GPy/GPy/testing/kernel_tests.py

# Copyright (c) 2012, 2013 GPy authors (see AUTHORS.txt).
# Licensed under the BSD 3-clause license (see LICENSE.txt)

import unittest
import numpy as np
import GPy
from GPy.core.parameterization.param import Param
from ..util.config import config

verbose = 0

try:
    from ..util import linalg_cython
    config.set('cython', 'working', 'True')
except ImportError:
    config.set('cython', 'working', 'False')


class Kern_check_model(GPy.core.Model):
    """
    This is a dummy model class used as a base class for checking that the
    gradients of a given kernel are implemented correctly. It enables
    checkgrad() to be called independently on a kernel.
    """
    def __init__(self, kernel=None, dL_dK=None, X=None, X2=None):
        super(Kern_check_model, self).__init__('kernel_test_model')
        if kernel==None:
            kernel = GPy.kern.RBF(1)
        kernel.randomize(loc=1, scale=0.1)
        if X is None:
            X = np.random.randn(20, kernel.input_dim)
        if dL_dK is None:
            if X2 is None:
                dL_dK = np.random.rand(X.shape[0], X.shape[0])
            else:
                dL_dK = np.random.rand(X.shape[0], X2.shape[0])

        self.kernel = kernel
        self.X = X
        self.X2 = X2
        self.dL_dK = dL_dK

    def is_positive_semi_definite(self):
        v = np.linalg.eig(self.kernel.K(self.X))[0]
        if any(v.real<=-1e-10):
            print(v.real.min())
            return False
        else:
            return True

    def log_likelihood(self):
        return np.sum(self.dL_dK*self.kernel.K(self.X, self.X2))

class Kern_check_dK_dtheta(Kern_check_model):
    """
    This class allows gradient checks for the gradient of a kernel with
    respect to parameters.
    """
    def __init__(self, kernel=None, dL_dK=None, X=None, X2=None):
        Kern_check_model.__init__(self,kernel=kernel,dL_dK=dL_dK, X=X, X2=X2)
        self.link_parameter(self.kernel)

    def parameters_changed(self):
        return self.kernel.update_gradients_full(self.dL_dK, self.X, self.X2)


class Kern_check_dKdiag_dtheta(Kern_check_model):
    """
    This class allows gradient checks of the gradient of the diagonal of a
    kernel with respect to the parameters.
    """
    def __init__(self, kernel=None, dL_dK=None, X=None):
        Kern_check_model.__init__(self,kernel=kernel,dL_dK=dL_dK, X=X, X2=None)
        self.link_parameter(self.kernel)

    def log_likelihood(self):
        return (np.diag(self.dL_dK)*self.kernel.Kdiag(self.X)).sum()

    def parameters_changed(self):
        self.kernel.update_gradients_diag(np.diag(self.dL_dK), self.X)

class Kern_check_dK_dX(Kern_check_model):
    """This class allows gradient checks for the gradient of a kernel with respect to X. """
    def __init__(self, kernel=None, dL_dK=None, X=None, X2=None):
        Kern_check_model.__init__(self,kernel=kernel,dL_dK=dL_dK, X=X, X2=X2)
        self.X = Param('X',X)
        self.link_parameter(self.X)

    def parameters_changed(self):
        self.X.gradient[:] =  self.kernel.gradients_X(self.dL_dK, self.X, self.X2)

class Kern_check_dKdiag_dX(Kern_check_dK_dX):
    """This class allows gradient checks for the gradient of a kernel diagonal with respect to X. """
    def __init__(self, kernel=None, dL_dK=None, X=None, X2=None):
        Kern_check_dK_dX.__init__(self,kernel=kernel,dL_dK=dL_dK, X=X, X2=None)

    def log_likelihood(self):
        return (np.diag(self.dL_dK)*self.kernel.Kdiag(self.X)).sum()

    def parameters_changed(self):
        self.X.gradient[:] =  self.kernel.gradients_X_diag(self.dL_dK.diagonal(), self.X)



def check_kernel_gradient_functions(kern, X=None, X2=None, output_ind=None, verbose=False, fixed_X_dims=None):
    """
    This function runs on kernels to check the correctness of their
    implementation. It checks that the covariance function is positive definite
    for a randomly generated data set.

