Minor edits to reading Lee data in datasets.py

GPy/Youter.txt

@@ -0,0 +1,12 @@
+models/generalized_FITC.py:        self.Youter = np.dot(self.mu_tilde,self.mu_tilde.T)
+models/generalized_FITC.py:        B = -.5*np.sum(self.Qi*self.Youter)
+models/GP_regression.py:            # then it's more efficient to store Youter
+models/GP_regression.py:            self.Youter = np.dot(self.Y, self.Y.T)
+models/GP_regression.py:            self.Youter = None
+models/GP_regression.py:        Computes the model fit using Youter if it's available
+models/GP_regression.py:        if self.Youter is None:
+models/GP_regression.py:            return -0.5*np.sum(np.multiply(self.Ki, self.Youter))
+models/GP_regression.py:        if self.Youter is None:
+models/GP_regression.py:            dL_dK = 0.5*(mdot(self.Ki, self.Youter, self.Ki) - self.D*self.Ki)
+models/warped_GP.py:            self.Youter = np.dot(self.Y, self.Y.T)
+models/warped_GP.py:            self.Youter = None

GPy/core/parameterization/tmp/observable_array.py

@@ -0,0 +1,137 @@
+# Copyright (c) 2012, GPy authors (see AUTHORS.txt).
+# Licensed under the BSD 3-clause license (see LICENSE.txt)
+
+__updated__ = '2014-03-31'
+
+import numpy as np
+from parameter_core import Observable, Pickleable
+
+class ObsAr(np.ndarray, Pickleable, Observable):
+    """
+    An ndarray which reports changes to its observers.
+    The observers can add themselves with a callable, which
+    will be called every time this array changes. The callable
+    takes exactly one argument, which is this array itself.
+    """
+    __array_priority__ = -1 # Never give back ObsAr
+    def __new__(cls, input_array, *a, **kw):
+        if not isinstance(input_array, ObsAr):
+            obj = np.atleast_1d(np.require(input_array, dtype=np.float64, requirements=['W', 'C'])).view(cls)
+        else: obj = input_array
+        #cls.__name__ = "ObsAr" # because of fixed printing of `array` in np printing
+        super(ObsAr, obj).__init__(*a, **kw)
+        return obj
+
+    def __array_finalize__(self, obj):
+        # see InfoArray.__array_finalize__ for comments
+        if obj is None: return
+        self._observer_callables_ = getattr(obj, '_observer_callables_', None)
+
+    def __array_wrap__(self, out_arr, context=None):
+        return out_arr.view(np.ndarray)
+
+    def copy(self):
+        memo = {}
+        memo[id(self)] = self
+        return self.__deepcopy__(memo)
+
+    def __deepcopy__(self, memo):
+        s = self.__new__(self.__class__, input_array=self.view(np.ndarray).copy())
+        memo[id(self)] = s
+        import copy
+        s.__dict__.update(copy.deepcopy(self.__dict__, memo))
+        return s
+
+    def __reduce__(self):
+        func, args, state = super(ObsAr, self).__reduce__()
+        return func, args, (state, Pickleable.__getstate__(self))
+
+    def __setstate__(self, state):
+        np.ndarray.__setstate__(self, state[0])
+        Pickleable.__setstate__(self, state[1])
+
+    def __setitem__(self, s, val):
+        super(ObsAr, self).__setitem__(s, val)
+        self.notify_observers()
+
+    def __getslice__(self, start, stop):
+        return self.__getitem__(slice(start, stop))
+
+    def __setslice__(self, start, stop, val):
+        return self.__setitem__(slice(start, stop), val)
+
+    def __ilshift__(self, *args, **kwargs):
+        r = np.ndarray.__ilshift__(self, *args, **kwargs)
+        self.notify_observers()
+        return r
+
+    def __irshift__(self, *args, **kwargs):
+        r = np.ndarray.__irshift__(self, *args, **kwargs)
+        self.notify_observers()
+        return r
+
+
+    def __ixor__(self, *args, **kwargs):
+        r = np.ndarray.__ixor__(self, *args, **kwargs)
+        self.notify_observers()
+        return r
+
+
+    def __ipow__(self, *args, **kwargs):
+        r = np.ndarray.__ipow__(self, *args, **kwargs)
+        self.notify_observers()
+        return r
+
+
+    def __ifloordiv__(self, *args, **kwargs):
+        r = np.ndarray.__ifloordiv__(self, *args, **kwargs)
+        self.notify_observers()
+        return r
+
+
+    def __isub__(self, *args, **kwargs):
+        r = np.ndarray.__isub__(self, *args, **kwargs)
+        self.notify_observers()
+        return r
+
+
+    def __ior__(self, *args, **kwargs):
+        r = np.ndarray.__ior__(self, *args, **kwargs)
+        self.notify_observers()
+        return r
+
+
+    def __itruediv__(self, *args, **kwargs):
+        r = np.ndarray.__itruediv__(self, *args, **kwargs)
+        self.notify_observers()
+        return r
+
+
+    def __idiv__(self, *args, **kwargs):
+        r = np.ndarray.__idiv__(self, *args, **kwargs)
+        self.notify_observers()
+        return r
+
+
+    def __iand__(self, *args, **kwargs):
+        r = np.ndarray.__iand__(self, *args, **kwargs)
+        self.notify_observers()
+        return r
+
+
+    def __imod__(self, *args, **kwargs):
+        r = np.ndarray.__imod__(self, *args, **kwargs)
+        self.notify_observers()
+        return r
+
+
+    def __iadd__(self, *args, **kwargs):
+        r = np.ndarray.__iadd__(self, *args, **kwargs)
+        self.notify_observers()
+        return r
+
+
+    def __imul__(self, *args, **kwargs):
+        r = np.ndarray.__imul__(self, *args, **kwargs)
+        self.notify_observers()
+        return r

GPy/core/tmp/domains.py

@@ -0,0 +1,26 @@
+'''
+Created on 4 Jun 2013
+
+@author: maxz
+
+(Hyper-)Parameter domains defined for :py:mod:`~GPy.core.priors` and :py:mod:`~GPy.kern`.
+These domains specify the legitimate realm of the parameters to live in.
+
+:const:`~GPy.core.domains.REAL` :
+    real domain, all values in the real numbers are allowed
+
+:const:`~GPy.core.domains.POSITIVE`:
+    positive domain, only positive real values are allowed
+    
+:const:`~GPy.core.domains.NEGATIVE`:
+    same as :const:`~GPy.core.domains.POSITIVE`, but only negative values are allowed
+    
+:const:`~GPy.core.domains.BOUNDED`:
+    only values within the bounded range are allowed,
+    the bounds are specified withing the object with the bounded range
+'''
+
+REAL = 'real'
+POSITIVE = "positive"
+NEGATIVE = 'negative'
+BOUNDED = 'bounded'

GPy/core/tmp/fitc.py

@@ -0,0 +1,248 @@
+# Copyright (c) 2012, GPy authors (see AUTHORS.txt).
+# Licensed under the BSD 3-clause license (see LICENSE.txt)
+
+import numpy as np
+import pylab as pb
+from ..util.linalg import mdot, jitchol, chol_inv, tdot, symmetrify, pdinv, dtrtrs
+from ..util.plot import gpplot
+from .. import kern
+from scipy import stats
+from sparse_gp import SparseGP
+
+class FITC(SparseGP):
+    """
+
+    Sparse FITC approximation
+
+    :param X: inputs
+    :type X: np.ndarray (num_data x Q)
+    :param likelihood: a likelihood instance, containing the observed data
+    :type likelihood: GPy.likelihood.(Gaussian | EP)
+    :param kernel: the kernel (covariance function). See link kernels
+    :type kernel: a GPy.kern.kern instance
+    :param Z: inducing inputs (optional, see note)
+    :type Z: np.ndarray (M x Q) | None
+    :param normalize_(X|Y): whether to normalize the data before computing (predictions will be in original scales)
+    :type normalize_(X|Y): bool
+
+    """
+
+    def __init__(self, X, likelihood, kernel, Z, normalize_X=False):
+        SparseGP.__init__(self, X, likelihood, kernel, Z, X_variance=None, normalize_X=False)
+        assert self.output_dim == 1, "FITC model is not defined for handling multiple outputs"
+
+    def update_likelihood_approximation(self, **kwargs):
+        """
+        Approximates a non-Gaussian likelihood using Expectation Propagation
+
+        For a Gaussian likelihood, no iteration is required:
+        this function does nothing
+        """
+        self.likelihood.restart()
+        self.likelihood.fit_FITC(self.Kmm,self.psi1,self.psi0, **kwargs)
+        self._set_params(self._get_params())
+
+    def _compute_kernel_matrices(self):
+        # kernel computations, using BGPLVM notation
+        self.Kmm = self.kern.K(self.Z)
+        self.psi0 = self.kern.Kdiag(self.X)
+        self.psi1 = self.kern.K(self.Z, self.X)
+        self.psi2 = None
+
+    def _computations(self):
+        #factor Kmm
+        self.Lm = jitchol(self.Kmm)
+        self.Lmi,info = dtrtrs(self.Lm,np.eye(self.num_inducing),lower=1)
+        Lmipsi1 = np.dot(self.Lmi,self.psi1)
+        self.Qnn = np.dot(Lmipsi1.T,Lmipsi1).copy()
+        self.Diag0 = self.psi0 - np.diag(self.Qnn)
+        self.beta_star = self.likelihood.precision/(1. + self.likelihood.precision*self.Diag0[:,None]) #NOTE: beta_star contains Diag0 and the precision
+        self.V_star = self.beta_star * self.likelihood.Y
+
+        # The rather complex computations of self.A
+        tmp = self.psi1 * (np.sqrt(self.beta_star.flatten().reshape(1, self.num_data)))
+        tmp, _ = dtrtrs(self.Lm, np.asfortranarray(tmp), lower=1)
+        self.A = tdot(tmp)
+
+        # factor B
+        self.B = np.eye(self.num_inducing) + self.A
+        self.LB = jitchol(self.B)
+        self.LBi = chol_inv(self.LB)
+        self.psi1V = np.dot(self.psi1, self.V_star)
+
+        Lmi_psi1V, info = dtrtrs(self.Lm, np.asfortranarray(self.psi1V), lower=1, trans=0)
+        self._LBi_Lmi_psi1V, _ = 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)
+        VVT = np.outer(self.V_star,self.V_star)
+        VV_p_Ki = np.dot(VVT,Kmmipsi1.T)
+        Ki_pVVp_Ki = np.dot(Kmmipsi1,VV_p_Ki)
+        psi1beta = self.psi1*self.beta_star.T
+        H = self.Kmm + mdot(self.psi1,psi1beta.T)
+        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 * gamma_2
+
+        self._dL_dpsi0 = -0.5 * self.beta_star#dA_dpsi0: logdet(self.beta_star)
+        self._dL_dpsi0 += .5 * self.V_star**2 #dA_psi0: yT*beta_star*y
+        self._dL_dpsi0 += .5 *alpha #dC_dpsi0
+        self._dL_dpsi0 += 0.5*mdot(self.beta_star*pHip,self.V_star)**2 - self.V_star * mdot(self.V_star.T,pHip*self.beta_star).T #dD_dpsi0
+
+        self._dL_dpsi1 = b_psi1_Ki.copy() #dA_dpsi1: logdet(self.beta_star)
+        self._dL_dpsi1 += -np.dot(psi1beta.T,LBL_inv) #dC_dpsi1
+        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*(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
+
+        self._dpsi1_dX_jkj = 0
+        self._dpsi1_dtheta_jkj = 0
+
+        for i,V_n,alpha_n,gamma_n,gamma_k in zip(range(self.num_data),self.V_star,alpha,gamma_2,gamma_3):
+            K_pp_K = np.dot(Kmmipsi1[:,i:(i+1)],Kmmipsi1[:,i:(i+1)].T)
+            _dpsi1 = (-V_n**2 - alpha_n + 2.*gamma_k - gamma_n**2) * Kmmipsi1.T[i:(i+1),:]
+            _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 += self.kern.dK_dX(_dKmm ,self.Z)
+            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.num_params == 0:
+            # save computation here.
+            self.partial_for_likelihood = None
+        elif self.likelihood.is_heteroscedastic:
+            raise NotImplementedError, "heteroscedatic derivates not implemented."
+        else:
+            # likelihood is not heterscedatic
+            dbstar_dnoise = self.likelihood.precision * (self.beta_star**2 * self.Diag0[:,None] - self.beta_star)
+            Lmi_psi1 = mdot(self.Lmi,self.psi1)
+            LBiLmipsi1 = np.dot(self.LBi,Lmi_psi1)
+            aux_0 = np.dot(self._LBi_Lmi_psi1V.T,LBiLmipsi1)
+            aux_1 = self.likelihood.Y.T * np.dot(self._LBi_Lmi_psi1V.T,LBiLmipsi1)
+            aux_2 = np.dot(LBiLmipsi1.T,self._LBi_Lmi_psi1V)
+
+            dA_dnoise = 0.5 * self.input_dim * (dbstar_dnoise/self.beta_star).sum() - 0.5 * self.input_dim * np.sum(self.likelihood.Y**2 * dbstar_dnoise)
+            dC_dnoise = -0.5 * np.sum(mdot(self.LBi.T,self.LBi,Lmi_psi1) *  Lmi_psi1 * dbstar_dnoise.T)
+
+            dD_dnoise_1 =  mdot(self.V_star*LBiLmipsi1.T,LBiLmipsi1*dbstar_dnoise.T*self.likelihood.Y.T)
+            alpha = mdot(LBiLmipsi1,self.V_star)
+            alpha_ = mdot(LBiLmipsi1.T,alpha)
+            dD_dnoise_2 = -0.5 * self.input_dim * np.sum(alpha_**2 * dbstar_dnoise )
+
+            dD_dnoise_1 = mdot(self.V_star.T,self.psi1.T,self.Lmi.T,self.LBi.T,self.LBi,self.Lmi,self.psi1,dbstar_dnoise*self.likelihood.Y)
+            dD_dnoise_2 = 0.5*mdot(self.V_star.T,self.psi1.T,Hi,self.psi1,dbstar_dnoise*self.psi1.T,Hi,self.psi1,self.V_star)
+            dD_dnoise = dD_dnoise_1 + dD_dnoise_2
+
+            self.partial_for_likelihood = dA_dnoise + dC_dnoise + dD_dnoise
+
+    def log_likelihood(self):
+        """ Compute the (lower bound on the) log marginal likelihood """
+        A = -0.5 * self.num_data * self.output_dim * np.log(2.*np.pi) + 0.5 * np.sum(np.log(self.beta_star)) - 0.5 * np.sum(self.V_star * self.likelihood.Y)
+        C = -self.output_dim * (np.sum(np.log(np.diag(self.LB))))
+        D = 0.5 * np.sum(np.square(self._LBi_Lmi_psi1V))
+        return A + C + D + self.likelihood.Z
+
+    def _log_likelihood_gradients(self):
+        pass
+        return np.hstack((self.dL_dZ().flatten(), self.dL_dtheta(), self.likelihood._gradients(partial=self.partial_for_likelihood)))
+
+    def dL_dtheta(self):
+        dL_dtheta = self.kern.dKdiag_dtheta(self._dL_dpsi0,self.X)
+        dL_dtheta += self.kern.dK_dtheta(self._dL_dpsi1,self.X,self.Z)
+        dL_dtheta += self.kern.dK_dtheta(self._dL_dKmm,X=self.Z)
+        dL_dtheta += self._dKmm_dtheta
+        dL_dtheta += self._dpsi1_dtheta
+        return dL_dtheta
+
+    def dL_dZ(self):
+        dL_dZ = self.kern.dK_dX(self._dL_dpsi1.T,self.Z,self.X)
+        dL_dZ += self.kern.dK_dX(self._dL_dKmm,X=self.Z)
+        dL_dZ += self._dpsi1_dX
+        dL_dZ += self._dKmm_dX
+        return dL_dZ
+
+    def _raw_predict(self, Xnew, X_variance_new=None, which_parts='all', full_cov=False):
+        assert X_variance_new is None, "FITC model is not defined for handling uncertain inputs."
+
+        if self.likelihood.is_heteroscedastic:
+            Iplus_Dprod_i = 1./(1.+ self.Diag0 * self.likelihood.precision.flatten())
+            self.Diag = self.Diag0 * Iplus_Dprod_i
+            self.P = Iplus_Dprod_i[:,None] * self.psi1.T
+            self.RPT0 = np.dot(self.Lmi,self.psi1)
+            self.L = np.linalg.cholesky(np.eye(self.num_inducing) + np.dot(self.RPT0,((1. - Iplus_Dprod_i)/self.Diag0)[:,None]*self.RPT0.T))
+            self.R,info = dtrtrs(self.L,self.Lmi,lower=1)
+            self.RPT = np.dot(self.R,self.P.T)
+            self.Sigma = np.diag(self.Diag) + np.dot(self.RPT.T,self.RPT)
+            self.w = self.Diag * self.likelihood.v_tilde
+            self.Gamma = np.dot(self.R.T, np.dot(self.RPT,self.likelihood.v_tilde))
+            self.mu = self.w + np.dot(self.P,self.Gamma)
+
+            """
+            Make a prediction for the generalized FITC model
+
+            Arguments
+            ---------
+            X : Input prediction data - Nx1 numpy array (floats)
+            """
+            # q(u|f) = N(u| R0i*mu_u*f, R0i*C*R0i.T)
+
+            # Ci = I + (RPT0)Di(RPT0).T
+            # C = I - [RPT0] * (input_dim+[RPT0].T*[RPT0])^-1*[RPT0].T
+            #   = I - [RPT0] * (input_dim + self.Qnn)^-1 * [RPT0].T
+            #   = I - [RPT0] * (U*U.T)^-1 * [RPT0].T
+            #   = I - V.T * V
+            U = np.linalg.cholesky(np.diag(self.Diag0) + self.Qnn)
+            V,info = dtrtrs(U,self.RPT0.T,lower=1)
+            C = np.eye(self.num_inducing) - np.dot(V.T,V)
+            mu_u = np.dot(C,self.RPT0)*(1./self.Diag0[None,:])
+            #self.C = C
+            #self.RPT0 = np.dot(self.R0,self.Knm.T) P0.T
+            #self.mu_u = mu_u
+            #self.U = U
+            # q(u|y) = N(u| R0i*mu_H,R0i*Sigma_H*R0i.T)
+            mu_H = np.dot(mu_u,self.mu)
+            self.mu_H = mu_H
+            Sigma_H = C + np.dot(mu_u,np.dot(self.Sigma,mu_u.T))
+            # q(f_star|y) = N(f_star|mu_star,sigma2_star)
+            Kx = self.kern.K(self.Z, Xnew, which_parts=which_parts)
+            KR0T = np.dot(Kx.T,self.Lmi.T)
+            mu_star = np.dot(KR0T,mu_H)
+            if full_cov:
+                Kxx = self.kern.K(Xnew,which_parts=which_parts)
+                var = Kxx + np.dot(KR0T,np.dot(Sigma_H - np.eye(self.num_inducing),KR0T.T))
+            else:
+                Kxx = self.kern.Kdiag(Xnew,which_parts=which_parts)
+                var = (Kxx + np.sum(KR0T.T*np.dot(Sigma_H - np.eye(self.num_inducing),KR0T.T),0))[:,None]
+            return mu_star[:,None],var
+        else:
+            raise NotImplementedError, "Heteroscedastic case not implemented."
+            """
+            Kx = self.kern.K(self.Z, Xnew)
+            mu = mdot(Kx.T, self.C/self.scale_factor, self.psi1V)
+            if full_cov:
+                Kxx = self.kern.K(Xnew)
+                var = Kxx - mdot(Kx.T, (self.Kmmi - self.C/self.scale_factor**2), Kx) #NOTE this won't work for plotting
+            else:
+                Kxx = self.kern.Kdiag(Xnew)
+                var = Kxx - np.sum(Kx*np.dot(self.Kmmi - self.C/self.scale_factor**2, Kx),0)
+            return mu,var[:,None]
+            """

GPy/core/tmp/gp_base.py

@@ -0,0 +1,275 @@
+import numpy as np
+from .. import kern
+from ..util.plot import gpplot, Tango, x_frame1D, x_frame2D
+import pylab as pb
+from GPy.core.model import Model
+import warnings
+from ..likelihoods import Gaussian, Gaussian_Mixed_Noise
+
+class GPBase(Model):
+    """
+    Gaussian process base model for holding shared behaviour between
+    sparse_GP and GP models, and potentially other models in the future.
+
+    Here we define some functions that are use
+    """
+    def __init__(self, X, likelihood, kernel, normalize_X=False):
+        if len(X.shape)==1:
+            X = X.reshape(-1,1)
+            warnings.warn("One dimension output (N,) being reshaped to (N,1)")
+        self.X = X
+        assert len(self.X.shape) == 2, "too many dimensions for X input"
+        self.num_data, self.input_dim = self.X.shape
+        assert isinstance(kernel, kern.kern)
+        self.kern = kernel
+        self.likelihood = likelihood
+        assert self.X.shape[0] == self.likelihood.data.shape[0]
+        self.num_data, self.output_dim = self.likelihood.data.shape
+
+        if normalize_X:
+            self._Xoffset = X.mean(0)[None, :]
+            self._Xscale = X.std(0)[None, :]
+            self.X = (X.copy() - self._Xoffset) / self._Xscale
+        else:
+            self._Xoffset = np.zeros((1, self.input_dim))
+            self._Xscale = np.ones((1, self.input_dim))
+
+        super(GPBase, self).__init__()
+        # Model.__init__(self)
+        # All leaf nodes should call self._set_params(self._get_params()) at
+        # the end
+
+
+    def posterior_samples_f(self,X,size=10,which_parts='all'):
+        """
+        Samples the posterior GP at the points X.
+
+        :param X: The points at which to take the samples.
+        :type X: np.ndarray, Nnew x self.input_dim.
+        :param size: the number of a posteriori samples to plot.
+        :type size: int.
+        :param which_parts: which of the kernel functions to plot (additively).
+        :type which_parts: 'all', or list of bools.
+        :param full_cov: whether to return the full covariance matrix, or just the diagonal.
+        :type full_cov: bool.
+        :returns: Ysim: set of simulations, a Numpy array (N x samples).
+        """
+        m, v = self._raw_predict(X, which_parts=which_parts, full_cov=True)
+        v = v.reshape(m.size,-1) if len(v.shape)==3 else v
+        Ysim = np.random.multivariate_normal(m.flatten(), v, size).T
+
+        return Ysim
+
+    def posterior_samples(self,X,size=10,which_parts='all',noise_model=None):
+        """
+        Samples the posterior GP at the points X.
+
+        :param X: the points at which to take the samples.
+        :type X: np.ndarray, Nnew x self.input_dim.
+        :param size: the number of a posteriori samples to plot.
+        :type size: int.
+        :param which_parts: which of the kernel functions to plot (additively).
+        :type which_parts: 'all', or list of bools.
+        :param full_cov: whether to return the full covariance matrix, or just the diagonal.
+        :type full_cov: bool.
+        :param noise_model: for mixed noise likelihood, the noise model to use in the samples.
+        :type noise_model: integer.
+        :returns: Ysim: set of simulations, a Numpy array (N x samples).
+        """
+        Ysim = self.posterior_samples_f(X, size, which_parts=which_parts)
+        if isinstance(self.likelihood,Gaussian):
+            noise_std = np.sqrt(self.likelihood._get_params())
+            Ysim += np.random.normal(0,noise_std,Ysim.shape)
+        elif isinstance(self.likelihood,Gaussian_Mixed_Noise):
+            assert noise_model is not None, "A noise model must be specified."
+            noise_std = np.sqrt(self.likelihood._get_params()[noise_model])
+            Ysim += np.random.normal(0,noise_std,Ysim.shape)
+        else:
+            Ysim = self.likelihood.noise_model.samples(Ysim)
+
+        return Ysim
+
+    def plot_f(self, *args, **kwargs):
+        """
+        Plot the GP's view of the world, where the data is normalized and before applying a likelihood.
+
+        This is a convenience function: we simply call self.plot with the
+        argument use_raw_predict set True. All args and kwargs are passed on to
+        plot.
+
+        see also: gp_base.plot
+        """
+        kwargs['plot_raw'] = True
+        self.plot(*args, **kwargs)
+
+    def plot(self, plot_limits=None, which_data_rows='all',
+            which_data_ycols='all', which_parts='all', fixed_inputs=[],
+            levels=20, samples=0, fignum=None, ax=None, resolution=None,
+            plot_raw=False,
+            linecol=Tango.colorsHex['darkBlue'],fillcol=Tango.colorsHex['lightBlue']):
+        """
+        Plot the posterior of the GP.
+          - In one dimension, the function is plotted with a shaded region identifying two standard deviations.
+          - In two dimsensions, a contour-plot shows the mean predicted function
+          - In higher dimensions, use fixed_inputs to plot the GP  with some of the inputs fixed.
+
+        Can plot only part of the data and part of the posterior functions
+        using which_data_rowsm which_data_ycols and which_parts
+
+        :param plot_limits: The limits of the plot. If 1D [xmin,xmax], if 2D [[xmin,ymin],[xmax,ymax]]. Defaluts to data limits
+        :type plot_limits: np.array
+        :param which_data_rows: which of the training data to plot (default all)
+        :type which_data_rows: 'all' or a slice object to slice self.X, self.Y
+        :param which_data_ycols: when the data has several columns (independant outputs), only plot these
+        :type which_data_rows: 'all' or a list of integers
+        :param which_parts: which of the kernel functions to plot (additively)
+        :type which_parts: 'all', or list of bools
+        :param fixed_inputs: a list of tuple [(i,v), (i,v)...], specifying that input index i should be set to value v.
+        :type fixed_inputs: a list of tuples
+        :param resolution: the number of intervals to sample the GP on. Defaults to 200 in 1D and 50 (a 50x50 grid) in 2D
+        :type resolution: int
+        :param levels: number of levels to plot in a contour plot.
+        :type levels: int
+        :param samples: the number of a posteriori samples to plot
+        :type samples: int
+        :param fignum: figure to plot on.
+        :type fignum: figure number
+        :param ax: axes to plot on.
+        :type ax: axes handle
+        :type output: integer (first output is 0)
+        :param linecol: color of line to plot.
+        :type linecol:
+        :param fillcol: color of fill
+        :param levels: for 2D plotting, the number of contour levels to use is ax is None, create a new figure
+        """
+        #deal with optional arguments
+        if which_data_rows == 'all':
+            which_data_rows = slice(None)
+        if which_data_ycols == 'all':
+            which_data_ycols = np.arange(self.output_dim)
+        if len(which_data_ycols)==0:
+            raise ValueError('No data selected for plotting')
+        if ax is None:
+            fig = pb.figure(num=fignum)
+            ax = fig.add_subplot(111)
+
+        #work out what the inputs are for plotting (1D or 2D)
+        fixed_dims = np.array([i for i,v in fixed_inputs])
+        free_dims = np.setdiff1d(np.arange(self.input_dim),fixed_dims)
+
+        #one dimensional plotting
+        if len(free_dims) == 1:
+
+            #define the frame on which to plot
+            resolution = resolution or 200
+            Xu = self.X * self._Xscale + self._Xoffset #NOTE self.X are the normalized values now
+            Xnew, xmin, xmax = x_frame1D(Xu[:,free_dims], plot_limits=plot_limits)
+            Xgrid = np.empty((Xnew.shape[0],self.input_dim))
+            Xgrid[:,free_dims] = Xnew
+            for i,v in fixed_inputs:
+                Xgrid[:,i] = v
+
+            #make a prediction on the frame and plot it
+            if plot_raw:
+                m, v = self._raw_predict(Xgrid, which_parts=which_parts)
+                lower = m - 2*np.sqrt(v)
+                upper = m + 2*np.sqrt(v)
+                Y = self.likelihood.Y
+            else:
+                m, v, lower, upper = self.predict(Xgrid, which_parts=which_parts, sampling=False) #Compute the exact mean
+                m_, v_, lower, upper = self.predict(Xgrid, which_parts=which_parts, sampling=True, num_samples=15000) #Apporximate the percentiles
+                Y = self.likelihood.data
+            for d in which_data_ycols:
+                gpplot(Xnew, m[:, d], lower[:, d], upper[:, d], axes=ax, edgecol=linecol, fillcol=fillcol)
+                ax.plot(Xu[which_data_rows,free_dims], Y[which_data_rows, d], 'kx', mew=1.5)
+
+            #optionally plot some samples
+            if samples: #NOTE not tested with fixed_inputs
+                Ysim = self.posterior_samples(Xgrid, samples, which_parts=which_parts)
+                for yi in Ysim.T:
+                    ax.plot(Xnew, yi[:,None], Tango.colorsHex['darkBlue'], linewidth=0.25)
+                    #ax.plot(Xnew, yi[:,None], marker='x', linestyle='--',color=Tango.colorsHex['darkBlue']) #TODO apply this line for discrete outputs.
+
+            #set the limits of the plot to some sensible values
+            ymin, ymax = min(np.append(Y[which_data_rows, which_data_ycols].flatten(), lower)), max(np.append(Y[which_data_rows, which_data_ycols].flatten(), upper))
+            ymin, ymax = ymin - 0.1 * (ymax - ymin), ymax + 0.1 * (ymax - ymin)
+            ax.set_xlim(xmin, xmax)
+            ax.set_ylim(ymin, ymax)
+
+        #2D plotting
+        elif len(free_dims) == 2:
+
+            #define the frame for plotting on
+            resolution = resolution or 50
+            Xu = self.X * self._Xscale + self._Xoffset #NOTE self.X are the normalized values now
+            Xnew, _, _, xmin, xmax = x_frame2D(Xu[:,free_dims], plot_limits, resolution)
+            Xgrid = np.empty((Xnew.shape[0],self.input_dim))
+            Xgrid[:,free_dims] = Xnew
+            for i,v in fixed_inputs:
+                Xgrid[:,i] = v
+            x, y = np.linspace(xmin[0], xmax[0], resolution), np.linspace(xmin[1], xmax[1], resolution)
+
+            #predict on the frame and plot
+            if plot_raw:
+                m, _ = self._raw_predict(Xgrid, which_parts=which_parts)
+                Y = self.likelihood.Y
+            else:
+                m, _, _, _ = self.predict(Xgrid, which_parts=which_parts,sampling=False)
+                Y = self.likelihood.data
+            for d in which_data_ycols:
+                m_d = m[:,d].reshape(resolution, resolution).T
+                contour = ax.contour(x, y, m_d, levels, vmin=m.min(), vmax=m.max(), cmap=pb.cm.jet)
+                scatter = ax.scatter(self.X[which_data_rows, free_dims[0]], self.X[which_data_rows, free_dims[1]], 40, Y[which_data_rows, d], cmap=pb.cm.jet, vmin=m.min(), vmax=m.max(), linewidth=0.)
+
+            #set the limits of the plot to some sensible values
+            ax.set_xlim(xmin[0], xmax[0])
+            ax.set_ylim(xmin[1], xmax[1])
+
+            if samples:
+                warnings.warn("Samples are rather difficult to plot for 2D inputs...")
+            return contour, scatter
+        else:
+            raise NotImplementedError, "Cannot define a frame with more than two input dimensions"
+
+    def getstate(self):
+        """
+        Get the curent state of the class. This is only used to efficiently
+        pickle the model. See also self.setstate
+        """
+        return Model.getstate(self) + [self.X,
+                self.num_data,
+                self.input_dim,
+                self.kern,
+                self.likelihood,
+                self.output_dim,
+                self._Xoffset,
+                self._Xscale]
+
+    def setstate(self, state):
+        """
+        Set the state of the model. Used for efficient pickling
+        """
+        self._Xscale = state.pop()
+        self._Xoffset = state.pop()
+        self.output_dim = state.pop()
+        self.likelihood = state.pop()
+        self.kern = state.pop()
+        self.input_dim = state.pop()
+        self.num_data = state.pop()
+        self.X = state.pop()
+        Model.setstate(self, state)
+
+    def log_predictive_density(self, x_test, y_test):
+        """
+        Calculation of the log predictive density
+
+        .. math:
+            p(y_{*}|D) = p(y_{*}|f_{*})p(f_{*}|\mu_{*}\\sigma^{2}_{*})
+
+        :param x_test: test observations (x_{*})
+        :type x_test: (Nx1) array
+        :param y_test: test observations (y_{*})
+        :type y_test: (Nx1) array
+        """
+        mu_star, var_star = self._raw_predict(x_test)
+        return self.likelihood.log_predictive_density(y_test, mu_star, var_star)

