, Y_metadata=None):
""" """
TODO: Doc strings TODO: Doc strings
""" """
if self.size > 0: if self.size > 0:
inv_link_f = self.gp_link.transf(f) if self.not_block_really:
dlink_df = self.gp_link.dtransf_df(f) raise NotImplementedError("Need to make a decorator for this!")
d2link_df2 = self.gp_link.d2transf_df2(f) if isinstance(self.gp_link, link_functions.Identity):
d2logpdf_dlink2_dtheta = self.d2logpdf_dlink2_dtheta(inv_link_f, y, Y_metadata=Y_metadata) return self.d2logpdf_dlink2_dtheta(f, y, Y_metadata=Y_metadata)
dlogpdf_dlink_dtheta = self.dlogpdf_dlink_dtheta(inv_link_f, y, Y_metadata=Y_metadata) else:
return chain_2(d2logpdf_dlink2_dtheta, dlink_df, dlogpdf_dlink_dtheta, d2link_df2) inv_link_f = self.gp_link.transf(f)
dlink_df = self.gp_link.dtransf_df(f)
d2link_df2 = self.gp_link.d2transf_df2(f)
d2logpdf_dlink2_dtheta = self.d2logpdf_dlink2_dtheta(inv_link_f, y, Y_metadata=Y_metadata)
dlogpdf_dlink_dtheta = self.dlogpdf_dlink_dtheta(inv_link_f, y, Y_metadata=Y_metadata)
d2logpdf_df2_dtheta = np.zeros((self.size, f.shape[0], f.shape[1]))
#Chain each parameter of hte likelihood seperately
for p in range(self.size):
d2logpdf_df2_dtheta[p, :, :] = chain_2(d2logpdf_dlink2_dtheta[p,:,:], dlink_df, dlogpdf_dlink_dtheta[p,:,:], d2link_df2)
return d2logpdf_df2_dtheta
#return chain_2(d2logpdf_dlink2_dtheta, dlink_df, dlogpdf_dlink_dtheta, d2link_df2)
else: else:
# There are no parameters so return an empty array for derivatives # There are no parameters so return an empty array for derivatives
return np.zeros([f.shape[0], 0]) return np.zeros((0, f.shape[0], f.shape[1]))
def _laplace_gradients(self, f, y, Y_metadata=None): def _laplace_gradients(self, f, y, Y_metadata=None):
dlogpdf_dtheta = self.dlogpdf_dtheta(f, y, Y_metadata=Y_metadata).sum(axis=0) dlogpdf_dtheta = self.dlogpdf_dtheta(f, y, Y_metadata=Y_metadata)
dlogpdf_df_dtheta = self.dlogpdf_df_dtheta(f, y, Y_metadata=Y_metadata) dlogpdf_df_dtheta = self.dlogpdf_df_dtheta(f, y, Y_metadata=Y_metadata)
d2logpdf_df2_dtheta = self.d2logpdf_df2_dtheta(f, y, Y_metadata=Y_metadata) d2logpdf_df2_dtheta = self.d2logpdf_df2_dtheta(f, y, Y_metadata=Y_metadata)
#Parameters are stacked vertically. Must be listed in same order as 'get_param_names' #Parameters are stacked vertically. Must be listed in same order as 'get_param_names'
# ensure we have gradients for every parameter we want to optimize # ensure we have gradients for every parameter we want to optimize
assert len(dlogpdf_dtheta) == self.size #1 x num_param array assert dlogpdf_dtheta.shape[0] == self.size #f, d x num_param array
assert dlogpdf_df_dtheta.shape[1] == self.size #f x num_param matrix assert dlogpdf_df_dtheta.shape[0] == self.size #f x d x num_param matrix or just f x num_param
assert d2logpdf_df2_dtheta.shape[1] == self.size #f x num_param matrix assert d2logpdf_df2_dtheta.shape[0] == self.size #f x num_param matrix or f x d x num_param matrix, f x f x num_param or f x f x d x num_param
return dlogpdf_dtheta, dlogpdf_df_dtheta, d2logpdf_df2_dtheta return dlogpdf_dtheta, dlogpdf_df_dtheta, d2logpdf_df2_dtheta
@ -458,19 +529,98 @@ class Likelihood(Parameterized):
def predictive_quantiles(self, mu, var, quantiles, Y_metadata=None): def predictive_quantiles(self, mu, var, quantiles, Y_metadata=None):
#compute the quantiles by sampling!!! #compute the quantiles by sampling!!!
N_samp = 1000 N_samp = 500
s = np.random.randn(mu.shape[0], N_samp)*np.sqrt(var) + mu s = np.random.randn(mu.shape[0], N_samp)*np.sqrt(var) + mu
#ss_f = s.flatten() #ss_f = s.flatten()
#ss_y = self.samples(ss_f, Y_metadata) #ss_y = self.samples(ss_f, Y_metadata)
#ss_y = self.samples(s, Y_metadata, samples=100)
ss_y = self.samples(s, Y_metadata) ss_y = self.samples(s, Y_metadata)
#ss_y = ss_y.reshape(mu.shape[0], N_samp) #ss_y = ss_y.reshape(mu.shape[0], N_samp)
return [np.percentile(ss_y ,q, axis=1)[:,None] for q in quantiles] return [np.percentile(ss_y ,q, axis=1)[:,None] for q in quantiles]
def samples(self, gp, Y_metadata=None): def samples(self, gp, Y_metadata=None, samples=1):
""" """
Returns a set of samples of observations based on a given value of the latent variable. Returns a set of samples of observations based on a given value of the latent variable.
:param gp: latent variable :param gp: latent variable
:param samples: number of samples to take for each f location
""" """
raise NotImplementedError raise NotImplementedError("""May be possible to use MCMC with user-tuning, see
MCMC_pdf_samples in likelihood.py and write samples function
using this, beware this is a simple implementation
of Metropolis and will not work well for all likelihoods""")
def MCMC_pdf_samples(self, fNew, num_samples=1000, starting_loc=None, stepsize=0.1, burn_in=1000, Y_metadata=None):
"""
Simple implementation of Metropolis sampling algorithm
Will run a parallel chain for each input dimension (treats each f independently)
Thus assumes f*_1 independant of f*_2 etc.
:param num_samples: Number of samples to take
:param fNew: f at which to sample around
:param starting_loc: Starting locations of the independant chains (usually will be conditional_mean of likelihood), often link_f
:param stepsize: Stepsize for the normal proposal distribution (will need modifying)
:param burnin: number of samples to use for burnin (will need modifying)
:param Y_metadata: Y_metadata for pdf
"""
print "Warning, using MCMC for sampling y*, needs to be tuned!"
if starting_loc is None:
starting_loc = fNew
from functools import partial
logpdf = partial(self.logpdf, f=fNew, Y_metadata=Y_metadata)
pdf = lambda y_star: np.exp(logpdf(y=y_star[:, None]))
#Should be the link function of f is a good starting point
#(i.e. the point before you corrupt it with the likelihood)
par_chains = starting_loc.shape[0]
chain_values = np.zeros((par_chains, num_samples))
chain_values[:, 0][:,None] = starting_loc
#Use same stepsize for all par_chains
stepsize = np.ones(par_chains)*stepsize
accepted = np.zeros((par_chains, num_samples+burn_in))
accept_ratio = np.zeros(num_samples+burn_in)
#Whilst burning in, only need to keep the previous lot
burnin_cache = np.zeros(par_chains)
burnin_cache[:] = starting_loc.flatten()
burning_in = True
for i in xrange(burn_in+num_samples):
next_ind = i-burn_in
if burning_in:
old_y = burnin_cache
else:
old_y = chain_values[:,next_ind-1]
old_lik = pdf(old_y)
#Propose new y from Gaussian proposal
new_y = np.random.normal(loc=old_y, scale=stepsize)
new_lik = pdf(new_y)
#Accept using Metropolis (not hastings) acceptance
#Always accepts if new_lik > old_lik
accept_probability = np.minimum(1, new_lik/old_lik)
u = np.random.uniform(0,1,par_chains)
#print "Accept prob: ", accept_probability
accepts = u < accept_probability
if burning_in:
burnin_cache[accepts] = new_y[accepts]
burnin_cache[~accepts] = old_y[~accepts]
if i == burn_in:
burning_in = False
chain_values[:,0] = burnin_cache
else:
#If it was accepted then new_y becomes the latest sample
chain_values[accepts, next_ind] = new_y[accepts]
#Otherwise use old y as the sample
chain_values[~accepts, next_ind] = old_y[~accepts]
accepted[~accepts, i] = 0
accepted[accepts, i] = 1
accept_ratio[i] = np.sum(accepted[:,i])/float(par_chains)
#Show progress
if i % int((burn_in+num_samples)*0.1) == 0:
print "{}% of samples taken ({})".format((i/int((burn_in+num_samples)*0.1)*10), i)
print "Last run accept ratio: ", accept_ratio[i]
print "Average accept ratio: ", np.mean(accept_ratio)
return chain_values

5
GPy/likelihoods/student_t.py
View file

@ -232,12 +232,13 @@ class StudentT(Likelihood):
def dlogpdf_dlink_dtheta(self, f, y, Y_metadata=None): def dlogpdf_dlink_dtheta(self, f, y, Y_metadata=None):
dlogpdf_dlink_dvar = self.dlogpdf_dlink_dvar(f, y, Y_metadata=Y_metadata) dlogpdf_dlink_dvar = self.dlogpdf_dlink_dvar(f, y, Y_metadata=Y_metadata)
dlogpdf_dlink_dv = np.zeros_like(dlogpdf_dlink_dvar) #FIXME: Not done yet dlogpdf_dlink_dv = np.zeros_like(dlogpdf_dlink_dvar) #FIXME: Not done yet
return np.hstack((dlogpdf_dlink_dvar, dlogpdf_dlink_dv)) return np.array((dlogpdf_dlink_dvar, dlogpdf_dlink_dv))
def d2logpdf_dlink2_dtheta(self, f, y, Y_metadata=None): def d2logpdf_dlink2_dtheta(self, f, y, Y_metadata=None):
d2logpdf_dlink2_dvar = self.d2logpdf_dlink2_dvar(f, y, Y_metadata=Y_metadata) d2logpdf_dlink2_dvar = self.d2logpdf_dlink2_dvar(f, y, Y_metadata=Y_metadata)
d2logpdf_dlink2_dv = np.zeros_like(d2logpdf_dlink2_dvar) #FIXME: Not done yet d2logpdf_dlink2_dv = np.zeros_like(d2logpdf_dlink2_dvar) #FIXME: Not done yet
return np.hstack((d2logpdf_dlink2_dvar, d2logpdf_dlink2_dv))
return np.array((d2logpdf_dlink2_dvar, d2logpdf_dlink2_dv))
def predictive_mean(self, mu, sigma, Y_metadata=None): def predictive_mean(self, mu, sigma, Y_metadata=None):
# The comment here confuses mean and median. # The comment here confuses mean and median.

5
GPy/models/ss_gplvm.py
View file

@ -39,7 +39,10 @@ class SSGPLVM(SparseGP_MPI):
X_variance = np.random.uniform(0,.1,X.shape) X_variance = np.random.uniform(0,.1,X.shape)
if Gamma is None: if Gamma is None:
gamma = np.random.randn(X.shape[0], input_dim) gamma = np.empty_like(X) # The posterior probabilities of the binary variable in the variational approximation
gamma[:] = 0.5 + 0.1 * np.random.randn(X.shape[0], input_dim)
gamma[gamma>1.-1e-9] = 1.-1e-9
gamma[gamma<1e-9] = 1e-9
else: else:
gamma = Gamma.copy() gamma = Gamma.copy()

8
GPy/testing/inference_tests.py
View file

@ -14,7 +14,6 @@ class InferenceXTestCase(unittest.TestCase):
def genData(self): def genData(self):
D1,D2,N = 12,12,50 D1,D2,N = 12,12,50
np.random.seed(1234)
x = np.linspace(0, 4 * np.pi, N)[:, None] x = np.linspace(0, 4 * np.pi, N)[:, None]
s1 = np.vectorize(lambda x: np.sin(x)) s1 = np.vectorize(lambda x: np.sin(x))
@ -63,10 +62,11 @@ class InferenceXTestCase(unittest.TestCase):
self.assertTrue(mi.checkgrad()) self.assertTrue(mi.checkgrad())
m.optimize(max_iters=10000) m.optimize(max_iters=10000)
x,mi = m.infer_newX(m.Y) x, mi = m.infer_newX(m.Y)
self.assertTrue(np.allclose(m.X.mean, mi.X.mean)) print m.X.mean - mi.X.mean
self.assertTrue(np.allclose(m.X.variance, mi.X.variance)) self.assertTrue(np.allclose(m.X.mean, mi.X.mean, rtol=1e-4, atol=1e-4))
self.assertTrue(np.allclose(m.X.variance, mi.X.variance, rtol=1e-4, atol=1e-4))
def test_inferenceX_GPLVM(self): def test_inferenceX_GPLVM(self):
Ys = self.genData() Ys = self.genData()

