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Kernel

src.geostat.kernel.Kernel

Bases: Op

Kernel class representing a covariance function for Gaussian Processes (GPs).

The Kernel class defines the structure of a GP's covariance function. It supports operations such as addition and multiplication with other kernels, enabling the construction of more complex kernels through combinations. The class also provides methods for computing the covariance matrix between sets of locations.

Parameters:

  • fa (dict or callable) –

    A dictionary or callable representing the functional attributes of the kernel.

  • autoinputs (dict) –

    A dictionary specifying the automatic input mappings for the kernel. If 'offset', 'locs1', or 'locs2' keys are not present, they are added with default values.

Examples:

Creating and using a Kernel object:

from geostat.kernel import Kernel
import numpy as np

# Construct kernel and call it on locations
locs1 = np.array([[0.0, 0.0], [1.0, 1.0]])
locs2 = np.array([[2.0, 2.0], [3.0, 3.0]])
kernel = Kernel(fa={'alpha': 1.0}, autoinputs={})
covariance_matrix = kernel({'locs1': locs1, 'locs2': locs2})
print(covariance_matrix) # Covariance matrix only has zero entries as no kernel function was given
# tf.Tensor(
# [[0. 0.]
#  [0. 0.]], shape=(2, 2), dtype=float32)

Combining two kernels using addition and multiplication:

kernel1 = Kernel(fa={'alpha': 1.0}, autoinputs={})
kernel2 = Kernel(fa={'range': 0.5}, autoinputs={})
combined_kernel = kernel1 + kernel2  # Adding kernels
product_kernel = kernel1 * kernel2   # Multiplying kernels

Notes:

  • The __call__ method computes the covariance matrix between two sets of locations (locs1 and locs2) and ensures the result is correctly broadcasted to the appropriate shape.
  • The report method provides a summary of the kernel's parameters and their values.
  • This class serves as a base class for more specialized kernel functions in GP modeling.
Source code in src/geostat/kernel.py 
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class Kernel(Op):
    """
    Kernel class representing a covariance function for Gaussian Processes (GPs).

    The `Kernel` class defines the structure of a GP's covariance function. It supports operations
    such as addition and multiplication with other kernels, enabling the construction of more
    complex kernels through combinations. The class also provides methods for computing the
    covariance matrix between sets of locations.

    Parameters:
        fa (dict or callable):
            A dictionary or callable representing the functional attributes of the kernel.
        autoinputs (dict):
            A dictionary specifying the automatic input mappings for the kernel. If 'offset',
            'locs1', or 'locs2' keys are not present, they are added with default values.

    Examples:
        Creating and using a `Kernel` object:

        ```python
        from geostat.kernel import Kernel
        import numpy as np

        # Construct kernel and call it on locations
        locs1 = np.array([[0.0, 0.0], [1.0, 1.0]])
        locs2 = np.array([[2.0, 2.0], [3.0, 3.0]])
        kernel = Kernel(fa={'alpha': 1.0}, autoinputs={})
        covariance_matrix = kernel({'locs1': locs1, 'locs2': locs2})
        print(covariance_matrix) # Covariance matrix only has zero entries as no kernel function was given
        # tf.Tensor(
        # [[0. 0.]
        #  [0. 0.]], shape=(2, 2), dtype=float32)
        ```

        Combining two kernels using addition and multiplication:

        ```python
        kernel1 = Kernel(fa={'alpha': 1.0}, autoinputs={})
        kernel2 = Kernel(fa={'range': 0.5}, autoinputs={})
        combined_kernel = kernel1 + kernel2  # Adding kernels
        product_kernel = kernel1 * kernel2   # Multiplying kernels
        ```

    Examples: Notes:
        - The `__call__` method computes the covariance matrix between two sets of locations 
            (`locs1` and `locs2`) and ensures the result is correctly broadcasted to the appropriate shape.
        - The `report` method provides a summary of the kernel's parameters and their values.
        - This class serves as a base class for more specialized kernel functions in GP modeling.
    """

    def __init__(self, fa, autoinputs):
        if 'offset' not in autoinputs: autoinputs['offset'] = 'offset'
        if 'locs1' not in autoinputs: autoinputs['locs1'] = 'locs1'
        if 'locs2' not in autoinputs: autoinputs['locs2'] = 'locs2'
        super().__init__(fa, autoinputs)

    def __add__(self, other):
        if other is None:
            return self
        else:
            return Stack([self]) + other

    def __mul__(self, other):
        return Product([self]) * other

    def call(self, e):
        """
        Returns covariance for locations.
        Return values may be unbroadcasted.
        """
        pass

    def __call__(self, e):
        """
        Returns covariance for locations.
        Return values have correct shapes.
        """
        C = self.call(e)
        if C is None: C = 0.
        n1 = tf.shape(e['locs1'])[0]
        n2 = tf.shape(e['locs2'])[0]
        C = tf.broadcast_to(C, [n1, n2])
        return C

    def report(self):
        string = ', '.join('%s %4.2f' % (v.name, p[v.name]) for v in self.vars())
        return '[' + string + ']'