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import functools
from itertools import chain
import operator
import numpy as np
from numpy.lib.stride_tricks import as_strided
def prod(x):
"""Product of a list/tuple of numbers; ~40x faster vs np.prod for Python tuples"""
if len(x) == 0:
return 1
return functools.reduce(operator.mul, x)
def to_2d(arr: np.ndarray, axis: int) -> np.ndarray:
"""Transforms the shape of N-D array to 2-D NxM array
The function transforms N-D array to 2-D NxM array along given axis,
where N is dimension and M is the nember of elements.
The function does not create a copy.
Parameters
----------
arr : np.array
N-D array
axis : int
Axis that will be used for transform array shape
Returns
-------
arr2d : np.ndarray
2-D NxM array view
Raises
------
ValueError : axis is out of array axes
See Also
--------
from_2d
Examples
--------
.. code-block:: python
>>> shape = (2, 3, 4)
>>> arr = np.arange(1, np.prod(shape)+1).reshape(shape)
>>> arr_2d = to_2d(arr, axis=1)
>>> print(arr)
[[[ 1 2 3 4]
[ 5 6 7 8]
[ 9 10 11 12]]
[[13 14 15 16]
[17 18 19 20]
[21 22 23 24]]]
>>> print(arr_2d)
[[ 1 5 9]
[ 2 6 10]
[ 3 7 11]
[ 4 8 12]
[13 17 21]
[14 18 22]
[15 19 23]
[16 20 24]]
"""
arr = np.asarray(arr)
axis = arr.ndim + axis if axis < 0 else axis
if axis >= arr.ndim: # pragma: no cover
raise ValueError(f'axis {axis} is out of array axes {arr.ndim}')
tr_axes = list(range(arr.ndim))
tr_axes.pop(axis)
tr_axes.append(axis)
new_shape = (np.prod(arr.shape) // arr.shape[axis], arr.shape[axis])
return arr.transpose(tr_axes).reshape(new_shape)
def umv_coeffs_to_canonical(arr: np.ndarray, pieces: int):
"""
Parameters
----------
arr : array
The 2-d array with shape (n, m) where:
n -- the number of spline dimensions (1 for univariate)
m -- order * pieces
pieces : int
The number of pieces
Returns
-------
arr_view : array view
The 2-d or 3-d array view with shape (k, p) or (k, p, n) where:
k -- spline order
p -- the number of spline pieces
n -- the number of spline dimensions (multivariate case)
"""
ndim: int = arr.shape[0]
order: int = arr.shape[1] // pieces
shape: tuple[int, ...]
strides: tuple[int, ...]
if ndim == 1:
shape = (order, pieces)
strides = (arr.strides[1] * pieces, arr.strides[1])
else:
shape = (order, pieces, ndim)
strides = (arr.strides[1] * pieces, arr.strides[1], arr.strides[0])
return as_strided(arr, shape=shape, strides=strides)
def umv_coeffs_to_flatten(arr: np.ndarray):
"""
Parameters
----------
arr : array
The 2-d or 3-d array with shape (k, m) or (k, m, n) where:
k -- the spline order
m -- the number of spline pieces
n -- the number of spline dimensions (multivariate case)
Returns
-------
arr_view : array view
The array 2-d view with shape (1, k * m) or (n, k * m)
"""
if arr.ndim == 2:
arr_view = arr.ravel()[np.newaxis]
elif arr.ndim == 3:
shape = (arr.shape[2], prod(arr.shape[:2]))
strides = arr.strides[:-3:-1]
arr_view = as_strided(arr, shape=shape, strides=strides)
else: # pragma: no cover
raise ValueError(f'The array ndim must be 2 or 3, but given array has ndim={arr.ndim}.')
return arr_view
def ndg_coeffs_to_canonical(arr: np.ndarray, pieces: tuple[int, ...]) -> np.ndarray:
"""Returns array canonical view for given n-d grid coeffs flatten array
Creates n-d array canonical view with shape (k0, ..., kn, p0, ..., pn) for given
array with shape (m0, ..., mn) and pieces (p0, ..., pn).
Parameters
----------
arr : array
The input array with shape (m0, ..., mn)
pieces : tuple
The number of pieces (p0, ..., pn)
Returns
-------
arr_view : array view
The canonical view for given array with shape (k0, ..., kn, p0, ..., pn)
"""
if arr.ndim > len(pieces):
return arr
shape = tuple(sz // p for sz, p in zip(arr.shape, pieces)) + pieces
strides = tuple(st * p for st, p in zip(arr.strides, pieces)) + arr.strides
return as_strided(arr, shape=shape, strides=strides)
def ndg_coeffs_to_flatten(arr: np.ndarray):
"""Creates flatten array view for n-d grid coeffs canonical array
For example for input array (4, 4, 20, 30) will be created the flatten view (80, 120)
Parameters
----------
arr : array
The input array with shape (k0, ..., kn, p0, ..., pn) where:
``k0, ..., kn`` -- spline orders
``p0, ..., pn`` -- spline pieces
Returns
-------
arr_view : array view
Flatten view of array with shape (m0, ..., mn)
"""
if arr.ndim == 2:
return arr
ndim = arr.ndim // 2
axes = tuple(chain.from_iterable(zip(range(ndim), range(ndim, arr.ndim))))
shape = tuple(prod(arr.shape[i::ndim]) for i in range(ndim))
return arr.transpose(axes).reshape(shape)
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