def test(self):
nxn= [
np.random.randint(-5,50,[2,2]),
np.random.randint(-5,50,[4,4]),
np.random.randint(-5,50,[8,8]),
np.random.randint(-5,50,[16,16])
]
had = [
linalg.hadamard(2),
linalg.hadamard(4),
linalg.hadamard(8),
linalg.hadamard(16)
]
vec = [
np.random.randint(-5,50,[2]),
np.random.randint(-5,50,[4]),
np.random.randint(-5,50,[8]),
np.random.randint(-5,50,[16])
]
for t in range(4):
#Problem 1: matmult(A,x). Multiply a matrix with a vector.
nt.assert_equal(p2.matmult(nxn[t],vec[t]),nxn[t].dot(vec[t]))
#Problem 2: hadmat(k). Create hadamard of size 2^k
# calls student hadmat with t=1,2,3,4
# it is supposed to generate hadmat of size 2,4,8,16
nt.assert_equal(p2.hadmat(t+1),had[t])
#Problem 4: hadmatmult(H,x). Takes hadamart H and vector x, multiplies.
nt.assert_equal(p2.hadmatmult(had[t],vec[t]),had[t].dot(vec[t]))
def MakeBinaryHadamard(n):
matrix = []
for i in range(len(hadamard(n))):
matrix.append([])
for entry in hadamard(n)[i]:
if (entry==-1):
matrix[i].append(0)
else:
matrix[i].append(entry)
return matrix
def initialize_cdma(n = len(members)):
"""Initialize_cdma program and assign codes to each name in members."""
from scipy.linalg import hadamard
code_list = hadamard(n) if is_power_of_two(n) else hadamard(closest_power_of_two(n))
code_list = code_list.tolist()
for index, name in enumerate(members):
codes[name] = code_list[index]
def test_basic(self):
y = hadamard(1)
assert_array_equal(y, [[1]])
y = hadamard(2, dtype=float)
assert_array_equal(y, [[1.0, 1.0], [1.0, -1.0]])
y = hadamard(4)
assert_array_equal(y, [[1, 1, 1, 1], [1, -1, 1, -1], [1, 1, -1, -1], [1, -1, -1, 1]])
assert_raises(ValueError, hadamard, 0)
assert_raises(ValueError, hadamard, 5)
def generate_contrast(problem):
num_vars = problem['num_vars']
# Find the smallest n, such that num_vars < k
k = [2 ** n for n in range(16)]
k_chosen = 2 ** find_smallest(num_vars)
# Generate the fractional factorial contrast
contrast = np.vstack([hadamard(k_chosen), -hadamard(k_chosen)])
return contrast
def test_basic(self):
y = hadamard(1)
assert_array_equal(y, [[1]])
y = hadamard(2, dtype=float)
assert_array_equal(y, [[1.0, 1.0], [1.0, -1.0]])
y = hadamard(4)
assert_array_equal(y, [[1,1,1,1], [1,-1,1,-1], [1,1,-1,-1], [1,-1,-1,1]])
assert_raises(ValueError, hadamard, 0)
assert_raises(ValueError, hadamard, 5)
def __init__(self, epsilon, hash_funcs, m):
self.epsilon = epsilon
self.hash_funcs = hash_funcs
self.k = len(hash_funcs)
self.m = m
self.prob = 1 / (1 + math.pow(math.e, self.epsilon / 2))
self.had = hadamard(self.m)
def __init__(self,
input_size,
output_size,
bias=True,
fixed_weights=True,
fixed_scale=None):
super(HadamardProj, self).__init__()
self.output_size = output_size
self.input_size = input_size
sz = 2**int(math.ceil(math.log(max(input_size, output_size), 2)))
mat = torch.from_numpy(hadamard(sz))
if fixed_weights:
self.proj = Variable(mat, requires_grad=False)
else:
self.proj = nn.Parameter(mat)
init_scale = 1. / math.sqrt(self.output_size)
if fixed_scale is not None:
self.scale = Variable(torch.Tensor([fixed_scale]),
requires_grad=False)
else:
self.scale = nn.Parameter(torch.Tensor([init_scale]))
if bias:
self.bias = nn.Parameter(
torch.Tensor(output_size).uniform_(-init_scale, init_scale))
else:
self.register_parameter('bias', None)
self.eps = 1e-8
def hadamard(k, eps):
""" The hadamard mechanism for general privacy regime
:param k: the domain size
:param eps: the privacy budget
"""
e_eps = np.exp(eps)
temp = min(e_eps, 2 * k)
B = 2**(np.ceil(np.log(temp) / np.log(2)) - 1)
temp1 = (k / B) + 1
b = 2**(np.ceil(np.log(temp1) / np.log(2)))
K = int(b * B)
M = -np.ones((K, K))
H = linalg.hadamard(int(b))
ll = []
for i in range(int(B)):
s = i * int(b)
f = (i + 1) * int(b)
M[s:f, s:f] = H
ll.append(s)
M = np.delete(M, ll, 1)
M[np.where(M == 1)] = e_eps
M[np.where(M == -1)] = 1
for i in range(M.shape[1]):
M[:, i] = M[:, i] / np.sum(M[:, i])
return M[:, :k]
def randomSubspace(subspaceDimension,
ambientDimension,
method="gaussian",
q=3.0):
print(method)
if method == "gaussian":
return np.random.normal(0,
1,
size=(subspaceDimension, ambientDimension))
elif method == "circulant":
cmatrix = circulant(np.random.normal(
0, 1, ambientDimension))[:subspaceDimension]