GPy/core/tmp/parameterized.py

@@ -0,0 +1,465 @@
+# Copyright (c) 2012, GPy authors (see AUTHORS.txt).
+# Licensed under the BSD 3-clause license (see LICENSE.txt)
+
+
+import numpy as np
+import re
+import copy
+import cPickle
+import warnings
+import transformations
+
+class Parameterized(object):
+    def __init__(self):
+        """
+        This is the base class for model and kernel. Mostly just handles tieing and constraining of parameters
+        """
+        self.tied_indices = []
+        self.fixed_indices = []
+        self.fixed_values = []
+        self.constrained_indices = []
+        self.constraints = []
+
+    def _get_params(self):
+        raise NotImplementedError, "this needs to be implemented to use the Parameterized class"
+    def _set_params(self, x):
+        raise NotImplementedError, "this needs to be implemented to use the Parameterized class"
+
+    def _get_param_names(self):
+        raise NotImplementedError, "this needs to be implemented to use the Parameterized class"
+    #def _get_print_names(self):
+    #    """ Override for which names to print out, when using print m """
+    #    return self._get_param_names()
+
+    def pickle(self, filename, protocol=-1):
+        with open(filename, 'wb') as f:
+            cPickle.dump(self, f, protocol=protocol)
+
+    def copy(self):
+        """Returns a (deep) copy of the current model """
+        return copy.deepcopy(self)
+
+    def __getstate__(self):
+        if self._has_get_set_state():
+            return self.getstate()
+        return self.__dict__
+
+    def __setstate__(self, state):
+        if self._has_get_set_state():
+            self.setstate(state) # set state
+            self._set_params(self._get_params()) # restore all values
+            return
+        self.__dict__ = state
+
+    def _has_get_set_state(self):
+        return 'getstate' in vars(self.__class__) and 'setstate' in vars(self.__class__)
+
+    def getstate(self):
+        """
+        Get the current state of the class,
+        here just all the indices, rest can get recomputed
+        For inheriting from Parameterized:
+
+        Allways append the state of the inherited object
+        and call down to the inherited object in setstate!!
+        """
+        return [self.tied_indices,
+                self.fixed_indices,
+                self.fixed_values,
+                self.constrained_indices,
+                self.constraints]
+
+    def setstate(self, state):
+        self.constraints = state.pop()
+        self.constrained_indices = state.pop()
+        self.fixed_values = state.pop()
+        self.fixed_indices = state.pop()
+        self.tied_indices = state.pop()
+
+    def __getitem__(self, regexp, return_names=False):
+        """
+        Get a model parameter by name.  The name is applied as a regular
+        expression and all parameters that match that regular expression are
+        returned.
+        """
+        matches = self.grep_param_names(regexp)
+        if len(matches):
+            if return_names:
+                return self._get_params()[matches], np.asarray(self._get_param_names())[matches].tolist()
+            else:
+                return self._get_params()[matches]
+        else:
+            raise AttributeError, "no parameter matches %s" % regexp
+
+    def __setitem__(self, name, val):
+        """
+        Set model parameter(s) by name. The name is provided as a regular
+        expression. All parameters matching that regular expression are set to
+        the given value.
+        """
+        matches = self.grep_param_names(name)
+        if len(matches):
+            val = np.array(val)
+            assert (val.size == 1) or val.size == len(matches), "Shape mismatch: {}:({},)".format(val.size, len(matches))
+            x = self._get_params()
+            x[matches] = val
+            self._set_params(x)
+        else:
+            raise AttributeError, "no parameter matches %s" % name
+
+    def tie_params(self, regexp):
+        """
+        Tie (all!) parameters matching the regular expression `regexp`. 
+        """
+        matches = self.grep_param_names(regexp)
+        assert matches.size > 0, "need at least something to tie together"
+        if len(self.tied_indices):
+            assert not np.any(matches[:, None] == np.hstack(self.tied_indices)), "Some indices are already tied!"
+        self.tied_indices.append(matches)
+        # TODO only one of the priors will be evaluated. Give a warning message if the priors are not identical
+        if hasattr(self, 'prior'):
+            pass
+
+        self._set_params_transformed(self._get_params_transformed()) # sets tied parameters to single value
+
+    def untie_everything(self):
+        """Unties all parameters by setting tied_indices to an empty list."""
+        self.tied_indices = []
+
+    def grep_param_names(self, regexp, transformed=False, search=False):
+        """
+        :param regexp: regular expression to select parameter names
+        :type regexp: re | str | int
+        :rtype: the indices of self._get_param_names which match the regular expression.
+
+        Note:-
+          Other objects are passed through - i.e. integers which weren't meant for grepping
+        """
+
+        if transformed:
+            names = self._get_param_names_transformed()
+        else:
+            names = self._get_param_names()
+
+        if type(regexp) in [str, np.string_, np.str]:
+            regexp = re.compile(regexp)
+        elif type(regexp) is re._pattern_type:
+            pass
+        else:
+            return regexp
+        if search:
+            return np.nonzero([regexp.search(name) for name in names])[0]
+        else:
+            return np.nonzero([regexp.match(name) for name in names])[0]
+
+    def num_params_transformed(self):
+        removed = 0
+        for tie in self.tied_indices:
+            removed += tie.size - 1
+
+        for fix in self.fixed_indices:
+            removed += fix.size
+
+        return len(self._get_params()) - removed
+
+    def unconstrain(self, regexp):
+        """Unconstrain matching parameters.  Does not untie parameters"""
+        matches = self.grep_param_names(regexp)
+
+        # tranformed contraints:
+        for match in matches:
+            self.constrained_indices = [i[i <> match] for i in self.constrained_indices]
+
+        # remove empty constraints
+        tmp = zip(*[(i, t) for i, t in zip(self.constrained_indices, self.constraints) if len(i)])
+        if tmp:
+            self.constrained_indices, self.constraints = zip(*[(i, t) for i, t in zip(self.constrained_indices, self.constraints) if len(i)])
+            self.constrained_indices, self.constraints = list(self.constrained_indices), list(self.constraints)
+
+        # fixed:
+        self.fixed_values = [np.delete(values, np.nonzero(np.sum(indices[:, None] == matches[None, :], 1))[0]) for indices, values in zip(self.fixed_indices, self.fixed_values)]
+        self.fixed_indices = [np.delete(indices, np.nonzero(np.sum(indices[:, None] == matches[None, :], 1))[0]) for indices in self.fixed_indices]
+
+        # remove empty elements
+        tmp = [(i, v) for i, v in zip(self.fixed_indices, self.fixed_values) if len(i)]
+        if tmp:
+            self.fixed_indices, self.fixed_values = zip(*tmp)
+            self.fixed_indices, self.fixed_values = list(self.fixed_indices), list(self.fixed_values)
+        else:
+            self.fixed_indices, self.fixed_values = [], []
+
+    def constrain_negative(self, regexp, warning=True):
+        """ Set negative constraints. """
+        self.constrain(regexp, transformations.negative_logexp(), warning=warning)
+
+    def constrain_positive(self, regexp, warning=True):
+        """ Set positive constraints. """
+        self.constrain(regexp, transformations.logexp(), warning=warning)
+
+    def constrain_bounded(self, regexp, lower, upper, warning=True):
+        """ Set bounded constraints. """
+        self.constrain(regexp, transformations.logistic(lower, upper), warning=warning)
+
+    def all_constrained_indices(self):
+        if len(self.constrained_indices) or len(self.fixed_indices):
+            return np.hstack(self.constrained_indices + self.fixed_indices)
+        else:
+            return np.empty(shape=(0,))
+
+    def constrain(self, regexp, transform, warning=True):
+        assert isinstance(transform, transformations.transformation)
+
+        matches = self.grep_param_names(regexp)
+        if warning:
+            overlap = set(matches).intersection(set(self.all_constrained_indices()))
+            if overlap:
+                self.unconstrain(np.asarray(list(overlap)))
+                print 'Warning: re-constraining these parameters'
+                pn = self._get_param_names()
+                for i in overlap:
+                    print pn[i]
+
+        self.constrained_indices.append(matches)
+        self.constraints.append(transform)
+        x = self._get_params()
+        x[matches] = transform.initialize(x[matches])
+        self._set_params(x)
+
+    def constrain_fixed(self, regexp, value=None, warning=True):
+        """
+
+        :param regexp: which parameters need to be fixed.
+        :type regexp: ndarray(dtype=int) or regular expression object or string
+        :param value: the vlaue to fix the parameters to. If the value is not specified,
+                 the parameter is fixed to the current value
+        :type value: float
+
+        **Notes**
+
+        Fixing a parameter which is tied to another, or constrained in some way will result in an error.
+
+        To fix multiple parameters to the same value, simply pass a regular expression which matches both parameter names, or pass both of the indexes.
+
+        """
+        matches = self.grep_param_names(regexp)
+        if warning:
+            overlap = set(matches).intersection(set(self.all_constrained_indices()))
+            if overlap:
+                self.unconstrain(np.asarray(list(overlap)))
+                print 'Warning: re-constraining these parameters'
+                pn = self._get_param_names()
+                for i in overlap:
+                    print pn[i]
+
+        self.fixed_indices.append(matches)
+        if value != None:
+            self.fixed_values.append(value)
+        else:
+            self.fixed_values.append(self._get_params()[self.fixed_indices[-1]])
+
+        # self.fixed_values.append(value)
+        self._set_params_transformed(self._get_params_transformed())
+
+    def _get_params_transformed(self):
+        """use self._get_params to get the 'true' parameters of the model, which are then tied, constrained and fixed"""
+        x = self._get_params()
+        [np.put(x, i, t.finv(x[i])) for i, t in zip(self.constrained_indices, self.constraints)]
+
+        to_remove = self.fixed_indices + [t[1:] for t in self.tied_indices]
+        if len(to_remove):
+            return np.delete(x, np.hstack(to_remove))
+        else:
+            return x
+
+    def _set_params_transformed(self, x):
+        """ takes the vector x, which is then modified (by untying, reparameterising or inserting fixed values), and then call self._set_params"""
+        self._set_params(self._untransform_params(x))
+
+    def _untransform_params(self, x):
+        """
+        The transformation required for _set_params_transformed.
+
+        This moves the vector x seen by the optimiser (unconstrained) to the
+        valid parameter vector seen by the model
+
+        Note:
+          - This function is separate from _set_params_transformed for downstream flexibility
+        """
+        # work out how many places are fixed, and where they are. tricky logic!
+        fix_places = self.fixed_indices + [t[1:] for t in self.tied_indices]
+        if len(fix_places):
+            fix_places = np.hstack(fix_places)
+            Nfix_places = fix_places.size
+        else:
+            Nfix_places = 0
+
+        free_places = np.setdiff1d(np.arange(Nfix_places + x.size, dtype=np.int), fix_places)
+
+        # put the models values in the vector xx
+        xx = np.zeros(Nfix_places + free_places.size, dtype=np.float64)
+
+        xx[free_places] = x
+        [np.put(xx, i, v) for i, v in zip(self.fixed_indices, self.fixed_values)]
+        [np.put(xx, i, v) for i, v in [(t[1:], xx[t[0]]) for t in self.tied_indices] ]
+
+        [np.put(xx, i, t.f(xx[i])) for i, t in zip(self.constrained_indices, self.constraints)]
+        if hasattr(self, 'debug'):
+            stop # @UndefinedVariable
+
+        return xx
+
+    def _get_param_names_transformed(self):
+        """
+        Returns the parameter names as propagated after constraining,
+        tying or fixing, i.e. a list of the same length as _get_params_transformed()
+        """
+        n = self._get_param_names()
+
+        # remove/concatenate the tied parameter names
+        if len(self.tied_indices):
+            for t in self.tied_indices:
+                n[t[0]] = "<tie>".join([n[tt] for tt in t])
+            remove = np.hstack([t[1:] for t in self.tied_indices])
+        else:
+            remove = np.empty(shape=(0,), dtype=np.int)
+
+        # also remove the fixed params
+        if len(self.fixed_indices):
+            remove = np.hstack((remove, np.hstack(self.fixed_indices)))
+
+        # add markers to show that some variables are constrained
+        for i, t in zip(self.constrained_indices, self.constraints):
+            for ii in i:
+                n[ii] = n[ii] + t.__str__()
+
+        n = [nn for i, nn in enumerate(n) if not i in remove]
+        return n
+
+    #@property
+    #def all(self):
+    #    return self.__str__(self._get_param_names())
+
+
+    #def __str__(self, names=None, nw=30):
+    def __str__(self, nw=30):
+        """
+        Return a string describing the parameter names and their ties and constraints
+        """
+        names = self._get_param_names()
+        #if names is None:
+        #    names = self._get_print_names()
+        #name_indices = self.grep_param_names("|".join(names))
+        N = len(names)
+
+        if not N:
+            return "This object has no free parameters."
+        header = ['Name', 'Value', 'Constraints', 'Ties']
+        values = self._get_params() # map(str,self._get_params())
+        #values = self._get_params()[name_indices] # map(str,self._get_params())
+        # sort out the constraints
+        constraints = [''] * len(names)
+        #constraints = [''] * len(self._get_param_names())
+        for i, t in zip(self.constrained_indices, self.constraints):
+            for ii in i:
+                constraints[ii] = t.__str__()
+        for i in self.fixed_indices:
+            for ii in i:
+                constraints[ii] = 'Fixed'
+        # sort out the ties
+        ties = [''] * len(names)
+        for i, tie in enumerate(self.tied_indices):
+            for j in tie:
+                ties[j] = '(' + str(i) + ')'
+
+        if values.size == 1:
+            values = ['%.4f' %float(values)]
+        else:
+            values = ['%.4f' % float(v) for v in values]
+        max_names = max([len(names[i]) for i in range(len(names))] + [len(header[0])])
+        max_values = max([len(values[i]) for i in range(len(values))] + [len(header[1])])
+        max_constraint = max([len(constraints[i]) for i in range(len(constraints))] + [len(header[2])])
+        max_ties = max([len(ties[i]) for i in range(len(ties))] + [len(header[3])])
+        cols = np.array([max_names, max_values, max_constraint, max_ties]) + 4
+        # columns = cols.sum()
+
+        header_string = ["{h:^{col}}".format(h=header[i], col=cols[i]) for i in range(len(cols))]
+        header_string = map(lambda x: '|'.join(x), [header_string])
+        separator = '-' * len(header_string[0])
+        param_string = ["{n:^{c0}}|{v:^{c1}}|{c:^{c2}}|{t:^{c3}}".format(n=names[i], v=values[i], c=constraints[i], t=ties[i], c0=cols[0], c1=cols[1], c2=cols[2], c3=cols[3]) for i in range(len(values))]
+
+
+        return ('\n'.join([header_string[0], separator] + param_string)) + '\n'
+
+    def grep_model(self,regexp):
+        regexp_indices = self.grep_param_names(regexp)
+        all_names = self._get_param_names()
+
+        names = [all_names[pj] for pj in regexp_indices]
+        N = len(names)
+
+        if not N:
+            return "Match not found."
+
+        header = ['Name', 'Value', 'Constraints', 'Ties']
+        all_values = self._get_params()
+        values = np.array([all_values[pj] for pj in regexp_indices])
+        constraints = [''] * len(names)
+
+        _constrained_indices,aux = self._pick_elements(regexp_indices,self.constrained_indices)
+        _constraints = [self.constraints[pj] for pj in aux]
+
+        for i, t in zip(_constrained_indices, _constraints):
+            for ii in i:
+                iii = regexp_indices.tolist().index(ii)
+                constraints[iii] = t.__str__()
+
+        _fixed_indices,aux = self._pick_elements(regexp_indices,self.fixed_indices)
+        for i in _fixed_indices:
+            for ii in i:
+                iii = regexp_indices.tolist().index(ii)
+                constraints[ii] = 'Fixed'
+
+        _tied_indices,aux = self._pick_elements(regexp_indices,self.tied_indices)
+        ties = [''] * len(names)
+        for i,ti in zip(_tied_indices,aux):
+            for ii in i:
+                iii = regexp_indices.tolist().index(ii)
+                ties[iii] = '(' + str(ti) + ')'
+
+        if values.size == 1:
+            values = ['%.4f' %float(values)]
+        else:
+            values = ['%.4f' % float(v) for v in values]
+
+        max_names = max([len(names[i]) for i in range(len(names))] + [len(header[0])])
+        max_values = max([len(values[i]) for i in range(len(values))] + [len(header[1])])
+        max_constraint = max([len(constraints[i]) for i in range(len(constraints))] + [len(header[2])])
+        max_ties = max([len(ties[i]) for i in range(len(ties))] + [len(header[3])])
+        cols = np.array([max_names, max_values, max_constraint, max_ties]) + 4
+
+        header_string = ["{h:^{col}}".format(h=header[i], col=cols[i]) for i in range(len(cols))]
+        header_string = map(lambda x: '|'.join(x), [header_string])
+        separator = '-' * len(header_string[0])
+        param_string = ["{n:^{c0}}|{v:^{c1}}|{c:^{c2}}|{t:^{c3}}".format(n=names[i], v=values[i], c=constraints[i], t=ties[i], c0=cols[0], c1=cols[1], c2=cols[2], c3=cols[3]) for i in range(len(values))]
+
+        print header_string[0]
+        print separator
+        for string in param_string:
+            print string
+
+    def _pick_elements(self,regexp_ind,array_list):
+        """Removes from array_list the elements different from regexp_ind"""
+        new_array_list = [] #New list with elements matching regexp_ind
+        array_indices = [] #Indices that matches the arrays in new_array_list and array_list
+
+        array_index = 0
+        for array in array_list:
+            _new = []
+            for ai in array:
+                if ai in regexp_ind:
+                    _new.append(ai)
+            if len(_new):
+                new_array_list.append(np.array(_new))
+                array_indices.append(array_index)
+            array_index += 1
+        return new_array_list, array_indices

GPy/core/tmp/priors.py

@@ -0,0 +1,217 @@
+# Copyright (c) 2012, GPy authors (see AUTHORS.txt).
+# Licensed under the BSD 3-clause license (see LICENSE.txt)
+
+
+import numpy as np
+import pylab as pb
+from scipy.special import gammaln, digamma
+from ..util.linalg import pdinv
+from GPy.core.domains import REAL, POSITIVE
+import warnings
+
+class Prior:
+    domain = None
+    def pdf(self, x):
+        return np.exp(self.lnpdf(x))
+
+    def plot(self):
+        rvs = self.rvs(1000)
+        pb.hist(rvs, 100, normed=True)
+        xmin, xmax = pb.xlim()
+        xx = np.linspace(xmin, xmax, 1000)
+        pb.plot(xx, self.pdf(xx), 'r', linewidth=2)
+
+
+class Gaussian(Prior):
+    """
+    Implementation of the univariate Gaussian probability function, coupled with random variables.
+
+    :param mu: mean
+    :param sigma: standard deviation
+
+    .. Note:: Bishop 2006 notation is used throughout the code
+
+    """
+    domain = REAL
+    def __init__(self, mu, sigma):
+        self.mu = float(mu)
+        self.sigma = float(sigma)
+        self.sigma2 = np.square(self.sigma)
+        self.constant = -0.5 * np.log(2 * np.pi * self.sigma2)
+
+    def __str__(self):
+        return "N(" + str(np.round(self.mu)) + ', ' + str(np.round(self.sigma2)) + ')'
+
+    def lnpdf(self, x):
+        return self.constant - 0.5 * np.square(x - self.mu) / self.sigma2
+
+    def lnpdf_grad(self, x):
+        return -(x - self.mu) / self.sigma2
+
+    def rvs(self, n):
+        return np.random.randn(n) * self.sigma + self.mu
+
+
+class LogGaussian(Prior):
+    """
+    Implementation of the univariate *log*-Gaussian probability function, coupled with random variables.
+
+    :param mu: mean
+    :param sigma: standard deviation
+
+    .. Note:: Bishop 2006 notation is used throughout the code
+
+    """
+    domain = POSITIVE
+    def __init__(self, mu, sigma):
+        self.mu = float(mu)
+        self.sigma = float(sigma)
+        self.sigma2 = np.square(self.sigma)
+        self.constant = -0.5 * np.log(2 * np.pi * self.sigma2)
+
+    def __str__(self):
+        return "lnN(" + str(np.round(self.mu)) + ', ' + str(np.round(self.sigma2)) + ')'
+
+    def lnpdf(self, x):
+        return self.constant - 0.5 * np.square(np.log(x) - self.mu) / self.sigma2 - np.log(x)
+
+    def lnpdf_grad(self, x):
+        return -((np.log(x) - self.mu) / self.sigma2 + 1.) / x
+
+    def rvs(self, n):
+        return np.exp(np.random.randn(n) * self.sigma + self.mu)
+
+
+class MultivariateGaussian:
+    """
+    Implementation of the multivariate Gaussian probability function, coupled with random variables.
+
+    :param mu: mean (N-dimensional array)
+    :param var: covariance matrix (NxN)
+
+    .. Note:: Bishop 2006 notation is used throughout the code
+
+    """
+    domain = REAL
+    def __init__(self, mu, var):
+        self.mu = np.array(mu).flatten()
+        self.var = np.array(var)
+        assert len(self.var.shape) == 2
+        assert self.var.shape[0] == self.var.shape[1]
+        assert self.var.shape[0] == self.mu.size
+        self.input_dim = self.mu.size
+        self.inv, self.hld = pdinv(self.var)
+        self.constant = -0.5 * self.input_dim * np.log(2 * np.pi) - self.hld
+
+    def summary(self):
+        raise NotImplementedError
+
+    def pdf(self, x):
+        return np.exp(self.lnpdf(x))
+
+    def lnpdf(self, x):
+        d = x - self.mu
+        return self.constant - 0.5 * np.sum(d * np.dot(d, self.inv), 1)
+
+    def lnpdf_grad(self, x):
+        d = x - self.mu
+        return -np.dot(self.inv, d)
+
+    def rvs(self, n):
+        return np.random.multivariate_normal(self.mu, self.var, n)
+
+    def plot(self):
+        if self.input_dim == 2:
+            rvs = self.rvs(200)
+            pb.plot(rvs[:, 0], rvs[:, 1], 'kx', mew=1.5)
+            xmin, xmax = pb.xlim()
+            ymin, ymax = pb.ylim()
+            xx, yy = np.mgrid[xmin:xmax:100j, ymin:ymax:100j]
+            xflat = np.vstack((xx.flatten(), yy.flatten())).T
+            zz = self.pdf(xflat).reshape(100, 100)
+            pb.contour(xx, yy, zz, linewidths=2)
+
+
+def gamma_from_EV(E, V):
+    warnings.warn("use Gamma.from_EV to create Gamma Prior", FutureWarning)
+    return Gamma.from_EV(E, V)
+
+
+class Gamma(Prior):
+    """
+    Implementation of the Gamma probability function, coupled with random variables.
+
+    :param a: shape parameter
+    :param b: rate parameter (warning: it's the *inverse* of the scale)
+
+    .. Note:: Bishop 2006 notation is used throughout the code
+
+    """
+    domain = POSITIVE
+    def __init__(self, a, b):
+        self.a = float(a)
+        self.b = float(b)
+        self.constant = -gammaln(self.a) + a * np.log(b)
+
+    def __str__(self):
+        return "Ga(" + str(np.round(self.a)) + ', ' + str(np.round(self.b)) + ')'
+
+    def summary(self):
+        ret = {"E[x]": self.a / self.b, \
+            "E[ln x]": digamma(self.a) - np.log(self.b), \
+            "var[x]": self.a / self.b / self.b, \
+            "Entropy": gammaln(self.a) - (self.a - 1.) * digamma(self.a) - np.log(self.b) + self.a}
+        if self.a > 1:
+            ret['Mode'] = (self.a - 1.) / self.b
+        else:
+            ret['mode'] = np.nan
+        return ret
+
+    def lnpdf(self, x):
+        return self.constant + (self.a - 1) * np.log(x) - self.b * x
+
+    def lnpdf_grad(self, x):
+        return (self.a - 1.) / x - self.b
+
+    def rvs(self, n):
+        return np.random.gamma(scale=1. / self.b, shape=self.a, size=n)
+    @staticmethod
+    def from_EV(E, V):
+        """
+        Creates an instance of a Gamma Prior  by specifying the Expected value(s)
+        and Variance(s) of the distribution.
+    
+        :param E: expected value
+        :param V: variance
+        """
+        a = np.square(E) / V
+        b = E / V
+        return Gamma(a, b)
+
+class inverse_gamma(Prior):
+    """
+    Implementation of the inverse-Gamma probability function, coupled with random variables.
+
+    :param a: shape parameter
+    :param b: rate parameter (warning: it's the *inverse* of the scale)
+
+    .. Note:: Bishop 2006 notation is used throughout the code
+
+    """
+    domain = POSITIVE
+    def __init__(self, a, b):
+        self.a = float(a)
+        self.b = float(b)
+        self.constant = -gammaln(self.a) + a * np.log(b)
+
+    def __str__(self):
+        return "iGa(" + str(np.round(self.a)) + ', ' + str(np.round(self.b)) + ')'
+
+    def lnpdf(self, x):
+        return self.constant - (self.a + 1) * np.log(x) - self.b / x
+
+    def lnpdf_grad(self, x):
+        return -(self.a + 1.) / x + self.b / x ** 2
+
+    def rvs(self, n):
+        return 1. / np.random.gamma(scale=1. / self.b, shape=self.a, size=n)

GPy/core/tmp/transformations.py

@@ -0,0 +1,143 @@
+# Copyright (c) 2012, GPy authors (see AUTHORS.txt).
+# Licensed under the BSD 3-clause license (see LICENSE.txt)
+
+
+import numpy as np
+from GPy.core.domains import POSITIVE, NEGATIVE, BOUNDED
+import sys 
+lim_val = -np.log(sys.float_info.epsilon) 
+
+class transformation(object):
+    domain = None
+    def f(self, x):
+        raise NotImplementedError
+
+    def finv(self, x):
+        raise NotImplementedError
+
+    def gradfactor(self, f):
+        """ df_dx evaluated at self.f(x)=f"""
+        raise NotImplementedError
+
+    def initialize(self, f):
+        """ produce a sensible initial value for f(x)"""
+        raise NotImplementedError
+
+    def __str__(self):
+        raise NotImplementedError
+
+class logexp(transformation):
+    domain = POSITIVE
+    def f(self, x):
+        return np.where(x<-lim_val, np.log(1+np.exp(-lim_val)), np.where(x>lim_val, x, np.log(1. + np.exp(x))))
+    def finv(self, f):
+        return np.where(f>lim_val, f, np.log(np.exp(f) - 1.))
+    def gradfactor(self, f):
+        return np.where(f>lim_val, 1., 1 - np.exp(-f))
+    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)'
+
+class negative_logexp(transformation):
+    domain = NEGATIVE
+    def f(self, x):
+        return -logexp.f(x)
+    def finv(self, f):
+        return logexp.finv(-f) 
+    def gradfactor(self, f):
+        return -logexp.gradfactor(-f)
+    def initialize(self, f):
+        return -logexp.initialize(f)
+    def __str__(self):
+        return '(-ve)'
+
+class logexp_clipped(logexp):
+    max_bound = 1e100
+    min_bound = 1e-10
+    log_max_bound = np.log(max_bound)
+    log_min_bound = np.log(min_bound)
+    domain = POSITIVE
+    def __init__(self, lower=1e-6):
+        self.lower = lower
+    def f(self, x):
+        exp = np.exp(np.clip(x, self.log_min_bound, self.log_max_bound))
+        f = np.log(1. + exp)
+#         if np.isnan(f).any():
+#             import ipdb;ipdb.set_trace()
+        return np.clip(f, self.min_bound, self.max_bound)
+    def finv(self, f):
+        return np.log(np.exp(f - 1.))
+    def gradfactor(self, f):
+        ef = np.exp(f) # np.clip(f, self.min_bound, self.max_bound))
+        gf = (ef - 1.) / ef
+        return gf # 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_c)'
+
+class exponent(transformation):
+    domain = POSITIVE
+    def f(self, x):
+        return np.where(x<lim_val, np.where(x>-lim_val, np.exp(x), np.exp(-lim_val)), np.exp(lim_val))
+    def finv(self, x):
+        return np.log(x)
+    def gradfactor(self, f):
+        return f
+    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)'
+
+class negative_exponent(exponent):
+    domain = NEGATIVE
+    def f(self, x):
+        return -exponent.f(x)
+    def finv(self, f):
+        return exponent.finv(-f)
+    def gradfactor(self, f):
+        return f
+    def initialize(self, f):
+        return -exponent.initialize(f) #np.abs(f)
+    def __str__(self):
+        return '(-ve)'
+
+class square(transformation):
+    domain = POSITIVE
+    def f(self, x):
+        return x ** 2
+    def finv(self, x):
+        return np.sqrt(x)
+    def gradfactor(self, f):
+        return 2 * np.sqrt(f)
+    def initialize(self, f):
+        return np.abs(f)
+    def __str__(self):
+        return '(+sq)'
+
+class logistic(transformation):
+    domain = BOUNDED
+    def __init__(self, lower, upper):
+        assert lower < upper
+        self.lower, self.upper = float(lower), float(upper)
+        self.difference = self.upper - self.lower
+    def f(self, x):
+        return self.lower + self.difference / (1. + np.exp(-x))
+    def finv(self, f):
+        return np.log(np.clip(f - self.lower, 1e-10, np.inf) / np.clip(self.upper - f, 1e-10, np.inf))
+    def gradfactor(self, f):
+        return (f - self.lower) * (self.upper - f) / self.difference
+    def initialize(self, f):
+        if np.any(np.logical_or(f < self.lower, f > self.upper)):
+            print "Warning: changing parameters to satisfy constraints"
+        return np.where(np.logical_or(f < self.lower, f > self.upper), self.f(f * 0.), f)
+    def __str__(self):
+        return '({},{})'.format(self.lower, self.upper)
+

GPy/examples/old_examples/GPLVM_demo.py

@@ -0,0 +1,28 @@
+# Copyright (c) 2012, GPy authors (see AUTHORS.txt).
+# Licensed under the BSD 3-clause license (see LICENSE.txt)
+
+
+import numpy as np
+import pylab as pb
+import GPy
+np.random.seed(1)
+print "GPLVM with RBF kernel"
+
+N = 100
+Q = 1
+D = 2
+X = np.random.rand(N, Q)
+k = GPy.kern.rbf(Q, 1.0, 2.0) + GPy.kern.white(Q, 0.00001)
+K = k.K(X)
+Y = np.random.multivariate_normal(np.zeros(N),K,D).T
+
+m = GPy.models.GPLVM(Y, Q)
+m.constrain_positive('(rbf|bias|white)')
+
+pb.figure()
+m.plot()
+pb.title('PCA initialisation')
+pb.figure()
+m.optimize(messages = 1)
+m.plot()
+pb.title('After optimisation')

GPy/examples/old_examples/GP_regression_demo.py

@@ -0,0 +1,51 @@
+# Copyright (c) 2012, GPy authors (see AUTHORS.txt).
+# Licensed under the BSD 3-clause license (see LICENSE.txt)
+
+
+"""
+Simple Gaussian Processes regression with an RBF kernel
+"""
+import pylab as pb
+import numpy as np
+import GPy
+pb.ion()
+pb.close('all')
+
+
+######################################
+## 1 dimensional example
+
+# sample inputs and outputs
+X = np.random.uniform(-3.,3.,(20,1))
+Y = np.sin(X)+np.random.randn(20,1)*0.05
+
+# create simple GP model
+m = GPy.models.GP_regression(X,Y)
+
+# contrain all parameters to be positive
+m.constrain_positive('')
+
+# optimize and plot
+m.optimize('tnc', max_f_eval = 1000)
+m.plot()
+print(m)
+
+######################################
+## 2 dimensional example
+
+# sample inputs and outputs
+X = np.random.uniform(-3.,3.,(40,2))
+Y = np.sin(X[:,0:1]) * np.sin(X[:,1:2])+np.random.randn(40,1)*0.05
+
+# create simple GP model
+m = GPy.models.GP_regression(X,Y)
+
+# contrain all parameters to be positive
+m.constrain_positive('')
+# optimize and plot
+pb.figure()
+m.optimize('tnc', max_f_eval = 1000)
+m.plot()
+print(m)
+
+

GPy/examples/old_examples/GP_regression_kern_demo.py

@@ -0,0 +1,33 @@
+# Copyright (c) 2012, GPy authors (see AUTHORS.txt).
+# Licensed under the BSD 3-clause license (see LICENSE.txt)
+
+
+"""
+Simple one-dimensional Gaussian Processes with assorted kernel functions
+"""
+import pylab as pb
+import numpy as np
+import GPy
+
+# sample inputs and outputs
+D = 1
+X = np.random.randn(10,D)*2
+X = np.linspace(-1.5,1.5,5)[:,None]
+X = np.append(X,[[5]],0)
+Y = np.sin(np.pi*X/2) #+np.random.randn(X.shape[0],1)*0.05
+
+models = [GPy.models.GP_regression(X,Y, k) for k in (GPy.kern.rbf(D), GPy.kern.Matern52(D), GPy.kern.Matern32(D), GPy.kern.exponential(D), GPy.kern.linear(D) + GPy.kern.white(D),  GPy.kern.bias(D) + GPy.kern.white(D))]
+
+pb.figure(figsize=(12,8))
+for i,m in enumerate(models):
+    m.constrain_positive('')
+    m.optimize()
+    pb.subplot(3,2,i+1)
+    m.plot()
+    #pb.title(m.kern.parts[0].name)
+
+GPy.util.plot.align_subplots(3,2,(-3,6),(-2.5,2.5))
+
+pb.show()
+
+

GPy/examples/old_examples/oil_flow_demo.py

@@ -0,0 +1,53 @@
+# Copyright (c) 2012, GPy authors (see AUTHORS.txt).
+# Licensed under the BSD 3-clause license (see LICENSE.txt)
+
+
+import cPickle as pickle
+import numpy as np
+import pylab as pb
+import GPy
+import pylab as plt
+np.random.seed(1)
+
+def plot_oil(X, theta, labels, label):
+    plt.figure()
+    X = X[:,np.argsort(theta)[:2]]
+    flow_type = (X[labels[:,0]==1])
+    plt.plot(flow_type[:,0], flow_type[:,1], 'rx')
+    flow_type = (X[labels[:,1]==1])
+    plt.plot(flow_type[:,0], flow_type[:,1], 'gx')
+    flow_type = (X[labels[:,2]==1])
+    plt.plot(flow_type[:,0], flow_type[:,1], 'bx')
+    plt.title(label)
+
+data = pickle.load(open('../util/datasets/oil_flow_3classes.pickle', 'r'))
+
+Y = data['DataTrn']
+N, D = Y.shape
+selected = np.random.permutation(N)[:200]
+labels = data['DataTrnLbls'][selected]
+Y = Y[selected]
+N, D = Y.shape
+Y -= Y.mean(axis=0)
+Y /= Y.std(axis=0)
+
+Q = 2
+m1 = GPy.models.sparse_GPLVM(Y, Q, M = 15)
+m1.constrain_positive('(rbf|bias|noise)')
+m1.constrain_bounded('white', 1e-6, 1.0)
+
+plot_oil(m1.X, np.array([1,1]), labels, 'PCA initialization')
+# m.optimize(messages = True)
+m1.optimize('bfgs', messages = True)
+plot_oil(m1.X, np.array([1,1]), labels, 'sparse GPLVM')
+# pb.figure()
+# m.plot()
+# pb.title('PCA initialisation')
+# pb.figure()
+# m.optimize(messages = 1)
+# m.plot()
+# pb.title('After optimisation')
+m = GPy.models.GPLVM(Y, Q)
+m.constrain_positive('(white|rbf|bias|noise)')
+m.optimize()
+plot_oil(m.X, np.array([1,1]), labels, 'GPLVM')

GPy/examples/old_examples/sparse_GPLVM_demo.py

@@ -0,0 +1,31 @@
+# Copyright (c) 2012, GPy authors (see AUTHORS.txt).
+# Licensed under the BSD 3-clause license (see LICENSE.txt)
+
+
+import numpy as np
+import pylab as pb
+import GPy
+np.random.seed(1)
+print "sparse GPLVM with RBF kernel"
+
+N = 100
+Q = 1
+D = 2
+#generate GPLVM-like data
+X = np.random.rand(N, Q)
+k = GPy.kern.rbf(Q, 1.0, 2.0) + GPy.kern.white(Q, 0.00001)
+K = k.K(X)
+Y = np.random.multivariate_normal(np.zeros(N),K,D).T
+
+m = GPy.models.sparse_GPLVM(Y, Q, M = 10)
+m.constrain_positive('(rbf|bias|noise)')
+m.constrain_bounded('white', 1e-3, 0.1)
+# m.plot()
+
+pb.figure()
+m.plot()
+pb.title('PCA initialisation')
+pb.figure()
+m.optimize(messages = 1)
+m.plot()
+pb.title('After optimisation')

GPy/examples/old_examples/sparse_GP_regression_demo.py

@@ -0,0 +1,70 @@
+# Copyright (c) 2012, GPy authors (see AUTHORS.txt).
+# Licensed under the BSD 3-clause license (see LICENSE.txt)
+
+
+import numpy as np
+"""
+Sparse Gaussian Processes regression with an RBF kernel
+"""
+import pylab as pb
+import numpy as np
+import GPy
+np.random.seed(2)
+pb.ion()
+N = 500
+
+######################################
+## 1 dimensional example
+
+# sample inputs and outputs
+X = np.random.uniform(-3.,3.,(N,1))
+Y = np.sin(X)+np.random.randn(N,1)*0.05
+
+# construct kernel
+rbf =  GPy.kern.rbf(1)
+noise = GPy.kern.white(1)
+kernel = rbf + noise
+
+# create simple GP model
+m1 = GPy.models.sparse_GP_regression(X,Y,kernel, M = 10)
+
+# contrain all parameters to be positive
+m1.constrain_positive('(variance|lengthscale|precision)')
+#m1.constrain_positive('(variance|lengthscale)')
+#m1.constrain_fixed('prec',10.)
+
+
+#check gradient FIXME unit test please
+m1.checkgrad()
+# optimize and plot
+m1.optimize('tnc', messages = 1)
+m1.plot()
+# print(m1)
+
+######################################
+## 2 dimensional example
+
+# # sample inputs and outputs
+# X = np.random.uniform(-3.,3.,(N,2))
+# Y = np.sin(X[:,0:1]) * np.sin(X[:,1:2])+np.random.randn(N,1)*0.05
+
+# # construct kernel
+# rbf =  GPy.kern.rbf(2)
+# noise = GPy.kern.white(2)
+# kernel = rbf + noise
+
+# # create simple GP model
+# m2 = GPy.models.sparse_GP_regression(X,Y,kernel, M = 50)
+# create simple GP model
+
+# # contrain all parameters to be positive (but not inducing inputs)
+# m2.constrain_positive('(variance|lengthscale|precision)')
+
+# #check gradient FIXME unit test please
+# m2.checkgrad()
+
+# # optimize and plot
+# pb.figure()
+# m2.optimize('tnc', messages = 1)
+# m2.plot()
+# print(m2)

GPy/examples/old_examples/uncertain_input_GP_regression_demo.py

@@ -0,0 +1,31 @@
+# Copyright (c) 2012, GPy authors (see AUTHORS.txt).
+# Licensed under the BSD 3-clause license (see LICENSE.txt)
+
+
+import pylab as pb
+import numpy as np
+import GPy
+pb.ion()
+pb.close('all')
+
+
+######################################
+## 1 dimensional example
+
+# sample inputs and outputs
+S = np.ones((20,1))
+X = np.random.uniform(-3.,3.,(20,1))
+Y = np.sin(X)+np.random.randn(20,1)*0.05
+
+k = GPy.kern.bias(1) + GPy.kern.white(1)
+
+# create simple GP model
+m = GPy.models.uncertain_input_GP_regression(X,Y,S,kernel=k)
+
+# contrain all parameters to be positive
+m.constrain_positive('(variance|prec)')
+
+# optimize and plot
+m.optimize('tnc', max_f_eval = 1000, messages=1)
+m.plot()
+print(m)

GPy/examples/old_examples/warped_GP_demo.py

@@ -0,0 +1,45 @@
+# Copyright (c) 2012, GPy authors (see AUTHORS.txt).
+# Licensed under the BSD 3-clause license (see LICENSE.txt)
+
+
+import numpy as np
+import scipy as sp
+import pdb, sys, pickle
+import matplotlib.pylab as plt
+import GPy
+np.random.seed(1)
+
+N = 100
+# sample inputs and outputs
+X = np.random.uniform(-np.pi,np.pi,(N,1))
+Y = np.sin(X)+np.random.randn(N,1)*0.05
+# Y += np.abs(Y.min()) + 0.5
+Z = np.exp(Y)# Y**(1/3.0)
+
+# rescaling targets?
+Zmax = Z.max()
+Zmin = Z.min()
+Z = (Z-Zmin)/(Zmax-Zmin) - 0.5
+
+m = GPy.models.warpedGP(X, Z, warping_terms = 2)
+m.constrain_positive('(tanh_a|tanh_b|rbf|white|bias)')
+m.randomize()
+plt.figure()
+plt.xlabel('predicted f(Z)')
+plt.ylabel('actual f(Z)')
+plt.plot(m.Y, Y, 'o', alpha = 0.5, label = 'before training')
+m.optimize(messages = True)
+plt.plot(m.Y, Y, 'o', alpha = 0.5, label = 'after training')
+plt.legend(loc = 0)
+m.plot_warping()
+plt.figure()
+plt.title('warped GP fit')
+m.plot()
+
+m1 = GPy.models.GP_regression(X, Z)
+m1.constrain_positive('(rbf|white|bias)')
+m1.randomize()
+m1.optimize(messages = True)
+plt.figure()
+plt.title('GP fit')
+m1.plot()

GPy/kern/__init__.py~

@@ -0,0 +1,14 @@
+from _src.kern import Kern
+from _src.rbf import RBF
+from _src.linear import Linear, LinearFull
+from _src.static import Bias, White
+from _src.brownian import Brownian
+from _src.sympykern import Sympykern
+from _src.stationary import Exponential, Matern32, Matern52, ExpQuad, RatQuad, Cosine
+from _src.mlp import MLP
+from _src.periodic import PeriodicExponential, PeriodicMatern32, PeriodicMatern52
+from _src.independent_outputs import IndependentOutputs, Hierarchical
+from _src.coregionalize import Coregionalize
+from _src.ssrbf import SSRBF # TODO: ZD: did you remove this?
+from _src.ODE_UY import ODE_UY
+

GPy/kern/_src/notes.txt

@@ -0,0 +1,5 @@
+Combination covariances, with a particular flag (partition?) allow interogation of the individual covariance contribution. So if we have k_3 = k_1 + k_2 because f_3 = f_1 + f_2 then we allow a multi output covariance over f_1, f_2 and f_3 jointly. Then users can make observations of f_3 and f_1 and build a posterior over f_2 using multiple output encoding. When this flag is set an extra input is added to deal with it. We allow for a new 'combination covariance' of the form scale and add so that
+
+f_3 = f_1*a + f_2
+
+Where a can also be negative.

