def test_graph_reverse_cuthill_mckee():
A = np.array(
[
[1, 0, 0, 0, 1, 0, 0, 0],
[0, 1, 1, 0, 0, 1, 0, 1],
[0, 1, 1, 0, 1, 0, 0, 0],
[0, 0, 0, 1, 0, 0, 1, 0],
[1, 0, 1, 0, 1, 0, 0, 0],
[0, 1, 0, 0, 0, 1, 0, 1],
[0, 0, 0, 1, 0, 0, 1, 0],
[0, 1, 0, 0, 0, 1, 0, 1],
],
dtype=int,
)
graph = csr_matrix(A)
perm = reverse_cuthill_mckee(graph)
correct_perm = np.array([6, 3, 7, 5, 1, 2, 4, 0])
assert_equal(perm, correct_perm)
# Test int64 indices input
graph.indices = graph.indices.astype("int64")
graph.indptr = graph.indptr.astype("int64")
perm = reverse_cuthill_mckee(graph, True)
assert_equal(perm, correct_perm)
def heuristica_bandwidth(file, symetric):
"""
Descrição
-----------
Reduz a largura de banda de uma Matriz grandes com a Heurística RCM (Reverse-Cuthill-Mckee).
Paramêtros
----------
Symetric_mode: True (ou False), se a Matriz for simetrica (ou nao simetrica)\n
filename: O nome do arquivo da matriz (extensoes .mtx, .mtz.gz)
Retorno
-------
O tempo de execução da heurística de redução de largura de banda.
Para maiores detalhes sobre a heurística desta classe:
--------------------------------------------------------------
Gonzaga de Oliveira, Sanderson L., "INTRODUÇÃO A HEURÍSTICAS PARA REDUÇÃO DE LARGURA DE BANDA DE MATRIZES", \
Notas em Matemática Aplicada, Volume 75, (2014). E-ISSN 2236-5915.
Para obter novas matrizes:
--------------------------
https://sparse.tamu.edu
"""
# Carregando o arquivo de formao Matriz Market filename
matriz = mmread(file)
# Convertendo com CSR uma Matriz Esparsa
G_sparse = csr_matrix(matriz)
print(" Aplicando a Heuristica REVERSE-CUTHIL-MCKEE")
t1 = time.time()
print("\tInicio\t- ", date.datetime.fromtimestamp(t1))
reverse_cuthill_mckee(G_sparse, symetric)
t2 = time.time()
print("\tTermino\t- ", date.datetime.fromtimestamp(t2))
print(" Tempo de Execucao da Heuristica REVERSE-CUTHIL-MCKEE: ", t2 - t1)
# Sumarizando o Dataset da Matriz
print(
"\n-------------------------------------------------------------------------------------------------"
)
print(" [SUMARIO] - Apresentando a Matriz")
print(
"-------------------------------------------------------------------------------------------------\n"
)
print(" Dimensao (NxN): \t", matriz.shape)
print(" Elementos NONZERO: \t", matriz.nnz)
print(" Arquivo da Matriz: \t", file)
if symetric == None or symetric == False:
texto = NONSYMETRIC
else:
texto = YESSYMETRIC
print(" Matriz Simétrica: \t", symetric, texto)
return (t2 - t1)
def salvar_permutacao_rcm(self):
"""Salva a permutação feita pelo algoritmo de redução da banda da matriz de rigidez Reverse Cuthill Mckee."""
# Interface Julia
julia = Main
julia.eval('include("julia_core/Deslocamentos.jl")')
julia.kelems = self.matrizes_rigidez_elementos_poligonais(
self.dados) + self.matrizes_rigidez_barras()
julia.gls_elementos = [
i + 1 for i in self.dados.graus_liberdade_elementos
]
julia.gls_estrutura = [
i + 1 if i != -1 else i
for i in self.dados.graus_liberdade_estrutura
]
julia.apoios = self.dados.apoios + 1
julia.eval(
'dados = Dict("kelems" => kelems, "gls_elementos" => gls_elementos, '
'"gls_estrutura" => gls_estrutura, "apoios" => apoios)')
linhas, colunas, termos = julia.eval(
'matriz_rigidez_estrutura(kelems, dados, true)')