472
GPy/testing/likelihood_tests.py
View file

@ -10,7 +10,7 @@ from GPy.likelihoods import link_functions
from GPy.core.parameterization import Param from GPy.core.parameterization import Param
from functools import partial from functools import partial
#np.random.seed(300) #np.random.seed(300)
#np.random.seed(7) #np.random.seed(4)
#np.seterr(divide='raise') #np.seterr(divide='raise')
def dparam_partial(inst_func, *args): def dparam_partial(inst_func, *args):
@ -52,8 +52,17 @@ def dparam_checkgrad(func, dfunc, params, params_names, args, constraints=None,
zipped_params = zip(params, params_names) zipped_params = zip(params, params_names)
for param_ind, (param_val, param_name) in enumerate(zipped_params): for param_ind, (param_val, param_name) in enumerate(zipped_params):
#Check one parameter at a time, make sure it is 2d (as some gradients only return arrays) then strip out the parameter #Check one parameter at a time, make sure it is 2d (as some gradients only return arrays) then strip out the parameter
fnum = np.atleast_2d(partial_f(param_val, param_name))[:, param_ind].shape[0] f_ = partial_f(param_val, param_name)
dfnum = np.atleast_2d(partial_df(param_val, param_name))[:, param_ind].shape[0] df_ = partial_df(param_val, param_name)
#Reshape it such that we have a 3d matrix incase, that is we want it (?, N, D) regardless of whether ? is num_params or not
f_ = f_.reshape(-1, f_.shape[0], f_.shape[1])
df_ = df_.reshape(-1, f_.shape[0], f_.shape[1])
#Get the number of f and number of dimensions
fnum = f_.shape[-2]
fdim = f_.shape[-1]
dfnum = df_.shape[-2]
for fixed_val in range(dfnum): for fixed_val in range(dfnum):
#dlik and dlik_dvar gives back 1 value for each #dlik and dlik_dvar gives back 1 value for each
f_ind = min(fnum, fixed_val+1) - 1 f_ind = min(fnum, fixed_val+1) - 1
@ -61,9 +70,13 @@ def dparam_checkgrad(func, dfunc, params, params_names, args, constraints=None,
#Make grad checker with this param moving, note that set_params is NOT being called #Make grad checker with this param moving, note that set_params is NOT being called
#The parameter is being set directly with __setattr__ #The parameter is being set directly with __setattr__
#Check only the parameter and function value we wish to check at a time #Check only the parameter and function value we wish to check at a time
grad = GradientChecker(lambda p_val: np.atleast_2d(partial_f(p_val, param_name))[f_ind, param_ind], #func = lambda p_val, fnum, fdim, param_ind, f_ind, param_ind: partial_f(p_val, param_name).reshape(-1, fnum, fdim)[param_ind, f_ind, :]
lambda p_val: np.atleast_2d(partial_df(p_val, param_name))[fixed_val, param_ind], #dfunc_dparam = lambda d_val, fnum, fdim, param_ind, fixed_val: partial_df(d_val, param_name).reshape(-1, fnum, fdim)[param_ind, fixed_val, :]
param_val, [param_name])
#First we reshape the output such that it is (num_params, N, D) then we pull out the relavent parameter-findex and checkgrad just this index at a time
func = lambda p_val: partial_f(p_val, param_name).reshape(-1, fnum, fdim)[param_ind, f_ind, :]
dfunc_dparam = lambda d_val: partial_df(d_val, param_name).reshape(-1, fnum, fdim)[param_ind, fixed_val, :]
grad = GradientChecker(func, dfunc_dparam, param_val, [param_name])
if constraints is not None: if constraints is not None:
for constrain_param, constraint in constraints: for constrain_param, constraint in constraints:
@ -104,37 +117,9 @@ class TestNoiseModels(object):
self.var = 0.2 self.var = 0.2
self.var = np.random.rand(1)
#Make a bigger step as lower bound can be quite curved #Make a bigger step as lower bound can be quite curved
self.step = 1e-4 self.step = 1e-4
def tearDown(self):
self.Y = None
self.f = None
self.X = None
def test_scale2_models(self):
self.setUp()
####################################################
# Constraint wrappers so we can just list them off #
####################################################
def constrain_fixed(regex, model):
model[regex].constrain_fixed()
def constrain_negative(regex, model):
model[regex].constrain_negative()
def constrain_positive(regex, model):
model[regex].constrain_positive()
def constrain_bounded(regex, model, lower, upper):
"""
Used like: partial(constrain_bounded, lower=0, upper=1)
"""
model[regex].constrain_bounded(lower, upper)
""" """
Dictionary where we nest models we would like to check Dictionary where we nest models we would like to check
Name: { Name: {
@ -149,136 +134,170 @@ class TestNoiseModels(object):
"link_f_constraints": [constraint_wrappers, listed_here] "link_f_constraints": [constraint_wrappers, listed_here]
} }
""" """
noise_models = {"Student_t_default": { self.noise_models = {"Student_t_default": {
"model": GPy.likelihoods.StudentT(deg_free=5, sigma2=self.var), "model": GPy.likelihoods.StudentT(deg_free=5, sigma2=self.var),
"grad_params": { "grad_params": {
"names": [".*t_scale2"], "names": [".*t_scale2"],
"vals": [self.var], "vals": [self.var],
"constraints": [(".*t_scale2", constrain_positive), (".*deg_free", constrain_fixed)] "constraints": [(".*t_scale2", self.constrain_positive), (".*deg_free", self.constrain_fixed)]
#"constraints": [("t_scale2", constrain_positive), ("deg_free", partial(constrain_fixed, value=5))] },
}, "laplace": True
"laplace": True },
}, "Student_t_1_var": {
"Student_t_1_var": { "model": GPy.likelihoods.StudentT(deg_free=5, sigma2=self.var),
"model": GPy.likelihoods.StudentT(deg_free=5, sigma2=self.var), "grad_params": {
"grad_params": { "names": [".*t_scale2"],
"names": [".*t_scale2"], "vals": [1.0],
"vals": [1.0], "constraints": [(".*t_scale2", self.constrain_positive), (".*deg_free", self.constrain_fixed)]
"constraints": [(".*t_scale2", constrain_positive), (".*deg_free", constrain_fixed)] },
}, "laplace": True
"laplace": True },
}, "Student_t_small_deg_free": {
"Student_t_small_deg_free": { "model": GPy.likelihoods.StudentT(deg_free=1.5, sigma2=self.var),
"model": GPy.likelihoods.StudentT(deg_free=1.5, sigma2=self.var), "grad_params": {
"grad_params": { "names": [".*t_scale2"],
"names": [".*t_scale2"], "vals": [self.var],
"vals": [self.var], "constraints": [(".*t_scale2", self.constrain_positive), (".*deg_free", self.constrain_fixed)]
"constraints": [(".*t_scale2", constrain_positive), (".*deg_free", constrain_fixed)] },
}, "laplace": True
"laplace": True },
}, "Student_t_small_var": {
"Student_t_small_var": { "model": GPy.likelihoods.StudentT(deg_free=5, sigma2=self.var),
"model": GPy.likelihoods.StudentT(deg_free=5, sigma2=self.var), "grad_params": {
"grad_params": { "names": [".*t_scale2"],
"names": [".*t_scale2"], "vals": [0.001],
"vals": [0.001], "constraints": [(".*t_scale2", self.constrain_positive), (".*deg_free", self.constrain_fixed)]
"constraints": [(".*t_scale2", constrain_positive), (".*deg_free", constrain_fixed)] },
}, "laplace": True
"laplace": True },
}, "Student_t_large_var": {
"Student_t_large_var": { "model": GPy.likelihoods.StudentT(deg_free=5, sigma2=self.var),
"model": GPy.likelihoods.StudentT(deg_free=5, sigma2=self.var), "grad_params": {
"grad_params": { "names": [".*t_scale2"],
"names": [".*t_scale2"], "vals": [10.0],
"vals": [10.0], "constraints": [(".*t_scale2", self.constrain_positive), (".*deg_free", self.constrain_fixed)]
"constraints": [(".*t_scale2", constrain_positive), (".*deg_free", constrain_fixed)] },
}, "laplace": True
"laplace": True },
}, "Student_t_approx_gauss": {
"Student_t_approx_gauss": { "model": GPy.likelihoods.StudentT(deg_free=1000, sigma2=self.var),
"model": GPy.likelihoods.StudentT(deg_free=1000, sigma2=self.var), "grad_params": {
"grad_params": { "names": [".*t_scale2"],
"names": [".*t_scale2"], "vals": [self.var],
"vals": [self.var], "constraints": [(".*t_scale2", self.constrain_positive), (".*deg_free", self.constrain_fixed)]
"constraints": [(".*t_scale2", constrain_positive), (".*deg_free", constrain_fixed)] },
}, "laplace": True
"laplace": True },
}, #"Student_t_log": {
"Student_t_log": { #"model": GPy.likelihoods.StudentT(gp_link=link_functions.Log(), deg_free=5, sigma2=self.var),
"model": GPy.likelihoods.StudentT(gp_link=link_functions.Log(), deg_free=5, sigma2=self.var), #"grad_params": {
"grad_params": { #"names": [".*t_noise"],
"names": [".*t_scale2"], #"vals": [self.var],
"vals": [self.var], #"constraints": [(".*t_noise", self.constrain_positive), (".*deg_free", self.constrain_fixed)]
"constraints": [(".*t_scale2", constrain_positive), (".*deg_free", constrain_fixed)] #},
}, #"laplace": True
"laplace": True #},
}, "Gaussian_default": {
"Gaussian_default": { "model": GPy.likelihoods.Gaussian(variance=self.var),
"model": GPy.likelihoods.Gaussian(variance=self.var), "grad_params": {
"grad_params": { "names": [".*variance"],
"names": [".*variance"], "vals": [self.var],
"vals": [self.var], "constraints": [(".*variance", self.constrain_positive)]
"constraints": [(".*variance", constrain_positive)] },
}, "laplace": True,
"laplace": True, "ep": False # FIXME: Should be True when we have it working again
"ep": False # FIXME: Should be True when we have it working again },
}, "Gaussian_log": {
#"Gaussian_log": { "model": GPy.likelihoods.Gaussian(gp_link=link_functions.Log(), variance=self.var),
#"model": GPy.likelihoods.gaussian(gp_link=link_functions.Log(), variance=self.var, D=self.D, N=self.N), "grad_params": {
#"grad_params": { "names": [".*variance"],
#"names": ["noise_model_variance"], "vals": [self.var],
#"vals": [self.var], "constraints": [(".*variance", self.constrain_positive)]
#"constraints": [constrain_positive] },
#}, "laplace": True
#"laplace": True },
#}, #"Gaussian_probit": {
#"Gaussian_probit": { #"model": GPy.likelihoods.gaussian(gp_link=link_functions.Probit(), variance=self.var, D=self.D, N=self.N),
#"model": GPy.likelihoods.gaussian(gp_link=link_functions.Probit(), variance=self.var, D=self.D, N=self.N), #"grad_params": {
#"grad_params": { #"names": ["noise_model_variance"],
#"names": ["noise_model_variance"], #"vals": [self.var],
#"vals": [self.var], #"constraints": [constrain_positive]
#"constraints": [constrain_positive] #},
#}, #"laplace": True
#"laplace": True #},
#}, #"Gaussian_log_ex": {
#"Gaussian_log_ex": { #"model": GPy.likelihoods.gaussian(gp_link=link_functions.Log_ex_1(), variance=self.var, D=self.D, N=self.N),
#"model": GPy.likelihoods.gaussian(gp_link=link_functions.Log_ex_1(), variance=self.var, D=self.D, N=self.N), #"grad_params": {
#"grad_params": { #"names": ["noise_model_variance"],
#"names": ["noise_model_variance"], #"vals": [self.var],
#"vals": [self.var], #"constraints": [constrain_positive]
#"constraints": [constrain_positive] #},
#}, #"laplace": True
#"laplace": True #},
#}, "Bernoulli_default": {
"Bernoulli_default": { "model": GPy.likelihoods.Bernoulli(),
"model": GPy.likelihoods.Bernoulli(), "link_f_constraints": [partial(self.constrain_bounded, lower=0, upper=1)],
"link_f_constraints": [partial(constrain_bounded, lower=0, upper=1)], "laplace": True,
"laplace": True, "Y": self.binary_Y,
"Y": self.binary_Y, "ep": False # FIXME: Should be True when we have it working again
"ep": False # FIXME: Should be True when we have it working again },
}, "Exponential_default": {
"Exponential_default": { "model": GPy.likelihoods.Exponential(),
"model": GPy.likelihoods.Exponential(), "link_f_constraints": [self.constrain_positive],
"link_f_constraints": [constrain_positive], "Y": self.positive_Y,
"Y": self.positive_Y, "laplace": True,
"laplace": True, },
}, "Poisson_default": {
"Poisson_default": { "model": GPy.likelihoods.Poisson(),
"model": GPy.likelihoods.Poisson(), "link_f_constraints": [self.constrain_positive],
"link_f_constraints": [constrain_positive], "Y": self.integer_Y,
"Y": self.integer_Y, "laplace": True,
"laplace": True, "ep": False #Should work though...
"ep": False #Should work though... },
}#, #,
#GAMMA needs some work!"Gamma_default": { #GAMMA needs some work!"Gamma_default": {
#"model": GPy.likelihoods.Gamma(), #"model": GPy.likelihoods.Gamma(),
#"link_f_constraints": [constrain_positive], #"link_f_constraints": [constrain_positive],
#"Y": self.positive_Y, #"Y": self.positive_Y,
#"laplace": True #"laplace": True
#} #}
} }
for name, attributes in noise_models.iteritems():
####################################################
# Constraint wrappers so we can just list them off #
####################################################
def constrain_fixed(self, regex, model):
model[regex].constrain_fixed()
def constrain_negative(self, regex, model):
model[regex].constrain_negative()
def constrain_positive(self, regex, model):
model[regex].constrain_positive()
def constrain_fixed_below(self, regex, model, up_to):
model[regex][0:up_to].constrain_fixed()
def constrain_fixed_above(self, regex, model, above):
model[regex][above:].constrain_fixed()
def constrain_bounded(self, regex, model, lower, upper):
"""
Used like: partial(constrain_bounded, lower=0, upper=1)
"""
model[regex].constrain_bounded(lower, upper)
def tearDown(self):
self.Y = None
self.f = None
self.X = None
def test_scale2_models(self):
self.setUp()
for name, attributes in self.noise_models.iteritems():
model = attributes["model"] model = attributes["model"]
if "grad_params" in attributes: if "grad_params" in attributes:
params = attributes["grad_params"] params = attributes["grad_params"]
@ -290,7 +309,7 @@ class TestNoiseModels(object):
param_vals = [] param_vals = []
param_names = [] param_names = []
constrain_positive = [] constrain_positive = []
param_constraints = [] # ??? TODO: Saul to Fix. param_constraints = []
if "link_f_constraints" in attributes: if "link_f_constraints" in attributes:
link_f_constraints = attributes["link_f_constraints"] link_f_constraints = attributes["link_f_constraints"]
else: else:
@ -303,6 +322,10 @@ class TestNoiseModels(object):
f = attributes["f"].copy() f = attributes["f"].copy()
else: else:
f = self.f.copy() f = self.f.copy()
if "Y_metadata" in attributes:
Y_metadata = attributes["Y_metadata"].copy()
else:
Y_metadata = None
if "laplace" in attributes: if "laplace" in attributes:
laplace = attributes["laplace"] laplace = attributes["laplace"]
else: else:
@ -317,30 +340,30 @@ class TestNoiseModels(object):
#Required by all #Required by all
#Normal derivatives #Normal derivatives
yield self.t_logpdf, model, Y, f yield self.t_logpdf, model, Y, f, Y_metadata
yield self.t_dlogpdf_df, model, Y, f yield self.t_dlogpdf_df, model, Y, f, Y_metadata
yield self.t_d2logpdf_df2, model, Y, f yield self.t_d2logpdf_df2, model, Y, f, Y_metadata
#Link derivatives #Link derivatives
yield self.t_dlogpdf_dlink, model, Y, f, link_f_constraints yield self.t_dlogpdf_dlink, model, Y, f, Y_metadata, link_f_constraints
yield self.t_d2logpdf_dlink2, model, Y, f, link_f_constraints yield self.t_d2logpdf_dlink2, model, Y, f, Y_metadata, link_f_constraints
if laplace: if laplace:
#Laplace only derivatives #Laplace only derivatives
yield self.t_d3logpdf_df3, model, Y, f yield self.t_d3logpdf_df3, model, Y, f, Y_metadata
yield self.t_d3logpdf_dlink3, model, Y, f, link_f_constraints yield self.t_d3logpdf_dlink3, model, Y, f, Y_metadata, link_f_constraints
#Params #Params
yield self.t_dlogpdf_dparams, model, Y, f, param_vals, param_names, param_constraints yield self.t_dlogpdf_dparams, model, Y, f, Y_metadata, param_vals, param_names, param_constraints
yield self.t_dlogpdf_df_dparams, model, Y, f, param_vals, param_names, param_constraints yield self.t_dlogpdf_df_dparams, model, Y, f, Y_metadata, param_vals, param_names, param_constraints
yield self.t_d2logpdf2_df2_dparams, model, Y, f, param_vals, param_names, param_constraints yield self.t_d2logpdf2_df2_dparams, model, Y, f, Y_metadata, param_vals, param_names, param_constraints
#Link params #Link params
yield self.t_dlogpdf_link_dparams, model, Y, f, param_vals, param_names, param_constraints yield self.t_dlogpdf_link_dparams, model, Y, f, Y_metadata, param_vals, param_names, param_constraints