custm = stats.rv_discrete(values=([-1, 1], [1.0 / 2, 1.0 / 2]))
dmatrix = np.diag(custm.rvs(size=ambientDimension))
return cmatrix.dot(dmatrix)
elif method == "sparse":
custm = stats.rv_discrete(
values=([-1, 0, 1], [1.0 / (2 * q), 1 - (1.0 / q), 1.0 / (2 * q)]))
return math.sqrt(q) * custm.rvs(size=(subspaceDimension,
ambientDimension))
elif method == "hadamard":
P = np.random.normal(0, 1, size=(subspaceDimension, ambientDimension))
H = hadamard(ambientDimension)
custm = stats.rv_discrete(values=([-1, 1], [1.0 / 2, 1.0 / 2]))
D = np.diag(custm.rvs(size=ambientDimension))
return (1 / math.sqrt(ambientDimension)) * P.dot(H.dot(D))
def test_fwht(seed_rng):
L=5
ar1=np.random.normal(size=(2**L,))
ar2=ar1.copy()
sparse.fwht(ar2)
ar1=scla.hadamard(2**L)@ar1
assert ar1==pytest.approx(ar2)
def walsh(N):
H = hadamard(N)
B = copy.copy(H)
ind = []
for x in range(N): ind.append(int(bin(N+x^x/2)[:2:-1],2))
for x in range(0,N): B[x,:] = H[ind[x],:]
return B
def nonlinearity(box):
rows = 256 #256
cols = 8 #8
boolarr = [[0] * 8 for i in range(256)]
for hh in range(rows):
for jj in range(cols):
boolarr[hh][cols - jj - 1] = (-1)**(bitlist(box[hh])[-(jj + 1)])
# print(boolarr)
h = hadamard(rows)
asum = 0
nn = [0 * i for i in range(cols)]
count = 0
for hh in range(cols):
maximum = 0
for kk in range(rows):
temp = 0
for jj in range(rows):
if boolarr[jj][hh] == h[kk][jj]:
temp += 1
else:
temp -= 1
temp = abs(temp)
count += 1
if temp > maximum:
maximum = temp
nn[cols - 1 - hh] = 128 - maximum / 2
asum = asum + nn[cols - 1 - hh]
avg = asum / cols
print(nn)
return avg
def efficient(X, r=2, l=5, d=2):
K_origin = (X.dot(X.T))**d
n = X.shape[0]
size = power_of_2(n)
samples = r + l
p = size - n
R = np.concatenate([
np.zeros((p, samples)),
np.identity(n)[:, np.random.permutation(n)[:samples]]
])
K = np.concatenate(
[np.concatenate([K_origin, np.zeros((p, n))]),
np.zeros((size, p))],
axis=1)
D = np.diag(np.random.randint(2, size=size) * 2 - 1)
H = hadamard(size)
W = R.T.dot(H.dot(D.dot(K)))
U, _, _ = np.linalg.svd(W.T)
Q = U[:, :samples]
A = D.dot(H.dot(R))
B = (np.linalg.inv(A.T.dot(Q))).dot(W.dot(Q))
U, E, _ = np.linalg.svd(B.T)
U = U[:, :r]
E = E[:r]
X_out = ((np.sqrt(E) * U).T.dot(Q.T)).T[:X.shape[0]]
K = X_out.dot(X_out.T)
return K, X_out
def __init__(self,
inputs: Union[str, List[str]],
outputs: Union[str, List[str]],
n_classes: int,
code_length: Optional[int] = None,
mode: Union[None, str, Iterable[str]] = None,
ds_id: Union[None, str, Iterable[str]] = None) -> None:
super().__init__(inputs=inputs,
outputs=outputs,
mode=mode,
ds_id=ds_id)
self.in_list, self.out_list = True, True
if len(self.inputs) != len(self.outputs):
raise ValueError(
"Hadamard requires the same number of input and output keys.")
self.n_classes = n_classes
if code_length is None:
code_length = 1 << (n_classes - 1).bit_length()
if code_length <= 0 or (code_length & (code_length - 1) != 0):
raise ValueError(
f"code_length must be a positive power of 2, but got {code_length}."
)
if code_length < n_classes:
raise ValueError(
f"code_length must be >= n_classes, but got {code_length} and {n_classes}."
)
self.code_length = code_length
labels = hadamard(self.code_length).astype(np.float32)
labels[np.arange(0, self.code_length, 2),
0] = -1 # Make first column alternate
labels = labels[:self.n_classes]
self.labels = labels
def theta(pi1, pi2, data):
"""
This function generates theta, a matrix used in the Fast Hadamard
Transform. This matrix is later multiplied by a scalar to obtain the
overview chromatogram.
:param pi1: The first permutation matrix used in the Fast Hadamard
Transform. Should be a column vector of length n, with values ranging from
1 to n. Can be generated using the function pi_one.
:param pi2: The second permutation matrix used in the Fast Hadamard
Transform. Should be a column vector of length n, with values ranging from
0 to n-1. Can be generated using the function pi_two.
:param data: The raw data or measurements output by the GC, after being
divided into the appropriate time bins. Should be a column vector of
length n.
:return: The matrix theta, which is used directly in the Fast Hadamard
Transform. Should be a column vector of length n.