# Número de graus de liberdade livres.
ngl = self.dados.num_graus_liberdade() - len(self.dados.apoios)
k = csr_matrix((termos, (linhas - 1, colunas - 1)), shape=(ngl, ngl))
rcm = reverse_cuthill_mckee(k)
# Salvar o vetor rcm.
self.dados.salvar_arquivo_numpy(rcm, 11)
def reduzir(self,matriz_nomeArquivo, simetrica = True):
matriz = self.lerMatriz(matriz_nomeArquivo)
#plot da matriz
plt.rcParams['figure.figsize'] = (15,15)
fig, axs = plt.subplots(1, 2)
ax1 = axs[0]
ax2 = axs[1]
matriz_densa = matriz.todense() #para auxiliar no plot e no calculo da largura de banda
ax1.spy(matriz_densa, markersize=1)
ax1.set_title('Matriz Original',y=1.08)
##segundo a documentação do RCM do Scipy essa transformação é necessária para matrizes assimetricas
if not simetrica:
matriz = matriz + matriz.T
print("Largura de banda original",self.larguraBanda(matriz_densa))
#vetor de permutação obtido ao aplicar o algoritmo Reverse Cuthill Mckee, utilizado para reordenar a matrix
perm_array = reverse_cuthill_mckee(matriz,symmetric_mode=True)
#reordenação da matriz
matriz = self.reordenarMatriz(matriz,perm_array)
matriz_densa = matriz.todense() #para auxiliar no plot
print("Largura de banda reduzida",self.larguraBanda(matriz_densa))
ax2.spy(matriz_densa, markersize=1)
ax2.set_title('Matriz Reordenada',y=1.08)
plt.show()
def rev_cuthill_mckee(C, return_order=True):
rorder = reverse_cuthill_mckee(csr_matrix(C))
if return_order:
return C[np.ix_(rorder, rorder)], rorder
else:
return C[np.ix_(rorder, rorder)]
def get_cuthill_mckee(weights) :
graph = csr_matrix(weights)
order = reverse_cuthill_mckee(graph)
permutation = [0 for i in range(len(weights))]
for i in range(len(weights)) :
permutation[order[i]] = i
return permutation
def find_permutation(graph, method, verbose=True):
n = len(graph)
if verbose:
identity_i2p = {i : i for i in range(n)}
bandwidth_initial = score(graph, 'max', identity_i2p)
MLA_initial = score(graph, 'sum', identity_i2p)
x = list(range(n))
random.shuffle(x)
random_i2p = {i : v for i, v in enumerate(x)}
bandwidth_random = score(graph, 'max', random_i2p)
MLA_random = score(graph, 'sum', random_i2p)
if method == 'max':
x = np.zeros((n,n))
for i in range(n):
for j in graph[i]['neighbors']:
x[i][j] = 1
x[j][i] = 1
csr = csr_matrix(x)
permutation = reverse_cuthill_mckee(csr, symmetric_mode=True)
I, J = np.ix_(permutation, permutation)
i2p = {v : i for i,v in enumerate(permutation)}
x2 = x[I,J]
permutation = list(permutation)
else:
i2p, permutation = MLA(graph, n)
if verbose:
bandwidth_final = score(graph, 'max', i2p)
MLA_final = score(graph, 'sum', i2p)
return i2p, permutation, {'Initial bandwidth' : bandwidth_initial, 'Random bandwidth' : bandwidth_random, 'Final bandwidth' : bandwidth_final,
'Initial MLA' : MLA_initial, 'Random MLA' : MLA_random, 'Final MLA' : MLA_final}
else:
return i2p, permutation
def transform_to_band(A, B, alg=False):
if not alg:
return A.A.tolist(), list(chain.from_iterable(B.A.tolist()))
# res = A @ B
# print("A=", A.A)
# print("b=", B.A)
#
# print()
a = csr_matrix(A)
p = reverse_cuthill_mckee(a, symmetric_mode=True)
band_a = A[np.ix_(p, p)]
band_b = csr_matrix(B.A[p, :])
# print("p=", p)
# band_result = band_a @ band_b
# print("band_a=", band_a.toarray())
# print("band_b=", band_b.toarray())
# print(are_equal(band_result.toarray(), res.A))
# print("a*b=", band_result.toarray())
# print("A*b=", res.A)
# print("nz", band_a.nnz)
# plt.spy(A.A, markersize=marksize)
# plt.show()
# plt.spy(band_a.toarray(), markersize=marksize)
# plt.show()
return band_a.toarray().tolist(), list(chain.from_iterable(band_b.toarray().tolist()))
def _best_subset(self, num_qubits, num_meas, num_cx):
"""Computes the qubit mapping with the best connectivity.