yield self.t_dlogpdf_dlink_dparams, model, Y, f, param_vals, param_names, param_constraints yield self.t_dlogpdf_dlink_dparams, model, Y, f, Y_metadata, param_vals, param_names, param_constraints
yield self.t_d2logpdf2_dlink2_dparams, model, Y, f, param_vals, param_names, param_constraints yield self.t_d2logpdf2_dlink2_dparams, model, Y, f, Y_metadata, param_vals, param_names, param_constraints
#laplace likelihood gradcheck #laplace likelihood gradcheck
yield self.t_laplace_fit_rbf_white, model, self.X, Y, f, self.step, param_vals, param_names, param_constraints yield self.t_laplace_fit_rbf_white, model, self.X, Y, f, Y_metadata, self.step, param_vals, param_names, param_constraints
if ep: if ep:
#ep likelihood gradcheck #ep likelihood gradcheck
yield self.t_ep_fit_rbf_white, model, self.X, Y, f, self.step, param_vals, param_names, param_constraints yield self.t_ep_fit_rbf_white, model, self.X, Y, f, Y_metadata, self.step, param_vals, param_names, param_constraints
self.tearDown() self.tearDown()
@ -349,41 +372,41 @@ class TestNoiseModels(object):
# dpdf_df's # # dpdf_df's #
############# #############
@with_setup(setUp, tearDown) @with_setup(setUp, tearDown)
def t_logpdf(self, model, Y, f): def t_logpdf(self, model, Y, f, Y_metadata):
print "\n{}".format(inspect.stack()[0][3]) print "\n{}".format(inspect.stack()[0][3])
print model print model
#print model._get_params() #print model._get_params()
np.testing.assert_almost_equal( np.testing.assert_almost_equal(
model.pdf(f.copy(), Y.copy()).prod(), model.pdf(f.copy(), Y.copy(), Y_metadata=Y_metadata).prod(),
np.exp(model.logpdf(f.copy(), Y.copy()).sum()) np.exp(model.logpdf(f.copy(), Y.copy(), Y_metadata=Y_metadata).sum())
) )
@with_setup(setUp, tearDown) @with_setup(setUp, tearDown)
def t_dlogpdf_df(self, model, Y, f): def t_dlogpdf_df(self, model, Y, f, Y_metadata):
print "\n{}".format(inspect.stack()[0][3]) print "\n{}".format(inspect.stack()[0][3])
self.description = "\n{}".format(inspect.stack()[0][3]) self.description = "\n{}".format(inspect.stack()[0][3])
logpdf = functools.partial(np.sum(model.logpdf), y=Y) logpdf = functools.partial(np.sum(model.logpdf), y=Y, Y_metadata=Y_metadata)
dlogpdf_df = functools.partial(model.dlogpdf_df, y=Y) dlogpdf_df = functools.partial(model.dlogpdf_df, y=Y, Y_metadata=Y_metadata)
grad = GradientChecker(logpdf, dlogpdf_df, f.copy(), 'g') grad = GradientChecker(logpdf, dlogpdf_df, f.copy(), 'g')
grad.randomize() grad.randomize()
print model print model
assert grad.checkgrad(verbose=1) assert grad.checkgrad(verbose=1)
@with_setup(setUp, tearDown) @with_setup(setUp, tearDown)
def t_d2logpdf_df2(self, model, Y, f): def t_d2logpdf_df2(self, model, Y, f, Y_metadata):
print "\n{}".format(inspect.stack()[0][3]) print "\n{}".format(inspect.stack()[0][3])
dlogpdf_df = functools.partial(model.dlogpdf_df, y=Y) dlogpdf_df = functools.partial(model.dlogpdf_df, y=Y, Y_metadata=Y_metadata)
d2logpdf_df2 = functools.partial(model.d2logpdf_df2, y=Y) d2logpdf_df2 = functools.partial(model.d2logpdf_df2, y=Y, Y_metadata=Y_metadata)
grad = GradientChecker(dlogpdf_df, d2logpdf_df2, f.copy(), 'g') grad = GradientChecker(dlogpdf_df, d2logpdf_df2, f.copy(), 'g')
grad.randomize() grad.randomize()
print model print model
assert grad.checkgrad(verbose=1) assert grad.checkgrad(verbose=1)
@with_setup(setUp, tearDown) @with_setup(setUp, tearDown)
def t_d3logpdf_df3(self, model, Y, f): def t_d3logpdf_df3(self, model, Y, f, Y_metadata):
print "\n{}".format(inspect.stack()[0][3]) print "\n{}".format(inspect.stack()[0][3])
d2logpdf_df2 = functools.partial(model.d2logpdf_df2, y=Y) d2logpdf_df2 = functools.partial(model.d2logpdf_df2, y=Y, Y_metadata=Y_metadata)
d3logpdf_df3 = functools.partial(model.d3logpdf_df3, y=Y) d3logpdf_df3 = functools.partial(model.d3logpdf_df3, y=Y, Y_metadata=Y_metadata)
grad = GradientChecker(d2logpdf_df2, d3logpdf_df3, f.copy(), 'g') grad = GradientChecker(d2logpdf_df2, d3logpdf_df3, f.copy(), 'g')
grad.randomize() grad.randomize()
print model print model
@ -393,32 +416,32 @@ class TestNoiseModels(object):
# df_dparams # # df_dparams #
############## ##############
@with_setup(setUp, tearDown) @with_setup(setUp, tearDown)
def t_dlogpdf_dparams(self, model, Y, f, params, params_names, param_constraints): def t_dlogpdf_dparams(self, model, Y, f, Y_metadata, params, params_names, param_constraints):
print "\n{}".format(inspect.stack()[0][3]) print "\n{}".format(inspect.stack()[0][3])
print model print model
assert ( assert (
dparam_checkgrad(model.logpdf, model.dlogpdf_dtheta, dparam_checkgrad(model.logpdf, model.dlogpdf_dtheta,
params, params_names, args=(f, Y), constraints=param_constraints, params, params_names, args=(f, Y, Y_metadata), constraints=param_constraints,
randomize=False, verbose=True) randomize=False, verbose=True)
) )
@with_setup(setUp, tearDown) @with_setup(setUp, tearDown)
def t_dlogpdf_df_dparams(self, model, Y, f, params, params_names, param_constraints): def t_dlogpdf_df_dparams(self, model, Y, f, Y_metadata, params, params_names, param_constraints):
print "\n{}".format(inspect.stack()[0][3]) print "\n{}".format(inspect.stack()[0][3])
print model print model
assert ( assert (
dparam_checkgrad(model.dlogpdf_df, model.dlogpdf_df_dtheta, dparam_checkgrad(model.dlogpdf_df, model.dlogpdf_df_dtheta,
params, params_names, args=(f, Y), constraints=param_constraints, params, params_names, args=(f, Y, Y_metadata), constraints=param_constraints,
randomize=False, verbose=True) randomize=False, verbose=True)
) )
@with_setup(setUp, tearDown) @with_setup(setUp, tearDown)
def t_d2logpdf2_df2_dparams(self, model, Y, f, params, params_names, param_constraints): def t_d2logpdf2_df2_dparams(self, model, Y, f, Y_metadata, params, params_names, param_constraints):
print "\n{}".format(inspect.stack()[0][3]) print "\n{}".format(inspect.stack()[0][3])
print model print model
assert ( assert (
dparam_checkgrad(model.d2logpdf_df2, model.d2logpdf_df2_dtheta, dparam_checkgrad(model.d2logpdf_df2, model.d2logpdf_df2_dtheta,
params, params_names, args=(f, Y), constraints=param_constraints, params, params_names, args=(f, Y, Y_metadata), constraints=param_constraints,
randomize=False, verbose=True) randomize=False, verbose=True)
) )
@ -426,10 +449,10 @@ class TestNoiseModels(object):
# dpdf_dlink's # # dpdf_dlink's #
################ ################
@with_setup(setUp, tearDown) @with_setup(setUp, tearDown)
def t_dlogpdf_dlink(self, model, Y, f, link_f_constraints): def t_dlogpdf_dlink(self, model, Y, f, Y_metadata, link_f_constraints):
print "\n{}".format(inspect.stack()[0][3]) print "\n{}".format(inspect.stack()[0][3])
logpdf = functools.partial(model.logpdf_link, y=Y) logpdf = functools.partial(model.logpdf_link, y=Y, Y_metadata=Y_metadata)
dlogpdf_dlink = functools.partial(model.dlogpdf_dlink, y=Y) dlogpdf_dlink = functools.partial(model.dlogpdf_dlink, y=Y, Y_metadata=Y_metadata)
grad = GradientChecker(logpdf, dlogpdf_dlink, f.copy(), 'g') grad = GradientChecker(logpdf, dlogpdf_dlink, f.copy(), 'g')
#Apply constraints to link_f values #Apply constraints to link_f values
@ -442,10 +465,10 @@ class TestNoiseModels(object):
assert grad.checkgrad(verbose=1) assert grad.checkgrad(verbose=1)
@with_setup(setUp, tearDown) @with_setup(setUp, tearDown)
def t_d2logpdf_dlink2(self, model, Y, f, link_f_constraints): def t_d2logpdf_dlink2(self, model, Y, f, Y_metadata, link_f_constraints):
print "\n{}".format(inspect.stack()[0][3]) print "\n{}".format(inspect.stack()[0][3])
dlogpdf_dlink = functools.partial(model.dlogpdf_dlink, y=Y) dlogpdf_dlink = functools.partial(model.dlogpdf_dlink, y=Y, Y_metadata=Y_metadata)
d2logpdf_dlink2 = functools.partial(model.d2logpdf_dlink2, y=Y) d2logpdf_dlink2 = functools.partial(model.d2logpdf_dlink2, y=Y, Y_metadata=Y_metadata)
grad = GradientChecker(dlogpdf_dlink, d2logpdf_dlink2, f.copy(), 'g') grad = GradientChecker(dlogpdf_dlink, d2logpdf_dlink2, f.copy(), 'g')
#Apply constraints to link_f values #Apply constraints to link_f values
@ -458,10 +481,10 @@ class TestNoiseModels(object):
assert grad.checkgrad(verbose=1) assert grad.checkgrad(verbose=1)
@with_setup(setUp, tearDown) @with_setup(setUp, tearDown)
def t_d3logpdf_dlink3(self, model, Y, f, link_f_constraints): def t_d3logpdf_dlink3(self, model, Y, f, Y_metadata, link_f_constraints):
print "\n{}".format(inspect.stack()[0][3]) print "\n{}".format(inspect.stack()[0][3])
d2logpdf_dlink2 = functools.partial(model.d2logpdf_dlink2, y=Y) d2logpdf_dlink2 = functools.partial(model.d2logpdf_dlink2, y=Y, Y_metadata=Y_metadata)
d3logpdf_dlink3 = functools.partial(model.d3logpdf_dlink3, y=Y) d3logpdf_dlink3 = functools.partial(model.d3logpdf_dlink3, y=Y, Y_metadata=Y_metadata)
grad = GradientChecker(d2logpdf_dlink2, d3logpdf_dlink3, f.copy(), 'g') grad = GradientChecker(d2logpdf_dlink2, d3logpdf_dlink3, f.copy(), 'g')
#Apply constraints to link_f values #Apply constraints to link_f values
@ -477,32 +500,32 @@ class TestNoiseModels(object):
# dlink_dparams # # dlink_dparams #
################# #################
@with_setup(setUp, tearDown) @with_setup(setUp, tearDown)
def t_dlogpdf_link_dparams(self, model, Y, f, params, param_names, param_constraints): def t_dlogpdf_link_dparams(self, model, Y, f, Y_metadata, params, param_names, param_constraints):
print "\n{}".format(inspect.stack()[0][3]) print "\n{}".format(inspect.stack()[0][3])
print model print model
assert ( assert (
dparam_checkgrad(model.logpdf_link, model.dlogpdf_link_dtheta, dparam_checkgrad(model.logpdf_link, model.dlogpdf_link_dtheta,
params, param_names, args=(f, Y), constraints=param_constraints, params, param_names, args=(f, Y, Y_metadata), constraints=param_constraints,
randomize=False, verbose=True) randomize=False, verbose=True)
) )
@with_setup(setUp, tearDown) @with_setup(setUp, tearDown)
def t_dlogpdf_dlink_dparams(self, model, Y, f, params, param_names, param_constraints): def t_dlogpdf_dlink_dparams(self, model, Y, f, Y_metadata, params, param_names, param_constraints):
print "\n{}".format(inspect.stack()[0][3]) print "\n{}".format(inspect.stack()[0][3])
print model print model
assert ( assert (
dparam_checkgrad(model.dlogpdf_dlink, model.dlogpdf_dlink_dtheta, dparam_checkgrad(model.dlogpdf_dlink, model.dlogpdf_dlink_dtheta,
params, param_names, args=(f, Y), constraints=param_constraints, params, param_names, args=(f, Y, Y_metadata), constraints=param_constraints,
randomize=False, verbose=True) randomize=False, verbose=True)
) )
@with_setup(setUp, tearDown) @with_setup(setUp, tearDown)
def t_d2logpdf2_dlink2_dparams(self, model, Y, f, params, param_names, param_constraints): def t_d2logpdf2_dlink2_dparams(self, model, Y, f, Y_metadata, params, param_names, param_constraints):
print "\n{}".format(inspect.stack()[0][3]) print "\n{}".format(inspect.stack()[0][3])
print model print model
assert ( assert (
dparam_checkgrad(model.d2logpdf_dlink2, model.d2logpdf_dlink2_dtheta, dparam_checkgrad(model.d2logpdf_dlink2, model.d2logpdf_dlink2_dtheta,
params, param_names, args=(f, Y), constraints=param_constraints, params, param_names, args=(f, Y, Y_metadata), constraints=param_constraints,
randomize=False, verbose=True) randomize=False, verbose=True)
) )
@ -510,14 +533,15 @@ class TestNoiseModels(object):
# laplace test # # laplace test #
################ ################
@with_setup(setUp, tearDown) @with_setup(setUp, tearDown)
def t_laplace_fit_rbf_white(self, model, X, Y, f, step, param_vals, param_names, constraints): def t_laplace_fit_rbf_white(self, model, X, Y, f, Y_metadata, step, param_vals, param_names, constraints):
print "\n{}".format(inspect.stack()[0][3]) print "\n{}".format(inspect.stack()[0][3])
#Normalize #Normalize
Y = Y/Y.max() Y = Y/Y.max()
white_var = 1e-6 white_var = 1e-5
kernel = GPy.kern.RBF(X.shape[1]) + GPy.kern.White(X.shape[1]) kernel = GPy.kern.RBF(X.shape[1]) + GPy.kern.White(X.shape[1])
laplace_likelihood = GPy.inference.latent_function_inference.Laplace() laplace_likelihood = GPy.inference.latent_function_inference.Laplace()
m = GPy.core.GP(X.copy(), Y.copy(), kernel, likelihood=model, inference_method=laplace_likelihood)
m = GPy.core.GP(X.copy(), Y.copy(), kernel, likelihood=model, Y_metadata=Y_metadata, inference_method=laplace_likelihood)
m['.*white'].constrain_fixed(white_var) m['.*white'].constrain_fixed(white_var)
#Set constraints #Set constraints
@ -526,6 +550,7 @@ class TestNoiseModels(object):
print m print m
m.randomize() m.randomize()
m.randomize()
#Set params #Set params
for param_num in range(len(param_names)): for param_num in range(len(param_names)):
@ -545,14 +570,15 @@ class TestNoiseModels(object):
# EP test # # EP test #
########### ###########
@with_setup(setUp, tearDown) @with_setup(setUp, tearDown)
def t_ep_fit_rbf_white(self, model, X, Y, f, step, param_vals, param_names, constraints): def t_ep_fit_rbf_white(self, model, X, Y, f, Y_metadata, step, param_vals, param_names, constraints):
print "\n{}".format(inspect.stack()[0][3]) print "\n{}".format(inspect.stack()[0][3])
#Normalize #Normalize
Y = Y/Y.max() Y = Y/Y.max()
white_var = 1e-6 white_var = 1e-6
kernel = GPy.kern.RBF(X.shape[1]) + GPy.kern.White(X.shape[1]) kernel = GPy.kern.RBF(X.shape[1]) + GPy.kern.White(X.shape[1])
ep_inf = GPy.inference.latent_function_inference.EP() ep_inf = GPy.inference.latent_function_inference.EP()
m = GPy.core.GP(X.copy(), Y.copy(), kernel=kernel, likelihood=model, inference_method=ep_inf)
m = GPy.core.GP(X.copy(), Y.copy(), kernel=kernel, likelihood=model, Y_metadata=Y_metadata, inference_method=ep_inf)
m['.*white'].constrain_fixed(white_var) m['.*white'].constrain_fixed(white_var)
for param_num in range(len(param_names)): for param_num in range(len(param_names)):
@ -571,8 +597,8 @@ class LaplaceTests(unittest.TestCase):
""" """
def setUp(self): def setUp(self):
self.N = 5 self.N = 15
self.D = 3 self.D = 1
self.X = np.random.rand(self.N, self.D)*10 self.X = np.random.rand(self.N, self.D)*10
self.real_std = 0.1 self.real_std = 0.1
@ -636,20 +662,20 @@ class LaplaceTests(unittest.TestCase):
exact_inf = GPy.inference.latent_function_inference.ExactGaussianInference() exact_inf = GPy.inference.latent_function_inference.ExactGaussianInference()
m1 = GPy.core.GP(X, Y.copy(), kernel=kernel1, likelihood=gauss_distr1, inference_method=exact_inf) m1 = GPy.core.GP(X, Y.copy(), kernel=kernel1, likelihood=gauss_distr1, inference_method=exact_inf)
m1['.*white'].constrain_fixed(1e-6) m1['.*white'].constrain_fixed(1e-6)
m1['.*rbf.variance'] = initial_var_guess m1['.*Gaussian_noise.variance'].constrain_bounded(1e-4, 10)
m1['.*rbf.variance'].constrain_bounded(1e-4, 10)
m1.randomize() m1.randomize()
gauss_distr2 = GPy.likelihoods.Gaussian(variance=initial_var_guess) gauss_distr2 = GPy.likelihoods.Gaussian(variance=initial_var_guess)
laplace_inf = GPy.inference.latent_function_inference.Laplace() laplace_inf = GPy.inference.latent_function_inference.Laplace()
m2 = GPy.core.GP(X, Y.copy(), kernel=kernel2, likelihood=gauss_distr2, inference_method=laplace_inf) m2 = GPy.core.GP(X, Y.copy(), kernel=kernel2, likelihood=gauss_distr2, inference_method=laplace_inf)
m2['.*white'].constrain_fixed(1e-6) m2['.*white'].constrain_fixed(1e-6)
m2['.*rbf.variance'].constrain_bounded(1e-4, 10) m2['.*Gaussian_noise.variance'].constrain_bounded(1e-4, 10)
m2.randomize() m2.randomize()
if debug: if debug:
print m1 print m1
print m2 print m2
optimizer = 'scg' optimizer = 'scg'
print "Gaussian" print "Gaussian"
m1.optimize(optimizer, messages=debug, ipython_notebook=False) m1.optimize(optimizer, messages=debug, ipython_notebook=False)
@ -687,8 +713,6 @@ class LaplaceTests(unittest.TestCase):
pb.scatter(X, m1.likelihood.Y, c='g') pb.scatter(X, m1.likelihood.Y, c='g')
pb.scatter(X, m2.likelihood.Y, c='r', marker='x') pb.scatter(X, m2.likelihood.Y, c='r', marker='x')
#Check Y's are the same #Check Y's are the same
np.testing.assert_almost_equal(m1.Y, m2.Y, decimal=5) np.testing.assert_almost_equal(m1.Y, m2.Y, decimal=5)
#Check marginals are the same #Check marginals are the same

