8645033486

Committed 11 Apr 2024 10:08AM CUT coverage: 88.264% (+0.04%) from 88.224%

Build # 8645033486

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Pull #629

github

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web-flow

Commit Message

Merge ca9ce7e3e into 15e8ef8e2

Pull Request Pull Request #629: [Main] Bump Version number after release

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61.9

/elephant/current_source_density_src/basis_functions.py

#!/usr/bin/env python
"""
This script is used to generate basis sources for the
kCSD method Jan et.al (2012) for 1D,2D and 3D cases.
Two 'types' are described here, gaussian and step source,
These can be easily extended.
These scripts are based on Grzegorz Parka's,
Google Summer of Code 2014, INFC/pykCSD
This was written by :
Michal Czerwinski, Chaitanya Chintaluri
Laboratory of Neuroinformatics,
Nencki Institute of Experimental Biology, Warsaw.
"""
from __future__ import division

import numpy as np

def gauss(d, stdev, dim):
    """Gaussian function
    Parameters
    ----------
    d : floats or np.arrays
        Distance array to the point of evaluation
    stdev : float
        cutoff range
    dim : int
        dimension of the gaussian function
    Returns
    -------
    Z : floats or np.arrays
        function evaluated
    """
    Z = np.exp(-(d**2) / (2* stdev**2) ) / (np.sqrt(2*np.pi)*stdev)**dim
    return Z

def step_1D(d, R):
    """Returns normalized 1D step function.
    Parameters
    ----------
    d : floats or np.arrays
        Distance array to the point of evaluation
    R : float
        cutoff range
    Returns
    -------
    s : Value of the function (d  <= R) / R
    """
    s = (d  <= R)
    s = s / R #normalize with width
    return s

def gauss_1D(d, three_stdev):
    """Returns normalized gaussian 2D scale function
    Parameters
    ----------
    d : floats or np.arrays
        Distance array to the point of evaluation
    three_stdev : float
        3 * standard deviation of the distribution
    Returns
    -------
    Z : (three_std/3)*(1/2*pi)*(exp(-0.5)*stddev**(-2) *(d**2))
    """
    stdev = three_stdev/3.0
    Z = gauss(d, stdev, 1)
    return Z

def gauss_lim_1D(d, three_stdev):
    """Returns gausian 2D function cut off after 3 standard deviations.
    Parameters
    ----------
    d : floats or np.arrays
        Distance array to the point of evaluation
    three_stdev : float
        3 * standard deviation of the distribution
    Returns
    -------
    Z : (three_std/3)*(1/2*pi)*(exp(-0.5)*stddev**(-2) *((x-mu)**2)),
        cut off = three_stdev
    """
    Z = gauss_1D(d, three_stdev)
    Z *= (d < three_stdev)
    return Z

def step_2D(d, R):
    """Returns normalized 2D step function.
    Parameters
    ----------
    d : float or np.arrays
        Distance array to the point of evaluation
    R : float
        cutoff range

    Returns
    -------
    s : step function
    """
    s = (d <= R) / (np.pi*(R**2))
    return s

def gauss_2D(d, three_stdev):
    """Returns normalized gaussian 2D scale function
    Parameters
    ----------
    d : floats or np.arrays
         distance at which we need the function evaluated
    three_stdev : float
        3 * standard deviation of the distribution
    Returns
    -------
    Z : function
        Normalized gaussian 2D function
    """
    stdev = three_stdev/3.0
    Z = gauss(d, stdev, 2)
    return Z

def gauss_lim_2D(d, three_stdev):
    """Returns gausian 2D function cut off after 3 standard deviations.
    Parameters
    ----------
    d : floats or np.arrays
         distance at which we need the function evaluated
    three_stdev : float
        3 * standard deviation of the distribution
    Returns
    -------
    Z : function
        Normalized gaussian 2D function cut off after three_stdev
    """
    Z = (d <= three_stdev)*gauss_2D(d, three_stdev)
    return Z