Args:
num_qubits (int): Number of subset qubits to consider.
Returns:
ndarray: Array of qubits to use for best connectivity mapping.
"""
from scipy.sparse import coo_matrix, csgraph
if num_qubits == 1:
return np.array([0])
if num_qubits == 0:
return []
rows, cols, best_map = best_subset(
num_qubits,
self.adjacency_matrix,
num_meas,
num_cx,
self._use_error,
self.coupling_map.is_symmetric,
self.error_mat,
)
data = [1] * len(rows)
sp_sub_graph = coo_matrix((data, (rows, cols)),
shape=(num_qubits, num_qubits)).tocsr()
perm = csgraph.reverse_cuthill_mckee(sp_sub_graph)
best_map = best_map[perm]
return best_map
def rcm_reorder(adj):
#---graph reordering using RCM---
node_count = adj.shape[0]
reindex_reverse = np.array(list(reverse_cuthill_mckee(adj.tocsr(),symmetric_mode=True)))
reindex = np.zeros((node_count,),int)
for i in range(node_count):
reindex[reindex_reverse[i]] = i
return reindex
def test_graph_reverse_cuthill_mckee():
A = np.array([[1, 0, 0, 0, 1, 0, 0, 0], [0, 1, 1, 0, 0, 1, 0, 1],
[0, 1, 1, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 1, 0],
[1, 0, 1, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 1, 0, 1],
[0, 0, 0, 1, 0, 0, 1, 0], [0, 1, 0, 0, 0, 1, 0, 1]],
dtype=int)
graph = csr_matrix(A)
perm = reverse_cuthill_mckee(graph)
correct_perm = np.array([6, 3, 7, 5, 1, 2, 4, 0])
assert_equal(perm, correct_perm)
# Test int64 indices input
graph.indices = graph.indices.astype('int64')
graph.indptr = graph.indptr.astype('int64')
perm = reverse_cuthill_mckee(graph, True)
assert_equal(perm, correct_perm)
def _best_subset(self, n_qubits):
"""Computes the qubit mapping with the best connectivity.
Args:
n_qubits (int): Number of subset qubits to consider.
Returns:
ndarray: Array of qubits to use for best connectivity mapping.
"""
if n_qubits == 1:
return np.array([0])
device_qubits = self.coupling_map.size()
cmap = np.asarray(self.coupling_map.get_edges())
data = np.ones_like(cmap[:, 0])
sp_cmap = sp.coo_matrix((data, (cmap[:, 0], cmap[:, 1])),
shape=(device_qubits, device_qubits)).tocsr()
best = 0
best_map = None
# do bfs with each node as starting point
for k in range(sp_cmap.shape[0]):
bfs = cs.breadth_first_order(sp_cmap,
i_start=k,
directed=False,
return_predecessors=False)
connection_count = 0
sub_graph = []
for i in range(n_qubits):
node_idx = bfs[i]
for j in range(sp_cmap.indptr[node_idx],
sp_cmap.indptr[node_idx + 1]):
node = sp_cmap.indices[j]
for counter in range(n_qubits):
if node == bfs[counter]:
connection_count += 1
sub_graph.append([node_idx, node])
break
if connection_count > best:
best = connection_count
best_map = bfs[0:n_qubits]
# Return a best mapping that has reduced bandwidth
mapping = {}
for edge in range(best_map.shape[0]):
mapping[best_map[edge]] = edge
new_cmap = [[mapping[c[0]], mapping[c[1]]] for c in sub_graph]
rows = [edge[0] for edge in new_cmap]
cols = [edge[1] for edge in new_cmap]
data = [1] * len(rows)
sp_sub_graph = sp.coo_matrix(
(data, (rows, cols)), shape=(n_qubits, n_qubits)).tocsr()
perm = cs.reverse_cuthill_mckee(sp_sub_graph)
best_map = best_map[perm]
return best_map
def compute_rcm_permutation(neighbor_list):
"""Computes the permutation that minimizes the bandwidth of the connectivity matrix
- uses Reverse CutHill-McKee (RCM) algorithm, which needs CSC or CSR sparse matrix format"""
A = convert_neighbor_list_to_compressed_matrix(neighbor_list, sparse.csr_matrix)
# Note we are always dealing with undirected (symmetric) graphs
permutation = graph.reverse_cuthill_mckee(A,symmetric_mode=True)
print_bandwidth_before_after_permutation(A,permutation)
return permutation.tolist()
def stability(self, omega, J_z, it=None):
"""Calculate B, Hills matrix.