    :param kern: the kernel to be tested.
    :type kern: GPy.kern.Kernpart
    :param X: X input values to test the covariance function.
    :type X: ndarray
    :param X2: X2 input values to test the covariance function.
    :type X2: ndarray

    """
    pass_checks = True
    if X is None:
        X = np.random.randn(10, kern.input_dim)
        if output_ind is not None:
            X[:, output_ind] = np.random.randint(kern.output_dim, X.shape[0])
    if X2 is None:
        X2 = np.random.randn(20, kern.input_dim)
        if output_ind is not None:
            X2[:, output_ind] = np.random.randint(kern.output_dim, X2.shape[0])

    if verbose:
        print("Checking covariance function is positive definite.")
    result = Kern_check_model(kern, X=X).is_positive_semi_definite()
    if result and verbose:
        print("Check passed.")
    if not result:
        print(("Positive definite check failed for " + kern.name + " covariance function."))
        pass_checks = False
        assert(result)
        return False

    if verbose:
        print("Checking gradients of K(X, X) wrt theta.")
    result = Kern_check_dK_dtheta(kern, X=X, X2=None).checkgrad(verbose=verbose)
    if result and verbose:
        print("Check passed.")
    if not result:
        print(("Gradient of K(X, X) wrt theta failed for " + kern.name + " covariance function. Gradient values as follows:"))
        Kern_check_dK_dtheta(kern, X=X, X2=None).checkgrad(verbose=True)
        pass_checks = False
        assert(result)
        return False

    if verbose:
        print("Checking gradients of K(X, X2) wrt theta.")
    result = Kern_check_dK_dtheta(kern, X=X, X2=X2).checkgrad(verbose=verbose)
    if result and verbose:
        print("Check passed.")
    if not result:
        print(("Gradient of K(X, X) wrt theta failed for " + kern.name + " covariance function. Gradient values as follows:"))
        Kern_check_dK_dtheta(kern, X=X, X2=X2).checkgrad(verbose=True)
        pass_checks = False
        assert(result)
        return False

    if verbose:
        print("Checking gradients of Kdiag(X) wrt theta.")
    try:
        result = Kern_check_dKdiag_dtheta(kern, X=X).checkgrad(verbose=verbose)
    except NotImplementedError:
        result=True
        if verbose:
            print(("update_gradients_diag not implemented for " + kern.name))
    if result and verbose:
        print("Check passed.")
    if not result:
        print(("Gradient of Kdiag(X) wrt theta failed for " + kern.name + " covariance function. Gradient values as follows:"))
        Kern_check_dKdiag_dtheta(kern, X=X).checkgrad(verbose=True)
        pass_checks = False
        assert(result)
        return False

    if verbose:
        print("Checking gradients of K(X, X) wrt X.")
    try:
        testmodel = Kern_check_dK_dX(kern, X=X, X2=None)
        if fixed_X_dims is not None:
            testmodel.X[:,fixed_X_dims].fix()
        result = testmodel.checkgrad(verbose=verbose)
    except NotImplementedError:
        result=True
        if verbose:
            print(("gradients_X not implemented for " + kern.name))
    if result and verbose:
        print("Check passed.")
    if not result:
        print(("Gradient of K(X, X) wrt X failed for " + kern.name + " covariance function. Gradient values as follows:"))
        testmodel.checkgrad(verbose=True)
        assert(result)
        pass_checks = False
        return False

