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some code to debug the sprase GP gradients with.
This commit is contained in:
James Hensman
parent
f92ff10e32
commit
1a135ca9f7
4 changed files with 144 additions and 24 deletions
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@ -363,7 +363,8 @@ class model(parameterised):
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grad_string = "{0:^{c0}}|{1:^{c1}}|{2:^{c2}}|{3:^{c3}}|{4:^{c4}}".format(formatted_name,r,d,g, ng, c0 = cols[0]+9, c1 = cols[1], c2 = cols[2], c3 = cols[3], c4 = cols[4])
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print grad_string
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print ''
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if verbose:
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print ''
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return False
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return True
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@ -3,7 +3,7 @@
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from GP_regression import GP_regression
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from sparse_GP_regression import sparse_GP_regression
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from sparse_GP_regression import sparse_GP_regression, sgp_debugB, sgp_debugC, sgp_debugE
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from GPLVM import GPLVM
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from warped_GP import warpedGP
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from GP_EP import GP_EP
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@ -197,3 +197,127 @@ class sparse_GP_regression(GP_regression):
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pb.errorbar(self.X[:,0], pb.ylim()[0]+np.zeros(self.N), xerr=2*np.sqrt(self.X_uncertainty.flatten()))
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if self.Q==2:
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pb.plot(self.Z[:,0],self.Z[:,1],'wo')
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class sgp_debugB(sparse_GP_regression):
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def _computations(self):
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self.V = self.beta*self.Y
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self.psi1V = np.dot(self.psi1, self.V)
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self.psi1VVpsi1 = np.dot(self.psi1V, self.psi1V.T)
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self.Kmmi, self.Lm, self.Lmi, self.Kmm_logdet = pdinv(self.Kmm)
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self.A = mdot(self.Lmi, self.beta*self.psi2, self.Lmi.T)
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self.B = np.eye(self.M) + self.A
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self.Bi, self.LB, self.LBi, self.B_logdet = pdinv(self.B)
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self.LLambdai = np.dot(self.LBi, self.Lmi)
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self.trace_K = self.psi0 - np.trace(self.A)/self.beta
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self.LBL_inv = mdot(self.Lmi.T, self.Bi, self.Lmi)
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self.C = mdot(self.LLambdai, self.psi1V)
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self.G = mdot(self.LBL_inv, self.psi1VVpsi1, self.LBL_inv.T)
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# Compute dL_dpsi
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self.dL_dpsi0 = - 0.5 * self.D * self.beta * np.ones(self.N)
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self.dL_dpsi1 = np.zeros_like(self.psi1)
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self.dL_dpsi2 = - 0.5 * self.beta * (self.D*( - self.Kmmi))
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# Compute dL_dKmm
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self.dL_dKmm = -0.5 * self.D * mdot(self.Lmi.T, self.A, self.Lmi) # dB
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def log_likelihood(self):
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A = -0.5*self.N*self.D*(np.log(2.*np.pi) - np.log(self.beta))
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B = -0.5*self.beta*self.D*self.trace_K
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C = -0.5*self.D * self.B_logdet
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D = -0.5*self.beta*self.trYYT
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E = +0.5*np.sum(self.psi1VVpsi1 * self.LBL_inv)
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return B
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def dL_dbeta(self):
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dA_dbeta = 0.5 * self.N*self.D/self.beta
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dB_dbeta = - 0.5 * self.D * self.trace_K
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dC_dbeta = - 0.5 * self.D * np.sum(self.Bi*self.A)/self.beta
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dD_dbeta = - 0.5 * self.trYYT
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tmp = mdot(self.LBi.T, self.LLambdai, self.psi1V)
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dE_dbeta = (np.sum(np.square(self.C)) - 0.5 * np.sum(self.A * np.dot(tmp, tmp.T)))/self.beta
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return np.squeeze(dB_dbeta)
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class sgp_debugC(sparse_GP_regression):
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def _computations(self):
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self.V = self.beta*self.Y
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self.psi1V = np.dot(self.psi1, self.V)
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self.psi1VVpsi1 = np.dot(self.psi1V, self.psi1V.T)
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self.Kmmi, self.Lm, self.Lmi, self.Kmm_logdet = pdinv(self.Kmm)
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self.A = mdot(self.Lmi, self.beta*self.psi2, self.Lmi.T)
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self.B = np.eye(self.M) + self.A