The 2n eigenvalues of B with lowest imaginary part, is the estimated
Floquet exponents. They are collected in B_tilde.
Returns
-------
B: ndarray (2Nh+1)2n x (2Nh+1)2n
Hills coefficients
"""
scale_x = self.hb.scale_x
scale_t = self.hb.scale_t
M0 = self.hb.M * scale_t**2 / scale_x
C0 = self.hb.C * scale_t / scale_x
K0 = self.hb.K / scale_x
n = self.hb.n
rcm_permute = self.hb.rcm_permute
NH = self.hb.NH
nu = self.hb.nu
Delta2 = self.Delta2
b2_inv = self.b2_inv
omega2 = omega / nu
# eq. 38
Delta1 = C0
for i in range(1, NH + 1):
blk = np.vstack((np.hstack((C0, -2 * i * omega2 / scale_t * M0)),
np.hstack((2 * i * omega2 / scale_t * M0, C0))))
Delta1 = block_diag(Delta1, blk)
# eq. 45
A0 = J_z / scale_x
A1 = Delta1
A2 = Delta2
b1 = np.vstack((np.hstack(
(A1, A0)), np.hstack((-np.eye(A0.shape[0]), np.zeros(A0.shape)))))
# eq. 46
mat_B = b2_inv @ b1
if rcm_permute:
# permute B to get smaller bandwidth which gives faster linalg comp.
p = reverse_cuthill_mckee(mat_B)
B = mat_B[p]
else:
B = mat_B
return B
def upper_bound_rcm(matrix=csr_matrix):
rcm = csgraph.reverse_cuthill_mckee(matrix, symmetric_mode=True)
matrix_aux = copy.deepcopy(matrix)
cont = 0
list_aux = list(range(0, len(rcm)))
rcm = list(rcm)
rcm.pop()
for x in rcm:
matrix_aux = swap_indices(list_aux.index(x), list_aux.index(cont),
matrix_aux)
list_aux[list_aux.index(x)], list_aux[list_aux.index(cont)] = \
list_aux[list_aux.index(cont)], list_aux[list_aux.index(x)]
cont += 1
return matrix_aux
def reverseCuthillMckee(df):
startTime = datetime.now()
print(" Calculating reverse Cuthill-McKee ordering...")
# We first change the DF to a np array
df_np = df.to_numpy()
# Which is then converted to a scipy CSR graph
graph = csr_matrix(df_np)
# On which the algorithm is run
graph_ordered = reverse_cuthill_mckee(graph, symmetric_mode=False)
# We return a list of the ordering (indices)
endTime = datetime.now() - startTime
print(" Done! (%s.%s seconds)" %
(endTime.seconds, endTime.microseconds))
return graph_ordered
def neighbor_argsort(nodes, m=None):
'''
Returns a permutation array that sorts `nodes` so that each node and
its `m` nearest neighbors are close together in memory. This is done
through the use of a KD Tree and the Reverse Cuthill-McKee
algorithm.
Parameters
----------
nodes : (n, d) float array
m : int, optional
Returns
-------
(N,) int array
Examples
--------
>>> nodes = np.array([[0.0, 1.0],
[2.0, 1.0],
[1.0, 1.0]])
>>> idx = neighbor_argsort(nodes, 2)
>>> nodes[idx]
array([[ 2., 1.],
[ 1., 1.],
[ 0., 1.]])