"""
n = len(pi1)
W = np.zeros((n, 1))
for i in range(n):
W[pi1[i] - 1] = data[i]
X = np.zeros((n + 1, 1))
for i in range(n):
X[i + 1] = W[i]
H = hadamard((n + 1))
Y = np.dot(H, X)
Y = np.delete(Y, (0), axis=0)
theta = np.zeros((n, 1))
for i in range(n):
theta[pi2[i]] = Y[i]
theta = theta * -1
# print theta, "<-- theta \n"
return theta
def create_Spreadcodes_Transmitter():
# This function makes Hadamard spread codes with the information of the
# amount of users and the length of the spread code, given in the config
# file.
# __________________
# OUTPUT: User 1 | Spreadcode user 1 | 0 0 0 0 0 0 0 0
# User 2 | Spreadcode user 2 | 0 1 0 1 0 1 0 1
# -------------------
# ------------------------------------------------------------------------
# JSON file as config file
with open('ConfigTransmitter.json') as json_file:
config = json.load(json_file)
# Generate spread code matrix #rows = #colums = config.order
spreadcode_Matrix = hadamard(config['order'])
# not necessary to transpose the matrix (symmetric matrix)
# Select spread codes for the users (bv: 2 users --> 2 spreadcodes)
spreadcode_Users_Matrix_Bip = spreadcode_Matrix[1:config['aantal_Users'] +
1]
# Make the spreadcode polar: '1' -->'1' '-1' --> '0'
spreadcode_Users_Matrix_Bip[spreadcode_Users_Matrix_Bip == -1] = 0
return spreadcode_Users_Matrix_Bip
def test_numerical_fuzzing_fht():
for length in [2, 4, 8, 16, 32, 64]:
input_ = np.random.normal(size=length)
copy = input_.copy()
H = hadamard(length)
cyfht(input_)
npt.assert_array_almost_equal(np.dot(copy, H), input_)
def compute_embedded(btsize, zdim, trgs, is_cond=False):
'''
Computes the embedded vector for the generator.
@param btsize batch size.
@param zdim embedded vector dimension.
@param trgs target inputs for conditional GAN.
@param is_cond conditional flag.
'''
# Computing random noise
zvar = torch.randn(btsize, zdim)
# Testing for conditional info
if is_cond:
# Computing Hadamard matrix
tdim = trgs.size(1)
had_mat = hadamard(zdim)[:tdim, :] / 128.0
had_mat = torch.from_numpy(had_mat).float()
# Converting targets to embedded dimension
zvar = zvar + torch.mm(trgs, had_mat)
# Return variables
return torch.autograd.Variable(zvar.cuda())
def srht(lin_op, m, indices=None, signs=None):
"""
Subsampled Randomized Hadamard Transform
Parameters
----------
lin_op : user-defined linear operator (see LinearOperator class for requirements), with shape (n,d)
m : sketch size, np.int
Returns
-------
np.ndarray with shape (m,d)
"""
lin_op = LinearOperator(lin_op)
n = lin_op.shape[0]
new_dim = 2**(np.int(np.ceil(np.log(n) / np.log(2))))
if indices is None:
indices = np.sort(
np.random.choice(np.arange(new_dim), m, replace=False))
if signs is None:
signs = np.random.choice([-1, 1], n, replace=True).reshape((-1, 1))
if hasattr(lin_op, 'row_slice'):
matrix = signs * lin_op.row_slice(range(n)).copy()
if n & (n - 1) != 0:
matrix = np.vstack(
[matrix, np.zeros((new_dim - n, matrix.shape[1]))])
return 1. / np.sqrt(m) * _srht(indices, matrix)
else:
RHD = 1. / np.sqrt(m) * hadamard(
new_dim)[:, :n][indices] * signs.squeeze()
return lin_op.hmul(RHD.T).T
def firstEval(nm):
escalar = 1. / (mt.sqrt(2))
hada=hadamard(2)*escalar
hada2= np.kron(hada,np.eye(2))
#Primer estado
r1 = hada2 @ nm
print("Evaluamos el primer estado")
print(r1)
print()
#Segundo estado
cnot = np.array([[1., 0., 0., 0.], [0., 1., 0., 0.], [0., 0., 0., 1.], [0., 0., 1., 0.]])
r2 = cnot@r1
print("Evaluamos el segundo estado")
print(r2)
#gatex(r2)
print()
#Tercera estado
r3 = hada2@r2
print("Evaluamos el tercera estado")
print(r3)
print()
def get_ruggedness_function(metric, N, gt_code):
"""
Return the correct ruggedness calculating function according to the input "metric"
"""
global phi, idx_1
if metric == 'N_max':
if N == 15:
return get_N_max
else:
return get_N_max
elif metric == 'r_s':
return cal_r_s
elif metric == 'epi':
return cal_epi
elif metric == 'open_ratio':
return cal_open_ratio
elif metric == 'E':
phi = hadamard(2**N, dtype='float32')
idx_1 = gt_code.sum(axis=1) == 1
return cal_E
elif metric == 'gamma':
return cal_gamma
elif metric == 'adptwalk_steps':
return cal_adptwalk_steps
elif metric == 'adptwalk_probs':
return cal_adptwalk_probs
def marginalQ(d, k, eps):
""" Fourier mechanism
:param d: number of dimensions
:param k: the order of the marginals of interest
e.g., 3 for 3 way marginals, d for all marginals, etc.
