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kerns
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Nicolo Fusi
parent
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commit
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18 changed files with 1861 additions and 0 deletions
234
GPy/kern/rbf_ARD.py
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234
GPy/kern/rbf_ARD.py
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from kernpart import kernpart
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import numpy as np
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import hashlib
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class rbf_ARD(kernpart):
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def __init__(self,D,variance=1.,lengthscales=None):
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"""
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Arguments
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----------
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D: int - the number of input dimensions
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variance: float
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lengthscales : np.ndarray of shape (D,)
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"""
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self.D = D
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if lengthscales is not None:
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assert lengthscales.shape==(self.D,)
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else:
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lengthscales = np.ones(self.D)
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self.Nparam = self.D + 1
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self.name = 'rbf_ARD'
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self.set_param(np.hstack((variance,lengthscales)))
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#initialize cache
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self._Z, self._mu, self._S = np.empty(shape=(3,1))
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self._X, self._X2, self._params = np.empty(shape=(3,1))
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def get_param(self):
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return np.hstack((self.variance,self.lengthscales))
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def set_param(self,x):
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assert x.size==(self.D+1)
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self.variance = x[0]
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self.lengthscales = x[1:]
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self.lengthscales2 = np.square(self.lengthscales)
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#reset cached results
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self._Z, self._mu, self._S = np.empty(shape=(3,1)) # cached versions of Z,mu,S
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def get_param_names(self):
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if self.D==1:
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return ['variance','lengthscale']
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else:
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return ['variance']+['lengthscale_%i'%i for i in range(self.lengthscales.size)]
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def K(self,X,X2,target):
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self._K_computations(X,X2)
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np.add(self.variance*self._K_dvar, target,target)
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def Kdiag(self,X,target):
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np.add(target,self.variance,target)
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def dK_dtheta(self,X,X2,target):
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"""Return shape is NxMx(Ntheta)"""
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self._K_computations(X,X2)
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dl = self._K_dvar[:,:,None]*self.variance*self._K_dist2/self.lengthscales
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np.add(target[:,:,0],self._K_dvar, target[:,:,0])
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np.add(target[:,:,1:],dl, target[:,:,1:])
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def dKdiag_dtheta(self,X,target):
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np.add(target[:,0],1.,target[:,0])
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def dK_dX(self,X,X2,target):
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self._K_computations(X,X2)
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dZ = self.variance*self._K_dvar[:,:,None]*self._K_dist/self.lengthscales2
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np.add(target,-dZ.transpose(1,0,2),target)
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def psi0(self,Z,mu,S,target):
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np.add(target, self.variance, target)
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def dpsi0_dtheta(self,Z,mu,S,target):
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target[:,0] += 1.
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def dpsi0_dmuS(self,Z,mu,S,target_mu,target_S):
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pass
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def psi1(self,Z,mu,S,target):
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"""Think N,M,Q """
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self._psi_computations(Z,mu,S)
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np.add(target, self._psi1,target)
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def dpsi1_dtheta(self,Z,mu,S,target):
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"""N,Q,(Ntheta)"""
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self._psi_computations(Z,mu,S)
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denom_deriv = S[:,None,:]/(self.lengthscales**3+self.lengthscales*S[:,None,:])
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d_length = self._psi1[:,:,None]*(self.lengthscales*np.square(self._psi1_dist/(self.lengthscales2+S[:,None,:])) + denom_deriv)
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target[:,:,0] += self._psi1/self.variance
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target[:,:,1:] += d_length
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def dpsi1_dZ(self,Z,mu,S,target):
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self._psi_computations(Z,mu,S)
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np.add(target,-self._psi1[:,:,None]*self._psi1_dist/self.lengthscales2/self._psi1_denom,target)
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def dpsi1_dmuS(self,Z,mu,S,target_mu,target_S):
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"""return shapes are N,M,Q"""
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self._psi_computations(Z,mu,S)
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tmp = self._psi1[:,:,None]/self.lengthscales2/self._psi1_denom
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np.add(target_mu,tmp*self._psi1_dist,target_mu)
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np.add(target_S, 0.5*tmp*(self._psi1_dist_sq-1), target_S)
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def psi2(self,Z,mu,S,target):
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"""shape N,M,M"""
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self._psi_computations(Z,mu,S)
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np.add(target, self._psi2,target)
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def dpsi2_dtheta(self,Z,mu,S,target):
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"""Shape N,M,M,Ntheta"""
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self._psi_computations(Z,mu,S)
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d_var = np.sum(2.*self._psi2/self.variance,0)
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d_length = self._psi2[:,:,:,None]*(0.5*self._psi2_Zdist_sq*self._psi2_denom + 2.*self._psi2_mudist_sq + 2.*S[:,None,None,:]/self.lengthscales2)/(self.lengthscales*self._psi2_denom)
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d_length = d_length.sum(0)
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target[:,:,0] += d_var
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target[:,:,1:] += d_length
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def dpsi2_dZ(self,Z,mu,S,target):
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"""Returns shape N,M,M,Q"""
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self._psi_computations(Z,mu,S)
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dZ = self._psi2[:,:,:,None]/self.lengthscales2*(-0.5*self._psi2_Zdist + self._psi2_mudist/self._psi2_denom)
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target += dZ
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def dpsi2_dmuS(self,Z,mu,S,target_mu,target_S):
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"""Think N,M,M,Q """
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self._psi_computations(Z,mu,S)
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tmp = self._psi2[:,:,:,None]/self.lengthscales2/self._psi2_denom
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np.add(target_mu, -tmp*(2.*self._psi2_mudist),target_mu) #N,M,M,Q
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np.add(target_S, tmp*(2.*self._psi2_mudist_sq-1), target_S) #N,M,M,Q
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def _K_computations(self,X,X2):
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if not (np.all(X==self._X) and np.all(X2==self._X2)):
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self._X = X
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self._X2 = X2
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if X2 is None: X2 = X
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self._K_dist = X[:,None,:]-X2[None,:,:] # this can be computationally heavy
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self._params = np.empty(shape=(1,0))#ensure the next section gets called
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if not np.all(self._params == self.get_param()):
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self._params == self.get_param()
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self._K_dist2 = np.square(self._K_dist/self.lengthscales)
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self._K_exponent = -0.5*self._K_dist2.sum(-1)
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self._K_dvar = np.exp(-0.5*self._K_dist2.sum(-1))
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def _psi_computations(self,Z,mu,S):
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#here are the "statistics" for psi1 and psi2
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if not np.all(Z==self._Z):
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#Z has changed, compute Z specific stuff
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self._psi2_Zhat = 0.5*(Z[:,None,:] +Z[None,:,:]) # M,M,Q
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self._psi2_Zdist = Z[:,None,:]-Z[None,:,:] # M,M,Q
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self._psi2_Zdist_sq = np.square(self._psi2_Zdist)/self.lengthscales2 # M,M,Q
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self._Z = Z
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if not (np.all(Z==self._Z) and np.all(mu==self._mu) and np.all(S==self._S)):
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#something's changed. recompute EVERYTHING
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#psi1
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self._psi1_denom = S[:,None,:]/self.lengthscales2 + 1.