    if verbose:
        print("Checking gradients of K(X, X2) wrt X.")
    try:
        testmodel = Kern_check_dK_dX(kern, X=X, X2=X2)
        if fixed_X_dims is not None:
            testmodel.X[:,fixed_X_dims].fix()
        result = testmodel.checkgrad(verbose=verbose)
    except NotImplementedError:
        result=True
        if verbose:
            print(("gradients_X not implemented for " + kern.name))
    if result and verbose:
        print("Check passed.")
    if not result:
        print(("Gradient of K(X, X2) wrt X failed for " + kern.name + " covariance function. Gradient values as follows:"))
        testmodel.checkgrad(verbose=True)
        assert(result)
        pass_checks = False
        return False

    if verbose:
        print("Checking gradients of Kdiag(X) wrt X.")
    try:
        testmodel = Kern_check_dKdiag_dX(kern, X=X)
        if fixed_X_dims is not None:
            testmodel.X[:,fixed_X_dims].fix()
        result = testmodel.checkgrad(verbose=verbose)
    except NotImplementedError:
        result=True
        if verbose:
            print(("gradients_X not implemented for " + kern.name))
    if result and verbose:
        print("Check passed.")
    if not result:
        print(("Gradient of Kdiag(X) wrt X failed for " + kern.name + " covariance function. Gradient values as follows:"))
        Kern_check_dKdiag_dX(kern, X=X).checkgrad(verbose=True)
        pass_checks = False
        assert(result)
        return False

    return pass_checks



class KernelGradientTestsContinuous(unittest.TestCase):
    def setUp(self):
        self.N, self.D = 10, 5
        self.X = np.random.randn(self.N,self.D)
        self.X2 = np.random.randn(self.N+10,self.D)

        continuous_kerns = ['RBF', 'Linear']
        self.kernclasses = [getattr(GPy.kern, s) for s in continuous_kerns]

    def test_MLP(self):
        k = GPy.kern.MLP(self.D,ARD=True)
        k.randomize()
        self.assertTrue(check_kernel_gradient_functions(k, X=self.X, X2=self.X2, verbose=verbose))

    def test_Matern32(self):
        k = GPy.kern.Matern32(self.D)
        k.randomize()
        self.assertTrue(check_kernel_gradient_functions(k, X=self.X, X2=self.X2, verbose=verbose))

    def test_Prod(self):
        k = GPy.kern.Matern32(2, active_dims=[2,3]) * GPy.kern.RBF(2, active_dims=[0,4]) + GPy.kern.Linear(self.D)
        k.randomize()
        self.assertTrue(check_kernel_gradient_functions(k, X=self.X, X2=self.X2, verbose=verbose))

    def test_Prod1(self):
        k = GPy.kern.RBF(self.D) * GPy.kern.Linear(self.D)
        k.randomize()
        self.assertTrue(check_kernel_gradient_functions(k, X=self.X, X2=self.X2, verbose=verbose))

    def test_Prod2(self):
        k = GPy.kern.RBF(2, active_dims=[0,4]) * GPy.kern.Linear(self.D)
        k.randomize()
        self.assertTrue(check_kernel_gradient_functions(k, X=self.X, X2=self.X2, verbose=verbose))

    def test_Prod3(self):
        k = GPy.kern.RBF(self.D) * GPy.kern.Linear(self.D) * GPy.kern.Bias(self.D)
        k.randomize()
        self.assertTrue(check_kernel_gradient_functions(k, X=self.X, X2=self.X2, verbose=verbose))

    def test_Prod4(self):
        k = GPy.kern.RBF(2, active_dims=[0,4]) * GPy.kern.Linear(self.D) * GPy.kern.Matern32(2, active_dims=[0,1])
        k.randomize()
        self.assertTrue(check_kernel_gradient_functions(k, X=self.X, X2=self.X2, verbose=verbose))

    def test_Add(self):
        k = GPy.kern.Matern32(2, active_dims=[2,3]) + GPy.kern.RBF(2, active_dims=[0,4]) + GPy.kern.Linear(self.D)
        k += GPy.kern.Matern32(2, active_dims=[2,3]) + GPy.kern.RBF(2, active_dims=[0,4]) + GPy.kern.Linear(self.D)
        k.randomize()
        self.assertTrue(check_kernel_gradient_functions(k, X=self.X, X2=self.X2, verbose=verbose))