:param eps: the privacy budget
"""
#d=4
#k=2
T = combo(d, k) #Set of putput index
T_int = [int(r, 2) for r in T] # int value of the output index
Input_item = combo(d, d)
U = 2**d
O = len(T)
Q = np.zeros((2 * O, U))
H = linalg.hadamard(2**d)
#eps=1.0
p = np.exp(eps) / (1 + np.exp(eps))
for i in range(O):
for j in range(2**d):
if H[T_int[i], j] == 1:
Q[i, j] = p * (1 / O)
Q[O + i, j] = (1 - p) * (1 / O)
else:
Q[i + O, j] = p * (1 / O)
Q[i, j] = (1 - p) * (1 / O)
return Q
def get_hash_targets(self, n_class, bit):
H_K = hadamard(bit)
H_2K = np.concatenate((H_K, -H_K), 0)
hash_targets = torch.from_numpy(H_2K[:n_class]).float()
if H_2K.shape[0] < n_class:
hash_targets.resize_(n_class, bit)
for k in range(20):
for index in range(H_2K.shape[0], n_class):
ones = torch.ones(bit)
# Bernouli distribution
sa = random.sample(list(range(bit)), bit // 2)
ones[sa] = -1
hash_targets[index] = ones
# to find average/min pairwise distance
c = []
for i in range(n_class):
for j in range(n_class):
if i < j:
TF = sum(hash_targets[i] != hash_targets[j])
c.append(TF)
c = np.array(c)
# choose min(c) in the range of K/4 to K/3
# see in https://github.com/yuanli2333/Hadamard-Matrix-for-hashing/issues/1
# but it is hard when bit is small
if c.min() > bit / 4 and c.mean() >= bit / 2:
print(c.min(), c.mean())
break
return hash_targets
def cake_cutting(n):
H = (hadamard(n) + np.ones(n)) / 2
structure = np.array([[0, 1, 0], [1, 1, 1], [0, 1, 0]])
nComp = []
for i in range(n):
basis = H[i, :]
#non tutti sono quadrati!-> 2^5 non lo è
#basis=basis.reshape((int(math.sqrt(n)),int(math.sqrt(n))))
basis = basis.reshape(int(n / 8), 8)
labeled, nC = label(basis, structure)
nComp.append(nC)
order = np.zeros((n, 1)) - 1
min_prev = -1
for i in range(n):
prev = 0
eq = 0
for j in range(n):
if nComp[j] < nComp[i]:
prev += 1
elif nComp[j] == nComp[i]:
if i > j:
eq += 1
order[i] = prev + eq
H1 = np.zeros((n, n))
for i in range(n):
H1[int(order[i]), :] = H[i, :]
H1 = 2 * H1 - 1
return H1
def generateSensingMatrix(self, m, n, type): #Generate sensing matrix of dim m by n of given type
if type == 'sdnormal':
self.sensing_matrix = np.random.randn(m,n)
#column normalize the matrix:
for i in range(n):
self.sensing_matrix[:,i] = self.sensing_matrix[:,i]/np.linalg.norm(self.sensing_matrix[:,i])
if type == 'uniform01':
self.sensing_matrix = np.random.rand(m,n)
for i in range(n):
self.sensing_matrix[:,i] = self.sensing_matrix[:,i]/np.linalg.norm(self.sensing_matrix[:,i])
if type == 'bernoulli':
#For small m and n, s columns has high prob. of being linearly dependent. This causes x_S feature to have components
#which blow up, which causes the output of the neural network to output a deterministic prob. dist. of all zeros and a single 1, and v to be nan(because it is so large)
self.sensing_matrix = np.random.binomial(1,1/2,(m,n))
self.sensing_matrix = self.sensing_matrix.astype(float)
for i in range(n):
self.sensing_matrix[:,i] = self.sensing_matrix[:,i]/np.linalg.norm(self.sensing_matrix[:,i])
if type == 'hadamard':
#n must be a power of 2 here!!! For small m and n, s columns has high prob. of being linearly dependent. This causes x_S feature to have components
#which blow up, which causes the output of the neural network to output a deterministic prob. dist. of all zeros and a single 1, and v to be nan(because it is so large)
A = hadamard(n)
S = sample(range(1, n), m) #sample m indices randomly
self.sensing_matrix = A[S,:]
self.sensing_matrix = self.sensing_matrix.astype(float)
for i in range(n):
self.sensing_matrix[:,i] = self.sensing_matrix[:,i]/np.linalg.norm(self.sensing_matrix[:,i])
if type == 'subsampled_haar':
A = ortho_group.rvs(n)
S = sample(range(1, n), m)
self.sensing_matrix = A[S,:]
for i in range(n):
self.sensing_matrix[:,i] = self.sensing_matrix[:,i]/np.linalg.norm(self.sensing_matrix[:,i])
def Apply(self, matrixA, applyLeft=True):
m, n = matrixA.shape
temp_state = np.random.get_state()
np.random.set_state(self.randstate)
if applyLeft:
#augmented dimension d(must be power of two)
d = 1 << int(np.ceil(np.log2(m)))
H = hadamard(d)
# Diagonal sign matrix
signs = 2 * np.random.binomial(n=1, p=.5,
size=d) - 1 # Random signs
D = np.diag(signs)
# Uniform sampling matrix
# Each column has a single 1; each row has at most one 1
inds = np.random.choice(a=d, size=self.sketchdim, replace=False)
P = csc_matrix(
(np.ones(self.sketchdim), (inds, range(self.sketchdim))),
shape=(d, self.sketchdim))
# print(P.T.shape, H.shape, D.shape)
matrixS = P.T @ H @ D * math.sqrt(1 / self.sketchdim)
print(matrixS.shape)
print(matrixA.shape)
return matrixS @ matrixA
else: # sanity check needed
#augmented dimension d(must be power of two)
d = 1 << int(np.ceil(np.log2(n)))
H = hadamard(d)
# Diagonal sign matrix
signs = 2 * np.random.binomial(n=1, p=.5,
size=d) - 1 # Random signs
D = np.diag(signs)