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self._psi1_dist = Z[None,:,:]-mu[:,None,:]
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self._psi1_dist_sq = np.square(self._psi1_dist)/self.lengthscales2/self._psi1_denom
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self._psi1_exponent = -0.5*np.sum(self._psi1_dist_sq+np.log(self._psi1_denom),-1)
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self._psi1 = self.variance*np.exp(self._psi1_exponent)
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#psi2
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self._psi2_denom = 2.*S[:,None,None,:]/self.lengthscales2+1. # N,M,M,Q
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self._psi2_mudist = mu[:,None,None,:]-self._psi2_Zhat #N,M,M,Q
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self._psi2_mudist_sq = np.square(self._psi2_mudist)/(self.lengthscales2*self._psi2_denom)
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self._psi2_exponent = np.sum(-self._psi2_Zdist_sq/4. -self._psi2_mudist_sq -0.5*np.log(self._psi2_denom),-1) #N,M,M
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self._psi2 = np.square(self.variance)*np.exp(self._psi2_exponent) # N,M,M
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self._Z, self._mu, self._S = Z, mu,S
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if __name__=='__main__':
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#run some simple tests on the kernel (TODO:move these to unititest)
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#TODO: these are broken in this new structure!
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N = 10
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M = 5
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Q = 3
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Z = np.random.randn(M,Q)
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mu = np.random.randn(N,Q)
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S = np.random.rand(N,Q)
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var = 2.5
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lengthscales = np.ones(Q)*0.7
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k = rbf(Q,var,lengthscales)
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from checkgrad import checkgrad
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def k_theta_test(param,k):
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k.set_param(param)
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K = k.K(Z)
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dK_dtheta = k.dK_dtheta(Z)
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f = np.sum(K)
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df = dK_dtheta.sum(0).sum(0)
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return f,np.array(df)
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print "dk_dtheta_test"
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checkgrad(k_theta_test,np.random.randn(1+Q),args=(k,))
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def psi1_mu_test(mu,k):
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mu = mu.reshape(N,Q)
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f = np.sum(k.psi1(Z,mu,S))
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df = k.dpsi1_dmuS(Z,mu,S)[0].sum(1)
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return f,df.flatten()
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print "psi1_mu_test"
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checkgrad(psi1_mu_test,np.random.randn(N*Q),args=(k,))
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def psi1_S_test(S,k):
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S = S.reshape(N,Q)
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f = np.sum(k.psi1(Z,mu,S))
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df = k.dpsi1_dmuS(Z,mu,S)[1].sum(1)
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return f,df.flatten()
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print "psi1_S_test"
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checkgrad(psi1_S_test,np.random.rand(N*Q),args=(k,))
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def psi1_theta_test(theta,k):
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k.set_param(theta)
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f = np.sum(k.psi1(Z,mu,S))
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df = np.array([np.sum(grad) for grad in k.dpsi1_dtheta(Z,mu,S)])
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return f,df
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print "psi1_theta_test"
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checkgrad(psi1_theta_test,np.random.rand(1+Q),args=(k,))
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def psi2_mu_test(mu,k):
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mu = mu.reshape(N,Q)
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f = np.sum(k.psi2(Z,mu,S))
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df = k.dpsi2_dmuS(Z,mu,S)[0].sum(1).sum(1)
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return f,df.flatten()
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print "psi2_mu_test"
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checkgrad(psi2_mu_test,np.random.randn(N*Q),args=(k,))
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def psi2_S_test(S,k):
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S = S.reshape(N,Q)
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f = np.sum(k.psi2(Z,mu,S))
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df = k.dpsi2_dmuS(Z,mu,S)[1].sum(1).sum(1)
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return f,df.flatten()
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print "psi2_S_test"
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checkgrad(psi2_S_test,np.random.rand(N*Q),args=(k,))
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def psi2_theta_test(theta,k):
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k.set_param(theta)
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f = np.sum(k.psi2(Z,mu,S))
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df = np.array([np.sum(grad) for grad in k.dpsi2_dtheta(Z,mu,S)])
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return f,df
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print "psi2_theta_test"
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checkgrad(psi2_theta_test,np.random.rand(1+Q),args=(k,))
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