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""" Contains extensions to gpflow.base."""
import tensorflow as tf
from typing import Tuple
from gpflow import Parameter, Module
from gpflow.utilities import positive
from gpflow.models.util import data_input_to_tensor
from gpflow.config import default_float
[docs]
class Variance(Module):
""" A non-diagonal Variance Matrix."""
CHOLESKY_DIAGONAL_LOWER_BOUND = 1e-3
@property
def shape(self) -> Tuple[int, int]:
""" Returns (L,L), which is the shape of self.value and self.cholesky."""
return self._shape
@property
def _c_l_t(self) -> tf.Tensor:
""" The (lower triangular) Cholesky decomposition of the covariance matrix."""
return tf.RaggedTensor.from_row_lengths(self._cholesky_lower_triangle, self._row_lengths).to_tensor(default_value=0, shape=self._shape)
@property
def cholesky(self) -> tf.Tensor:
""" The (lower triangular) Cholesky decomposition of the covariance matrix."""
return tf.linalg.set_diag(self._c_l_t, self._cholesky_diagonal)
@property
def value(self):
""" The covariance matrix, shape (L,L)."""
return tf.matmul(self.cholesky, self.cholesky, transpose_b=True)
@property
def value_to_broadcast(self):
""" The covariance matrix, shape (L,1,L,1) ready to broadcast."""
return tf.reshape(self.value, self._broadcast_shape)
[docs]
def value_times_eye(self, N: int) -> tf.Tensor:
""" The cartesian product variance[:L, :L] * eye[:N, :N], transposed.
Args:
N: The dimension of the identity matrix we are multiplying by.
Returns: An [:L, :N, :L, :N] Tensor, after transposition.
"""
return self.value_to_broadcast * tf.eye(N, dtype=default_float())[tf.newaxis, :, tf.newaxis, :]
[docs]
def __init__(self, value, name: str = 'Variance', cholesky_diagonal_lower_bound: float = CHOLESKY_DIAGONAL_LOWER_BOUND):
""" Construct a non-diagonal covariance matrix. Mutable only through it's properties cholesky_diagonal and cholesky_lower_triangle.
Args:
value: A symmetric, positive definite matrix, expressed in tensorflow or numpy.
cholesky_diagonal_lower_bound: Lower bound on the diagonal of the Cholesky decomposition.
"""
super().__init__(name=name)
value = data_input_to_tensor(value)
self._shape = (value.shape[-1], value.shape[-1])
self._broadcast_shape = (value.shape[-1], 1, value.shape[-1], 1)
if value.shape != self._shape:
raise ValueError('Variance must have shape (L,L).')
cholesky = tf.linalg.cholesky(value)
self._cholesky_diagonal = tf.linalg.diag_part(cholesky)
if min(self._cholesky_diagonal) <= cholesky_diagonal_lower_bound:
raise ValueError(f'The Cholesky diagonal of {name} must be strictly greater than {cholesky_diagonal_lower_bound}.')
self._cholesky_diagonal = Parameter(self._cholesky_diagonal, transform=positive(lower=cholesky_diagonal_lower_bound),
name=name+'.cholesky_diagonal')
mask = sum([list(range(i * self._shape[0], i * (self._shape[0] + 1))) for i in range(1, self._shape[0])], start=[])
self._cholesky_lower_triangle = Parameter(tf.gather(tf.reshape(cholesky, [-1]), mask), name=name+'.cholesky_lower_triangle')
self._row_lengths = tuple(range(self._shape[0]))