18
GPy/testing/misc_tests.py Normal file
View file

@ -0,0 +1,18 @@
import numpy as np
import scipy as sp
import GPy
class MiscTests(np.testing.TestCase):
"""
Testing some utilities of misc
"""
def setUp(self):
self._lim_val = np.finfo(np.float64).max
self._lim_val_exp = np.log(self._lim_val)
def test_safe_exp_upper(self):
assert np.exp(self._lim_val_exp + 1) == np.inf
assert GPy.util.misc.safe_exp(self._lim_val_exp + 1) < np.inf
def test_safe_exp_lower(self):
assert GPy.util.misc.safe_exp(1e-10) < np.inf

50
GPy/util/block_matrices.py
View file

@ -17,6 +17,54 @@ def get_blocks(A, blocksizes):
count_i += i count_i += i
return B return B
def get_block_shapes(B):
assert B.dtype is np.dtype('object'), "Must be a block matrix"
return [B[b,b].shape[0] for b in range(0, B.shape[0])]
def unblock(B):
assert B.dtype is np.dtype('object'), "Must be a block matrix"
block_shapes = get_block_shapes(B)
num_elements = np.sum(block_shapes)
A = np.empty(shape=(num_elements, num_elements))
count_i = 0
for Bi, i in enumerate(block_shapes):
count_j = 0
for Bj, j in enumerate(block_shapes):
A[count_i:count_i + i, count_j:count_j + j] = B[Bi, Bj]
count_j += j
count_i += i
return A
def block_dot(A, B):
"""
Element wise dot product on block matricies
+------+------+ +------+------+ +-------+-------+
| | | | | | |A11.B11|B12.B12|
| A11 | A12 | | B11 | B12 | | | |
+------+------+ o +------+------| = +-------+-------+
| | | | | | |A21.B21|A22.B22|
| A21 | A22 | | B21 | B22 | | | |
+-------------+ +------+------+ +-------+-------+
..Note
If either (A or B) of the diagonal matrices are stored as vectors then a more
efficient dot product using numpy broadcasting will be used, i.e. A11*B11
"""
#Must have same number of blocks and be a block matrix
assert A.dtype is np.dtype('object'), "Must be a block matrix"
assert B.dtype is np.dtype('object'), "Must be a block matrix"
Ashape = A.shape
Bshape = B.shape
assert Ashape == Bshape
def f(A,B):
if Ashape[0] == Ashape[1] or Bshape[0] == Bshape[1]:
#FIXME: Careful if one is transpose of other, would make a matrix
return A*B
else:
return np.dot(A,B)
dot = np.vectorize(f, otypes = [np.object])
return dot(A,B)
if __name__=='__main__': if __name__=='__main__':
@ -24,3 +72,5 @@ if __name__=='__main__':
B = get_blocks(A,[2,3]) B = get_blocks(A,[2,3])
B[0,0] += 7 B[0,0] += 7
print B print B
assert np.all(unblock(B) == A)

78
GPy/util/misc.py
View file

@ -4,6 +4,16 @@
import numpy as np import numpy as np
from config import * from config import *
_lim_val = np.finfo(np.float64).max
_lim_val_exp = np.log(_lim_val)
_lim_val_square = np.sqrt(_lim_val)
_lim_val_cube = np.power(_lim_val, -3)
def safe_exp(f):
clip_f = np.clip(f, -np.inf, _lim_val_exp)
return np.exp(clip_f)
def chain_1(df_dg, dg_dx): def chain_1(df_dg, dg_dx):
""" """
Generic chaining function for first derivative Generic chaining function for first derivative
@ -11,6 +21,11 @@ def chain_1(df_dg, dg_dx):
.. math:: .. math::
\\frac{d(f . g)}{dx} = \\frac{df}{dg} \\frac{dg}{dx} \\frac{d(f . g)}{dx} = \\frac{df}{dg} \\frac{dg}{dx}
""" """
if np.all(dg_dx==1.):
return df_dg
if len(df_dg) > 1 and df_dg.shape[-1] > 1:
import ipdb; ipdb.set_trace() # XXX BREAKPOINT
raise NotImplementedError('Not implemented for matricies yet')
return df_dg * dg_dx return df_dg * dg_dx
def chain_2(d2f_dg2, dg_dx, df_dg, d2g_dx2): def chain_2(d2f_dg2, dg_dx, df_dg, d2g_dx2):
@ -20,7 +35,13 @@ def chain_2(d2f_dg2, dg_dx, df_dg, d2g_dx2):
.. math:: .. math::
\\frac{d^{2}(f . g)}{dx^{2}} = \\frac{d^{2}f}{dg^{2}}(\\frac{dg}{dx})^{2} + \\frac{df}{dg}\\frac{d^{2}g}{dx^{2}} \\frac{d^{2}(f . g)}{dx^{2}} = \\frac{d^{2}f}{dg^{2}}(\\frac{dg}{dx})^{2} + \\frac{df}{dg}\\frac{d^{2}g}{dx^{2}}
""" """
return d2f_dg2*(dg_dx**2) + df_dg*d2g_dx2 if np.all(dg_dx==1.) and np.all(d2g_dx2 == 0):
return d2f_dg2
if len(d2f_dg2) > 1 and d2f_dg2.shape[-1] > 1:
raise NotImplementedError('Not implemented for matricies yet')
#dg_dx_2 = np.clip(dg_dx, 1e-12, _lim_val_square)**2
dg_dx_2 = dg_dx**2
return d2f_dg2*(dg_dx_2) + df_dg*d2g_dx2
def chain_3(d3f_dg3, dg_dx, d2f_dg2, d2g_dx2, df_dg, d3g_dx3): def chain_3(d3f_dg3, dg_dx, d2f_dg2, d2g_dx2, df_dg, d3g_dx3):
""" """
@ -29,11 +50,18 @@ def chain_3(d3f_dg3, dg_dx, d2f_dg2, d2g_dx2, df_dg, d3g_dx3):
.. math:: .. math::
\\frac{d^{3}(f . g)}{dx^{3}} = \\frac{d^{3}f}{dg^{3}}(\\frac{dg}{dx})^{3} + 3\\frac{d^{2}f}{dg^{2}}\\frac{dg}{dx}\\frac{d^{2}g}{dx^{2}} + \\frac{df}{dg}\\frac{d^{3}g}{dx^{3}} \\frac{d^{3}(f . g)}{dx^{3}} = \\frac{d^{3}f}{dg^{3}}(\\frac{dg}{dx})^{3} + 3\\frac{d^{2}f}{dg^{2}}\\frac{dg}{dx}\\frac{d^{2}g}{dx^{2}} + \\frac{df}{dg}\\frac{d^{3}g}{dx^{3}}
""" """
return d3f_dg3*(dg_dx**3) + 3*d2f_dg2*dg_dx*d2g_dx2 + df_dg*d3g_dx3 if np.all(dg_dx==1.) and np.all(d2g_dx2==0) and np.all(d3g_dx3==0):
return d3f_dg3
if ( (len(d2f_dg2) > 1 and d2f_dg2.shape[-1] > 1)
or (len(d3f_dg3) > 1 and d3f_dg3.shape[-1] > 1)):
raise NotImplementedError('Not implemented for matricies yet')
#dg_dx_3 = np.clip(dg_dx, 1e-12, _lim_val_cube)**3
dg_dx_3 = dg_dx**3
return d3f_dg3*(dg_dx_3) + 3*d2f_dg2*dg_dx*d2g_dx2 + df_dg*d3g_dx3
def opt_wrapper(m, **kwargs): def opt_wrapper(m, **kwargs):
""" """
This function just wraps the optimization procedure of a GPy Thit function just wraps the optimization procedure of a GPy
object so that optimize() pickleable (necessary for multiprocessing). object so that optimize() pickleable (necessary for multiprocessing).
""" """
m.optimize(**kwargs) m.optimize(**kwargs)
@ -96,3 +124,47 @@ from :class:ndarray)"""
if len(param) == 1: if len(param) == 1:
return param[0].view(np.ndarray) return param[0].view(np.ndarray)
return [x.view(np.ndarray) for x in param] return [x.view(np.ndarray) for x in param]
def blockify_hessian(func):
def wrapper_func(self, *args, **kwargs):
# Invoke the wrapped function first
retval = func(self, *args, **kwargs)
# Now do something here with retval and/or action
if self.not_block_really and (retval.shape[0] != retval.shape[1]):
return np.diagflat(retval)
else:
return retval
return wrapper_func
def blockify_third(func):
def wrapper_func(self, *args, **kwargs):
# Invoke the wrapped function first
retval = func(self, *args, **kwargs)
# Now do something here with retval and/or action
if self.not_block_really and (len(retval.shape) < 3):
num_data = retval.shape[0]
d3_block_cache = np.zeros((num_data, num_data, num_data))
diag_slice = range(num_data)
d3_block_cache[diag_slice, diag_slice, diag_slice] = np.squeeze(retval)
return d3_block_cache
else:
return retval
return wrapper_func
def blockify_dhess_dtheta(func):
def wrapper_func(self, *args, **kwargs):
# Invoke the wrapped function first
retval = func(self, *args, **kwargs)
# Now do something here with retval and/or action
if self.not_block_really and (len(retval.shape) < 3):
num_data = retval.shape[0]
num_params = retval.shape[-1]
dhess_dtheta = np.zeros((num_data, num_data, num_params))
diag_slice = range(num_data)
for param_ind in range(num_params):
dhess_dtheta[diag_slice, diag_slice, param_ind] = np.squeeze(retval[:,param_ind])
return dhess_dtheta
else:
return retval
return wrapper_func

44
benchmarks/boston_housing.py Normal file
View file

@ -0,0 +1,44 @@
import numpy as np
import GPy
def load_housing_data():
X = np.loadtxt('housing.data')
X, Y = X[:,:-1], X[:,-1:]
#scale the X data
xmax, xmin = X.max(0), X.min(0)
X = (X-xmin)/(xmax-xmin)
#loy the response
Y = np.log(Y)
return X, Y
def fit_full_GP():
X, Y = load_housing_data()
k = GPy.kern.RBF(X.shape[1], ARD=True) + GPy.kern.Linear(X.shape[1])
m = GPy.models.GPRegression(X, Y, kernel=k)
m.optimize('bfgs', max_iters=400, gtol=0)
return m
def fit_svgp_st():
np.random.seed(0)
X, Y = load_housing_data()
Z = X[np.random.permutation(X.shape[0])[:100]]
k = GPy.kern.RBF(X.shape[1], ARD=True) + GPy.kern.Linear(X.shape[1], ARD=True) + GPy.kern.White(1,0.01) + GPy.kern.Bias(1)
lik = GPy.likelihoods.StudentT(deg_free=3.)
m = GPy.core.SVGP(X, Y, Z=Z, kernel=k, likelihood=lik)
[m.optimize('scg', max_iters=40, gtol=0, messages=1, xtol=0, ftol=0) for i in range(10)]
m.optimize('bfgs', max_iters=4000, gtol=0, messages=1, xtol=0, ftol=0)
return m
if __name__=="__main__":
import timeit