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self.Bi, self.LB, self.LBi, self.B_logdet = pdinv(self.B)
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self.LLambdai = np.dot(self.LBi, self.Lmi)
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self.trace_K = self.psi0 - np.trace(self.A)/self.beta
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self.LBL_inv = mdot(self.Lmi.T, self.Bi, self.Lmi)
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self.C = mdot(self.LLambdai, self.psi1V)
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self.G = mdot(self.LBL_inv, self.psi1VVpsi1, self.LBL_inv.T)
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# Compute dL_dpsi
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self.dL_dpsi0 = np.zeros(self.N)
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self.dL_dpsi1 = np.zeros_like(self.psi1)
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self.dL_dpsi2 = - 0.5 * self.beta * (self.D*(self.LBL_inv))
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# Compute dL_dKmm
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self.dL_dKmm = -0.5 * self.D * (- self.LBL_inv - 2.*self.beta*mdot(self.LBL_inv, self.psi2, self.Kmmi) + self.Kmmi) # dC
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def log_likelihood(self):
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A = -0.5*self.N*self.D*(np.log(2.*np.pi) - np.log(self.beta))
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B = -0.5*self.beta*self.D*self.trace_K
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C = -0.5*self.D * self.B_logdet
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D = -0.5*self.beta*self.trYYT
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E = +0.5*np.sum(self.psi1VVpsi1 * self.LBL_inv)
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return C
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def dL_dbeta(self):
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dA_dbeta = 0.5 * self.N*self.D/self.beta
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dB_dbeta = - 0.5 * self.D * self.trace_K
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dC_dbeta = - 0.5 * self.D * np.sum(self.Bi*self.A)/self.beta
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dD_dbeta = - 0.5 * self.trYYT
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tmp = mdot(self.LBi.T, self.LLambdai, self.psi1V)
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dE_dbeta = (np.sum(np.square(self.C)) - 0.5 * np.sum(self.A * np.dot(tmp, tmp.T)))/self.beta
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return np.squeeze(dC_dbeta)
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class sgp_debugE(sparse_GP_regression):
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def _computations(self):
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self.V = self.beta*self.Y
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self.psi1V = np.dot(self.psi1, self.V)
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self.psi1VVpsi1 = np.dot(self.psi1V, self.psi1V.T)
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self.Kmmi, self.Lm, self.Lmi, self.Kmm_logdet = pdinv(self.Kmm)
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self.A = mdot(self.Lmi, self.beta*self.psi2, self.Lmi.T)
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self.B = np.eye(self.M) + self.A
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self.Bi, self.LB, self.LBi, self.B_logdet = pdinv(self.B)
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self.LLambdai = np.dot(self.LBi, self.Lmi)
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self.trace_K = self.psi0 - np.trace(self.A)/self.beta
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self.LBL_inv = mdot(self.Lmi.T, self.Bi, self.Lmi)
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self.C = mdot(self.LLambdai, self.psi1V)
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self.G = mdot(self.LBL_inv, self.psi1VVpsi1, self.LBL_inv.T)
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# Compute dL_dpsi
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self.dL_dpsi0 = np.zeros(self.N)
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self.dL_dpsi1 = np.zeros_like(self.psi1)
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self.dL_dpsi2 = - 0.5 * self.beta * (self.G)
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# Compute dL_dKmm
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self.dL_dKmm = np.dot(np.dot(self.G,self.beta*self.psi2) - np.dot(self.LBL_inv, self.psi1VVpsi1), self.Kmmi) + 0.5*self.G # dE
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def log_likelihood(self):
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A = -0.5*self.N*self.D*(np.log(2.*np.pi) - np.log(self.beta))
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B = -0.5*self.beta*self.D*self.trace_K
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C = -0.5*self.D * self.B_logdet
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D = -0.5*self.beta*self.trYYT
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E = +0.5*np.sum(self.psi1VVpsi1 * self.LBL_inv)
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return E
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def dL_dbeta(self):
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dA_dbeta = 0.5 * self.N*self.D/self.beta
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dB_dbeta = - 0.5 * self.D * self.trace_K
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dC_dbeta = - 0.5 * self.D * np.sum(self.Bi*self.A)/self.beta
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dD_dbeta = - 0.5 * self.trYYT
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tmp = mdot(self.LBi.T, self.LLambdai, self.psi1V)
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dE_dbeta = (np.sum(np.square(self.C)) - 0.5 * np.sum(self.A * np.dot(tmp, tmp.T)))/self.beta
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return np.squeeze(dE_dbeta)
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@ -16,11 +16,14 @@ Y = np.sin(X) + np.random.randn(*X.shape)/np.sqrt(50.)