    def test_Add_dims(self):
        k = GPy.kern.Matern32(2, active_dims=[2,self.D]) + GPy.kern.RBF(2, active_dims=[0,4]) + GPy.kern.Linear(self.D)
        k.randomize()
        self.assertRaises(IndexError, k.K, self.X)
        k = GPy.kern.Matern32(2, active_dims=[2,self.D-1]) + GPy.kern.RBF(2, active_dims=[0,4]) + GPy.kern.Linear(self.D)
        k.randomize()
        # assert it runs:
        try:
            k.K(self.X)
        except AssertionError:
            raise AssertionError("k.K(X) should run on self.D-1 dimension")

    def test_Matern52(self):
        k = GPy.kern.Matern52(self.D)
        k.randomize()
        self.assertTrue(check_kernel_gradient_functions(k, X=self.X, X2=self.X2, verbose=verbose))

    def test_RBF(self):
        k = GPy.kern.RBF(self.D, ARD=True)
        k.randomize()
        self.assertTrue(check_kernel_gradient_functions(k, X=self.X, X2=self.X2, verbose=verbose))

    def test_Linear(self):
        k = GPy.kern.Linear(self.D)
        k.randomize()
        self.assertTrue(check_kernel_gradient_functions(k, X=self.X, X2=self.X2, verbose=verbose))

    def test_LinearFull(self):
        k = GPy.kern.LinearFull(self.D, self.D-1)
        k.randomize()
        self.assertTrue(check_kernel_gradient_functions(k, X=self.X, X2=self.X2, verbose=verbose))

    def test_Poly(self):
        k = GPy.kern.Poly(self.D, order=5)
        k.randomize()
        self.assertTrue(check_kernel_gradient_functions(k, X=self.X, X2=self.X2, verbose=verbose))

    def test_WhiteHeteroscedastic(self):
        k = GPy.kern.WhiteHeteroscedastic(self.D, self.X.shape[0])
        k.randomize()
        self.assertTrue(check_kernel_gradient_functions(k, X=self.X, X2=self.X2, verbose=verbose))

    def test_standard_periodic(self):
        k = GPy.kern.StdPeriodic(self.D)
        k.randomize()
        self.assertTrue(check_kernel_gradient_functions(k, X=self.X, X2=self.X2, verbose=verbose))

class KernelTestsMiscellaneous(unittest.TestCase):
    def setUp(self):
        N, D = 100, 10
        self.X = np.linspace(-np.pi, +np.pi, N)[:,None] * np.random.uniform(-10,10,D)
        self.rbf = GPy.kern.RBF(2, active_dims=np.arange(0,4,2))
        self.rbf.randomize()
        self.linear = GPy.kern.Linear(2, active_dims=(3,9))
        self.linear.randomize()
        self.matern = GPy.kern.Matern32(3, active_dims=np.array([1,7,9]))
        self.matern.randomize()
        self.sumkern = self.rbf + self.linear
        self.sumkern += self.matern
        #self.sumkern.randomize()

    def test_which_parts(self):
        self.assertTrue(np.allclose(self.sumkern.K(self.X, which_parts=[self.linear, self.matern]), self.linear.K(self.X)+self.matern.K(self.X)))
        self.assertTrue(np.allclose(self.sumkern.K(self.X, which_parts=[self.linear, self.rbf]), self.linear.K(self.X)+self.rbf.K(self.X)))
        self.assertTrue(np.allclose(self.sumkern.K(self.X, which_parts=self.sumkern.parts[0]), self.rbf.K(self.X)))