506
benchmarks/housing.data Normal file
View file

@ -0,0 +1,506 @@
0.00632 18.00 2.310 0 0.5380 6.5750 65.20 4.0900 1 296.0 15.30 396.90 4.98 24.00
0.02731 0.00 7.070 0 0.4690 6.4210 78.90 4.9671 2 242.0 17.80 396.90 9.14 21.60
0.02729 0.00 7.070 0 0.4690 7.1850 61.10 4.9671 2 242.0 17.80 392.83 4.03 34.70
0.03237 0.00 2.180 0 0.4580 6.9980 45.80 6.0622 3 222.0 18.70 394.63 2.94 33.40
0.06905 0.00 2.180 0 0.4580 7.1470 54.20 6.0622 3 222.0 18.70 396.90 5.33 36.20
0.02985 0.00 2.180 0 0.4580 6.4300 58.70 6.0622 3 222.0 18.70 394.12 5.21 28.70
0.08829 12.50 7.870 0 0.5240 6.0120 66.60 5.5605 5 311.0 15.20 395.60 12.43 22.90
0.14455 12.50 7.870 0 0.5240 6.1720 96.10 5.9505 5 311.0 15.20 396.90 19.15 27.10
0.21124 12.50 7.870 0 0.5240 5.6310 100.00 6.0821 5 311.0 15.20 386.63 29.93 16.50
0.17004 12.50 7.870 0 0.5240 6.0040 85.90 6.5921 5 311.0 15.20 386.71 17.10 18.90
0.22489 12.50 7.870 0 0.5240 6.3770 94.30 6.3467 5 311.0 15.20 392.52 20.45 15.00
0.11747 12.50 7.870 0 0.5240 6.0090 82.90 6.2267 5 311.0 15.20 396.90 13.27 18.90
0.09378 12.50 7.870 0 0.5240 5.8890 39.00 5.4509 5 311.0 15.20 390.50 15.71 21.70
0.62976 0.00 8.140 0 0.5380 5.9490 61.80 4.7075 4 307.0 21.00 396.90 8.26 20.40
0.63796 0.00 8.140 0 0.5380 6.0960 84.50 4.4619 4 307.0 21.00 380.02 10.26 18.20
0.62739 0.00 8.140 0 0.5380 5.8340 56.50 4.4986 4 307.0 21.00 395.62 8.47 19.90
1.05393 0.00 8.140 0 0.5380 5.9350 29.30 4.4986 4 307.0 21.00 386.85 6.58 23.10
0.78420 0.00 8.140 0 0.5380 5.9900 81.70 4.2579 4 307.0 21.00 386.75 14.67 17.50
0.80271 0.00 8.140 0 0.5380 5.4560 36.60 3.7965 4 307.0 21.00 288.99 11.69 20.20
0.72580 0.00 8.140 0 0.5380 5.7270 69.50 3.7965 4 307.0 21.00 390.95 11.28 18.20
1.25179 0.00 8.140 0 0.5380 5.5700 98.10 3.7979 4 307.0 21.00 376.57 21.02 13.60
0.85204 0.00 8.140 0 0.5380 5.9650 89.20 4.0123 4 307.0 21.00 392.53 13.83 19.60
1.23247 0.00 8.140 0 0.5380 6.1420 91.70 3.9769 4 307.0 21.00 396.90 18.72 15.20
0.98843 0.00 8.140 0 0.5380 5.8130 100.00 4.0952 4 307.0 21.00 394.54 19.88 14.50
0.75026 0.00 8.140 0 0.5380 5.9240 94.10 4.3996 4 307.0 21.00 394.33 16.30 15.60
0.84054 0.00 8.140 0 0.5380 5.5990 85.70 4.4546 4 307.0 21.00 303.42 16.51 13.90
0.67191 0.00 8.140 0 0.5380 5.8130 90.30 4.6820 4 307.0 21.00 376.88 14.81 16.60
0.95577 0.00 8.140 0 0.5380 6.0470 88.80 4.4534 4 307.0 21.00 306.38 17.28 14.80
0.77299 0.00 8.140 0 0.5380 6.4950 94.40 4.4547 4 307.0 21.00 387.94 12.80 18.40
1.00245 0.00 8.140 0 0.5380 6.6740 87.30 4.2390 4 307.0 21.00 380.23 11.98 21.00
1.13081 0.00 8.140 0 0.5380 5.7130 94.10 4.2330 4 307.0 21.00 360.17 22.60 12.70
1.35472 0.00 8.140 0 0.5380 6.0720 100.00 4.1750 4 307.0 21.00 376.73 13.04 14.50
1.38799 0.00 8.140 0 0.5380 5.9500 82.00 3.9900 4 307.0 21.00 232.60 27.71 13.20
1.15172 0.00 8.140 0 0.5380 5.7010 95.00 3.7872 4 307.0 21.00 358.77 18.35 13.10
1.61282 0.00 8.140 0 0.5380 6.0960 96.90 3.7598 4 307.0 21.00 248.31 20.34 13.50
0.06417 0.00 5.960 0 0.4990 5.9330 68.20 3.3603 5 279.0 19.20 396.90 9.68 18.90
0.09744 0.00 5.960 0 0.4990 5.8410 61.40 3.3779 5 279.0 19.20 377.56 11.41 20.00
0.08014 0.00 5.960 0 0.4990 5.8500 41.50 3.9342 5 279.0 19.20 396.90 8.77 21.00
0.17505 0.00 5.960 0 0.4990 5.9660 30.20 3.8473 5 279.0 19.20 393.43 10.13 24.70
0.02763 75.00 2.950 0 0.4280 6.5950 21.80 5.4011 3 252.0 18.30 395.63 4.32 30.80
0.03359 75.00 2.950 0 0.4280 7.0240 15.80 5.4011 3 252.0 18.30 395.62 1.98 34.90
0.12744 0.00 6.910 0 0.4480 6.7700 2.90 5.7209 3 233.0 17.90 385.41 4.84 26.60
0.14150 0.00 6.910 0 0.4480 6.1690 6.60 5.7209 3 233.0 17.90 383.37 5.81 25.30
0.15936 0.00 6.910 0 0.4480 6.2110 6.50 5.7209 3 233.0 17.90 394.46 7.44 24.70
0.12269 0.00 6.910 0 0.4480 6.0690 40.00 5.7209 3 233.0 17.90 389.39 9.55 21.20
0.17142 0.00 6.910 0 0.4480 5.6820 33.80 5.1004 3 233.0 17.90 396.90 10.21 19.30
0.18836 0.00 6.910 0 0.4480 5.7860 33.30 5.1004 3 233.0 17.90 396.90 14.15 20.00
0.22927 0.00 6.910 0 0.4480 6.0300 85.50 5.6894 3 233.0 17.90 392.74 18.80 16.60
0.25387 0.00 6.910 0 0.4480 5.3990 95.30 5.8700 3 233.0 17.90 396.90 30.81 14.40
0.21977 0.00 6.910 0 0.4480 5.6020 62.00 6.0877 3 233.0 17.90 396.90 16.20 19.40
0.08873 21.00 5.640 0 0.4390 5.9630 45.70 6.8147 4 243.0 16.80 395.56 13.45 19.70
0.04337 21.00 5.640 0 0.4390 6.1150 63.00 6.8147 4 243.0 16.80 393.97 9.43 20.50
0.05360 21.00 5.640 0 0.4390 6.5110 21.10 6.8147 4 243.0 16.80 396.90 5.28 25.00
0.04981 21.00 5.640 0 0.4390 5.9980 21.40 6.8147 4 243.0 16.80 396.90 8.43 23.40
0.01360 75.00 4.000 0 0.4100 5.8880 47.60 7.3197 3 469.0 21.10 396.90 14.80 18.90
0.01311 90.00 1.220 0 0.4030 7.2490 21.90 8.6966 5 226.0 17.90 395.93 4.81 35.40
0.02055 85.00 0.740 0 0.4100 6.3830 35.70 9.1876 2 313.0 17.30 396.90 5.77 24.70
0.01432 100.00 1.320 0 0.4110 6.8160 40.50 8.3248 5 256.0 15.10 392.90 3.95 31.60
0.15445 25.00 5.130 0 0.4530 6.1450 29.20 7.8148 8 284.0 19.70 390.68 6.86 23.30
0.10328 25.00 5.130 0 0.4530 5.9270 47.20 6.9320 8 284.0 19.70 396.90 9.22 19.60
0.14932 25.00 5.130 0 0.4530 5.7410 66.20 7.2254 8 284.0 19.70 395.11 13.15 18.70
0.17171 25.00 5.130 0 0.4530 5.9660 93.40 6.8185 8 284.0 19.70 378.08 14.44 16.00
0.11027 25.00 5.130 0 0.4530 6.4560 67.80 7.2255 8 284.0 19.70 396.90 6.73 22.20
0.12650 25.00 5.130 0 0.4530 6.7620 43.40 7.9809 8 284.0 19.70 395.58 9.50 25.00
0.01951 17.50 1.380 0 0.4161 7.1040 59.50 9.2229 3 216.0 18.60 393.24 8.05 33.00
0.03584 80.00 3.370 0 0.3980 6.2900 17.80 6.6115 4 337.0 16.10 396.90 4.67 23.50
0.04379 80.00 3.370 0 0.3980 5.7870 31.10 6.6115 4 337.0 16.10 396.90 10.24 19.40
0.05789 12.50 6.070 0 0.4090 5.8780 21.40 6.4980 4 345.0 18.90 396.21 8.10 22.00
0.13554 12.50 6.070 0 0.4090 5.5940 36.80 6.4980 4 345.0 18.90 396.90 13.09 17.40
0.12816 12.50 6.070 0 0.4090 5.8850 33.00 6.4980 4 345.0 18.90 396.90 8.79 20.90
0.08826 0.00 10.810 0 0.4130 6.4170 6.60 5.2873 4 305.0 19.20 383.73 6.72 24.20
0.15876 0.00 10.810 0 0.4130 5.9610 17.50 5.2873 4 305.0 19.20 376.94 9.88 21.70
0.09164 0.00 10.810 0 0.4130 6.0650 7.80 5.2873 4 305.0 19.20 390.91 5.52 22.80
0.19539 0.00 10.810 0 0.4130 6.2450 6.20 5.2873 4 305.0 19.20 377.17 7.54 23.40
0.07896 0.00 12.830 0 0.4370 6.2730 6.00 4.2515 5 398.0 18.70 394.92 6.78 24.10
0.09512 0.00 12.830 0 0.4370 6.2860 45.00 4.5026 5 398.0 18.70 383.23 8.94 21.40
0.10153 0.00 12.830 0 0.4370 6.2790 74.50 4.0522 5 398.0 18.70 373.66 11.97 20.00
0.08707 0.00 12.830 0 0.4370 6.1400 45.80 4.0905 5 398.0 18.70 386.96 10.27 20.80
0.05646 0.00 12.830 0 0.4370 6.2320 53.70 5.0141 5 398.0 18.70 386.40 12.34 21.20
0.08387 0.00 12.830 0 0.4370 5.8740 36.60 4.5026 5 398.0 18.70 396.06 9.10 20.30
0.04113 25.00 4.860 0 0.4260 6.7270 33.50 5.4007 4 281.0 19.00 396.90 5.29 28.00
0.04462 25.00 4.860 0 0.4260 6.6190 70.40 5.4007 4 281.0 19.00 395.63 7.22 23.90
0.03659 25.00 4.860 0 0.4260 6.3020 32.20 5.4007 4 281.0 19.00 396.90 6.72 24.80
0.03551 25.00 4.860 0 0.4260 6.1670 46.70 5.4007 4 281.0 19.00 390.64 7.51 22.90
0.05059 0.00 4.490 0 0.4490 6.3890 48.00 4.7794 3 247.0 18.50 396.90 9.62 23.90
0.05735 0.00 4.490 0 0.4490 6.6300 56.10 4.4377 3 247.0 18.50 392.30 6.53 26.60
0.05188 0.00 4.490 0 0.4490 6.0150 45.10 4.4272 3 247.0 18.50 395.99 12.86 22.50
0.07151 0.00 4.490 0 0.4490 6.1210 56.80 3.7476 3 247.0 18.50 395.15 8.44 22.20
0.05660 0.00 3.410 0 0.4890 7.0070 86.30 3.4217 2 270.0 17.80 396.90 5.50 23.60
0.05302 0.00 3.410 0 0.4890 7.0790 63.10 3.4145 2 270.0 17.80 396.06 5.70 28.70
0.04684 0.00 3.410 0 0.4890 6.4170 66.10 3.0923 2 270.0 17.80 392.18 8.81 22.60
0.03932 0.00 3.410 0 0.4890 6.4050 73.90 3.0921 2 270.0 17.80 393.55 8.20 22.00
0.04203 28.00 15.040 0 0.4640 6.4420 53.60 3.6659 4 270.0 18.20 395.01 8.16 22.90
0.02875 28.00 15.040 0 0.4640 6.2110 28.90 3.6659 4 270.0 18.20 396.33 6.21 25.00
0.04294 28.00 15.040 0 0.4640 6.2490 77.30 3.6150 4 270.0 18.20 396.90 10.59 20.60
0.12204 0.00 2.890 0 0.4450 6.6250 57.80 3.4952 2 276.0 18.00 357.98 6.65 28.40
0.11504 0.00 2.890 0 0.4450 6.1630 69.60 3.4952 2 276.0 18.00 391.83 11.34 21.40
0.12083 0.00 2.890 0 0.4450 8.0690 76.00 3.4952 2 276.0 18.00 396.90 4.21 38.70
0.08187 0.00 2.890 0 0.4450 7.8200 36.90 3.4952 2 276.0 18.00 393.53 3.57 43.80
0.06860 0.00 2.890 0 0.4450 7.4160 62.50 3.4952 2 276.0 18.00 396.90 6.19 33.20
0.14866 0.00 8.560 0 0.5200 6.7270 79.90 2.7778 5 384.0 20.90 394.76 9.42 27.50
0.11432 0.00 8.560 0 0.5200 6.7810 71.30 2.8561 5 384.0 20.90 395.58 7.67 26.50
0.22876 0.00 8.560 0 0.5200 6.4050 85.40 2.7147 5 384.0 20.90 70.80 10.63 18.60
0.21161 0.00 8.560 0 0.5200 6.1370 87.40 2.7147 5 384.0 20.90 394.47 13.44 19.30
0.13960 0.00 8.560 0 0.5200 6.1670 90.00 2.4210 5 384.0 20.90 392.69 12.33 20.10
0.13262 0.00 8.560 0 0.5200 5.8510 96.70 2.1069 5 384.0 20.90 394.05 16.47 19.50
0.17120 0.00 8.560 0 0.5200 5.8360 91.90 2.2110 5 384.0 20.90 395.67 18.66 19.50
0.13117 0.00 8.560 0 0.5200 6.1270 85.20 2.1224 5 384.0 20.90 387.69 14.09 20.40
0.12802 0.00 8.560 0 0.5200 6.4740 97.10 2.4329 5 384.0 20.90 395.24 12.27 19.80
0.26363 0.00 8.560 0 0.5200 6.2290 91.20 2.5451 5 384.0 20.90 391.23 15.55 19.40
0.10793 0.00 8.560 0 0.5200 6.1950 54.40 2.7778 5 384.0 20.90 393.49 13.00 21.70
0.10084 0.00 10.010 0 0.5470 6.7150 81.60 2.6775 6 432.0 17.80 395.59 10.16 22.80
0.12329 0.00 10.010 0 0.5470 5.9130 92.90 2.3534 6 432.0 17.80 394.95 16.21 18.80
0.22212 0.00 10.010 0 0.5470 6.0920 95.40 2.5480 6 432.0 17.80 396.90 17.09 18.70
0.14231 0.00 10.010 0 0.5470 6.2540 84.20 2.2565 6 432.0 17.80 388.74 10.45 18.50
0.17134 0.00 10.010 0 0.5470 5.9280 88.20 2.4631 6 432.0 17.80 344.91 15.76 18.30
0.13158 0.00 10.010 0 0.5470 6.1760 72.50 2.7301 6 432.0 17.80 393.30 12.04 21.20
0.15098 0.00 10.010 0 0.5470 6.0210 82.60 2.7474 6 432.0 17.80 394.51 10.30 19.20
0.13058 0.00 10.010 0 0.5470 5.8720 73.10 2.4775 6 432.0 17.80 338.63 15.37 20.40
0.14476 0.00 10.010 0 0.5470 5.7310 65.20 2.7592 6 432.0 17.80 391.50 13.61 19.30
0.06899 0.00 25.650 0 0.5810 5.8700 69.70 2.2577 2 188.0 19.10 389.15 14.37 22.00
0.07165 0.00 25.650 0 0.5810 6.0040 84.10 2.1974 2 188.0 19.10 377.67 14.27 20.30
0.09299 0.00 25.650 0 0.5810 5.9610 92.90 2.0869 2 188.0 19.10 378.09 17.93 20.50
0.15038 0.00 25.650 0 0.5810 5.8560 97.00 1.9444 2 188.0 19.10 370.31 25.41 17.30
0.09849 0.00 25.650 0 0.5810 5.8790 95.80 2.0063 2 188.0 19.10 379.38 17.58 18.80
0.16902 0.00 25.650 0 0.5810 5.9860 88.40 1.9929 2 188.0 19.10 385.02 14.81 21.40
0.38735 0.00 25.650 0 0.5810 5.6130 95.60 1.7572 2 188.0 19.10 359.29 27.26 15.70
