"""
The tools module of pentapy.
The following functions are provided
.. currentmodule:: pentapy.tools
.. autosummary::
:toctree:
diag_indices
shift_banded
create_banded
create_full
"""
# pylint: disable=C0103
import numpy as np
[docs]
def diag_indices(n, offset=0):
"""
Get indices for the main or minor diagonals of a matrix.
This returns a tuple of indices that can be used to access the main
diagonal of an array `a` with ``a.ndim == 2`` dimensions and shape
(n, n).
Parameters
----------
n : int
The size, along each dimension, of the arrays for which the returned
indices can be used.
offset : int, optional
The diagonal offset.
Returns
-------
idx : :class:`numpy.ndarray`
row indices
idy : :class:`numpy.ndarray`
col indices
"""
idx = np.arange(n - np.abs(offset)) - np.min((0, offset))
idy = np.arange(n - np.abs(offset)) + np.max((0, offset))
return idx, idy
[docs]
def shift_banded(mat, up=2, low=2, col_to_row=True, copy=True):
"""Shift rows of a banded matrix.
Either from column-wise to row-wise storage or vice versa.
The Matrix has to be given as a flattend matrix.
Either in a column-wise flattend form::
[[0 0 Dup2[2] ... Dup2[N-2] Dup2[N-1] Dup2[N] ]
[0 Dup1[1] Dup1[2] ... Dup1[N-2] Dup1[N-1] Dup1[N] ]
[Diag[0] Diag[1] Diag[2] ... Diag[N-2] Diag[N-1] Diag[N] ]
[Dlow1[0] Dlow1[1] Dlow1[2] ... Dlow1[N-2] Dlow1[N-1] 0 ]
[Dlow2[0] Dlow2[1] Dlow2[2] ... Dlow2[N-2] 0 0 ]]
Then use::
col_to_row=True
Or in a row-wise flattend form::
[[Dup2[0] Dup2[1] Dup2[2] ... Dup2[N-2] 0 0 ]
[Dup1[0] Dup1[1] Dup1[2] ... Dup1[N-2] Dup1[N-1] 0 ]
[Diag[0] Diag[1] Diag[2] ... Diag[N-2] Diag[N-1] Diag[N] ]
[0 Dlow1[1] Dlow1[2] ... Dlow1[N-2] Dlow1[N-1] Dlow1[N]]
[0 0 Dlow2[2] ... Dlow2[N-2] Dlow2[N-2] Dlow2[N]]]
Then use::
col_to_row=False
Dup1 and Dup2 are the first and second upper minor-diagonals
and Dlow1 resp. Dlow2 are the lower ones.
The number of upper and lower minor-diagonals can be altered.
Parameters
----------
mat : :class:`numpy.ndarray`
The Matrix or the flattened Version of the pentadiagonal matrix.
up : :class:`int`
The number of upper minor-diagonals. Default: 2
low : :class:`int`
The number of lower minor-diagonals. Default: 2
col_to_row : :class:`bool`, optional
Shift from column-wise to row-wise storage or vice versa.
Default: ``True``
copy : :class:`bool`, optional
Copy the input matrix or overwrite it. Default: ``True``
Returns
-------
:class:`numpy.ndarray`
Shifted bandend matrix
"""
if copy:
mat_flat = np.copy(mat)
else:
mat_flat = mat
if col_to_row:
for i in range(up):
mat_flat[i, : -(up - i)] = mat_flat[i, (up - i) :]
mat_flat[i, -(up - i) :] = 0
for i in range(low):
mat_flat[-i - 1, (low - i) :] = mat_flat[-i - 1, : -(low - i)]
mat_flat[-i - 1, : (low - i)] = 0
else:
for i in range(up):
mat_flat[i, (up - i) :] = mat_flat[i, : -(up - i)]
mat_flat[i, : (up - i)] = 0
for i in range(low):
mat_flat[-i - 1, : -(low - i)] = mat_flat[-i - 1, (low - i) :]
mat_flat[-i - 1, -(low - i) :] = 0
return mat_flat
[docs]
def create_banded(mat, up=2, low=2, col_wise=True, dtype=None):
"""Create a banded matrix from a given quadratic Matrix.
The Matrix will to be returned as a flattend matrix.
Either in a column-wise flattend form::
[[0 0 Dup2[2] ... Dup2[N-2] Dup2[N-1] Dup2[N] ]
[0 Dup1[1] Dup1[2] ... Dup1[N-2] Dup1[N-1] Dup1[N] ]
[Diag[0] Diag[1] Diag[2] ... Diag[N-2] Diag[N-1] Diag[N] ]
[Dlow1[0] Dlow1[1] Dlow1[2] ... Dlow1[N-2] Dlow1[N-1] 0 ]
[Dlow2[0] Dlow2[1] Dlow2[2] ... Dlow2[N-2] 0 0 ]]
Then use::
col_wise=True
Or in a row-wise flattend form::
[[Dup2[0] Dup2[1] Dup2[2] ... Dup2[N-2] 0 0 ]
[Dup1[0] Dup1[1] Dup1[2] ... Dup1[N-2] Dup1[N-1] 0 ]
[Diag[0] Diag[1] Diag[2] ... Diag[N-2] Diag[N-1] Diag[N] ]
[0 Dlow1[1] Dlow1[2] ... Dlow1[N-2] Dlow1[N-1] Dlow1[N]]
[0 0 Dlow2[2] ... Dlow2[N-2] Dlow2[N-2] Dlow2[N]]]
Then use::
col_wise=False
Dup1 and Dup2 or the first and second upper minor-diagonals and Dlow1 resp.