    def test_active_dims(self):
        np.testing.assert_array_equal(self.sumkern.active_dims, [0,1,2,3,7,9])
        np.testing.assert_array_equal(self.sumkern._all_dims_active, range(10))
        tmp = self.linear+self.rbf
        np.testing.assert_array_equal(tmp.active_dims, [0,2,3,9])
        np.testing.assert_array_equal(tmp._all_dims_active, range(10))
        tmp = self.matern+self.rbf
        np.testing.assert_array_equal(tmp.active_dims, [0,1,2,7,9])
        np.testing.assert_array_equal(tmp._all_dims_active, range(10))
        tmp = self.matern+self.rbf*self.linear
        np.testing.assert_array_equal(tmp.active_dims, [0,1,2,3,7,9])
        np.testing.assert_array_equal(tmp._all_dims_active, range(10))
        tmp = self.matern+self.rbf+self.linear
        np.testing.assert_array_equal(tmp.active_dims, [0,1,2,3,7,9])
        np.testing.assert_array_equal(tmp._all_dims_active, range(10))
        tmp = self.matern*self.rbf*self.linear
        np.testing.assert_array_equal(tmp.active_dims, [0,1,2,3,7,9])
        np.testing.assert_array_equal(tmp._all_dims_active, range(10))

class KernelTestsNonContinuous(unittest.TestCase):
    def setUp(self):
        N0 = 3
        N1 = 9
        N2 = 4
        N = N0+N1+N2
        self.D = 3
        self.X = np.random.randn(N, self.D+1)
        indices = np.random.random_integers(0, 2, size=N)
        self.X[indices==0, -1] = 0
        self.X[indices==1, -1] = 1
        self.X[indices==2, -1] = 2
        #self.X = self.X[self.X[:, -1].argsort(), :]
        self.X2 = np.random.randn((N0+N1)*2, self.D+1)
        self.X2[:(N0*2), -1] = 0
        self.X2[(N0*2):, -1] = 1

    @unittest.expectedFailure
    def test_IndependentOutputs(self):
        k = GPy.kern.RBF(self.D, active_dims=range(self.D))
        kern = GPy.kern.IndependentOutputs(k, -1, 'ind_single')
        self.assertTrue(check_kernel_gradient_functions(kern, X=self.X, X2=self.X2, verbose=verbose, fixed_X_dims=-1))
        k = [GPy.kern.RBF(1, active_dims=[1], name='rbf1'), GPy.kern.RBF(self.D, active_dims=range(self.D), name='rbf012'), GPy.kern.RBF(2, active_dims=[0,2], name='rbf02')]
        kern = GPy.kern.IndependentOutputs(k, -1, name='ind_split')
        self.assertTrue(check_kernel_gradient_functions(kern, X=self.X, X2=self.X2, verbose=verbose, fixed_X_dims=-1))

    @unittest.expectedFailure
    def test_Hierarchical(self):
        k = [GPy.kern.RBF(2, active_dims=[0,2], name='rbf1'), GPy.kern.RBF(2, active_dims=[0,2], name='rbf2')]
        kern = GPy.kern.IndependentOutputs(k, -1, name='ind_split')
        self.assertTrue(check_kernel_gradient_functions(kern, X=self.X, X2=self.X2, verbose=verbose, fixed_X_dims=-1))


    def test_ODE_UY(self):
        kern = GPy.kern.ODE_UY(2, active_dims=[0, self.D])
        X = self.X[self.X[:,-1]!=2]
        X2 = self.X2[self.X2[:,-1]!=2]
        self.assertTrue(check_kernel_gradient_functions(kern, X=X, X2=X2, verbose=verbose, fixed_X_dims=-1))

@unittest.skipIf(not config.getboolean('cython', 'working'),"Cython modules have not been built on this machine")
class Coregionalize_cython_test(unittest.TestCase):
    """
    Make sure that the coregionalize kernel work with and without cython enabled
    """
    def setUp(self):
        self.k = GPy.kern.Coregionalize(1, output_dim=12)
        self.N1, self.N2 = 100, 200
        self.X = np.random.randint(0,12,(self.N1,1))
        self.X2 = np.random.randint(0,12,(self.N2,1))

    def test_sym(self):
        dL_dK = np.random.randn(self.N1, self.N1)
        GPy.util.config.config.set('cython', 'working', 'True')
        K_cython = self.k.K(self.X)
        self.k.update_gradients_full(dL_dK, self.X)
        grads_cython = self.k.gradient.copy()