GPy/kern/_src/ode1_eq_lfm.py

@@ -0,0 +1,52 @@
+try:
+    import sympy as sym
+    sympy_available=True
+except ImportError:
+    sympy_available=False
+
+import numpy as np
+from GPy.util.symbolic import differfln
+from symbolic import Symbolic
+from sympy import Function, S, oo, I, cos, sin, asin, log, erf, pi, exp, sqrt, sign, gamma, polygamma
+
+class Ode1_eq_lfm(Symbolic):
+    """
+    A symbolic covariance based on a first order differential equation being driven by a latent force that is an exponentiated quadratic. 
+
+    """
+    def __init__(self, output_dim=1, param=None, name='Ode1_eq_lfm'):
+
+        input_dim = 2
+        x_0, z_0, decay_i, decay_j, lengthscale = sym.symbols('x_0, z_0, decay_i, decay_j, lengthscale', positive=True)
+        scale_i, scale_j = sym.symbols('scale_i, scale_j')
+        # note that covariance only valid for positive time.
+        
+        class sim_h(Function):
+            nargs = 5
+            @classmethod
+            def eval(cls, t, tprime, d_i, d_j, l):
+                half_l_di = 0.5*l*d_i
+                arg_1 = half_l_di + tprime/l
+                arg_2 = half_l_di - (t-tprime)/l
+                ln_part_1 = differfln(arg_1, arg_2)
+                arg_1 = half_l_di 
+                arg_2 = half_l_di - t/l
+                ln_part_2 = differfln(half_l_di, half_l_di - t/l)
+
+                
+                return (exp(half_l_di*half_l_di
+                                     - d_i*(t-tprime)
+                                     + ln_part_1
+                                     - log(d_i + d_j))
+                        - exp(half_l_di*half_l_di
+                              - d_i*t - d_j*tprime
+                              + ln_part_2
+                              - log(d_i + d_j)))
+            
+
+        f = scale_i*scale_j*(sim_h(x_0, z_0, decay_i, decay_j, lengthscale)
+                             + sim_h(z_0, x_0, decay_j, decay_i, lengthscale))
+        # extra input dim is to signify the output dimension. 
+        super(Ode1_eq_lfm, self).__init__(input_dim, k=f, output_dim=output_dim, name=name)
+        self.lengthscale.constrain_positive()
+        self.decay.constrain_positive()

GPy/kern/_src/old_symbolic.py

@@ -0,0 +1,445 @@
+# Check Matthew Rocklin's blog post.
+try:
+    import sympy as sym
+    sympy_available=True
+    from sympy.utilities.lambdify import lambdify
+    from GPy.util.symbolic import stabilise
+except ImportError:
+    sympy_available=False
+
+import numpy as np
+from kern import Kern
+from scipy.special import gammaln, gamma, erf, erfc, erfcx, polygamma
+from GPy.util.functions import normcdf, normcdfln, logistic, logisticln, differfln
+from ...core.parameterization import Param
+
+class Symbolic(Kern):
+    """
+    A kernel object, where all the hard work is done by sympy.
+
+    :param k: the covariance function
+    :type k: a positive definite sympy function of x_0, z_0, x_1, z_1, x_2, z_2...
+
+    To construct a new sympy kernel, you'll need to define:
+     - a kernel function using a sympy object. Ensure that the kernel is of the form k(x,z).
+     - that's it! we'll extract the variables from the function k.
+
+    Note:
+     - to handle multiple inputs, call them x_1, z_1, etc
+     - to handle multpile correlated outputs, you'll need to add parameters with an index, such as lengthscale_i and lengthscale_j.
+    """
+    def __init__(self, input_dim, k=None, output_dim=1, name='symbolic', param=None, active_dims=None, operators=None, func_modules=[]):
+
+        if k is None:
+            raise ValueError, "You must provide an argument for the covariance function."
+
+        self.func_modules = func_modules
+        self.func_modules += [{'gamma':gamma,
+                               'gammaln':gammaln,
+                               'erf':erf, 'erfc':erfc,
+                               'erfcx':erfcx,
+                               'polygamma':polygamma,
+                               'differfln':differfln,
+                               'normcdf':normcdf,
+                               'normcdfln':normcdfln,
+                               'logistic':logistic,
+                               'logisticln':logisticln},
+                              'numpy']
+
+        super(Symbolic, self).__init__(input_dim, active_dims, name)
+
+        self._sym_k = k
+
+        # pull the variable names out of the symbolic covariance function.
+        sym_vars = [e for e in k.atoms() if e.is_Symbol]
+        self._sym_x= sorted([e for e in sym_vars if e.name[0:2]=='x_'],key=lambda x:int(x.name[2:]))
+        self._sym_z= sorted([e for e in sym_vars if e.name[0:2]=='z_'],key=lambda z:int(z.name[2:]))
+
+        # Check that variable names make sense.
+        assert all([x.name=='x_%i'%i for i,x in enumerate(self._sym_x)])
+        assert all([z.name=='z_%i'%i for i,z in enumerate(self._sym_z)])
+        assert len(self._sym_x)==len(self._sym_z)
+        x_dim=len(self._sym_x)
+
+        self._sym_kdiag = k
+        for x, z in zip(self._sym_x, self._sym_z):
+            self._sym_kdiag = self._sym_kdiag.subs(z, x)
+
+        # If it is a multi-output covariance, add an input for indexing the outputs.
+        self._real_input_dim = x_dim
+        # Check input dim is number of xs + 1 if output_dim is >1
+        assert self.input_dim == x_dim + int(output_dim > 1)
+        self.output_dim = output_dim
+
+        # extract parameter names from the covariance
+        thetas = sorted([e for e in sym_vars if not (e.name[0:2]=='x_' or e.name[0:2]=='z_')],key=lambda e:e.name)
+
+        # Look for parameters with index (subscripts), they are associated with different outputs.
+        if self.output_dim>1:
+            self._sym_theta_i = sorted([e for e in thetas if (e.name[-2:]=='_i')], key=lambda e:e.name)
+            self._sym_theta_j = sorted([e for e in thetas if (e.name[-2:]=='_j')], key=lambda e:e.name)
+
+            # Make sure parameter appears with both indices!
+            assert len(self._sym_theta_i)==len(self._sym_theta_j)
+            assert all([theta_i.name[:-2]==theta_j.name[:-2] for theta_i, theta_j in zip(self._sym_theta_i, self._sym_theta_j)])
+
+            # Extract names of shared parameters (those without a subscript)
+            self._sym_theta = [theta for theta in thetas if theta not in self._sym_theta_i and theta not in self._sym_theta_j]
+
+            self.num_split_params = len(self._sym_theta_i)
+            self._split_theta_names = ["%s"%theta.name[:-2] for theta in self._sym_theta_i]
+            # Add split parameters to the model.
+            for theta in self._split_theta_names:
+                # TODO: what if user has passed a parameter vector, how should that be stored and interpreted?
+                setattr(self, theta, Param(theta, np.ones(self.output_dim), None))
+                self.add_parameter(getattr(self, theta))
+
+
+            self.num_shared_params = len(self._sym_theta)
+            for theta_i, theta_j in zip(self._sym_theta_i, self._sym_theta_j):
+                self._sym_kdiag = self._sym_kdiag.subs(theta_j, theta_i)
+
+        else:
+            self.num_split_params = 0
+            self._split_theta_names = []
+            self._sym_theta = thetas
+            self.num_shared_params = len(self._sym_theta)
+
+        # Add parameters to the model.
+        for theta in self._sym_theta:
+            val = 1.0
+            # TODO: what if user has passed a parameter vector, how should that be stored and interpreted? This is the old way before params class.
+            if param is not None:
+                if param.has_key(theta.name):
+                    val = param[theta.name]
+            setattr(self, theta.name, Param(theta.name, val, None))
+            self.add_parameters(getattr(self, theta.name))
+
+        # Differentiate with respect to parameters.
+        derivative_arguments = self._sym_x + self._sym_theta
+        if self.output_dim > 1:
+            derivative_arguments += self._sym_theta_i
+
+        self.derivatives = {theta.name : stabilise(sym.diff(self._sym_k,theta)) for theta in derivative_arguments}
+        self.diag_derivatives = {theta.name : stabilise(sym.diff(self._sym_kdiag,theta)) for theta in derivative_arguments}
+
+        # This gives the parameters for the arg list.
+        self.arg_list = self._sym_x + self._sym_z + self._sym_theta
+        self.diag_arg_list = self._sym_x + self._sym_theta
+        if self.output_dim > 1:
+            self.arg_list += self._sym_theta_i + self._sym_theta_j
+            self.diag_arg_list += self._sym_theta_i
+
+        # Check if there are additional linear operators on the covariance.
+        self._sym_operators = operators
+        # TODO: Deal with linear operators
+        #if self._sym_operators:
+        #    for operator in self._sym_operators:
+                
+        # psi_stats aren't yet implemented.
+        if False:
+            self.compute_psi_stats()
+
+        # generate the code for the covariance functions
+        self._gen_code()
+
+    def __add__(self,other):
+        return spkern(self._sym_k+other._sym_k)
+
+    def _gen_code(self):
+        #fn_theano = theano_function([self.arg_lists], [self._sym_k + self.derivatives], dims={x: 1}, dtypes={x_0: 'float64', z_0: 'float64'})
+        self._K_function = lambdify(self.arg_list, self._sym_k, self.func_modules)
+        self._K_derivatives_code = {key: lambdify(self.arg_list, self.derivatives[key], self.func_modules) for key in self.derivatives.keys()}
+        self._Kdiag_function = lambdify(self.diag_arg_list, self._sym_kdiag, self.func_modules)
+        self._Kdiag_derivatives_code = {key: lambdify(self.diag_arg_list, self.diag_derivatives[key], self.func_modules) for key in self.diag_derivatives.keys()}
+
+    def K(self,X,X2=None):
+        self._K_computations(X, X2)
+        return self._K_function(**self._arguments)
+
+
+    def Kdiag(self,X):
+        self._K_computations(X)
+        return self._Kdiag_function(**self._diag_arguments)
+
+    def _param_grad_helper(self,partial,X,Z,target):
+        pass
+
+
+    def gradients_X(self, dL_dK, X, X2=None):
+        #if self._X is None or X.base is not self._X.base or X2 is not None:
+        self._K_computations(X, X2)
+        gradients_X = np.zeros_like(X)
+        for i, x in enumerate(self._sym_x):
+            gf = self._K_derivatives_code[x.name]
+            gradients_X[:, i] = (gf(**self._arguments)*dL_dK).sum(1)
+        if X2 is None:
+            gradients_X *= 2
+        return gradients_X
+
+    def gradients_X_diag(self, dL_dK, X):
+        self._K_computations(X)
+        dX = np.zeros_like(X)
+        for i, x in enumerate(self._sym_x):
+            gf = self._Kdiag_derivatives_code[x.name]
+            dX[:, i] = gf(**self._diag_arguments)*dL_dK
+        return dX
+
+    def update_gradients_full(self, dL_dK, X, X2=None):
+        # Need to extract parameters to local variables first
+        self._K_computations(X, X2)
+        for theta in self._sym_theta:
+            parameter = getattr(self, theta.name)
+            gf = self._K_derivatives_code[theta.name]
+            gradient = (gf(**self._arguments)*dL_dK).sum()
+            if X2 is not None:
+                gradient += (gf(**self._reverse_arguments)*dL_dK).sum()
+            setattr(parameter, 'gradient', gradient)
+        if self.output_dim>1:
+            for theta in self._sym_theta_i:
+                parameter = getattr(self, theta.name[:-2])
+                gf = self._K_derivatives_code[theta.name]
+                A = gf(**self._arguments)*dL_dK
+                gradient = np.asarray([A[np.where(self._output_ind==i)].T.sum()
+                                       for i in np.arange(self.output_dim)])
+                if X2 is None:
+                    gradient *= 2
+                else:
+                    A = gf(**self._reverse_arguments)*dL_dK.T
+                    gradient += np.asarray([A[np.where(self._output_ind2==i)].T.sum()
+                                 for i in np.arange(self.output_dim)])
+                setattr(parameter, 'gradient', gradient)
+
+
+    def update_gradients_diag(self, dL_dKdiag, X):
+        self._K_computations(X)
+        for theta in self._sym_theta:
+            parameter = getattr(self, theta.name)
+            gf = self._Kdiag_derivatives_code[theta.name]
+            setattr(parameter, 'gradient', (gf(**self._diag_arguments)*dL_dKdiag).sum())
+        if self.output_dim>1:
+            for theta in self._sym_theta_i:
+                parameter = getattr(self, theta.name[:-2])
+                gf = self._Kdiag_derivatives_code[theta.name]
+                a = gf(**self._diag_arguments)*dL_dKdiag
+                setattr(parameter, 'gradient',
+                        np.asarray([a[np.where(self._output_ind==i)].sum()
+                         for i in np.arange(self.output_dim)]))
+
+    def _K_computations(self, X, X2=None):
+        """Set up argument lists for the derivatives."""
+        # Could check if this needs doing or not, there could
+        # definitely be some computational savings by checking for
+        # parameter updates here.
+        self._arguments = {}
+        self._diag_arguments = {}
+        for i, x in enumerate(self._sym_x):
+            self._arguments[x.name] =  X[:, i][:, None]
+            self._diag_arguments[x.name] =  X[:, i][:, None]
+        if self.output_dim > 1:
+            self._output_ind = np.asarray(X[:, -1], dtype='int')
+            for i, theta in enumerate(self._sym_theta_i):
+                self._arguments[theta.name] = np.asarray(getattr(self, theta.name[:-2])[self._output_ind])[:, None]
+                self._diag_arguments[theta.name] = self._arguments[theta.name]
+        for theta in self._sym_theta:
+            self._arguments[theta.name] = np.asarray(getattr(self, theta.name))
+            self._diag_arguments[theta.name] = self._arguments[theta.name]
+
+        if X2 is not None:
+            for i, z in enumerate(self._sym_z):
+                self._arguments[z.name] =  X2[:, i][None, :]
+            if self.output_dim > 1:
+                self._output_ind2 = np.asarray(X2[:, -1], dtype='int')
+                for i, theta in enumerate(self._sym_theta_j):
+                    self._arguments[theta.name] = np.asarray(getattr(self, theta.name[:-2])[self._output_ind2])[None, :]
+        else:
+            for z in self._sym_z:
+                self._arguments[z.name] =  self._arguments['x_'+z.name[2:]].T
+            if self.output_dim > 1:
+                self._output_ind2 = self._output_ind
+                for theta in self._sym_theta_j:
+                    self._arguments[theta.name] = self._arguments[theta.name[:-2] + '_i'].T
+        if X2 is not None:
+            # These arguments are needed in gradients when X2 is not equal to X.
+            self._reverse_arguments = self._arguments
+            for x, z in zip(self._sym_x, self._sym_z):
+                self._reverse_arguments[x.name] = self._arguments[z.name].T
+                self._reverse_arguments[z.name] = self._arguments[x.name].T
+            if self.output_dim > 1:
+                for theta_i, theta_j in zip(self._sym_theta_i, self._sym_theta_j):
+                    self._reverse_arguments[theta_i.name] = self._arguments[theta_j.name].T
+                    self._reverse_arguments[theta_j.name] = self._arguments[theta_i.name].T
+
+if False:
+    class Symcombine(CombinationKernel):
+        """
+        Combine list of given sympy covariances together with the provided operations.
+        """
+        def __init__(self, subkerns, operations, name='sympy_combine'):
+            super(Symcombine, self).__init__(subkerns, name)
+            for subkern, operation in zip(subkerns, operations):
+                self._sym_k += self._k_double_operate(subkern._sym_k, operation)
+
+        #def _double_operate(self, k, operation):
+
+
+        @Cache_this(limit=2, force_kwargs=['which_parts'])
+        def K(self, X, X2=None, which_parts=None):
+            """
+            Combine covariances with a linear operator.
+            """
+            assert X.shape[1] == self.input_dim
+            if which_parts is None:
+                which_parts = self.parts
+            elif not isinstance(which_parts, (list, tuple)):
+                # if only one part is given
+                which_parts = [which_parts]
+            return reduce(np.add, (p.K(X, X2) for p in which_parts))
+
+        @Cache_this(limit=2, force_kwargs=['which_parts'])
+        def Kdiag(self, X, which_parts=None):
+            assert X.shape[1] == self.input_dim
+            if which_parts is None:
+                which_parts = self.parts
+            elif not isinstance(which_parts, (list, tuple)):
+                # if only one part is given
+                which_parts = [which_parts]
+            return reduce(np.add, (p.Kdiag(X) for p in which_parts))
+
+        def update_gradients_full(self, dL_dK, X, X2=None):
+            [p.update_gradients_full(dL_dK, X, X2) for p in self.parts]
+
+        def update_gradients_diag(self, dL_dK, X):
+            [p.update_gradients_diag(dL_dK, X) for p in self.parts]
+
+        def gradients_X(self, dL_dK, X, X2=None):
+            """Compute the gradient of the objective function with respect to X.
+
+            :param dL_dK: An array of gradients of the objective function with respect to the covariance function.
+            :type dL_dK: np.ndarray (num_samples x num_inducing)
+            :param X: Observed data inputs
+            :type X: np.ndarray (num_samples x input_dim)
+            :param X2: Observed data inputs (optional, defaults to X)
+            :type X2: np.ndarray (num_inducing x input_dim)"""
+
+            target = np.zeros(X.shape)
+            [target.__iadd__(p.gradients_X(dL_dK, X, X2)) for p in self.parts]
+            return target
+
+        def gradients_X_diag(self, dL_dKdiag, X):
+            target = np.zeros(X.shape)
+            [target.__iadd__(p.gradients_X_diag(dL_dKdiag, X)) for p in self.parts]
+            return target
+
+        def psi0(self, Z, variational_posterior):
+            return reduce(np.add, (p.psi0(Z, variational_posterior) for p in self.parts))
+
+        def psi1(self, Z, variational_posterior):
+            return reduce(np.add, (p.psi1(Z, variational_posterior) for p in self.parts))
+
+        def psi2(self, Z, variational_posterior):
+            psi2 = reduce(np.add, (p.psi2(Z, variational_posterior) for p in self.parts))
+            #return psi2
+            # compute the "cross" terms
+            from static import White, Bias
+            from rbf import RBF
+            #from rbf_inv import RBFInv
+            from linear import Linear
+            #ffrom fixed import Fixed
+
+            for p1, p2 in itertools.combinations(self.parts, 2):
+                # i1, i2 = p1.active_dims, p2.active_dims
+                # white doesn;t combine with anything
+                if isinstance(p1, White) or isinstance(p2, White):
+                    pass
+                # rbf X bias
+                #elif isinstance(p1, (Bias, Fixed)) and isinstance(p2, (RBF, RBFInv)):
+                elif isinstance(p1,  Bias) and isinstance(p2, (RBF, Linear)):
+                    tmp = p2.psi1(Z, variational_posterior)
+                    psi2 += p1.variance * (tmp[:, :, None] + tmp[:, None, :])
+                #elif isinstance(p2, (Bias, Fixed)) and isinstance(p1, (RBF, RBFInv)):
+                elif isinstance(p2, Bias) and isinstance(p1, (RBF, Linear)):
+                    tmp = p1.psi1(Z, variational_posterior)
+                    psi2 += p2.variance * (tmp[:, :, None] + tmp[:, None, :])
+                elif isinstance(p2, (RBF, Linear)) and isinstance(p1, (RBF, Linear)):
+                    assert np.intersect1d(p1.active_dims, p2.active_dims).size == 0, "only non overlapping kernel dimensions allowed so far"
+                    tmp1 = p1.psi1(Z, variational_posterior)
+                    tmp2 = p2.psi1(Z, variational_posterior)
+                    psi2 += (tmp1[:, :, None] * tmp2[:, None, :]) + (tmp2[:, :, None] * tmp1[:, None, :])
+                else:
+                    raise NotImplementedError, "psi2 cannot be computed for this kernel"
+            return psi2
+
+        def update_gradients_expectations(self, dL_dpsi0, dL_dpsi1, dL_dpsi2, Z, variational_posterior):
+            from static import White, Bias
+            for p1 in self.parts:
+                #compute the effective dL_dpsi1. Extra terms appear becaue of the cross terms in psi2!
+                eff_dL_dpsi1 = dL_dpsi1.copy()
+                for p2 in self.parts:
+                    if p2 is p1:
+                        continue
+                    if isinstance(p2, White):
+                        continue
+                    elif isinstance(p2, Bias):
+                        eff_dL_dpsi1 += dL_dpsi2.sum(1) * p2.variance * 2.
+                    else:# np.setdiff1d(p1.active_dims, ar2, assume_unique): # TODO: Careful, not correct for overlapping active_dims
+                        eff_dL_dpsi1 += dL_dpsi2.sum(1) * p2.psi1(Z, variational_posterior) * 2.
+                p1.update_gradients_expectations(dL_dpsi0, eff_dL_dpsi1, dL_dpsi2, Z, variational_posterior)
+
+        def gradients_Z_expectations(self, dL_dpsi1, dL_dpsi2, Z, variational_posterior):
+            from static import White, Bias
+            target = np.zeros(Z.shape)
+            for p1 in self.parts:
+                #compute the effective dL_dpsi1. extra terms appear becaue of the cross terms in psi2!
+                eff_dL_dpsi1 = dL_dpsi1.copy()
+                for p2 in self.parts:
+                    if p2 is p1:
+                        continue
+                    if isinstance(p2, White):
+                        continue
+                    elif isinstance(p2, Bias):
+                        eff_dL_dpsi1 += dL_dpsi2.sum(1) * p2.variance * 2.
+                    else:
+                        eff_dL_dpsi1 += dL_dpsi2.sum(1) * p2.psi1(Z, variational_posterior) * 2.
+                target += p1.gradients_Z_expectations(eff_dL_dpsi1, dL_dpsi2, Z, variational_posterior)
+            return target
+
+        def gradients_qX_expectations(self, dL_dpsi0, dL_dpsi1, dL_dpsi2, Z, variational_posterior):
+            from static import White, Bias
+            target_mu = np.zeros(variational_posterior.shape)
+            target_S = np.zeros(variational_posterior.shape)
+            for p1 in self._parameters_:
+                #compute the effective dL_dpsi1. extra terms appear becaue of the cross terms in psi2!
+                eff_dL_dpsi1 = dL_dpsi1.copy()
+                for p2 in self._parameters_:
+                    if p2 is p1:
+                        continue
+                    if isinstance(p2, White):
+                        continue
+                    elif isinstance(p2, Bias):
+                        eff_dL_dpsi1 += dL_dpsi2.sum(1) * p2.variance * 2.
+                    else:
+                        eff_dL_dpsi1 += dL_dpsi2.sum(1) * p2.psi1(Z, variational_posterior) * 2.
+                a, b = p1.gradients_qX_expectations(dL_dpsi0, eff_dL_dpsi1, dL_dpsi2, Z, variational_posterior)
+                target_mu += a
+                target_S += b
+            return target_mu, target_S
+
+        def _getstate(self):
+            """
+            Get the current state of the class,
+            here just all the indices, rest can get recomputed
+            """
+            return super(Add, self)._getstate()
+
+        def _setstate(self, state):
+            super(Add, self)._setstate(state)
+
+        def add(self, other, name='sum'):
+            if isinstance(other, Add):
+                other_params = other._parameters_.copy()
+                for p in other_params:
+                    other.remove_parameter(p)
+                self.add_parameters(*other_params)
+            else: self.add_parameter(other)
+            return self

GPy/kern/_src/old_sympykern.py

@@ -0,0 +1,564 @@
+# Check Matthew Rocklin's blog post.
+try: 
+    import sympy as sp
+    sympy_available=True
+    from sympy.utilities.autowrap import ufuncify
+except ImportError:
+    sympy_available=False
+    exit()
+
+from sympy.core.cache import clear_cache
+from sympy.utilities.codegen import codegen
+
+try:
+    from scipy import weave
+    weave_available = True
+except ImportError:
+    weave_available = False
+
+import os
+current_dir = os.path.dirname(os.path.abspath(os.path.dirname(__file__)))
+import sys
+import numpy as np
+import re
+import tempfile
+import pdb
+import ast
+
+from kernpart import Kernpart
+from ...core.parameterization import Param
+from ...core.parameterization.transformations import Logexp
+# TODO have this set up in a set up file!
+user_code_storage = tempfile.gettempdir()
+
+class spkern(Kern):
+    """
+    A kernel object, where all the hard work in done by sympy.
+
+    :param k: the covariance function
+    :type k: a positive definite sympy function of x_0, z_0, x_1, z_1, x_2, z_2...
+
+    To construct a new sympy kernel, you'll need to define:
+     - a kernel function using a sympy object. Ensure that the kernel is of the form k(x,z).
+     - that's it! we'll extract the variables from the function k.
+
+    Note:
+     - to handle multiple inputs, call them x_1, z_1, etc
+     - to handle multpile correlated outputs, you'll need to add parameters with an index, such as lengthscale_i and lengthscale_j.
+    """
+    def __init__(self, input_dim, k=None, output_dim=1, name=None, param=None):
+
+        if name is None:
+            name='sympykern'
+        if k is None:
+            raise ValueError, "You must provide an argument for the covariance function."
+        super(spkern, self).__init__(input_dim, name)
+
+        self._sp_k = k
+
+        # pull the variable names out of the symbolic covariance function.
+        sp_vars = [e for e in k.atoms() if e.is_Symbol]
+        self._sp_x= sorted([e for e in sp_vars if e.name[0:2]=='x_'],key=lambda x:int(x.name[2:]))
+        self._sp_z= sorted([e for e in sp_vars if e.name[0:2]=='z_'],key=lambda z:int(z.name[2:]))
+
+        # Check that variable names make sense.
+        assert all([x.name=='x_%i'%i for i,x in enumerate(self._sp_x)])
+        assert all([z.name=='z_%i'%i for i,z in enumerate(self._sp_z)])
+        assert len(self._sp_x)==len(self._sp_z)
+        x_dim=len(self._sp_x)
+
+        # If it is a multi-output covariance, add an input for indexing the outputs.
+        self._real_input_dim = x_dim
+        # Check input dim is number of xs + 1 if output_dim is >1
+        assert self.input_dim == x_dim + int(output_dim > 1)
+        self.output_dim = output_dim
+
+        # extract parameter names from the covariance
+        thetas = sorted([e for e in sp_vars if not (e.name[0:2]=='x_' or e.name[0:2]=='z_')],key=lambda e:e.name)
+
+
+        # Look for parameters with index (subscripts), they are associated with different outputs.
+        if self.output_dim>1:
+            self._sp_theta_i = sorted([e for e in thetas if (e.name[-2:]=='_i')], key=lambda e:e.name)
+            self._sp_theta_j = sorted([e for e in thetas if (e.name[-2:]=='_j')], key=lambda e:e.name)
+
+            # Make sure parameter appears with both indices!
+            assert len(self._sp_theta_i)==len(self._sp_theta_j)
+            assert all([theta_i.name[:-2]==theta_j.name[:-2] for theta_i, theta_j in zip(self._sp_theta_i, self._sp_theta_j)])
+
+            # Extract names of shared parameters (those without a subscript)
+            self._sp_theta = [theta for theta in thetas if theta not in self._sp_theta_i and theta not in self._sp_theta_j]
+            
+            self.num_split_params = len(self._sp_theta_i)
+            self._split_theta_names = ["%s"%theta.name[:-2] for theta in self._sp_theta_i]
+            for theta in self._split_theta_names:
+                setattr(self, theta, Param(theta, np.ones(self.output_dim), None))
+                self.add_parameters(getattr(self, theta))
+
+                #setattr(self, theta, np.ones(self.output_dim))
+            
+            self.num_shared_params = len(self._sp_theta)
+            #self.num_params = self.num_shared_params+self.num_split_params*self.output_dim
+            
+        else:
+            self.num_split_params = 0
+            self._split_theta_names = []
+            self._sp_theta = thetas
+            self.num_shared_params = len(self._sp_theta)
+            #self.num_params = self.num_shared_params
+
+        # Add parameters to the model.
+        for theta in self._sp_theta:
+            val = 1.0
+            if param is not None:
+                if param.has_key(theta):
+                    val = param[theta]
+            #setattr(self, theta.name, val)
+            setattr(self, theta.name, Param(theta.name, val, None))
+            self.add_parameters(getattr(self, theta.name))
+        #deal with param            
+        #self._set_params(self._get_params())
+
+        # Differentiate with respect to parameters.
+        self._sp_dk_dtheta = [sp.diff(k,theta).simplify() for theta in self._sp_theta]
+        if self.output_dim > 1:
+            self._sp_dk_dtheta_i = [sp.diff(k,theta).simplify() for theta in self._sp_theta_i]
+
+        # differentiate with respect to input variables.
+        self._sp_dk_dx = [sp.diff(k,xi).simplify() for xi in self._sp_x]
+
+        # psi_stats aren't yet implemented.
+        if False:
+            self.compute_psi_stats()
+
+        self._code = {}
+
+        # generate the code for the covariance functions
+        self._gen_code()
+
+        if weave_available:
+            if False:
+                extra_compile_args = ['-ftree-vectorize', '-mssse3', '-ftree-vectorizer-verbose=5']
+            else:
+                extra_compile_args = []
+            
+                self.weave_kwargs = {
+                    'support_code': None, #self._function_code,
+                    'include_dirs':[user_code_storage, os.path.join(current_dir,'parts/')],
+                    'headers':['"sympy_helpers.h"', '"'+self.name+'.h"'],
+                    'sources':[os.path.join(current_dir,"parts/sympy_helpers.cpp"), os.path.join(user_code_storage, self.name+'.cpp')],
+                    'extra_compile_args':extra_compile_args,
+                    'extra_link_args':['-lgomp'],
+                    'verbose':True}
+        self.parameters_changed() # initializes caches
+
+
+    def __add__(self,other):
+        return spkern(self._sp_k+other._sp_k)
+
+    def _gen_code(self):
+
+        argument_sequence = self._sp_x+self._sp_z+self._sp_theta
+        code_list = [('k',self._sp_k)]
+        # gradients with respect to covariance input
+        code_list += [('dk_d%s'%x.name,dx) for x,dx in zip(self._sp_x,self._sp_dk_dx)]
+        # gradient with respect to parameters
+        code_list += [('dk_d%s'%theta.name,dtheta) for theta,dtheta in zip(self._sp_theta,self._sp_dk_dtheta)]
+        # gradient with respect to multiple output parameters
+        if self.output_dim > 1:
+            argument_sequence += self._sp_theta_i + self._sp_theta_j
+            code_list += [('dk_d%s'%theta.name,dtheta) for theta,dtheta in zip(self._sp_theta_i,self._sp_dk_dtheta_i)]
+        # generate c functions from sympy objects
+        if weave_available:
+            code_type = "C"
+        else:
+            code_type = "PYTHON"
+        # Need to add the sympy_helpers header in here.
+        (foo_c,self._function_code), (foo_h,self._function_header) = \
+                                     codegen(code_list,
+                                             code_type,
+                                             self.name,
+                                             argument_sequence=argument_sequence)
+
+
+        # Use weave to compute the underlying functions.
+        if weave_available:
+            # put the header file where we can find it
+            f = file(os.path.join(user_code_storage, self.name + '.h'),'w')
+            f.write(self._function_header)
+            f.close()
+    
+
+        if weave_available:
+            # Substitute any known derivatives which sympy doesn't compute
+            self._function_code = re.sub('DiracDelta\(.+?,.+?\)','0.0',self._function_code)
+            # put the cpp file in user code storage (defaults to temp file location)
+            f = file(os.path.join(user_code_storage, self.name + '.cpp'),'w')
+        else:
+            # put the python file in user code storage
+            f = file(os.path.join(user_code_storage, self.name + '.py'),'w')
+        f.write(self._function_code)
+        f.close()
+
+        if weave_available:
+            # arg_list will store the arguments required for the C code.
+            input_arg_list = (["X2(i, %s)"%x.name[2:] for x in self._sp_x]
+                        + ["Z2(j, %s)"%z.name[2:] for z in self._sp_z])
+
+            # for multiple outputs reverse argument list is also required
+            if self.output_dim>1:
+                reverse_input_arg_list = list(input_arg_list)
+                reverse_input_arg_list.reverse()
+
+            # This gives the parameters for the arg list.
+            param_arg_list = [shared_params.name for shared_params in self._sp_theta]
+            arg_list = input_arg_list + param_arg_list
+
+            precompute_list=[]
+            if self.output_dim > 1:
+                reverse_arg_list= reverse_input_arg_list + list(param_arg_list)
+                # For multiple outputs, also need the split parameters.
+                split_param_arg_list = ["%s1(%s)"%(theta.name[:-2].upper(),index) for index in ['ii', 'jj'] for theta in self._sp_theta_i]
+                split_param_reverse_arg_list = ["%s1(%s)"%(theta.name[:-2].upper(),index) for index in ['jj', 'ii'] for theta in self._sp_theta_i]
+                arg_list += split_param_arg_list
+                reverse_arg_list += split_param_reverse_arg_list
+                # Extract the right output indices from the inputs.
+                c_define_output_indices = [' '*16 + "int %s=(int)%s(%s, %i);"%(index, var, index2, self.input_dim-1) for index, var, index2 in zip(['ii', 'jj'], ['X2', 'Z2'], ['i', 'j'])]
+                precompute_list += c_define_output_indices
+                reverse_arg_string = ", ".join(reverse_arg_list)
+            arg_string = ", ".join(arg_list)
+            precompute_string = "\n".join(precompute_list)
+
+            # Now we use the arguments in code that computes the separate parts.
+
+            # Any precomputations will be done here eventually.
+            self._precompute = \
+                """
+                // Precompute code would go here. It will be called when parameters are updated. 
+                """
+
+            # Here's the code to do the looping for K
+            self._code['K'] =\
+            """
+            // _K_code
+            // Code for computing the covariance function.
+            int i;
+            int j;
+            int n = target_array->dimensions[0];
+            int num_inducing = target_array->dimensions[1];
+            int input_dim = X_array->dimensions[1];
+            //#pragma omp parallel for private(j)
+            for (i=0;i<n;i++){
+                for (j=0;j<num_inducing;j++){
+                    %s
+                    //target[i*num_inducing+j] = 
+                    TARGET2(i, j) += k(%s);
+                }
+            }
+            %s
+            """%(precompute_string,arg_string,"/*"+str(self._sp_k)+"*/")
+           # adding a string representation of the function in the
+           # comment forces recompile when needed
+            self._code['K_X'] = self._code['K'].replace('Z2(', 'X2(')
+
+
+            # Code to compute diagonal of covariance.
+            diag_arg_string = re.sub('Z','X',arg_string)
+            diag_arg_string = re.sub('int jj','//int jj',diag_arg_string)
+            diag_arg_string = re.sub('j','i',diag_arg_string)
+            diag_precompute_string = re.sub('int jj','//int jj',precompute_string)
+            diag_precompute_string = re.sub('Z','X',diag_precompute_string)
+            diag_precompute_string = re.sub('j','i',diag_precompute_string)
+            # Code to do the looping for Kdiag
+            self._code['Kdiag'] =\
+            """
+            // _code['Kdiag']
+            // Code for computing diagonal of covariance function.
+            int i;
+            int n = target_array->dimensions[0];
+            int input_dim = X_array->dimensions[1];
+            //#pragma omp parallel for
+            for (i=0;i<n;i++){
+                    %s
+                    //target[i] =
+                    TARGET1(i)=k(%s);
+            }
+            %s
+            """%(diag_precompute_string,diag_arg_string,"/*"+str(self._sp_k)+"*/") #adding a string representation forces recompile when needed
+
+            # Code to compute gradients
+            if self.output_dim>1:
+                for i, theta in enumerate(self._sp_theta_i):
+                    grad_func_list = [' '*26 + 'TARGET1(ii) += PARTIAL2(i, j)*dk_d%s(%s);'%(theta.name, arg_string)]
+                    grad_func_list += [' '*26 + 'TARGET1(jj) += PARTIAL2(i, j)*dk_d%s(%s);'%(theta.name, reverse_arg_string)]
+                    grad_func_list = c_define_output_indices+grad_func_list
+
+                    grad_func_string = '\n'.join(grad_func_list) 
+                    self._code['dK_d' + theta.name] =\
+                      """
+                      int i;
+                      int j;
+                      int n = partial_array->dimensions[0];
+                      int num_inducing = partial_array->dimensions[1];
+                      int input_dim = X_array->dimensions[1];
+                      //#pragma omp parallel for private(j)
+                      for (i=0;i<n;i++){
+                        for (j=0;j<num_inducing;j++){
+%s
+                        }
+                      }
+                      %s
+                      """%(grad_func_string,"/*"+str(self._sp_k)+"*/") # adding a string representation forces recompile when needed
+                    self._code['dK_d' +theta.name + '_X'] = self._code['dK_d' + theta.name].replace('Z2(', 'X2(')
+                    # Code to compute gradients for Kdiag TODO: needs clean up
+                    diag_grad_func_string = re.sub('Z','X',grad_func_string,count=0)
+                    diag_grad_func_string = re.sub('int jj','//int jj',diag_grad_func_string)
+                    diag_grad_func_string = re.sub('j','i',diag_grad_func_string)
+                    diag_grad_func_string = re.sub('PARTIAL2\(i, i\)','PARTIAL(i)',diag_grad_func_string)
+                    self._code['dKdiag_d' + theta.name] =\
+                      """
+                      // _dKdiag_dtheta_code
+                      // Code for computing gradient of diagonal with respect to parameters.
+                      int i;
+                      int n = partial_array->dimensions[0];
+                      int input_dim = X_array->dimensions[1];
+                      for (i=0;i<n;i++){
+                        %s
+                      }
+                      %s
+                      """%(diag_grad_func_string,"/*"+str(self._sp_k)+"*/") #adding a string representation forces recompile when needed
+
+            for i, theta in enumerate(self._sp_theta):
+                grad_func_list = [' '*26 + 'TARGET1(%i) += PARTIAL2(i, j)*dk_d%s(%s);'%(i,theta.name,arg_string)]
+                grad_func_string = '\n'.join(grad_func_list) 
+
+                self._code['dK_d' + theta.name] =\
+                  """
+                  // _dK_dtheta_code
+                  // Code for computing gradient of covariance with respect to parameters.
+                  int i;
+                  int j;
+                  int n = partial_array->dimensions[0];
+                  int num_inducing = partial_array->dimensions[1];
+                  int input_dim = X_array->dimensions[1];
+                  //#pragma omp parallel for private(j)
+                  for (i=0;i<n;i++){
+                    for (j=0;j<num_inducing;j++){
+                      %s
+                    }
+                  }
+                  %s
+                  """%(grad_func_string,"/*"+str(self._sp_k)+"*/") # adding a string representation forces recompile when needed
+                self._code['dK_d' + theta.name +'_X'] = self._code['dK_d' + theta.name].replace('Z2(', 'X2(')
+                # Code to compute gradients for Kdiag TODO: needs clean up
+                diag_grad_func_string = re.sub('Z','X',grad_func_string,count=0)
+                diag_grad_func_string = re.sub('int jj','//int jj',diag_grad_func_string)
+                diag_grad_func_string = re.sub('j','i',diag_grad_func_string)
+                diag_grad_func_string = re.sub('PARTIAL2\(i, i\)','PARTIAL(i)',diag_grad_func_string)
+                self._code['dKdiag_d' + theta.name] =\
+                   """
+                   // _dKdiag_dtheta_code
+                   // Code for computing gradient of diagonal with respect to parameters.
+                   int i;
+                   int n = partial_array->dimensions[0];
+                   int input_dim = X_array->dimensions[1];
+                   for (i=0;i<n;i++){
+                     %s
+                   }
+                   %s
+                   """%(diag_grad_func_string,"/*"+str(self._sp_k)+"*/") #adding a string representation forces recompile when needed
+
+
+
+            # Code for gradients wrt X, TODO: may need to deal with special case where one input is actually an output.
+            gradX_func_list = []
+            if self.output_dim>1:
+                gradX_func_list += c_define_output_indices
+            gradX_func_list += ["TARGET2(i, %i) += partial[i*num_inducing+j]*dk_dx_%i(%s);"%(q,q,arg_string) for q in range(self._real_input_dim)]
+            gradX_func_string = "\n".join(gradX_func_list)
+
+            self._code['dK_dX'] = \
+            """
+            // _dK_dX_code
+            // Code for computing gradient of covariance with respect to inputs.
+            int i;
+            int j;
+            int n = partial_array->dimensions[0];
+            int num_inducing = partial_array->dimensions[1];
+            int input_dim = X_array->dimensions[1];
+            //#pragma omp parallel for private(j)
+            for (i=0;i<n; i++){
+              for (j=0; j<num_inducing; j++){
+                %s
+              }
+            }
+            %s
+            """%(gradX_func_string,"/*"+str(self._sp_k)+"*/") #adding a string representation forces recompile when needed
+            self._code['dK_dX_X'] = self._code['dK_dX'].replace('Z2(', 'X2(')
+
+
+            diag_gradX_func_string = re.sub('Z','X',gradX_func_string,count=0)
+            diag_gradX_func_string = re.sub('int jj','//int jj',diag_gradX_func_string)
+            diag_gradX_func_string = re.sub('j','i',diag_gradX_func_string)
+            diag_gradX_func_string = re.sub('PARTIAL2\(i\, i\)','2*PARTIAL(i)',diag_gradX_func_string)
+
+            # Code for gradients of Kdiag wrt X
+            self._code['dKdiag_dX'] = \
+            """
+            // _dKdiag_dX_code
+            // Code for computing gradient of diagonal with respect to inputs.
+            int n = partial_array->dimensions[0];
+            int input_dim = X_array->dimensions[1];
+            for (int i=0;i<n; i++){
+                %s
+            }
+            %s
+            """%(diag_gradX_func_string,"/*"+str(self._sp_k)+"*/") #adding a
+            # string representation forces recompile when needed Get rid
+            # of Zs in argument for diagonal. TODO: Why wasn't
+            # diag_func_string called here? Need to check that.
+
+            
+
+
+            #TODO: insert multiple functions here via string manipulation
+            #TODO: similar functions for psi_stats
+            #TODO: similar functions when cython available.
+            #TODO: similar functions when only python available.
+            
+    def _get_arg_names(self, target=None, Z=None, partial=None):
+        arg_names = ['X']
+        if target is not None:
+            arg_names += ['target']
+        for shared_params in self._sp_theta:
+            arg_names += [shared_params.name]
+        if Z is not None:
+            arg_names += ['Z']
+        if partial is not None:
+            arg_names += ['partial']
+        if self.output_dim>1:
+            arg_names += self._split_theta_names
+            arg_names += ['output_dim']
+        return arg_names
+
+    def _generate_inline(self, code, X, target=None, Z=None, partial=None):
+        output_dim = self.output_dim
+        # Need to extract parameters to local variables first
+        for shared_params in self._sp_theta:
+            locals()[shared_params.name] = getattr(self, shared_params.name)
+            
+        for split_params in self._split_theta_names:
+            locals()[split_params] = np.asarray(getattr(self, split_params))
+        arg_names = self._get_arg_names(target, Z, partial)        
+
+        if weave_available:
+            return weave.inline(code=code, arg_names=arg_names,**self.weave_kwargs)
+        else:
+            raise RuntimeError('Weave not available and other variants of sympy covariance not yet implemented')
+
+    def K(self,X,Z,target):        
+        if Z is None:
+            self._generate_inline(self._code['K_X'], X, target)
+        else:
+            self._generate_inline(self._code['K'], X, target, Z)
+
+
+    def Kdiag(self,X,target):
+        self._generate_inline(self._code['Kdiag'], X, target)
+
+    def _param_grad_helper(self,partial,X,Z,target):
+        if Z is None:
+            self._generate_inline(self._code['dK_dtheta_X'], X, target, Z, partial)
+        else:
+            self._generate_inline(self._code['dK_dtheta'], X, target, Z, partial)
+
+    def dKdiag_dtheta(self,partial,X,target):
+        self._generate_inline(self._code['dKdiag_dtheta'], X, target, Z=None, partial=partial).namelocals()[shared_params.name] = getattr(self, shared_params.name)
+               
+    def gradients_X(self,partial,X,Z,target):
+        if Z is None:
+            self._generate_inline(self._code['dK_dX_X'], X, target, Z, partial)
+        else:
+            self._generate_inline(self._code['dK_dX'], X, target, Z, partial)
+
+    def dKdiag_dX(self,partial,X,target):
+        self._generate_inline(self._code['dKdiag_dX'], X, target, Z, partial)
+
+    def compute_psi_stats(self):
+        #define some normal distributions
+        mus = [sp.var('mu_%i'%i,real=True) for i in range(self.input_dim)]
+        Ss = [sp.var('S_%i'%i,positive=True) for i in range(self.input_dim)]
+        normals = [(2*sp.pi*Si)**(-0.5)*sp.exp(-0.5*(xi-mui)**2/Si) for xi, mui, Si in zip(self._sp_x, mus, Ss)]
+
+        #do some integration!
+        #self._sp_psi0 = ??
+        self._sp_psi1 = self._sp_k
+        for i in range(self.input_dim):
+            print 'perfoming integrals %i of %i'%(i+1,2*self.input_dim)
+            sys.stdout.flush()
+            self._sp_psi1 *= normals[i]
+            self._sp_psi1 = sp.integrate(self._sp_psi1,(self._sp_x[i],-sp.oo,sp.oo))
+            clear_cache()
+        self._sp_psi1 = self._sp_psi1.simplify()
+
+        #and here's psi2 (eek!)
+        zprime = [sp.Symbol('zp%i'%i) for i in range(self.input_dim)]
+        self._sp_psi2 = self._sp_k.copy()*self._sp_k.copy().subs(zip(self._sp_z,zprime))
+        for i in range(self.input_dim):
+            print 'perfoming integrals %i of %i'%(self.input_dim+i+1,2*self.input_dim)
+            sys.stdout.flush()
+            self._sp_psi2 *= normals[i]
+            self._sp_psi2 = sp.integrate(self._sp_psi2,(self._sp_x[i],-sp.oo,sp.oo))
+            clear_cache()
+        self._sp_psi2 = self._sp_psi2.simplify()
+
+    def parameters_changed(self):
+        # Reset the caches
+        self._cache, self._cache2 = np.empty(shape=(2, 1))
+        self._cache3, self._cache4, self._cache5 = np.empty(shape=(3, 1)) 
+
+    def update_gradients_full(self, dL_dK, X):
+        # Need to extract parameters to local variables first
+        self._K_computations(X, None)
+        for shared_params in self._sp_theta:
+            parameter = getattr(self, shared_params.name)
+            code = self._code['dK_d' + shared_params.name]
+            setattr(parameter, 'gradient', self._generate_inline(code, X, target=None, Z=None, partial=dL_dK))
+            
+        for split_params in self._split_theta_names:
+            parameter = getattr(self, split_params.name)
+            code = self._code['dK_d' + split_params.name]
+            setattr(parameter, 'gradient', self._generate_inline(code, X, target=None, Z=None, partial=dL_dK))
+    
+
+    # def update_gradients_sparse(self, dL_dKmm, dL_dKnm, dL_dKdiag, X, Z):
+    #     #contributions from Kdiag
+    #     self.variance.gradient = np.sum(dL_dKdiag)
+        
+    #     #from Knm
+    #     self._K_computations(X, Z)
+    #     self.variance.gradient += np.sum(dL_dKnm * self._K_dvar)
+    #     if self.ARD:
+    #         self.lengthscale.gradient = self._dL_dlengthscales_via_K(dL_dKnm, X, Z)
+            
+    #     else:
+    #         self.lengthscale.gradient = (self.variance / self.lengthscale) * np.sum(self._K_dvar * self._K_dist2 * dL_dKnm)
+            
+    #     #from Kmm
+    #     self._K_computations(Z, None)
+    #     self.variance.gradient += np.sum(dL_dKmm * self._K_dvar)
+    #     if self.ARD:
+    #         self.lengthscale.gradient += self._dL_dlengthscales_via_K(dL_dKmm, Z, None)
+    #     else:
+    #         self.lengthscale.gradient += (self.variance / self.lengthscale) * np.sum(self._K_dvar * self._K_dist2 * dL_dKmm)
+            
+            
+    #---------------------------------------#
+    #            Precomputations            #
+    #---------------------------------------#
+
+    def _K_computations(self, X, Z):
+        if Z is None:
+            self._generate_inline(self._precompute, X)
+        else:
+            self._generate_inline(self._precompute, X, Z=Z)