Dlow2 are the lower ones. The number of upper and lower minor-diagonals can
be altered.
Parameters
----------
mat : :class:`numpy.ndarray`
The full (n x n) Matrix.
up : :class:`int`
The number of upper minor-diagonals. Default: 2
low : :class:`int`
The number of lower minor-diagonals. Default: 2
col_wise : :class:`bool`, optional
Use column-wise storage. If False, use row-wise storage.
Default: ``True``
Returns
-------
:class:`numpy.ndarray`
Bandend matrix
"""
mat = np.asanyarray(mat)
if mat.ndim != 2:
msg = "create_banded: matrix has to be 2D"
raise ValueError(msg)
if mat.shape[0] != mat.shape[1]:
msg = "create_banded: matrix has to be n x n"
raise ValueError(msg)
size = mat.shape[0]
mat_flat = np.zeros((5, size), dtype=dtype)
mat_flat[up, :] = mat.diagonal()
if col_wise:
for i in range(up):
mat_flat[i, (up - i) :] = mat.diagonal(up - i)
for i in range(low):
mat_flat[-i - 1, : -(low - i)] = mat.diagonal(-(low - i))
else:
for i in range(up):
mat_flat[i, : -(up - i)] = mat.diagonal(up - i)
for i in range(low):
mat_flat[-i - 1, (low - i) :] = mat.diagonal(-(low - i))
return mat_flat
[docs]
def create_full(mat, up=2, low=2, col_wise=True):
"""Create a (n x n) Matrix from a given banded matrix.
The given Matrix has to be a flattend matrix.
Either in a column-wise flattend form::
[[0 0 Dup2[2] ... Dup2[N-2] Dup2[N-1] Dup2[N] ]
[0 Dup1[1] Dup1[2] ... Dup1[N-2] Dup1[N-1] Dup1[N] ]
[Diag[0] Diag[1] Diag[2] ... Diag[N-2] Diag[N-1] Diag[N] ]
[Dlow1[0] Dlow1[1] Dlow1[2] ... Dlow1[N-2] Dlow1[N-1] 0 ]
[Dlow2[0] Dlow2[1] Dlow2[2] ... Dlow2[N-2] 0 0 ]]
Then use::
col_wise=True
Or in a row-wise flattend form::
[[Dup2[0] Dup2[1] Dup2[2] ... Dup2[N-2] 0 0 ]
[Dup1[0] Dup1[1] Dup1[2] ... Dup1[N-2] Dup1[N-1] 0 ]
[Diag[0] Diag[1] Diag[2] ... Diag[N-2] Diag[N-1] Diag[N] ]
[0 Dlow1[1] Dlow1[2] ... Dlow1[N-2] Dlow1[N-1] Dlow1[N]]
[0 0 Dlow2[2] ... Dlow2[N-2] Dlow2[N-2] Dlow2[N]]]
Then use::
col_wise=False
Dup1 and Dup2 or the first and second upper minor-diagonals and Dlow1 resp.
Dlow2 are the lower ones. The number of upper and lower minor-diagonals can
be altered.
Parameters
----------
mat : :class:`numpy.ndarray`
The flattened Matrix.
up : :class:`int`
The number of upper minor-diagonals. Default: 2
low : :class:`int`
The number of lower minor-diagonals. Default: 2
col_wise : :class:`bool`, optional
Input is in column-wise storage. If False, use as row-wise storage.
Default: ``True``
Returns
-------
:class:`numpy.ndarray`
Full matrix.
"""
mat = np.asanyarray(mat)
if mat.ndim != 2:
msg = "create_full: matrix has to be 2D"
raise ValueError(msg)
if mat.shape[0] != up + low + 1:
msg = "create_full: matrix has wrong count of bands"
raise ValueError(msg)
if mat.shape[1] < max(up, low) + 1:
msg = "create_full: matrix has to few information"
raise ValueError(msg)
size = mat.shape[1]
mat_full = np.diag(mat[up])
if col_wise:
for i in range(up):
mat_full[diag_indices(size, up - i)] = mat[i, (up - i) :]
for i in range(low):
mat_full[diag_indices(size, -(low - i))] = mat[-i - 1, : -(low - i)]
else:
for i in range(up):
mat_full[diag_indices(size, up - i)] = mat[i, : -(up - i)]
for i in range(low):
mat_full[diag_indices(size, -(low - i))] = mat[-i - 1, (low - i) :]
return mat_full
def _check_penta(mat):
if mat.ndim != 2:
msg = "pentapy: matrix has to be 2D"
raise ValueError(msg)
if mat.shape[0] != 5:
msg = "pentapy: matrix needs 5 bands"
raise ValueError(msg)
if mat.shape[1] < 3:
msg = "pentapy: matrix needs at least 3 rows"
raise ValueError(msg)