def qubit2_conv_comp_base_rep_to_svd_diag_rep(rho: np.ndarray):
a, b, t = qubit2_conv_comp_base_rep_to_hilbert_schmidt_rep(rho)
u, s, vh = np.linalg.svd(t)
if MF.check_matrix_symmetric(t):
print(concurrency(rho))
if MF.check_matrixy_antisymmetric(t):
print("nant")
return np.dot(u.T, a).real, np.dot(vh, b).real, s, u, vh
def test_analyse_matrix_sparse(self):
m1 = np.zeros((100, 100))
m1[0][0] = 0.0004
non_zero, N_total = MF.analyse_matrix_sparse(m1)
self.assertTrue(non_zero == 1)
self.assertTrue(N_total == 100 * 100)
non_zero, N_total = MF.analyse_matrix_sparse(m1, rtol_places=2)
self.assertTrue(non_zero == 0)
m2 = np.ones((20, 20))
non_zero, N_total = MF.analyse_matrix_sparse(m2, rtol_places=2)
self.assertTrue(non_zero == N_total)
def make_pure_random_2qbit_density_matrix_by_unitary_partial_trace2(p, n):
"""Create an ensemble of density matrices by first constructing an Seperable
state of 8 uncoupled qubits, then applying a random unitary matrix and then
tracing out to 2 qbits. The state should in principle be closer to the
totally mixed state than in the procedure with only 4 uncoupled qubits"""
N = 2**8
rho = np.zeros((N, N)) + 0.j
rho += np.kron(
make_random_1qubit_density_matrix(1),
np.kron(
make_random_1qubit_density_matrix(1),
np.kron(
make_random_1qubit_density_matrix(1),
np.kron(
make_random_1qubit_density_matrix(1),
np.kron(
make_random_1qubit_density_matrix(1),
np.kron(
make_random_1qubit_density_matrix(1),
np.kron(make_random_1qubit_density_matrix(1),
make_random_1qubit_density_matrix(1))))))))
U = MF.make_matrix_random_unitary(N, N)
rho = np.dot(U, np.dot(rho, np.conjugate(np.transpose(U))))
rho = partial_trace(
partial_trace(
partial_trace(partial_trace(partial_trace(partial_trace(rho))))))
return rho
def fitnessFunction(individual, algorithm, n_labels, ground_truth, m1, m2, m3):
w1 = individual[0]
w2 = individual[1]
# w3 = individual[2]
w3 = 0
corr = mf.calculateCorrelationMatrix(m1, m2, m3, w1, w2, w3)
if algorithm == 'complete':
agglomerative = AgglomerativeClustering(affinity='precomputed', n_clusters=n_labels, linkage='complete').fit(corr)
labels = agglomerative.labels_
elif algorithm == 'average':
agglomerative = AgglomerativeClustering(affinity='precomputed', n_clusters=n_labels, linkage='average').fit(corr)
labels = agglomerative.labels_
elif algorithm == 'kmedoids':
_, clusters = km.kMedoids(corr, n_labels, 100)
labels = km.sortLabels(clusters)
#fitness = metrics.homogeneity_score(labels, ground_truth)
#fitness = metrics.adjusted_rand_score(labels, ground_truth)
#fitness = sum(individual)
fitness = metrics.calinski_harabaz_score(corr, labels)
corr = None
m1 = None
m2 = None
m3 = None
return fitness
def mutual_information(p_x: np.ndarray, p_yx: np.ndarray) -> float:
assert MF.check_matrix_simple_stochastic(p_yx), "conditional matrix p_yx is not \
simple stochastic."
assert check_l1_norm(p_x), "p_x is not l1-normed"
p_y = np.dot(np.transpose(p_yx), p_x)
assert check_l1_norm(p_y), "p_y is not l1-normed"
return classical_entropy(p_y) - conditional_entropy(p_x, p_yx)
def create_random_ensemble_arcsin(N: int, K: int,
size: int) -> List[np.ndarray]:
"""TODO: Need more verification.