GPy/kern/_src/poly_tmp.py

@@ -0,0 +1,134 @@
+# Copyright (c) 2013, GPy authors (see AUTHORS.txt).
+# Licensed under the BSD 3-clause license (see LICENSE.txt)
+
+from kernpart import Kernpart
+import numpy as np
+four_over_tau = 2./np.pi
+
+class POLY(Kernpart):
+    """
+
+    Polynomial kernel parameter initialisation.  Included for completeness, but generally not recommended, is the polynomial kernel:
+
+    .. math::
+        k(x, y) = \sigma^2\*(\sigma_w^2 x'y+\sigma_b^b)^d
+
+    The kernel parameters are :math:`\sigma^2` (variance), :math:`\sigma^2_w`
+    (weight_variance), :math:`\sigma^2_b` (bias_variance) and d
+    (degree). Only gradients of the first three are provided for
+    kernel optimisation, it is assumed that polynomial degree would
+    be set by hand.
+
+    The kernel is not recommended as it is badly behaved when the
+    :math:`\sigma^2_w\*x'\*y + \sigma^2_b` has a magnitude greater than one. For completeness
+    there is an automatic relevance determination version of this
+    kernel provided (NOTE YET IMPLEMENTED!).
+    :param input_dim: the number of input dimensions
+    :type input_dim: int 
+    :param variance: the variance :math:`\sigma^2`
+    :type variance: float
+    :param weight_variance: the vector of the variances of the prior over input weights in the neural network :math:`\sigma^2_w`
+    :type weight_variance: array or list of the appropriate size (or float if there is only one weight variance parameter)
+    :param bias_variance: the variance of the prior over bias parameters :math:`\sigma^2_b`
+    :param degree: the degree of the polynomial.
+    :type degree: int
+    :param ARD: Auto Relevance Determination. If equal to "False", the kernel is isotropic (ie. one weight variance parameter :math:`\sigma^2_w`), otherwise there is one weight variance parameter per dimension.
+    :type ARD: Boolean
+    :rtype: Kernpart object
+
+    """
+
+    def __init__(self, input_dim, variance=1., weight_variance=None, bias_variance=1., degree=2, ARD=False):
+        self.input_dim = input_dim
+        self.ARD = ARD
+        if not ARD:
+            self.num_params=3
+            if weight_variance is not None:
+                weight_variance = np.asarray(weight_variance)
+                assert weight_variance.size == 1, "Only one weight variance needed for non-ARD kernel"
+            else:
+                weight_variance = 1.*np.ones(1)
+        else:
+            self.num_params = self.input_dim + 2
+            if weight_variance is not None:
+                weight_variance = np.asarray(weight_variance)
+                assert weight_variance.size == self.input_dim, "bad number of weight variances"
+            else:
+                weight_variance = np.ones(self.input_dim)
+            raise NotImplementedError
+        self.degree=degree
+        self.name='poly_deg' + str(self.degree)
+        self._set_params(np.hstack((variance, weight_variance.flatten(), bias_variance)))
+
+    def _get_params(self):
+        return np.hstack((self.variance, self.weight_variance.flatten(), self.bias_variance))
+
+    def _set_params(self, x):
+        assert x.size == (self.num_params)
+        self.variance = x[0]
+        self.weight_variance = x[1:-1]
+        self.weight_std = np.sqrt(self.weight_variance)
+        self.bias_variance = x[-1]
+
+    def _get_param_names(self):
+        if self.num_params == 3:
+            return ['variance', 'weight_variance', 'bias_variance']
+        else:
+            return ['variance'] + ['weight_variance_%i' % i for i in range(self.lengthscale.size)] + ['bias_variance']
+
+    def K(self, X, X2, target):
+        """Return covariance between X and X2."""
+        self._K_computations(X, X2)
+        target += self.variance*self._K_dvar
+
+    def Kdiag(self, X, target):
+        """Compute the diagonal of the covariance matrix for X."""
+        self._K_diag_computations(X)
+        target+= self.variance*self._K_diag_dvar
+
+    def dK_dtheta(self, dL_dK, X, X2, target):
+        """Derivative of the covariance with respect to the parameters."""
+        self._K_computations(X, X2)
+        base = self.variance*self.degree*self._K_poly_arg**(self.degree-1)
+        base_cov_grad = base*dL_dK
+
+
+            
+        target[0] += np.sum(self._K_dvar*dL_dK)
+        target[1] += (self._K_inner_prod*base_cov_grad).sum()
+        target[2] += base_cov_grad.sum()
+
+
+    def dK_dX(self, dL_dK, X, X2, target):
+        """Derivative of the covariance matrix with respect to X"""
+        self._K_computations(X, X2)
+        arg = self._K_poly_arg
+        if X2 is None:
+            target += 2*self.weight_variance*self.degree*self.variance*(((X[None,:, :])) *(arg**(self.degree-1))[:, :, None]*dL_dK[:, :, None]).sum(1)
+        else:
+            target += self.weight_variance*self.degree*self.variance*(((X2[None,:, :])) *(arg**(self.degree-1))[:, :, None]*dL_dK[:, :, None]).sum(1)
+            
+    def dKdiag_dX(self, dL_dKdiag, X, target):
+        """Gradient of diagonal of covariance with respect to X"""
+        self._K_diag_computations(X)
+        arg = self._K_diag_poly_arg
+        target += 2.*self.weight_variance*self.degree*self.variance*X*dL_dKdiag[:, None]*(arg**(self.degree-1))[:, None]
+    
+    
+    def _K_computations(self, X, X2):
+        if self.ARD:
+            pass
+        else:
+            if X2 is None:
+                self._K_inner_prod = np.dot(X,X.T)
+            else:
+                self._K_inner_prod = np.dot(X,X2.T)
+            self._K_poly_arg = self._K_inner_prod*self.weight_variance + self.bias_variance
+        self._K_dvar = self._K_poly_arg**self.degree
+
+    def _K_diag_computations(self, X):
+        if self.ARD:
+            pass
+        else:
+            self._K_diag_poly_arg = (X*X).sum(1)*self.weight_variance + self.bias_variance
+        self._K_diag_dvar = self._K_diag_poly_arg**self.degree

GPy/kern/_src/symbolic2.py

@@ -0,0 +1,70 @@
+# Check Matthew Rocklin's blog post.
+import sympy as sym
+import numpy as np
+from kern import Kern
+from ...core.symbolic import Symbolic_core
+
+
+class Symbolic(Kern, Symbolic_core):
+    """
+    """
+    def __init__(self, input_dim, k=None, output_dim=1, name='symbolic', parameters=None, active_dims=None, operators=None, func_modules=[]):
+
+        if k is None:
+            raise ValueError, "You must provide an argument for the covariance function."
+
+        Kern.__init__(self, input_dim, active_dims, name=name)
+        kdiag = k
+        self.cacheable = ['X', 'Z']
+        Symbolic_core.__init__(self, {'k':k,'kdiag':kdiag}, cacheable=self.cacheable, derivatives = ['X', 'theta'], parameters=parameters, func_modules=func_modules)        
+        self.output_dim = output_dim
+
+    def __add__(self,other):
+        return spkern(self._sym_k+other._sym_k)
+
+    def _set_expressions(self, expressions):
+        """This method is overwritten because we need to modify kdiag by substituting z for x. We do this by calling the parent expression method to extract variables from expressions, then subsitute the z variables that are present with x."""
+        Symbolic_core._set_expressions(self, expressions)
+        Symbolic_core._set_variables(self, self.cacheable)
+        # Substitute z with x to obtain kdiag.
+        for x, z in zip(self.variables['X'], self.variables['Z']):
+            expressions['kdiag'] = expressions['kdiag'].subs(z, x)
+        Symbolic_core._set_expressions(self, expressions)
+            
+        
+    def K(self,X,X2=None):
+        if X2 is None:
+            return self.eval_function('k', X=X, Z=X)
+        else:
+            return self.eval_function('k', X=X, Z=X2)
+
+
+    def Kdiag(self,X):
+        d = self.eval_function('kdiag', X=X)
+        if not d.shape[0] == X.shape[0]:
+            d = np.tile(d, (X.shape[0], 1))
+        return d
+
+
+    def gradients_X(self, dL_dK, X, X2=None):
+        #if self._X is None or X.base is not self._X.base or X2 is not None:
+        g = self.eval_gradients_X('k', dL_dK, X=X, Z=X2)
+        if X2 is None:
+            g *= 2
+        return g
+
+    def gradients_X_diag(self, dL_dK, X):
+        return self.eval_gradients_X('kdiag', dL_dK, X=X)
+
+    def update_gradients_full(self, dL_dK, X, X2=None):
+        # Need to extract parameters to local variables first
+        if X2 is None:
+            # need to double this inside ...
+            self.eval_update_gradients('k', dL_dK, X=X)
+        else:
+            self.eval_update_gradients('k', dL_dK, X=X, Z=X2)
+
+
+    def update_gradients_diag(self, dL_dKdiag, X):
+        self.eval_update_gradients('kdiag', dL_dKdiag, X)
+

GPy/kern/matlab_construct.py

@@ -0,0 +1,17 @@
+# Copyright (c) 2013, GPy authors (see AUTHORS.txt).
+# Licensed under the BSD 3-clause license (see LICENSE.txt)
+
+# Construct covariance functions from matlab saves.
+import numpy as np
+from kern import kern
+import parts
+import scipy.io
+
+def read_matlab(mat_data)
+    mat_data = scipy.io.loadmat(os.path.join(data_path, data_set, 'frey_rawface.mat'))
+    if mat_data['type']=='cmpnd':
+        # cmpnd kernel
+        types = []
+        for i in range(mat_data['comp'][0][0]):
+            types.append(mat_data['comp'][0][0][i]
+        

GPy/kern/parts/eq.py

@@ -0,0 +1,318 @@
+# Copyright (c) 2012, GPy authors (see AUTHORS.txt).
+# Licensed under the BSD 3-clause license (see LICENSE.txt)
+
+
+from kernpart import Kernpart
+import numpy as np
+from scipy import weave
+from ...util.linalg import tdot
+from ...util.misc import fast_array_equal
+
+class EQ(Kernpart_stationary):
+    """
+    Exponentiated Quadratic covariance function als known as radial basis function, squared-exponential or Gaussian kernel.
+
+    .. math::
+
+       k(r) = \sigma^2 \exp \\bigg(- \\frac{1}{2} r^2 \\bigg) \ \ \ \ \  \\text{ where  } r^2 = \sum_{i=1}^d \\frac{ (x_i-x^\prime_i)^2}{\ell_i^2}
+
+    where \ell_i is the lengthscale, \sigma^2 the variance and d the dimensionality of the input.
+
+    :param input_dim: the number of input dimensions
+    :type input_dim: int
+    :param variance: the variance of the kernel
+    :type variance: float
+    :param lengthscale: the vector of lengthscale of the kernel
+    :type lengthscale: array or list of the appropriate size (or float if there is only one lengthscale parameter)
+    :param ARD: Auto Relevance Determination. If equal to "False", the kernel is isotropic (ie. one single lengthscale parameter \ell), otherwise there is one lengthscale parameter per dimension.
+    :type ARD: Boolean
+    :rtype: kernel object
+
+    .. Note: this object implements both the ARD and 'spherical' version of the function
+    """
+
+    def __init__(self, input_dim, variance=1., lengthscale=None, ARD=False):
+        Kernpart_stationary.__init__(self, input_dim, lengthscale, ARD)
+        self.name = 'rbf'
+        self._set_params(np.hstack((variance, self.lengthscale.flatten())))
+
+        # a set of optional args to pass to weave
+        self.weave_options = {'headers'           : ['<omp.h>'],
+                         'extra_compile_args': ['-fopenmp -O3'], # -march=native'],
+                         'extra_link_args'   : ['-lgomp']}
+
+
+
+    def _get_params(self):
+        return np.hstack((self.variance, self.lengthscale))
+
+    def _set_params(self, x):
+        assert x.size == (self.num_params)
+        self.variance = x[0]
+        Kernpart_stationary._set_params(self, x[1:])
+
+    def _get_param_names(self):
+        if self.num_params == 2:
+            return ['variance', 'lengthscale']
+        else:
+            return ['variance'] + ['lengthscale_%i' % i for i in range(self.lengthscale.size)]
+
+    def K(self, X, X2, target):
+        self._K_computations(X, X2)
+        target += self.variance * self._K_dvar
+
+    def Kdiag(self, X, target):
+        np.add(target, self.variance, target)
+
+    def dK_dtheta(self, dL_dK, X, X2, target):
+        self._K_computations(X, X2)
+        target[0] += np.sum(self._K_dvar * dL_dK)
+        if self.ARD:
+            dvardLdK = self._K_dvar * dL_dK
+            var_len3 = self.variance / np.power(self.lengthscale, 3)
+            if X2 is None:
+                # save computation for the symmetrical case
+                dvardLdK = dvardLdK + dvardLdK.T
+                code = """
+                int q,i,j;
+                double tmp;
+                for(q=0; q<input_dim; q++){
+                  tmp = 0;
+                  for(i=0; i<num_data; i++){
+                    for(j=0; j<i; j++){
+                      tmp += (X(i,q)-X(j,q))*(X(i,q)-X(j,q))*dvardLdK(i,j);
+                    }
+                  }
+                  target(q+1) += var_len3(q)*tmp;
+                }
+                """
+                num_data, num_inducing, input_dim = X.shape[0], X.shape[0], self.input_dim
+                weave.inline(code, arg_names=['num_data',
+                                              'num_inducing',
+                                              'input_dim',
+                                              'X', 'X2',
+                                              'target',
+                                              'dvardLdK',
+                                              'var_len3'],
+                             type_converters=weave.converters.blitz,
+                             **self.weave_options)
+            else:
+                code = """
+                int q,i,j;
+                double tmp;
+                for(q=0; q<input_dim; q++){
+                  tmp = 0;
+                  for(i=0; i<num_data; i++){
+                    for(j=0; j<num_inducing; j++){
+                      tmp += (X(i,q)-X2(j,q))*(X(i,q)-X2(j,q))*dvardLdK(i,j);
+                    }
+                  }
+                  target(q+1) += var_len3(q)*tmp;
+                }
+                """
+                num_data, num_inducing, input_dim = X.shape[0], X2.shape[0], self.input_dim
+                # [np.add(target[1+q:2+q],var_len3[q]*np.sum(dvardLdK*np.square(X[:,q][:,None]-X2[:,q][None,:])),target[1+q:2+q]) for q in range(self.input_dim)]
+                weave.inline(code, arg_names=['num_data',
+                                              'num_inducing',
+                                              'input_dim',
+                                              'X', 'X2',
+                                              'target',
+                                              'dvardLdK',
+                                              'var_len3'],
+                             type_converters=weave.converters.blitz,
+                             **self.weave_options)
+        else:
+            target[1] += (self.variance / self.lengthscale) * np.sum(self._K_dvar * self._K_dist2 * dL_dK)
+
+
+    def dK_dX(self, dL_dK, X, X2, target):
+        self._K_computations(X, X2)
+        _K_dist = X[:, None, :] - X2[None, :, :] # don't cache this in _K_computations because it is high memory. If this function is being called, chances are we're not in the high memory arena.
+        dK_dX = (-self.variance / self.lengthscale2) * np.transpose(self._K_dvar[:, :, np.newaxis] * _K_dist, (1, 0, 2))
+        target += np.sum(dK_dX * dL_dK.T[:, :, None], 0)
+
+    def dKdiag_dX(self, dL_dKdiag, X, target):
+        pass
+
+
+    #---------------------------------------#
+    #             PSI statistics            #
+    #---------------------------------------#
+
+    def psi0(self, Z, mu, S, target):
+        target += self.variance
+
+    def dpsi0_dtheta(self, dL_dpsi0, Z, mu, S, target):
+        target[0] += np.sum(dL_dpsi0)
+
+    def dpsi0_dmuS(self, dL_dpsi0, Z, mu, S, target_mu, target_S):
+        pass
+
+    def psi1(self, Z, mu, S, target):
+        self._psi_computations(Z, mu, S)
+        target += self._psi1
+
+    def dpsi1_dtheta(self, dL_dpsi1, Z, mu, S, target):
+        self._psi_computations(Z, mu, S)
+        target[0] += np.sum(dL_dpsi1 * self._psi1 / self.variance)
+        d_length = self._psi1[:,:,None] * ((self._psi1_dist_sq - 1.)/(self.lengthscale*self._psi1_denom) +1./self.lengthscale)
+        dpsi1_dlength = d_length * dL_dpsi1[:, :, None]
+        if not self.ARD:
+            target[1] += dpsi1_dlength.sum()
+        else:
+            target[1:] += dpsi1_dlength.sum(0).sum(0)
+
+    def dpsi1_dZ(self, dL_dpsi1, Z, mu, S, target):
+        self._psi_computations(Z, mu, S)
+        denominator = (self.lengthscale2 * (self._psi1_denom))
+        dpsi1_dZ = -self._psi1[:, :, None] * ((self._psi1_dist / denominator))
+        target += np.sum(dL_dpsi1[:, :, None] * dpsi1_dZ, 0)
+
+    def dpsi1_dmuS(self, dL_dpsi1, Z, mu, S, target_mu, target_S):
+        self._psi_computations(Z, mu, S)
+        tmp = self._psi1[:, :, None] / self.lengthscale2 / self._psi1_denom
+        target_mu += np.sum(dL_dpsi1[:, :, None] * tmp * self._psi1_dist, 1)
+        target_S += np.sum(dL_dpsi1[:, :, None] * 0.5 * tmp * (self._psi1_dist_sq - 1), 1)
+
+    def psi2(self, Z, mu, S, target):
+        self._psi_computations(Z, mu, S)
+        target += self._psi2
+
+    def dpsi2_dtheta(self, dL_dpsi2, Z, mu, S, target):
+        """Shape N,num_inducing,num_inducing,Ntheta"""
+        self._psi_computations(Z, mu, S)
+        d_var = 2.*self._psi2 / self.variance
+        d_length = 2.*self._psi2[:, :, :, None] * (self._psi2_Zdist_sq * self._psi2_denom + self._psi2_mudist_sq + S[:, None, None, :] / self.lengthscale2) / (self.lengthscale * self._psi2_denom)
+
+        target[0] += np.sum(dL_dpsi2 * d_var)
+        dpsi2_dlength = d_length * dL_dpsi2[:, :, :, None]
+        if not self.ARD:
+            target[1] += dpsi2_dlength.sum()
+        else:
+            target[1:] += dpsi2_dlength.sum(0).sum(0).sum(0)
+
+    def dpsi2_dZ(self, dL_dpsi2, Z, mu, S, target):
+        self._psi_computations(Z, mu, S)
+        term1 = self._psi2_Zdist / self.lengthscale2 # num_inducing, num_inducing, input_dim
+        term2 = self._psi2_mudist / self._psi2_denom / self.lengthscale2 # N, num_inducing, num_inducing, input_dim
+        dZ = self._psi2[:, :, :, None] * (term1[None] + term2)
+        target += (dL_dpsi2[:, :, :, None] * dZ).sum(0).sum(0)
+
+    def dpsi2_dmuS(self, dL_dpsi2, Z, mu, S, target_mu, target_S):
+        """Think N,num_inducing,num_inducing,input_dim """
+        self._psi_computations(Z, mu, S)
+        tmp = self._psi2[:, :, :, None] / self.lengthscale2 / self._psi2_denom
+        target_mu += -2.*(dL_dpsi2[:, :, :, None] * tmp * self._psi2_mudist).sum(1).sum(1)
+        target_S += (dL_dpsi2[:, :, :, None] * tmp * (2.*self._psi2_mudist_sq - 1)).sum(1).sum(1)
+
+    #---------------------------------------#
+    #            Precomputations            #
+    #---------------------------------------#
+
+    def _K_computations(self, X, X2):
+        params = self._get_params()
+        if not (fast_array_equal(X, self._X) and fast_array_equal(X2, self._X2) and fast_array_equal(self._params , params)):
+            self._X = X.copy()
+            self._params = params.copy()
+            if X2 is None:
+                self._X2 = None
+                X = X / self.lengthscale
+                Xsquare = np.sum(np.square(X), 1)
+                self._K_dist2 = -2.*tdot(X) + (Xsquare[:, None] + Xsquare[None, :])
+            else:
+                self._X2 = X2.copy()
+                X = X / self.lengthscale
+                X2 = X2 / self.lengthscale
+                self._K_dist2 = -2.*np.dot(X, X2.T) + (np.sum(np.square(X), 1)[:, None] + np.sum(np.square(X2), 1)[None, :])
+            self._K_dvar = np.exp(-0.5 * self._K_dist2)
+
+    def _psi_computations(self, Z, mu, S):
+        # here are the "statistics" for psi1 and psi2
+        if not fast_array_equal(Z, self._Z):
+            # Z has changed, compute Z specific stuff
+            self._psi2_Zhat = 0.5 * (Z[:, None, :] + Z[None, :, :]) # M,M,Q
+            self._psi2_Zdist = 0.5 * (Z[:, None, :] - Z[None, :, :]) # M,M,Q
+            self._psi2_Zdist_sq = np.square(self._psi2_Zdist / self.lengthscale) # M,M,Q
+
+        if not fast_array_equal(Z, self._Z) or not fast_array_equal(mu, self._mu) or not fast_array_equal(S, self._S):
+            # something's changed. recompute EVERYTHING
+
+            # psi1
+            self._psi1_denom = S[:, None, :] / self.lengthscale2 + 1.
+            self._psi1_dist = Z[None, :, :] - mu[:, None, :]
+            self._psi1_dist_sq = np.square(self._psi1_dist) / self.lengthscale2 / self._psi1_denom
+            self._psi1_exponent = -0.5 * np.sum(self._psi1_dist_sq + np.log(self._psi1_denom), -1)
+            self._psi1 = self.variance * np.exp(self._psi1_exponent)
+
+            # psi2
+            self._psi2_denom = 2.*S[:, None, None, :] / self.lengthscale2 + 1. # N,M,M,Q
+            self._psi2_mudist, self._psi2_mudist_sq, self._psi2_exponent, _ = self.weave_psi2(mu, self._psi2_Zhat)
+            # self._psi2_mudist = mu[:,None,None,:]-self._psi2_Zhat #N,M,M,Q
+            # self._psi2_mudist_sq = np.square(self._psi2_mudist)/(self.lengthscale2*self._psi2_denom)
+            # self._psi2_exponent = np.sum(-self._psi2_Zdist_sq -self._psi2_mudist_sq -0.5*np.log(self._psi2_denom),-1) #N,M,M,Q
+            self._psi2 = np.square(self.variance) * np.exp(self._psi2_exponent) # N,M,M,Q
+
+            # store matrices for caching
+            self._Z, self._mu, self._S = Z, mu, S
+
+    def weave_psi2(self, mu, Zhat):
+        N, input_dim = mu.shape
+        num_inducing = Zhat.shape[0]
+
+        mudist = np.empty((N, num_inducing, num_inducing, input_dim))
+        mudist_sq = np.empty((N, num_inducing, num_inducing, input_dim))
+        psi2_exponent = np.zeros((N, num_inducing, num_inducing))
+        psi2 = np.empty((N, num_inducing, num_inducing))
+
+        psi2_Zdist_sq = self._psi2_Zdist_sq
+        _psi2_denom = self._psi2_denom.squeeze().reshape(N, self.input_dim)
+        half_log_psi2_denom = 0.5 * np.log(self._psi2_denom).squeeze().reshape(N, self.input_dim)
+        variance_sq = float(np.square(self.variance))
+        if self.ARD:
+            lengthscale2 = self.lengthscale2
+        else:
+            lengthscale2 = np.ones(input_dim) * self.lengthscale2
+        code = """
+        double tmp;
+
+        #pragma omp parallel for private(tmp)
+        for (int n=0; n<N; n++){
+            for (int m=0; m<num_inducing; m++){
+               for (int mm=0; mm<(m+1); mm++){
+                   for (int q=0; q<input_dim; q++){
+                       //compute mudist
+                       tmp = mu(n,q) - Zhat(m,mm,q);
+                       mudist(n,m,mm,q) = tmp;
+                       mudist(n,mm,m,q) = tmp;
+
+                       //now mudist_sq
+                       tmp = tmp*tmp/lengthscale2(q)/_psi2_denom(n,q);
+                       mudist_sq(n,m,mm,q) = tmp;
+                       mudist_sq(n,mm,m,q) = tmp;
+
+                       //now psi2_exponent
+                       tmp = -psi2_Zdist_sq(m,mm,q) - tmp - half_log_psi2_denom(n,q);
+                       psi2_exponent(n,mm,m) += tmp;
+                       if (m !=mm){
+                           psi2_exponent(n,m,mm) += tmp;
+                       }
+                   //psi2 would be computed like this, but np is faster
+                   //tmp = variance_sq*exp(psi2_exponent(n,m,mm));
+                   //psi2(n,m,mm) = tmp;
+                   //psi2(n,mm,m) = tmp;
+                   }
+                }
+            }
+        }
+
+        """
+
+        support_code = """
+        #include <omp.h>
+        #include <math.h>
+        """
+        weave.inline(code, support_code=support_code, libraries=['gomp'],
+                     arg_names=['N', 'num_inducing', 'input_dim', 'mu', 'Zhat', 'mudist_sq', 'mudist', 'lengthscale2', '_psi2_denom', 'psi2_Zdist_sq', 'psi2_exponent', 'half_log_psi2_denom', 'psi2', 'variance_sq'],
+                     type_converters=weave.converters.blitz, **self.weave_options)
+
+        return mudist, mudist_sq, psi2_exponent, psi2

GPy/kern/parts/ode1.py

@@ -0,0 +1,428 @@
+# Copyright (c) 2012, James Hensman and Ricardo Andrade
+# Licensed under the BSD 3-clause license (see LICENSE.txt)
+
+from kernpart import Kernpart
+import numpy as np
+from GPy.util.linalg import mdot, pdinv
+from GPy.util import ln_diff_erfs
+import pdb
+from scipy import weave
+
+class Ode1(Kernpart):
+    """
+    Covariance function for first order differential equation driven by an exponetiated quadratic covariance.
+
+    This kernel has the form
+    .. math::
+
+    :param num_outputs: number of outputs driven by latent function.
+    :type num_outputs: int
+
+    .. Note: see first order differential equation examples in GPy.examples.regression for some usage.
+    """
+    def __init__(self,num_outputs, W=None, rank=1, delay=None, kappa=None):
+        self.rank = rank
+        self.input_dim = 1
+        self.name = 'ode1'
+        self.num_outputs = num_outputs
+        self.num_params = self.num_outputs*(1. + self.rank) + 1
+        if kappa is not None:
+            self.num_params+=num_outputs
+        if delay is not None:
+            self.num_params+=num_outputs
+        self.rank = rank
+        if W is None:
+            self.W = 0.5*np.random.randn(self.num_outputs,self.rank)/np.sqrt(self.rank)
+        else:
+            assert W.shape==(self.num_outputs,self.rank)
+            self.W = W
+            
+        if kappa is not None:
+            assert kappa.shape==(self.num_outputs,)
+        self.kappa = kappa
+
+        if delay is not None:
+            assert delay.shape==(self.num_outputs,)
+        self.delay = delay
+        self._set_params(self._get_params())
+
+    def _get_params(self):
+        param_list = [self.W.flatten()]
+        if self.kappa is not None:
+            param_list.append(self.kappa)
+        param_list.append(self.decay)
+        if self.delay is not None:
+            param_list.append(self.delay)
+        param_list.append(self.length_scale)
+        return np.hstack(param_list)
+
+    def _set_params(self,x):
+        assert x.size == self.num_params
+        end = self.num_outputs*self.rank
+        self.W = x[:end].reshape(self.num_outputs,self.rank)
+        start = end
+        self.B = np.dot(self.W,self.W.T)
+        if self.kappa is not None:
+            end+=self.num_outputs
+            self.kappa = x[start:end]
+            self.B += np.diag(self.kappa)
+            start=end
+        end+=num_outputs
+        self.decay = x[start:end]
+        start=end
+        if self.delay is not None:
+            end+=num_outputs
+            self.delay = x[start:end]
+            start=end
+        end+=1
+        self.length_scale = x[start]
+        self.sigma = np.sqrt(2)*self.length_scale
+
+
+    def _get_param_names(self):
+        param_names = sum([['W%i_%i'%(i,j) for j in range(self.rank)] for i in range(self.num_outputs)],[])
+        if self.kappa is not None:
+            param_names += ['kappa_%i'%i for i in range(self.num_outputs)]
+        param_names += ['decay_%i'%i for i in range(self.num_outputs)]
+        if self.delay is not None:
+            param_names += ['delay_%i'%i for i in range(self.num_outputs)]
+        param_names+= ['length_scale'] 
+        return param_names
+
+    def K(self,X,X2,target):
+        
+        if X.shape[1] > 2:
+            raise ValueError('Input matrix for ode1 covariance should have at most two columns, one containing times, the other output indices')
+
+        self._K_computations()
+        target += self._scales*self._dK_dvar
+
+        if self.gaussian_initial:
+            # Add covariance associated with initial condition.
+            t1_mat = self._t[self._rorder, None]
+            t2_mat = self._t2[None, self._rorder2]
+            target+=self.initial_variance * np.exp(- self.decay * (t1_mat + t2_mat))
+
+
+
+    def Kdiag(self,index,target):
+        #target += np.diag(self.B)[np.asarray(index,dtype=np.int).flatten()]
+        pass
+    
+    def dK_dtheta(self,dL_dK,index,index2,target):
+        pass
+
+    def dKdiag_dtheta(self,dL_dKdiag,index,target):
+        pass
+
+    def dK_dX(self,dL_dK,X,X2,target):
+        pass
+
+    def _extract_t_indices(X, X2=None):
+        """Extract times and output indices from the input matrix X. Times are ordered according to their index for convenience of computation, this ordering is stored in self._order and self.order2. These orderings are then mapped back to the original ordering (in X) using self._rorder and self._rorder2. """
+
+        # TODO: some fast checking here to see if this needs recomputing?
+        self._t = X[:, 0]
+        if X.shape[1]==1:
+            # No index passed, assume single output of ode model.
+            self._index = np.ones_like(X[:, 1],dtype=np.int)
+        self._index = np.asarray(X[:, 1],dtype=np.int)
+        # Sort indices so that outputs are in blocks for computational
+        # convenience.
+        self._order = self._index.argsort()
+        self._index = self._index[self._order]
+        self._t = self._t[self._order]
+        self._rorder = self._order.argsort() # rorder is for reversing the order
+        
+        if X2 is None:
+            self._t2 = None
+            self._index2 = None
+            self._rorder2 = self._rorder
+        else:
+            if X2.shape[1] > 2:
+                raise ValueError('Input matrix for ode1 covariance should have at most two columns, one containing times, the other output indices')
+            self._t2 = X2[:, 0]
+            if X.shape[1]==1:
+                # No index passed, assume single output of ode model.
+                self._index2 = np.ones_like(X2[:, 1],dtype=np.int)
+            self._index2 = np.asarray(X2[:, 1],dtype=np.int)
+            self._order2 = self._index2.argsort()
+            slef._index2 = self._index2[self._order2]
+            self._t2 = self._t2[self._order2]
+            self._rorder2 = self._order2.argsort() # rorder2 is for reversing order
+
+    def _K_computations(X, X2):
+        """Perform main body of computations for the ode1 covariance function."""
+        # First extract times and indices.
+        self._extract_t_indices(X, X2)
+
+        self._K_compute_eq()
+        self._K_compute_eq_x_ode()
+        if X2 is None:
+            self._K_ode_eq = self._K_ode_eq.T
+        else:
+            self._K_compute_eq_x_ode(transpose=True)
+        self._K_compute_ode()
+        
+        # Reorder values of blocks for placing back into _K_dvar.
+        self._K_dvar[self._rorder, :] = np.vstack((
+            np.hstack((self._K_eq, self._Keq_ode))
+            np.hstack((self._K_ode_eq, self.K_ode))))[:, self._rorder2]
+
+
+    def _K_compute_eq():
+        """Compute covariance for latent covariance."""
+        t_eq = self._t[self._index==0]
+        if t_eq.shape[0]==0:
+            self._K_eq = np.zeros((0, 0))
+            return
+        
+        if self._t2 is None:
+            self._dist2 = np.square(t_eq[:, None] - t_eq[None, :])
+        else:
+            t2_eq = self._t2[self._index2==0]
+            if t2_eq.shape[0]==0:
+                self._K_eq_eq = np.zeros((0, 0))
+                return
+            self._dist2 = np.square(t_eq[:, None] - t2_eq[None, :])
+        
+        self._K_eq = np.exp(-self._dist2/(2*self.length_scale*self.length_scale))
+        if self.is_normalise:
+            self._K_eq/=(np.sqrt(2*np.pi)*self.length_scale)
+
+    def _K_compute_ode_eq(transpose=False):
+        """Compute the cross covariances between latent exponentiated quadratic and observed ordinary differential equations.
+
+        :param transpose: if set to false the exponentiated quadratic is on the rows of the matrix and is computed according to self._t, if set to true it is on the columns and is computed according to self._t2 (default=False).
+        :type transpose: bool"""
+
+        if transpose:
+            t_ode = self._t2[self._index>0]
+            index_ode = self._index2[self._index>0]-1
+            if t_ode.shape[0]==0:
+                self._K_ode = np.zeros((0, 0))
+                return
+        
+            if self._t2 is not None:            
+                t2_ode = self._t2[self._index2>0]
+                index2_ode = self._index2[self._index2>0]-1
+                if t2_eq.shape[0]==0:
+                    self._K_ode = np.zeros((0, 0))
+                    return
+        else:
+
+        # Matrix giving scales of each output
+        self._scale = np.zeros((t_ode.shape[0], t_eq.shape[0]))
+        code="""
+        for(int i=0;i<N; i++){
+              for(int j=0; j<N2; j++){
+                  scale_mat[i+j*N] = self.W[index_sim[i]+index_eq[j]*num_outputs];
+                }
+              }
+            """
+            scale_mat, B = self._scale, self._B
+            N, N2, num_outputs = index_ode.size, index_eq.size, self.num_outputs
+            weave.inline(code,['index_ode', 'index_eq',
+                               'scale_mat', 'B',
+                               'N', 'N2', 'num_outputs'])
+        else:
+            self._scale = np.zeros((t_ode.shape[0], t2_ode.shape[0]))
+            code = """
+            for(int i=0; i<N; i++){
+              for(int j=0; j<N2; j++){
+                scale_mat[i+j*N] = B[index_ode[i]+num_outputs*index2_ode[j]]
+              }
+            }
+            """
+            scale_mat, B = self._scale, self._B
+            N, N2, num_outputs = index_ode.size, index2.size, self.num_outputs
+            weave.inline(code, ['index_ode', 'index2_ode',
+                                'scale_mat', 'B',
+                                'N', 'N2', 'num_outputs'])
+        if transpose:
+            t_ode = t2 - self.delay
+            t_eq_mat = t1[None, :]
+        else:
+            t_ode = t1 - self.delay
+            t_eq_mat = t2[None, :]
+        t_ode_mat = t_ode[:, None]
+        diff_t = (t_ode_mat - t_eq_mat)
+        sigma = sqrt(2/self.inverseWidth)
+
+        invSigmaDiffT = 1/sigma*diff_t
+        halfSigmaD_i = 0.5*sigma*self.decay
+
+        if self.isStationary == false
+          [ln_part, signs] = ln_diff_erfs(halfSigmaD_i + t2Mat/sigma, halfSigmaD_i - invSigmaDiffT)
+        else
+          [ln_part, signs] = ln_diff_erfs(inf, halfSigmaD_i - invSigmaDiffT)
+        end
+        sK = signs .* exp(halfSigmaD_i*halfSigmaD_i - self.decay*diff_t + ln_part)
+
+        sK *= 0.5
+
+        if not self.is_normalised:
+            sK *= sqrt(pi)*self.sigma
+
+
+        if transpose:
+            self._K_eq_ode = 
+        else:
+            self._K_ode_eq = sK
+        return K
+        
+    def _K_compute_ode():
+        # Compute covariances between outputs of the ODE models.
+
+        t_ode = self._t[self._index>0]
+        index_ode = self._index[self._index>0]-1
+        if t_ode.shape[0]==0:
+            self._K_ode = np.zeros((0, 0))
+            return
+        
+        if self._t2 is not None:            
+            t2_ode = self._t2[self._index2>0]
+            index2_ode = self._index2[self._index2>0]-1
+            if t2_eq.shape[0]==0:
+                self._K_ode = np.zeros((0, 0))
+                return
+        
+        if self._index2 is None:
+            # Matrix giving scales of each output
+            self._scale = np.zeros((t_ode.shape[0], t_ode.shape[0]))
+            code="""
+            for(int i=0;i<N; i++){
+              scale_mat[i+i*N] = B[index_ode[i]+num_outputs*(index_ode[i])];
+              for(int j=0; j<i; j++){
+                  scale_mat[j+i*N] = B[index_ode[i]+num_outputs*index_ode[j]];
+                  scale_mat[i+j*N] = scale_mat[j+i*N];
+                }
+              }
+            """
+            scale_mat, B = self._scale, self._B
+            N, num_outputs = index_ode.size, self.num_outputs
+            weave.inline(code,['index_ode',
+                               'scale_mat', 'B',
+                               'N', 'num_outputs'])
+        else:
+            self._scale = np.zeros((t_ode.shape[0], t2_ode.shape[0]))
+            code = """
+            for(int i=0; i<N; i++){
+              for(int j=0; j<N2; j++){
+                scale_mat[i+j*N] = B[index_ode[i]+num_outputs*index2_ode[j]]
+              }
+            }
+            """
+            scale_mat, B = self._scale, self._B
+            N, N2, num_outputs = index_ode.size, index2.size, self.num_outputs
+            weave.inline(code, ['index_ode', 'index2_ode',
+                                'scale_mat', 'B',
+                                'N', 'N2', 'num_outputs'])
+        
+        # When index is identical
+        if self.is_stationary:
+            h = self._compute_H_stat(t_ode, index_ode, t2_ode, index2_ode)
+        else:
+            h = self._compute_H(t_ode, index_ode, t2_ode, index2_ode)
+
+        if t2 is None:
+            self._K_ode = 0.5 * (h + h.T)
+        else:
+            if self.is_stationary:
+                h2 = self._compute_H_stat(t2, index2, t, index)
+            else:
+                h2 = self._compute_H(t2, index2, t, index)                
+            self._K_ode += 0.5 * (h + h2.T)
+
+        if not self.is_normalized:
+            self._K_ode *= np.sqrt(np.pi)*sigma
+    
+    def _compute_H(t, index, t2, index2, update_derivatives=False):
+        """Helper function for computing part of the ode1 covariance function.
+
+        :param t: first time input.
+        :type t: array
+        :param index: Indices of first output.
+        :type index: array of int
+        :param t2: second time input.
+        :type t2: array
+        :param index2: Indices of second output.
+        :type index2: array of int
+        :param update_derivatives: whether to update derivatives (default is False)
+        :return h : result of this subcomponent of the kernel for the given values.
+        :rtype: ndarray
+"""
+
+        if t.shape[1] > 1 or t2.shape[1] > 1:
+            raise error('Input can only have one column')
+
+        # Vector of decays and delays associated with each output.
+        Decay = np.zeros(t.shape[0])
+        Delay = np.zeros(t.shape[0])
+        Decay2 = np.zeros(t2.shape[0])
+        Delay2 = np.zeros(t2.shape[0])
+        code="""
+        for(int i=0;i<N; i++){
+          Delay[i] = decays[index[i]];
+          Decay[i] = delays[index[i]];
+          }
+        for(int i=0; i<N2; i++){
+          Delay2[i] = decays[index2[i]];
+          Decay2[i] = delays[index2[i]];
+          }
+        """
+        delays, decays = self.delays, self.decays
+        N, N2 = index.size, index2.size
+        weave.inline(code,['index_ode',
+                           'Delay', 'Decay',
+                           'Delay2', 'Decay2',
+                           'delays', 'decays',
+                           'N', 'N2'])
+
+        t_mat = t[:, None]-Delay[:, None]
+        t2_mat = t2[None, :]-Delay2[None, :]
+        diff_t = (t_mat - t2_mat)
+        inv_sigma_diff_t = 1./self.sigma*diff_t
+        half_sigma_decay_i = 0.5*self.sigma*Decay[:, None]
+
+        ln_part_1, sign1 = ln_diff_erfs(half_sigma_decay_i + t2_mat/self.sigma, 
+                                        half_sigma_decay_i - inv_sigma_diff_t)
+        ln_part_2, sign2 = ln_diff_erfs(half_sigma_decay_i,
+                                        half_sigma_decay_i - t_mat/self.sigma)
+
+        h = sign1*np.exp(half_sigma_decay_i
+                         *half_sigma_decay_i
+                         -Decay[:, None]*diff_t+ln_part_1
+                         -np.log(Decay[:, None] + Decay2[None, :]))
+        h -= sign2*np.exp(half_sigma_decay_i*half_sigma_decay_i
+                          -Decay[:, None]*t_mat-Decay2[None, :]*t2_mat+ln_part_2
+                          -np.log(Decay[:, None] + Decay2[None, :]))
+
+
+        # if update_derivatives:
+        #     sigma2 = self.sigma*self.sigma
+        #     # Update ith decay gradient
+        #     dh_ddecay += (0.5*self.decay[i]*sigma2*(self.decay[i] + decay[j])-1)*h
+        #     + (-diff_t*sign1*np.exp(half_sigma_decay_i*half_sigma_decay_i-self.decay[i]*diff_t+ln_part_1) 
+        #        +t_mat*sign2*np.exp(half_sigma_decay_i*half_sigma_decay_i-self.decay[i]*t_mat - decay[j]*t2_mat+ln_part_2)) ...
+        #     +self.sigma/sqrt(pi)*(-np.exp(-diff_t*diff_t/sigma2)
+        #                           +np.exp(-t2_mat*t2_mat/sigma2-self.decay[i]*t_mat) 
+        #                           +np.exp(-t_mat*t_mat/sigma2-decay[j]*t2_mat) ...
+        #                           -np.exp(-(self.decay[i]*t_mat + decay[j]*t2_mat)))
+        #     self._dh_ddecay[i] += real(dh_ddecay/(self.decay[i]+decay[j]))
+
+        #     # Update jth decay gradient
+        #     dh_ddecay = t2_mat*sign2*np.exp(half_sigma_decay_i*half_sigma_decay_i-(self.decay[i]*t_mat + decay[j]*t2_mat)+ln_part_2)-h
+        #     self._dh_ddecay[j] += real(dh_ddecay/(self.decay[i] + decay[j]))
+            
+        #     # Update sigma gradient
+        #     self._dh_dsigma += 0.5*self.decay[i]*self.decay[i]*self.sigma*h + 2/(np.sqrt(np.pi)*(self.decay[i]+decay[j]))*((-diff_t/sigma2-self.decay[i]/ 
+        #                                                                                                                     2)*np.exp(-diff_t*
+        #                                                                                                                               diff_t/sigma2) 
+        #                                                                                                                    + (-t2_mat/sigma2+self.decay[i]/2)
+        #                                                                                                                    *np.exp(-t2_mat*t2_mat/sigma2 
+        #                                                                                                                            -self.decay[i]*t_mat) 
+        #                                                                                                                    - (-t_mat/sigma2-self.decay[i]/2) 
+        #                                                                                                                    *np.exp(-t_mat*t_mat/sigma2-decay[j]*t2_mat) 
+        #                                                                                                                    - self.decay[i]/2*np.exp(-(self.decay[i]*t_mat+decay[j]*t2_mat)))
+                

