Merge branch 'devel' of github.com:SheffieldML/GPy into devel

.gitignore

@@ -39,3 +39,11 @@ nosetests.xml
 
 #bfgs optimiser leaves this lying around
 iterate.dat
+
+# Nosetests #
+#############
+*.noseids
+
+# git merge files #
+###################
+*.orig

GPy/core/transformations.py

@@ -39,23 +39,29 @@ class logexp(transformation):
         return '(+ve)'
 
 class logexp_clipped(transformation):
-    def __init__(self):
+    max_bound = 1e300
+    min_bound = 1e-10
+    log_max_bound = np.log(max_bound)
+    log_min_bound = np.log(min_bound)
+    def __init__(self, lower=1e-6):
         self.domain = 'positive'
+        self.lower = lower
     def f(self, x):
-        f = np.log(1. + np.exp(x))
+        exp = np.exp(np.clip(x, self.log_min_bound, self.log_max_bound))
+        f = np.log(1. + exp)
         return f
     def finv(self, f):
-        return np.log(np.exp(f) - 1.)
+        return np.log(np.exp(np.clip(f, self.min_bound, self.max_bound)) - 1.)
     def gradfactor(self, f):
         ef = np.exp(f)
         gf = (ef - 1.) / ef
-        return np.where(f < 1e-6, 0, gf)
+        return np.where(f < self.lower, 0, gf)
     def initialize(self, f):
         if np.any(f < 0.):
             print "Warning: changing parameters to satisfy constraints"
         return np.abs(f)
     def __str__(self):
-        return '(+ve)'
+        return '(+ve_c)'
 
 class exponent(transformation):
     def __init__(self):

GPy/examples/classification.py

@@ -79,7 +79,6 @@ def toy_linear_1d_classification(seed=default_seed):
 
     data = GPy.util.datasets.toy_linear_1d_classification(seed=seed)
     Y = data['Y'][:, 0:1]
-    Y[Y == -1] = 0
 
     # Kernel object
     kernel = GPy.kern.rbf(1)
@@ -96,7 +95,7 @@ def toy_linear_1d_classification(seed=default_seed):
     m.update_likelihood_approximation()
     # Parameters optimization:
     m.optimize()
-    #m.EPEM() #FIXME
+    #m.pseudo_EM() #FIXME
 
     # Plot
     pb.subplot(211)
@@ -109,14 +108,13 @@ def toy_linear_1d_classification(seed=default_seed):
 
 def sparse_toy_linear_1d_classification(seed=default_seed):
     """
-    Simple 1D classification example
+    Sparse 1D classification example
     :param seed : seed value for data generation (default is 4).
     :type seed: int
     """
 
     data = GPy.util.datasets.toy_linear_1d_classification(seed=seed)
     Y = data['Y'][:, 0:1]
-    Y[Y == -1] = 0
 
     # Kernel object
     kernel = GPy.kern.rbf(1) + GPy.kern.white(1)
@@ -168,7 +166,6 @@ def sparse_crescent_data(inducing=10, seed=default_seed):
 
     sample = np.random.randint(0,data['X'].shape[0],inducing)
     Z = data['X'][sample,:]
-    #Z = (np.random.random_sample(2*inducing)*(data['X'].max()-data['X'].min())+data['X'].min()).reshape(inducing,-1)
 
     # create sparse GP EP model
     m = GPy.models.sparse_GP(data['X'],likelihood=likelihood,kernel=kernel,Z=Z)

GPy/examples/dimensionality_reduction.py

@@ -2,13 +2,11 @@
 # Licensed under the BSD 3-clause license (see LICENSE.txt)
 
 import numpy as np
-import pylab as pb
+from matplotlib import pyplot as plt
-from matplotlib import pyplot as plt, pyplot
 
 import GPy
 from GPy.models.Bayesian_GPLVM import Bayesian_GPLVM
-from GPy.util.datasets import simulation_BGPLVM
+from GPy.util.datasets import swiss_roll_generated
-from GPy.core.transformations import square, logexp_clipped
 
 default_seed = np.random.seed(123344)
 
@@ -47,10 +45,11 @@ def BGPLVM(seed=default_seed):
 
 def GPLVM_oil_100(optimize=True):
     data = GPy.util.datasets.oil_100()
+    Y = data['X']
 
     # create simple GP model
     kernel = GPy.kern.rbf(6, ARD=True) + GPy.kern.bias(6)
-    m = GPy.models.GPLVM(data['X'], 6, kernel=kernel)
+    m = GPy.models.GPLVM(Y, 6, kernel=kernel)
     m.data_labels = data['Y'].argmax(axis=1)
 
     # optimize
@@ -63,27 +62,88 @@ def GPLVM_oil_100(optimize=True):
     m.plot_latent(labels=m.data_labels)
     return m
 
-def BGPLVM_oil(optimize=True, N=100, Q=10, M=20, max_f_eval=300, plot=False):
+def swiss_roll(optimize=True, N=1000, M=15, Q=4, sigma=.2, plot=False):
+    from GPy.util.datasets import swiss_roll
+    from GPy.core.transformations import logexp_clipped
+
+    data = swiss_roll_generated(N=N, sigma=sigma)
+    Y = data['Y']
+    Y -= Y.mean()
+    Y /= Y.std()
+
+    t = data['t']
+    c = data['colors']
+
+    try:
+        from sklearn.manifold.isomap import Isomap
+        iso = Isomap().fit(Y)
+        X = iso.embedding_
+        if Q > 2:
+            X = np.hstack((X, np.random.randn(N, Q - 2)))
+    except ImportError:
+        X = np.random.randn(N, Q)
+
+    if plot:
+        from mpl_toolkits import mplot3d
+        import pylab
+        fig = pylab.figure("Swiss Roll Data")
+        ax = fig.add_subplot(121, projection='3d')
+        ax.scatter(*Y.T, c=c)
+        ax.set_title("Swiss Roll")
+
+        ax = fig.add_subplot(122)
+        ax.scatter(*X.T[:2], c=c)
+        ax.set_title("Initialization")
+
+
+    var = .5
+    S = (var * np.ones_like(X) + np.clip(np.random.randn(N, Q) * var ** 2,
+                                         - (1 - var),
+                                         (1 - var))) + .001
+    Z = np.random.permutation(X)[:M]
+
+    kernel = GPy.kern.rbf(Q, ARD=True) + GPy.kern.bias(Q, np.exp(-2)) + GPy.kern.white(Q, np.exp(-2))
+
+    m = Bayesian_GPLVM(Y, Q, X=X, X_variance=S, M=M, Z=Z, kernel=kernel)
+    m.data_colors = c
+    m.data_t = t
+
+    m.constrain('variance|length', logexp_clipped())
+    m['lengthscale'] = 1. # X.var(0).max() / X.var(0)
+    m['noise'] = Y.var() / 100.
+    m.ensure_default_constraints()
+
+    if optimize:
+        m.optimize('scg', messages=1)
+    return m
+
+def BGPLVM_oil(optimize=True, N=100, Q=5, M=25, max_f_eval=4e3, plot=False, **k):
     data = GPy.util.datasets.oil()
+    from GPy.core.transformations import logexp_clipped
+    np.random.seed(0)
 
