"""
Functions to create 2D patterns.
Note, in the hopfield model, we define patterns as vectors. To make
the exercise more visual, we use 2D patterns (N by N ndarrays).
"""
# This file is part of the exercise code repository accompanying
# the book: Neuronal Dynamics (see http://neuronaldynamics.epfl.ch)
# located at http://github.com/EPFL-LCN/neuronaldynamics-exercises.
# This free software: you can redistribute it and/or modify it under
# the terms of the GNU General Public License 2.0 as published by the
# Free Software Foundation. You should have received a copy of the
# GNU General Public License along with the repository. If not,
# see http://www.gnu.org/licenses/.
# Should you reuse and publish the code for your own purposes,
# please cite the book or point to the webpage http://neuronaldynamics.epfl.ch.
# Wulfram Gerstner, Werner M. Kistler, Richard Naud, and Liam Paninski.
# Neuronal Dynamics: From Single Neurons to Networks and Models of Cognition.
# Cambridge University Press, 2014.
import numpy as np
from scipy import linalg
import pickle
import gzip
from pkg_resources import resource_filename
import sys
[docs]class PatternFactory:
"""
Creates square patterns of size pattern_length x pattern_width
If pattern length is omitted, square patterns are produced
"""
def __init__(self, pattern_length, pattern_width=None):
"""
Constructor
Args:
pattern_length: the length of a pattern
pattern_width: width or None. If None, patterns are squares of size (pattern_length x pattern_length)
"""
self.pattern_length = pattern_length
self.pattern_width = pattern_length if pattern_width is None else pattern_width
[docs] def create_random_pattern(self, on_probability=0.5):
"""
Creates a pattern_length by pattern_width 2D random pattern
Args:
on_probability:
Returns:
a new random pattern
"""
p = np.random.binomial(1, on_probability, self.pattern_length * self.pattern_width)
p = p * 2 - 1 # map {0, 1} to {-1 +1}
return p.reshape((self.pattern_length, self.pattern_width))
[docs] def create_random_pattern_list(self, nr_patterns, on_probability=0.5):
"""
Creates a list of nr_patterns random patterns
Args:
nr_patterns: length of the new list
on_probability:
Returns:
a list of new random patterns of size (pattern_length x pattern_width)
"""
p = list()
for i in range(nr_patterns):
p.append(self.create_random_pattern(on_probability))
return p
[docs] def create_row_patterns(self, nr_patterns=None):
"""
creates a list of n patterns, the i-th pattern in the list
has all states of the i-th row set to active.
This is convenient to create a list of orthogonal patterns which
are easy to visually identify
Args:
nr_patterns:
Returns:
list of orthogonal patterns
"""
n = self.pattern_width if nr_patterns is None else nr_patterns
pattern_list = []
for i in range(n):
p = self.create_all_off()
p[i, :] = np.ones((1, self.pattern_length))
pattern_list.append(p)
return pattern_list
[docs] def create_all_on(self):
"""
Returns:
2d pattern, all pixels on
"""
return np.ones((self.pattern_length, self.pattern_width), np.int)
[docs] def create_all_off(self):
"""
Returns:
2d pattern, all pixels off
"""
return -1 * np.ones((self.pattern_length, self.pattern_width), np.int)
[docs] def create_checkerboard(self):
"""
creates a checkerboard pattern of size (pattern_length x pattern_width)
Returns:
checkerboard pattern
"""
pw = np.ones(self.pattern_length, np.int)
# set every second value to -1
pw[1::2] = -1
pl = np.ones(self.pattern_width, np.int)
# set every second value to -1
pl[1::2] = -1
t = linalg.toeplitz(pw, pl)
t = t.reshape((self.pattern_length, self.pattern_width))
return t
[docs] def create_L_pattern(self, l_width=1):
"""
creates a pattern with column 0 (left) and row n (bottom) set to +1.
Increase l_width to set more columns and rows (default is 1)
Args:
l_width (int): nr of rows and columns to set
Returns:
an L shaped pattern.
"""
l_pat = -1 * np.ones((self.pattern_length, self.pattern_width), np.int)
for i in range(l_width):
l_pat[-i - 1, :] = np.ones(self.pattern_length, np.int)
l_pat[:, i] = np.ones(self.pattern_length, np.int)
return l_pat
[docs] def reshape_patterns(self, pattern_list):
"""
reshapes all patterns in pattern_list to have shape = (self.pattern_length, self.pattern_width)
Args:
self:
pattern_list:
Returns:
"""
new_shape = (self.pattern_length, self.pattern_width)
return reshape_patterns(pattern_list, new_shape)
[docs]def reshape_patterns(pattern_list, shape):
"""
reshapes each pattern in pattern_list to the given shape
Args:
pattern_list:
shape:
Returns:
"""
reshaped_patterns = [p.reshape(shape) for p in pattern_list]
return reshaped_patterns
[docs]def get_pattern_diff(pattern1, pattern2, diff_code=0):
"""
Creates a new pattern of same size as the two patterns.
the diff pattern has the values pattern1 = pattern2 where the two patterns have
the same value. Locations that differ between the two patterns are set to
diff_code (default = 0)
Args:
pattern1:
pattern2:
diff_code: the values of the new pattern, at locations that differ between
the two patterns are set to diff_code.