GPy/kern/parts/sympykern_old.py

@@ -0,0 +1,461 @@
+import numpy as np
+import sympy as sp
+from sympy.utilities.codegen import codegen
+from sympy.core.cache import clear_cache
+from scipy import weave
+import re
+import os
+import sys
+current_dir = os.path.dirname(os.path.abspath(os.path.dirname(__file__)))
+import tempfile
+import pdb
+import ast
+from kernpart import Kernpart
+from ...util.config import config
+
+class spkern(Kernpart):
+    """
+    A kernel object, where all the hard work in done by sympy.
+
+    :param k: the covariance function
+    :type k: a positive definite sympy function of x_0, z_0, x_1, z_1, x_2, z_2...
+
+    To construct a new sympy kernel, you'll need to define:
+     - a kernel function using a sympy object. Ensure that the kernel is of the form k(x,z).
+     - that's it! we'll extract the variables from the function k.
+
+    Note:
+     - to handle multiple inputs, call them x_1, z_1, etc
+     - to handle multpile correlated outputs, you'll need to add parameters with an index, such as lengthscale_i and lengthscale_j.
+    """
+    def __init__(self, input_dim, k=None, output_dim=1, name=None, param=None):
+        if name is None:
+            self.name='sympykern'
+        else:
+            self.name = name
+        if k is None:
+            raise ValueError, "You must provide an argument for the covariance function."
+        self._sp_k = k
+        sp_vars = [e for e in k.atoms() if e.is_Symbol]
+        self._sp_x= sorted([e for e in sp_vars if e.name[0:2]=='x_'],key=lambda x:int(x.name[2:]))
+        self._sp_z= sorted([e for e in sp_vars if e.name[0:2]=='z_'],key=lambda z:int(z.name[2:]))
+        # Check that variable names make sense.
+        assert all([x.name=='x_%i'%i for i,x in enumerate(self._sp_x)])
+        assert all([z.name=='z_%i'%i for i,z in enumerate(self._sp_z)])
+        assert len(self._sp_x)==len(self._sp_z)
+        self.input_dim = len(self._sp_x)
+        self._real_input_dim = self.input_dim
+        if output_dim > 1:
+            self.input_dim += 1
+        assert self.input_dim == input_dim
+        self.output_dim = output_dim
+        # extract parameter names
+        thetas = sorted([e for e in sp_vars if not (e.name[0:2]=='x_' or e.name[0:2]=='z_')],key=lambda e:e.name)
+
+
+        # Look for parameters with index.
+        if self.output_dim>1:
+            self._sp_theta_i = sorted([e for e in thetas if (e.name[-2:]=='_i')], key=lambda e:e.name)
+            self._sp_theta_j = sorted([e for e in thetas if (e.name[-2:]=='_j')], key=lambda e:e.name)
+            # Make sure parameter appears with both indices!
+            assert len(self._sp_theta_i)==len(self._sp_theta_j)
+            assert all([theta_i.name[:-2]==theta_j.name[:-2] for theta_i, theta_j in zip(self._sp_theta_i, self._sp_theta_j)])
+
+            # Extract names of shared parameters
+            self._sp_theta = [theta for theta in thetas if theta not in self._sp_theta_i and theta not in self._sp_theta_j]
+            
+            self.num_split_params = len(self._sp_theta_i)
+            self._split_theta_names = ["%s"%theta.name[:-2] for theta in self._sp_theta_i]
+            for theta in self._split_theta_names:
+                setattr(self, theta, np.ones(self.output_dim))
+            
+            self.num_shared_params = len(self._sp_theta)
+            self.num_params = self.num_shared_params+self.num_split_params*self.output_dim
+            
+        else:
+            self.num_split_params = 0
+            self._split_theta_names = []
+            self._sp_theta = thetas
+            self.num_shared_params = len(self._sp_theta)
+            self.num_params = self.num_shared_params
+        
+        for theta in self._sp_theta:
+            val = 1.0
+            if param is not None:
+                if param.has_key(theta):
+                    val = param[theta]
+            setattr(self, theta.name, val)
+        #deal with param            
+        self._set_params(self._get_params())
+
+        #Differentiate!
+        self._sp_dk_dtheta = [sp.diff(k,theta).simplify() for theta in self._sp_theta]
+        if self.output_dim > 1:
+            self._sp_dk_dtheta_i = [sp.diff(k,theta).simplify() for theta in self._sp_theta_i]
+            
+        self._sp_dk_dx = [sp.diff(k,xi).simplify() for xi in self._sp_x]
+
+        if False:
+            self.compute_psi_stats()
+
+        self._gen_code()
+
+        if False:
+            extra_compile_args = ['-ftree-vectorize', '-mssse3', '-ftree-vectorizer-verbose=5']
+        else:
+            extra_compile_args = []
+            
+        self.weave_kwargs = {
+            'support_code':self._function_code,
+            'include_dirs':[tempfile.gettempdir(), os.path.join(current_dir,'parts/')],
+            'headers':['"sympy_helpers.h"'],
+            'sources':[os.path.join(current_dir,"parts/sympy_helpers.cpp")],
+            'extra_compile_args':extra_compile_args,
+            'extra_link_args':[],
+            'verbose':True}
+        if config.getboolean('parallel', 'openmp'): self.weave_kwargs.append('-lgomp')
+
+    def __add__(self,other):
+        return spkern(self._sp_k+other._sp_k)
+
+    def _gen_code(self):
+        """Generates the C functions necessary for computing the covariance function using the sympy objects as input."""
+        #TODO: maybe generate one C function only to save compile time? Also easier to take that as a basis and hand craft other covariances??
+
+        #generate c functions from sympy objects        
+        argument_sequence = self._sp_x+self._sp_z+self._sp_theta
+        code_list = [('k',self._sp_k)]
+        # gradients with respect to covariance input
+        code_list += [('dk_d%s'%x.name,dx) for x,dx in zip(self._sp_x,self._sp_dk_dx)]
+        # gradient with respect to parameters
+        code_list += [('dk_d%s'%theta.name,dtheta) for theta,dtheta in zip(self._sp_theta,self._sp_dk_dtheta)]
+        # gradient with respect to multiple output parameters
+        if self.output_dim > 1:
+            argument_sequence += self._sp_theta_i + self._sp_theta_j
+            code_list += [('dk_d%s'%theta.name,dtheta) for theta,dtheta in zip(self._sp_theta_i,self._sp_dk_dtheta_i)]
+        (foo_c,self._function_code), (foo_h,self._function_header) = \
+                                     codegen(code_list, "C",'kernel_code',argument_sequence=argument_sequence)
+        #put the header file where we can find it
+        f = file(os.path.join(tempfile.gettempdir(),'kernel_code.h'),'w')
+        f.write(self._function_header)
+        f.close()
+
+        # Substitute any known derivatives which sympy doesn't compute
+        self._function_code = re.sub('DiracDelta\(.+?,.+?\)','0.0',self._function_code)
+
+
+        ############################################################
+        # This is the basic argument construction for the C code.  #
+        ############################################################
+        
+        arg_list = (["X2(i, %s)"%x.name[2:] for x in self._sp_x]
+                    + ["Z2(j, %s)"%z.name[2:] for z in self._sp_z])
+
+        # for multiple outputs need to also provide these arguments reversed.
+        if self.output_dim>1:
+            reverse_arg_list = list(arg_list)
+            reverse_arg_list.reverse()
+
+        # Add in any 'shared' parameters to the list.
+        param_arg_list = [shared_params.name for shared_params in self._sp_theta]
+        arg_list += param_arg_list
+
+        precompute_list=[]
+        if self.output_dim > 1:
+            reverse_arg_list+=list(param_arg_list)
+            split_param_arg_list = ["%s1(%s)"%(theta.name[:-2].upper(),index) for index in ['ii', 'jj'] for theta in self._sp_theta_i]
+            split_param_reverse_arg_list = ["%s1(%s)"%(theta.name[:-2].upper(),index) for index in ['jj', 'ii'] for theta in self._sp_theta_i]
+            arg_list += split_param_arg_list
+            reverse_arg_list += split_param_reverse_arg_list
+            # Extract the right output indices from the inputs.
+            c_define_output_indices = [' '*16 + "int %s=(int)%s(%s, %i);"%(index, var, index2, self.input_dim-1) for index, var, index2 in zip(['ii', 'jj'], ['X2', 'Z2'], ['i', 'j'])]
+            precompute_list += c_define_output_indices
+            reverse_arg_string = ", ".join(reverse_arg_list)
+        arg_string = ", ".join(arg_list)
+        precompute_string = "\n".join(precompute_list)
+
+        # Code to compute argments string needed when only X is provided.
+        X_arg_string = re.sub('Z','X',arg_string)
+        # Code to compute argument string when only diagonal is required.
+        diag_arg_string = re.sub('int jj','//int jj',X_arg_string)
+        diag_arg_string = re.sub('j','i',diag_arg_string)
+        if precompute_string == '':
+            # if it's not multioutput, the precompute strings are set to zero
+            diag_precompute_string = ''
+            diag_precompute_replace = ''
+        else:
+            # for multioutput we need to extract the index of the output form the input.
+            diag_precompute_string = precompute_list[0]
+            diag_precompute_replace = precompute_list[1]
+        
+
+        # Here's the code to do the looping for K
+        self._K_code =\
+        """
+        // _K_code
+        // Code for computing the covariance function.
+        int i;
+        int j;
+        int N = target_array->dimensions[0];
+        int num_inducing = target_array->dimensions[1];
+        int input_dim = X_array->dimensions[1];
+        //#pragma omp parallel for private(j)
+        for (i=0;i<N;i++){
+            for (j=0;j<num_inducing;j++){
+%s
+                //target[i*num_inducing+j] = 
+                TARGET2(i, j) += k(%s);
+            }
+        }
+        %s
+        """%(precompute_string,arg_string,"/*"+str(self._sp_k)+"*/") #adding a string representation forces recompile when needed
+
+        self._K_code_X = """
+        // _K_code_X
+        // Code for computing the covariance function.
+        int i;
+        int j;
+        int N = target_array->dimensions[0];
+        int num_inducing = target_array->dimensions[1];
+        int input_dim = X_array->dimensions[1];
+        //#pragma omp parallel for private(j)
+        for (i=0;i<N;i++){
+            %s // int ii=(int)X2(i, 1);
+            TARGET2(i, i) += k(%s);
+            for (j=0;j<i;j++){
+              %s //int jj=(int)X2(j, 1);
+              double kval = k(%s); //double kval = k(X2(i, 0), shared_lengthscale, LENGTHSCALE1(ii), SCALE1(ii));
+              TARGET2(i, j) += kval;
+              TARGET2(j, i) += kval;
+            }
+        }
+        /*%s*/
+        """%(diag_precompute_string, diag_arg_string, re.sub('Z2', 'X2', diag_precompute_replace), X_arg_string,str(self._sp_k)) #adding a string representation forces recompile when needed
+
+        # Code to do the looping for Kdiag
+        self._Kdiag_code =\
+        """
+        // _Kdiag_code
+        // Code for computing diagonal of covariance function.
+        int i;
+        int N = target_array->dimensions[0];
+        int input_dim = X_array->dimensions[1];
+        //#pragma omp parallel for
+        for (i=0;i<N;i++){
+                %s
+                //target[i] =
+                TARGET1(i)=k(%s);
+        }
+        %s
+        """%(diag_precompute_string,diag_arg_string,"/*"+str(self._sp_k)+"*/") #adding a string representation forces recompile when needed
+
+        # Code to compute gradients
+        grad_func_list = []
+        if self.output_dim>1:
+            grad_func_list += c_define_output_indices
+            grad_func_list += [' '*16 + 'TARGET1(%i+ii) += PARTIAL2(i, j)*dk_d%s(%s);'%(self.num_shared_params+i*self.output_dim, theta.name, arg_string) for i, theta in enumerate(self._sp_theta_i)]
+            grad_func_list += [' '*16 + 'TARGET1(%i+jj) += PARTIAL2(i, j)*dk_d%s(%s);'%(self.num_shared_params+i*self.output_dim, theta.name, reverse_arg_string) for i, theta in enumerate(self._sp_theta_i)]
+        grad_func_list += ([' '*16 + 'TARGET1(%i) += PARTIAL2(i, j)*dk_d%s(%s);'%(i,theta.name,arg_string) for i,theta in  enumerate(self._sp_theta)])
+        grad_func_string = '\n'.join(grad_func_list) 
+
+        self._dK_dtheta_code =\
+        """
+        // _dK_dtheta_code
+        // Code for computing gradient of covariance with respect to parameters.
+        int i;
+        int j;
+        int N = partial_array->dimensions[0];
+        int num_inducing = partial_array->dimensions[1];
+        int input_dim = X_array->dimensions[1];
+        //#pragma omp parallel for private(j)
+        for (i=0;i<N;i++){
+            for (j=0;j<num_inducing;j++){
+%s
+            }
+        }
+        %s
+        """%(grad_func_string,"/*"+str(self._sp_k)+"*/") # adding a string representation forces recompile when needed
+
+
+        # Code to compute gradients for Kdiag TODO: needs clean up
+        diag_grad_func_string = re.sub('Z','X',grad_func_string,count=0)
+        diag_grad_func_string = re.sub('int jj','//int jj',diag_grad_func_string)
+        diag_grad_func_string = re.sub('j','i',diag_grad_func_string)
+        diag_grad_func_string = re.sub('PARTIAL2\(i, i\)','PARTIAL1(i)',diag_grad_func_string)
+        self._dKdiag_dtheta_code =\
+        """
+        // _dKdiag_dtheta_code
+        // Code for computing gradient of diagonal with respect to parameters.
+        int i;
+        int N = partial_array->dimensions[0];
+        int input_dim = X_array->dimensions[1];
+        for (i=0;i<N;i++){
+                %s
+        }
+        %s
+        """%(diag_grad_func_string,"/*"+str(self._sp_k)+"*/") #adding a string representation forces recompile when needed
+
+        # Code for gradients wrt X, TODO: may need to deal with special case where one input is actually an output.
+        gradX_func_list = []
+        if self.output_dim>1:
+            gradX_func_list += c_define_output_indices
+        gradX_func_list += ["TARGET2(i, %i) += PARTIAL2(i, j)*dk_dx_%i(%s);"%(q,q,arg_string) for q in range(self._real_input_dim)]
+        gradX_func_string = "\n".join(gradX_func_list)
+
+        self._dK_dX_code = \
+        """
+        // _dK_dX_code
+        // Code for computing gradient of covariance with respect to inputs.
+        int i;
+        int j;
+        int N = partial_array->dimensions[0];
+        int num_inducing = partial_array->dimensions[1];
+        int input_dim = X_array->dimensions[1];
+        //#pragma omp parallel for private(j)
+        for (i=0;i<N; i++){
+          for (j=0; j<num_inducing; j++){
+            %s
+          }
+        }
+        %s
+        """%(gradX_func_string,"/*"+str(self._sp_k)+"*/") #adding a string representation forces recompile when needed
+  
+
+        diag_gradX_func_string = re.sub('Z','X',gradX_func_string,count=0)
+        diag_gradX_func_string = re.sub('int jj','//int jj',diag_gradX_func_string)
+        diag_gradX_func_string = re.sub('j','i',diag_gradX_func_string)
+        diag_gradX_func_string = re.sub('PARTIAL2\(i, i\)','2*PARTIAL1(i)',diag_gradX_func_string)
+
+        # Code for gradients of Kdiag wrt X
+        self._dKdiag_dX_code= \
+        """
+        // _dKdiag_dX_code
+        // Code for computing gradient of diagonal with respect to inputs.
+        int N = partial_array->dimensions[0];
+        int input_dim = X_array->dimensions[1];
+        for (int i=0;i<N; i++){
+            %s
+        }
+        %s
+        """%(diag_gradX_func_string,"/*"+str(self._sp_k)+"*/") #adding a
+        # string representation forces recompile when needed Get rid
+        # of Zs in argument for diagonal. TODO: Why wasn't
+        # diag_func_string called here? Need to check that.
+        #self._dKdiag_dX_code = self._dKdiag_dX_code.replace('Z[j', 'X[i')
+
+        # Code to use when only X is provided. 
+        self._dK_dtheta_code_X = self._dK_dtheta_code.replace('Z[', 'X[')
+        self._dK_dX_code_X = self._dK_dX_code.replace('Z[', 'X[').replace('+= PARTIAL2(', '+= 2*PARTIAL2(') 
+        self._dK_dtheta_code_X = self._dK_dtheta_code_X.replace('Z2(', 'X2(')
+        self._dK_dX_code_X = self._dK_dX_code_X.replace('Z2(', 'X2(')
+
+
+        #TODO: insert multiple functions here via string manipulation
+        #TODO: similar functions for psi_stats
+    def _get_arg_names(self, Z=None, partial=None):
+        arg_names = ['target','X']
+        for shared_params in self._sp_theta:
+            arg_names += [shared_params.name]
+        if Z is not None:
+            arg_names += ['Z']
+        if partial is not None:
+            arg_names += ['partial']
+        if self.output_dim>1:
+            arg_names += self._split_theta_names
+            arg_names += ['output_dim']
+        return arg_names
+        
+    def _weave_inline(self, code, X, target, Z=None, partial=None):
+        output_dim = self.output_dim
+        for shared_params in self._sp_theta:
+            locals()[shared_params.name] = getattr(self, shared_params.name)
+
+        # Need to extract parameters first
+        for split_params in self._split_theta_names:
+            locals()[split_params] = getattr(self, split_params)
+        arg_names = self._get_arg_names(Z, partial)        
+        weave.inline(code=code, arg_names=arg_names,**self.weave_kwargs)
+
+    def K(self,X,Z,target):        
+        if Z is None:
+            self._weave_inline(self._K_code_X, X, target)
+        else:
+            self._weave_inline(self._K_code, X, target, Z)
+
+
+    def Kdiag(self,X,target):
+        self._weave_inline(self._Kdiag_code, X, target)
+
+    def dK_dtheta(self,partial,X,Z,target):
+        if Z is None:
+            self._weave_inline(self._dK_dtheta_code_X, X, target, Z, partial)
+        else:
+            self._weave_inline(self._dK_dtheta_code, X, target, Z, partial)
+            
+    def dKdiag_dtheta(self,partial,X,target):
+        self._weave_inline(self._dKdiag_dtheta_code, X, target, Z=None, partial=partial)
+               
+    def dK_dX(self,partial,X,Z,target):
+        if Z is None:
+            self._weave_inline(self._dK_dX_code_X, X, target, Z, partial)
+        else:
+            self._weave_inline(self._dK_dX_code, X, target, Z, partial)
+
+    def dKdiag_dX(self,partial,X,target):
+        self._weave_inline(self._dKdiag_dX_code, X, target, Z=None, partial=partial)
+
+    def compute_psi_stats(self):
+        #define some normal distributions
+        mus = [sp.var('mu_%i'%i,real=True) for i in range(self.input_dim)]
+        Ss = [sp.var('S_%i'%i,positive=True) for i in range(self.input_dim)]
+        normals = [(2*sp.pi*Si)**(-0.5)*sp.exp(-0.5*(xi-mui)**2/Si) for xi, mui, Si in zip(self._sp_x, mus, Ss)]
+
+        #do some integration!
+        #self._sp_psi0 = ??
+        self._sp_psi1 = self._sp_k
+        for i in range(self.input_dim):
+            print 'perfoming integrals %i of %i'%(i+1,2*self.input_dim)
+            sys.stdout.flush()
+            self._sp_psi1 *= normals[i]
+            self._sp_psi1 = sp.integrate(self._sp_psi1,(self._sp_x[i],-sp.oo,sp.oo))
+            clear_cache()
+        self._sp_psi1 = self._sp_psi1.simplify()
+
+        #and here's psi2 (eek!)
+        zprime = [sp.Symbol('zp%i'%i) for i in range(self.input_dim)]
+        self._sp_psi2 = self._sp_k.copy()*self._sp_k.copy().subs(zip(self._sp_z,zprime))
+        for i in range(self.input_dim):
+            print 'perfoming integrals %i of %i'%(self.input_dim+i+1,2*self.input_dim)
+            sys.stdout.flush()
+            self._sp_psi2 *= normals[i]
+            self._sp_psi2 = sp.integrate(self._sp_psi2,(self._sp_x[i],-sp.oo,sp.oo))
+            clear_cache()
+        self._sp_psi2 = self._sp_psi2.simplify()
+
+
+    def _set_params(self,param):        
+        assert param.size == (self.num_params)
+        for i, shared_params in enumerate(self._sp_theta):
+            setattr(self, shared_params.name, param[i])
+            
+        if self.output_dim>1:
+            for i, split_params in enumerate(self._split_theta_names):
+                start = self.num_shared_params + i*self.output_dim
+                end = self.num_shared_params + (i+1)*self.output_dim
+                setattr(self, split_params, param[start:end])
+
+
+    def _get_params(self):
+        params = np.zeros(0)
+        for shared_params in self._sp_theta:
+            params = np.hstack((params, getattr(self, shared_params.name)))
+        if self.output_dim>1:
+            for split_params in self._split_theta_names:
+                params = np.hstack((params, getattr(self, split_params).flatten()))
+        return params
+
+    def _get_param_names(self):
+        if self.output_dim>1:
+            return [x.name for x in self._sp_theta] + [x.name[:-2] + str(i)  for x in self._sp_theta_i for i in range(self.output_dim)]
+        else:
+            return [x.name for x in self._sp_theta]

GPy/kern/ratquad.py

@@ -0,0 +1,179 @@
+# Copyright (c) 2012, GPy authors (see AUTHORS.txt).
+# Licensed under the BSD 3-clause license (see LICENSE.txt)
+
+
+from kernpart import kernpart
+import numpy as np
+import hashlib
+
+class rbf(kernpart):
+    """
+    Rational quadratic kernel.
+    .. math::
+
+       k(r) = \sigma^2 \left(\frac{(\ell^{-2} +  r^2)}{2*\alpha}\right)^{-\alpha} \qquad \qquad \\text{ where  } r = \sqrt{\frac{\sum_{i=1}^d (x_i-x^\prime_i)^2}{\ell^2}}
+
+    where \ell is the lengthscale, \alpha the smoothness, \sigma^2 the variance and d the dimensionality of the input.
+
+    :param D: the number of input dimensions
+    :type D: int
+    :param variance: the variance of the kernel
+    :type variance: float
+    :param lengthscale: the lengthscale of the kernel (l)
+    :type lengthscale: float
+    :param smoothness: the smoothness parameter of the kernel
+    :type lengthscale: float
+
+    .. Note: for rational quadratic with different lengthscale on each dimension, see ratquad_ARD
+    """
+
+    def __init__(self,D,variance=1.,lengthscale=1.,smoothness)=1.:
+        self.D = D
+        self.Nparam = 3
+        self.name = 'ratquad'
+        self._set_params(np.hstack((variance,lengthscale,smoothness)))
+
+        #initialize cache
+        self._Z, self._mu, self._S = np.empty(shape=(3,1))
+        self._X, self._X2, self._params = np.empty(shape=(3,1))
+
+    def _get_params(self):
+        return np.hstack((self.variance,self.lengthscale,self.smoothness))
+
+    def _set_params(self,x):
+        self.variance, self.lengthscale, self.smoothness = x
+        self.lengthscale2 = np.square(self.lengthscale)
+        #reset cached results
+        self._X, self._X2, self._params = np.empty(shape=(3,1))
+        self._Z, self._mu, self._S = np.empty(shape=(3,1)) # cached versions of Z,mu,S
+
+    def _get_param_names(self):
+        return ['variance','lengthscale','smoothness']
+
+    def K(self,X,X2,target):
+        if X2 is None:
+            X2 = X
+        self._K_computations(X,X2)
+        np.add(self.variance*self._K_dvar, target,target)
+
+    def Kdiag(self,X,target):
+        np.add(target,self.variance,target)
+
+    def dK_dtheta(self,partial,X,X2,target):
+        self._K_computations(X,X2)
+        target[0] += np.sum(self._K_dvar*partial)
+        target[1] += np.sum(self._K_dvar*self.variance*self._K_dist2/self.lengthscale*partial)
+        target[2] += 
+    def dKdiag_dtheta(self,partial,X,target):
+        #NB: derivative of diagonal elements wrt lengthscale is 0
+        target[0] += np.sum(partial)
+
+    def dK_dX(self,partial,X,X2,target):
+        self._K_computations(X,X2)
+        if X2 is None:
+            _K_dist = 2*X[:, None, :] - X[None, :, :]
+        else:
+            _K_dist = X[:,None,:]-X2[None,:,:]
+        dK_dX = np.transpose(-self.variance*self._K_dvar[:,:,np.newaxis]*_K_dist/self.lengthscale2,(1,0,2))
+        target += np.sum(dK_dX*partial.T[:,:,None],0)
+
+    def dKdiag_dX(self,partial,X,target):
+        pass
+
+    def _K_computations(self,X,X2):
+        if not (np.all(X==self._X) and np.all(X2==self._X2)):
+            self._X = X
+            self._X2 = X2
+            if X2 is None: X2 = X
+            XXT = np.dot(X,X2.T)
+            if X is X2:
+                self._K_dist2 = (-2.*XXT + np.diag(XXT)[:,np.newaxis] + np.diag(XXT)[np.newaxis,:])/self.lengthscale2
+            else:
+                self._K_dist2 = (-2.*XXT + np.sum(np.square(X),1)[:,np.newaxis] + np.sum(np.square(X2),1)[np.newaxis,:])/self.lengthscale2
+            self._K_dvar = (0.5./self.smoothness*(1./self.lengthscale2 + self._K_dist2))**(-self.smoothness)
+
+    def psi0(self,Z,mu,S,target):
+        target += self.variance
+
+    def dpsi0_dtheta(self,partial,Z,mu,S,target):
+        target[0] += 1.
+
+    def dpsi0_dmuS(self,Z,mu,S,target_mu,target_S):
+        pass
+
+    def psi1(self,Z,mu,S,target):
+        self._psi_computations(Z,mu,S)
+        target += self._psi1
+
+    def dpsi1_dtheta(self,partial,Z,mu,S,target):
+        self._psi_computations(Z,mu,S)
+        denom_deriv = S[:,None,:]/(self.lengthscale**3+self.lengthscale*S[:,None,:])
+        d_length = self._psi1[:,:,None]*(self.lengthscale*np.square(self._psi1_dist/(self.lengthscale2+S[:,None,:])) + denom_deriv)
+        target[0] += np.sum(partial*self._psi1/self.variance)
+        target[1] += np.sum(d_length*partial[:,:,None])
+
+    def dpsi1_dZ(self,partial,Z,mu,S,target):
+        self._psi_computations(Z,mu,S)
+        target += np.sum(partial[:,:,None]*-self._psi1[:,:,None]*self._psi1_dist/self.lengthscale2/self._psi1_denom,0)
+
+    def dpsi1_dmuS(self,partial,Z,mu,S,target_mu,target_S):
+        self._psi_computations(Z,mu,S)
+        tmp = self._psi1[:,:,None]/self.lengthscale2/self._psi1_denom
+        target_mu += np.sum(partial*tmp*self._psi1_dist,1)
+        target_S += np.sum(partial*0.5*tmp*(self._psi1_dist_sq-1),1)
+
+    def psi2(self,Z,mu,S,target):
+        self._psi_computations(Z,mu,S)
+        target += self._psi2.sum(0) #TODO: psi2 should be NxMxM (for het. noise)
+
+    def dpsi2_dtheta(self,partial,Z,mu,S,target):
+        """Shape N,M,M,Ntheta"""
+        self._psi_computations(Z,mu,S)
+        d_var = np.sum(2.*self._psi2/self.variance,0)
+        d_length = self._psi2[:,:,:,None]*(0.5*self._psi2_Zdist_sq*self._psi2_denom + 2.*self._psi2_mudist_sq + 2.*S[:,None,None,:]/self.lengthscale2)/(self.lengthscale*self._psi2_denom)
+        d_length = d_length.sum(0)
+        target[0] += np.sum(partial*d_var)
+        target[1] += np.sum(d_length*partial)
+
+    def dpsi2_dZ(self,partial,Z,mu,S,target):
+        """Returns shape N,M,M,Q"""
+        self._psi_computations(Z,mu,S)
+        dZ = self._psi2[:,:,:,None]/self.lengthscale2*(-0.5*self._psi2_Zdist + self._psi2_mudist/self._psi2_denom)
+        target += np.sum(partial[None,:,:,None]*dZ,0).sum(1)
+
+    def dpsi2_dmuS(self,Z,mu,S,target_mu,target_S):
+        """Think N,M,M,Q """
+        self._psi_computations(Z,mu,S)
+        tmp = self._psi2[:,:,:,None]/self.lengthscale2/self._psi2_denom
+        target_mu += (partial*-tmp*2.*self._psi2_mudist).sum(1).sum(1)
+        target_S += (partial*tmp*(2.*self._psi2_mudist_sq-1)).sum(1).sum(1)
+
+    def _psi_computations(self,Z,mu,S):
+        #here are the "statistics" for psi1 and psi2
+        if not np.all(Z==self._Z):
+            #Z has changed, compute Z specific stuff
+            self._psi2_Zhat = 0.5*(Z[:,None,:] +Z[None,:,:]) # M,M,Q
+            self._psi2_Zdist = Z[:,None,:]-Z[None,:,:] # M,M,Q
+            self._psi2_Zdist_sq = np.square(self._psi2_Zdist)/self.lengthscale2 # M,M,Q
+            self._Z = Z
+
+        if not (np.all(Z==self._Z) and np.all(mu==self._mu) and np.all(S==self._S)):
+            #something's changed. recompute EVERYTHING
+
+            #TODO: make more efficient for large Q (using NDL's dot product trick)
+            #psi1
+            self._psi1_denom = S[:,None,:]/self.lengthscale2 + 1.
+            self._psi1_dist = Z[None,:,:]-mu[:,None,:]
+            self._psi1_dist_sq = np.square(self._psi1_dist)/self.lengthscale2/self._psi1_denom
+            self._psi1_exponent = -0.5*np.sum(self._psi1_dist_sq+np.log(self._psi1_denom),-1)
+            self._psi1 = self.variance*np.exp(self._psi1_exponent)
+
+            #psi2
+            self._psi2_denom = 2.*S[:,None,None,:]/self.lengthscale2+1. # N,M,M,Q
+            self._psi2_mudist = mu[:,None,None,:]-self._psi2_Zhat #N,M,M,Q
+            self._psi2_mudist_sq = np.square(self._psi2_mudist)/(self.lengthscale2*self._psi2_denom)
+            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
+            self._psi2 = np.square(self.variance)*np.exp(self._psi2_exponent) # N,M,M
+
+            self._Z, self._mu, self._S = Z, mu,S
+

GPy/likelihoods/negative_binomial.py~

@@ -0,0 +1,31 @@
+# Copyright (c) 2014 The GPy authors (see AUTHORS.txt)
+# Licensed under the BSD 3-clause license (see LICENSE.txt)
+
+import numpy as np
+from ..util.univariate_Gaussian import std_norm_pdf, std_norm_cdf
+import link_functions
+from likelihood import Likelihood
+from scipy import stats
+
+class Negative_binomial(Symbolic):
+    """
+    Negative binomial
+
+    .. math::
+        p(y_{i}|\pi(f_{i})) = \\lambda(f_{i})^{y_{i}}(1-f_{i})^{1-y_{i}}
+
+    .. Note::
+        Y takes values in either {-1, 1} or {0, 1}.
+        link function should have the domain [0, 1], e.g. probit (default) or Heaviside
+
+    .. See also::
+        likelihood.py, for the parent class
+    """
+    def __init__(self, gp_link=None):
+        if gp_link is None:
+            gp_link = link_functions.Probit()
+
+        super(Bernoulli, self).__init__(gp_link, 'Bernoulli')
+
+        if isinstance(gp_link , (link_functions.Heaviside, link_functions.Probit)):
+            self.log_concave = True

GPy/likelihoods/null_category.py

@@ -0,0 +1,53 @@
+# Copyright (c) 2014 The GPy authors (see AUTHORS.txt)
+# Licensed under the BSD 3-clause license (see LICENSE.txt)
+
+
+try:
+    import sympy as sym
+    sympy_available=True
+    from sympy.utilities.lambdify import lambdify
+    from GPy.util.symbolic import gammaln, normcdfln, normcdf
+    from sympy.functions.elementary.piecewise import Piecewise
+except ImportError:
+    sympy_available=False
+
+import numpy as np
+from ..util.univariate_Gaussian import std_norm_pdf, std_norm_cdf
+import link_functions
+from symbolic import Symbolic
+from scipy import stats
+
+if sympy_available:
+    class Null_category(Symbolic):
+        """
+        Null category noise model.
+
+        .. math::
+
+        .. Note::
+            Y takes -1, 0 or 1.
+
+        .. See also::
+            symbolic.py, for the parent class
+        """
+        def __init__(self, gp_link=None):
+            if gp_link is None:
+                gp_link = link_functions.Identity()
+            # width of the null category.
+            width = sym.Symbol('width', positive=True, real=True)
+            # prior probability of positive class
+            p = sym.Symbol('p', positive=True, real=True)
+            y = sym.Symbol('y', binary=True)            
+            f = sym.Symbol('f', positive=True, real=True) 
+
+            log_pdf_missing = sym.log((1-p)*normcdf(-f-width/2)
+                                      +p*normcdf(f+width/2))
+            log_pdf = (y-1)*normcdfln(-f-width/2)+y*normcdfln(f+width/2)
+            super(Null_category, self).__init__(log_pdf=log_pdf, missing_log_pdf=log_pdf_missing, gp_link=gp_link, name='Null_category')
+
+            self.p=0.5
+            self.p.constrain_bounded(0., 1.)
+            self.width = 1.
+            self.width.constrain_fixed()
+            self.log_concave = False
+

GPy/likelihoods/null_category.py~

@@ -0,0 +1,46 @@
+# Copyright (c) 2014 The GPy authors (see AUTHORS.txt)
+# Licensed under the BSD 3-clause license (see LICENSE.txt)
+
+
+try:
+    import sympy as sym
+    sympy_available=True
+    from sympy.utilities.lambdify import lambdify
+    from GPy.util.symbolic import gammaln, ln_cum_gaussian, cum_gaussian
+except ImportError:
+    sympy_available=False
+
+import numpy as np
+from ..util.univariate_Gaussian import std_norm_pdf, std_norm_cdf
+import link_functions
+from symbolic import Symbolic
+from scipy import stats
+
+if sympy_available:
+    class Negative_binomial(Symbolic):
+        """
+        Negative binomial
+
+        .. math::
+            p(y_{i}|\pi(f_{i})) = \left(\frac{r}{r+f_i}\right)^r \frac{\Gamma(r+y_i)}{y!\Gamma(r)}\left(\frac{f_i}{r+f_i}\right)^{y_i}
+
+        .. Note::
+            Y takes non zero integer values..
+            link function should have a positive domain, e.g. log (default).
+
+        .. See also::
+            symbolic.py, for the parent class
+        """
+        def __init__(self, gp_link=None):
+            if gp_link is None:
+                gp_link = link_functions.Log()
+
+            dispersion = sym.Symbol('dispersion', positive=True, real=True)
+            y = sym.Symbol('y', nonnegative=True, integer=True)
+            f = sym.Symbol('f', positive=True, real=True) 
+            log_pdf=dispersion*sym.log(dispersion) - (dispersion+y)*sym.log(dispersion+f) + gammaln(y+dispersion) - gammaln(y+1) - gammaln(dispersion) + y*sym.log(f)  
+            super(Negative_binomial, self).__init__(log_pdf=log_pdf, gp_link=gp_link, name='Negative_binomial')
+
+            # TODO: Check this.
+            self.log_concave = False
+