@see: ZyPeNeCo2011"""
rho_list = []
n = int(N / 2)
phi1 = create_maximally_entangled_state(N, 0, 0)
for i in range(size):
U = np.zeros((N**2, N**2)) + 0.j
for k in range(1, K):
U += np.kron(np.eye(N), MF.make_matrix_random_unitary(N, N))
#U += np.kron(MF.make_matrix_random_unitary(N, N), np.eye(N))
phi2 = np.dot(U, phi1)
psi = (phi1 + phi2)
psi /= np.sqrt(np.dot(psi, psi))
rho = density_matrix(psi)
for k in range(n):
rho = partial_trace(rho) / np.trace(rho)
rho /= np.trace(rho)
assert check_density_operator(rho), "rho is not a density matrix"
rho_list.append(rho)
return rho_list
def conditional_entropy(p_x: np.ndarray, p_yx: np.ndarray) -> float:
assert MF.check_matrix_simple_stochastic(p_yx), "conditional matrix p_yx is not \
simple stochastic."
assert check_l1_norm(p_x), "p_x is not l1-normed"
H = 0
for i, p in enumerate(p_x):
H += p * classical_entropy(p_yx[i])
return H
def create_random_ensemble_pure(N: int, n=4) -> List[np.ndarray]:
list = []
for i in range(N):
rho = np.kron(make_random_1qubit_density_matrix(1),
make_random_1qubit_density_matrix(1))
U = MF.make_matrix_random_unitary(4, 4)
rho = np.dot(U, np.dot(rho, np.conjugate(np.transpose(U))))
list.append(rho)
return list
def make_pure_random_2qbit_density_matrix_by_unitary(p, n):
rho = np.zeros((4, 4)) + 0.j
pp = np.random.rand(n)
pp = pp / np.sum(pp)
for i in range(n):
rho += np.kron(make_random_1qubit_density_matrix(p),
make_random_1qubit_density_matrix(p)) * pp[i]
U = MF.make_matrix_random_unitary(4, 4)
rho = np.dot(U, np.dot(rho, np.conjugate(np.transpose(U))))
return rho
def make_cue_matrix(N: int) -> np.ndarray:
"""
mu = 0
ep = 1/np.sqrt(N)
sigma = ep**2 / 8
K = np.random.normal(mu, sigma**0.5, (N ,N)) + 0.j
H = K + np.transpose(K)"""
m = MF.make_matrix_ginibre(N)
H, R = np.linalg.qr(m)
return H
def get_conditional_prob_from_joint_prob(p_xy: np.ndarray) -> np.ndarray:
assert check_joint_probability_matrix(p_xy), "p_xy is not a joint probability \
matrix."
size_a, size_b = p_xy.shape
p_x = np.dot(p_xy, np.ones(size_b))
assert check_l1_norm(p_x), "p_x is not l1-normed."
for i in range(size_a):
p_xy[i] *= 1/p_x[i]
assert MF.check_matrix_simple_stochastic(p_xy), "after calculation the matrix \
is not a conditional probability matrix"
return p_xy
def test_check_matrix_triagonal(self):
m1 = MF.make_matrix_random_triagonal(3, 5)
m2 = MF.make_matrix_random_triagonal(3, 5).T
self.assertTrue(MF.check_matrix_triagonal(m1))
self.assertTrue(MF.check_matrix_triagonal(m2))
m3 = MF.make_matrix_random_unitary(5, 5)
self.assertFalse(MF.check_matrix_triagonal(m3))
def make_pure_random_2qbit_density_matrix_by_unitary_partial_trace(p, n):
"""Create an ensemble of density matrices by first constructing an Seperable
state of 4 uncoupled qubits, then applying a random unitary matrix and then
tracing out 2 qbits."""