# Uniform sampling matrix
# Each column has a single 1; each row has at most one 1
inds = np.random.choice(a=d, size=self.sketchdim, replace=False)
P = csc_matrix(
(np.ones(self.sketchdim), (inds, range(self.sketchdim))),
shape=(d, self.sketchdim))
matrixS = P.T @ H @ D * math.sqrt(1 / self.sketchdim)
matrixC = matrixA @ matrixS
np.random.set_state(temp_state)
def __init__(self, vec_dim=512, vec_norm=10, L=10, K=8, bucket_limit=None):
self.vec_dim = vec_dim # must be power of 2
self.vec_norm = vec_norm
self.bucket_limit = bucket_limit
self.L = L
self.K = K
self.H_dim = linalg.hadamard(vec_dim).astype(np.float32)
self.reset_params()
def setUp(self):
self.data = dict()
self.data['hadamard'] = hadamard(32)
n_rows = 64
n_cols = 77
X = np.random.randn(n_rows, n_cols)
self.data['random matrix'] = X
def getH(s):
n_by_s = int(n / s)
# print(n_by_s)
Is = np.eye(s)
Hs = np.multiply(1 / np.sqrt(s), hadamard(s))
Gs = np.vstack([Hs, Is])
H_bar = block_diag(*([Gs] * n_by_s))
print("Normalized H shape", H_bar.shape)
return H_bar
def __init__(self, epsilon, hash_funcs, m):
self.epsilon = epsilon
self.hash_funcs = hash_funcs
self.k = len(hash_funcs)
self.m = m
if (self.m & (self.m - 1)) == 0:
self.hadamard_matrix = hadamard(
self.m) # Cache hadamard for performance
def fjlt_derive(n,N):
S = np.zeros((n,N))
for i in xrange(n):
S[i,np.random.randint(0,N)] = 1
S = S * np.sqrt(N)/np.sqrt(n)
T = random_bernoulli(n,n)
H = hadamard(N)
return np.matrix(T) * np.matrix(S) * np.matrix(H)
def gen_walsh_masks(rank,invert=False):
res = 2**rank
vol = (res)**2 # volume
H = hadamard(vol)
H[H==-1]=0
if invert:
H = -H+1
return [H[:,k].reshape(res,res) for k in range(vol)]
def masks(self):
rank = self.rank
res = 2**rank
H = hadamard(res**2)
H[H==-1]=0
if self.invert:
H = -H+1
return [H[:,k].reshape(res,res) for k in range(res**2)]
def walsh(N):
H = hadamard(N)
B = copy.copy(H)
ind = []
for x in range(N):
ind.append(int(bin(N + x ^ x / 2)[:2:-1], 2))
for x in range(0, N):
B[x, :] = H[ind[x], :]
return B
def generate_contrast(problem):
"""Generates the raw sample from the problem file
Arguments
=========
problem : dict
The problem definition
"""
num_vars = problem['num_vars']
# Find the smallest n, such that num_vars < k
k = [2 ** n for n in range(16)]
k_chosen = 2 ** find_smallest(num_vars)
# Generate the fractional factorial contrast
contrast = np.vstack([hadamard(k_chosen), -hadamard(k_chosen)])
return contrast
def setUp(self):
self.nxn= [
np.random.randint(-5,50,[2,2]),
np.random.randint(-5,50,[4,4]),
np.random.randint(-5,50,[8,8]),
np.random.randint(-5,50,[16,16])
]
self.had = [
linalg.hadamard(2),
linalg.hadamard(4),
linalg.hadamard(8),
linalg.hadamard(16)
]
self.vec = [
np.random.randint(-5,50,[2]),
np.random.randint(-5,50,[4]),
np.random.randint(-5,50,[8]),
np.random.randint(-5,50,[16])
]
def multiresolutional_walsh_hadamard_transform(grayscale_image):
"""
MR-WHT implementation.
Outputs 1-level MR-WHT transformed image
23-July-2015
"""
def is_power2(num):
return num != 0 and ((num & (num - 1)) == 0)
assert is_power2(grayscale_image.shape[0]) and (
grayscale_image.shape[0] == grayscale_image.shape[1]), 'Grayscale Image size is not a power of 2 or not square!'
# image = Image.fromarray(numpy.uint8(grayscale_image))
# image.show()
# print 'Pre-transformed_grayscale_image:\r\n',grayscale_image
# Do usual WHT
n = grayscale_image.shape[0]
h = hadamard(n)
transformed_grayscale_image = numpy.dot(h, grayscale_image)
# print 'transformed_grayscale_image:\r\n',transformed_grayscale_image
# RowWiseTransformedGrayscaleImage = numpy.zeros(transformed_grayscale_image.shape)
#
# for row in range(0,n):
# for column in range(1,int(n/2)):
# RowWiseTransformedGrayscaleImage[row][column] = math.floor(float(transformed_grayscale_image[row][2*column-1]+transformed_grayscale_image[row][2*column])/2)
# RowWiseTransformedGrayscaleImage[row][column+int(n/2)-1] = transformed_grayscale_image[row][2*column-1]-transformed_grayscale_image[row][2*column]
#
# print 'Row wise transformed_grayscale_image:\r\n',RowWiseTransformedGrayscaleImage
# ColumnWiseTransformedGrayscaleImage = numpy.zeros(transformed_grayscale_image.shape)
#
# for column in range(0,n):
# for row in range(1,int(n/2)):
# ColumnWiseTransformedGrayscaleImage[row][column] = math.floor(float(RowWiseTransformedGrayscaleImage[2*row-1][column]+RowWiseTransformedGrayscaleImage[2*row][column])/2)
# ColumnWiseTransformedGrayscaleImage[row+int(n/2)-1][column] = RowWiseTransformedGrayscaleImage[2*row-1][column]-RowWiseTransformedGrayscaleImage[2*row][column]
#
# print 'Column wise transformed_grayscale_image:\r\n',ColumnWiseTransformedGrayscaleImage
# transformed_grayscale_image = RowWiseTransformedGrayscaleImage
return transformed_grayscale_image
def inverse_multiresolutional_walsh_hadamard_transform(transformed_grayscale_image):
"""
MR-WHT implementation.