GPy/likelihoods/old_symbolic.py

@@ -0,0 +1,316 @@
+# Copyright (c) 2014 GPy Authors
+# Licensed under the BSD 3-clause license (see LICENSE.txt)
+
+try:
+    import sympy as sym
+    sympy_available=True
+    from sympy.utilities.lambdify import lambdify
+except ImportError:
+    sympy_available=False
+
+import numpy as np
+import link_functions
+from scipy import stats, integrate
+from scipy.special import gammaln, gamma, erf, erfc, erfcx, polygamma
+from GPy.util.functions import normcdf, normcdfln, logistic, logisticln
+from likelihood import Likelihood
+from ..core.parameterization import Param
+
+
+if sympy_available:
+    class Symbolic(Likelihood):
+        """
+        Symbolic likelihood.
+
+        Likelihood where the form of the likelihood is provided by a sympy expression.
+
+        """
+        def __init__(self, log_pdf=None, logZ=None, missing_log_pdf=None, gp_link=None, name='symbolic', log_concave=False, param=None, func_modules=[]):
+
+            if gp_link is None:
+                gp_link = link_functions.Identity()
+
+            if log_pdf is None:
+                raise ValueError, "You must provide an argument for the log pdf."
+
+            self.func_modules = func_modules
+            self.func_modules += [{'gamma':gamma,
+                                   'gammaln':gammaln,
+                                   'erf':erf, 'erfc':erfc,
+                                   'erfcx':erfcx,
+                                   'polygamma':polygamma,
+                                   'normcdf':normcdf,
+                                   'normcdfln':normcdfln,
+                                   'logistic':logistic,
+                                   'logisticln':logisticln},
+                                  'numpy']
+
+            super(Symbolic, self).__init__(gp_link, name=name)
+            self.missing_data = False
+            self._sym_log_pdf = log_pdf
+            if missing_log_pdf:
+                self.missing_data = True
+                self._sym_missing_log_pdf = missing_log_pdf
+
+            # pull the variable names out of the symbolic pdf
+            sym_vars = [e for e in self._sym_log_pdf.atoms() if e.is_Symbol]
+            self._sym_f = [e for e in sym_vars if e.name=='f']
+            if not self._sym_f:
+                raise ValueError('No variable f in log pdf.')
+            self._sym_y = [e for e in sym_vars if e.name=='y']
+            if not self._sym_y:
+                raise ValueError('No variable y in log pdf.')
+            self._sym_theta = sorted([e for e in sym_vars if not (e.name=='f' or e.name=='y')],key=lambda e:e.name)
+
+            theta_names = [theta.name for theta in self._sym_theta]
+            if self.missing_data:
+                # pull the variable names out of missing data
+                sym_vars = [e for e in self._sym_missing_log_pdf.atoms() if e.is_Symbol]
+                sym_f = [e for e in sym_vars if e.name=='f']
+                if not sym_f:
+                    raise ValueError('No variable f in missing data log pdf.')
+                sym_y = [e for e in sym_vars if e.name=='y']
+                if sym_y:
+                    raise ValueError('Data is present in missing data portion of likelihood.')
+                # additional missing data parameters
+                missing_theta = sorted([e for e in sym_vars if not (e.name=='f' or e.name=='missing' or e.name in theta_names)],key=lambda e:e.name)
+                self._sym_theta += missing_theta
+                self._sym_theta = sorted(self._sym_theta, key=lambda e:e.name)
+
+            # These are all the arguments need to compute likelihoods.
+            self.arg_list = self._sym_y + self._sym_f + self._sym_theta
+
+            # these are arguments for computing derivatives.
+            derivative_arguments = self._sym_f + self._sym_theta
+
+            # Do symbolic work to compute derivatives.
+            self._log_pdf_derivatives = {theta.name : stabilise(sym.diff(self._sym_log_pdf,theta)) for theta in derivative_arguments}
+            self._log_pdf_second_derivatives = {theta.name : stabilise(sym.diff(self._log_pdf_derivatives['f'],theta)) for theta in derivative_arguments}
+            self._log_pdf_third_derivatives = {theta.name : stabilise(sym.diff(self._log_pdf_second_derivatives['f'],theta)) for theta in derivative_arguments}
+
+            if self.missing_data:
+                # Do symbolic work to compute derivatives.
+                self._missing_log_pdf_derivatives = {theta.name : stabilise(sym.diff(self._sym_missing_log_pdf,theta)) for theta in derivative_arguments}
+                self._missing_log_pdf_second_derivatives = {theta.name : stabilise(sym.diff(self._missing_log_pdf_derivatives['f'],theta)) for theta in derivative_arguments}
+                self._missing_log_pdf_third_derivatives = {theta.name : stabilise(sym.diff(self._missing_log_pdf_second_derivatives['f'],theta)) for theta in derivative_arguments}
+
+            
+            # Add parameters to the model.
+            for theta in self._sym_theta:
+                val = 1.0
+                # TODO: need to decide how to handle user passing values for the se parameter vectors.
+                if param is not None:
+                    if param.has_key(theta.name):
+                        val = param[theta.name]
+                setattr(self, theta.name, Param(theta.name, val, None))
+                self.add_parameters(getattr(self, theta.name))
+
+
+            # TODO: Is there an easy way to check whether the pdf is log
+            # concave? For the moment, need user to specify.
+            self.log_concave = log_concave
+
+            # initialise code arguments
+            self._arguments = {} 
+
+            # generate the code for the pdf and derivatives
+            self._gen_code()
+
+        def list_functions(self):
+            """Return a list of all symbolic functions in the model and their names."""
+        def _gen_code(self):
+            """Generate the code from the symbolic parts that will be used for likleihod computation."""
+            # TODO: Check here whether theano is available and set up
+            # functions accordingly.
+            symbolic_functions = [self._sym_log_pdf]
+            deriv_list = [self._log_pdf_derivatives, self._log_pdf_second_derivatives, self._log_pdf_third_derivatives]
+            symbolic_functions += [deriv[key] for key in sorted(deriv.keys()) for deriv in deriv_list]
+            if self.missing_data:
+                symbolic_functions+=[self._sym_missing_log_pdf]
+                deriv_list = [self._missing_log_pdf_derivatives, self._missing_log_pdf_second_derivatives, self._missing_log_pdf_third_derivatives]
+                symbolic_functions += [deriv[key] for key in sorted(deriv.keys()) for deriv in deriv_list]
+            # self._log_pdf_function = lambdify(self.arg_list, self._sym_log_pdf, self.func_modules)
+
+            # # compute code for derivatives 
+            # self._derivative_code = {key: lambdify(self.arg_list, self._log_pdf_derivatives[key], self.func_modules) for key in self._log_pdf_derivatives.keys()}
+            # self._second_derivative_code = {key: lambdify(self.arg_list, self._log_pdf_second_derivatives[key], self.func_modules) for key in self._log_pdf_second_derivatives.keys()}
+            # self._third_derivative_code = {key: lambdify(self.arg_list, self._log_pdf_third_derivatives[key], self.func_modules) for key in self._log_pdf_third_derivatives.keys()}
+
+            # if self.missing_data:
+            #     self._missing_derivative_code = {key: lambdify(self.arg_list, self._missing_log_pdf_derivatives[key], self.func_modules) for key in self._missing_log_pdf_derivatives.keys()}
+            #     self._missing_second_derivative_code = {key: lambdify(self.arg_list, self._missing_log_pdf_second_derivatives[key], self.func_modules) for key in self._missing_log_pdf_second_derivatives.keys()}
+            #     self._missing_third_derivative_code = {key: lambdify(self.arg_list, self._missing_log_pdf_third_derivatives[key], self.func_modules) for key in self._missing_log_pdf_third_derivatives.keys()}
+
+            # TODO: compute EP code parts based on logZ. We need dlogZ/dmu, d2logZ/dmu2 and dlogZ/dtheta
+
+        def parameters_changed(self):
+            pass
+
+        def update_gradients(self, grads):
+            """
+            Pull out the gradients, be careful as the order must match the order
+            in which the parameters are added
+            """
+            # The way the Laplace approximation is run requires the
+            # covariance function to compute the true gradient (because it
+            # is dependent on the mode). This means we actually compute
+            # the gradient outside this object. This function would
+            # normally ask the object to update its gradients internally,
+            # but here it provides them externally, because they are
+            # computed in the inference code. TODO: Thought: How does this
+            # effect EP? Shouldn't this be done by a separate
+            # Laplace-approximation specific call?
+            for grad, theta in zip(grads, self._sym_theta):
+                parameter = getattr(self, theta.name)
+                setattr(parameter, 'gradient', grad)
+
+        def _arguments_update(self, f, y):
+            """Set up argument lists for the derivatives."""
+            # If we do make use of Theano, then at this point we would
+            # need to do a lot of precomputation to ensure that the
+            # likelihoods and gradients are computed together, then check
+            # for parameter changes before updating.
+            for i, fvar in enumerate(self._sym_f):
+                self._arguments[fvar.name] =  f
+            for i, yvar in enumerate(self._sym_y):
+                self._arguments[yvar.name] = y
+            for theta in self._sym_theta:
+                self._arguments[theta.name] = np.asarray(getattr(self, theta.name))
+
+        def pdf_link(self, inv_link_f, y, Y_metadata=None):
+            """
+            Likelihood function given inverse link of f.
+
+            :param inv_link_f: inverse link of latent variables.
+            :type inv_link_f: Nx1 array
+            :param y: data
+            :type y: Nx1 array
+            :param Y_metadata: Y_metadata which is not used in student t distribution
+            :returns: likelihood evaluated for this point
+            :rtype: float
+            """
+            return np.exp(self.logpdf_link(inv_link_f, y, Y_metadata=None))
+
+        def logpdf_link(self, inv_link_f, y, Y_metadata=None):
+            """
+            Log Likelihood Function given inverse link of latent variables.
+
+            :param inv_inv_link_f: latent variables (inverse link of f)
+            :type inv_inv_link_f: Nx1 array
+            :param y: data
+            :type y: Nx1 array
+            :param Y_metadata: Y_metadata 
+            :returns: likelihood evaluated for this point
+            :rtype: float
+
+            """
+            assert np.atleast_1d(inv_link_f).shape == np.atleast_1d(y).shape
+            self._arguments_update(inv_link_f, y)
+            if self.missing_data:
+                ll = np.where(np.isnan(y), self._missing_log_pdf_function(**self._missing_arguments), self._log_pdf_function(**self._arguments))
+            else:
+                ll = np.where(np.isnan(y), 0., self._log_pdf_function(**self._arguments))
+            return np.sum(ll)
+
+        def dlogpdf_dlink(self, inv_link_f, y, Y_metadata=None):
+            """
+            Gradient of log likelihood with respect to the inverse link function.
+
+            :param inv_inv_link_f: latent variables (inverse link of f)
+            :type inv_inv_link_f: Nx1 array
+            :param y: data
+            :type y: Nx1 array
+            :param Y_metadata: Y_metadata 
+            :returns: gradient of likelihood with respect to each point.
+            :rtype: Nx1 array
+
+            """
+            assert np.atleast_1d(inv_link_f).shape == np.atleast_1d(y).shape 
+            self._arguments_update(inv_link_f, y)
+            if self.missing_data:
+                return np.where(np.isnan(y), self._missing_derivative_code['f'](**self._missing_argments), self._derivative_code['f'](**self._argments)) 
+            else:
+                return np.where(np.isnan(y), 0., self._derivative_code['f'](**self._arguments))
+
+        def d2logpdf_dlink2(self, inv_link_f, y, Y_metadata=None):
+            """
+            Hessian of log likelihood given inverse link of latent variables with respect to that inverse link.
+            i.e. second derivative logpdf at y given inv_link(f_i) and inv_link(f_j)  w.r.t inv_link(f_i) and inv_link(f_j).
+
+
+            :param inv_link_f: inverse link of the latent variables.
+            :type inv_link_f: Nx1 array
+            :param y: data
+            :type y: Nx1 array
+            :param Y_metadata: Y_metadata which is not used in student t distribution
+            :returns: Diagonal of Hessian matrix (second derivative of likelihood evaluated at points f)
+            :rtype: Nx1 array
+
+            .. Note::
+                Returns diagonal of Hessian, since every where else it is
+                0, as the likelihood factorizes over cases (the
+                distribution for y_i depends only on link(f_i) not on
+                link(f_(j!=i))
+            """
+            assert np.atleast_1d(inv_link_f).shape == np.atleast_1d(y).shape 
+            self._arguments_update(inv_link_f, y)
+            if self.missing_data:
+                return np.where(np.isnan(y), self._missing_second_derivative_code['f'](**self._missing_argments), self._second_derivative_code['f'](**self._argments)) 
+            else:
+                return np.where(np.isnan(y), 0., self._second_derivative_code['f'](**self._arguments))
+
+        def d3logpdf_dlink3(self, inv_link_f, y, Y_metadata=None):
+            assert np.atleast_1d(inv_link_f).shape == np.atleast_1d(y).shape 
+            self._arguments_update(inv_link_f, y)
+            if self.missing_data:
+                return np.where(np.isnan(y), self._missing_third_derivative_code['f'](**self._missing_argments), self._third_derivative_code['f'](**self._argments)) 
+            else:
+                return np.where(np.isnan(y), 0., self._third_derivative_code['f'](**self._arguments))
+
+        def dlogpdf_link_dtheta(self, inv_link_f, y, Y_metadata=None):
+            assert np.atleast_1d(inv_link_f).shape == np.atleast_1d(y).shape 
+            self._arguments_update(inv_link_f, y)
+            g = np.zeros((np.atleast_1d(y).shape[0], len(self._sym_theta)))
+            for i, theta in enumerate(self._sym_theta):
+                if self.missing_data:
+                    g[:, i:i+1] = np.where(np.isnan(y), self._missing_derivative_code[theta.name](**self._arguments), self._derivative_code[theta.name](**self._arguments))
+                else:
+                    g[:, i:i+1] = np.where(np.isnan(y), 0., self._derivative_code[theta.name](**self._arguments))
+            return g.sum(0)
+
+        def dlogpdf_dlink_dtheta(self, inv_link_f, y, Y_metadata=None):
+            assert np.atleast_1d(inv_link_f).shape == np.atleast_1d(y).shape 
+            self._arguments_update(inv_link_f, y)
+            g = np.zeros((np.atleast_1d(y).shape[0], len(self._sym_theta)))
+            for i, theta in enumerate(self._sym_theta):
+                if self.missing_data:
+                    g[:, i:i+1] = np.where(np.isnan(y), self._missing_second_derivative_code[theta.name](**self._arguments), self._second_derivative_code[theta.name](**self._arguments))
+                else:
+                    g[:, i:i+1] = np.where(np.isnan(y), 0., self._second_derivative_code[theta.name](**self._arguments))
+            return g
+
+        def d2logpdf_dlink2_dtheta(self, inv_link_f, y, Y_metadata=None):
+            assert np.atleast_1d(inv_link_f).shape == np.atleast_1d(y).shape 
+            self._arguments_update(inv_link_f, y)
+            g = np.zeros((np.atleast_1d(y).shape[0], len(self._sym_theta)))
+            for i, theta in enumerate(self._sym_theta):
+                if self.missing_data:
+                    g[:, i:i+1] = np.where(np.isnan(y), self._missing_third_derivative_code[theta.name](**self._arguments), self._third_derivative_code[theta.name](**self._arguments))
+                else:
+                    g[:, i:i+1] = np.where(np.isnan(y), 0., self._third_derivative_code[theta.name](**self._arguments))
+            return g
+
+        def predictive_mean(self, mu, sigma, Y_metadata=None):
+            raise NotImplementedError
+
+        def predictive_variance(self, mu,variance, predictive_mean=None, Y_metadata=None):
+            raise NotImplementedError
+
+        def conditional_mean(self, gp):
+            raise NotImplementedError
+
+        def conditional_variance(self, gp):
+            raise NotImplementedError
+
+        def samples(self, gp, Y_metadata=None):
+            raise NotImplementedError

GPy/likelihoods/symbolic.py~

@@ -0,0 +1,234 @@
+# Copyright (c) 2014 GPy Authors
+# Licensed under the BSD 3-clause license (see LICENSE.txt)
+
+import numpy as np
+import sympy as sp
+from scipy import stats, special
+import scipy as sp
+import link_functions
+from scipy import stats, integrate
+from scipy.special import gammaln, gamma
+from likelihood import Likelihood
+from ..core.parameterization import Param
+from ..core.parameterization.transformations import Logexp
+
+class Symbolic(Likelihood):
+    """
+    Symbolic likelihood.
+
+    Likelihood where the form of the likelihood is provided by a sympy expression.
+
+    """
+    def __init__(self, likelihood=None, log_likelihood=None, gp_link=None, name='symbolic', log_concave=False):
+        if gp_link is None:
+            gp_link = link_functions.Identity()
+
+        if likelihood is None and log_likelihood is None:
+            raise ValueError, "You must provide an argument for the likelihood or the log likelihood."
+
+        super(Symbolic, self).__init__(gp_link, name=name)
+
+        if likelihood is None:
+            self._sp_likelihood = sp.exp(log_likelihood).simplify()
+            self._sp_log_likelihood = log_likelihood
+
+        if log_likelihood is None:
+            self._sp_likelihood = likelihood
+            self._sp_log_likelihood = sp.log(likelihood).simplify()
+
+        # extract parameter names from the covariance
+        # pull the variable names out of the symbolic covariance function.
+        sp_vars = [e for e in self._sp_likelihood.atoms() if e.is_Symbol]
+        # f subscript allows the likelihood of y to be dependent on multiple functions of f. The index of these functions would need to be specified in y_meta.
+        self._sp_f = sorted([e for e in sp_vars if e.name[0:2]=='f_'],key=lambda x:int(x.name[2:]))
+        self._sp_y = sorted([e for e in sp_vars if e.name=='y'],key=lambda x:int(x.name[2:]))
+        self._sp_theta = sorted([e for e in sp_vars if not (e.name[0:2]=='f_' or e.name=='y')],key=lambda e:e.name)
+
+        self.arg_list = self._sp_y + self._sp_f + self._sp_theta
+        # this gives us the arguments for first derivative
+        first_derivative_arguments = self._sp_f + self._sp_theta
+        second_derivative_arguments = {}
+        for arg in first_derivative_arguments:
+            if arg.name[0:2] == 'f_':
+                # take all second derivatives with respect to everything
+                second_derivative_arguments[arg.name] = first_derivative_arguments
+        second_derivative_arguments = self._sp_f + self._sp_theta
+        third_derivative_arguments = self._sp_f + self._sp_theta
+        self._likelihood_derivatives = {theta.name : sp.diff(self._sp_likelihood,theta).simplify() for theta in derivative_arguments}
+        self._log_likelihood_derivatives = {theta.name : sp.diff(self._sp_log_likelihood,theta).simplify() for theta in derivative_arguments}
+
+        # Add parameters to the model.
+        for theta in self._sp_theta:
+            val = 1.0
+            # TODO: what if user has passed a parameter vector, how should that be stored and interpreted? This is the old way before params class.
+            if param is not None:
+                if param.has_key(theta):
+                    val = param[theta]
+            setattr(self, theta.name, Param(theta.name, val, None))
+            self.add_parameters(getattr(self, theta.name))
+
+
+        # By default it won't be log concave. It would be nice to check for this somehow though!
+        self.log_concave = log_concave
+
+        # initialise code arguments
+        self._arguments = {} 
+
+        # generate the code for the likelihood and derivatives
+        self._gen_code()
+
+    def _gen_code(self):
+        # Potentially run theano here as an option.
+        self._likelihood_function = lambdify(self.arg_list, self._sp_likelihood, 'numpy')
+        self._log_likelihood_function = lambdify(self.arg_list, self._sp_log_likelihood, 'numpy')
+        # for derivatives we need gradient of the likelihood, gradient of log likelihood
+        for key in self.derivatives.keys():
+            setattr(self, '_log_likelihood_diff_' + key, lambdify(self.arg_list, self.derivatives[key], 'numpy'))
+            
+
+        pass
+
+    def parameters_changed(self):
+        pass
+
+    def update_gradients(self, grads):
+        """
+        Pull out the gradients, be careful as the order must match the order
+        in which the parameters are added
+        """
+        for grad, theta in zip(grads, self._sp_theta):
+            parameter = getattr(self, theta.name)
+            setattr(parameter, 'gradient', grad)
+
+    def _arguments_update(self, f, y):
+        """Set up argument lists for the derivatives."""
+        # Could check if this needs doing or not, there could
+        # definitely be some computational savings by checking for
+        # parameter updates here.
+        for i, f in enumerate(self._sp_f):
+            self._arguments[f.name] =  f[:, i][:, None]
+        for i, y in enumerate(self._sp_y):
+            self._arguments[y.name] = y[:, i][:, None]
+
+        for theta in self._sp_theta:
+            self._arguments[theta.name] = np.asarray(getattr(self, theta.name))
+
+    def pdf_link(self, inv_link_f, y, Y_metadata=None):
+        """
+        Likelihood function given inverse link of f.
+
+        :param inv_link_f: inverse link of latent variables.
+        :type inv_link_f: Nx1 array
+        :param y: data
+        :type y: Nx1 array
+        :param Y_metadata: Y_metadata which is not used in student t distribution
+        :returns: likelihood evaluated for this point
+        :rtype: float
+        """
+        assert np.atleast_1d(inv_link_f).shape == np.atleast_1d(y).shape
+        self._arguments_update(inv_link_f, y)
+        l = self._likelihood_function(**self._arguments)
+        return np.prod(l)
+
+    def logpdf_link(self, inv_link_f, y, Y_metadata=None):
+        """
+        Log Likelihood Function given inverse link of latent variables.
+
+        :param inv_inv_link_f: latent variables (inverse link of f)
+        :type inv_inv_link_f: Nx1 array
+        :param y: data
+        :type y: Nx1 array
+        :param Y_metadata: Y_metadata 
+        :returns: likelihood evaluated for this point
+        :rtype: float
+
+        """
+        assert np.atleast_1d(inv_link_f).shape == np.atleast_1d(y).shape
+        self._arguments_update(inv_link_f, y)
+        ll = self._log_likelihood_function(**self._arguments)
+        return np.sum(ll)
+
+    def dlogpdf_dlink(self, inv_link_f, y, Y_metadata=None):
+        """
+        Gradient of log likelihood with respect to the inverse link function.
+
+        :param inv_inv_link_f: latent variables (inverse link of f)
+        :type inv_inv_link_f: Nx1 array
+        :param y: data
+        :type y: Nx1 array
+        :param Y_metadata: Y_metadata 
+        :returns: gradient of likelihood with respect to each point.
+        :rtype: Nx1 array
+
+        """
+
+        assert np.atleast_1d(inv_link_f).shape == np.atleast_1d(y).shape
+        self._arguments_update(inv_link_f, y)
+        return self._log_likelihood_diff['f_0'](**self._arguments)
+
+    def d2logpdf_dlink2(self, inv_link_f, y, Y_metadata=None):
+        raise NotImplementedError
+
+    def d3logpdf_dlink3(self, inv_link_f, y, Y_metadata=None):
+        raise NotImplementedError
+
+    def dlogpdf_link_dtheta(self, inv_link_f, y, Y_metadata=None):
+        raise NotImplementedError
+
+    def dlogpdf_dlink_dtheta(self, inv_link_f, y, Y_metadata=None):
+        raise NotImplementedError
+
+    def d2logpdf_dlink2_dtheta(self, inv_link_f, y, Y_metadata=None):
+        raise NotImplementedError
+
+
+    def d2logpdf_dlink2(self, inv_link_f, y, Y_metadata=None):
+        """
+        Hessian at y, given link(f), w.r.t link(f)
+        i.e. second derivative logpdf at y given link(f_i) and link(f_j)  w.r.t link(f_i) and link(f_j)
+        The hessian will be 0 unless i == j
+
+        .. math::
+            \\frac{d^{2} \\ln p(y_{i}|\lambda(f_{i}))}{d^{2}\\lambda(f)} = \\frac{(v+1)((y_{i}-\lambda(f_{i}))^{2} - \\sigma^{2}v)}{((y_{i}-\lambda(f_{i}))^{2} + \\sigma^{2}v)^{2}}
+
+        :param inv_link_f: latent variables link(f)
+        :type inv_link_f: Nx1 array
+        :param y: data
+        :type y: Nx1 array
+        :param Y_metadata: Y_metadata which is not used in student t distribution
+        :returns: Diagonal of hessian matrix (second derivative of likelihood evaluated at points f)
+        :rtype: Nx1 array
+
+        .. Note::
+            Will return diagonal of hessian, since every where else it is 0, as the likelihood factorizes over cases
+            (the distribution for y_i depends only on link(f_i) not on link(f_(j!=i))
+        """
+        assert np.atleast_1d(inv_link_f).shape == np.atleast_1d(y).shape
+        e = y - inv_link_f
+        hess = ((self.v + 1)*(e**2 - self.v*self.sigma2)) / ((self.sigma2*self.v + e**2)**2)
+        return hess
+
+    def predictive_mean(self, mu, sigma, Y_metadata=None):
+        return self.gp_link.transf(mu) # only true in link is monotoci, which it is.
+
+    def predictive_variance(self, mu,variance, predictive_mean=None, Y_metadata=None):
+        if self.deg_free <2.:
+            return np.empty(mu.shape)*np.nan #not defined for small degress fo freedom
+        else:
+            return super(StudentT, self).predictive_variance(mu, variance, predictive_mean, Y_metadata)
+
+    def conditional_mean(self, gp):
+        return self.gp_link.transf(gp)
+
+    def conditional_variance(self, gp):
+        return self.deg_free/(self.deg_free - 2.)
+
+    def samples(self, gp, Y_metadata=None):
+        """
+        Returns a set of samples of observations based on a given value of the latent variable.
+
+        :param gp: latent variable
+        """
+        orig_shape = gp.shape
+        gp = gp.flatten()
+        pass

GPy/likelihoods/symlikelihood.py~

@@ -0,0 +1,318 @@
+# Copyright (c) 2012, 2013 Ricardo Andrade
+# Licensed under the BSD 3-clause license (see LICENSE.txt)
+
+import numpy as np
+import sympy as sp
+from scipy import stats, special
+import scipy as sp
+import link_functions
+from scipy import stats, integrate
+from scipy.special import gammaln, gamma
+from likelihood import Likelihood
+from ..core.parameterization import Param
+from ..core.parameterization.transformations import Logexp
+
+class Symbolic(Likelihood):
+    """
+    Symbolic likelihood.
+
+    Likelihood where the form of the likelihood is provided by a sympy expression.
+
+    """
+    def __init__(self, likelihood=None, log_likelihood=None, gp_link=None, name='symbolic', log_concave=False):
+        if gp_link is None:
+            gp_link = link_functions.Identity()
+
+        if likelihood is None and log_likelihood is None:
+            raise ValueError, "You must provide an argument for the likelihood or the log likelihood."
+
+        super(Symbolic, self).__init__(gp_link, name=name)
+
+        if likelihood is None:
+            self._sp_likelihood = sp.exp(log_likelihood).simplify()
+            self._sp_log_likelihood = log_likelihood
+
+        if log_likelihood is None:
+            self._sp_likelihood = likelihood
+            self._sp_log_likelihood = sp.log(likelihood).simplify()
+
+        # extract parameter names from the covariance
+        # pull the variable names out of the symbolic covariance function.
+        sp_vars = [e for e in self._sp_likelihood.atoms() if e.is_Symbol]
+        self._sp_f = sorted([e for e in sp_vars if e.name[0:2]=='f_'],key=lambda x:int(x.name[2:]))
+        self._sp_y = sorted([e for e in sp_vars if e.name[0:2]=='y_'],key=lambda x:int(x.name[2:]))
+        self._sp_theta = sorted([e for e in sp_vars if not (e.name[0:2]=='f_' or e.name[0:2]=='y_')],key=lambda e:e.name)
+
+        self.arg_list = self._sp_y + self._sp_f + self._sp_theta
+        first_derivative_arguments = self._sp_f + self._sp_theta
+        second_derivative_arguments = self._sp_f + self._sp_theta
+        third_derivative_arguments = self._sp_f + self._sp_theta
+        self._likelihood_derivatives = {theta.name : sp.diff(self._sp_likelihood,theta).simplify() for theta in derivative_arguments}
+        self._log_likelihood_derivatives = {theta.name : sp.diff(self._sp_log_likelihood,theta).simplify() for theta in derivative_arguments}
+
+        # Add parameters to the model.
+        for theta in self._sp_theta:
+            val = 1.0
+            # TODO: what if user has passed a parameter vector, how should that be stored and interpreted? This is the old way before params class.
+            if param is not None:
+                if param.has_key(theta):
+                    val = param[theta]
+            setattr(self, theta.name, Param(theta.name, val, None))
+            self.add_parameters(getattr(self, theta.name))
+
+
+        # By default it won't be log concave. It would be nice to check for this somehow though!
+        self.log_concave = log_concave
+
+        # initialise code arguments
+        self._arguments = {} 
+
+        # generate the code for the covariance functions
+        self._gen_code()
+
+    def _gen_code(self):
+        # Potentially run theano here as an option.
+        self._likelihood_function = lambdify(self.arg_list, self._sp_likelihood, 'numpy')
+        self._log_likelihood_function = lambdify(self.arg_list, self._sp_log_likelihood, 'numpy')
+        for key in self.derivatives.keys():
+            setattr(self, '_likelihood_diff_' + key, lambdify(self.arg_list, self.derivatives[key], 'numpy'))
+
+
+        pass
+
+    def parameters_changed(self):
+        pass
+
+    def update_gradients(self, grads):
+        """
+        Pull out the gradients, be careful as the order must match the order
+        in which the parameters are added
+        """
+        #self.sigma2.gradient = grads[0]
+        #self.v.gradient = grads[1]
+        pass
+
+    def _arguments_update(self, f, y):
+        """Set up argument lists for the derivatives."""
+        # Could check if this needs doing or not, there could
+        # definitely be some computational savings by checking for
+        # parameter updates here.
+        for i, f in enumerate(self._sp_f):
+            self._arguments[f.name] =  f[:, i][:, None]
+        for i, y in enumerate(self._sp_y):
+            self._arguments[f.name] = y[:, i][:, None]
+
+        for theta in self._sp_theta:
+            self._arguments[theta.name] = np.asarray(getattr(self, theta.name))
+
+    def pdf_link(self, link_f, y, Y_metadata=None):
+        """
+        Likelihood function given link(f)
+
+        .. math::
+            p(y_{i}|\\lambda(f_{i})) = \\frac{\\Gamma\\left(\\frac{v+1}{2}\\right)}{\\Gamma\\left(\\frac{v}{2}\\right)\\sqrt{v\\pi\\sigma^{2}}}\\left(1 + \\frac{1}{v}\\left(\\frac{(y_{i} - \\lambda(f_{i}))^{2}}{\\sigma^{2}}\\right)\\right)^{\\frac{-v+1}{2}}
+
+        :param link_f: latent variables link(f)
+        :type link_f: Nx1 array
+        :param y: data
+        :type y: Nx1 array
+        :param Y_metadata: Y_metadata which is not used in student t distribution
+        :returns: likelihood evaluated for this point
+        :rtype: float
+        """
+        assert np.atleast_1d(link_f).shape == np.atleast_1d(y).shape
+        self._arguments_update(link_f, y)
+        l = self._likelihood_function(**self._arguments)
+        return np.prod(l)
+
+    def logpdf_link(self, link_f, y, Y_metadata=None):
+        """
+        Log Likelihood Function given link(f)
+
+        .. math::
+            \\ln p(y_{i}|\lambda(f_{i})) = \\ln \\Gamma\\left(\\frac{v+1}{2}\\right) - \\ln \\Gamma\\left(\\frac{v}{2}\\right) - \\ln \\sqrt{v \\pi\\sigma^{2}} - \\frac{v+1}{2}\\ln \\left(1 + \\frac{1}{v}\\left(\\frac{(y_{i} - \lambda(f_{i}))^{2}}{\\sigma^{2}}\\right)\\right)
+
+        :param link_f: latent variables (link(f))
+        :type link_f: Nx1 array
+        :param y: data
+        :type y: Nx1 array
+        :param Y_metadata: Y_metadata which is not used in student t distribution
+        :returns: likelihood evaluated for this point
+        :rtype: float
+
+        """
+        assert np.atleast_1d(link_f).shape == np.atleast_1d(y).shape
+        self._arguments_update(link_f, y)
+        ll = self._log_likelihood_function(**self._arguments)
+        return np.sum(ll)
+
+    def dlogpdf_dlink(self, link_f, y, Y_metadata=None):
+        """
+        Gradient of the log likelihood function at y, given link(f) w.r.t link(f)
+
+        .. math::
+            \\frac{d \\ln p(y_{i}|\lambda(f_{i}))}{d\\lambda(f)} = \\frac{(v+1)(y_{i}-\lambda(f_{i}))}{(y_{i}-\lambda(f_{i}))^{2} + \\sigma^{2}v}
+
+        :param link_f: latent variables (f)
+        :type link_f: Nx1 array
+        :param y: data
+        :type y: Nx1 array
+        :param Y_metadata: Y_metadata which is not used in student t distribution
+        :returns: gradient of likelihood evaluated at points
+        :rtype: Nx1 array
+
+        """
+        assert np.atleast_1d(link_f).shape == np.atleast_1d(y).shape
+        e = y - link_f
+        grad = ((self.v + 1) * e) / (self.v * self.sigma2 + (e**2))
+        return grad
+
+    def d2logpdf_dlink2(self, link_f, y, Y_metadata=None):
+        """
+        Hessian at y, given link(f), w.r.t link(f)
+        i.e. second derivative logpdf at y given link(f_i) and link(f_j)  w.r.t link(f_i) and link(f_j)
+        The hessian will be 0 unless i == j
+
+        .. math::
+            \\frac{d^{2} \\ln p(y_{i}|\lambda(f_{i}))}{d^{2}\\lambda(f)} = \\frac{(v+1)((y_{i}-\lambda(f_{i}))^{2} - \\sigma^{2}v)}{((y_{i}-\lambda(f_{i}))^{2} + \\sigma^{2}v)^{2}}
+
+        :param link_f: latent variables link(f)
+        :type link_f: Nx1 array
+        :param y: data
+        :type y: Nx1 array
+        :param Y_metadata: Y_metadata which is not used in student t distribution
+        :returns: Diagonal of hessian matrix (second derivative of likelihood evaluated at points f)
+        :rtype: Nx1 array
+
+        .. Note::
+            Will return diagonal of hessian, since every where else it is 0, as the likelihood factorizes over cases
+            (the distribution for y_i depends only on link(f_i) not on link(f_(j!=i))
+        """
+        assert np.atleast_1d(link_f).shape == np.atleast_1d(y).shape
+        e = y - link_f
+        hess = ((self.v + 1)*(e**2 - self.v*self.sigma2)) / ((self.sigma2*self.v + e**2)**2)
+        return hess
+
+    def d3logpdf_dlink3(self, link_f, y, Y_metadata=None):
+        """
+        Third order derivative log-likelihood function at y given link(f) w.r.t link(f)
+
+        .. math::
+            \\frac{d^{3} \\ln p(y_{i}|\lambda(f_{i}))}{d^{3}\\lambda(f)} = \\frac{-2(v+1)((y_{i} - \lambda(f_{i}))^3 - 3(y_{i} - \lambda(f_{i})) \\sigma^{2} v))}{((y_{i} - \lambda(f_{i})) + \\sigma^{2} v)^3}
+
+        :param link_f: latent variables link(f)
+        :type link_f: Nx1 array
+        :param y: data
+        :type y: Nx1 array
+        :param Y_metadata: Y_metadata which is not used in student t distribution
+        :returns: third derivative of likelihood evaluated at points f
+        :rtype: Nx1 array
+        """
+        assert np.atleast_1d(link_f).shape == np.atleast_1d(y).shape
+        e = y - link_f
+        d3lik_dlink3 = ( -(2*(self.v + 1)*(-e)*(e**2 - 3*self.v*self.sigma2)) /
+                       ((e**2 + self.sigma2*self.v)**3)
+                    )
+        return d3lik_dlink3
+
+    def dlogpdf_link_dvar(self, link_f, y, Y_metadata=None):
+        """
+        Gradient of the log-likelihood function at y given f, w.r.t variance parameter (t_noise)
+
+        .. math::
+            \\frac{d \\ln p(y_{i}|\lambda(f_{i}))}{d\\sigma^{2}} = \\frac{v((y_{i} - \lambda(f_{i}))^{2} - \\sigma^{2})}{2\\sigma^{2}(\\sigma^{2}v + (y_{i} - \lambda(f_{i}))^{2})}
+
+        :param link_f: latent variables link(f)
+        :type link_f: Nx1 array
+        :param y: data
+        :type y: Nx1 array
+        :param Y_metadata: Y_metadata which is not used in student t distribution
+        :returns: derivative of likelihood evaluated at points f w.r.t variance parameter
+        :rtype: float
+        """
+        assert np.atleast_1d(link_f).shape == np.atleast_1d(y).shape
+        e = y - link_f
+        dlogpdf_dvar = self.v*(e**2 - self.sigma2)/(2*self.sigma2*(self.sigma2*self.v + e**2))
+        return np.sum(dlogpdf_dvar)
+
+    def dlogpdf_dlink_dvar(self, link_f, y, Y_metadata=None):
+        """
+        Derivative of the dlogpdf_dlink w.r.t variance parameter (t_noise)
+
+        .. math::
+            \\frac{d}{d\\sigma^{2}}(\\frac{d \\ln p(y_{i}|\lambda(f_{i}))}{df}) = \\frac{-2\\sigma v(v + 1)(y_{i}-\lambda(f_{i}))}{(y_{i}-\lambda(f_{i}))^2 + \\sigma^2 v)^2}
+
+        :param link_f: latent variables link_f
+        :type link_f: Nx1 array
+        :param y: data
+        :type y: Nx1 array
+        :param Y_metadata: Y_metadata which is not used in student t distribution
+        :returns: derivative of likelihood evaluated at points f w.r.t variance parameter
+        :rtype: Nx1 array
+        """
+        assert np.atleast_1d(link_f).shape == np.atleast_1d(y).shape
+        e = y - link_f
+        dlogpdf_dlink_dvar = (self.v*(self.v+1)*(-e))/((self.sigma2*self.v + e**2)**2)
+        return dlogpdf_dlink_dvar
+
+    def d2logpdf_dlink2_dvar(self, link_f, y, Y_metadata=None):
+        """
+        Gradient of the hessian (d2logpdf_dlink2) w.r.t variance parameter (t_noise)
+
+        .. math::
+            \\frac{d}{d\\sigma^{2}}(\\frac{d^{2} \\ln p(y_{i}|\lambda(f_{i}))}{d^{2}f}) = \\frac{v(v+1)(\\sigma^{2}v - 3(y_{i} - \lambda(f_{i}))^{2})}{(\\sigma^{2}v + (y_{i} - \lambda(f_{i}))^{2})^{3}}
+
+        :param link_f: latent variables link(f)
+        :type link_f: Nx1 array
+        :param y: data
+        :type y: Nx1 array
+        :param Y_metadata: Y_metadata which is not used in student t distribution
+        :returns: derivative of hessian evaluated at points f and f_j w.r.t variance parameter
+        :rtype: Nx1 array
+        """
+        assert np.atleast_1d(link_f).shape == np.atleast_1d(y).shape
+        e = y - link_f
+        d2logpdf_dlink2_dvar = ( (self.v*(self.v+1)*(self.sigma2*self.v - 3*(e**2)))
+                              / ((self.sigma2*self.v + (e**2))**3)
+                           )
+        return d2logpdf_dlink2_dvar
+
+    def dlogpdf_link_dtheta(self, f, y, Y_metadata=None):
+        dlogpdf_dvar = self.dlogpdf_link_dvar(f, y, Y_metadata=Y_metadata)
+        dlogpdf_dv = np.zeros_like(dlogpdf_dvar) #FIXME: Not done yet
+        return np.hstack((dlogpdf_dvar, dlogpdf_dv))
+
+    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_dv = np.zeros_like(dlogpdf_dlink_dvar) #FIXME: Not done yet
+        return np.hstack((dlogpdf_dlink_dvar, dlogpdf_dlink_dv))
+
+    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_dv = np.zeros_like(d2logpdf_dlink2_dvar) #FIXME: Not done yet
+        return np.hstack((d2logpdf_dlink2_dvar, d2logpdf_dlink2_dv))
+
+    def predictive_mean(self, mu, sigma, Y_metadata=None):
+        return self.gp_link.transf(mu) # only true in link is monotoci, which it is.
+
+    def predictive_variance(self, mu,variance, predictive_mean=None, Y_metadata=None):
+        if self.deg_free <2.:
+            return np.empty(mu.shape)*np.nan #not defined for small degress fo freedom
+        else:
+            return super(StudentT, self).predictive_variance(mu, variance, predictive_mean, Y_metadata)
+
+    def conditional_mean(self, gp):
+        return self.gp_link.transf(gp)
+
+    def conditional_variance(self, gp):
+        return self.deg_free/(self.deg_free - 2.)
+
+    def samples(self, gp, Y_metadata=None):
+        """
+        Returns a set of samples of observations based on a given value of the latent variable.
+
+        :param gp: latent variable
+        """
+        orig_shape = gp.shape
+        gp = gp.flatten()
+        pass