rho = np.zeros((16, 16)) + 0.j
rho += np.kron(
make_random_1qubit_density_matrix(1),
np.kron(
make_random_1qubit_density_matrix(1),
np.kron(make_random_1qubit_density_matrix(1),
make_random_1qubit_density_matrix(1))))
U = MF.make_matrix_random_unitary(16, 16)
rho = np.dot(U, np.dot(rho, np.conjugate(np.transpose(U))))
rho = partial_trace(partial_trace(rho))
return rho
def fitness(indv):
w1, w2, w3 = indv.solution
#return x + 10*sin(5*x) + 7*cos(4*x)
corr = mf.calculateCorrelationMatrix(matrix1, matrix2, matrix3, w1, w2, w3)
agglomerative = AgglomerativeClustering(affinity='precomputed',
n_clusters=n_labels,
linkage='complete').fit(corr)
labels = agglomerative.labels_
metrics = cl.clusterEvaluation(corr, labels, ground_truth)
if metrics[0] <= 0:
return 1
print(metrics[0] * 100)
return float(metrics[0]) * 100
def fitness(indv):
w1, w2, w3 = indv.solution
corr = mf.calculateCorrelationMatrix(matrix1, matrix2, matrix3, w1, w2, w3)
if algorithm == 'complete':
agglomerative = AgglomerativeClustering(affinity='precomputed', n_clusters=n_labels, linkage='complete').fit(corr)
labels = agglomerative.labels_
elif algorithm == 'average':
agglomerative = AgglomerativeClustering(affinity='precomputed', n_clusters=n_labels, linkage='average').fit(corr)
labels = agglomerative.labels_
elif algorithm == 'kmedoids':
_, clusters = km.kMedoids(corr, n_labels, 100)
labels = km.sortLabels(clusters)
metrics = ce.clusterEvaluation(corr, labels, ground_truth)
writer.write(str(current_iteration)+': '+str(w1)+' '+str(w2)+' '+str(w3)+' '.join(str(x) for x in metrics)+'\n')
def fitness(indv):
w1, w2, w3 = indv.solution
corr = mf.calculateCorrelationMatrix(matrix1, matrix2, matrix3, w1, w2, w3)
if algorithm == 'complete':
agglomerative = AgglomerativeClustering(affinity='precomputed',
n_clusters=n_labels,
linkage='complete').fit(corr)
labels = agglomerative.labels_
elif algorithm == 'average':
agglomerative = AgglomerativeClustering(affinity='precomputed',
n_clusters=n_labels,
linkage='average').fit(corr)
labels = agglomerative.labels_
elif algorithm == 'kmedoids':
_, clusters = km.kMedoids(corr, n_labels, 100)
labels = km.sortLabels(clusters)
metrics = ce.clusterEvaluation(corr, labels, ground_truth)
return float(metrics[0]) * 100
sample_for_domains = spl
sample = str(spl) + '.'
matrix1 = rs.loadMatrixFromFile(sample, measure1)
matrix2 = rs.loadMatrixFromFile(sample, measure2)
matrix3 = rs.loadMatrixFromFile(sample, measure3)
domains = rs.loadDomainListFromFile(sample)
n_labels = scop.getUniqueClassifications(sample_for_domains)
ground_truth = scop.getDomainLabels(domains)
ground_truth = map(int, ground_truth)
ground_truth = list(map(int, ground_truth))
matrix1 = mf.minMaxScale(matrix1)
matrix2 = mf.minMaxScale(matrix2)
matrix3 = mf.minMaxScale(matrix3)
matrix1 = mf.calculateDistances(matrix1)
matrix2 = mf.calculateDistances(matrix2)
matrix3 = mf.calculateDistances(matrix3)
for w1 in np.arange(0.05, 1.05, 0.05):
w2 = 0
w3 = 1 - w1
corr = mf.calculateCorrelationMatrix(matrix1, matrix2, matrix3, w1,
w2, w3)