Returns:
the diff pattern.
"""
if pattern1.shape != pattern2.shape:
raise ValueError("patterns are not of equal shape")
diffs = np.multiply(pattern1, pattern2)
pattern_with_diffs = np.where(diffs < 0, diff_code, pattern1)
return pattern_with_diffs
[docs]def flip_n(template, nr_of_flips):
"""
makes a copy of the template pattern and flips
exactly n randomly selected states.
Args:
template:
nr_of_flips:
Returns:
a new pattern
"""
n = np.prod(template.shape)
# pick nrOfMutations indices (without replacement)
idx_reassignment = np.random.choice(n, nr_of_flips, replace=False)
linear_template = template.flatten()
linear_template[idx_reassignment] = -linear_template[idx_reassignment]
return linear_template.reshape(template.shape)
[docs]def get_noisy_copy(template, noise_level):
"""
Creates a copy of the template pattern and reassigns N pixels. N is determined
by the noise_level
Note: reassigning a random value is not the same as flipping the state. This
function reassigns a random value.
Args:
template:
noise_level: a value in [0,1]. for 0, this returns a copy of the template.
for 1, a random pattern of the same size as template is returned.
Returns:
"""
if noise_level == 0:
return template.copy()
if noise_level < 0 or noise_level > 1:
raise ValueError("noise level is not in [0,1] but {}0".format(noise_level))
linear_template = template.copy().flatten()
n = np.prod(template.shape)
nr_mutations = int(round(n * noise_level))
idx_reassignment = np.random.choice(n, nr_mutations, replace=False)
rand_values = np.random.binomial(1, 0.5, nr_mutations)
rand_values = rand_values * 2 - 1 # map {0,1} to {-1, +1}
linear_template[idx_reassignment] = rand_values
return linear_template.reshape(template.shape)
[docs]def compute_overlap(pattern1, pattern2):
"""
compute overlap
Args:
pattern1:
pattern2:
Returns: Overlap between pattern1 and pattern2
"""
shape1 = pattern1.shape
if shape1 != pattern2.shape:
raise ValueError("patterns are not of equal shape")
dot_prod = np.dot(pattern1.flatten(), pattern2.flatten())
return float(dot_prod) / (np.prod(shape1))
[docs]def compute_overlap_list(reference_pattern, pattern_list):
"""
Computes the overlap between the reference_pattern and each pattern
in pattern_list
Args:
reference_pattern:
pattern_list: list of patterns
Returns:
A list of the same length as pattern_list
"""
overlap = np.zeros(len(pattern_list))
for i in range(0, len(pattern_list)):
overlap[i] = compute_overlap(reference_pattern, pattern_list[i])
return overlap
[docs]def compute_overlap_matrix(pattern_list):
"""
For each pattern, it computes the overlap to all other patterns.
Args:
pattern_list:
Returns:
the matrix m(i,k) = overlap(pattern_list[i], pattern_list[k]
"""
nr_patterns = len(pattern_list)
overlap = np.zeros((nr_patterns, nr_patterns))
for i in range(nr_patterns):
for k in range(i, nr_patterns):
if i == k:
overlap[i, i] = 1 # no need to compute the overlap with itself
else:
overlap[i, k] = compute_overlap(pattern_list[i], pattern_list[k])
overlap[k, i] = overlap[i, k] # because overlap is symmetric
return overlap
[docs]def load_alphabet():
"""Load alphabet dict from the file
``data/alphabet.pickle.gz``, which is included in
the neurodynex3 release.
Returns:
dict: Dictionary of 10x10 patterns
Raises:
ImportError: Raised if ``neurodynex``
can not be imported. Please install
`neurodynex <pypi.python.org/pypi/neurodynex/>`_.
"""
# Todo: consider removing the zip file and explicitly store the strings here.
file_str = "data/alphabet.pickle.gz"
try:
file_name = resource_filename("neurodynex3", file_str)
except ImportError:
raise ImportError(
"Could not import data file %s. " % file_str +
"Make sure the pypi package `neurodynex` is installed!"
)
with gzip.open("%s" % file_name) as f:
if sys.version_info < (3, 0, 0):
# python2 pickle.loads has no attribute "encoding"
abc_dict = pickle.load(f)
else:
# latin1 is required for python3 compatibility
abc_dict = pickle.load(f, encoding="latin1")
# shape the patterns and provide upper case keys
ABC_dict = dict()
for key in abc_dict:
ABC_dict[key.upper()] = abc_dict[key].reshape((10, 10))
return ABC_dict
if __name__ == "__main__":
pf = PatternFactory(5)
L = pf.create_L_pattern(l_width=2)
print(L)