GPy/log_like_grad.txt

@@ -0,0 +1 @@
+core/model.py:    def get(self,name):

GPy/mappings/symbolic.py~

@@ -0,0 +1,149 @@
+# Copyright (c) 2014 GPy Authors
+# Licensed under the BSD 3-clause license (see LICENSE.txt)
+
+try:
+    import sympy as sym
+    sympy_available=True
+    from sympy.utilities.lambdify import lambdify
+    from GPy.util.symbolic import stabilise
+except ImportError:
+    sympy_available=False
+
+from ..core.mapping import Mapping, Bijective_mapping
+import numpy as np
+from scipy.special import gammaln, gamma, erf, erfc, erfcx, polygamma
+from GPy.util.functions import normcdf, normcdfln, logistic, logisticln
+from ..core.parameterization import Param
+
+
+if sympy_available:
+    class Symbolic(Mapping):
+        """
+        Symbolic likelihood.
+
+        Likelihood where the form of the likelihood is provided by a sympy expression.
+
+        """
+        def __init__(self, f=None, logZ=None, name='symbolic', param=None, func_modules=[]):
+
+
+            if f is None:
+                raise ValueError, "You must provide an argument for the function."
+
+            self.func_modules = func_modules
+            self.func_modules += [{'gamma':gamma,
+                                   'gammaln':gammaln,
+                                   'erf':erf, 'erfc':erfc,
+                                   'erfcx':erfcx,
+                                   'polygamma':polygamma,
+                                   'normcdf':normcdf,
+                                   'normcdfln':normcdfln,
+                                   'logistic':logistic,
+                                   'logisticln':logisticln},
+                                  'numpy']
+
+            super(Symbolic, self).__init__(gp_link, name=name)
+            self.symbolic['function'] = f
+
+            # pull the variable names out of the symbolic pdf
+            sym_vars = [e for e in f.atoms() if e.is_Symbol]
+            self.symbolic['x'] = [e for e in sym_vars if e.name[:2]=='x_']
+            if not self.symbolic['f']:
+                raise ValueError('No variable x in f().')
+            self.symbolic['theta'] = sorted([e for e in sym_vars if not e.name[:2]=='x_'],key=lambda e:e.name)
+
+            theta_names = [theta.name for theta in self.symbolic['theta']
+
+            # These are all the arguments need to compute the mapping.
+            self.arg_list = self.symbolic['x'] + self.symbolic['theta']
+
+            # these are arguments for computing derivatives.
+            derivative_arguments = self.arg_list
+
+            # Do symbolic work to compute derivatives.
+            self.symbolic['derivatives'] = {theta.name : stabilise(sym.diff(f,theta)) for theta in derivative_arguments}
+            
+            # Add parameters to the model.
+            for theta in self._sym_theta:
+                val = 1.0
+                # TODO: need to decide how to handle user passing values for the se parameter vectors.
+                if param is not None:
+                    if param.has_key(theta.name):
+                        val = param[theta.name]
+                setattr(self, theta.name, Param(theta.name, val, None))
+                self.add_parameters(getattr(self, theta.name))
+
+            # initialise code arguments
+            self._arguments = {} 
+
+            # generate the code for the pdf and derivatives
+            self._gen_code()
+
+        def _gen_code(self):
+            """Generate the code from the symbolic parts that will be used for likleihod computation."""
+
+            self.code = GPy.util.function.gen_code(self.symbolic)
+
+        def parameters_changed(self):
+            # do all the precomputation codes.
+            for variable, code in self.code['precompute'].items():
+                self.setattr(variable, eval(code, self.namespace))
+
+        def update_gradients(self, grads):
+            """
+            """
+            for param, code in self.code['derivatives'].items():
+                self.getattr(param).setattr('gradient',
+                                            eval(code, self.namespace))
+            pass
+
+        def _arguments_update(self, x):
+            """Set up argument lists for the derivatives."""
+            # If we do make use of Theano, then at this point we would
+            # need to do a lot of precomputation to ensure that the
+            # likelihoods and gradients are computed together, then check
+            # for parameter changes before updating.
+            for i, fvar in enumerate(self._sym_x):
+                self._arguments[fvar.name] =  x[:, i]
+            for theta in self._sym_theta:
+                self._arguments[theta.name] = np.asarray(getattr(self, theta.name))
+
+        def f(self, x):
+            """
+            Likelihood function given inverse link of f.
+
+            :param inv_link_f: inverse link of latent variables.
+            :type inv_link_f: Nx1 array
+            :param y: data
+            :type y: Nx1 array
+            :param Y_metadata: Y_metadata which is not used in student t distribution
+            :returns: likelihood evaluated for this point
+            :rtype: float
+            """
+            self._arguments_update(inv_link_f, y)
+            return self._f_function(x)
+
+
+        def df_dX(self, X):
+            """
+            Gradient of log likelihood with respect to the inverse link function.
+
+            :param inv_inv_link_f: latent variables (inverse link of f)
+            :type inv_inv_link_f: Nx1 array
+            :param y: data
+            :type y: Nx1 array
+            :param Y_metadata: Y_metadata 
+            :returns: gradient of likelihood with respect to each point.
+            :rtype: Nx1 array
+
+            """
+            self._arguments_update(X)
+            return self._derivative_code['X'](**self._arguments)
+
+        def df_dtheta(self, X):
+            self._arguments_update(X)
+            g = np.zeros((np.atleast_1d(X).shape[0], len(self._sym_theta)))
+            for i, theta in enumerate(self._sym_theta):
+                g[:, i:i+1] = self._derivative_code[theta.name](**self._arguments)
+            return g.sum(0)
+

GPy/util/datasets.py

@@ -405,11 +405,11 @@ def lee_yeast_ChIP(data_set='lee_yeast_ChIP'):
     import zipfile
     dir_path = os.path.join(data_path, data_set)
     filename = os.path.join(dir_path, 'binding_by_gene.tsv')
-    X = read_csv(filename, header=1, index_col=0, sep='\t')
-    transcription_factors = [col for col in X.columns if col[:7] != 'Unnamed']    
-    annotations = X[['Unnamed: 1', 'Unnamed: 2', 'Unnamed: 3']]
-    X = X[transcription_factors]
-    return data_details_return({'annotations' : annotations, 'X' : X, 'transcription_factors': transcription_factors}, data_set)
+    S = read_csv(filename, header=1, index_col=0, sep='\t')
+    transcription_factors = [col for col in S.columns if col[:7] != 'Unnamed']    
+    annotations = S[['Unnamed: 1', 'Unnamed: 2', 'Unnamed: 3']]
+    S = S[transcription_factors]
+    return data_details_return({'annotations' : annotations, 'Y' : S, 'transcription_factors': transcription_factors}, data_set)
     
 
 def fruitfly_tomancak(data_set='fruitfly_tomancak', gene_number=None):

GPy/util/osu_accad/camper_04TXT.ZIP

@@ -0,0 +1,213 @@
+<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
+<html xmlns="http://www.w3.org/1999/xhtml">
+<head>
+<base href="http://accad.osu.edu/" />
+<meta http-equiv="Content-Type" content="text/html; charset=UTF-8" />
+<title>ACCAD | Page Not Found</title>
+<link rel="alternate" type="application/rss+xml" title="ACCAD RSS feed" href="125.html">
+
+<!-- OSU Navigation Bar: Required CSS. -->
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+<!-- OSU Navigation Bar: Required Conditional CSS. -->
+<!--[if lte IE 6]>  
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+<![endif]-->
+<!--[if IE 7]>  
+<link rel="stylesheet" type="text/css" href="/assets/osu-navbar-media/css/navbar-ie7.css" />
+<![endif]-->
+  
+<style type="text/css">
+<!--#page-content {width: 100%;}-->
+</style>
+
+<!-- OSU: Optional Favicon -->
+<link rel="icon" href="/assets/osu-navbar-media/img/favicon.ico" type="image/x-icon" />
+<link rel="shortcut icon" href="/assets/osu-navbar-media/img/favicon.ico" type="image/x-icon" /> 
+    
+<!-- Blueprint: Base CSS -->
+<link href="/assets/css/screen.css" rel="stylesheet" type="text/css" media="screen, projection" />
+<link href="/assets/css/print.css" rel="stylesheet" type="text/css" media="print" />
+<!-- site specific styles -->
+<link href="/assets/css/accad_styles.css" rel="stylesheet" type="text/css" media="screen, projection" />
+
+<!-- [if IE]>
+<link href="/assets/css/ie.css" rel="stylesheet" type="text/css" media="screen, projection" />
+<![endif]--> 
+
+<!-- Base Javascript -->
+<script type="text/javascript" src="http://ajax.googleapis.com/ajax/libs/jquery/1.4/jquery.min.js"></script> <!-- base jquery library -->
+<!-- Drop-down menu -->
+<script type="text/javascript" src="/assets/js/hoverIntent.js"></script>
+<script type="text/javascript" src="/assets/js/superfish.js"></script>
+<script type="text/javascript">
+// initialize plugins
+		jQuery(function(){
+			jQuery('ul#topnav').superfish({ 
+            delay: 1000,                          // one second delay on mouseout 
+            animation: {height:'show'},    // slide-down animation 
+            speed:'fast',                           // faster animation speed 
+            dropShadows: false              // disable drop shadows 
+        }); 
+    }); 
+ 
+</script>
+
+<script type="text/javascript">
+
+  var _gaq = _gaq || [];
+  _gaq.push(['_setAccount', 'UA-22129230-1']);
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+    var s = document.getElementsByTagName?('script')[0]; s.parentNode.insertBefore(ga, s);
+  })();
+
+</script> 
+
+</head>
+
+<body>
+
+<div id="osu_navbar">
+	<div id="osu-Navbar">
+ 	<div class="container">
+      <p>
+        <a href="#page-content" id="skip" class="osu-semantic">skip to main content</a>
+      </p>
+      <h2 class="osu-semantic">OSU Navigation Bar</h2>
+      <div id="osu-NavbarBreadcrumb">
+        <p id="osu">
+          <a title="The Ohio State University homepage" href="http://www.osu.edu/">The Ohio State University</a>
+        </p>
+        <p id="site-name">
+           Arts and Sciences
+        </p>
+      </div>
+      <div id="osu-NavbarLinks">
+        <ul>
+          <li><a href="http://www.osu.edu/help.php" title="OSU Help">Help</a></li>
+          <li><a href="http://buckeyelink.osu.edu/" title="Buckeye Link">Buckeye Link</a></li>
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+          <li><a href="http://www.osu.edu/search.php" title="Ohio State's main search page">Search Ohio State</a>
+          </li>       
+        </ul>
+      </div>
+		</div>
+   </div>  
+</div>
+
+<div id="header" style="z-index:99999;">
+<div class="container">
+	<h1 class="osu-semantic">ACCAD Advanced Computing Center for the Arts and Design</h1>
+<a href="index.html" title="ACCAD Home"><img src="/assets/images/site/accad_name.png" class="accad_name" alt="Advanced Computing Center for the Arts and Design"/></a>
+<a href="http://www.osu.edu"><img src="/assets/images/site/logo-ohiostate.gif" class="osu_logo" alt="The Ohio State University" /></a>
+</div><!-- end container -->
+</div><!-- end header -->
+
+<div id="global_nav">
+<div class="container">
+   <ul id="topnav">
+			<li ><a href="/about_us.html"  >About Us</a></li>
+			<li ><a href="researchmain/gallery.html"  >Research</a></li>
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+
+</ul>
+</div><!-- end container -->
+</div><!-- end global_nav -->
+
+
+
+<div id="content" class="container">
+	
+	<div id="subnav" class="span-6 prepend-1 column first">
+
+	</div>
+	<!-- end subnav -->
+  
+  <div id="page_body" class="span-15 prepend-1 column last">
+<h2>Page Not Found</h2>
+<h4>Sorry, we couldn't find the page you are looking for</h4>
+<p>The page may have moved, or been deleted. Please use the upper navigation menu to find what you are looking for, and don't forget to update your bookmarks. Thanks for your understanding.</p>
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+  
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+       1224 Kinnear Rd., Columbus, OH 43212
+<br>accad [at] accad [dot] osu [dot] edu
+
+<br><img src="assets/images/Footer_underline2.png"></td>
+<td style="text-align: left;" width="470px">        
+            <div id="searchbox">                
+                
+<form id="ajaxSearch_form" action="316.html" method="post">
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+      <input id="ajaxSearch_input" class="cleardefault" type="text" name="search" value="Search here..." onfocus="this.value=(this.value=='Search here...')? '' : this.value ;" />
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+" target="_blank">Privacy Policy</a>
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+</span></td>
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+</table>
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+</html>

GPy/util/osu_accad/connections.txt

@@ -0,0 +1,22 @@
+LFHD, RFHD
+RFHD, RBHD
+RBHD, LBHD
+LBHD, LFHD
+LELB, LWRB
+LWRB, LFIN
+LELB, LSHO
+LSHO, RSHO
+RSHO, STRN
+LSHO, STRN
+RSHO, RELB
+RELB, RWRB
+RWRB, RFIN
+LSHO, LFWT
+RSHO, RFWT
+LFWT, RFWT
+LFWT, LKNE
+RFWT, RKNE
+LKNE, LHEE
+RKNE, RHEE
+RMT5, RHEE
+LMT5, LHEE

GPy/util/osu_run1/Aug210107.txt

@@ -0,0 +1,266 @@
+Field	Time	EricAutoLabel:C7:X	EricAutoLabel:C7:Y	EricAutoLabel:C7:Z	EricAutoLabel:CLAV:X	EricAutoLabel:CLAV:Y	EricAutoLabel:CLAV:Z	EricAutoLabel:LANK:X	EricAutoLabel:LANK:Y	EricAutoLabel:LANK:Z	EricAutoLabel:LBHD:X	EricAutoLabel:LBHD:Y	EricAutoLabel:LBHD:Z	EricAutoLabel:LBWT:X	EricAutoLabel:LBWT:Y	EricAutoLabel:LBWT:Z	EricAutoLabel:LELB:X	EricAutoLabel:LELB:Y	EricAutoLabel:LELB:Z	EricAutoLabel:LFHD:X	EricAutoLabel:LFHD:Y	EricAutoLabel:LFHD:Z	EricAutoLabel:LFIN:X	EricAutoLabel:LFIN:Y	EricAutoLabel:LFIN:Z	EricAutoLabel:LFRM:X	EricAutoLabel:LFRM:Y	EricAutoLabel:LFRM:Z	EricAutoLabel:LFWT:X	EricAutoLabel:LFWT:Y	EricAutoLabel:LFWT:Z	EricAutoLabel:LHEE:X	EricAutoLabel:LHEE:Y	EricAutoLabel:LHEE:Z	EricAutoLabel:LKNE:X	EricAutoLabel:LKNE:Y	EricAutoLabel:LKNE:Z	EricAutoLabel:LMT5:X	EricAutoLabel:LMT5:Y	EricAutoLabel:LMT5:Z	EricAutoLabel:LSHN:X	EricAutoLabel:LSHN:Y	EricAutoLabel:LSHN:Z	EricAutoLabel:LSHO:X	EricAutoLabel:LSHO:Y	EricAutoLabel:LSHO:Z	EricAutoLabel:LTHI:X	EricAutoLabel:LTHI:Y	EricAutoLabel:LTHI:Z	EricAutoLabel:LTOE:X	EricAutoLabel:LTOE:Y	EricAutoLabel:LTOE:Z	EricAutoLabel:LUPA:X	EricAutoLabel:LUPA:Y	EricAutoLabel:LUPA:Z	EricAutoLabel:LWRA:X	EricAutoLabel:LWRA:Y	EricAutoLabel:LWRA:Z	EricAutoLabel:LWRB:X	EricAutoLabel:LWRB:Y	EricAutoLabel:LWRB:Z	EricAutoLabel:RANK:X	EricAutoLabel:RANK:Y	EricAutoLabel:RANK:Z	EricAutoLabel:RBAC:X	EricAutoLabel:RBAC:Y	EricAutoLabel:RBAC:Z	EricAutoLabel:RBHD:X	EricAutoLabel:RBHD:Y	EricAutoLabel:RBHD:Z	EricAutoLabel:RBWT:X	EricAutoLabel:RBWT:Y	EricAutoLabel:RBWT:Z	EricAutoLabel:RELB:X	EricAutoLabel:RELB:Y	EricAutoLabel:RELB:Z	EricAutoLabel:RFHD:X	EricAutoLabel:RFHD:Y	EricAutoLabel:RFHD:Z	EricAutoLabel:RFIN:X	EricAutoLabel:RFIN:Y	EricAutoLabel:RFIN:Z	EricAutoLabel:RFRM:X	EricAutoLabel:RFRM:Y	EricAutoLabel:RFRM:Z	EricAutoLabel:RFWT:X	EricAutoLabel:RFWT:Y	EricAutoLabel:RFWT:Z	EricAutoLabel:RHEE:X	EricAutoLabel:RHEE:Y	EricAutoLabel:RHEE:Z	EricAutoLabel:RKNE:X	EricAutoLabel:RKNE:Y	EricAutoLabel:RKNE:Z	EricAutoLabel:RMT5:X	EricAutoLabel:RMT5:Y	EricAutoLabel:RMT5:Z	EricAutoLabel:RSHN:X	EricAutoLabel:RSHN:Y	EricAutoLabel:RSHN:Z	EricAutoLabel:RSHO:X	EricAutoLabel:RSHO:Y	EricAutoLabel:RSHO:Z	EricAutoLabel:RTHI:X	EricAutoLabel:RTHI:Y	EricAutoLabel:RTHI:Z	EricAutoLabel:RTOE:X	EricAutoLabel:RTOE:Y	EricAutoLabel:RTOE:Z	EricAutoLabel:RUPA:X	EricAutoLabel:RUPA:Y	EricAutoLabel:RUPA:Z	EricAutoLabel:RWRA:X	EricAutoLabel:RWRA:Y	EricAutoLabel:RWRA:Z	EricAutoLabel:RWRB:X	EricAutoLabel:RWRB:Y	EricAutoLabel:RWRB:Z	EricAutoLabel:STRN:X	EricAutoLabel:STRN:Y	EricAutoLabel:STRN:Z	EricAutoLabel:T10:X	EricAutoLabel:T10:Y	EricAutoLabel:T10:Z
+1	0.0000	-2114.7	-1520.2	1369.2	-9999.99	-9999.99	-9999.99	-2080.1	-1275.6	108.89	-2053.5	-1435.7	1485.6	-2279.6	-1465.8	934.99	-2175.1	-1228.9	999.83	-1937.4	-1376.6	1538.5	-2080.3	-1212.9	708.05	-2174.2	-1234.3	880.67	-2101.2	-1402.6	839.51	-2123.7	-1337.2	27.412	-2068.7	-1303.1	456.76	-1986.1	-1198.3	30.383	-2090.1	-1274.2	329.88	-2076.5	-1328.4	1341.4	-2081	-1315.8	688.45	-1907.8	-1219.2	57.456	-2144.7	-1246.1	1186.5	-2044.7	-1265.6	791.05	-2159.9	-1202	791.99	-2307.5	-1779.3	98.701	-2154.1	-1623.9	1289.1	-2002.2	-1571.7	1479.5	-2243.7	-1639.3	955.61	-1975	-1802.8	1012	-1856.9	-1482.8	1545.2	-1939.7	-1781.1	682.85	-1946.1	-1802.3	835.1	-2033.6	-1668.4	848.59	-2381.8	-1723.1	32.929	-2216.9	-1767.9	453.96	-2196.4	-1800.4	31.401	-2282.2	-1790.9	253.92	-1987.4	-1655.2	1329	-2129	-1749.6	592.38	-2107.2	-1753.5	46.253	-1970.5	-1731.1	1254	-1904.1	-1724.2	778.83	-1990.1	-1828.3	765.59	-9999.99	-9999.99	-9999.99	-2227.4	-1551.7	1212.3
+2	0.0083	-2110.4	-1516.5	1368	-9999.99	-9999.99	-9999.99	-2079.8	-1275.4	109.23	-2049.1	-1432.1	1483.7	-2276.3	-1462.8	933.8	-2173.6	-1225.8	999.49	-1931.3	-1373.2	1536.2	-2082.4	-1211.2	706.7	-2174	-1232	879.83	-2092.2	-1399.4	838.66	-2124	-1337.3	28.006	-2066.4	-1302	458.03	-1985.9	-1198.7	30.128	-2087.8	-1273.1	330.31	-2072	-1324.7	1339.9	-2077.8	-1313.6	688.45	-1907.7	-1219.6	57.456	-2141.3	-1243	1185.5	-2045.4	-1264.3	788.85	-2159.3	-1199.8	790.29	-2307.6	-1779.3	98.532	-2149.6	-1620.4	1288	-1997.5	-1567.9	1477.5	-2241.1	-1636.3	955.27	-1970.3	-1800.1	1010.7	-1852.3	-1479	1543.4	-1936.3	-1775.8	681.66	-1942.1	-1798.8	834.17	-2030.9	-1666.1	847.15	-2381.8	-1723.2	32.929	-2217.3	-1767.6	454.13	-2196.1	-1800.7	31.062	-2282.4	-1790.9	254.01	-1982.4	-1651.3	1327.4	-2128.6	-1748.5	592.21	-2107.4	-1753.8	46.338	-1965.4	-1727.7	1252.7	-1900.9	-1719.2	777.9	-1984.7	-1824.1	764.15	-1938.4	-1463.5	1078.3	-2223.2	-1548.4	1211.4
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+237	1.9667	1684.5	1238.5	1422.7	1862.8	1343.5	1384.1	1553.1	1221.8	154.97	1676.6	1313.4	1575.1	1629.6	1305	991.68	1735.8	1565.9	1110.8	1775.7	1361.9	1663.1	2041.8	1551.6	1133.2	1852	1552.1	1082.7	1780.5	1441.4	908.77	1502.2	1129.3	128.49	1648.6	1348	470.34	1601.4	1257.8	30.383	1595.3	1320.3	352.2	1681.8	1424.1	1445.7	1718.3	1446.1	698.55	1689.9	1245.3	46.253	1664.4	1520.2	1283.3	1962.1	1500	1186.6	1941.9	1580.4	1088.2	1770.9	1117.9	208.01	1678.9	1154.6	1336.7	1737	1181.7	1554.1	1726.6	1146	968.85	1813.1	945.6	1174.5	1857.7	1260.2	1664.9	1999.8	1063.4	951.96	1915.1	1001.4	1044.1	1924.3	1218.9	901.72	1662.1	1132.2	183.23	1960.2	1219.1	492.06	1834.3	1133.2	93.015	1852	1143.8	339.13	1832	1139.4	1428.9	1987.7	1222.7	630.65	1889.3	1207.8	59.153	1851.2	1063.4	1382.6	1968.3	1087.6	1055.1	1916.9	1011.9	961.38	1926.4	1373.8	1205.5	1647.6	1215.6	1238.4
+238	1.9750	1703.6	1251.4	1428.3	1882	1353.7	1388.9	1556.8	1231.1	163.03	1696.3	1323.5	1579.1	1647.8	1319.2	996.43	1757.9	1584.6	1122.6	1795	1372.3	1667.1	2063.6	1560	1139.2	1872	1567.3	1091.1	1798.5	1455	914.54	1505.1	1138.9	140.97	1660.6	1359.5	476.11	1602.3	1259.9	31.656	1603.8	1332	359.76	1703.8	1435.4	1453.5	1733.8	1458.6	702.79	1690.2	1248.3	46.592	1685.8	1534.5	1293.6	1982.2	1509.9	1193.1	1963.2	1593.2	1096.7	1813.7	1154.5	192.74	1696.3	1167.7	1341.8	1755.7	1192.6	1557.8	1745.6	1161.1	974.11	1825.1	956.63	1182.6	1876.2	1270.6	1668.8	2014.6	1071.2	960.87	1928.3	1010.7	1052.7	1942	1233.6	907.24	1706.8	1169.3	161.93	1984.2	1238.8	495.2	1883.7	1175.9	81.982	1886.3	1172.5	330.73	1848.3	1151.2	1434.2	2009.1	1240.8	638.04	1940.6	1253.3	55.164	1868.5	1075.3	1389.5	1984.5	1094.6	1064.9	1930.2	1022.3	969.53	1946.1	1384.3	1211.2	1662.6	1228.6	1245
+239	1.9833	1722.9	1263.7	1433.5	1901.8	1364.4	1394	1560.2	1241.3	171.43	1715.4	1333.8	1582.4	1667.6	1333.3	1000.5	1778.5	1601.5	1132.3	1814.1	1382.7	1670.9	2084.2	1569.2	1142.6	1891.7	1581.9	1098.4	1817.2	1468.6	921.16	1507.9	1149	153.53	1672.3	1371.8	481.63	1603.8	1263.3	33.947	1612.6	1343.9	367.14	1725.2	1446.4	1460.7	1749.8	1471.6	706.95	1691.2	1253.3	48.12	1706.9	1548.9	1303.6	2002.3	1520.8	1198.3	1983.4	1606.1	1103.1	1857.8	1191.5	178.56	1718.7	1181	1345.3	1774.5	1202.3	1561.6	1763.7	1174.9	978.7	1836.9	967.75	1190.2	1894.6	1280.6	1672.2	2030	1079	969.02	1941.8	1020.1	1060.4	1961	1248.3	912.58	1753.2	1207.7	142.58	2007.6	1257.4	498.26	1934.4	1220.6	73.326	1921.4	1201	322.16	1865.4	1162.9	1439.1	2029.6	1257.8	644.83	1991.1	1298.6	51.515	1885.3	1087.1	1395.7	2001.4	1101	1073.7	1943.1	1033.1	976.66	1966.2	1395	1216.6	1692.4	1242	1245.8
+240	1.9917	1741.9	1275.8	1437.7	1921.9	1375.3	1398.4	1563.9	1251.9	179.92	1734.2	1344.6	1585	1688.3	1347.2	1004.1	1797.8	1616.7	1139.9	1833.1	1392.6	1673.7	2104	1579.1	1143.8	1911.1	1596.4	1104.6	1836.3	1482.2	927.35	1510.9	1159.5	165.83	1684	1384.5	486.8	1605.2	1267.6	37.596	1621.2	1355.6	374.1	1746.6	1457.4	1466.6	1766.4	1485.3	711.02	1692.2	1259.9	49.648	1728	1563	1312.4	2022.1	1532.6	1202	2002.5	1619.1	1107.6	1903.1	1228.4	165.41	1742.1	1194	1348.1	1792.8	1212.1	1565	1782.7	1188.3	982.35	1848.6	979.38	1196.3	1913.3	1290.2	1675	2045.7	1087.2	976.58	1955.6	1029.9	1067	1980.6	1262.7	917.76	1800.4	1246.6	125.94	2030	1274.5	499.96	1985	1265	64.839	1956.8	1229.1	313.42	1883.8	1175	1443.5	2049.2	1274.1	650.51	2041.6	1343.7	49.223	1901.6	1098.5	1401.2	2018.5	1107.2	1082	1956.7	1044.8	983.19	1986.2	1407.4	1220.9	1708.1	1256.6	1252.8
+241	2.0000	1760.6	1288.4	1440.5	1941.5	1386.1	1401.8	1568.4	1262.4	188.49	1753.1	1355.6	1586.9	1708.6	1361.3	1006.9	1816.6	1631.8	1146.4	1852	1402.3	1676	2123.7	1590	1143.3	1929.2	1611.1	1109.1	1855.6	1496.1	931.6	1514.8	1170.5	177.2	1696	1397.4	491.55	1606.2	1274	42.773	1631	1367.4	380.63	1767.6	1468.5	1471.2	1783.2	1498.4	714.08	1692.7	1267.6	50.581	1749	1576.5	1320	2041.7	1544.7	1203.6	2021	1632.4	1111.2	1949.1	1265	153.78	1766.5	1207.8	1350.1	1811.3	1222	1566.7	1802	1203.1	985.83	1860.9	991.85	1201.1	1932.1	1299.8	1677	2062.3	1096.1	982.94	1970.1	1040.2	1072.6	2000.1	1277.1	922.6	1848.3	1285.7	111.69	2051.7	1290.6	500.3	2035.3	1307.9	56.607	1991.9	1256.6	305.61	1902.2	1187.4	1446.7	2067.9	1289	654.5	2091.9	1388	47.271	1917.2	1110.4	1406	2036	1113.6	1089.4	1971.2	1057.3	988.97	2006.4	1419.2	1224.6	1729.3	1269.7	1255.8
+242	2.0083	1778.9	1300.3	1442.8	1961	1397.1	1404.2	1573.5	1273.3	196.98	1772.1	1366	1588.1	1728.1	1375.7	1009.8	1834.9	1646.7	1152.3	1871	1412	1677.3	2142	1601.5	1141.2	1946.9	1626	1112.9	1875.2	1510.2	933.55	1520.3	1180.7	187.73	1708.6	1410.3	495.97	1607.1	1282.6	48.969	1641.9	1379.6	386.57	1788.1	1479.1	1475.2	1800.9	1510.8	716.12	1692.5	1278.3	52.279	1769.6	1589.7	1326.4	2060.4	1557.3	1203.6	2039	1646.7	1113.6	1995.2	1301.2	143.77	1780.4	1219.9	1352.2	1829.8	1231.9	1567.4	1820.6	1217.9	988.63	1873.7	1004.7	1205.1	1950.7	1309.3	1678.3	2079.8	1105.6	988.12	1985.2	1050.5	1077.1	2018.8	1291.1	925.57	1897.1	1324.1	100.14	2072.6	1305.8	499.36	2085.3	1350.2	49.648	2027.1	1283.5	298.57	1919.4	1199.4	1448.8	2086.3	1303	657.3	2141	1430.8	44.301	1932.3	1122.7	1409.7	2053.7	1120.9	1095.8	1987.3	1069.8	994.06	2026.3	1431.2	1227.8	1750.9	1280.9	1257.4
+243	2.0167	1797.2	1311.5	1444.4	1980.6	1408.3	1405.8	1579.1	1283.7	205.21	1790.7	1376	1588.6	1747.3	1390.5	1012.7	1852.4	1660.4	1156.4	1889.8	1421.8	1678	2160.2	1613.9	1138.3	1963.8	1641	1115.5	1895.3	1524.1	934.4	1527.5	1190	197.57	1721.5	1423.5	499.79	1607.6	1293.6	56.013	1652.5	1391.6	391.92	1808.7	1490.1	1478.6	1819.1	1523.2	717.9	1692.2	1291.9	55.334	1790.1	1602.4	1331.3	2078.9	1570.2	1202.5	2056	1661.7	1114.7	2041.7	1336.1	136.04	1807.4	1233.6	1351.3	1848.6	1241.2	1567.4	1839.3	1232.2	990.92	1886.8	1017.7	1207.6	1969.3	1319.1	1678.9	2099.1	1115.8	992.87	2000.2	1060.2	1080.5	2036.8	1304.1	926.5	1946	1361.5	91.827	2092.2	1320.9	497.92	2134.3	1390.9	44.301	2062.3	1310	292.12	1936.6	1211	1450.1	2104.2	1315.8	658.32	2188.1	1472	41.585	1948	1134.9	1412.3	2072.3	1128.5	1101.8	2005.4	1082.2	998.13	2046.2	1443.6	1230.5	1779.8	1294.5	1252.3
+244	2.0250	1815.6	1322.9	1445.2	2000.1	1419.3	1406.5	1585.7	1294.2	213.36	1809.5	1385.3	1588.3	1767	1405.8	1014.9	1869.1	1673.6	1159.5	1908.4	1431.5	1678.2	2179.3	1627.2	1134.6	1981.1	1656.5	1117.2	1915.5	1537.9	934.9	1536.1	1198.7	206.23	1735.6	1436.7	503.1	1608.2	1306.3	63.396	1663.5	1402.9	397.27	1829.3	1501.7	1481	1837.6	1536	718.92	1692.3	1307.5	58.983	1810.1	1615	1334.9	2097.3	1583.3	1200	2072.5	1677.2	1114.1	2087.4	1369.3	131.04	1816.5	1243.6	1352.2	1867.3	1251.6	1566.8	1858.8	1246.3	991.85	1900.4	1030.9	1208.4	1988.3	1328.8	1679.1	2120.2	1126.6	997.88	2018.9	1071.4	1084.4	2056.3	1316.9	927.1	1994.1	1396.7	86.65	2111.2	1336.6	495.46	2182.4	1429.2	40.482	2096.7	1335.4	286.6	1954.9	1222.9	1450.3	2121.8	1327.7	656.88	2234.1	1511.2	39.973	1964.9	1147.3	1413.5	2091.6	1136.9	1107.4	2025.5	1093.9	1001.4	2066	1456.2	1231.7	1780.4	1308.6	1262.1
+245	2.0333	1834	1334.4	1445.3	2019.5	1430.6	1406.4	1593.5	1304.4	221.34	1828.2	1394.7	1587.1	1786.8	1420.3	1015.4	1886.1	1687.8	1162.8	1927	1440.8	1677.4	2197.1	1641.3	1128.8	1996.5	1670.8	1116.4	1935.7	1551.6	935.24	1545.5	1207.6	214.55	1749.9	1450.5	506.58	1610.9	1320	71.204	1675	1414.2	402.7	1850	1513.2	1482.6	1856.2	1549.6	718.92	1694	1323.4	62.802	1829.7	1627.5	1337.8	2115.4	1597.2	1195.8	2088.3	1692.6	1112.4	2131	1400.4	127.73	1834.8	1255.5	1352.4	1885.8	1262.2	1565.4	1878.6	1260.8	990.32	1915	1044.4	1207.5	2006.5	1338	1677.1	2142.9	1138	1001.8	2037.6	1082.6	1086.6	2078.8	1330.2	927.1	2039.8	1429.4	83.765	2129.6	1351.9	491.81	2228.9	1464.8	38.785	2129.5	1360.1	282.53	1973.3	1234.6	1449.6	2139.2	1339	653.48	2278.4	1547.5	38.191	1981.5	1159.1	1412.8	2111.4	1146.1	1111.9	2047.4	1105.6	1004.2	2085.1	1468.7	1232	1795.8	1320.8	1264
+246	2.0417	1852.6	1346.5	1443.9	2038.8	1442.2	1405.8	1602.3	1314.8	229.06	1846.9	1404.9	1585.8	1806.8	1433.4	1014.5	1902.8	1701.7	1165	1945.9	1450.3	1676.1	2212	1655.9	1120.4	2011.8	1684.6	1115.8	1955.8	1565	934.9	1555.9	1217.8	223.54	1765.1	1464	509.63	1615.6	1333.4	79.436	1687.3	1425.8	408.13	1870.4	1524.7	1483	1875.2	1564.6	719.34	1698.3	1338.5	68.064	1849	1640	1339.7	2133.4	1611.9	1190.2	2103.4	1708.4	1109.1	2171.4	1429.8	126.28	1853.1	1267.1	1350.4	1904	1272.1	1563.4	1898.4	1275.1	986.93	1931.2	1057.8	1205.1	2024.6	1347.2	1675	2166.3	1149.7	1004.7	2057.3	1093.9	1087.8	2094.5	1342.9	922.94	2082.4	1460.1	82.322	2147.9	1366.8	487.14	2271.7	1497.1	37.851	2160.1	1384.3	279.3	1991.6	1245.9	1447.4	2156.7	1350	649.07	2319.8	1581.1	36.578	1998	1170.1	1410.3	2132.1	1155.8	1115.8	2070.9	1117.6	1006.1	2104	1481.3	1231.5	1815.9	1330.6	1260.9
+247	2.0500	1871.3	1358.1	1441.1	2057.9	1453.8	1404.4	1612.6	1325.7	236.87	1865.4	1415.3	1583.6	1826.7	1446.9	1012.8	1919.2	1715.4	1165.8	1964.3	1459.6	1673.7	-9999.99	-9999.99	-9999.99	2026.7	1699.6	1113.7	1975.8	1578.4	934.48	1567	1229.4	232.03	1781.8	1478.2	511.67	1623.4	1346.6	88.772	1700.9	1438.1	412.97	1890.4	1536.6	1482.5	1894.3	1580.2	719.76	1705.4	1353.3	75.278	1868.3	1652.5	1340.4	2150.8	1627.3	1183.3	2118	1724.9	1104.6	2208.9	1457.3	126.37	1876.5	1278.4	1345.4	1921.9	1282.6	1559.6	1917.4	1288.8	982.86	1948.7	1070.9	1201.2	2043.1	1356.3	1672.2	2190.4	1161.7	1006.9	2078.7	1105.6	1088	2122.5	1358.2	920.65	2121.2	1488.7	82.237	2166.6	1381.9	482.13	2308.9	1526.1	36.918	2188.3	1407.1	276.41	2010.4	1257	1443.8	2174.7	1361.5	644.15	2357.5	1611.9	34.541	2016.3	1181.2	1406.2	2153.2	1165.5	1119.4	2095.3	1129.7	1006.7	2123.6	1494.4	1230.5	1835.4	1342.3	1255.5
+248	2.0583	1890.4	1369.8	1437.5	2076.9	1465.2	1401.8	1624.6	1338	244.67	1883.8	1426.5	1580.1	1845.8	1461.3	1010.3	1934.5	1727.5	1164.6	1982.5	1468.8	1671.1	-9999.99	-9999.99	-9999.99	2041.2	1714.5	1109.9	1995.6	1592	933.55	1579.3	1241.3	239.92	1800.4	1494.7	513.37	1633.6	1360	98.107	1716.2	1452.1	417.55	1910.7	1548.8	1480.9	1913.3	1595.2	719.09	1714.2	1367.4	82.661	1887	1665.5	1340.1	2168	1643.3	1175.6	2132	1741.5	1099	2241.7	1482.8	126.71	1893.2	1289.9	1341.8	1940.6	1293.1	1554.5	1935.4	1302	979.29	1967.2	1083.7	1195	2061.7	1365.5	1668.8	2216.2	1174.4	1008	2101.4	1117.7	1086.4	2138.9	1370.7	915.72	2155.1	1516.8	85.123	2185.1	1397.1	477.38	2341.3	1552	36.663	2214.3	1428.8	274.12	2029.8	1268	1439	2194.1	1373.7	638.72	2391	1639.5	31.825	2036.4	1192.3	1400.9	2175.6	1175.9	1121.6	2120.9	1141.7	1005.5	2136.4	1504.9	1225.7	1854.5	1353.5	1251.6
+249	2.0667	1909.8	1381.4	1433	2095.7	1476.6	1398.4	1638.5	1351.1	252.99	1901.9	1438.7	1575.8	1864.4	1475.2	1007.5	1950	1740.1	1162.9	2001.3	1478.1	1667.7	-9999.99	-9999.99	-9999.99	2054.9	1728.6	1104.6	2014.8	1605.7	931.93	1593	1253.3	248.92	1821.4	1512.9	513.37	1644.2	1374.2	107.36	1734	1468.5	421.79	1930.9	1560.8	1478.7	1932.3	1610.6	717.13	1723.4	1381.2	89.281	1905.7	1678.3	1339	2184.6	1660	1167.3	2145.3	1758	1092.3	2269.1	1506	126.28	1911	1300.8	1337.6	1959.3	1302.2	1550.1	1953.2	1316	974.88	1986.8	1096.8	1186.7	2080.3	1374.6	1664.6	2242.8	1187.1	1007.9	2124.7	1129.7	1083.1	2161.2	1385	910.72	2183.6	1543.5	89.111	2203.7	1412.7	472.88	2369.6	1575.1	36.154	2238.5	1449.5	271.92	2049.7	1278.9	1433.8	2214.4	1385.9	632.78	2419.1	1664.1	29.279	2057.4	1203	1394.5	2199.6	1187.3	1121.3	2147.6	1154	1002.6	2152.6	1516.5	1221.1	1874.1	1365.3	1247.4
+250	2.0750	1929.3	1393	1428	2114.5	1488.1	1394.3	1654.3	1364.8	261.9	1920.3	1450.1	1571.5	1882.7	1488.2	1003.7	1964.9	1752.3	1159.8	2019.9	1487.2	1663.7	-9999.99	-9999.99	-9999.99	2068	1742.8	1098.2	2033.8	1619.2	929.22	1608.9	1266.1	259.61	1844.3	1531.7	511.5	1654.8	1388.4	116.52	1754.6	1485.6	424.51	1951.2	1572.7	1475.4	1952	1627.4	714.84	1733	1395.4	95.731	1924.6	1691	1336.8	2201.6	1677.5	1158	2157.6	1774.7	1084.4	2292.3	1526.5	125.35	1930	1311.5	1332.2	1977.8	1312.1	1545.1	1971.1	1330.2	969.11	2008.7	1110.1	1176.8	2098.7	1383.7	1660	2270.9	1200.4	1007.4	2149	1142.2	1080	2178.4	1397.9	904.61	2207.2	1565	91.403	2222.9	1428.8	469.15	2392.7	1595.3	34.966	2260.4	1468.6	269.54	2068.7	1289.2	1427.3	2234.3	1398.1	626.92	2442.2	1687.2	27.667	2078.3	1213.5	1386.7	2224.3	1199	1119.2	2174.2	1167.4	999.4	2171.9	1528.9	1216.9	1892.4	1377.4	1242.4
+251	2.0833	1948.7	1404.2	1422.7	2132.9	1498.9	1389.7	1672.2	1379	270.47	1938.8	1460.4	1566.7	1899.9	1501.7	998.9	1979	1763.7	1155.5	2038.4	1496.3	1659.4	-9999.99	-9999.99	-9999.99	2080.7	1757.2	1091.1	2052.2	1632.8	925.99	1627.4	1279.7	270.98	1868.7	1551.6	508.36	1666.1	1402.4	125.77	1777.1	1503.3	425.87	1971.5	1585.2	1471.2	1972.7	1645.4	711.96	1743.9	1410.7	102.35	1943.6	1703.6	1334.2	2219.2	1695.5	1147.9	2169.2	1791.3	1075.4	2310.7	1544.2	123.99	1949.2	1322.2	1326.3	1995.3	1323.3	1537.9	1989	1343.5	963.42	2032.7	1123.1	1166	2116.9	1392.7	1655	2300.8	1214.6	1006.5	2176.9	1155.9	1075	2196.7	1411.4	898.92	2225	1581.6	90.639	2242.4	1444.5	465.92	2409.5	1611.6	33.777	2279.6	1486.2	266.65	2087.2	1299.3	1419.9	2253.3	1411.9	621.66	2460.8	1706	25.46	2099.3	1224.2	1378	2250	1211.3	1116.4	2202	1182	994.74	2192.9	1541.7	1212.9	1910.3	1388.4	1237.3
+252	2.0917	1968.2	1415.4	1417	2151	1509.7	1384.6	1691.5	1394.3	278.79	1957.4	1470.7	1561.2	1917	1514.8	993.8	1992.4	1775.2	1150.1	2056.6	1505.5	1654.9	-9999.99	-9999.99	-9999.99	2093	1771.9	1083.3	2070.8	1647.1	922.85	1647.9	1294.6	282.02	1894.3	1573	504.62	1679.7	1417.3	134.6	1801.3	1522.8	426.38	1993	1598.3	1466.8	1994.4	1663.2	707.97	1756.7	1426.3	108.89	1962.5	1716.9	1331	2235	1713.7	1136.5	2180	1808.6	1065.5	2322.2	1558.7	121.28	1968.9	1332.1	1319.5	2010.9	1334.9	1528.2	2006.7	1357.5	957.23	2057.5	1136	1153.9	2134.9	1401.4	1649.4	2331.5	1229.1	1005.2	2204.4	1169.6	1067.8	2214.6	1424.6	893.66	2235.5	1595.4	86.141	2261.9	1460.2	462.95	2420.3	1622.8	32.929	2295.8	1502.4	263.85	2106	1309.3	1412.1	2270.9	1426.8	617.58	2474.2	1718.2	22.151	2120.4	1235.1	1367.6	2276.8	1224.3	1113	2231.6	1196.9	989.31	2214.3	1554.6	1208.8	1929	1398.8	1231.9
+253	2.1000	1988.5	1427	1410.9	2169.5	1521.2	1379.4	1713	1410.9	286.6	1976.2	1481.3	1555.6	1936.1	1527.6	986.76	2006	1787	1144.3	2074.7	1514.7	1649.9	-9999.99	-9999.99	-9999.99	2104.8	1787.5	1075.2	2089.6	1661.2	918.7	1670.3	1310.7	292.29	1921.3	1595.3	500.89	1695.5	1433.2	143.09	1827.3	1543.4	426.8	2014.7	1611.9	1461.9	2017.1	1680.7	703.05	1771.3	1442.5	115	1981.5	1730.7	1327.2	2249.4	1732.7	1124.3	2189.9	1825.3	1054	2325.9	1568.3	116.78	1986.8	1342.5	1312.1	2025.1	1346.3	1520.8	2024.3	1371.2	950.18	2083.7	1149.3	1140.5	2152.8	1410.2	1643.9	2362	1243.4	1002.5	2232.9	1183.9	1059.8	2231.3	1437.2	889.25	2238.3	1604.3	78.503	2281.5	1475.8	461.26	2424.6	1628.1	32.504	2307.6	1515.7	260.71	2125.1	1319.4	1404	2287.5	1442.2	614.78	2482.1	1724.7	18.162	2141.5	1246	1356.3	2304.3	1238.1	1108.1	2262.9	1212	983.7	2234.8	1567.1	1204.3	1946.4	1410.1	1226.2
+254	2.1083	2007.9	1438.4	1405.1	2189.2	1532.6	1374.4	1736.4	1429.2	294.07	1995.2	1492	1549.6	1955.1	1541.1	978.19	2020.3	1798.9	1138.6	2092.9	1524.1	1645.2	-9999.99	-9999.99	-9999.99	2116.2	1802.2	1066.8	2108.6	1674.4	913.52	1694.5	1328.3	301.79	1949.8	1617.8	497.41	1713.3	1451.4	152.59	1854.8	1563.9	427.31	2034.7	1625.2	1456	2040.5	1697.9	698.46	1788	1460.2	120.51	2000.2	1743.7	1321.9	2264.4	1752.4	1112	2199.6	1842.4	1042.1	2324.4	1573	112.03	2004.7	1353.4	1304.9	2037.3	1357	1516.1	2040.6	1383.9	943.56	2111.1	1163	1126.5	2170.4	1419.2	1638.4	2392.9	1257.1	999.07	2261.9	1198.3	1051.4	2246.8	1449.3	885.94	2236	1606.4	69.337	2300.7	1490.8	459.98	2424.8	1629.9	32.844	2315.2	1525.1	257.83	2144.7	1329.5	1395.7	2304.8	1457.6	612.75	2483.8	1724.4	21.387	2162.3	1256.6	1344.2	2332.3	1251.8	1102.3	2295.4	1227.4	977.25	2253.2	1578.9	1199.3	1962.5	1422.5	1220.1
+255	2.1167	2025.1	1450.5	1399	2208.6	1543.9	1369.3	1761.4	1448.4	300.43	2013.7	1502.5	1543.2	1971.7	1554.9	970.29	2034.1	1810.3	1132.3	2111	1533.1	1640.7	-9999.99	-9999.99	-9999.99	2127.1	1816.9	1057.8	2127.6	1687.8	908	1720.3	1347.6	310.53	1980	1640.4	494.53	1734.2	1470.7	161.42	1883.7	1585	428.58	2053.7	1638.5	1449.5	2064.7	1714.5	693.88	1807.7	1479.1	125.35	2018.5	1755.3	1315	2278.2	1771.7	1097.9	2208.3	1860.6	1030.7	2323.9	1575.3	108.38	2023.1	1364.3	1298.1	2049.5	1367.4	1512.6	2055.5	1396.5	937.28	2139.4	1176.9	1111.9	2187.8	1428	1632.9	2424.1	1271.3	995.08	2291.9	1212.8	1042.1	2262.3	1460.6	883.14	2233.5	1604.9	61.36	2318	1504.4	458.37	2424.5	1630.3	33.014	2321.7	1530.9	255.11	2164.6	1339.9	1387	2322.1	1471.8	610.37	2484.3	1724.7	22.405	2182.8	1267.4	1331.6	2360.8	1266	1095.8	2327.5	1243.1	969.45	2269.6	1590	1193.6	1978	1434.9	1214.7
+256	2.1250	2041.2	1463.5	1393.3	2226.8	1554.9	1364.1	1788.1	1468.6	305.86	2032.2	1513.3	1537.6	1987.4	1569	963.25	2047.6	1821.9	1125.8	2128.6	1541.8	1636.3	-9999.99	-9999.99	-9999.99	2137.6	1832.2	1048.3	2146.9	1701	902.74	1747.2	1368.5	318.25	2010.9	1662.6	492.06	1758.5	1491.3	167.87	1913.9	1607.1	429.6	2072.6	1651.9	1443.2	2089.4	1730.5	689.21	1830.9	1499.3	130.19	2036	1766.5	1307.2	2289.9	1791.6	1082.1	2216.2	1878.4	1018.9	2325.9	1576.9	105.41	2040.2	1375	1292	2063.8	1378	1508.8	2069.2	1409.4	931.26	2168.1	1191.2	1097.1	2205	1436	1627.9	2454.7	1285.8	989.73	2323.1	1229.3	1033.3	2278.6	1471.2	880.59	2231.9	1602.6	56.607	2333.2	1515.7	456.17	2424.8	1629.8	32.844	2329.9	1535.9	252.91	2183.8	1349.7	1378.2	2339	1485.2	608.33	2484	1724.9	22.32	2203.5	1278.7	1318.6	2389.5	1280.9	1089	2359.6	1261.1	961.81	2287.4	1601.1	1188.2	1993	1447.3	1209.5
+257	2.1333	2057.8	1475.3	1388.9	2244.7	1565.3	1359	1816.5	1490.3	311.04	2050.3	1524.2	1532	2002.5	1583.1	956.8	2061.4	1833.4	1119.7	2146	1550.5	1632.3	-9999.99	-9999.99	-9999.99	2147.4	1846.8	1038.7	2166.2	1713.3	898.24	1774.8	1390.9	325.04	2042.4	1684.6	490.11	1785.3	1513.5	173.55	1945.1	1628.7	429.94	2091.2	1665.2	1437.2	2114.2	1746.3	686.16	1856.9	1520.2	134.6	2052.7	1777.3	1300.1	2301.4	1812.8	1066.8	2223	1896	1006.5	2327.3	1578.4	102.27	2056.8	1384.4	1285.4	2082.3	1389.2	1503.2	2082.1	1422.6	927.1	2197.6	1206.1	1083.3	2222.1	1444.8	1623.7	2485.8	1302	988.46	2354.2	1245.5	1024.6	2294.3	1482.2	876.35	2230.5	1602.1	53.467	2347.3	1525.4	453.7	2425.1	1629.3	32.759	2338.9	1541.5	249	2202.7	1359.4	1369.8	2355.3	1497.2	606.21	2483.6	1725	21.726	2224.3	1290.6	1305.9	2418.8	1296.1	1082	2391.9	1283.5	955.19	2306.2	1612.2	1183.8	2007.5	1460.6	1204.2
+258	2.1417	2076	1486.1	1386.1	2262.1	1574.8	1358.1	1846.3	1513.2	314.86	2068.7	1535.2	1526.7	2017.1	1596.7	952.05	2074.7	1843.6	1114.1	2163.1	1559.4	1629	-9999.99	-9999.99	-9999.99	2156.4	1860.1	1029.4	2184.7	1725.8	894.85	1803	1414.6	329.88	2075.3	1706.4	488.84	1814.6	1536.4	178.22	1977.3	1650.7	429.86	2108.7	1677.9	1432.2	2138.9	1763	685.14	1885.5	1541.7	138.08	2068.9	1788.8	1294.8	2312.8	1834	1051.4	2228.4	1913.5	993.72	2327.5	1579.7	99.465	2070.4	1397.6	1283.9	2107.3	1401.3	1494.2	2093.9	1436.3	924.47	2227.9	1222.3	1070.9	2238.5	1453.3	1620	2517.6	1317.8	984.55	2386.3	1261.7	1016.3	2308.5	1492.7	871.76	2229.6	1603.3	50.666	2361.1	1533.6	450.9	2425.5	1629.6	33.353	2344.6	1546.6	241.19	2221.4	1369.5	1362.3	2369.8	1507.2	604	2483.4	1724.9	21.472	2245.3	1302.7	1294.9	2448.9	1311.5	1074.5	2424.5	1299.3	946.79	2323.4	1618	1179.5	2024.1	1473	1204.4
+259	2.1500	2093.9	1496.1	1384.1	2280	1584.5	1357.5	1877	1536.4	316.56	2087	1546	1522.5	2031.5	1610.5	949.59	2087.9	1854	1109.8	2179.8	1567.8	1626.5	-9999.99	-9999.99	-9999.99	2164.3	1872.9	1020.6	2202.1	1737.2	895.1	1831.7	1438.3	332.26	2108.7	1727.3	488.33	1846	1560.6	181.28	2010.4	1673.2	430.03	2124.4	1689.6	1428.2	2163.5	1780.2	685.48	1917	1564.1	140.71	2084.8	1800	1290.8	2322.5	1856.6	1036.2	2232.1	1929.5	980.48	2327.4	1581.3	97.598	2073	1410.6	1289.6	2138.7	1414.5	1481.9	2105.9	1449.5	922.6	2259.4	1239.8	1060.2	2254.5	1461.1	1617.1	2548.3	1332.9	977.76	2418.3	1278.4	1008.6	2321.7	1501.7	869.73	2229.5	1604.9	48.46	2372.9	1540.3	448.19	2425.8	1630.6	34.796	2355	1552.5	245.35	2239.9	1380.3	1356.6	2382.3	1515.1	601.88	2483.4	1724.9	21.472	2265.6	1315.2	1285.8	2479.6	1327.6	1067.3	2456.5	1313.7	940.08	2336.1	1624.3	1177.3	2040	1485.4	1202.5
+260	2.1583	2110.5	1505.6	1382.8	2297.5	1594.3	1356.5	1908.8	1559.4	316.81	2104.4	1556.3	1519.4	2046	1624.7	948.99	2101.4	1864.7	1107.5	2196.1	1576.3	1624.7	-9999.99	-9999.99	-9999.99	2170.9	1885.3	1012.4	2218.6	1744.6	900.36	1861	1462.8	332.85	2141.7	1747.4	487.57	1878.6	1586.2	182.98	2043.4	1696.3	430.7	2140.1	1700.2	1425.4	2187.7	1796.4	685.9	1951.2	1586.4	142.24	2100.1	1810.6	1288	2330.2	1879.1	1021.6	2233.8	1944.6	967.92	2327	1582.6	96.834	-9999.99	-9999.99	-9999.99	2155.1	1424.9	1478.1	2117.8	1460.7	922.17	2290.8	1257.9	1052.4	2270.6	1469.1	1614.4	2577.9	1347.2	969.87	2447.8	1295.3	999.91	2334.5	1509.3	869.39	2229.6	1606.7	47.526	2381.8	1545.5	445.56	2425.9	1631.2	35.645	2355.4	1553.4	243.74	2257.7	1391.2	1352.8	2392.4	1520.7	599.42	2483.4	1724.7	21.387	2286.6	1327.8	1279.1	2510.2	1344.4	1060.6	-9999.99	-9999.99	-9999.99	2349.3	1632.6	1175.4	-9999.99	-9999.99	-9999.99
+261	2.1667	2125.6	1514.8	1382.3	2314.2	1603.7	1354.8	1941.1	1582.8	316.22	2120.7	1565.9	1517.5	2059.4	1639	949.93	2112.8	1874.7	1105.7	2212.2	1584.3	1623.9	2342.1	1964.4	920.82	2175.9	1898.8	1006.1	2231	1756.1	901.13	1890.6	1487.6	331.41	2174.5	1767.5	487.65	1913.7	1606.8	179.58	2076.1	1719	430.96	2156.4	1710.1	1424.1	2211.2	1810.7	686.16	1986.8	1608.7	142.83	2115.5	1821.1	1286.9	2335.6	1899.1	1006.2	2232.8	1958.8	956.29	2326.9	1583	96.41	-9999.99	-9999.99	-9999.99	2172.1	1434.2	1474.5	2128.6	1471.1	922.94	2320.8	1276.2	1047.4	2286.3	1477.1	1612.6	2608.2	1361.8	962.83	2478.1	1313.5	995.5	2346.3	1516.3	868.45	2229.6	1607.7	47.611	2388.2	1549.8	443.43	2425.9	1631.1	35.475	2356.4	1554.4	243.06	2274.9	1402	1350.4	2400.9	1525.2	597.22	2483.3	1724.3	20.878	2308.4	1341.1	1275.1	2540.6	1361.7	1054.7	-9999.99	-9999.99	-9999.99	2362.8	1640.8	1172.6	-9999.99	-9999.99	-9999.99
+262	2.1750	2139.9	1524	1382.4	2329.9	1612.1	1352.7	1973.9	1607.2	314.78	2136.5	1575.3	1516.9	2072.3	1652.2	951.28	2122.7	1884.6	1105.2	2227.8	1592.3	1624.1	2335.1	1985.9	909.7	2179.5	1911.4	1002.1	2242.3	1766.6	904.1	1920.8	1512.2	328.18	2206.6	1787.5	489.52	1950.6	1630.6	176.1	2108.6	1740.4	430.96	2172.2	1718.8	1423.7	2234.8	1824.5	686.58	2024.1	1631.4	141.73	2131.4	1831.6	1288.3	2338.4	1918	991.43	2230	1971.4	946.28	2327.1	1583.3	96.325	-9999.99	-9999.99	-9999.99	2187.6	1443.9	1472.5	2138.1	1482.8	923.79	2349.1	1293.6	1044.6	2301.7	1484.8	1611.3	2637	1377.2	957.65	2507.8	1331.4	991.85	2357.1	1522.5	867.01	2229.5	1607.3	48.29	2393.9	1553.6	442.67	2425.9	1631	35.305	2358.1	1555.5	242.72	2291.4	1412.6	1349.8	2408.9	1529.7	595.6	2483.2	1724	20.453	2328.7	1354	1273	2570.4	1379.1	1050.1	-9999.99	-9999.99	-9999.99	2376.6	1648.5	1168.8	-9999.99	-9999.99	-9999.99
+263	2.1833	2153.7	1533.3	1382.8	2345.8	1619.9	1351.4	2007.1	1631.9	311.55	2151.5	1584.2	1517.4	2086.5	1663.9	952.05	2134.2	1894.5	1107.9	2243	1600.1	1624.6	2326.6	2005.4	899.85	2182.1	1921.8	1000.3	2266.6	1772.1	898.84	1951.2	1537.9	323.18	2238.1	1805.5	493.59	1990	1656.6	172.71	2141.3	1761.2	431.13	2187.8	1726.8	1424.3	2258.4	1838.7	692.01	2064	1653.5	139.78	2147.8	1841.4	1290.8	2339.3	1937.3	979.63	2225.7	1982.9	938.98	2327.7	1584.1	97.513	-9999.99	-9999.99	-9999.99	2201.3	1453.4	1471.9	2146.5	1494.8	924.98	2376.2	1310.4	1043.5	2316.9	1492.8	1610.5	2663	1393.6	953.32	2536.7	1349.2	989.73	2367.1	1527.5	865.91	2228.8	1607.7	49.139	2400.4	1557.4	442.42	2425.5	1630.7	34.372	2361	1557.1	243.23	2306.4	1422.5	1349.9	2416.4	1534	593.82	2483.4	1724.2	20.708	2346.9	1366.1	1272.1	2599.7	1396.5	1047.8	-9999.99	-9999.99	-9999.99	2392.7	1656	1165.2	-9999.99	-9999.99	-9999.99
+264	2.1917	2166.9	1542.5	1383.3	2362	1627.7	1350.4	2041.4	1656.5	305.86	2165.6	1592.4	1518.5	2100.7	1674.7	953.24	2146.9	1904.7	1112.9	2257.3	1608.1	1625.1	2316.6	2023.3	892.56	2184.6	1932.4	1000.9	2285.2	1778.7	897.22	1982.5	1563.7	315.28	2268.9	1822.5	499.19	2031.3	1683.2	168.97	2174	1781.1	431.81	2203	1734.4	1425.4	2280.5	1851.2	695.83	2106.6	1677.4	138.16	2165	1851.6	1295.1	2339	1955.8	970.8	2220.6	1993.5	935.16	2328.4	1585.5	99.465	-9999.99	-9999.99	-9999.99	2214.8	1461.5	1472.5	2154.8	1506.1	926.33	2402.8	1326.3	1044.3	2331.6	1501.5	1610.5	2690.3	1411.7	953.92	2564.2	1367	989.14	2376.4	1531.3	865.65	2228.4	1610.5	50.327	2407.7	1561.5	442.25	2424.3	1630.1	33.098	2364.9	1559.1	244.67	2319.9	1431.6	1350.6	2423.8	1537.9	592.46	2483.9	1724.2	21.472	2363.5	1377.4	1272.6	2628.3	1413.6	1047.6	-9999.99	-9999.99	-9999.99	2407.4	1663.2	1161.8	-9999.99	-9999.99	-9999.99
+265	2.2000	2180	1550.5	1383.9	2374.9	1635.2	1350.7	2076.1	1681.1	299.75	2179.3	1600.6	1519.8	2113.1	1686.8	954.25	2158.5	1915	1118.6	2271.2	1616.5	1625.6	2305.7	2039.8	887.04	2187.6	1943.9	1004.5	2300.5	1785.9	898.5	2015.1	1589.3	304.93	2298	1838.7	505.3	2073.1	1710.7	164.05	2205.8	1800.4	432.91	2217.6	1741.9	1427	2300.5	1863.5	699.91	2149.3	1701.4	134.18	2180.9	1862.3	1300.7	2337.5	1973.1	963	2215.3	2003.6	934.57	2328.3	1586.8	100.14	-9999.99	-9999.99	-9999.99	2227.2	1468.8	1474.2	2163.2	1516.3	926.93	2428.5	1340.9	1046.1	2345.5	1509.7	1611.4	2715.8	1430.6	955.27	2590.1	1383.9	990.41	2385.2	1535.3	865.91	2228.2	1613.7	52.194	2414.7	1565.3	442.42	2423.1	1630.1	32.165	2368.5	1561.1	245.52	2333.3	1440.2	1352.5	2430.9	1541.9	592.29	2484	1723.9	21.387	2378.6	1387.5	1274	2656.8	1430.4	1048.9	-9999.99	-9999.99	-9999.99	2420.3	1669.8	1159.8	-9999.99	-9999.99	-9999.99

