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import warnings
from typing import Any, List, Optional, Tuple
import numpy as np
from docarray.computation import AbstractComputationalBackend
from docarray.computation.abstract_numpy_based_backend import AbstractNumpyBasedBackend
def _expand_if_single_axis(*matrices: np.ndarray) -> List[np.ndarray]:
"""Expands arrays that only have one axis, at dim 0.
This ensures that all outputs can be treated as matrices, not vectors.
:param matrices: Matrices to be expanded
:return: List of the input matrices,
where single axis matrices are expanded at dim 0.
"""
expanded = []
for m in matrices:
if len(m.shape) == 1:
expanded.append(np.expand_dims(m, axis=0))
else:
expanded.append(m)
return expanded
def _expand_if_scalar(arr: np.ndarray) -> np.ndarray:
if len(arr.shape) == 0: # avoid scalar output
arr = np.expand_dims(arr, axis=0)
return arr
def identity(array: np.ndarray) -> np.ndarray:
return array
class NumpyCompBackend(AbstractNumpyBasedBackend):
"""
Computational backend for Numpy.
"""
_module = np
_cast_output = identity
_get_tensor = identity
@classmethod
def to_device(cls, tensor: 'np.ndarray', device: str) -> 'np.ndarray':
"""Move the tensor to the specified device."""
raise NotImplementedError('Numpy does not support devices (GPU).')
@classmethod
def device(cls, tensor: 'np.ndarray') -> Optional[str]:
"""Return device on which the tensor is allocated."""
return None
@classmethod
def to_numpy(cls, array: 'np.ndarray') -> 'np.ndarray':
return array
@classmethod
def none_value(cls) -> Any:
"""Provide a compatible value that represents None in numpy."""
return None
@classmethod
def detach(cls, tensor: 'np.ndarray') -> 'np.ndarray':
"""
Returns the tensor detached from its current graph.
:param tensor: tensor to be detached
:return: a detached tensor with the same data.
"""
return tensor
@classmethod
def dtype(cls, tensor: 'np.ndarray') -> np.dtype:
"""Get the data type of the tensor."""
return tensor.dtype
@classmethod
def minmax_normalize(
cls,
tensor: 'np.ndarray',
t_range: Tuple = (0, 1),
x_range: Optional[Tuple] = None,
eps: float = 1e-7,
) -> 'np.ndarray':
"""
Normalize values in `tensor` into `t_range`.
`tensor` can be a 1D array or a 2D array. When `tensor` is a 2D array, then
normalization is row-based.
!!! note
- with `t_range=(0, 1)` will normalize the min-value of data to 0, max to 1;
- with `t_range=(1, 0)` will normalize the min-value of data to 1, max value
of the data to 0.
:param tensor: the data to be normalized
:param t_range: a tuple represents the target range.
:param x_range: a tuple represents tensors range.
:param eps: a small jitter to avoid divide by zero
:return: normalized data in `t_range`
"""
a, b = t_range
min_d = x_range[0] if x_range else np.min(tensor, axis=-1, keepdims=True)
max_d = x_range[1] if x_range else np.max(tensor, axis=-1, keepdims=True)
r = (b - a) * (tensor - min_d) / (max_d - min_d + eps) + a
return np.clip(r, *((a, b) if a < b else (b, a)))
@classmethod
def equal(cls, tensor1: 'np.ndarray', tensor2: 'np.ndarray') -> bool:
"""
Check if two tensors are equal.
:param tensor1: the first array
:param tensor2: the second array
:return: True if two arrays are equal, False otherwise.
If one or more of the inputs is not an ndarray, return False.
"""
are_np_arrays = isinstance(tensor1, np.ndarray) and isinstance(
tensor2, np.ndarray
)
return are_np_arrays and np.array_equal(tensor1, tensor2)
class Retrieval(AbstractComputationalBackend.Retrieval[np.ndarray]):
"""
Abstract class for retrieval and ranking functionalities
"""
@staticmethod
def top_k(
values: 'np.ndarray',
k: int,
descending: bool = False,
device: Optional[str] = None,
) -> Tuple['np.ndarray', 'np.ndarray']:
"""
Retrieves the top k smallest values in `values`,
and returns them alongside their indices in the input `values`.
Can also be used to retrieve the top k largest values,
by setting the `descending` flag.
:param values: Torch tensor of values to rank.
Should be of shape (n_queries, n_values_per_query).
Inputs of shape (n_values_per_query,) will be expanded
to (1, n_values_per_query).
:param k: number of values to retrieve
:param descending: retrieve largest values instead of smallest values
:param device: Not supported for this backend
:return: Tuple containing the retrieved values, and their indices.