     # create simple GP model
     kernel = GPy.kern.rbf(Q, ARD=True) + GPy.kern.bias(Q, np.exp(-2)) + GPy.kern.white(Q, np.exp(-2))
     Y = data['X'][:N]
-    m = GPy.models.Bayesian_GPLVM(Y, Q, kernel=kernel, M=M)
+    Yn = Y - Y.mean(0)
+    Yn /= Yn.std(0)
+
+    m = GPy.models.Bayesian_GPLVM(Yn, Q, kernel=kernel, M=M, **k)
     m.data_labels = data['Y'][:N].argmax(axis=1)
 
-    m.constrain('variance', logexp_clipped())
+#     m.constrain('variance', logexp_clipped())
-    m.constrain('length', logexp_clipped())
+#     m.constrain('length', logexp_clipped())
-    m['lengt'] = 100.
+    m['lengt'] = m.X.var(0).max() / m.X.var(0)
+    m['noise'] = Yn.var() / 100.
+
     m.ensure_default_constraints()
 
     # optimize
     if optimize:
-        m.unconstrain('noise'); m.constrain_fixed('noise', Y.var() / 100.)
+#         m.unconstrain('noise'); m.constrain_fixed('noise')
-        m.optimize('scg', messages=1, max_f_eval=150)
+#         m.optimize('scg', messages=1, max_f_eval=200)
-
+#         m.unconstrain('noise')
-        m.unconstrain('noise')
+#         m.constrain('noise', logexp_clipped())
-        m.constrain('noise', logexp_clipped())
         m.optimize('scg', messages=1, max_f_eval=max_f_eval)
 
     if plot:
@@ -115,6 +175,8 @@ def oil_100():
     # m.plot_latent(labels=data['Y'].argmax(axis=1))
     return m
 
+
+
 def _simulate_sincos(D1, D2, D3, N, M, Q, plot_sim=False):
     x = np.linspace(0, 4 * np.pi, N)[:, None]
     s1 = np.vectorize(lambda x: np.sin(x))
@@ -178,6 +240,7 @@ def _simulate_sincos(D1, D2, D3, N, M, Q, plot_sim=False):
     return slist, [S1, S2, S3], Ylist
 
 def bgplvm_simulation_matlab_compare():
+    from GPy.util.datasets import simulation_BGPLVM
     sim_data = simulation_BGPLVM()
     Y = sim_data['Y']
     S = sim_data['S']
@@ -213,6 +276,8 @@ def bgplvm_simulation(burnin='scg', plot_sim=False,
                       max_burnin=100, true_X=False,
                       do_opt=True,
                       max_f_eval=1000):
+    from GPy.core.transformations import logexp_clipped
+
     D1, D2, D3, N, M, Q = 15, 8, 8, 350, 3, 6
     slist, Slist, Ylist = _simulate_sincos(D1, D2, D3, N, M, Q, plot_sim)
 
@@ -317,6 +382,8 @@ def mrd_simulation(plot_sim=False):
 
     from GPy.models import mrd
     from GPy import kern
+    from GPy.core.transformations import logexp_clipped
+
     reload(mrd); reload(kern)
 
 #    k = kern.rbf(2, ARD=True) + kern.bias(2) + kern.white(2)
@@ -365,13 +432,23 @@ def mrd_silhouette():
     pass
 
 def brendan_faces():
+    from GPy import kern
     data = GPy.util.datasets.brendan_faces()
-    Y = data['Y'][0:-1:10, :]
+    Q = 2
-    m = GPy.models.GPLVM(data['Y'], 2)
+    # Y = data['Y'][0:-1:2, :]
+    Y = data['Y']
+    Yn = Y - Y.mean()
+    Yn /= Yn.std()
+
+    m = GPy.models.GPLVM(Yn, Q)#, M=Y.shape[0]/4)
 
     # optimize
+    # m.constrain_fixed('white', 1e-2)
+    # m.constrain_bounded('noise', 1e-6, 10)
+    m.constrain('rbf', GPy.core.transformations.logexp_clipped())
+
     m.ensure_default_constraints()
-    m.optimize(messages=1, max_f_eval=10000)
+    m.optimize('scg', messages=1, max_f_eval=10000)
 
     ax = m.plot_latent()
     y = m.likelihood.Y[0, :]

GPy/inference/SCG.py

@@ -111,7 +111,7 @@ def SCG(f, gradf, x, optargs=(), maxiters=500, max_f_eval=500, display=True, xto
         iteration += 1
         if display:
             print '\r',
-            print 'i: {0:>5g}  f:{1:> 12e}  b:{2:> 12e} |g|:{3:> 12e}'.format(iteration, fnow, beta, current_grad),
+            print 'Iter: {0:>0{mi}g}  Obj:{1:> 12e}  Scale:{2:> 12e}  |g|:{3:> 12e}'.format(iteration, float(fnow), float(beta), float(current_grad), mi=len(str(maxiters))),
             # print 'Iteration:', iteration, ' Objective:', fnow, '  Scale:', beta, '\r',
             sys.stdout.flush()
 
@@ -130,7 +130,8 @@ def SCG(f, gradf, x, optargs=(), maxiters=500, max_f_eval=500, display=True, xto
                 # If the gradient is zero then we are done.
                 if current_grad <= gtol:
                     status = 'converged'
-                    return x, flog, function_eval, status
+                    break
+                    # return x, flog, function_eval, status
 