##################################################### # LOAD PROTEIN DATA ##################################################### path_to_results = 'C:/ShareSSD/scop/tests/' measure1 = 'rmsd' measure2 = 'gdt_2' measure3 = 'seq' algorithm = 'complete' sample = 'a.1.' sample_for_domains = 'a.1' matrix1 = rs.loadMatrixFromFile(sample, measure1) matrix2 = rs.loadMatrixFromFile(sample, measure2) matrix3 = rs.loadMatrixFromFile(sample, measure3) matrix1 = mf.minMaxScale(matrix1) matrix2 = mf.minMaxScale(matrix2) matrix3 = mf.minMaxScale(matrix3) matrix1 = mf.calculateDistances(matrix1) matrix2 = mf.calculateDistances(matrix2) matrix3 = mf.calculateDistances(matrix3) domains = rs.loadDomainListFromFile(sample_for_domains) n_labels = scop.getUniqueClassifications(sample_for_domains) ground_truth = scop.getDomainLabels(domains) ##################################################### # GENETIC ALGORITHM CONFIG ##################################################### # Define population. indv_template = DecimalIndividual(ranges=[(0.1, 0.9),(0.1, 0.9),(0.1, 0.9)], eps=[0.001,0.001,0.001])
def test_check_matrix_diagonal(self):
m = np.eye(5)
self.assertTrue(MF.check_matrix_diagonal(m))
m[0][1] = 1
self.assertFalse(MF.check_matrix_diagonal(m))
def readDistances(sample, measure):
path_to_matrix = 'C:/ShareSSD/scop/data_old/sim_' + sample + '_' + measure
counter = 0
matrix = []
with open(path_to_matrix, 'r') as fp:
size = 0
domains = []
#get number of structures
line = fp.readline()
while line:
if 'PDB :' in str(line):
if '#' not in str(line):
size += 1
domain = str(line).strip().split()[-1].split('/')[-1]
domains.append(str(domain))
if 'Distance records' in str(line):
break
line = fp.readline()
#get distance matrix
while line:
if 'DIST :' in str(line):
if '#' not in str(line):
print(line)
parsed = str(line).strip().split()
current_row = parsed[2]
value = float(parsed[4])
while current_row == parsed[2]:
matrix.append(value)
line = fp.readline()
parsed = str(line).strip().split()
value = float(parsed[4])
counter += 1
i = 0
while i < counter:
matrix.append(0)
i += 1
i = 0
matrix.append(value)
line = fp.readline()
counter += 1
i = 0
while i < counter:
matrix.append(0)
i += 1
i = 0
matrix = np.asmatrix(matrix)
matrix = matrix.reshape(size, size - 1)
n, _ = matrix.shape
X0 = np.zeros((n, 1))
matrix = np.hstack((X0, matrix))
#np.savetxt("C:/ShareSSD/scop/data_old/matrix2.txt", matrix,delimiter=' ', newline='\n')
#if 'rmsd' in path_to_matrix:
#matrix = matrix/(matrix.max()/1)
matrix = mf.symmetrizeMatrix(matrix)
#if 'gdt' in path_to_matrix:
#matrix = mf.processGDTMatrix(matrix)
#np.savetxt("C:/ShareSSD/scop/data_old/matrix3.txt", matrix,delimiter=' ', newline='\n')
return domains, matrix
from sklearn.cluster import AgglomerativeClustering # load protein data before loop path_to_results = 'C:/ShareSSD/scop/clustering_results/' measure1 = 'gdt_2' measure2 = 'gdt_2' measure3 = 'seq' sample = 'a.3.' sample_for_domains = 'a.3' matrix1 = rs.loadMatrixFromFile(sample, measure1) matrix2 = rs.loadMatrixFromFile(sample, measure2) matrix3 = rs.loadMatrixFromFile(sample, measure3) matrix1 = mf.minMaxScale(matrix1) matrix2 = mf.minMaxScale(matrix2) matrix3 = mf.minMaxScale(matrix3) #experimentar divisoes com medias e desvio padrao #matrix1 = mf.calculateDistances(matrix1) #matrix2 = mf.calculateDistances(matrix2) #matrix3 = mf.calculateDistances(matrix3) domains = rs.loadDomainListFromFile(sample_for_domains) # read existing labels n_labels = scop.getUniqueClassifications(sample_for_domains) ground_truth = scop.getDomainLabels(domains)
def readDistances(sample, measure):
path_to_matrix = 'C:/ShareSSD/scop/data/sim_' + sample + '_' + measure
path_to_values = 'C:/ShareSSD/scop/values_' + sample + '_' + measure
counter = 0
matrix = []
with open(path_to_matrix, 'r') as fp:
size = 0
domains = []
#get structures
line = fp.readline()
while line:
if 'PDB :' in str(line):
if '#' not in str(line):