Both ar of shape (n_queries, k)
"""
if device is not None:
warnings.warn('`device` is not supported for numpy operations')
if len(values.shape) == 1:
values = np.expand_dims(values, axis=0)
if descending:
values = -values
if k >= values.shape[1]:
idx = values.argsort(axis=1)[:, :k]
values = np.take_along_axis(values, idx, axis=1)
else:
idx_ps = values.argpartition(kth=k, axis=1)[:, :k]
values = np.take_along_axis(values, idx_ps, axis=1)
idx_fs = values.argsort(axis=1)
idx = np.take_along_axis(idx_ps, idx_fs, axis=1)
values = np.take_along_axis(values, idx_fs, axis=1)
if descending:
values = -values
return values, idx
class Metrics(AbstractComputationalBackend.Metrics[np.ndarray]):
"""
Abstract base class for metrics (distances and similarities).
"""
@staticmethod
def cosine_sim(
x_mat: np.ndarray,
y_mat: np.ndarray,
eps: float = 1e-7,
device: Optional[str] = None,
) -> np.ndarray:
"""Pairwise cosine similarities between all vectors in x_mat and y_mat.
:param x_mat: np.ndarray of shape (n_vectors, n_dim), where n_vectors is
the number of vectors and n_dim is the number of dimensions of each
example.
:param y_mat: np.ndarray of shape (n_vectors, n_dim), where n_vectors is
the number of vectors and n_dim is the number of dimensions of each
example.
:param eps: a small jitter to avoid divde by zero
:param device: Not supported for this backend
:return: np.ndarray of shape (n_vectors, n_vectors) containing all
pairwise cosine distances.
The index [i_x, i_y] contains the cosine distance between
x_mat[i_x] and y_mat[i_y].
"""
if device is not None:
warnings.warn('`device` is not supported for numpy operations')
x_mat, y_mat = _expand_if_single_axis(x_mat, y_mat)
sims = np.clip(
(np.dot(x_mat, y_mat.T) + eps)
/ (
np.outer(
np.linalg.norm(x_mat, axis=1), np.linalg.norm(y_mat, axis=1)
)
+ eps
),
-1,
1,
).squeeze()
return _expand_if_scalar(sims)
@classmethod
def euclidean_dist(
cls, x_mat: np.ndarray, y_mat: np.ndarray, device: Optional[str] = None
) -> np.ndarray:
"""Pairwise Euclidian distances between all vectors in x_mat and y_mat.
:param x_mat: np.ndarray of shape (n_vectors, n_dim), where n_vectors is
the number of vectors and n_dim is the number of dimensions of each
example.
:param y_mat: np.ndarray of shape (n_vectors, n_dim), where n_vectors is
the number of vectors and n_dim is the number of dimensions of each
example.
:param eps: a small jitter to avoid divde by zero
:param device: Not supported for this backend
:return: np.ndarray of shape (n_vectors, n_vectors) containing all
pairwise euclidian distances.
The index [i_x, i_y] contains the euclidian distance between
x_mat[i_x] and y_mat[i_y].
"""
if device is not None:
warnings.warn('`device` is not supported for numpy operations')
x_mat, y_mat = _expand_if_single_axis(x_mat, y_mat)
return _expand_if_scalar(
np.sqrt(cls.sqeuclidean_dist(x_mat, y_mat)).squeeze()
)
@staticmethod
def sqeuclidean_dist(
x_mat: np.ndarray,
y_mat: np.ndarray,
device: Optional[str] = None,
) -> np.ndarray:
"""Pairwise Squared Euclidian distances between all vectors in
x_mat and y_mat.
:param x_mat: np.ndarray of shape (n_vectors, n_dim), where n_vectors is
the number of vectors and n_dim is the number of dimensions of each
example.
:param y_mat: np.ndarray of shape (n_vectors, n_dim), where n_vectors is
the number of vectors and n_dim is the number of dimensions of each
example.
:param device: Not supported for this backend
:return: np.ndarray of shape (n_vectors, n_vectors) containing all
pairwise Squared Euclidian distances.
The index [i_x, i_y] contains the cosine Squared Euclidian between
x_mat[i_x] and y_mat[i_y].
"""
eps: float = 1e-7 # avoid problems with numerical inaccuracies
if device is not None:
warnings.warn('`device` is not supported for numpy operations')
x_mat, y_mat = _expand_if_single_axis(x_mat, y_mat)
dists = (
np.sum(y_mat**2, axis=1)
+ np.sum(x_mat**2, axis=1)[:, np.newaxis]
- 2 * np.dot(x_mat, y_mat.T)
).squeeze()
# remove numerical artifacts
dists = np.where(np.logical_and(dists < 0, dists > -eps), 0, dists)
return _expand_if_scalar(dists)