         # Adjust beta according to comparison ratio.
         if Delta < 0.25:
@@ -147,9 +148,10 @@ def SCG(f, gradf, x, optargs=(), maxiters=500, max_f_eval=500, display=True, xto
         elif success:
             gamma = np.dot(gradold - gradnew, gradnew) / (mu)
             d = gamma * d - gradnew
-
+    else:
         # If we get here, then we haven't terminated in the given number of
         # iterations.
         status = "maxiter exceeded"
 
+    print ""
     return x, flog, function_eval, status

GPy/inference/natural_gradient_scg.py

@@ -1,146 +0,0 @@
-#Copyright I. Nabney, N.Lawrence and James Hensman (1996 - 2012)
-
-#Scaled Conjuagte Gradients, originally in Matlab as part of the Netlab toolbox by I. Nabney, converted to python N. Lawrence and given a pythonic interface by James Hensman
-
-#      THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT
-#      HOLDERS AND CONTRIBUTORS "AS IS" AND ANY
-#      EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT
-#      NOT LIMITED TO, THE IMPLIED WARRANTIES OF
-#      MERCHANTABILITY AND FITNESS FOR A PARTICULAR
-#      PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
-#      REGENTS OR CONTRIBUTORS BE LIABLE FOR ANY
-#      DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
-#      EXEMPLARY, OR CONSEQUENTIAL DAMAGES
-#      (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT
-#      OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
-#      DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
-#      HOWEVER CAUSED AND ON ANY THEORY OF
-#      LIABILITY, WHETHER IN CONTRACT, STRICT
-#      LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR
-#      OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
-#      OF THIS SOFTWARE, EVEN IF ADVISED OF THE
-#      POSSIBILITY OF SUCH DAMAGE.
-
-
-import numpy as np
-import sys
-
-def SCG(f, gradf, x, optargs=(), maxiters=500, max_f_eval=500, display=True, xtol=1e-6, ftol=1e-6):
-    """
-    Optimisation through Scaled Conjugate Gradients (SCG)
-
-    f: the objective function
-    gradf : the gradient function (should return a 1D np.ndarray)
-    x : the initial condition
-
-    Returns
-    x the optimal value for x
-    flog : a list of all the objective values
-
-    """
-
-    sigma0 = 1.0e-4
-    fold = f(x, *optargs)	# Initial function value.
-    function_eval = 1
-    fnow = fold
-    gradnew = gradf(x, *optargs)	# Initial gradient.
-    gradold = gradnew.copy()
-    d = -gradnew				# Initial search direction.
-    success = True				# Force calculation of directional derivs.
-    nsuccess = 0				# nsuccess counts number of successes.
-    beta = 1.0				# Initial scale parameter.
-    betamin = 1.0e-15 			# Lower bound on scale.
-    betamax = 1.0e100			# Upper bound on scale.
-    status = "Not converged"
-
-    flog = [fold]
-
-    iteration = 0
-
-    # Main optimization loop.
-    while iteration < maxiters:
-
-        # Calculate first and second directional derivatives.
-        if success:
-            mu = np.dot(d, gradnew)
-            if mu >= 0:
-                d = -gradnew
-                mu = np.dot(d, gradnew)
-            kappa = np.dot(d, d)
-            sigma = sigma0/np.sqrt(kappa)
-            xplus = x + sigma*d
-            gplus = gradf(xplus, *optargs)
-            theta = np.dot(d, (gplus - gradnew))/sigma
-
-        # Increase effective curvature and evaluate step size alpha.
-        delta = theta + beta*kappa
-        if delta <= 0:
-            delta = beta*kappa
-            beta = beta - theta/kappa
-
-        alpha = - mu/delta
-
-        # Calculate the comparison ratio.
-        xnew = x + alpha*d
-        fnew = f(xnew, *optargs)
-        function_eval += 1
-
-        if function_eval >= max_f_eval:
-            status = "Maximum number of function evaluations exceeded"
-            return x, flog, function_eval, status
-
-        Delta = 2.*(fnew - fold)/(alpha*mu)
-        if Delta  >= 0.:
-            success = True
-            nsuccess += 1
-            x = xnew
-            fnow = fnew
-        else:
-            success = False
-            fnow = fold
-
-        # Store relevant variables
-        flog.append(fnow)		# Current function value
-
-        iteration += 1
-        if display:
-            print '\r',
-            print 'Iteration: {0:>5g}  Objective:{1:> 12e}  Scale:{2:> 12e}'.format(iteration, fnow, beta),
-            # print 'Iteration:', iteration, ' Objective:', fnow, '  Scale:', beta, '\r',
-            sys.stdout.flush()
-
-        if success:
-            # Test for termination
-            if (np.max(np.abs(alpha*d)) < xtol) or (np.abs(fnew-fold) < ftol):
-                status='converged'
-                return x, flog, function_eval, status
-
-            else:
-                # Update variables for new position
-                fold = fnew
-                gradold = gradnew
-                gradnew = gradf(x, *optargs)
-                # If the gradient is zero then we are done.
-                if np.dot(gradnew,gradnew) == 0:
-                    return x, flog, function_eval, status
-
-        # Adjust beta according to comparison ratio.
-        if Delta < 0.25:
-            beta = min(4.0*beta, betamax)
-        if Delta > 0.75:
-            beta = max(0.5*beta, betamin)
-
-        # Update search direction using Polak-Ribiere formula, or re-start
-        # in direction of negative gradient after nparams steps.
-        if nsuccess == x.size:
-            d = -gradnew
-            nsuccess = 0
-        elif success:
-            gamma = np.dot(gradold - gradnew,gradnew)/(mu)
-            d = gamma*d - gradnew
-
-    # If we get here, then we haven't terminated in the given number of
-    # iterations.
-    status = "maxiter exceeded"
-
-    return x, flog, function_eval, status

GPy/kern/kern.py

@@ -61,7 +61,7 @@ class kern(parameterised):
 
                 ax.bar(np.arange(len(ard_params)) - 0.4, ard_params)
                 ax.set_xticks(np.arange(len(ard_params)))
-                ax.set_xticklabels([r"${}$".format(i + 1) for i in range(len(ard_params))])
+                ax.set_xticklabels([r"${}$".format(i) for i in range(len(ard_params))])
         return ax
 
     def _transform_gradients(self, g):
@@ -176,8 +176,8 @@ class kern(parameterised):
         prev_constr_ind = [K1.constrained_indices] + [K1.Nparam + i for i in K2.constrained_indices]
         prev_constr = K1.constraints + K2.constraints
 
