# -*- coding: utf-8 -*-
"""
This file is part of FElupe.
FElupe is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
FElupe is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with FElupe. If not, see <http://www.gnu.org/licenses/>.
"""
import numpy as np
[docs]
def linsteps(points, num=10, endpoint=True, axis=None, axes=None, values=0.0):
"""Return a sequence from batches of evenly spaced samples between pairs of
milestone points.
Parameters
----------
points : array_like
The milestone values of the sequence.
num : int, optional
Number of samples (without the end point) to generate. Must be non-negative
(default is 10).
endpoint : bool, optional
If True, ``points[-1]`` is the last sample. Otherwise, it is not included
(default is True).
axis : int or None, optional
The axis in the result to store the samples. By default (None), the samples will
be concatenated along the existing first axis. If ``axis > 0``, the samples will
be inserted at column ``axis``. Only positive integers are supported.
axes : int or None, optional
Number of output columns if ``axis`` is not None. Requires ``axes > axis`` and
will be set to ``axes = axis + 1`` by default (None).
values : array_like, optional
Default values if ``axis`` is not None (not used for column ``axis``). Default
is 0.0.
Returns
-------
samples : ndarray
Concatenated batches of ``num`` equally spaced samples.
Examples
--------
>>> import felupe as fem
>>>
>>> fem.math.linsteps([0, 0.5, 1.5, 3.5], num=2)
array([0. , 0.25, 0.5 , 1. , 1.5 , 2.5 , 3.5 ])
Not including the end value of the sequence does not change the step size.
>>> fem.math.linsteps([0, 0.5, 1.5, 3.5], num=2, endpoint=False)
array([0. , 0.25, 0.5 , 1. , 1.5 , 2.5 ])
>>> fem.math.linsteps([0, 0.5, 1.5, 3.5], num=2, axis=1, values=[-1, 0])
array([[-1. , 0. ],
[-1. , 0.25],
[-1. , 0.5 ],
[-1. , 1. ],
[-1. , 1.5 ],
[-1. , 2.5 ],
[-1. , 3.5 ]])
Output with four columns:
>>> fem.math.linsteps([0, 0.5, 1.5, 3.5], num=2, axis=1, axes=4)
array([[0. , 0. , 0. , 0. ],
[0. , 0.25, 0. , 0. ],
[0. , 0.5 , 0. , 0. ],
[0. , 1. , 0. , 0. ],
[0. , 1.5 , 0. , 0. ],
[0. , 2.5 , 0. , 0. ],
[0. , 3.5 , 0. , 0. ]])
The ouput degenerates to the end value
>>> fem.math.linsteps([0, 0.5, 1.5, 3.5], num=0)
array([3.5])
or an empty array.
>>> fem.math.linsteps([0, 0.5, 1.5, 3.5], num=0, endpoint=False)
array([], dtype=float64)
See Also
--------
numpy.linspace : Return evenly spaced numbers over a specified interval.
"""
points = np.array(points).ravel()
start = points[:-1]
end = points[1:]
num = np.array([num]).ravel()
if len(num) == 1:
num = np.tile(num, max(1, len(start)))
num = np.pad(num, (0, max(0, len(start) - len(num))), mode="edge")
steplist = [
np.linspace(a, b, n, endpoint=False) for a, b, n in zip(start, end, num)
]
if len(steplist) > 0:
steps = np.concatenate(
[np.linspace(a, b, n, endpoint=False) for a, b, n in zip(start, end, num)]
)
else:
steps = np.array([])
if endpoint:
steps = np.append(steps, points[-1])
if axis is not None:
if axes is None:
axes = axis + 1
steps_1d = steps
steps = np.ones((len(steps_1d), axes)) * np.atleast_2d(values)
steps[:, axis] = steps_1d
return steps