        GPy.util.config.config.set('cython', 'working', 'False')
        K_numpy = self.k.K(self.X)
        self.k.update_gradients_full(dL_dK, self.X)
        grads_numpy = self.k.gradient.copy()

        self.assertTrue(np.allclose(K_numpy, K_cython))
        self.assertTrue(np.allclose(grads_numpy, grads_cython))

        #reset the cython state for any other tests
        GPy.util.config.config.set('cython', 'working', 'true')

    def test_nonsym(self):
        dL_dK = np.random.randn(self.N1, self.N2)
        GPy.util.config.config.set('cython', 'working', 'True')
        K_cython = self.k.K(self.X, self.X2)
        self.k.gradient = 0.
        self.k.update_gradients_full(dL_dK, self.X, self.X2)
        grads_cython = self.k.gradient.copy()

        GPy.util.config.config.set('cython', 'working', 'False')
        K_numpy = self.k.K(self.X, self.X2)
        self.k.gradient = 0.
        self.k.update_gradients_full(dL_dK, self.X, self.X2)
        grads_numpy = self.k.gradient.copy()

        self.assertTrue(np.allclose(K_numpy, K_cython))
        self.assertTrue(np.allclose(grads_numpy, grads_cython))

        #reset the cython state for any other tests
        GPy.util.config.config.set('cython', 'working', 'true')



class KernelTestsProductWithZeroValues(unittest.TestCase):

    def setUp(self):
        self.X = np.array([[0,1],[1,0]])
        self.k = GPy.kern.Linear(2) * GPy.kern.Bias(2)

    def test_zero_valued_kernel_full(self):
        self.k.update_gradients_full(1, self.X)
        self.assertFalse(np.isnan(self.k['linear.variances'].gradient),
                         "Gradient resulted in NaN")

    def test_zero_valued_kernel_gradients_X(self):
        target = self.k.gradients_X(1, self.X)
        self.assertFalse(np.any(np.isnan(target)),
                         "Gradient resulted in NaN")

class Kernel_Psi_statistics_GradientTests(unittest.TestCase):

    def setUp(self):
        from GPy.core.parameterization.variational import NormalPosterior
        N,M,Q = 100,20,3

        X = np.random.randn(N,Q)
        X_var = np.random.rand(N,Q)+0.01
        self.Z = np.random.randn(M,Q)
        self.qX = NormalPosterior(X, X_var)

        self.w1 = np.random.randn(N)
        self.w2 = np.random.randn(N,M)
        self.w3 = np.random.randn(M,M)
        self.w3 = self.w3#+self.w3.T
        self.w3n = np.random.randn(N,M,M)
        self.w3n = self.w3n+np.swapaxes(self.w3n, 1,2)

    def test_kernels(self):
        from GPy.kern import RBF,Linear,MLP,Bias,White
        Q = self.Z.shape[1]
        kernels = [RBF(Q,ARD=True), Linear(Q,ARD=True),MLP(Q,ARD=True), RBF(Q,ARD=True)+Linear(Q,ARD=True)+Bias(Q)+White(Q)
                  ,RBF(Q,ARD=True)+Bias(Q)+White(Q),  Linear(Q,ARD=True)+Bias(Q)+White(Q)]

        for k in kernels:
            k.randomize()
            self._test_kernel_param(k)
            self._test_Z(k)
            self._test_qX(k)
            self._test_kernel_param(k, psi2n=True)
            self._test_Z(k, psi2n=True)
            self._test_qX(k, psi2n=True)

    def _test_kernel_param(self, kernel, psi2n=False):

        def f(p):
            kernel.param_array[:] = p
            psi0 = kernel.psi0(self.Z, self.qX)
            psi1 = kernel.psi1(self.Z, self.qX)
            if not psi2n:
                psi2 = kernel.psi2(self.Z, self.qX)
                return (self.w1*psi0).sum() + (self.w2*psi1).sum() + (self.w3*psi2).sum()
            else:
                psi2 = kernel.psi2n(self.Z, self.qX)
                return (self.w1*psi0).sum() + (self.w2*psi1).sum() + (self.w3n*psi2).sum()