-        prev_constr_fix = K1.fixed_indices + [arr + K1.Nparam for arr in K2.fixed_indices]
+        # prev_constr_fix = K1.fixed_indices + [arr + K1.Nparam for arr in K2.fixed_indices]
-        prev_constr_fix_values = K1.fixed_values + K2.fixed_values
+        # prev_constr_fix_values = K1.fixed_values + K2.fixed_values
 
         # follow the previous ties
         for arr in prev_ties:

GPy/likelihoods/EP.py

@@ -1,6 +1,6 @@
 import numpy as np
 from scipy import stats, linalg
-from ..util.linalg import pdinv,mdot,jitchol,DSYR
+from ..util.linalg import pdinv,mdot,jitchol,chol_inv,DSYR,tdot
 from likelihood import likelihood
 
 class EP(likelihood):
@@ -117,8 +117,6 @@ class EP(likelihood):
                 self.v_tilde[i] += Delta_v
                 #Posterior distribution parameters update
                 DSYR(Sigma,Sigma[:,i].copy(), -float(Delta_tau/(1.+ Delta_tau*Sigma[i,i])))
-                #si=Sigma[:,i:i+1]
-                #Sigma -= Delta_tau/(1.+ Delta_tau*Sigma[i,i])*np.dot(si,si.T)#DSYR
                 mu = np.dot(Sigma,self.v_tilde)
                 self.iterations += 1
             #Sigma recomptutation with Cholesky decompositon
@@ -135,12 +133,12 @@ class EP(likelihood):
 
         return self._compute_GP_variables()
 
-    #def fit_DTC(self, Knn_diag, Kmn, Kmm):
     def fit_DTC(self, Kmm, Kmn):
         """
         The expectation-propagation algorithm with sparse pseudo-input.
         For nomenclature see ... 2013.
         """
+        M = Kmm.shape[0]
 
         #TODO: this doesn't work with uncertain inputs!
 
@@ -149,12 +147,20 @@ class EP(likelihood):
         q(f|X) = int_{df}{N(f|KfuKuu_invu,diag(Kff-Qff)*N(u|0,Kuu)} = N(f|0,Sigma0)
         Sigma0 = Qnn = Knm*Kmmi*Kmn
         """
-        Kmmi, Lm, Lmi, Kmm_logdet = pdinv(Kmm)
         KmnKnm = np.dot(Kmn,Kmn.T)
+        Lm = jitchol(Kmm)
+        Lmi = chol_inv(Lm)
+        Kmmi = np.dot(Lmi.T,Lmi)
         KmmiKmn = np.dot(Kmmi,Kmn)
         Qnn_diag = np.sum(Kmn*KmmiKmn,-2)
         LLT0 = Kmm.copy()
 
+        #Kmmi, Lm, Lmi, Kmm_logdet = pdinv(Kmm)
+        #KmnKnm = np.dot(Kmn, Kmn.T)
+        #KmmiKmn = np.dot(Kmmi,Kmn)
+        #Qnn_diag = np.sum(Kmn*KmmiKmn,-2)
+        #LLT0 = Kmm.copy()
+
         """
         Posterior approximation: q(f|y) = N(f| mu, Sigma)
         Sigma = Diag + P*R.T*R*P.T + K
@@ -197,19 +203,19 @@ class EP(likelihood):
                 #Site parameters update
                 Delta_tau = self.delta/self.eta*(1./sigma2_hat[i] - 1./Sigma_diag[i])
                 Delta_v = self.delta/self.eta*(mu_hat[i]/sigma2_hat[i] - mu[i]/Sigma_diag[i])
-                self.tau_tilde[i] = self.tau_tilde[i] + Delta_tau
+                self.tau_tilde[i] += Delta_tau
-                self.v_tilde[i] = self.v_tilde[i] + Delta_v
+                self.v_tilde[i] += Delta_v
                 #Posterior distribution parameters update
-                LLT = LLT + np.outer(Kmn[:,i],Kmn[:,i])*Delta_tau
+                DSYR(LLT,Kmn[:,i].copy(),Delta_tau) #LLT = LLT + np.outer(Kmn[:,i],Kmn[:,i])*Delta_tau
                 L = jitchol(LLT)
                 #cholUpdate(L,Kmn[:,i]*np.sqrt(Delta_tau))
                 V,info = linalg.lapack.flapack.dtrtrs(L,Kmn,lower=1)
                 Sigma_diag = np.sum(V*V,-2)
                 si = np.sum(V.T*V[:,i],-1)
-                mu = mu + (Delta_v-Delta_tau*mu[i])*si
+                mu += (Delta_v-Delta_tau*mu[i])*si
                 self.iterations += 1
             #Sigma recomputation with Cholesky decompositon
-            LLT0 = LLT0 + np.dot(Kmn*self.tau_tilde[None,:],Kmn.T)
+            LLT = LLT0 + np.dot(Kmn*self.tau_tilde[None,:],Kmn.T)
             L = jitchol(LLT)
             V,info = linalg.lapack.flapack.dtrtrs(L,Kmn,lower=1)
             V2,info = linalg.lapack.flapack.dtrtrs(L.T,V,lower=0)
@@ -235,7 +241,9 @@ class EP(likelihood):
         q(f|X) = int_{df}{N(f|KfuKuu_invu,diag(Kff-Qff)*N(u|0,Kuu)} = N(f|0,Sigma0)
         Sigma0 = diag(Knn-Qnn) + Qnn, Qnn = Knm*Kmmi*Kmn
         """
-        Kmmi, self.Lm, self.Lmi, Kmm_logdet = pdinv(Kmm)
+        Lm = jitchol(Kmm)
+        Lmi = chol_inv(Lm)
+        Kmmi = np.dot(Lmi.T,Lmi)
         P0 = Kmn.T
         KmnKnm = np.dot(P0.T, P0)
         KmmiKmn = np.dot(Kmmi,P0.T)
@@ -290,8 +298,8 @@ class EP(likelihood):
                 #Site parameters update
                 Delta_tau = self.delta/self.eta*(1./sigma2_hat[i] - 1./Sigma_diag[i])
                 Delta_v = self.delta/self.eta*(mu_hat[i]/sigma2_hat[i] - mu[i]/Sigma_diag[i])
-                self.tau_tilde[i] = self.tau_tilde[i] + Delta_tau
+                self.tau_tilde[i] += Delta_tau
-                self.v_tilde[i] = self.v_tilde[i] + Delta_v
+                self.v_tilde[i] += Delta_v
                 #Posterior distribution parameters update
                 dtd1 = Delta_tau*Diag[i] + 1.
                 dii = Diag[i]
@@ -301,8 +309,8 @@ class EP(likelihood):
                 Rp_i = np.dot(R,pi_.T)
                 RTR = np.dot(R.T,np.dot(np.eye(M) - Delta_tau/(1.+Delta_tau*Sigma_diag[i]) * np.dot(Rp_i,Rp_i.T),R))
                 R = jitchol(RTR).T
-                self.w[i] = self.w[i] + (Delta_v - Delta_tau*self.w[i])*dii/dtd1
+                self.w[i] += (Delta_v - Delta_tau*self.w[i])*dii/dtd1
-                self.gamma = self.gamma + (Delta_v - Delta_tau*mu[i])*np.dot(RTR,P[i,:].T)
+                self.gamma += (Delta_v - Delta_tau*mu[i])*np.dot(RTR,P[i,:].T)
                 RPT = np.dot(R,P.T)
                 Sigma_diag = Diag + np.sum(RPT.T*RPT.T,-1)
                 mu = self.w + np.dot(P,self.gamma)