Outputs 1-level inverse MR-WHT transformed image
23-July-2015
"""
n = transformed_grayscale_image.shape[0]
# ColumnWiseTransformedGrayscaleImage = numpy.zeros(transformed_grayscale_image.shape)
#
# for column in range(0,n):
# for row in range(1,int(n/2)):
# ColumnWiseTransformedGrayscaleImage[2*row-1][column] = transformed_grayscale_image[row][column] + math.floor(float(transformed_grayscale_image[n/2 + row][column] + 1)/2)
# ColumnWiseTransformedGrayscaleImage[2*row][column] = transformed_grayscale_image[2*row-1][column] - transformed_grayscale_image[n/2 + row][column]
#
# print 'Column wise inverse_transformed_grayscale_image:\r\n',ColumnWiseTransformedGrayscaleImage
# RowWiseTransformedGrayscaleImage = numpy.zeros(transformed_grayscale_image.shape)
#
# for row in range(0,n):
# for column in range(1,int(n/2)):
# RowWiseTransformedGrayscaleImage[row][2*column-1] = transformed_grayscale_image[row][column] + math.floor(float(transformed_grayscale_image[row][n/2 + column] + 1)/2)
# RowWiseTransformedGrayscaleImage[row][2*column] = transformed_grayscale_image[row][2*column-1] - transformed_grayscale_image[row][n/2 + column]
#
# print 'Row wise inverse_transformed_grayscale_image:\r\n',RowWiseTransformedGrayscaleImage
# Do usual IWHT
h = hadamard(n)
inverse_transformed_grayscale_image = numpy.dot(h, transformed_grayscale_image) / n
# image = Image.fromarray(numpy.uint8(inverse_transformed_grayscale_image))
# image.show()
return inverse_transformed_grayscale_image
if((i*i)%p==v):
f=1;
break;
i+=1
return f;
#for key in keys:
#print ("%d %d",key*key,len(s[key]))
t=int(raw_input())
for q in range(t):
n=int(raw_input())
if(is_power2(n)):
print "YES"
mat=linalg.hadamard(n)
#print mat
for j in range(n):
for k in range(n):
print mat[j][k],
print ""
elif(n in keys):
print "YES"
for symb in s[n]:
if symb=='+':
print 1,
else:
print -1,
print ""
elif(n in keys1):
print "YES"
def run( defaultVolt, maxVolt, offsetChannel, listChannels, orderChannel,
activateZeroSlopes, log, repeatMeas, fracBits):
dimHadamard = int( 2**(_numpy.ceil(_numpy.log2( len(orderChannel) ))) )
hadamardMat = hadamard( dimHadamard )
hadamardMat[len(orderChannel):dimHadamard,:] = 0
log.write("_hadamardMat:\n%s\n" % ( hadamardMat ))
_numpy.set_printoptions(threshold='nan')
#print hadamardMat
assert (defaultVolt-maxVolt) >= 0, \
"defaultVolt-maxVolt must be greater zero for hadamard application"
# open comedi device
device = _device(filename='/dev/comedi0')
device.open()
ao_subdevice = device.find_subdevice_by_type(
_constant.SUBDEVICE_TYPE.ao)
mem_subdevice = device.find_subdevice_by_type(
_constant.SUBDEVICE_TYPE.memory)
#print ao_subdevice
insnR = mem_subdevice.insn()
insnR2 = mem_subdevice.insn()
insnR.data = 256*[0]
insnR2.data = 256*[0]
insnSHWFSTrigger = [mem_subdevice.insn(), mem_subdevice.insn(), mem_subdevice.insn()]
insnSHWFSTrigger[0].insn = insnSHWFSTrigger[2].insn = _constant.INSN.gtod
insnSHWFSTrigger[0].data = insnSHWFSTrigger[2].data = [0, 0]
insnSHWFSTrigger[1].data = [1]
