sfepy.linalg.utils module¶
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sfepy.linalg.utils.
apply_to_sequence
(seq, fun, ndim, out_item_shape)[source]¶ Applies function fun() to each item of the sequence seq. An item corresponds to the last ndim dimensions of seq.
Parameters: - seq : array
The sequence array with shape (n_1, …, n_r, m_1, …, m_{ndim}).
- fun : function
The function taking an array argument of shape of length ndim.
- ndim : int
The number of dimensions of an item in seq.
- out_item_shape : tuple
The shape an output item.
Returns: - out : array
The resulting array of shape (n_1, …, n_r) + out_item_shape. The out_item_shape must be compatible with the fun.
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sfepy.linalg.utils.
argsort_rows
(seq)[source]¶ Returns an index array that sorts the sequence seq. Works along rows if seq is two-dimensional.
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sfepy.linalg.utils.
assemble1d
(ar_out, indx, ar_in)[source]¶ Perform ar_out[indx] += ar_in, where items of ar_in corresponding to duplicate indices in indx are summed together.
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sfepy.linalg.utils.
combine
(seqs)[source]¶ Same as cycle, but with general sequences.
Example:
In [19]: c = combine( [[‘a’, ‘x’], [‘b’, ‘c’], [‘dd’]] )
In [20]: list(c) Out[20]: [[‘a’, ‘b’, ‘dd’], [‘a’, ‘c’, ‘dd’], [‘x’, ‘b’, ‘dd’], [‘x’, ‘c’, ‘dd’]]
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sfepy.linalg.utils.
cycle
(bounds)[source]¶ Cycles through all combinations of bounds, returns a generator.
More specifically, let bounds=[a, b, c, …], so cycle returns all combinations of lists [0<=i<a, 0<=j<b, 0<=k<c, …] for all i,j,k,…
Examples: In [9]: list(cycle([3, 2])) Out[9]: [[0, 0], [0, 1], [1, 0], [1, 1], [2, 0], [2, 1]]
In [14]: list(cycle([3, 4])) [[0, 0], [0, 1], [0, 2], [0, 3], [1, 0], [1, 1], [1, 2], [1, 3], [2, 0], [2, 1], [2, 2], [2, 3]]
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sfepy.linalg.utils.
dets_fast
(a)[source]¶ Fast determinant calculation of 3-dimensional array.
Parameters: - a : array
The input array with shape (m, n, n).
Returns: - out : array
The output array with shape (m,): out[i] = det(a[i, :, :]).
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sfepy.linalg.utils.
dot_sequences
(mtx, vec, mode=’AB’)[source]¶ Computes dot product for each pair of items in the two sequences.
Equivalent to
>>> out = nm.empty((vec.shape[0], mtx.shape[1], vec.shape[2]), >>> dtype=vec.dtype) >>> for ir in range(mtx.shape[0]): >>> out[ir] = nm.dot(mtx[ir], vec[ir])
Parameters: - mtx : array
The array of matrices with shape (n_item, m, n).
- vec : array
The array of vectors with shape (n_item, a) or matrices with shape (n_item, a, b).
- mode : one of ‘AB’, ‘ATB’, ‘ABT’, ‘ATBT’
The mode of the dot product - the corresponding axes are dotted together:
‘AB’ : a = n ‘ATB’ : a = m ‘ABT’ : b = n (*) ‘ATBT’ : b = m (*)
(*) The ‘BT’ part is ignored for the vector second argument.
Returns: - out : array
The resulting array.
Notes
Uses numpy.core.umath_tests.matrix_multiply() if available, which is much faster than the default implementation.
The default implementation uses numpy.sum() and element-wise multiplication. For r-D arrays (n_1, …, n_r, ?, ?) the arrays are first reshaped to (n_1 * … * n_r, ?, ?), then the dot is performed, and finally the shape is restored to (n_1, …, n_r, ?, ?).
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sfepy.linalg.utils.
insert_strided_axis
(ar, axis, length)[source]¶ Insert a new axis of given length into an array using numpy stride tricks, i.e. no copy is made.
Parameters: - ar : array
The input array.
- axis : int
The axis before which the new axis will be inserted.
- length : int
The length of the inserted axis.
Returns: - out : array
The output array sharing data with ar.
Examples
>>> import numpy as nm >>> from sfepy.linalg import insert_strided_axis >>> ar = nm.random.rand(2, 1, 2) >>> ar array([[[ 0.18905119, 0.44552425]],
[[ 0.78593989, 0.71852473]]])>>> ar.shape (2, 1, 2) >>> ar2 = insert_strided_axis(ar, 1, 3) >>> ar2 array([[[[ 0.18905119, 0.44552425]],
[[ 0.18905119, 0.44552425]],
[[ 0.18905119, 0.44552425]]],
[[[ 0.78593989, 0.71852473]],
[[ 0.78593989, 0.71852473]],
[[ 0.78593989, 0.71852473]]]])
>>> ar2.shape (2, 3, 1, 2)
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sfepy.linalg.utils.
map_permutations
(seq1, seq2, check_same_items=False)[source]¶ Returns an index array imap such that seq1[imap] == seq2, if both sequences have the same items - this is not checked by default!
In other words, finds the indices of items of seq2 in seq1.
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sfepy.linalg.utils.
norm_l2_along_axis
(ar, axis=1, n_item=None, squared=False)[source]¶ Compute l2 norm of rows (axis=1) or columns (axis=0) of a 2D array.
n_item … use only the first n_item columns/rows squared … if True, return the norm squared