GPy/likelihoods/Gaussian.py

@@ -53,10 +53,10 @@ class Gaussian(likelihood):
     def _set_params(self, x):
         x = float(x)
         if self._variance != x:
-            self._variance = x
+            self.precision = 1. / x
-            self.covariance_matrix = np.eye(self.N) * self._variance
+            self.covariance_matrix = np.eye(self.N) * x
-            self.precision = 1. / self._variance
             self.V = (self.precision) * self.Y
+            self._variance = x
 
     def predictive_values(self, mu, var, full_cov):
         """
@@ -69,6 +69,7 @@ class Gaussian(likelihood):
                 # Note. for D>1, we need to re-normalise all the outputs independently.
                 # This will mess up computations of diag(true_var), below.
                 # note that the upper, lower quantiles should be the same shape as mean
+            # Augment the output variance with the likelihood variance and rescale.
             true_var = (var + np.eye(var.shape[0]) * self._variance) * self._scale ** 2
             _5pc = mean - 2.*np.sqrt(np.diag(true_var))
             _95pc = mean + 2.*np.sqrt(np.diag(true_var))

GPy/likelihoods/likelihood_functions.py

@@ -58,7 +58,7 @@ class probit(likelihood_function):
         norm_975 = [stats.norm.ppf(.975,m,v) for m,v in zip(mu,var)]
         p_025 = stats.norm.cdf(norm_025/np.sqrt(1+var))
         p_975 = stats.norm.cdf(norm_975/np.sqrt(1+var))
-        return mean, np.nan*var, p_025, p_975 # TODO: var
+        return mean[:,None], np.nan*var, p_025[:,None], p_975[:,None] # TODO: var
 
 class Poisson(likelihood_function):
     """

GPy/models/Bayesian_GPLVM.py

@@ -27,7 +27,7 @@ class Bayesian_GPLVM(sparse_GP, GPLVM):
 
     """
     def __init__(self, Y, Q, X=None, X_variance=None, init='PCA', M=10,
-                 Z=None, kernel=None, oldpsave=5, _debug=False,
+                 Z=None, kernel=None, oldpsave=10, _debug=False,
                  **kwargs):
         if X == None:
             X = self.initialise_latent(init, Q, Y)
@@ -87,19 +87,19 @@ class Bayesian_GPLVM(sparse_GP, GPLVM):
         return x
 
     def _set_params(self, x, save_old=True, save_count=0):
-        try:
+#         try:
             N, Q = self.N, self.Q
             self.X = x[:self.X.size].reshape(N, Q).copy()
             self.X_variance = x[(N * Q):(2 * N * Q)].reshape(N, Q).copy()
             sparse_GP._set_params(self, x[(2 * N * Q):])
-            self.oldps = x
+#             self.oldps = x
-        except (LinAlgError, FloatingPointError, ZeroDivisionError):
+#         except (LinAlgError, FloatingPointError, ZeroDivisionError):
-            print "\rWARNING: Caught LinAlgError, continueing without setting            "
+#             print "\rWARNING: Caught LinAlgError, continueing without setting            "
-            if self._debug:
+#             if self._debug:
-                self._savederrors.append(self.f_call)
+#                 self._savederrors.append(self.f_call)
-            if save_count > 10:
+#             if save_count > 10:
-                raise
+#                 raise
-            self._set_params(self.oldps[-1], save_old=False, save_count=save_count + 1)
+#             self._set_params(self.oldps[-1], save_old=False, save_count=save_count + 1)
 
     def dKL_dmuS(self):
         dKL_dS = (1. - (1. / (self.X_variance))) * 0.5
@@ -167,8 +167,12 @@ class Bayesian_GPLVM(sparse_GP, GPLVM):
 #         d_dmu = (dL_dmu).flatten()
 #         d_dS = (dL_dS).flatten()
         # ========================
-        dbound_dmuS = np.hstack((d_dmu, d_dS))
+        self.dbound_dmuS = np.hstack((d_dmu, d_dS))
-        return np.hstack((dbound_dmuS.flatten(), sparse_GP._log_likelihood_gradients(self)))
+        self.dbound_dZtheta = sparse_GP._log_likelihood_gradients(self)
+        return np.hstack((self.dbound_dmuS.flatten(), self.dbound_dZtheta))
+
+    def _log_likelihood_normal_gradients(self):
+        Si, _, _, _ = pdinv(self.X_variance)
 
     def plot_latent(self, which_indices=None, *args, **kwargs):
 
@@ -263,7 +267,7 @@ class Bayesian_GPLVM(sparse_GP, GPLVM):
 
         param_dict = dict(self._savedparams)
         gradient_dict = dict(self._savedgradients)
-        kmm_dict = dict(self._savedpsiKmm)
+#         kmm_dict = dict(self._savedpsiKmm)
         iters = np.array(param_dict.keys())
         ABCD_dict = np.array(self._savedABCD)
         self.showing = 0

GPy/models/FITC.py

@@ -3,8 +3,7 @@
 
 import numpy as np
 import pylab as pb
-from ..util.linalg import mdot, jitchol, tdot, symmetrify,pdinv
+from ..util.linalg import mdot, jitchol, chol_inv, tdot, symmetrify,pdinv
-#from ..util.linalg import mdot, jitchol, chol_inv, pdinv, trace_dot
 from ..util.plot import gpplot
 from .. import kern
 from scipy import stats, linalg
@@ -33,7 +32,6 @@ class FITC(sparse_GP):
             self.likelihood.fit_FITC(self.Kmm,self.psi1,self.psi0)
             self._set_params(self._get_params()) # update the GP
 
