示例#1
0
def covfunc_se(amplitude, lengthscale, x1, x2=None, gradient=False):

    # Make sure that hyperparameters are scalars, not an array objects
    amplitude = utils.array_to_scalar(amplitude)
    lengthscale = utils.array_to_scalar(lengthscale)

    # Compute covariance matrix
    if x2 is None:
        x1 = gp_preprocess_inputs(x1)
        #x = inputs[0]
        # Compute variance vector
        N = np.shape(x1)[0]
        K = np.ones(N)
        np.multiply(K, amplitude**2, out=K)
        # Compute gradient w.r.t. lengthscale
        if gradient:
            # TODO: Use sparse matrices?
            gradient_lengthscale = np.zeros(N)
    else:
        (x1,x2) = gp_preprocess_inputs(x1,x2)
        x1 = x1 / (lengthscale)
        x2 = x2 / (lengthscale)
        # Compute distance matrix
        K = squared_distance(x1, x2)
        # Compute gradient partly
        if gradient:
            gradient_lengthscale = np.divide(K, lengthscale)
        # Compute covariance matrix
        gp_cov_se(K, overwrite=True)
        np.multiply(K, amplitude**2, out=K)
        # Compute gradient w.r.t. lengthscale
        if gradient:
            gradient_lengthscale *= K

    # Gradient w.r.t. amplitude
    if gradient:
        gradient_amplitude = K * (2 / amplitude)

    # Return values
    if gradient:
        print("se grad", gradient_amplitude, gradient_lengthscale)
        return (K, (gradient_amplitude, gradient_lengthscale))
    else:
        return K
示例#2
0
def covfunc_se(amplitude, lengthscale, x1, x2=None, gradient=False):

    # Make sure that hyperparameters are scalars, not an array objects
    amplitude = utils.array_to_scalar(amplitude)
    lengthscale = utils.array_to_scalar(lengthscale)

    # Compute covariance matrix
    if x2 is None:
        x1 = gp_preprocess_inputs(x1)
        #x = inputs[0]
        # Compute variance vector
        N = np.shape(x1)[0]
        K = np.ones(N)
        np.multiply(K, amplitude**2, out=K)
        # Compute gradient w.r.t. lengthscale
        if gradient:
            # TODO: Use sparse matrices?
            gradient_lengthscale = np.zeros(N)
    else:
        (x1, x2) = gp_preprocess_inputs(x1, x2)
        x1 = x1 / (lengthscale)
        x2 = x2 / (lengthscale)
        # Compute distance matrix
        K = squared_distance(x1, x2)
        # Compute gradient partly
        if gradient:
            gradient_lengthscale = np.divide(K, lengthscale)
        # Compute covariance matrix
        gp_cov_se(K, overwrite=True)
        np.multiply(K, amplitude**2, out=K)
        # Compute gradient w.r.t. lengthscale
        if gradient:
            gradient_lengthscale *= K

    # Gradient w.r.t. amplitude
    if gradient:
        gradient_amplitude = K * (2 / amplitude)

    # Return values
    if gradient:
        print("se grad", gradient_amplitude, gradient_lengthscale)
        return (K, (gradient_amplitude, gradient_lengthscale))
    else:
        return K
示例#3
0
def covfunc_delta(amplitude, x1, x2=None, gradient=False):

    # Make sure that amplitude is a scalar, not an array object
    amplitude = utils.array_to_scalar(amplitude)

    ## if gradient:
    ##     gradient_amplitude = gradient[0]
    ## else:
    ##     gradient_amplitude = []

    ## inputs = gp_preprocess_inputs(*inputs)

    # Compute distance and covariance matrix
    if x2 is None:
        x1 = gp_preprocess_inputs(x1)
        # Only variance vector asked
        #x = inputs[0]
        N = np.shape(x1)[0]
        K = np.ones(N) * amplitude**2

    else:
        (x1,x2) = gp_preprocess_inputs(x1,x2)
        # Full covariance matrix asked
        #x1 = inputs[0]
        #x2 = inputs[1]
        # Number of inputs x1
        N1 = np.shape(x1)[0]