size += 1
domain = str(line).strip().split()[-1].split('/')[-1]
domains.append(str(domain))
if 'Distance records' in str(line):
break
line = fp.readline()
#get distance matrix
while line:
if 'DIST :' in str(line):
if '#' not in str(line):
print(line)
parsed = str(line).strip().split()
current_row = parsed[2]
value = float(parsed[4])
while current_row == parsed[2]:
matrix.append(value)
line = fp.readline()
parsed = str(line).strip().split()
value = float(parsed[4])
counter += 1
i = 0
while i < counter:
matrix.append(0)
i += 1
i = 0
matrix.append(value)
line = fp.readline()
counter += 1
i = 0
while i < counter:
matrix.append(0)
i += 1
i = 0
matrix = np.asmatrix(matrix)
matrix = matrix.reshape(size, size - 1)
n, m = matrix.shape
X0 = np.zeros((n, 1))
matrix = np.hstack((X0, matrix))
# np.savetxt("C:/ShareSSD/scop/data_old2/kernel_"+measure, matrix, delimiter=' ', newline='\n')
# if 'rmsd' in path_to_matrix:
# matrix = matrix/(matrix.max()/1)
# if 'gdt' in path_to_matrix:
# matrix = mf.processgdtmatrix(matrix)
matrix = mf.symmetrizeMatrix(matrix)
# save kernel values
with open(path_to_values, 'w') as nf:
for i in range(0, n):
for j in range(0, m):
nf.write(str(matrix[i, j]) + '\n')
# np.savetxt("C:/ShareSSD/scop/data_old2/matrix_"+measure, matrix, delimiter=' ', newline='\n')
matrix.dump('C:/ShareSSD/scop/matrix_' + sample + '_' + measure)
return domains, matrix
ground_truth = list(map(int, ground_truth))
#matrix1 = mf.minMaxScale(matrix1)
#matrix2 = mf.minMaxScale(matrix2)
#matrix3 = mf.minMaxScale(matrix3)
# matrix1 = mf.calculatedistances(matrix1)
# matrix2 = mf.calculatedistances(matrix2)
# matrix3 = mf.calculatedistances(matrix3)
#for w1 in [0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9]:
w1 = 0.5
w2 = 0.5
w3 = 0
corr = mf.calculateCorrelationMatrix(matrix1, matrix2, matrix3, w1, w2, w3)
# Hierarchical
for link in ['complete', 'average']:
agglomerative = AgglomerativeClustering(affinity='precomputed',
n_clusters=n_labels,
linkage='complete').fit(corr)
labels = agglomerative.labels_
metrics = cl.clusterEvaluation(corr, labels, ground_truth)
cl.saveResults(measure1, measure2, 'hierarchical_' + link, sample, metrics)
# K-Medoids
medoids, clusters = km.kMedoids(corr, n_labels, 100)
labels = km.sortLabels(clusters)
metrics = cl.clusterEvaluation(corr, labels, ground_truth)
cl.saveResults(measure1, measure2, 'kmedoids', sample, metrics)
def test_operation_matrix_commutation(self):
m1 = np.array([[0, 1], [1, 0]]) + 0.j
m2 = np.array([[1, 0], [0, -1]]) + 0.j
m3 = np.array([[0, -1.j], [1.j, 0]])
self.assertTrue(
np.allclose(MF.operation_matrix_commutation(m1, m2), -2.j * m3))
n = scop.getUniqueClassifications('a.1')
measure1 = 'seq'
measure2 = 'seq'
#measure2 = 'maxsub'
#read matrices
domains, matrix1 = ff.readDistances('a.1.', 'rmsd')
matrix1 = ff.loadMatrixFromFile('a.1.', measure1)
#matrix2 = matrix1
#domains, matrix2 = ff.readDistances('a.1.', measure2)
matrix2 = ff.loadMatrixFromFile('a.1.', measure2)
ground_truth = scop.getDomainLabels(domains)
matrix1 = mf.calculateDistances(matrix1, matrix1)
matrix2 = mf.calculateDistances(matrix2, matrix2)
for w1 in [0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9]:
corr = mf.calculateCorrelation(w1, matrix1, matrix2)
for link in ['complete','average']:
with open(path_to_results+'euclhiearchical_'+link+'_'+str(w1)+'_'+measure1+'_'+measure2,'w') as file:
agglo = AgglomerativeClustering(affinity='precomputed', n_clusters=n, linkage=link).fit(corr)
labels = agglo.labels_