-    #@profile
     def _computations(self):
 
         #factor Kmm
@@ -58,18 +56,15 @@ class FITC(sparse_GP):
         # factor B
         self.B = np.eye(self.M) + self.A
         self.LB = jitchol(self.B)
-        self.LBi,info = linalg.lapack.flapack.dtrtrs(self.LB,np.eye(self.M),lower=1)
+        self.LBi = chol_inv(self.LB)
         self.psi1V = np.dot(self.psi1, self.V_star)
 
-        # back substutue C into psi1V
+        Lmi_psi1V, info = linalg.lapack.flapack.dtrtrs(self.Lm, np.asfortranarray(self.psi1V), lower=1, trans=0)
-        Lmi_psi1V, info1 = linalg.lapack.flapack.dtrtrs(self.Lm, np.asfortranarray(self.psi1V), lower=1, trans=0)
         self._LBi_Lmi_psi1V, _ = linalg.lapack.flapack.dtrtrs(self.LB, np.asfortranarray(Lmi_psi1V), lower=1, trans=0)
 
-
         Kmmipsi1 = np.dot(self.Lmi.T,Lmipsi1)
         b_psi1_Ki = self.beta_star * Kmmipsi1.T
         Ki_pbp_Ki = np.dot(Kmmipsi1,b_psi1_Ki)
-
         Kmmi = np.dot(self.Lmi.T,self.Lmi)
         LBiLmi = np.dot(self.LBi,self.Lmi)
         LBL_inv = np.dot(LBiLmi.T,LBiLmi)
@@ -78,13 +73,15 @@ class FITC(sparse_GP):
         Ki_pVVp_Ki = np.dot(Kmmipsi1,VV_p_Ki)
         psi1beta = self.psi1*self.beta_star.T
         H = self.Kmm + mdot(self.psi1,psi1beta.T)
-        Hi, LH, LHi, logdetH = pdinv(H)
+        LH = jitchol(H)
+        LHi = chol_inv(LH)
+        Hi = np.dot(LHi.T,LHi)
+
         betapsi1TLmiLBi = np.dot(psi1beta.T,LBiLmi.T)
         alpha = np.array([np.dot(a.T,a) for a in betapsi1TLmiLBi])[:,None]
         gamma_1 = mdot(VVT,self.psi1.T,Hi)
         pHip = mdot(self.psi1.T,Hi,self.psi1)
         gamma_2 = mdot(self.beta_star*pHip,self.V_star)
-        #gamma_3 = self.V_star * mdot(self.V_star.T,pHip*self.beta_star).T
         gamma_3 = self.V_star * gamma_2
 
         self._dL_dpsi0 = -0.5 * self.beta_star#dA_dpsi0: logdet(self.beta_star)
@@ -97,31 +94,31 @@ class FITC(sparse_GP):
         self._dL_dpsi1 += gamma_1 - mdot(psi1beta.T,Hi,self.psi1,gamma_1) #dD_dpsi1
 
         self._dL_dKmm = -0.5 * np.dot(Kmmipsi1,b_psi1_Ki) #dA_dKmm: logdet(self.beta_star)
-        self._dL_dKmm += -.5*Kmmi + .5*LBL_inv + mdot(LBL_inv,psi1beta,Kmmipsi1.T) #dC_dKmm
+        self._dL_dKmm += .5*(LBL_inv - Kmmi) + mdot(LBL_inv,psi1beta,Kmmipsi1.T) #dC_dKmm
         self._dL_dKmm += -.5 * mdot(Hi,self.psi1,gamma_1) #dD_dKmm
 
         self._dpsi1_dtheta = 0
         self._dpsi1_dX = 0
         self._dKmm_dtheta = 0
         self._dKmm_dX = 0
-        for psi1_n,V_n,X_n,alpha_n,gamma_n,gamma_k in zip(self.psi1.T,self.V_star,self.X,alpha,gamma_2,gamma_3):
 
-            psin_K = np.dot(psi1_n[None,:],Kmmi)
+        self._dpsi1_dX_jkj = 0
+        self._dpsi1_dtheta_jkj = 0
 
-            _dpsi1 = -V_n**2 * psin_K #dA_dpsi1: yT*beta_star*y
+        for i,V_n,alpha_n,gamma_n,gamma_k in zip(range(self.N),self.V_star,alpha,gamma_2,gamma_3):
-            _dpsi1 += - alpha_n * psin_K #Diag_dC_dpsi1
+            K_pp_K = np.dot(Kmmipsi1[:,i:(i+1)],Kmmipsi1[:,i:(i+1)].T)
-            _dpsi1 += - gamma_n**2 * psin_K + 2. * gamma_k * psin_K #Diag_dD_dpsi1
 
-            _dKmm = .5*V_n**2 * np.dot(psin_K.T,psin_K) #dA_dKmm: yT*beta_star*y
+            #Diag_dpsi1 = Diag_dA_dpsi1: yT*beta_star*y + Diag_dC_dpsi1 +Diag_dD_dpsi1
-            _dKmm += .5 * alpha_n * np.dot(psin_K.T,psin_K) #Diag_dC_dKmm
+            _dpsi1 = (-V_n**2 - alpha_n + 2.*gamma_k - gamma_n**2) * Kmmipsi1.T[i:(i+1),:]
-            _dKmm += .5*gamma_n**2 * np.dot(psin_K.T,psin_K) - gamma_k * np.dot(psin_K.T,psin_K) #Diag_dD_dKmm
 
-            self._dpsi1_dtheta += self.kern.dK_dtheta(_dpsi1,X_n[None,:],self.Z)
+            #Diag_dKmm = Diag_dA_dKmm: yT*beta_star*y +Diag_dC_dKmm +Diag_dD_dKmm
+            _dKmm = .5*(V_n**2 + alpha_n + gamma_n**2 - 2.*gamma_k) * K_pp_K #Diag_dD_dKmm
+
+            self._dpsi1_dtheta += self.kern.dK_dtheta(_dpsi1,self.X[i:i+1,:],self.Z)
             self._dKmm_dtheta += self.kern.dK_dtheta(_dKmm,self.Z)
 
             self._dKmm_dX += 2.*self.kern.dK_dX(_dKmm ,self.Z)
-            self._dpsi1_dX += self.kern.dK_dX(_dpsi1.T,self.Z,X_n[None,:])
+            self._dpsi1_dX += self.kern.dK_dX(_dpsi1.T,self.Z,self.X[i:i+1,:])
-
 