        # x1 == x2?
        if x1 is x2:
            delta = True
            # Delta covariance
            #
            # FIXME: Broadcasting doesn't work with sparse matrices,
            # so must use scalar multiplication
            K = gp_cov_delta(N1) * amplitude**2
            #K = gp_cov_delta(N1).multiply(amplitude**2)
        else:
            delta = False
            # Number of inputs x2
            N2 = np.shape(x2)[0]
            # Zero covariance
            if N1 > 0 and N2 > 0:
                K = sp.csc_matrix((N1,N2))
            else:
                K = np.zeros((N1,N2))

    # Gradient w.r.t. amplitude
    if gradient:
        # FIXME: Broadcasting doesn't work with sparse matrices,
        # so must use scalar multiplication
        gradient_amplitude = K*(2/amplitude)
        print("noise grad", gradient_amplitude)
        return (K, (gradient_amplitude,))
    else:
        return K
示例#4
0
def covfunc_delta(amplitude, x1, x2=None, gradient=False):

    # Make sure that amplitude is a scalar, not an array object
    amplitude = utils.array_to_scalar(amplitude)

    ## if gradient:
    ##     gradient_amplitude = gradient[0]
    ## else:
    ##     gradient_amplitude = []

    ## inputs = gp_preprocess_inputs(*inputs)

    # Compute distance and covariance matrix
    if x2 is None:
        x1 = gp_preprocess_inputs(x1)
        # Only variance vector asked
        #x = inputs[0]
        N = np.shape(x1)[0]
        K = np.ones(N) * amplitude**2

    else:
        (x1, x2) = gp_preprocess_inputs(x1, x2)
        # Full covariance matrix asked
        #x1 = inputs[0]
        #x2 = inputs[1]
        # Number of inputs x1
        N1 = np.shape(x1)[0]

        # x1 == x2?
        if x1 is x2:
            delta = True
            # Delta covariance
            #
            # FIXME: Broadcasting doesn't work with sparse matrices,
            # so must use scalar multiplication
            K = gp_cov_delta(N1) * amplitude**2
            #K = gp_cov_delta(N1).multiply(amplitude**2)
        else:
            delta = False
            # Number of inputs x2
            N2 = np.shape(x2)[0]
            # Zero covariance
            if N1 > 0 and N2 > 0:
                K = sp.csc_matrix((N1, N2))
            else:
                K = np.zeros((N1, N2))

    # Gradient w.r.t. amplitude
    if gradient:
        # FIXME: Broadcasting doesn't work with sparse matrices,
        # so must use scalar multiplication
        gradient_amplitude = K * (2 / amplitude)
        print("noise grad", gradient_amplitude)
        return (K, (gradient_amplitude, ))
    else:
        return K
示例#5
0
def covfunc_pp2(amplitude, lengthscale, x1, x2=None, gradient=False):

    # Make sure that hyperparameters are scalars, not an array objects
    amplitude = utils.array_to_scalar(amplitude)
    lengthscale = utils.array_to_scalar(lengthscale)
    #amplitude = theta[0]
    #lengthscale = theta[1]

    ## if gradient:
    ##     gradient_amplitude = gradient[0]
    ##     gradient_lengthscale = gradient[1]
    ## else:
    ##     gradient_amplitude = []
    ##     gradient_lengthscale = []

    ## inputs = gp_preprocess_inputs(*inputs)

    # Compute covariance matrix
    if x2 is None:
        x1 = gp_preprocess_inputs(x1)
        # Compute variance vector
        K = np.ones(np.shape(x)[:-1])
        K *= amplitude**2
        # Compute gradient w.r.t. lengthscale
        if gradient:
            gradient_lengthscale = np.zeros(np.shape(x1)[:-1])
    
    else:
        (x1,x2) = gp_preprocess_inputs(x1,x2)
        # Compute (sparse) distance matrix
        if x1 is x2:
            x1 = x1 / (lengthscale)
            x2 = x1
            D2 = distance.sparse_pdist(x1, 1.0, form="full", format="csc")
        else:
            x1 = x1 / (lengthscale)
            x2 = x2 / (lengthscale)
            D2 = distance.sparse_cdist(x1, x2, 1.0, format="csc")
        r = np.sqrt(D2.data)