GPy/util/osu_run1/connections.txt

@@ -0,0 +1,22 @@
+LFHD, RFHD
+RFHD, RBHD
+RBHD, LBHD
+LBHD, LFHD
+LELB, LWRB
+LWRB, LFIN
+LELB, LSHO
+LSHO, RSHO
+RSHO, STRN
+LSHO, STRN
+RSHO, RELB
+RELB, RWRB
+RWRB, RFIN
+LSHO, LFWT
+RSHO, RFWT
+LFWT, RFWT
+LFWT, LKNE
+RFWT, RKNE
+LKNE, LHEE
+RKNE, RHEE
+RMT5, RHEE
+LMT5, LHEE

GPy/util/sinc.py

@@ -0,0 +1,34 @@
+from sympy import Function, S, oo, I, cos, sin
+
+
+class sinc_grad(Function):
+    nargs = 1
+    
+    def fdiff(self, argindex=1):
+        return ((2-x*x)*sin(self.args[0]) - 2*x*cos(x))/(x*x*x)
+    
+    @classmethod
+    def eval(cls, x):
+        if x.is_Number:
+            if x is S.Zero:
+                return S.Zero
+            else:
+                return (x*cos(x) - sin(x))/(x*x)
+            
+class sinc(Function):
+    
+    nargs = 1
+    
+    def fdiff(self, argindex=1):
+        return sinc_grad(self.args[0])
+    
+    @classmethod
+    def eval(cls, x):
+        if x.is_Number:
+            if x is S.Zero:
+                return S.One
+            else:
+                return sin(x)/x
+    
+    def _eval_is_real(self):
+        return self.args[0].is_real

Untitled0.ipynb

@@ -0,0 +1,73 @@
+{
+ "metadata": {
+  "name": ""
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+  {
+   "cells": [
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "import numpy\n",
+      "np.where?"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "Object `np.where` not found.\n"
+       ]
+      }
+     ],
+     "prompt_number": 1
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "numpy.where?"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [],
+     "prompt_number": 2
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "numpy.exp(-36)"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "metadata": {},
+       "output_type": "pyout",
+       "prompt_number": 3,
+       "text": [
+        "2.3195228302435696e-16"
+       ]
+      }
+     ],
+     "prompt_number": 3
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [],
+     "language": "python",
+     "metadata": {},
+     "outputs": []
+    }
+   ],
+   "metadata": {}
+  }
+ ]
+}

svm_gui.py

@@ -0,0 +1,330 @@
+"""
+==========
+Libsvm GUI
+==========
+
+A simple graphical frontend for Libsvm mainly intended for didactic
+purposes. You can create data points by point and click and visualize
+the decision region induced by different kernels and parameter settings.
+
+To create positive examples click the left mouse button; to create
+negative examples click the right button.
+
+If all examples are from the same class, it uses a one-class SVM.
+
+"""
+from __future__ import division, print_function
+
+print(__doc__)
+
+# Author: Peter Prettenhoer <peter.prettenhofer@gmail.com>
+#
+# License: BSD Style.
+
+import matplotlib
+matplotlib.use('TkAgg')
+
+from matplotlib.backends.backend_tkagg import FigureCanvasTkAgg
+from matplotlib.backends.backend_tkagg import NavigationToolbar2TkAgg
+from matplotlib.figure import Figure
+from matplotlib.contour import ContourSet
+
+import Tkinter as Tk
+import sys
+import numpy as np
+
+from sklearn import svm
+from sklearn.datasets import dump_svmlight_file
+from sklearn.externals.six.moves import xrange
+
+y_min, y_max = -50, 50
+x_min, x_max = -50, 50
+
+
+class Model(object):
+    """The Model which hold the data. It implements the
+    observable in the observer pattern and notifies the
+    registered observers on change event.
+    """
+
+    def __init__(self):
+        self.observers = []
+        self.surface = None
+        self.data = []
+        self.cls = None
+        self.surface_type = 0
+
+    def changed(self, event):
+        """Notify the observers. """
+        for observer in self.observers:
+            observer.update(event, self)
+
+    def add_observer(self, observer):
+        """Register an observer. """
+        self.observers.append(observer)
+
+    def set_surface(self, surface):
+        self.surface = surface
+
+    def dump_svmlight_file(self, file):
+        data = np.array(self.data)
+        X = data[:, 0:2]
+        y = data[:, 2]
+        dump_svmlight_file(X, y, file)
+
+
+class Controller(object):
+    def __init__(self, model):
+        self.model = model
+        self.kernel = Tk.IntVar()
+        self.surface_type = Tk.IntVar()
+        # Whether or not a model has been fitted
+        self.fitted = False
+
+    def fit(self):
+        print("fit the model")
+        train = np.array(self.model.data)
+        X = train[:, 0:2]
+        y = train[:, 2]
+
+        C = float(self.complexity.get())
+        gamma = float(self.gamma.get())
+        coef0 = float(self.coef0.get())
+        degree = int(self.degree.get())
+        kernel_map = {0: "linear", 1: "rbf", 2: "poly"}
+        if len(np.unique(y)) == 1:
+            clf = svm.OneClassSVM(kernel=kernel_map[self.kernel.get()],
+                                  gamma=gamma, coef0=coef0, degree=degree)
+            clf.fit(X)
+        else:
+            clf = svm.SVC(kernel=kernel_map[self.kernel.get()], C=C,
+                          gamma=gamma, coef0=coef0, degree=degree)
+            clf.fit(X, y)
+        if hasattr(clf, 'score'):
+            print("Accuracy:", clf.score(X, y) * 100)
+        X1, X2, Z = self.decision_surface(clf)
+        self.model.clf = clf
+        self.model.set_surface((X1, X2, Z))
+        self.model.surface_type = self.surface_type.get()
+        self.fitted = True
+        self.model.changed("surface")
+
+    def decision_surface(self, cls):
+        delta = 1
+        x = np.arange(x_min, x_max + delta, delta)
+        y = np.arange(y_min, y_max + delta, delta)
+        X1, X2 = np.meshgrid(x, y)
+        Z = cls.decision_function(np.c_[X1.ravel(), X2.ravel()])
+        Z = Z.reshape(X1.shape)
+        return X1, X2, Z
+
+    def clear_data(self):
+        self.model.data = []
+        self.fitted = False
+        self.model.changed("clear")
+
+    def add_example(self, x, y, label):
+        self.model.data.append((x, y, label))
+        self.model.changed("example_added")
+
+        # update decision surface if already fitted.
+        self.refit()
+
+    def refit(self):
+        """Refit the model if already fitted. """
+        if self.fitted:
+            self.fit()
+
+
+class View(object):
+    """Test docstring. """
+    def __init__(self, root, controller):
+        f = Figure()
+        ax = f.add_subplot(111)
+        ax.set_xticks([])
+        ax.set_yticks([])
+        ax.set_xlim((x_min, x_max))
+        ax.set_ylim((y_min, y_max))
+        canvas = FigureCanvasTkAgg(f, master=root)
+        canvas.show()
+        canvas.get_tk_widget().pack(side=Tk.TOP, fill=Tk.BOTH, expand=1)
+        canvas._tkcanvas.pack(side=Tk.TOP, fill=Tk.BOTH, expand=1)
+        canvas.mpl_connect('button_press_event', self.onclick)
+        toolbar = NavigationToolbar2TkAgg(canvas, root)
+        toolbar.update()
+        self.controllbar = ControllBar(root, controller)
+        self.f = f
+        self.ax = ax
+        self.canvas = canvas
+        self.controller = controller
+        self.contours = []
+        self.c_labels = None
+        self.plot_kernels()
+
+    def plot_kernels(self):
+        self.ax.text(-50, -60, "Linear: $u^T v$")
+        self.ax.text(-20, -60, "RBF: $\exp (-\gamma \| u-v \|^2)$")
+        self.ax.text(10, -60, "Poly: $(\gamma \, u^T v + r)^d$")
+
+    def onclick(self, event):
+        if event.xdata and event.ydata:
+            if event.button == 1:
+                self.controller.add_example(event.xdata, event.ydata, 1)
+            elif event.button == 3:
+                self.controller.add_example(event.xdata, event.ydata, -1)
+
+    def update_example(self, model, idx):
+        x, y, l = model.data[idx]
+        if l == 1:
+            color = 'w'
+        elif l == -1:
+            color = 'k'
+        self.ax.plot([x], [y], "%so" % color, scalex=0.0, scaley=0.0)
+
+    def update(self, event, model):
+        if event == "examples_loaded":
+            for i in xrange(len(model.data)):
+                self.update_example(model, i)
+
+        if event == "example_added":
+            self.update_example(model, -1)
+
+        if event == "clear":
+            self.ax.clear()
+            self.ax.set_xticks([])
+            self.ax.set_yticks([])
+            self.contours = []
+            self.c_labels = None
+            self.plot_kernels()
+
+        if event == "surface":
+            self.remove_surface()
+            self.plot_support_vectors(model.clf.support_vectors_)
+            self.plot_decision_surface(model.surface, model.surface_type)
+
+        self.canvas.draw()
+
+    def remove_surface(self):
+        """Remove old decision surface."""
+        if len(self.contours) > 0:
+            for contour in self.contours:
+                if isinstance(contour, ContourSet):
+                    for lineset in contour.collections:
+                        lineset.remove()
+                else:
+                    contour.remove()
+            self.contours = []
+
+    def plot_support_vectors(self, support_vectors):
+        """Plot the support vectors by placing circles over the
+        corresponding data points and adds the circle collection
+        to the contours list."""
+        cs = self.ax.scatter(support_vectors[:, 0], support_vectors[:, 1],
+                             s=80, edgecolors="k", facecolors="none")
+        self.contours.append(cs)
+
+    def plot_decision_surface(self, surface, type):
+        X1, X2, Z = surface
+        if type == 0:
+            levels = [-1.0, 0.0, 1.0]
+            linestyles = ['dashed', 'solid', 'dashed']
+            colors = 'k'
+            self.contours.append(self.ax.contour(X1, X2, Z, levels,
+                                                 colors=colors,
+                                                 linestyles=linestyles))
+        elif type == 1:
+            self.contours.append(self.ax.contourf(X1, X2, Z, 10,
+                                                  cmap=matplotlib.cm.bone,
+                                                  origin='lower', alpha=0.85))
+            self.contours.append(self.ax.contour(X1, X2, Z, [0.0], colors='k',
+                                                 linestyles=['solid']))
+        else:
+            raise ValueError("surface type unknown")
+
+
+class ControllBar(object):
+    def __init__(self, root, controller):
+        fm = Tk.Frame(root)
+        kernel_group = Tk.Frame(fm)
+        Tk.Radiobutton(kernel_group, text="Linear", variable=controller.kernel,
+                       value=0, command=controller.refit).pack(anchor=Tk.W)
+        Tk.Radiobutton(kernel_group, text="RBF", variable=controller.kernel,
+                       value=1, command=controller.refit).pack(anchor=Tk.W)
+        Tk.Radiobutton(kernel_group, text="Poly", variable=controller.kernel,
+                       value=2, command=controller.refit).pack(anchor=Tk.W)
+        kernel_group.pack(side=Tk.LEFT)
+
+        valbox = Tk.Frame(fm)
+        controller.complexity = Tk.StringVar()
+        controller.complexity.set("1.0")
+        c = Tk.Frame(valbox)
+        Tk.Label(c, text="C:", anchor="e", width=7).pack(side=Tk.LEFT)
+        Tk.Entry(c, width=6, textvariable=controller.complexity).pack(
+            side=Tk.LEFT)
+        c.pack()
+
+        controller.gamma = Tk.StringVar()
+        controller.gamma.set("0.01")
+        g = Tk.Frame(valbox)
+        Tk.Label(g, text="gamma:", anchor="e", width=7).pack(side=Tk.LEFT)
+        Tk.Entry(g, width=6, textvariable=controller.gamma).pack(side=Tk.LEFT)
+        g.pack()
+
+        controller.degree = Tk.StringVar()
+        controller.degree.set("3")
+        d = Tk.Frame(valbox)
+        Tk.Label(d, text="degree:", anchor="e", width=7).pack(side=Tk.LEFT)
+        Tk.Entry(d, width=6, textvariable=controller.degree).pack(side=Tk.LEFT)
+        d.pack()
+
+        controller.coef0 = Tk.StringVar()
+        controller.coef0.set("0")
+        r = Tk.Frame(valbox)
+        Tk.Label(r, text="coef0:", anchor="e", width=7).pack(side=Tk.LEFT)
+        Tk.Entry(r, width=6, textvariable=controller.coef0).pack(side=Tk.LEFT)
+        r.pack()
+        valbox.pack(side=Tk.LEFT)
+
+        cmap_group = Tk.Frame(fm)
+        Tk.Radiobutton(cmap_group, text="Hyperplanes",
+                       variable=controller.surface_type, value=0,
+                       command=controller.refit).pack(anchor=Tk.W)
+        Tk.Radiobutton(cmap_group, text="Surface",
+                       variable=controller.surface_type, value=1,
+                       command=controller.refit).pack(anchor=Tk.W)
+
+        cmap_group.pack(side=Tk.LEFT)
+
+        train_button = Tk.Button(fm, text='Fit', width=5,
+                                 command=controller.fit)
+        train_button.pack()
+        fm.pack(side=Tk.LEFT)
+        Tk.Button(fm, text='Clear', width=5,
+                  command=controller.clear_data).pack(side=Tk.LEFT)
+
+
+def get_parser():
+    from optparse import OptionParser
+    op = OptionParser()
+    op.add_option("--output",
+                  action="store", type="str", dest="output",
+                  help="Path where to dump data.")
+    return op
+
+
+def main(argv):
+    op = get_parser()
+    opts, args = op.parse_args(argv[1:])
+    root = Tk.Tk()
+    model = Model()
+    controller = Controller(model)
+    root.wm_title("Scikit-learn Libsvm GUI")
+    view = View(root, controller)
+    model.add_observer(view)
+    Tk.mainloop()
+
+    if opts.output:
+        model.dump_svmlight_file(opts.output)
+
+if __name__ == "__main__":
+    main(sys.argv)

test6.py

@@ -0,0 +1,95 @@
+from matplotlib import pyplot as plt
+import GPy
+import numpy as np
+
+class lvm_visualise:
+    def __init__(self, visualise, ax):
+        self.cid = ax.figure.canvas.mpl_connect('button_press_event', self.on_click)
+        self.cid = ax.figure.canvas.mpl_connect('motion_notify_event', self.on_move)
+        self.visualise = visualise
+        self.ax = ax
+        # This is vectorDisplay code
+        self.called = False
+        self.move_on = False
+
+    def on_click(self, event):
+        print 'click', event.xdata, event.ydata
+        if event.inaxes!=self.ax: return
+        self.move_on = not self.move_on
+        print
+        if self.called:
+            self.xs.append(event.xdata)
+            self.ys.append(event.ydata)
+            self.line.set_data(self.xs, self.ys)
+            self.line.figure.canvas.draw()
+        else:
+            self.xs = [event.xdata]
+            self.ys = [event.ydata]
+            self.line, = ax.plot(event.xdata, event.ydata)
+        self.called = True
+    def on_move(self, event):
+        if event.inaxes!=self.ax: return
+        if self.called and self.move_on:
+            # This is vectorModify code
+            #print 'move', event.xdata, event.ydata
+            latent_values = np.array((event.xdata, event.ydata))
+            self.visualise.modify(latent_values)
+            #print 'y', y
+
+class data_visualiser:
+    def __init__(self, model):
+        self.model = model
+
+    def modify(self, latent_values):
+        raise NotImplementedError, "this needs to be implemented to use the data_visualiser class"
+
+class vector_visualise(data_visualiser):
+    def __init__(self, model):
+        data_visualiser.__init__(self, model)
+        self.fig_display = plt.figure()
+        self.model = model
+        self.y = model.predict(np.zeros((1, model.input_dim)))[0]
+        self.handle = plt.plot(np.arange(0, model.output_dim)[:, None], self.y.T)[0]
+
+    def modify(self, latent_values):
+        y = self.model.predict(latent_values)[0]
+        xdata, ydata = self.handle.get_data()
+        self.handle.set_data(xdata, y.T)
+        plt.show()
+
+class image_visualise(data_visualiser):
+    def __init__(self, model, dimensions=(16,16), transpose=False, invert=False):
+        data_visualiser.__init__(self, model)
+        self.fig_display = plt.figure()
+        self.model = model
+        self.imvals = self.get_array(model, np.zeros((1, model.input_dim)))
+        self.handle = plt.imshow(self.imvals)
+        self.transpose = transpose
+        self.invert = invert
+
+    def modify(self, latent_values):
+        xdata, ydata = self.handle.get_data()
+        self.imvals = self.get_array(model, latent_values)
+        self.handle.set_array(self.imvals)
+        plt.show()
+
+    def get_array(self, latent_values):
+        self.y = self.model.predict(latent_values)[0]
+        imvals = np.reshape(self.y, dimensions)
+        if self.transpose:
+            imvals = imvals.T
+        if self.invert:
+            imvals = -imvals
+
+model = GPy.examples.dimensionality_reduction.oil_100()
+visualise = vector_visualise(model)
+fig = plt.figure()
+ax = fig.add_subplot(111)
+plt.ylim((-1, 1))
+plt.xlim((-1, 1))
+
+ax.set_title('latent space')
+
+linebuilder = lvm_visualise(visualise, ax)
+
+plt.show()