         # the partial derivative vector for the likelihood
         if self.likelihood.Nparams == 0:
@@ -235,8 +232,6 @@ class FITC(sparse_GP):
                 var = Kxx + np.dot(KR0T,np.dot(Sigma_H - np.eye(self.M),KR0T.T))
             else:
                 Kxx = self.kern.Kdiag(Xnew,which_parts=which_parts)
-                Kxx_ = self.kern.K(Xnew,which_parts=which_parts) # TODO: RA, is this line needed?
-                var_ = Kxx_ + np.dot(KR0T,np.dot(Sigma_H - np.eye(self.M),KR0T.T)) # TODO: RA, is this line needed?
                 var = (Kxx + np.sum(KR0T.T*np.dot(Sigma_H - np.eye(self.M),KR0T.T),0))[:,None]
             return mu_star[:,None],var
         else:

GPy/models/GPLVM.py

@@ -28,7 +28,7 @@ class GPLVM(GP):
         if X is None:
             X = self.initialise_latent(init, Q, Y)
         if kernel is None:
-            kernel = kern.rbf(Q) + kern.bias(Q)
+            kernel = kern.rbf(Q, ARD=Q>1) + kern.bias(Q, np.exp(-2)) + kern.white(Q, np.exp(-2))
         likelihood = Gaussian(Y, normalize=normalize_Y)
         GP.__init__(self, X, likelihood, kernel, **kwargs)
 

GPy/models/sparse_GP.py

@@ -76,7 +76,7 @@ class sparse_GP(GP):
 #                 psi2_beta_scaled = (self.psi2 * (self.likelihood.precision.flatten().reshape(self.N, 1, 1) / sf2)).sum(0)
                 psi2_beta_scaled = (self.psi2 * (self.likelihood.precision.flatten().reshape(self.N, 1, 1))).sum(0)
                 evals, evecs = linalg.eigh(psi2_beta_scaled)
-                clipped_evals = np.clip(evals, 0., 1e15)  # TODO: make clipping configurable
+                clipped_evals = np.clip(evals, 0., 1e6) # TODO: make clipping configurable
                 if not np.allclose(evals, clipped_evals):
                     print "Warning: clipping posterior eigenvalues"
                 tmp = evecs * np.sqrt(clipped_evals)

GPy/util/datasets.py

@@ -4,6 +4,7 @@ import numpy as np
 import GPy
 import scipy.sparse
 import scipy.io
+import cPickle as pickle
 data_path = os.path.join(os.path.dirname(__file__), 'datasets')
 default_seed = 10000
 
@@ -96,16 +97,29 @@ def stick():
     lbls = 'connect'
     return {'Y': Y, 'connect' : connect, 'info': "Stick man data from Ohio."}
 
+def swiss_roll_generated(N=1000, sigma=0.0):
+    with open(os.path.join(data_path, 'swiss_roll.pickle')) as f:
+        data = pickle.load(f)
+    Na = data['Y'].shape[0]
+    perm = np.random.permutation(np.r_[:Na])[:N]
+    Y = data['Y'][perm, :]
+    t = data['t'][perm]
+    c = data['colors'][perm, :]
+    so = np.argsort(t)
+    Y = Y[so, :]
+    t = t[so]
+    c = c[so, :]
+    return {'Y':Y, 't':t, 'colors':c}
 
 def swiss_roll_1000():
     mat_data = scipy.io.loadmat(os.path.join(data_path, 'swiss_roll_data'))
     Y = mat_data['X_data'][:, 0:1000].transpose()
     return {'Y': Y, 'info': "Subsample of the swiss roll data extracting only the first 1000 values."}
 
-def swiss_roll():
+def swiss_roll(N=3000):
     mat_data = scipy.io.loadmat(os.path.join(data_path, 'swiss_roll_data.mat'))
-    Y = mat_data['X_data'][:, 0:3000].transpose()
+    Y = mat_data['X_data'][:, 0:N].transpose()
-    return {'Y': Y, 'info': "The first 3,000 points from the swiss roll data of Tennenbaum, de Silva and Langford (2001)."}
+    return {'Y': Y, 'X': mat_data['X_data'], 'info': "The first 3,000 points from the swiss roll data of Tennenbaum, de Silva and Langford (2001)."}
 
 def toy_rbf_1d(seed=default_seed):
     np.random.seed(seed=seed)

GPy/util/linalg.py

@@ -237,6 +237,16 @@ def tdot(*args, **kwargs):
         return tdot_numpy(*args,**kwargs)
 
 def DSYR(A,x,alpha=1.):
+    """
+    Performs a symmetric rank-1 update operation:
+    A <- A + alpha * np.dot(x,x.T)
+
+    Arguments
+    ---------
+    :param A: Symmetric NxN np.array
+    :param x: Nx1 np.array
+    :param alpha: scalar
+    """
     N = c_int(A.shape[0])
     LDA = c_int(A.shape[0])
     UPLO = c_char('l')

GPy/util/visualize.py

@@ -44,7 +44,7 @@ class vector_show(data_show):
 
 
 class lvm(data_show):
-    def __init__(self, vals, model, data_visualize, latent_axes=None, latent_index=[0,1]):
+    def __init__(self, vals, model, data_visualize, latent_axes=None, sense_axes=None, latent_index=[0,1]):
         """Visualize a latent variable model
 
         :param model: the latent variable model to visualize.
@@ -71,7 +71,7 @@ class lvm(data_show):
         self.data_visualize = data_visualize
         self.model = model
         self.latent_axes = latent_axes
-
+        self.sense_axes = sense_axes
         self.called = False
         self.move_on = False
         self.latent_index = latent_index
@@ -81,10 +81,12 @@ class lvm(data_show):
         self.latent_values = vals
         self.latent_handle = self.latent_axes.plot([0],[0],'rx',mew=2)[0]
         self.modify(vals)
+        self.show_sensitivities()
 
     def modify(self, vals):
         """When latent values are modified update the latent representation and ulso update the output visualization."""
         y = self.model.predict(vals)[0]
+        print y
         self.data_visualize.modify(y)
         self.latent_handle.set_data(vals[self.latent_index[0]], vals[self.latent_index[1]])
         self.axes.figure.canvas.draw()
@@ -99,6 +101,7 @@ class lvm(data_show):
         if event.inaxes!=self.latent_axes: return
         self.move_on = not self.move_on
         self.called = True
+
     def on_move(self, event):
         if event.inaxes!=self.latent_axes: return
         if self.called and self.move_on:
@@ -107,38 +110,9 @@ class lvm(data_show):
             self.latent_values[self.latent_index[1]]=event.ydata
             self.modify(self.latent_values)
 