'''
nodes = np.asarray(nodes, dtype=float)
assert_shape(nodes, (None, None), 'nodes')
if m is None:
# this should be roughly equal to the stencil size for the RBF-FD
# problem
m = 5**nodes.shape[1]
m = min(m, nodes.shape[0])
# find the indices of the nearest m nodes for each node
_, idx = KDTree(nodes).query(nodes, m)
# efficiently form adjacency matrix
col = idx.ravel()
row = np.repeat(np.arange(nodes.shape[0]), m)
data = np.ones(nodes.shape[0]*m, dtype=bool)
mat = csc_matrix((data, (row, col)), dtype=bool)
permutation = reverse_cuthill_mckee(mat)
return permutation
def test_graph_reverse_cuthill_mckee_ordering():
data = np.ones(63, dtype=int)
rows = np.array([
0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5,
6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 10, 10, 10, 10, 10, 11, 11,
11, 11, 12, 12, 12, 13, 13, 13, 13, 14, 14, 14, 14, 15, 15, 15, 15, 15
])
cols = np.array([
0, 2, 5, 8, 10, 1, 3, 9, 11, 0, 2, 7, 10, 1, 3, 11, 4, 6, 12, 14, 0, 7,
13, 15, 4, 6, 14, 2, 5, 7, 15, 0, 8, 10, 13, 1, 9, 11, 0, 2, 8, 10, 15,
1, 3, 9, 11, 4, 12, 14, 5, 8, 13, 15, 4, 6, 12, 14, 5, 7, 10, 13, 15
])
graph = coo_matrix((data, (rows, cols))).tocsr()
perm = reverse_cuthill_mckee(graph)
correct_perm = np.array(
[12, 14, 4, 6, 10, 8, 2, 15, 0, 13, 7, 5, 9, 11, 1, 3])
assert_equal(perm, correct_perm)
def neighbor_argsort(nodes, m=10, vert=None, smp=None):
'''
Returns a permutation array that sorts *nodes* so that each node and
its *m* nearest neighbors are close together in memory. This is done
through the use of a KD Tree and the Reverse Cuthill-McKee
algorithm.
Parameters
----------
nodes : (N,D) array
Node positions.
m : int, optional
Number of neighboring nodes to place close together in memory.
This should be about equal to the stencil size for RBF-FD method.
Returns
-------
permutation: (N,) array
Sorting indices.
Examples
--------
>>> nodes = np.array([[0.0,1.0],
[2.0,1.0],
[1.0,1.0]])
>>> idx = neighbor_argsort(nodes,2)
>>> nodes[idx]
array([[ 2., 1.],
[ 1., 1.],
[ 0., 1.]])
'''
nodes = np.asarray(nodes, dtype=float)
m = min(m, nodes.shape[0])
# find the indices of the nearest n nodes for each node
idx, dist = neighbors(nodes, m, vert=vert, smp=smp)
# efficiently form adjacency matrix
col = idx.ravel()
row = np.repeat(np.arange(nodes.shape[0]), m)
data = np.ones(nodes.shape[0] * m, dtype=bool)
mat = csr_matrix((data, (row, col)), dtype=bool)
permutation = reverse_cuthill_mckee(mat)
return permutation
def test_graph_reverse_cuthill_mckee_ordering():
data = np.ones(63,dtype=int)
rows = np.array([0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2,
2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5,
6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9,
9, 10, 10, 10, 10, 10, 11, 11, 11, 11,
12, 12, 12, 13, 13, 13, 13, 14, 14, 14,
14, 15, 15, 15, 15, 15])
cols = np.array([0, 2, 5, 8, 10, 1, 3, 9, 11, 0, 2,
7, 10, 1, 3, 11, 4, 6, 12, 14, 0, 7, 13,
15, 4, 6, 14, 2, 5, 7, 15, 0, 8, 10, 13,
1, 9, 11, 0, 2, 8, 10, 15, 1, 3, 9, 11,
4, 12, 14, 5, 8, 13, 15, 4, 6, 12, 14,
5, 7, 10, 13, 15])
graph = coo_matrix((data, (rows,cols))).tocsr()
perm = reverse_cuthill_mckee(graph)