insnSHWFSTrigger[1].insn = _constant.INSN.config
# deactivate repositioning if enabled!
insnDeactivateRePos = mem_subdevice.insn()
insnDeactivateRePos.data = [3, 0, 0]
device.do_insn(insnDeactivateRePos)
time.sleep(0.1)
# set selected channels to defaultVoltage
#print listChannels
setInsn = setDefaultVoltage( ao_subdevice, offsetChannel, listChannels, defaultVolt )
device.do_insn(setInsn)
time.sleep(1)
# average slopeZero measurement
slopeZero = averageMeasurements( device, repeatMeas, insnSHWFSTrigger, insnR, fracBits )
print "-------------------------------"
# create empty matrix for slopes measured from now on
shwfsData = _numpy.uint32(_numpy.zeros( (dimHadamard,2*len(insnR.data)) ))
shwfsData_ref_previous = _numpy.uint32(_numpy.zeros( (dimHadamard,2*len(insnR.data)) ))
#print shwfsData.shape
kk = True
while kk == True:
for k in range( dimHadamard ):
insnsW = setDefaultVoltage( ao_subdevice, offsetChannel, listChannels, defaultVolt )
time.sleep(1)
# average zeroSlopes for each set
ret2 = averageMeasurements( device, repeatMeas, insnSHWFSTrigger, insnR, fracBits )
for l in range(0,11):
tmp = _numpy.floor( defaultVolt + hadamardMat[:,k] * maxVolt/10*l )
dat = insnsW.data
dat[orderChannel] = tmp
insnsW.data = dat
device.do_insn(insnsW)
# wait 50 ms
time.sleep(0.05)
time.sleep(1)
# average max slope for set
slope = averageMeasurements( device, repeatMeas, insnSHWFSTrigger, insnR, fracBits )
slopeX = slope.slopeX
slopeY = slope.slopeY
if activateZeroSlopes == True:
shwfsData_ref_previous[k,:] = _numpy.append(_numpy.uint32(ret2.slopeX),_numpy.uint32(ret2.slopeY))
print " activateZeroSlopes true"
print " captured wavefront"
# store captured slope data into matrix
shwfsData[k,:] = _numpy.append(slopeX,slopeY)
insnsW = setDefaultVoltage( ao_subdevice, offsetChannel, listChannels, defaultVolt )
for l in reversed(range(0,11)):
tmp = _numpy.floor( defaultVolt + hadamardMat[:,k] * maxVolt/10*l )
dat = insnsW.data
dat[orderChannel] = tmp
insnsW.data = dat
device.do_insn(insnsW)
# wait 50 ms
time.sleep(0.05)
print "number %d" % k+" of %d" % dimHadamard
kk = False
print "-------------------------------"
time.sleep(1)
# average slopeZero2 measurement
slopeZero2 = averageMeasurements( device, repeatMeas, insnSHWFSTrigger, insnR, fracBits )
# set previous selected channels to zero volt
clearInsn = setDefaultVoltage( ao_subdevice, offsetChannel, listChannels, 0)
device.do_insn(clearInsn)
timeD = datetime.now()
c = ao_subdevice.channel(index=0)
chanVolt = c.get_range(index=0)
log.write("_comediVoltMin:\n%s\n" % ( chanVolt.min ))
log.write("_comediVoltMax:\n%s\n" % ( chanVolt.max ))
log.write("_time:\n%s\n" % ( timeD.strftime("%Y-%m-%d_%H-%M") ) )
# close comedi device
device.close()
#print(shwfsData)
saveData( time, shwfsData, slopeZero, slopeZero2, shwfsData_ref_previous, activateZeroSlopes, log, hadamardMat )
def hadet(n):
a = hadamard(n)
da = det(a)
ina = inv(a)
return da, a, ina
def hadamard_transform(n):
H = hadamard(n)
d = np.random.choice([-1, 1], size=n)
D = np.zeros((n, n))
np.fill_diagonal(D, d)
return H, D
def alvarez_embed(grayscale_container_path, binary_watermark_path, watermarked_image_path):
"""
Alvarez embedding method implementation.
Outputs the resulting watermarked image to watermarked_image_path
23-July-2015
"""
binary_watermark_1darray = numpy.asarray(genetic_algorithm_pretreatment(binary_watermark_path))
m = int(math.sqrt(binary_watermark_1darray.shape[0]))
grayscale_container_2darray = numpy.asarray(Image.open(grayscale_container_path).convert("L"))
while grayscale_container_2darray.shape[0] != grayscale_container_2darray.shape[1]:
if grayscale_container_2darray.shape[0] > grayscale_container_2darray.shape[1]:
grayscale_container_2darray = numpy.c_[
grayscale_container_2darray, numpy.zeros(grayscale_container_2darray.shape[0])]
elif grayscale_container_2darray.shape[0] < grayscale_container_2darray.shape[1]:
grayscale_container_2darray = numpy.r_[
grayscale_container_2darray, numpy.zeros(grayscale_container_2darray.shape[1])[numpy.newaxis]]
n = grayscale_container_2darray.shape[0]
# Now try to find a normalized Hadamard matrix of size 4t closest to floor(n/m)
hadamard_matrix_size = int(math.floor(float(n) / float(m)))
hadamard_matrix_size_right = hadamard_matrix_size
hadamard_matrix_size_left = hadamard_matrix_size
# Find hadamard_matrix_size as an integer, divisible by 4 and a power of 2 and bigger than m/n
while (hadamard_matrix_size_right % 4 != 0) or (
(hadamard_matrix_size_right & (hadamard_matrix_size_right - 1)) != 0):
hadamard_matrix_size_right += 1
# Find hadamard_matrix_size as an integer, divisible by 4 and a power of 2 and less than m/n
while (hadamard_matrix_size_left % 4 != 0) or ((hadamard_matrix_size_left & (hadamard_matrix_size_left - 1)) != 0):
hadamard_matrix_size_left -= 1