-class lvm_subplots(lvm):
-    """
-    latent_axes is a np array of dimension np.ceil(Q/2) + 1,
-    one for each pair of the axes, and the last one for the sensitiity bar chart
-    """
-    def __init__(self, vals, model, data_visualize, latent_axes=None, latent_index=[0,1]):
-        lvm.__init__(self, vals, model,data_visualize,latent_axes,[0,1])
-        self.nplots = int(np.ceil(model.Q/2.))+1
-        lvm.__init__(self,model,data_visualize,latent_axes,latent_index)
-        self.latent_values = np.zeros(2*np.ceil(self.model.Q/2.)) # possibly an extra dimension on this
-        assert latent_axes.size == self.nplots
-
-
-class lvm_dimselect(lvm):
-    """
-    A visualizer for latent variable models which allows selection of the latent dimensions to use by clicking on a bar chart of their length scales.
-    """
-    def __init__(self, vals, model, data_visualize, latent_axes=None, sense_axes=None, latent_index=[0, 1]):
-        if latent_axes==None and sense_axes==None:
-            self.fig,(latent_axes,self.sense_axes) = plt.subplots(1,2)
-        elif sense_axes==None:
-            fig=plt.figure()
-            self.sense_axes = fig.add_subplot(111)
-        else:
-            self.sense_axes = sense_axes
-        
-        lvm.__init__(self,vals,model,data_visualize,latent_axes,latent_index)
-        self.show_sensitivities()
-        print "use left and right mouse butons to select dimensions"
-
     def show_sensitivities(self):
         # A click in the bar chart axis for selection a dimension.
+        if self.sense_axes != None:
             self.sense_axes.cla()
             self.sense_axes.bar(np.arange(self.model.Q),1./self.model.input_sensitivity(),color='b')
 
@@ -152,6 +126,52 @@ class lvm_dimselect(lvm):
 
             self.sense_axes.figure.canvas.draw()
 
+
+class lvm_subplots(lvm):
+    """
+    latent_axes is a np array of dimension np.ceil(Q/2),
+    one for each pair of the latent dimensions.
+    """
+    def __init__(self, vals, model, data_visualize, latent_axes=None, sense_axes=None):
+        self.nplots = int(np.ceil(model.Q/2.))+1
+        assert len(latent_axes)==self.nplots
+        if vals==None:
+            vals = model.X[0, :]
+        self.latent_values = vals 
+
+        for i, axis in enumerate(latent_axes):
+            if i == self.nplots-1:
+                if self.nplots*2!=model.Q:
+                    latent_index = [i*2, i*2]
+                lvm.__init__(self, self.latent_vals, model, data_visualize, axis, sense_axes, latent_index=latent_index)
+            else:
+                latent_index = [i*2, i*2+1]
+                lvm.__init__(self, self.latent_vals, model, data_visualize, axis, latent_index=latent_index)
+
+
+
+class lvm_dimselect(lvm):
+    """
+    A visualizer for latent variable models which allows selection of the latent dimensions to use by clicking on a bar chart of their length scales.
+
+    For an example of the visualizer's use try:
+    
+    GPy.examples.dimensionality_reduction.BGPVLM_oil()
+
+    """
+    def __init__(self, vals, model, data_visualize, latent_axes=None, sense_axes=None, latent_index=[0, 1]):
+        if latent_axes==None and sense_axes==None:
+            self.fig,(latent_axes,self.sense_axes) = plt.subplots(1,2)
+        elif sense_axes==None:
+            fig=plt.figure()
+            self.sense_axes = fig.add_subplot(111)
+        else:
+            self.sense_axes = sense_axes
+        
+        lvm.__init__(self,vals,model,data_visualize,latent_axes,sense_axes,latent_index)
+        print "use left and right mouse butons to select dimensions"
+
+
     def on_click(self, event):
 
         if event.inaxes==self.sense_axes:
@@ -177,12 +197,6 @@ class lvm_dimselect(lvm):
         self.called = True
 
 
-    def on_move(self, event):
-        if event.inaxes!=self.latent_axes: return
-        if self.called and self.move_on:
-            self.latent_values[self.latent_index[0]]=event.xdata
-            self.latent_values[self.latent_index[1]]=event.ydata            
-            self.modify(self.latent_values)
 
     def on_leave(self,event):
         latent_values = self.latent_values.copy()
@@ -214,15 +228,30 @@ class image_show(data_show):
     def modify(self, vals):
         self.set_image(vals)
         self.handle.set_array(self.vals)
-        self.axes.figure.canvas.draw() # Teo - original line: plt.show()
+        self.axes.figure.canvas.draw() 
 
     def set_image(self, vals):
         dim = self.dimensions[0] * self.dimensions[1]
+        nImg = np.sqrt(vals[0,].size/dim)
+        if nImg > 1 and nImg.is_integer(): # Show a mosaic of images
+            nImg = np.int(nImg)
+            self.vals = np.zeros((self.dimensions[0]*nImg, self.dimensions[1]*nImg))
+            for iR in range(nImg):
+                for iC in range(nImg):
+                    currImgId = iR*nImg + iC
+                    currImg = np.reshape(vals[0,dim*currImgId+np.array(range(dim))], self.dimensions, order='F')
+                    firstRow = iR*self.dimensions[0]
+                    lastRow = (iR+1)*self.dimensions[0]
+                    firstCol = iC*self.dimensions[1]
+                    lastCol = (iC+1)*self.dimensions[1]
+                    self.vals[firstRow:lastRow, firstCol:lastCol] = currImg
+
+        else: 
             self.vals = np.reshape(vals[0,dim*self.selectImage+np.array(range(dim))], self.dimensions, order='F')
         if self.transpose:
             self.vals = self.vals.T.copy()
-        if not self.scale:
+        # if not self.scale:
-            self.vals = self.vals
+        #     self.vals = self.vals
         if self.invert:
             self.vals = -self.vals