correct_perm = np.array([12, 14, 4, 6, 10, 8, 2, 15,
0, 13, 7, 5, 9, 11, 1, 3])
assert_equal(perm, correct_perm)
def cramers_corrected_matrix(df, reorder_cuthill_mckee = True):
"""
Calculate Cramers V statistic with bias correction for all
combinations of columns in pandas DataFrame df
Parameters
--------------------------
df : pandas DataFrame - all columns must be categorical
reorder_cuthill_mckee : boolean - whether to reorder to the columns
based on the reverse Cuthill McKee algorithm applied to the
matrix of Cramers V statistics
Returns
---------------------------
Z : numpy array with Cramers V statistics
"""
cols = df.columns.tolist()
Z = np.zeros((len(cols),len(cols)))
for i,j in combinations_with_replacement(range(len(cols)),2):
z = cramers_corrected_stat(
pd.crosstab(df[cols[i]],df[cols[j]]).values
)
Z[i,j] = Z[j,i] = z
if reorder_cuthill_mckee is True:
perm = reverse_cuthill_mckee(
csr_matrix(Z),
symmetric_mode = True
)
cols = [cols[i] for i in perm]
gx,gy = np.meshgrid(perm,perm)
Z = (csr_matrix(Z)[gx,gy]).toarray()
Z = pd.DataFrame(
Z,
index = cols,
columns = cols
)
return(Z)
def _neighbor_argsort(nodes, m=None, vert=None, smp=None):
'''
Returns a permutation array that sorts `nodes` so that each node and
its `m` nearest neighbors are close together in memory. This is done
through the use of a KD Tree and the Reverse Cuthill-McKee
algorithm.
Returns
-------
(N,) int array
Sorting indices.
Examples
--------
>>> nodes = np.array([[0.0, 1.0],
[2.0, 1.0],
[1.0, 1.0]])
>>> idx = neighbor_argsort(nodes, 2)
>>> nodes[idx]
array([[ 2., 1.],
[ 1., 1.],
[ 0., 1.]])
'''
if m is None:
# this should be roughly equal to the stencil size for the RBF-FD
# problem
if nodes.shape[1] == 2:
m = 30
elif nodes.shape[1] == 3:
m = 50
m = min(m, nodes.shape[0])
# find the indices of the nearest n nodes for each node
idx, dist = _neighbors(nodes, m, vert=vert, smp=smp)
# efficiently form adjacency matrix
col = idx.ravel()
row = np.repeat(np.arange(nodes.shape[0]), m)
data = np.ones(nodes.shape[0] * m, dtype=bool)
mat = csc_matrix((data, (row, col)), dtype=bool)
permutation = reverse_cuthill_mckee(mat)
return permutation
def reduzir_medirTempo(self,matriz_nomeArquivo, simetrica = True):
#calcula o tempo de execução para reduzir a largura de banda, reordenando a matrix
matriz = self.lerMatriz(matriz_nomeArquivo)
inicio = time.time()
##segundo a documentação do RCM do Scipy essa transformação é necessária para matrizes assimetricas
if not simetrica:
matriz = matriz + matriz.T
#vetor de permutação obtido ao aplicar o algoritmo Reverse Cuthill Mckee, utilizado para reordenar a matrix
perm_array = reverse_cuthill_mckee(matriz,symmetric_mode=True)
#reordenação da matriz
matriz = self.reordenarMatriz(matriz,perm_array)
fim = time.time()
print("Tempo de execução: ",fim - inicio)
def reorder_matrix(self, matrix, index_order):
"""Return dataframe with matrix row/columns in index_order.
Parameters
----------
matrix : a SciPy COO sparse matrix
input sparse matrix
index_order : list of ensembles or None
order to list ensembles. If None, defaults to reverse
Cuthill-McKee order.
