# BEGIN OF LICENSE NOTE
# This file is part of Pyoints.
# Copyright (c) 2018, Sebastian Lamprecht, Trier University,
# lamprecht@uni-trier.de
#
# Pyoints 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.
#
# Pyoints 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 Pyoints. If not, see <https://www.gnu.org/licenses/>.
# END OF LICENSE NOTE
"""Various distance metrics.
"""
import numpy as np
from . import (
assertion,
)
from .misc import print_rounded
[docs]def norm(coords):
"""Normalization of coordinates.
Parameters
----------
coords : array_like(Number, shape=(k)) or array_like(Number, shape=(n, k))
Represents `n` points or a single point of `k` dimensions.
Returns
-------
array_like(shape=(n, ))
Normed values.
See Also
--------
snorm
Examples
--------
>>> coords = [(3, 4), (0, 1), (4, 3), (0, 0), (8, 6)]
>>> print_rounded(norm(coords))
[ 5. 1. 5. 0. 10.]
"""
return np.sqrt(snorm(coords))
[docs]def snorm(coords):
"""Squared normalization of coordinates.
Parameters
----------
coords: array_like(Number, shape=(k)) or array_like(Number, shape=(n, k))
Represents `n` points or a single point of `k` dimensions.
Returns
-------
Number or array_like(Number, shape=(n))
Squared normed values.
See Also
--------
norm
Examples
--------
>>> coords = [(3, 4), (0, 1), (4, 3), (0, 0), (8, 6)]
>>> print_rounded(snorm(coords))
[ 25 1 25 0 100]
"""
coords = assertion.ensure_numarray(coords)
if len(coords.shape) == 1:
res = (coords * coords).sum()
else:
res = (coords * coords).sum(1)
return res
[docs]def dist(p, coords):
"""Calculates the distances between points.
Parameters
----------
p : array_like(Number, shape=(n, k)) or array_like(Number, shape=(k))
Represents `n` points or a single point of `k` dimensions.
coords : array_like(Number, shape=(n, k))
Represents `n` points of `k` dimensions.
Returns
-------
Number or array_like(Number, shape=(n))
Normed values.
See Also
--------
sdist
Examples
--------
Point to points distance.
>>> p = (1, 2)
>>> coords = [(2, 2), (1, 1), (1, 2), (9, 8)]
>>> print_rounded(dist(p, coords))
[ 1. 1. 0. 10.]
Points to points distance.
>>> A = [(2, 2), (1, 1), (1, 2)]
>>> B = [(4, 2), (2, 1), (9, 8)]
>>> print_rounded(dist(A, B))
[ 2. 1. 10.]
"""
return np.sqrt(sdist(p, coords))
[docs]def sdist(p, coords):
"""Calculates the squared distances between points.
Parameters
----------
p : array_like(Number, shape=(n, k)) or array_like(Number, shape=(k))
Represents `n` points or a single point of `k` dimensions.
coords : array_like(Number, shape=(n, k))
Represents `n` points of `k` dimensions.
Returns
-------
Number or array_like(Number, shape=(n))
Squared distances between the points.
See Also
--------
dist
Examples
--------
Squared point to points distance.
>>> p = (1, 2)
>>> coords = [(2, 4), (1, 1), (1, 2), (9, 8)]
>>> print_rounded(sdist(p, coords))
[ 5 1 0 100]
Squared points to points distance.
>>> A = [(2, 2), (1, 1), (1, 2)]
>>> B = [(4, 2), (2, 1), (9, 8)]
>>> print_rounded(sdist(A, B))
[ 4 1 100]
"""
p = assertion.ensure_numarray(p)
coords = assertion.ensure_numarray(coords)
if not p.shape == coords.shape:
if not (len(coords.shape) == 2 and p.shape[0] == coords.shape[1]):
m = "Dimensions %s and %s do not match"
raise ValueError(m % (str(p.shape), str(coords.shape)))
return snorm(coords - p)
[docs]def rmse(A, B=None):
"""Calculates the Root Mean Squared Error of corresponding data sets.
Parameters
----------
A, B : array_like(Number, shape=(n, k))
Represent `n` points or a single point of `k` dimensions.
Returns
-------
Number
Root Mean Squared Error.
Examples
--------
>>> A = [(2, 2), (1, 1), (1, 2)]
>>> B = [(2.2, 2), (0.9, 1.1), (1, 2.1)]
>>> print_rounded(rmse(A, B))
0.15
"""
if B is None:
d = snorm(A)
else:
d = sdist(A, B)
return np.sqrt(np.mean(d))
[docs]def idw(dists, p=2):
"""Calculates the weights for Inverse Distance Weighting method.
Parameters
----------
dists : Number or array_like(Number, shape=(n))
Represent `n` distance values.
p : optional, Number
Weighting power.
Returns
-------
Number or array_like(Number, shape=(n))
Weights according to Inverse Distance Weighting.
Examples
--------
>>> dists = [0, 1, 4]
>>> print_rounded(idw(dists))
[ 1. 0.25 0.04]
>>> print_rounded(idw(dists, p=1))
[ 1. 0.5 0.2]
"""
dists = assertion.ensure_numvector(dists)
return 1.0 / (1 + dists)**p