def gauss_3D(d, three_stdev):
    """Returns normalized gaussian 3D scale function
    Parameters
    ----------
    d : floats or np.arrays
        distance at which we need the function evaluated
    three_stdev : float
        3 * standard deviation of the distribution
    Returns
    -------
    Z : funtion
        Normalized gaussian 3D function
    """
    stdev = three_stdev/3.0
    Z = gauss(d, stdev, 3)
    return Z

def gauss_lim_3D(d, three_stdev):
    """Returns normalized gaussian 3D scale function cut off after 3stdev
    Parameters
    ----------
    d : floats or np.arrays
        distance at which we need the function evaluated
    three_stdev : float
        3 * standard deviation of the distribution
    Returns
    -------
    Z : funtion
        Normalized gaussian 3D function cutoff three_Stdev
    """
    Z = gauss_3D(d, three_stdev)
    Z = Z * (d < (three_stdev))
    return Z

def step_3D(d, R):
    """Returns normalized 3D step function.
    Parameters
    ----------
    d : floats or np.arrays
        distance at which we need the function evaluated
    R : float
        cutoff range
    Returns
    -------
    s : step function in 3D
    """

    s = 3/(4*np.pi*R**3)*(d <= R)
    return s

basis_1D = {
    "step": step_1D,
    "gauss": gauss_1D,
    "gauss_lim": gauss_lim_1D,
}


basis_2D = {
    "step": step_2D,
    "gauss": gauss_2D,
    "gauss_lim": gauss_lim_2D,
}

basis_3D = {
    "step": step_3D,
    "gauss": gauss_3D,
    "gauss_lim": gauss_lim_3D,
}