        N1 = np.shape(x1)[0]
        N2 = np.shape(x2)[0]
        
        # Compute the covariances
        if gradient:
            (k, dk) = gp_cov_pp2(r, np.shape(x1)[-1], gradient=True)
        else:
            k = gp_cov_pp2(r, np.shape(x1)[-1])
        k *= amplitude**2
        # Compute gradient w.r.t. lengthscale
        if gradient:
            if N1 >= 1 and N2 >= 1:
                dk *= r * (-amplitude**2 / lengthscale)
                gradient_lengthscale = sp.csc_matrix((dk, D2.indices, D2.indptr),
                                                     shape=(N1,N2))
            else:
                gradient_lengthscale = np.empty((N1,N2))
            
        # Form sparse covariance matrix
        if N1 >= 1 and N2 >= 1:
            ## K = sp.csc_matrix((k, ij), shape=(N1,N2))
            K = sp.csc_matrix((k, D2.indices, D2.indptr), shape=(N1,N2))
        else:
            K = np.empty((N1, N2))
        #print(K.__class__)

    # Gradient w.r.t. amplitude
    if gradient:
        gradient_amplitude = K * (2 / amplitude)

    # Return values
    if gradient:
        print("pp2 grad", gradient_lengthscale)
        return (K, (gradient_amplitude, gradient_lengthscale))
    else:
        return K
示例#6
0
def covfunc_pp2(amplitude, lengthscale, x1, x2=None, gradient=False):

    # Make sure that hyperparameters are scalars, not an array objects
    amplitude = utils.array_to_scalar(amplitude)
    lengthscale = utils.array_to_scalar(lengthscale)
    #amplitude = theta[0]
    #lengthscale = theta[1]

    ## if gradient:
    ##     gradient_amplitude = gradient[0]
    ##     gradient_lengthscale = gradient[1]
    ## else:
    ##     gradient_amplitude = []
    ##     gradient_lengthscale = []

    ## inputs = gp_preprocess_inputs(*inputs)

    # Compute covariance matrix
    if x2 is None:
        x1 = gp_preprocess_inputs(x1)
        # Compute variance vector
        K = np.ones(np.shape(x)[:-1])
        K *= amplitude**2
        # Compute gradient w.r.t. lengthscale
        if gradient:
            gradient_lengthscale = np.zeros(np.shape(x1)[:-1])

    else:
        (x1, x2) = gp_preprocess_inputs(x1, x2)
        # Compute (sparse) distance matrix
        if x1 is x2:
            x1 = x1 / (lengthscale)
            x2 = x1
            D2 = distance.sparse_pdist(x1, 1.0, form="full", format="csc")
        else:
            x1 = x1 / (lengthscale)
            x2 = x2 / (lengthscale)
            D2 = distance.sparse_cdist(x1, x2, 1.0, format="csc")
        r = np.sqrt(D2.data)

        N1 = np.shape(x1)[0]
        N2 = np.shape(x2)[0]

        # Compute the covariances
        if gradient:
            (k, dk) = gp_cov_pp2(r, np.shape(x1)[-1], gradient=True)
        else:
            k = gp_cov_pp2(r, np.shape(x1)[-1])
        k *= amplitude**2
        # Compute gradient w.r.t. lengthscale
        if gradient:
            if N1 >= 1 and N2 >= 1:
                dk *= r * (-amplitude**2 / lengthscale)
                gradient_lengthscale = sp.csc_matrix(
                    (dk, D2.indices, D2.indptr), shape=(N1, N2))
            else:
                gradient_lengthscale = np.empty((N1, N2))

        # Form sparse covariance matrix
        if N1 >= 1 and N2 >= 1:
            ## K = sp.csc_matrix((k, ij), shape=(N1,N2))
            K = sp.csc_matrix((k, D2.indices, D2.indptr), shape=(N1, N2))
        else:
            K = np.empty((N1, N2))
        #print(K.__class__)

    # Gradient w.r.t. amplitude
    if gradient:
        gradient_amplitude = K * (2 / amplitude)

    # Return values
    if gradient:
        print("pp2 grad", gradient_lengthscale)
        return (K, (gradient_amplitude, gradient_lengthscale))
    else:
        return K