0.25915 0.00 21.890 0 0.6240 5.6930 96.00 1.7883 4 437.0 21.20 392.11 17.19 16.20
0.32543 0.00 21.890 0 0.6240 6.4310 98.80 1.8125 4 437.0 21.20 396.90 15.39 18.00
0.88125 0.00 21.890 0 0.6240 5.6370 94.70 1.9799 4 437.0 21.20 396.90 18.34 14.30
0.34006 0.00 21.890 0 0.6240 6.4580 98.90 2.1185 4 437.0 21.20 395.04 12.60 19.20
1.19294 0.00 21.890 0 0.6240 6.3260 97.70 2.2710 4 437.0 21.20 396.90 12.26 19.60
0.59005 0.00 21.890 0 0.6240 6.3720 97.90 2.3274 4 437.0 21.20 385.76 11.12 23.00
0.32982 0.00 21.890 0 0.6240 5.8220 95.40 2.4699 4 437.0 21.20 388.69 15.03 18.40
0.97617 0.00 21.890 0 0.6240 5.7570 98.40 2.3460 4 437.0 21.20 262.76 17.31 15.60
0.55778 0.00 21.890 0 0.6240 6.3350 98.20 2.1107 4 437.0 21.20 394.67 16.96 18.10
0.32264 0.00 21.890 0 0.6240 5.9420 93.50 1.9669 4 437.0 21.20 378.25 16.90 17.40
0.35233 0.00 21.890 0 0.6240 6.4540 98.40 1.8498 4 437.0 21.20 394.08 14.59 17.10
0.24980 0.00 21.890 0 0.6240 5.8570 98.20 1.6686 4 437.0 21.20 392.04 21.32 13.30
0.54452 0.00 21.890 0 0.6240 6.1510 97.90 1.6687 4 437.0 21.20 396.90 18.46 17.80
0.29090 0.00 21.890 0 0.6240 6.1740 93.60 1.6119 4 437.0 21.20 388.08 24.16 14.00
1.62864 0.00 21.890 0 0.6240 5.0190 100.00 1.4394 4 437.0 21.20 396.90 34.41 14.40
3.32105 0.00 19.580 1 0.8710 5.4030 100.00 1.3216 5 403.0 14.70 396.90 26.82 13.40
4.09740 0.00 19.580 0 0.8710 5.4680 100.00 1.4118 5 403.0 14.70 396.90 26.42 15.60
2.77974 0.00 19.580 0 0.8710 4.9030 97.80 1.3459 5 403.0 14.70 396.90 29.29 11.80
2.37934 0.00 19.580 0 0.8710 6.1300 100.00 1.4191 5 403.0 14.70 172.91 27.80 13.80
2.15505 0.00 19.580 0 0.8710 5.6280 100.00 1.5166 5 403.0 14.70 169.27 16.65 15.60
2.36862 0.00 19.580 0 0.8710 4.9260 95.70 1.4608 5 403.0 14.70 391.71 29.53 14.60
2.33099 0.00 19.580 0 0.8710 5.1860 93.80 1.5296 5 403.0 14.70 356.99 28.32 17.80
2.73397 0.00 19.580 0 0.8710 5.5970 94.90 1.5257 5 403.0 14.70 351.85 21.45 15.40
1.65660 0.00 19.580 0 0.8710 6.1220 97.30 1.6180 5 403.0 14.70 372.80 14.10 21.50
1.49632 0.00 19.580 0 0.8710 5.4040 100.00 1.5916 5 403.0 14.70 341.60 13.28 19.60
1.12658 0.00 19.580 1 0.8710 5.0120 88.00 1.6102 5 403.0 14.70 343.28 12.12 15.30
2.14918 0.00 19.580 0 0.8710 5.7090 98.50 1.6232 5 403.0 14.70 261.95 15.79 19.40
1.41385 0.00 19.580 1 0.8710 6.1290 96.00 1.7494 5 403.0 14.70 321.02 15.12 17.00
3.53501 0.00 19.580 1 0.8710 6.1520 82.60 1.7455 5 403.0 14.70 88.01 15.02 15.60
2.44668 0.00 19.580 0 0.8710 5.2720 94.00 1.7364 5 403.0 14.70 88.63 16.14 13.10
1.22358 0.00 19.580 0 0.6050 6.9430 97.40 1.8773 5 403.0 14.70 363.43 4.59 41.30
1.34284 0.00 19.580 0 0.6050 6.0660 100.00 1.7573 5 403.0 14.70 353.89 6.43 24.30
1.42502 0.00 19.580 0 0.8710 6.5100 100.00 1.7659 5 403.0 14.70 364.31 7.39 23.30
1.27346 0.00 19.580 1 0.6050 6.2500 92.60 1.7984 5 403.0 14.70 338.92 5.50 27.00
1.46336 0.00 19.580 0 0.6050 7.4890 90.80 1.9709 5 403.0 14.70 374.43 1.73 50.00
1.83377 0.00 19.580 1 0.6050 7.8020 98.20 2.0407 5 403.0 14.70 389.61 1.92 50.00
1.51902 0.00 19.580 1 0.6050 8.3750 93.90 2.1620 5 403.0 14.70 388.45 3.32 50.00
2.24236 0.00 19.580 0 0.6050 5.8540 91.80 2.4220 5 403.0 14.70 395.11 11.64 22.70
2.92400 0.00 19.580 0 0.6050 6.1010 93.00 2.2834 5 403.0 14.70 240.16 9.81 25.00
2.01019 0.00 19.580 0 0.6050 7.9290 96.20 2.0459 5 403.0 14.70 369.30 3.70 50.00
1.80028 0.00 19.580 0 0.6050 5.8770 79.20 2.4259 5 403.0 14.70 227.61 12.14 23.80
2.30040 0.00 19.580 0 0.6050 6.3190 96.10 2.1000 5 403.0 14.70 297.09 11.10 23.80
2.44953 0.00 19.580 0 0.6050 6.4020 95.20 2.2625 5 403.0 14.70 330.04 11.32 22.30
1.20742 0.00 19.580 0 0.6050 5.8750 94.60 2.4259 5 403.0 14.70 292.29 14.43 17.40
2.31390 0.00 19.580 0 0.6050 5.8800 97.30 2.3887 5 403.0 14.70 348.13 12.03 19.10
0.13914 0.00 4.050 0 0.5100 5.5720 88.50 2.5961 5 296.0 16.60 396.90 14.69 23.10
0.09178 0.00 4.050 0 0.5100 6.4160 84.10 2.6463 5 296.0 16.60 395.50 9.04 23.60
0.08447 0.00 4.050 0 0.5100 5.8590 68.70 2.7019 5 296.0 16.60 393.23 9.64 22.60
0.06664 0.00 4.050 0 0.5100 6.5460 33.10 3.1323 5 296.0 16.60 390.96 5.33 29.40
0.07022 0.00 4.050 0 0.5100 6.0200 47.20 3.5549 5 296.0 16.60 393.23 10.11 23.20
0.05425 0.00 4.050 0 0.5100 6.3150 73.40 3.3175 5 296.0 16.60 395.60 6.29 24.60
0.06642 0.00 4.050 0 0.5100 6.8600 74.40 2.9153 5 296.0 16.60 391.27 6.92 29.90
0.05780 0.00 2.460 0 0.4880 6.9800 58.40 2.8290 3 193.0 17.80 396.90 5.04 37.20
0.06588 0.00 2.460 0 0.4880 7.7650 83.30 2.7410 3 193.0 17.80 395.56 7.56 39.80
0.06888 0.00 2.460 0 0.4880 6.1440 62.20 2.5979 3 193.0 17.80 396.90 9.45 36.20
0.09103 0.00 2.460 0 0.4880 7.1550 92.20 2.7006 3 193.0 17.80 394.12 4.82 37.90
0.10008 0.00 2.460 0 0.4880 6.5630 95.60 2.8470 3 193.0 17.80 396.90 5.68 32.50
0.08308 0.00 2.460 0 0.4880 5.6040 89.80 2.9879 3 193.0 17.80 391.00 13.98 26.40
0.06047 0.00 2.460 0 0.4880 6.1530 68.80 3.2797 3 193.0 17.80 387.11 13.15 29.60
0.05602 0.00 2.460 0 0.4880 7.8310 53.60 3.1992 3 193.0 17.80 392.63 4.45 50.00
0.07875 45.00 3.440 0 0.4370 6.7820 41.10 3.7886 5 398.0 15.20 393.87 6.68 32.00
0.12579 45.00 3.440 0 0.4370 6.5560 29.10 4.5667 5 398.0 15.20 382.84 4.56 29.80
0.08370 45.00 3.440 0 0.4370 7.1850 38.90 4.5667 5 398.0 15.20 396.90 5.39 34.90
0.09068 45.00 3.440 0 0.4370 6.9510 21.50 6.4798 5 398.0 15.20 377.68 5.10 37.00
0.06911 45.00 3.440 0 0.4370 6.7390 30.80 6.4798 5 398.0 15.20 389.71 4.69 30.50
0.08664 45.00 3.440 0 0.4370 7.1780 26.30 6.4798 5 398.0 15.20 390.49 2.87 36.40
0.02187 60.00 2.930 0 0.4010 6.8000 9.90 6.2196 1 265.0 15.60 393.37 5.03 31.10
0.01439 60.00 2.930 0 0.4010 6.6040 18.80 6.2196 1 265.0 15.60 376.70 4.38 29.10
0.01381 80.00 0.460 0 0.4220 7.8750 32.00 5.6484 4 255.0 14.40 394.23 2.97 50.00
0.04011 80.00 1.520 0 0.4040 7.2870 34.10 7.3090 2 329.0 12.60 396.90 4.08 33.30
0.04666 80.00 1.520 0 0.4040 7.1070 36.60 7.3090 2 329.0 12.60 354.31 8.61 30.30
0.03768 80.00 1.520 0 0.4040 7.2740 38.30 7.3090 2 329.0 12.60 392.20 6.62 34.60
0.03150 95.00 1.470 0 0.4030 6.9750 15.30 7.6534 3 402.0 17.00 396.90 4.56 34.90
0.01778 95.00 1.470 0 0.4030 7.1350 13.90 7.6534 3 402.0 17.00 384.30 4.45 32.90
0.03445 82.50 2.030 0 0.4150 6.1620 38.40 6.2700 2 348.0 14.70 393.77 7.43 24.10
0.02177 82.50 2.030 0 0.4150 7.6100 15.70 6.2700 2 348.0 14.70 395.38 3.11 42.30
0.03510 95.00 2.680 0 0.4161 7.8530 33.20 5.1180 4 224.0 14.70 392.78 3.81 48.50
0.02009 95.00 2.680 0 0.4161 8.0340 31.90 5.1180 4 224.0 14.70 390.55 2.88 50.00
0.13642 0.00 10.590 0 0.4890 5.8910 22.30 3.9454 4 277.0 18.60 396.90 10.87 22.60
0.22969 0.00 10.590 0 0.4890 6.3260 52.50 4.3549 4 277.0 18.60 394.87 10.97 24.40
0.25199 0.00 10.590 0 0.4890 5.7830 72.70 4.3549 4 277.0 18.60 389.43 18.06 22.50
0.13587 0.00 10.590 1 0.4890 6.0640 59.10 4.2392 4 277.0 18.60 381.32 14.66 24.40
0.43571 0.00 10.590 1 0.4890 5.3440 100.00 3.8750 4 277.0 18.60 396.90 23.09 20.00
0.17446 0.00 10.590 1 0.4890 5.9600 92.10 3.8771 4 277.0 18.60 393.25 17.27 21.70
0.37578 0.00 10.590 1 0.4890 5.4040 88.60 3.6650 4 277.0 18.60 395.24 23.98 19.30
0.21719 0.00 10.590 1 0.4890 5.8070 53.80 3.6526 4 277.0 18.60 390.94 16.03 22.40
0.14052 0.00 10.590 0 0.4890 6.3750 32.30 3.9454 4 277.0 18.60 385.81 9.38 28.10
0.28955 0.00 10.590 0 0.4890 5.4120 9.80 3.5875 4 277.0 18.60 348.93 29.55 23.70
0.19802 0.00 10.590 0 0.4890 6.1820 42.40 3.9454 4 277.0 18.60 393.63 9.47 25.00
0.04560 0.00 13.890 1 0.5500 5.8880 56.00 3.1121 5 276.0 16.40 392.80 13.51 23.30
0.07013 0.00 13.890 0 0.5500 6.6420 85.10 3.4211 5 276.0 16.40 392.78 9.69 28.70
0.11069 0.00 13.890 1 0.5500 5.9510 93.80 2.8893 5 276.0 16.40 396.90 17.92 21.50
0.11425 0.00 13.890 1 0.5500 6.3730 92.40 3.3633 5 276.0 16.40 393.74 10.50 23.00
0.35809 0.00 6.200 1 0.5070 6.9510 88.50 2.8617 8 307.0 17.40 391.70 9.71 26.70
0.40771 0.00 6.200 1 0.5070 6.1640 91.30 3.0480 8 307.0 17.40 395.24 21.46 21.70
0.62356 0.00 6.200 1 0.5070 6.8790 77.70 3.2721 8 307.0 17.40 390.39 9.93 27.50
0.61470 0.00 6.200 0 0.5070 6.6180 80.80 3.2721 8 307.0 17.40 396.90 7.60 30.10
0.31533 0.00 6.200 0 0.5040 8.2660 78.30 2.8944 8 307.0 17.40 385.05 4.14 44.80
0.52693 0.00 6.200 0 0.5040 8.7250 83.00 2.8944 8 307.0 17.40 382.00 4.63 50.00
0.38214 0.00 6.200 0 0.5040 8.0400 86.50 3.2157 8 307.0 17.40 387.38 3.13 37.60
0.41238 0.00 6.200 0 0.5040 7.1630 79.90 3.2157 8 307.0 17.40 372.08 6.36 31.60
0.29819 0.00 6.200 0 0.5040 7.6860 17.00 3.3751 8 307.0 17.40 377.51 3.92 46.70
0.44178 0.00 6.200 0 0.5040 6.5520 21.40 3.3751 8 307.0 17.40 380.34 3.76 31.50
0.53700 0.00 6.200 0 0.5040 5.9810 68.10 3.6715 8 307.0 17.40 378.35 11.65 24.30
0.46296 0.00 6.200 0 0.5040 7.4120 76.90 3.6715 8 307.0 17.40 376.14 5.25 31.70
0.57529 0.00 6.200 0 0.5070 8.3370 73.30 3.8384 8 307.0 17.40 385.91 2.47 41.70
0.33147 0.00 6.200 0 0.5070 8.2470 70.40 3.6519 8 307.0 17.40 378.95 3.95 48.30
0.44791 0.00 6.200 1 0.5070 6.7260 66.50 3.6519 8 307.0 17.40 360.20 8.05 29.00
0.33045 0.00 6.200 0 0.5070 6.0860 61.50 3.6519 8 307.0 17.40 376.75 10.88 24.00
0.52058 0.00 6.200 1 0.5070 6.6310 76.50 4.1480 8 307.0 17.40 388.45 9.54 25.10
0.51183 0.00 6.200 0 0.5070 7.3580 71.60 4.1480 8 307.0 17.40 390.07 4.73 31.50
0.08244 30.00 4.930 0 0.4280 6.4810 18.50 6.1899 6 300.0 16.60 379.41 6.36 23.70
0.09252 30.00 4.930 0 0.4280 6.6060 42.20 6.1899 6 300.0 16.60 383.78 7.37 23.30
0.11329 30.00 4.930 0 0.4280 6.8970 54.30 6.3361 6 300.0 16.60 391.25 11.38 22.00
0.10612 30.00 4.930 0 0.4280 6.0950 65.10 6.3361 6 300.0 16.60 394.62 12.40 20.10
0.10290 30.00 4.930 0 0.4280 6.3580 52.90 7.0355 6 300.0 16.60 372.75 11.22 22.20
0.12757 30.00 4.930 0 0.4280 6.3930 7.80 7.0355 6 300.0 16.60 374.71 5.19 23.70
0.20608 22.00 5.860 0 0.4310 5.5930 76.50 7.9549 7 330.0 19.10 372.49 12.50 17.60
0.19133 22.00 5.860 0 0.4310 5.6050 70.20 7.9549 7 330.0 19.10 389.13 18.46 18.50
0.33983 22.00 5.860 0 0.4310 6.1080 34.90 8.0555 7 330.0 19.10 390.18 9.16 24.30
0.19657 22.00 5.860 0 0.4310 6.2260 79.20 8.0555 7 330.0 19.10 376.14 10.15 20.50
0.16439 22.00 5.860 0 0.4310 6.4330 49.10 7.8265 7 330.0 19.10 374.71 9.52 24.50
0.19073 22.00 5.860 0 0.4310 6.7180 17.50 7.8265 7 330.0 19.10 393.74 6.56 26.20
0.14030 22.00 5.860 0 0.4310 6.4870 13.00 7.3967 7 330.0 19.10 396.28 5.90 24.40
0.21409 22.00 5.860 0 0.4310 6.4380 8.90 7.3967 7 330.0 19.10 377.07 3.59 24.80
0.08221 22.00 5.860 0 0.4310 6.9570 6.80 8.9067 7 330.0 19.10 386.09 3.53 29.60
0.36894 22.00 5.860 0 0.4310 8.2590 8.40 8.9067 7 330.0 19.10 396.90 3.54 42.80