1	#!/usr/bin/env python
2	"""	5✔
3	This script is used to generate basis sources for the
4	kCSD method Jan et.al (2012) for 1D,2D and 3D cases.
5	Two 'types' are described here, gaussian and step source,
6	These can be easily extended.
7	These scripts are based on Grzegorz Parka's,
8	Google Summer of Code 2014, INFC/pykCSD
9	This was written by :
10	Michal Czerwinski, Chaitanya Chintaluri
11	Laboratory of Neuroinformatics,
12	Nencki Institute of Experimental Biology, Warsaw.
13	"""
14	from __future__ import division	5✔
15
16	import numpy as np	5✔
17
18	def gauss(d, stdev, dim):	5✔
19	"""Gaussian function
20	Parameters
21	----------
22	d : floats or np.arrays
23	Distance array to the point of evaluation
24	stdev : float
25	cutoff range
26	dim : int
27	dimension of the gaussian function
28	Returns
29	-------
30	Z : floats or np.arrays
31	function evaluated
32	"""
33	Z = np.exp(-(d*2) / (2 stdev*2) ) / (np.sqrt(2np.pi)stdev)*dim	5✔
34	return Z	5✔
35
36	def step_1D(d, R):	5✔
37	"""Returns normalized 1D step function.
38	Parameters
39	----------
40	d : floats or np.arrays
41	Distance array to the point of evaluation
42	R : float
43	cutoff range
44	Returns
45	-------
46	s : Value of the function (d <= R) / R
47	"""
48	s = (d <= R)	×
49	s = s / R #normalize with width	×
50	return s	×
51
52	def gauss_1D(d, three_stdev):	5✔
53	"""Returns normalized gaussian 2D scale function
54	Parameters
55	----------
56	d : floats or np.arrays
57	Distance array to the point of evaluation
58	three_stdev : float
59	3 * standard deviation of the distribution
60	Returns
61	-------
62	Z : (three_std/3)(1/2pi)(exp(-0.5)stddev*(-2) (d**2))
63	"""
64	stdev = three_stdev/3.0	5✔
65	Z = gauss(d, stdev, 1)	5✔
66	return Z	5✔
67
68	def gauss_lim_1D(d, three_stdev):	5✔
69	"""Returns gausian 2D function cut off after 3 standard deviations.
70	Parameters
71	----------
72	d : floats or np.arrays
73	Distance array to the point of evaluation
74	three_stdev : float
75	3 * standard deviation of the distribution
76	Returns
77	-------
78	Z : (three_std/3)(1/2pi)(exp(-0.5)stddev*(-2) ((x-mu)**2)),
79	cut off = three_stdev
80	"""
81	Z = gauss_1D(d, three_stdev)	×
82	Z *= (d < three_stdev)	×
83	return Z	×
84
85	def step_2D(d, R):	5✔
86	"""Returns normalized 2D step function.
87	Parameters
88	----------
89	d : float or np.arrays
90	Distance array to the point of evaluation
91	R : float
92	cutoff range
93
94	Returns
95	-------
96	s : step function
97	"""
98	s = (d <= R) / (np.pi(R*2))	×
99	return s	×
100
101	def gauss_2D(d, three_stdev):	5✔
102	"""Returns normalized gaussian 2D scale function
103	Parameters
104	----------
105	d : floats or np.arrays
106	distance at which we need the function evaluated
107	three_stdev : float
108	3 * standard deviation of the distribution
109	Returns
110	-------
111	Z : function
112	Normalized gaussian 2D function
113	"""
114	stdev = three_stdev/3.0	5✔
115	Z = gauss(d, stdev, 2)	5✔
116	return Z	5✔
117
118	def gauss_lim_2D(d, three_stdev):	5✔
119	"""Returns gausian 2D function cut off after 3 standard deviations.
120	Parameters
121	----------
122	d : floats or np.arrays
123	distance at which we need the function evaluated
124	three_stdev : float
125	3 * standard deviation of the distribution
126	Returns
127	-------
128	Z : function
129	Normalized gaussian 2D function cut off after three_stdev
130	"""
131	Z = (d <= three_stdev)*gauss_2D(d, three_stdev)	×
132	return Z	×
133
134	def gauss_3D(d, three_stdev):	5✔
135	"""Returns normalized gaussian 3D scale function
136	Parameters
137	----------
138	d : floats or np.arrays
139	distance at which we need the function evaluated
140	three_stdev : float
141	3 * standard deviation of the distribution
142	Returns
143	-------
144	Z : funtion
145	Normalized gaussian 3D function
146	"""
147	stdev = three_stdev/3.0	×
148	Z = gauss(d, stdev, 3)	×
149	return Z	×
150
151	def gauss_lim_3D(d, three_stdev):	5✔
152	"""Returns normalized gaussian 3D scale function cut off after 3stdev
153	Parameters
154	----------
155	d : floats or np.arrays
156	distance at which we need the function evaluated
157	three_stdev : float
158	3 * standard deviation of the distribution
159	Returns
160	-------
161	Z : funtion
162	Normalized gaussian 3D function cutoff three_Stdev
163	"""
164	Z = gauss_3D(d, three_stdev)	×
165	Z = Z * (d < (three_stdev))	×
166	return Z	×
167
168	def step_3D(d, R):	5✔
169	"""Returns normalized 3D step function.
170	Parameters
171	----------
172	d : floats or np.arrays
173	distance at which we need the function evaluated
174	R : float
175	cutoff range
176	Returns
177	-------
178	s : step function in 3D
179	"""
180
181	s = 3/(4np.piR*3)(d <= R)	5✔
182	return s	5✔
183
184	basis_1D = {	5✔
185	"step": step_1D,
186	"gauss": gauss_1D,
187	"gauss_lim": gauss_lim_1D,
188	}
189
190
191	basis_2D = {	5✔
192	"step": step_2D,
193	"gauss": gauss_2D,
194	"gauss_lim": gauss_lim_2D,
195	}
196
197	basis_3D = {	5✔
198	"step": step_3D,
199	"gauss": gauss_3D,
200	"gauss_lim": gauss_lim_3D,
201	}

NeuralEnsemble / elephant / 8645033486

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