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.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, ?, ?).

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.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().