0.04819 80.00 3.640 0 0.3920 6.1080 32.00 9.2203 1 315.0 16.40 392.89 6.57 21.90
0.03548 80.00 3.640 0 0.3920 5.8760 19.10 9.2203 1 315.0 16.40 395.18 9.25 20.90
0.01538 90.00 3.750 0 0.3940 7.4540 34.20 6.3361 3 244.0 15.90 386.34 3.11 44.00
0.61154 20.00 3.970 0 0.6470 8.7040 86.90 1.8010 5 264.0 13.00 389.70 5.12 50.00
0.66351 20.00 3.970 0 0.6470 7.3330 100.00 1.8946 5 264.0 13.00 383.29 7.79 36.00
0.65665 20.00 3.970 0 0.6470 6.8420 100.00 2.0107 5 264.0 13.00 391.93 6.90 30.10
0.54011 20.00 3.970 0 0.6470 7.2030 81.80 2.1121 5 264.0 13.00 392.80 9.59 33.80
0.53412 20.00 3.970 0 0.6470 7.5200 89.40 2.1398 5 264.0 13.00 388.37 7.26 43.10
0.52014 20.00 3.970 0 0.6470 8.3980 91.50 2.2885 5 264.0 13.00 386.86 5.91 48.80
0.82526 20.00 3.970 0 0.6470 7.3270 94.50 2.0788 5 264.0 13.00 393.42 11.25 31.00
0.55007 20.00 3.970 0 0.6470 7.2060 91.60 1.9301 5 264.0 13.00 387.89 8.10 36.50
0.76162 20.00 3.970 0 0.6470 5.5600 62.80 1.9865 5 264.0 13.00 392.40 10.45 22.80
0.78570 20.00 3.970 0 0.6470 7.0140 84.60 2.1329 5 264.0 13.00 384.07 14.79 30.70
0.57834 20.00 3.970 0 0.5750 8.2970 67.00 2.4216 5 264.0 13.00 384.54 7.44 50.00
0.54050 20.00 3.970 0 0.5750 7.4700 52.60 2.8720 5 264.0 13.00 390.30 3.16 43.50
0.09065 20.00 6.960 1 0.4640 5.9200 61.50 3.9175 3 223.0 18.60 391.34 13.65 20.70
0.29916 20.00 6.960 0 0.4640 5.8560 42.10 4.4290 3 223.0 18.60 388.65 13.00 21.10
0.16211 20.00 6.960 0 0.4640 6.2400 16.30 4.4290 3 223.0 18.60 396.90 6.59 25.20
0.11460 20.00 6.960 0 0.4640 6.5380 58.70 3.9175 3 223.0 18.60 394.96 7.73 24.40
0.22188 20.00 6.960 1 0.4640 7.6910 51.80 4.3665 3 223.0 18.60 390.77 6.58 35.20
0.05644 40.00 6.410 1 0.4470 6.7580 32.90 4.0776 4 254.0 17.60 396.90 3.53 32.40
0.09604 40.00 6.410 0 0.4470 6.8540 42.80 4.2673 4 254.0 17.60 396.90 2.98 32.00
0.10469 40.00 6.410 1 0.4470 7.2670 49.00 4.7872 4 254.0 17.60 389.25 6.05 33.20
0.06127 40.00 6.410 1 0.4470 6.8260 27.60 4.8628 4 254.0 17.60 393.45 4.16 33.10
0.07978 40.00 6.410 0 0.4470 6.4820 32.10 4.1403 4 254.0 17.60 396.90 7.19 29.10
0.21038 20.00 3.330 0 0.4429 6.8120 32.20 4.1007 5 216.0 14.90 396.90 4.85 35.10
0.03578 20.00 3.330 0 0.4429 7.8200 64.50 4.6947 5 216.0 14.90 387.31 3.76 45.40
0.03705 20.00 3.330 0 0.4429 6.9680 37.20 5.2447 5 216.0 14.90 392.23 4.59 35.40
0.06129 20.00 3.330 1 0.4429 7.6450 49.70 5.2119 5 216.0 14.90 377.07 3.01 46.00
0.01501 90.00 1.210 1 0.4010 7.9230 24.80 5.8850 1 198.0 13.60 395.52 3.16 50.00
0.00906 90.00 2.970 0 0.4000 7.0880 20.80 7.3073 1 285.0 15.30 394.72 7.85 32.20
0.01096 55.00 2.250 0 0.3890 6.4530 31.90 7.3073 1 300.0 15.30 394.72 8.23 22.00
0.01965 80.00 1.760 0 0.3850 6.2300 31.50 9.0892 1 241.0 18.20 341.60 12.93 20.10
0.03871 52.50 5.320 0 0.4050 6.2090 31.30 7.3172 6 293.0 16.60 396.90 7.14 23.20
0.04590 52.50 5.320 0 0.4050 6.3150 45.60 7.3172 6 293.0 16.60 396.90 7.60 22.30
0.04297 52.50 5.320 0 0.4050 6.5650 22.90 7.3172 6 293.0 16.60 371.72 9.51 24.80
0.03502 80.00 4.950 0 0.4110 6.8610 27.90 5.1167 4 245.0 19.20 396.90 3.33 28.50
0.07886 80.00 4.950 0 0.4110 7.1480 27.70 5.1167 4 245.0 19.20 396.90 3.56 37.30
0.03615 80.00 4.950 0 0.4110 6.6300 23.40 5.1167 4 245.0 19.20 396.90 4.70 27.90
0.08265 0.00 13.920 0 0.4370 6.1270 18.40 5.5027 4 289.0 16.00 396.90 8.58 23.90
0.08199 0.00 13.920 0 0.4370 6.0090 42.30 5.5027 4 289.0 16.00 396.90 10.40 21.70
0.12932 0.00 13.920 0 0.4370 6.6780 31.10 5.9604 4 289.0 16.00 396.90 6.27 28.60
0.05372 0.00 13.920 0 0.4370 6.5490 51.00 5.9604 4 289.0 16.00 392.85 7.39 27.10
0.14103 0.00 13.920 0 0.4370 5.7900 58.00 6.3200 4 289.0 16.00 396.90 15.84 20.30
0.06466 70.00 2.240 0 0.4000 6.3450 20.10 7.8278 5 358.0 14.80 368.24 4.97 22.50
0.05561 70.00 2.240 0 0.4000 7.0410 10.00 7.8278 5 358.0 14.80 371.58 4.74 29.00
0.04417 70.00 2.240 0 0.4000 6.8710 47.40 7.8278 5 358.0 14.80 390.86 6.07 24.80
0.03537 34.00 6.090 0 0.4330 6.5900 40.40 5.4917 7 329.0 16.10 395.75 9.50 22.00
0.09266 34.00 6.090 0 0.4330 6.4950 18.40 5.4917 7 329.0 16.10 383.61 8.67 26.40
0.10000 34.00 6.090 0 0.4330 6.9820 17.70 5.4917 7 329.0 16.10 390.43 4.86 33.10
0.05515 33.00 2.180 0 0.4720 7.2360 41.10 4.0220 7 222.0 18.40 393.68 6.93 36.10
0.05479 33.00 2.180 0 0.4720 6.6160 58.10 3.3700 7 222.0 18.40 393.36 8.93 28.40
0.07503 33.00 2.180 0 0.4720 7.4200 71.90 3.0992 7 222.0 18.40 396.90 6.47 33.40
0.04932 33.00 2.180 0 0.4720 6.8490 70.30 3.1827 7 222.0 18.40 396.90 7.53 28.20
0.49298 0.00 9.900 0 0.5440 6.6350 82.50 3.3175 4 304.0 18.40 396.90 4.54 22.80
0.34940 0.00 9.900 0 0.5440 5.9720 76.70 3.1025 4 304.0 18.40 396.24 9.97 20.30
2.63548 0.00 9.900 0 0.5440 4.9730 37.80 2.5194 4 304.0 18.40 350.45 12.64 16.10
0.79041 0.00 9.900 0 0.5440 6.1220 52.80 2.6403 4 304.0 18.40 396.90 5.98 22.10
0.26169 0.00 9.900 0 0.5440 6.0230 90.40 2.8340 4 304.0 18.40 396.30 11.72 19.40
0.26938 0.00 9.900 0 0.5440 6.2660 82.80 3.2628 4 304.0 18.40 393.39 7.90 21.60
0.36920 0.00 9.900 0 0.5440 6.5670 87.30 3.6023 4 304.0 18.40 395.69 9.28 23.80
0.25356 0.00 9.900 0 0.5440 5.7050 77.70 3.9450 4 304.0 18.40 396.42 11.50 16.20
0.31827 0.00 9.900 0 0.5440 5.9140 83.20 3.9986 4 304.0 18.40 390.70 18.33 17.80
0.24522 0.00 9.900 0 0.5440 5.7820 71.70 4.0317 4 304.0 18.40 396.90 15.94 19.80
0.40202 0.00 9.900 0 0.5440 6.3820 67.20 3.5325 4 304.0 18.40 395.21 10.36 23.10
0.47547 0.00 9.900 0 0.5440 6.1130 58.80 4.0019 4 304.0 18.40 396.23 12.73 21.00
0.16760 0.00 7.380 0 0.4930 6.4260 52.30 4.5404 5 287.0 19.60 396.90 7.20 23.80
0.18159 0.00 7.380 0 0.4930 6.3760 54.30 4.5404 5 287.0 19.60 396.90 6.87 23.10
0.35114 0.00 7.380 0 0.4930 6.0410 49.90 4.7211 5 287.0 19.60 396.90 7.70 20.40
0.28392 0.00 7.380 0 0.4930 5.7080 74.30 4.7211 5 287.0 19.60 391.13 11.74 18.50
0.34109 0.00 7.380 0 0.4930 6.4150 40.10 4.7211 5 287.0 19.60 396.90 6.12 25.00
0.19186 0.00 7.380 0 0.4930 6.4310 14.70 5.4159 5 287.0 19.60 393.68 5.08 24.60
0.30347 0.00 7.380 0 0.4930 6.3120 28.90 5.4159 5 287.0 19.60 396.90 6.15 23.00
0.24103 0.00 7.380 0 0.4930 6.0830 43.70 5.4159 5 287.0 19.60 396.90 12.79 22.20
0.06617 0.00 3.240 0 0.4600 5.8680 25.80 5.2146 4 430.0 16.90 382.44 9.97 19.30
0.06724 0.00 3.240 0 0.4600 6.3330 17.20 5.2146 4 430.0 16.90 375.21 7.34 22.60
0.04544 0.00 3.240 0 0.4600 6.1440 32.20 5.8736 4 430.0 16.90 368.57 9.09 19.80
0.05023 35.00 6.060 0 0.4379 5.7060 28.40 6.6407 1 304.0 16.90 394.02 12.43 17.10
0.03466 35.00 6.060 0 0.4379 6.0310 23.30 6.6407 1 304.0 16.90 362.25 7.83 19.40
0.05083 0.00 5.190 0 0.5150 6.3160 38.10 6.4584 5 224.0 20.20 389.71 5.68 22.20
0.03738 0.00 5.190 0 0.5150 6.3100 38.50 6.4584 5 224.0 20.20 389.40 6.75 20.70
0.03961 0.00 5.190 0 0.5150 6.0370 34.50 5.9853 5 224.0 20.20 396.90 8.01 21.10
0.03427 0.00 5.190 0 0.5150 5.8690 46.30 5.2311 5 224.0 20.20 396.90 9.80 19.50
0.03041 0.00 5.190 0 0.5150 5.8950 59.60 5.6150 5 224.0 20.20 394.81 10.56 18.50
0.03306 0.00 5.190 0 0.5150 6.0590 37.30 4.8122 5 224.0 20.20 396.14 8.51 20.60
0.05497 0.00 5.190 0 0.5150 5.9850 45.40 4.8122 5 224.0 20.20 396.90 9.74 19.00
0.06151 0.00 5.190 0 0.5150 5.9680 58.50 4.8122 5 224.0 20.20 396.90 9.29 18.70
0.01301 35.00 1.520 0 0.4420 7.2410 49.30 7.0379 1 284.0 15.50 394.74 5.49 32.70
0.02498 0.00 1.890 0 0.5180 6.5400 59.70 6.2669 1 422.0 15.90 389.96 8.65 16.50
0.02543 55.00 3.780 0 0.4840 6.6960 56.40 5.7321 5 370.0 17.60 396.90 7.18 23.90
0.03049 55.00 3.780 0 0.4840 6.8740 28.10 6.4654 5 370.0 17.60 387.97 4.61 31.20
0.03113 0.00 4.390 0 0.4420 6.0140 48.50 8.0136 3 352.0 18.80 385.64 10.53 17.50
0.06162 0.00 4.390 0 0.4420 5.8980 52.30 8.0136 3 352.0 18.80 364.61 12.67 17.20
0.01870 85.00 4.150 0 0.4290 6.5160 27.70 8.5353 4 351.0 17.90 392.43 6.36 23.10
0.01501 80.00 2.010 0 0.4350 6.6350 29.70 8.3440 4 280.0 17.00 390.94 5.99 24.50
0.02899 40.00 1.250 0 0.4290 6.9390 34.50 8.7921 1 335.0 19.70 389.85 5.89 26.60
0.06211 40.00 1.250 0 0.4290 6.4900 44.40 8.7921 1 335.0 19.70 396.90 5.98 22.90
0.07950 60.00 1.690 0 0.4110 6.5790 35.90 10.7103 4 411.0 18.30 370.78 5.49 24.10
0.07244 60.00 1.690 0 0.4110 5.8840 18.50 10.7103 4 411.0 18.30 392.33 7.79 18.60
0.01709 90.00 2.020 0 0.4100 6.7280 36.10 12.1265 5 187.0 17.00 384.46 4.50 30.10
0.04301 80.00 1.910 0 0.4130 5.6630 21.90 10.5857 4 334.0 22.00 382.80 8.05 18.20
0.10659 80.00 1.910 0 0.4130 5.9360 19.50 10.5857 4 334.0 22.00 376.04 5.57 20.60
8.98296 0.00 18.100 1 0.7700 6.2120 97.40 2.1222 24 666.0 20.20 377.73 17.60 17.80
3.84970 0.00 18.100 1 0.7700 6.3950 91.00 2.5052 24 666.0 20.20 391.34 13.27 21.70
5.20177 0.00 18.100 1 0.7700 6.1270 83.40 2.7227 24 666.0 20.20 395.43 11.48 22.70
4.26131 0.00 18.100 0 0.7700 6.1120 81.30 2.5091 24 666.0 20.20 390.74 12.67 22.60
4.54192 0.00 18.100 0 0.7700 6.3980 88.00 2.5182 24 666.0 20.20 374.56 7.79 25.00
3.83684 0.00 18.100 0 0.7700 6.2510 91.10 2.2955 24 666.0 20.20 350.65 14.19 19.90
3.67822 0.00 18.100 0 0.7700 5.3620 96.20 2.1036 24 666.0 20.20 380.79 10.19 20.80
4.22239 0.00 18.100 1 0.7700 5.8030 89.00 1.9047 24 666.0 20.20 353.04 14.64 16.80
3.47428 0.00 18.100 1 0.7180 8.7800 82.90 1.9047 24 666.0 20.20 354.55 5.29 21.90
4.55587 0.00 18.100 0 0.7180 3.5610 87.90 1.6132 24 666.0 20.20 354.70 7.12 27.50
3.69695 0.00 18.100 0 0.7180 4.9630 91.40 1.7523 24 666.0 20.20 316.03 14.00 21.90
13.52220 0.00 18.100 0 0.6310 3.8630 100.00 1.5106 24 666.0 20.20 131.42 13.33 23.10
4.89822 0.00 18.100 0 0.6310 4.9700 100.00 1.3325 24 666.0 20.20 375.52 3.26 50.00
5.66998 0.00 18.100 1 0.6310 6.6830 96.80 1.3567 24 666.0 20.20 375.33 3.73 50.00
6.53876 0.00 18.100 1 0.6310 7.0160 97.50 1.2024 24 666.0 20.20 392.05 2.96 50.00
9.23230 0.00 18.100 0 0.6310 6.2160 100.00 1.1691 24 666.0 20.20 366.15 9.53 50.00
8.26725 0.00 18.100 1 0.6680 5.8750 89.60 1.1296 24 666.0 20.20 347.88 8.88 50.00
11.10810 0.00 18.100 0 0.6680 4.9060 100.00 1.1742 24 666.0 20.20 396.90 34.77 13.80
18.49820 0.00 18.100 0 0.6680 4.1380 100.00 1.1370 24 666.0 20.20 396.90 37.97 13.80
19.60910 0.00 18.100 0 0.6710 7.3130 97.90 1.3163 24 666.0 20.20 396.90 13.44 15.00
15.28800 0.00 18.100 0 0.6710 6.6490 93.30 1.3449 24 666.0 20.20 363.02 23.24 13.90
9.82349 0.00 18.100 0 0.6710 6.7940 98.80 1.3580 24 666.0 20.20 396.90 21.24 13.30
23.64820 0.00 18.100 0 0.6710 6.3800 96.20 1.3861 24 666.0 20.20 396.90 23.69 13.10
17.86670 0.00 18.100 0 0.6710 6.2230 100.00 1.3861 24 666.0 20.20 393.74 21.78 10.20
88.97620 0.00 18.100 0 0.6710 6.9680 91.90 1.4165 24 666.0 20.20 396.90 17.21 10.40
