"""Conversion tools."""
import math
import numbers
import numpy as np
import scipy
from scipy.stats import norm
pi = math.pi
def int2bitarray(n, k):
"""Change an array's base from int (base 10) to binary (base 2)."""
binary_string = bin(n)
length = len(binary_string)
bitarray = np.zeros(k, 'int')
for i in range(length - 2):
bitarray[k - i - 1] = int(binary_string[length - i - 1])
return bitarray
def bitarray2int(bitarray):
"""Change array's base from binary (base 2) to int (base 10)."""
bitstring = "".join([str(i) for i in bitarray])
return int(bitstring, 2)
def binaryproduct(X, Y):
"""Compute a matrix-matrix / vector product in Z/2Z."""
A = X.dot(Y)
try:
A = A.toarray()
except AttributeError:
pass
return A % 2
def gaussjordan(X, change=0):
"""Compute the binary row reduced echelon form of X.
Parameters
----------
X: array (m, n)
change : boolean (default, False). If True returns the inverse transform
Returns
-------
if `change` == 'True':
A: array (m, n). row reduced form of X.
P: tranformations applied to the identity
else:
A: array (m, n). row reduced form of X.
"""
A = np.copy(X)
m, n = A.shape
if change:
P = np.identity(m).astype(int)
pivot_old = -1
for j in range(n):
filtre_down = A[pivot_old+1:m, j]
pivot = np.argmax(filtre_down)+pivot_old+1
if A[pivot, j]:
pivot_old += 1
if pivot_old != pivot:
aux = np.copy(A[pivot, :])
A[pivot, :] = A[pivot_old, :]
A[pivot_old, :] = aux
if change:
aux = np.copy(P[pivot, :])
P[pivot, :] = P[pivot_old, :]
P[pivot_old, :] = aux
for i in range(m):
if i != pivot_old and A[i, j]:
if change:
P[i, :] = abs(P[i, :]-P[pivot_old, :])
A[i, :] = abs(A[i, :]-A[pivot_old, :])
if pivot_old == m-1:
break
if change:
return A, P
return A
def binaryrank(X):
"""Compute rank of a binary Matrix using Gauss-Jordan algorithm."""
A = np.copy(X)
m, n = A.shape
A = gaussjordan(A)
return sum([a.any() for a in A])
def f1(y, sigma):
"""Compute normal density N(1,sigma)."""
f = norm.pdf(y, loc=1, scale=sigma)
return f
def fm1(y, sigma):
"""Compute normal density N(-1,sigma)."""
f = norm.pdf(y, loc=-1, scale=sigma)
return f
def _bitsandnodes(H):
"""Return bits and nodes of a parity-check matrix H."""
if type(H) != scipy.sparse.csr_matrix:
bits_indices, bits = np.where(H)
nodes_indices, nodes = np.where(H.T)
else:
bits_indices, bits = scipy.sparse.find(H)[:2]
nodes_indices, nodes = scipy.sparse.find(H.T)[:2]
bits_histogram = np.bincount(bits_indices)
nodes_histogram = np.bincount(nodes_indices)
return bits_histogram, bits, nodes_histogram, nodes
def bits2i(H, i):
"""Compute list of variables (bits) connected to Parity node i."""
if type(H) != scipy.sparse.csr_matrix:
m, n = H.shape
return list(np.where(H[i])[0])
indj = H.indptr
indi = H.indices
return [indi[a] for a in range(indj[i], indj[i+1])]
def nodes2j(H, j):
"""Compute list of nodes (PC equations) connecting variable j."""
return bits2i(H.T, j)
def bitsandnodes(H):
"""Return bits and nodes of a parity-check matrix H."""
m, n = H.shape
bits = [bits2i(H, i) for i in range(m)]
nodes = [nodes2j(H, j) for j in range(n)]
bits = np.array(bits)
nodes = np.array(nodes)
return bits, nodes
def incode(H, x):
"""Compute Binary Product of H and x."""
return (binaryproduct(H, x) == 0).all()
def gausselimination(A, b):
"""Solve linear system in Z/2Z via Gauss Gauss elimination."""
if type(A) == scipy.sparse.csr_matrix:
A = A.toarray().copy()
else:
A = A.copy()
b = b.copy()
n, k = A.shape
for j in range(min(k, n)):
listedepivots = [i for i in range(j, n) if A[i, j]]
if len(listedepivots):
pivot = np.min(listedepivots)
else:
continue
if pivot != j:
aux = (A[j, :]).copy()
A[j, :] = A[pivot, :]
A[pivot, :] = aux
aux = b[j].copy()
b[j] = b[pivot]
b[pivot] = aux
for i in range(j+1, n):
if A[i, j]:
A[i, :] = abs(A[i, :]-A[j, :])
b[i] = abs(b[i]-b[j])
return A, b
def check_random_state(seed):
"""Turn seed into a np.random.RandomState instance
Parameters
----------
seed : None | int | instance of RandomState
If seed is None, return the RandomState singleton used by np.random.
If seed is an int, return a new RandomState instance seeded with seed.
If seed is already a RandomState instance, return it.
Otherwise raise ValueError.
"""
if seed is None or seed is np.random:
return np.random.mtrand._rand
if isinstance(seed, numbers.Integral):
return np.random.RandomState(seed)
if isinstance(seed, np.random.RandomState):
return seed
raise ValueError('%r cannot be used to seed a numpy.random.RandomState'
' instance' % seed)
