sfepy.linalg.utils module

class sfepy.linalg.utils.MatrixAction(**kwargs)

static from_array(arr)

static from_function(fun, expected_shape, dtype)

to_array()

sfepy.linalg.utils.apply_to_sequence(seq, fun, ndim, out_item_shape)

Applies function fun() to each item of the sequence seq. An item corresponds to the last ndim dimensions of seq.

Parameters:

seqarray

The sequence array with shape (n_1, …, n_r, m_1, …, m_{ndim}).

funfunction

The function taking an array argument of shape of length ndim.

ndimint

The number of dimensions of an item in seq.

out_item_shapetuple

The shape an output item.

Returns:

outarray

The resulting array of shape (n_1, …, n_r) + out_item_shape. The out_item_shape must be compatible with the fun.

sfepy.linalg.utils.argsort_rows(seq)

Returns an index array that sorts the sequence seq. Works along rows if seq is two-dimensional.

sfepy.linalg.utils.assemble1d(ar_out, indx, ar_in)

Perform ar_out[indx] += ar_in, where items of ar_in corresponding to duplicate indices in indx are summed together.

sfepy.linalg.utils.combine(seqs)

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’]]

sfepy.linalg.utils.cycle(bounds)

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]]

sfepy.linalg.utils.dets_fast(a)

Fast determinant calculation of 3-dimensional array.

Parameters:

aarray

The input array with shape (m, n, n).

Returns:

outarray

The output array with shape (m,): out[i] = det(a[i, :, :]).

sfepy.linalg.utils.dot_sequences(mtx, vec, mode='AB')

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:

mtxarray

The array of matrices with shape (n_item, m, n).

vecarray

The array of vectors with shape (n_item, a) or matrices with shape (n_item, a, b).

modeone 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:

outarray

The resulting array.

Notes

Uses numpy.matmul() via the @ operator.

sfepy.linalg.utils.get_blocks_stats(blocks, *args)

Return statistics of array/matrix blocks defined by indices in args.

Returns:

stats: structured array

The array with ‘shape’, ‘min’, ‘mean’ and ‘max’ fields at positions of each matrix block.

Examples

>>> import numpy as nm
>>> from sfepy.linalg.utils import get_blocks_stats
>>>
>>> A = nm.eye(3)
>>> B = nm.full((3,2), 2)
>>> C = nm.full((1,3), 3)
>>> D = nm.full((1,2), 4)
>>> M = nm.block([[A, B], [C, D]])
>>>
>>> sr = [slice(0, 3), slice(3, 5)]
>>> sc = [slice(0, 3), slice(3, 4)]
>>> stats = get_blocks_stats(M, sr, sc)
>>>
>>> print(stats['shape'])
[[(3, 3) (3, 1)]
 [(1, 3) (1, 1)]]
>>>
>>> print(stats['min'])
[[0. 2.]
 [3. 4.]]

sfepy.linalg.utils.insert_strided_axis(ar, axis, length)

Insert a new axis of given length into an array using numpy stride tricks, i.e. no copy is made.

Parameters:

ararray

The input array.

axisint

The axis before which the new axis will be inserted.

lengthint

The length of the inserted axis.

Returns:

outarray

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)

sfepy.linalg.utils.invs_fast(a, det=None)

Fast inversion calculation of 4-dimensional array.

Parameters:

aarray

The input array with shape (c, q, n, n).

det: array

To speed up the calculation, enter the already calculated determinant.

Returns:

outarray

The output array with shape (c, q, n, n): out[c, q] = inv(a[c, q, :, :]).

sfepy.linalg.utils.map_permutations(seq1, seq2, check_same_items=False)

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.

sfepy.linalg.utils.max_diff_csr(mtx1, mtx2)

sfepy.linalg.utils.mini_newton(fun, x0, dfun, i_max=100, eps=1e-08)

sfepy.linalg.utils.norm_l2_along_axis(ar, axis=1, n_item=None, squared=False)

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

sfepy.linalg.utils.normalize_vectors(vecs, eps=1e-08)

Normalize an array of vectors in place.

Parameters:

vecsarray

The 2D array of vectors in rows.

epsfloat

The tolerance for considering a vector to have zero norm. Such vectors are left unchanged.

sfepy.linalg.utils.output_array_stats(ar, name, verbose=True)

sfepy.linalg.utils.permutations(seq)

sfepy.linalg.utils.print_array_info(ar)

Print array shape and other basic information.

sfepy.linalg.utils.split_range(n_item, step)

sfepy.linalg.utils.unique_rows(ar, return_index=False, return_inverse=False)

Return unique rows of a two-dimensional array ar. The arguments follow numpy.unique().