15.87440 0.00 18.100 0 0.6710 6.5450 99.10 1.5192 24 666.0 20.20 396.90 21.08 10.90
9.18702 0.00 18.100 0 0.7000 5.5360 100.00 1.5804 24 666.0 20.20 396.90 23.60 11.30
7.99248 0.00 18.100 0 0.7000 5.5200 100.00 1.5331 24 666.0 20.20 396.90 24.56 12.30
20.08490 0.00 18.100 0 0.7000 4.3680 91.20 1.4395 24 666.0 20.20 285.83 30.63 8.80
16.81180 0.00 18.100 0 0.7000 5.2770 98.10 1.4261 24 666.0 20.20 396.90 30.81 7.20
24.39380 0.00 18.100 0 0.7000 4.6520 100.00 1.4672 24 666.0 20.20 396.90 28.28 10.50
22.59710 0.00 18.100 0 0.7000 5.0000 89.50 1.5184 24 666.0 20.20 396.90 31.99 7.40
14.33370 0.00 18.100 0 0.7000 4.8800 100.00 1.5895 24 666.0 20.20 372.92 30.62 10.20
8.15174 0.00 18.100 0 0.7000 5.3900 98.90 1.7281 24 666.0 20.20 396.90 20.85 11.50
6.96215 0.00 18.100 0 0.7000 5.7130 97.00 1.9265 24 666.0 20.20 394.43 17.11 15.10
5.29305 0.00 18.100 0 0.7000 6.0510 82.50 2.1678 24 666.0 20.20 378.38 18.76 23.20
11.57790 0.00 18.100 0 0.7000 5.0360 97.00 1.7700 24 666.0 20.20 396.90 25.68 9.70
8.64476 0.00 18.100 0 0.6930 6.1930 92.60 1.7912 24 666.0 20.20 396.90 15.17 13.80
13.35980 0.00 18.100 0 0.6930 5.8870 94.70 1.7821 24 666.0 20.20 396.90 16.35 12.70
8.71675 0.00 18.100 0 0.6930 6.4710 98.80 1.7257 24 666.0 20.20 391.98 17.12 13.10
5.87205 0.00 18.100 0 0.6930 6.4050 96.00 1.6768 24 666.0 20.20 396.90 19.37 12.50
7.67202 0.00 18.100 0 0.6930 5.7470 98.90 1.6334 24 666.0 20.20 393.10 19.92 8.50
38.35180 0.00 18.100 0 0.6930 5.4530 100.00 1.4896 24 666.0 20.20 396.90 30.59 5.00
9.91655 0.00 18.100 0 0.6930 5.8520 77.80 1.5004 24 666.0 20.20 338.16 29.97 6.30
25.04610 0.00 18.100 0 0.6930 5.9870 100.00 1.5888 24 666.0 20.20 396.90 26.77 5.60
14.23620 0.00 18.100 0 0.6930 6.3430 100.00 1.5741 24 666.0 20.20 396.90 20.32 7.20
9.59571 0.00 18.100 0 0.6930 6.4040 100.00 1.6390 24 666.0 20.20 376.11 20.31 12.10
24.80170 0.00 18.100 0 0.6930 5.3490 96.00 1.7028 24 666.0 20.20 396.90 19.77 8.30
41.52920 0.00 18.100 0 0.6930 5.5310 85.40 1.6074 24 666.0 20.20 329.46 27.38 8.50
67.92080 0.00 18.100 0 0.6930 5.6830 100.00 1.4254 24 666.0 20.20 384.97 22.98 5.00
20.71620 0.00 18.100 0 0.6590 4.1380 100.00 1.1781 24 666.0 20.20 370.22 23.34 11.90
11.95110 0.00 18.100 0 0.6590 5.6080 100.00 1.2852 24 666.0 20.20 332.09 12.13 27.90
7.40389 0.00 18.100 0 0.5970 5.6170 97.90 1.4547 24 666.0 20.20 314.64 26.40 17.20
14.43830 0.00 18.100 0 0.5970 6.8520 100.00 1.4655 24 666.0 20.20 179.36 19.78 27.50
51.13580 0.00 18.100 0 0.5970 5.7570 100.00 1.4130 24 666.0 20.20 2.60 10.11 15.00
14.05070 0.00 18.100 0 0.5970 6.6570 100.00 1.5275 24 666.0 20.20 35.05 21.22 17.20
18.81100 0.00 18.100 0 0.5970 4.6280 100.00 1.5539 24 666.0 20.20 28.79 34.37 17.90
28.65580 0.00 18.100 0 0.5970 5.1550 100.00 1.5894 24 666.0 20.20 210.97 20.08 16.30
45.74610 0.00 18.100 0 0.6930 4.5190 100.00 1.6582 24 666.0 20.20 88.27 36.98 7.00
18.08460 0.00 18.100 0 0.6790 6.4340 100.00 1.8347 24 666.0 20.20 27.25 29.05 7.20
10.83420 0.00 18.100 0 0.6790 6.7820 90.80 1.8195 24 666.0 20.20 21.57 25.79 7.50
25.94060 0.00 18.100 0 0.6790 5.3040 89.10 1.6475 24 666.0 20.20 127.36 26.64 10.40
73.53410 0.00 18.100 0 0.6790 5.9570 100.00 1.8026 24 666.0 20.20 16.45 20.62 8.80
11.81230 0.00 18.100 0 0.7180 6.8240 76.50 1.7940 24 666.0 20.20 48.45 22.74 8.40
11.08740 0.00 18.100 0 0.7180 6.4110 100.00 1.8589 24 666.0 20.20 318.75 15.02 16.70
7.02259 0.00 18.100 0 0.7180 6.0060 95.30 1.8746 24 666.0 20.20 319.98 15.70 14.20
12.04820 0.00 18.100 0 0.6140 5.6480 87.60 1.9512 24 666.0 20.20 291.55 14.10 20.80
7.05042 0.00 18.100 0 0.6140 6.1030 85.10 2.0218 24 666.0 20.20 2.52 23.29 13.40
8.79212 0.00 18.100 0 0.5840 5.5650 70.60 2.0635 24 666.0 20.20 3.65 17.16 11.70
15.86030 0.00 18.100 0 0.6790 5.8960 95.40 1.9096 24 666.0 20.20 7.68 24.39 8.30
12.24720 0.00 18.100 0 0.5840 5.8370 59.70 1.9976 24 666.0 20.20 24.65 15.69 10.20
37.66190 0.00 18.100 0 0.6790 6.2020 78.70 1.8629 24 666.0 20.20 18.82 14.52 10.90
7.36711 0.00 18.100 0 0.6790 6.1930 78.10 1.9356 24 666.0 20.20 96.73 21.52 11.00
9.33889 0.00 18.100 0 0.6790 6.3800 95.60 1.9682 24 666.0 20.20 60.72 24.08 9.50
8.49213 0.00 18.100 0 0.5840 6.3480 86.10 2.0527 24 666.0 20.20 83.45 17.64 14.50
10.06230 0.00 18.100 0 0.5840 6.8330 94.30 2.0882 24 666.0 20.20 81.33 19.69 14.10
6.44405 0.00 18.100 0 0.5840 6.4250 74.80 2.2004 24 666.0 20.20 97.95 12.03 16.10
5.58107 0.00 18.100 0 0.7130 6.4360 87.90 2.3158 24 666.0 20.20 100.19 16.22 14.30
13.91340 0.00 18.100 0 0.7130 6.2080 95.00 2.2222 24 666.0 20.20 100.63 15.17 11.70
11.16040 0.00 18.100 0 0.7400 6.6290 94.60 2.1247 24 666.0 20.20 109.85 23.27 13.40
14.42080 0.00 18.100 0 0.7400 6.4610 93.30 2.0026 24 666.0 20.20 27.49 18.05 9.60
15.17720 0.00 18.100 0 0.7400 6.1520 100.00 1.9142 24 666.0 20.20 9.32 26.45 8.70
13.67810 0.00 18.100 0 0.7400 5.9350 87.90 1.8206 24 666.0 20.20 68.95 34.02 8.40
9.39063 0.00 18.100 0 0.7400 5.6270 93.90 1.8172 24 666.0 20.20 396.90 22.88 12.80
22.05110 0.00 18.100 0 0.7400 5.8180 92.40 1.8662 24 666.0 20.20 391.45 22.11 10.50
9.72418 0.00 18.100 0 0.7400 6.4060 97.20 2.0651 24 666.0 20.20 385.96 19.52 17.10
5.66637 0.00 18.100 0 0.7400 6.2190 100.00 2.0048 24 666.0 20.20 395.69 16.59 18.40
9.96654 0.00 18.100 0 0.7400 6.4850 100.00 1.9784 24 666.0 20.20 386.73 18.85 15.40
12.80230 0.00 18.100 0 0.7400 5.8540 96.60 1.8956 24 666.0 20.20 240.52 23.79 10.80
10.67180 0.00 18.100 0 0.7400 6.4590 94.80 1.9879 24 666.0 20.20 43.06 23.98 11.80
6.28807 0.00 18.100 0 0.7400 6.3410 96.40 2.0720 24 666.0 20.20 318.01 17.79 14.90
9.92485 0.00 18.100 0 0.7400 6.2510 96.60 2.1980 24 666.0 20.20 388.52 16.44 12.60
9.32909 0.00 18.100 0 0.7130 6.1850 98.70 2.2616 24 666.0 20.20 396.90 18.13 14.10
7.52601 0.00 18.100 0 0.7130 6.4170 98.30 2.1850 24 666.0 20.20 304.21 19.31 13.00
6.71772 0.00 18.100 0 0.7130 6.7490 92.60 2.3236 24 666.0 20.20 0.32 17.44 13.40
5.44114 0.00 18.100 0 0.7130 6.6550 98.20 2.3552 24 666.0 20.20 355.29 17.73 15.20
5.09017 0.00 18.100 0 0.7130 6.2970 91.80 2.3682 24 666.0 20.20 385.09 17.27 16.10
8.24809 0.00 18.100 0 0.7130 7.3930 99.30 2.4527 24 666.0 20.20 375.87 16.74 17.80
9.51363 0.00 18.100 0 0.7130 6.7280 94.10 2.4961 24 666.0 20.20 6.68 18.71 14.90
4.75237 0.00 18.100 0 0.7130 6.5250 86.50 2.4358 24 666.0 20.20 50.92 18.13 14.10
4.66883 0.00 18.100 0 0.7130 5.9760 87.90 2.5806 24 666.0 20.20 10.48 19.01 12.70
8.20058 0.00 18.100 0 0.7130 5.9360 80.30 2.7792 24 666.0 20.20 3.50 16.94 13.50
7.75223 0.00 18.100 0 0.7130 6.3010 83.70 2.7831 24 666.0 20.20 272.21 16.23 14.90
6.80117 0.00 18.100 0 0.7130 6.0810 84.40 2.7175 24 666.0 20.20 396.90 14.70 20.00
4.81213 0.00 18.100 0 0.7130 6.7010 90.00 2.5975 24 666.0 20.20 255.23 16.42 16.40
3.69311 0.00 18.100 0 0.7130 6.3760 88.40 2.5671 24 666.0 20.20 391.43 14.65 17.70
6.65492 0.00 18.100 0 0.7130 6.3170 83.00 2.7344 24 666.0 20.20 396.90 13.99 19.50
5.82115 0.00 18.100 0 0.7130 6.5130 89.90 2.8016 24 666.0 20.20 393.82 10.29 20.20
7.83932 0.00 18.100 0 0.6550 6.2090 65.40 2.9634 24 666.0 20.20 396.90 13.22 21.40
3.16360 0.00 18.100 0 0.6550 5.7590 48.20 3.0665 24 666.0 20.20 334.40 14.13 19.90
3.77498 0.00 18.100 0 0.6550 5.9520 84.70 2.8715 24 666.0 20.20 22.01 17.15 19.00
4.42228 0.00 18.100 0 0.5840 6.0030 94.50 2.5403 24 666.0 20.20 331.29 21.32 19.10
15.57570 0.00 18.100 0 0.5800 5.9260 71.00 2.9084 24 666.0 20.20 368.74 18.13 19.10
13.07510 0.00 18.100 0 0.5800 5.7130 56.70 2.8237 24 666.0 20.20 396.90 14.76 20.10
4.34879 0.00 18.100 0 0.5800 6.1670 84.00 3.0334 24 666.0 20.20 396.90 16.29 19.90
4.03841 0.00 18.100 0 0.5320 6.2290 90.70 3.0993 24 666.0 20.20 395.33 12.87 19.60
3.56868 0.00 18.100 0 0.5800 6.4370 75.00 2.8965 24 666.0 20.20 393.37 14.36 23.20
4.64689 0.00 18.100 0 0.6140 6.9800 67.60 2.5329 24 666.0 20.20 374.68 11.66 29.80
8.05579 0.00 18.100 0 0.5840 5.4270 95.40 2.4298 24 666.0 20.20 352.58 18.14 13.80
6.39312 0.00 18.100 0 0.5840 6.1620 97.40 2.2060 24 666.0 20.20 302.76 24.10 13.30
4.87141 0.00 18.100 0 0.6140 6.4840 93.60 2.3053 24 666.0 20.20 396.21 18.68 16.70
15.02340 0.00 18.100 0 0.6140 5.3040 97.30 2.1007 24 666.0 20.20 349.48 24.91 12.00
10.23300 0.00 18.100 0 0.6140 6.1850 96.70 2.1705 24 666.0 20.20 379.70 18.03 14.60
14.33370 0.00 18.100 0 0.6140 6.2290 88.00 1.9512 24 666.0 20.20 383.32 13.11 21.40
5.82401 0.00 18.100 0 0.5320 6.2420 64.70 3.4242 24 666.0 20.20 396.90 10.74 23.00
5.70818 0.00 18.100 0 0.5320 6.7500 74.90 3.3317 24 666.0 20.20 393.07 7.74 23.70
5.73116 0.00 18.100 0 0.5320 7.0610 77.00 3.4106 24 666.0 20.20 395.28 7.01 25.00
2.81838 0.00 18.100 0 0.5320 5.7620 40.30 4.0983 24 666.0 20.20 392.92 10.42 21.80
2.37857 0.00 18.100 0 0.5830 5.8710 41.90 3.7240 24 666.0 20.20 370.73 13.34 20.60
3.67367 0.00 18.100 0 0.5830 6.3120 51.90 3.9917 24 666.0 20.20 388.62 10.58 21.20
5.69175 0.00 18.100 0 0.5830 6.1140 79.80 3.5459 24 666.0 20.20 392.68 14.98 19.10
4.83567 0.00 18.100 0 0.5830 5.9050 53.20 3.1523 24 666.0 20.20 388.22 11.45 20.60
0.15086 0.00 27.740 0 0.6090 5.4540 92.70 1.8209 4 711.0 20.10 395.09 18.06 15.20
0.18337 0.00 27.740 0 0.6090 5.4140 98.30 1.7554 4 711.0 20.10 344.05 23.97 7.00
0.20746 0.00 27.740 0 0.6090 5.0930 98.00 1.8226 4 711.0 20.10 318.43 29.68 8.10
0.10574 0.00 27.740 0 0.6090 5.9830 98.80 1.8681 4 711.0 20.10 390.11 18.07 13.60
0.11132 0.00 27.740 0 0.6090 5.9830 83.50 2.1099 4 711.0 20.10 396.90 13.35 20.10
0.17331 0.00 9.690 0 0.5850 5.7070 54.00 2.3817 6 391.0 19.20 396.90 12.01 21.80
0.27957 0.00 9.690 0 0.5850 5.9260 42.60 2.3817 6 391.0 19.20 396.90 13.59 24.50
0.17899 0.00 9.690 0 0.5850 5.6700 28.80 2.7986 6 391.0 19.20 393.29 17.60 23.10
0.28960 0.00 9.690 0 0.5850 5.3900 72.90 2.7986 6 391.0 19.20 396.90 21.14 19.70
0.26838 0.00 9.690 0 0.5850 5.7940 70.60 2.8927 6 391.0 19.20 396.90 14.10 18.30
0.23912 0.00 9.690 0 0.5850 6.0190 65.30 2.4091 6 391.0 19.20 396.90 12.92 21.20
0.17783 0.00 9.690 0 0.5850 5.5690 73.50 2.3999 6 391.0 19.20 395.77 15.10 17.50
0.22438 0.00 9.690 0 0.5850 6.0270 79.70 2.4982 6 391.0 19.20 396.90 14.33 16.80
0.06263 0.00 11.930 0 0.5730 6.5930 69.10 2.4786 1 273.0 21.00 391.99 9.67 22.40
0.04527 0.00 11.930 0 0.5730 6.1200 76.70 2.2875 1 273.0 21.00 396.90 9.08 20.60
0.06076 0.00 11.930 0 0.5730 6.9760 91.00 2.1675 1 273.0 21.00 396.90 5.64 23.90
0.10959 0.00 11.930 0 0.5730 6.7940 89.30 2.3889 1 273.0 21.00 393.45 6.48 22.00
0.04741 0.00 11.930 0 0.5730 6.0300 80.80 2.5050 1 273.0 21.00 396.90 7.88 11.90