# Pick the closest or the least if equally distant
if hadamard_matrix_size_right - hadamard_matrix_size < hadamard_matrix_size - hadamard_matrix_size_left:
hadamard_matrix_size = hadamard_matrix_size_right
else:
hadamard_matrix_size = hadamard_matrix_size_left
# print 'Hadamard matrix size: ', hadamard_matrix_size
h = hadamard(hadamard_matrix_size)
# print 'Hadamard matrix h: ', h
block_size = int(math.floor(float(n) / float(m)))
watermarked_image_2darray = numpy.copy(grayscale_container_2darray)
for i in range(0, m * m - 1):
col_index = i % (n / block_size)
row_index = i / (n / block_size)
a = grayscale_container_2darray[col_index * block_size:col_index * block_size + hadamard_matrix_size,
row_index * block_size:row_index * block_size + hadamard_matrix_size]
# if i == 0 :
# print a
_b = numpy.dot(numpy.dot(h, a), h.transpose()) / hadamard_matrix_size
# if i == 0 :
# print b
b1 = _b[3][3]
b2 = _b[3][5]
# let b equal hadamard_matrix_size/4, as proposed by authors in 3.1 -> 1
b = hadamard_matrix_size / 4
d = abs((b1 - b2) / 2)
if binary_watermark_1darray[i]:
_b[3][3] = b1 - d - b
_b[3][5] = b2 + d + b
else:
_b[3][3] = b1 + d + b
_b[3][5] = b2 - d - b
a = numpy.dot(numpy.dot(h.transpose(), _b), h) / hadamard_matrix_size
# After HT, some values are more than 255 and less than 0, so fix it
a[a > 255] = 255
a[a < 0] = 0
# if i == 0 :
# print a
watermarked_image_2darray[col_index * block_size:col_index * block_size + hadamard_matrix_size,
row_index * block_size:row_index * block_size + hadamard_matrix_size] = a
watermarked_image = Image.fromarray(numpy.uint8(watermarked_image_2darray))
# watermarked_image.show()
# Write image to file
watermarked_image.save(watermarked_image_path)
return
def time_hadamard(self, size):
sl.hadamard(size)
print "Norm of inverse is %g" % (inv_norm) print "Norm of residual is %g" % (res_norm) sgn, det = slogdet(Rkk) print "Log-determinant of selected columns is %g with sign %g" %\ (det, sgn) print "Conditioning of selected columns is %g" %(cond(Rkk)) p = p[:k] return Q, R, p if __name__ == '__main__': from scipy.linalg import hadamard A = np.random.randn(100,30) k = 30 Q, R, p = srrqr(A, k, verbose = True) print p print np.allclose(A[:,p],np.dot(Q,R[:,:k])) A = hadamard(32, dtype = 'd') k = 5 Q, R, p = srrqr(A, k, verbose = True) print p print np.allclose(A[:,p],np.dot(Q,R[:,:k])) A = np.random.randn(30,100) k = 30 Q, R, p = srrqr(A, k, verbose = True) print p print np.allclose(A[:,p],np.dot(Q,R[:,:k]))
def alvarez_extract(grayscale_stego_path, extracted_watermark_path, watermark_size):
"""
Alvarez extracting method implementation.
Outputs the extracted watermark to extracted_watermark_path
23-July-2015
"""
grayscale_stego_2darray = numpy.asarray(Image.open(grayscale_stego_path).convert("L"))
assert grayscale_stego_2darray.shape[0] == grayscale_stego_2darray.shape[1], 'Grayscale Stego is not square!'
n = grayscale_stego_2darray.shape[0]
m = watermark_size
# Now try to find a normalized Hadamard matrix of size 4t closest to floor(n/m)
hadamard_matrix_size = int(math.floor(float(n) / float(m)))
hadamard_matrix_size_right = hadamard_matrix_size
hadamard_matrix_size_left = hadamard_matrix_size
# Find hadamard_matrix_size as an integer, divisible by 4 and a power of 2 and bigger than m/n
while (hadamard_matrix_size_right % 4 != 0) or (
(hadamard_matrix_size_right & (hadamard_matrix_size_right - 1)) != 0):
hadamard_matrix_size_right += 1
# Find hadamard_matrix_size as an integer, divisible by 4 and a power of 2 and less than m/n
while (hadamard_matrix_size_left % 4 != 0) or ((hadamard_matrix_size_left & (hadamard_matrix_size_left - 1)) != 0):
hadamard_matrix_size_left -= 1
# Pick the closest or the least if equally distant
if hadamard_matrix_size_right - hadamard_matrix_size < hadamard_matrix_size - hadamard_matrix_size_left:
hadamard_matrix_size = hadamard_matrix_size_right
else:
hadamard_matrix_size = hadamard_matrix_size_left
# print 'Hadamard matrix size: ', hadamard_matrix_size
h = hadamard(hadamard_matrix_size)
# print 'Hadamard matrix h: ', h
block_size = int(math.floor(float(n) / float(m)))
extracted_watermark = numpy.zeros(m * m)
for i in range(0, m * m - 1):
col_index = i % (n / block_size)
row_index = i / (n / block_size)
a = grayscale_stego_2darray[col_index * block_size:col_index * block_size + hadamard_matrix_size,
row_index * block_size:row_index * block_size + hadamard_matrix_size]
# if i == 0 :
# print a
b = numpy.dot(numpy.dot(h, a), h.transpose()) / hadamard_matrix_size
# if i == 0 :
# print b
b1 = b[3][3]
b2 = b[3][5]
extracted_watermark[i] = 255 if b1 > b2 else 0
extracted_watermark_image = Image.fromarray(numpy.uint8(extracted_watermark.reshape(m, m)))
# Write image to file
extracted_watermark_image.save(extracted_watermark_path)
return