        def df(p):
            kernel.param_array[:] = p
            kernel.update_gradients_expectations(self.w1, self.w2, self.w3 if not psi2n else self.w3n, self.Z, self.qX)
            return kernel.gradient.copy()

        from GPy.models import GradientChecker
        m = GradientChecker(f, df, kernel.param_array.copy())
        m.checkgrad(verbose=1)
        self.assertTrue(m.checkgrad())

    def _test_Z(self, kernel, psi2n=False):

        def f(p):
            psi0 = kernel.psi0(p, self.qX)
            psi1 = kernel.psi1(p, self.qX)
            psi2 = kernel.psi2(p, self.qX)
            if not psi2n:
                psi2 = kernel.psi2(p, self.qX)
                return (self.w1*psi0).sum() + (self.w2*psi1).sum() + (self.w3*psi2).sum()
            else:
                psi2 = kernel.psi2n(p, self.qX)
                return (self.w1*psi0).sum() + (self.w2*psi1).sum() + (self.w3n*psi2).sum()

        def df(p):
            return kernel.gradients_Z_expectations(self.w1, self.w2, self.w3 if not psi2n else self.w3n, p, self.qX)

        from GPy.models import GradientChecker
        m = GradientChecker(f, df, self.Z.copy())
        self.assertTrue(m.checkgrad())

    def _test_qX(self, kernel, psi2n=False):

        def f(p):
            self.qX.param_array[:] = p
            self.qX._trigger_params_changed()
            psi0 = kernel.psi0(self.Z, self.qX)
            psi1 = kernel.psi1(self.Z, self.qX)
            if not psi2n:
                psi2 = kernel.psi2(self.Z, self.qX)
                return (self.w1*psi0).sum() + (self.w2*psi1).sum() + (self.w3*psi2).sum()
            else:
                psi2 = kernel.psi2n(self.Z, self.qX)
                return (self.w1*psi0).sum() + (self.w2*psi1).sum() + (self.w3n*psi2).sum()

        def df(p):
            self.qX.param_array[:] = p
            self.qX._trigger_params_changed()
            grad =  kernel.gradients_qX_expectations(self.w1, self.w2, self.w3 if not psi2n else self.w3n, self.Z, self.qX)
            self.qX.set_gradients(grad)
            return self.qX.gradient.copy()

        from GPy.models import GradientChecker
        m = GradientChecker(f, df, self.qX.param_array.copy())
        self.assertTrue(m.checkgrad())

if __name__ == "__main__":
    print("Running unit tests, please be (very) patient...")
    unittest.main()

#     np.random.seed(0)
#     N0 = 3
#     N1 = 9
#     N2 = 4
#     N = N0+N1+N2
#     D = 3
#     X = np.random.randn(N, D+1)
#     indices = np.random.random_integers(0, 2, size=N)
#     X[indices==0, -1] = 0
#     X[indices==1, -1] = 1
#     X[indices==2, -1] = 2
#     #X = X[X[:, -1].argsort(), :]
#     X2 = np.random.randn((N0+N1)*2, D+1)
#     X2[:(N0*2), -1] = 0
#     X2[(N0*2):, -1] = 1
#     k = [GPy.kern.RBF(1, active_dims=[1], name='rbf1'), GPy.kern.RBF(D, name='rbf012'), GPy.kern.RBF(2, active_dims=[0,2], name='rbf02')]
#     kern = GPy.kern.IndependentOutputs(k, -1, name='ind_split')
#     assert(check_kernel_gradient_functions(kern, X=X, X2=X2, verbose=verbose, fixed_X_dims=-1))
#     k = GPy.kern.RBF(D)
#     kern = GPy.kern.IndependentOutputs(k, -1, 'ind_single')
#     assert(check_kernel_gradient_functions(kern, X=X, X2=X2, verbose=verbose, fixed_X_dims=-1))