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k = GPy.kern.rbf(1)
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m = GPy.models.sparse_GP_regression(X,Y,Z=Z,kernel=k)
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m.constrain_fixed('iip')
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models = [GPy.models.sparse_GP_regression(X,Y,Z=Z,kernel=k),
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GPy.models.sgp_debugB(X,Y,Z=Z,kernel=k),
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GPy.models.sgp_debugC(X,Y,Z=Z,kernel=k),
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GPy.models.sgp_debugE(X,Y,Z=Z,kernel=k)]
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#[m.constrain_fixed('iip') for m in models]
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#m.constrain_fixed('white',1e-6)
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m.constrain_fixed('precision',50)
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m.ensure_default_constraints()
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#[m.constrain_fixed('precision',50) for m in models]
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#[m.ensure_default_constraints() for m in models]
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xx,yy = np.mgrid[1.5:4:0+resolution*1j,-2:2:0+resolution*1j]
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@ -28,24 +31,16 @@ xx,yy = np.mgrid[1.5:4:0+resolution*1j,-2:2:0+resolution*1j]
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lls = []
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cgs = []
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for l,v in zip(xx.flatten(),yy.flatten()):
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m.set('lengthscale',l)
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m.set('rbf_variance',10.**v)
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lls.append(m.log_likelihood())
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cgs.append(m.checkgrad())
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#m.plot()
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[m.set('lengthscale',l) for m in models]
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[m.set('rbf_variance',10.**v) for m in models]
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lls.append(models[0].log_likelihood())
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cgs.append([m.checkgrad(verbose=0) for m in models])
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lls = np.array(lls).reshape(resolution,resolution)
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cgs = np.array(cgs,dtype=np.float64).reshape(resolution,resolution)
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cgs = np.array(zip(*cgs),dtype=np.float64).reshape(-1,resolution,resolution)
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pb.contourf(xx,yy,lls,np.linspace(-500,560,100),linewidths=2,cmap=pb.cm.jet)
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pb.colorbar()
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pb.scatter(xx.flatten(),yy.flatten(),10,cgs.flatten(),linewidth=0,cmap=pb.cm.gray)
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pb.figure()
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#pb.imshow(lls,origin='upper',cmap=pb.cm.jet,extent=[xx[0,0],xx[-1,0],yy[0].min(),yy[0].max()],vmin=-500)
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pb.scatter(xx.flatten(),yy.flatten(),10,lls.flatten(),linewidth=0,cmap=pb.cm.jet)
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pb.colorbar()
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pb.figure()
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#pb.imshow(cgs,origin='upper',cmap=pb.cm.jet,extent=[xx[0,0],xx[-1,0],yy[0].min(),yy[0].max()])
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pb.scatter(xx.flatten(),yy.flatten(),10,cgs.flatten(),linewidth=0,cmap=pb.cm.jet)
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pb.colorbar()
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for cg in cgs:
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pb.figure()
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pb.contourf(xx,yy,lls,cmap=pb.cm.jet)
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pb.scatter(xx.flatten(),yy.flatten(),12,cg.flatten(),cmap=pb.cm.gray)
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