metrics = ce.clusterEvaluation(corr, labels, ground_truth)
print(w1)
from sklearn.cluster import AgglomerativeClustering # load protein data before loop path_to_results = '/home/pedro/Desktop/scop/clustering_results/' measure1 = 'rmsd' sample = 'a.1.' sample_for_domains = 'a.1' X = rs.loadMatrixFromFile(sample, measure1) mean = 1.79197547637771 std_dev = 0.669382812243833 #X = (X - (mean/std_dev)) X = mf.minMaxScale(X) X = mf.calculateDistances(X) domains = rs.loadDomainListFromFile(sample_for_domains) # read existing labels n_labels = scop.getUniqueClassifications(sample_for_domains) ground_truth = scop.getDomainLabels(domains) ground_truth = map(int, ground_truth) ground_truth = list(map(int, ground_truth)) X = np.asmatrix(X) M, C = kmedoids.kMedoids(X, n_labels, 100)
def test_check_matrix_unitary(self):
m1 = np.array([[1 + 1.j, 2, 3], [4, 5, 6]])
m2 = MF.make_matrix_random_unitary(5, 6)
self.assertFalse(MF.check_matrix_unitary(m1))
self.assertTrue(MF.check_matrix_unitary(m2))
from sklearn.cluster import AgglomerativeClustering
# load protein data before loop
path_to_results = 'C:/ShareSSD/scop/clustering_results/'
measure1 = 'rmsd'
sample = 'a.1.'
sample_for_domains = 'a.1'
X = rs.loadMatrixFromFile(sample, measure1)
mean = 1.79197547637771
std_dev = 0.669382812243833
#X = (X - (mean/std_dev))
X = mf.calculateDistances(X)
domains = rs.loadDomainListFromFile(sample)
# read existing labels
n_labels = scop.getUniqueClassifications(sample_for_domains)
ground_truth = scop.getDomainLabels(domains)
ground_truth = map(int, ground_truth)
ground_truth = list(map(int, ground_truth))
X = np.asmatrix(X)
agglomerative = AgglomerativeClustering(affinity='precomputed',
n_clusters=n_labels,
linkage='complete').fit(X)
def make_random_density_matrix_from_ginibre(N: int) -> np.ndarray:
"""Creates a random density matrix of size N from a ginibre matrix.
@see MatrixFunctions.make_matrix_ginibre"""
m = MF.make_matrix_ginibre(N) # Defines Measure of matrix and positiv
m2 = np.dot(np.conjugate(m.T), m) # Make hermitian
return m2 / np.trace(m2) # Trace to one normation
def readSimilaritiesToMatrix(sample, measure):
path_to_matrix = 'C:/ShareSSD/scop/data/values_' + sample + '_' + measure
path_to_domains = 'C:/ShareSSD/scop/data/domains_' + sample
counter = 0
matrix = []
row = []
with open(path_to_matrix, 'r') as fp:
domains = set()
line = fp.readline()
while line:
if 'END' in line:
break
parsed = str(line).strip().split(' ')
structure1 = parsed[0]
structure2 = parsed[1]
value = float(parsed[2])
domains.add(structure1)
domains.add(structure2)
# add the respective amount of zeroes to the current row
counter += 1
i = 0
while i < counter:
row.append(0)
i += 1
i = 0
# track the current structure and read its alignments
current_row = parsed[0]
while current_row == parsed[0] and line:
row.append(value)
line = fp.readline()
if 'END' in line:
break
parsed = str(line).strip().split(' ')
print(parsed)
value = float(parsed[2])
matrix.append(row)
row = []
line = fp.readline()
counter += 1
i = 0
while i < counter:
row.append(0)
i += 1
i = 0
matrix.append(row)
matrix = np.asmatrix(matrix)
# symmetrize and write results to file
matrix = mf.symmetrizeMatrix(matrix)
matrix = np.matrix(matrix)
matrix.dump("C:/ShareSSD/scop/data/matrix_" + sample + '_' + measure)
# write domain list to file
if not os.path.isfile(path_to_domains):
with open(path_to_domains, 'w') as nf:
domains = list(domains)
for domain in domains:
nf.write(domain + '\n')
nf.write('END')