Returns
-------
pandas.DataFrame
dataframe with rows/columns ordered as desired
"""
#""" matrix must be a coo_matrix (I think): do other have same `data`
#attrib?"""
if index_order is None:
# reorder based on RCM from scipy.sparse.csgraph
rcm_perm = reverse_cuthill_mckee(matrix.tocsr())
rev_perm_dict = {k: rcm_perm.tolist().index(k) for k in rcm_perm}
perm_i = [rev_perm_dict[ii] for ii in matrix.row]
perm_j = [rev_perm_dict[jj] for jj in matrix.col]
new_matrix = scipy.sparse.coo_matrix(
(matrix.data, (perm_i, perm_j)),
shape=(self.n_ensembles, self.n_ensembles))
reordered_labels = [self.number_to_string[k] for k in rcm_perm]
else:
reordered_labels = [
self.number_to_string[k] for k in self.number_to_string.keys()
]
new_matrix = matrix
reordered = pd.DataFrame(new_matrix.todense())
reordered.index = reordered_labels
reordered.columns = reordered_labels
return reordered
def reorder_matrix(self, matrix, index_order):
"""Return dataframe with matrix row/columns in index_order.
Parameters
----------
matrix : a SciPy COO sparse matrix
input sparse matrix
index_order : list of ensembles or None
order to list ensembles. If None, defaults to reverse
Cuthill-McKee order.
Returns
-------
pandas.DataFrame
dataframe with rows/columns ordered as desired
"""
#""" matrix must be a coo_matrix (I think): do other have same `data`
#attrib?"""
if index_order == None:
# reorder based on RCM from scipy.sparse.csgraph
rcm_perm = reverse_cuthill_mckee(matrix.tocsr())
rev_perm_dict = {k : rcm_perm.tolist().index(k) for k in rcm_perm}
perm_i = [rev_perm_dict[ii] for ii in matrix.row]
perm_j = [rev_perm_dict[jj] for jj in matrix.col]
new_matrix = scipy.sparse.coo_matrix(
(matrix.data, (perm_i, perm_j)),
shape=(self.n_ensembles, self.n_ensembles)
)
reordered_labels = [self.number_to_string[k] for k in rcm_perm]
else:
reordered_labels = [self.number_to_string[k]
for k in self.number_to_string.keys()]
new_matrix = matrix
reordered = pd.DataFrame(new_matrix.todense())
reordered.index = reordered_labels
reordered.columns = reordered_labels
return reordered
def ordered_graph(self, filename=None, dpi=600, width=None, height=None):
def get_distances(xs, ys):
z = np.abs(xs - ys) / 2
return np.sqrt(2 * z**2) / MAX_DIST
def get_colors(distances):
cmap = plt.get_cmap("Dark2")
return cmap(distances)
def unroll(data):
return [list(row) for row in data]
nm = reverse_cuthill_mckee(self.matrix)
ro = self.matrix[nm, :][:, nm]
as_coo = ro.tocoo()
y, x = as_coo.shape
MAX_DIST = np.sqrt(2 * (x / 2.0)**2)
colors = unroll(get_colors(get_distances(as_coo.col, as_coo.row)))
plt.figure(figsize=(width or x / 1000, height or y / 1000))
ax = plt.axes([0, 0, 1, 1])
plt.scatter(
list(as_coo.shape[1] - as_coo.col),
list(as_coo.row),
s=10,
c=colors,
marker=".",
edgecolors="None",
)
ax.xaxis.set_ticks_position("none")
ax.yaxis.set_ticks_position("none")
ax.xaxis.set_ticklabels([])
ax.yaxis.set_ticklabels([])
ax.set_ylim((0, self.matrix.shape[0]))
ax.set_xlim((0, self.matrix.shape[1]))
plt.box(False)
if filename:
plt.savefig(filename, dpi=dpi)
def GetCuthillMcKeePermutation(self,A):
"""Applies Cuthill-Mckee permutation to reduce the sparse matrix bandwidth
input:
A: [csc_matrix or csr_matrix]
returns:
perm: [1D array] of permutation such that A[perm,:][:,perm]
has its non-zero elements closer to the diagonal
"""
if not (isspmatrix_csc(A) or isspmatrix_csr(A)):
raise TypeError("Matrix must be in CSC or CSR sparse format "
"for Cuthill-McKee permutation")
if int(sp.__version__.split('.')[1]) >= 15:
from scipy.sparse.csgraph import reverse_cuthill_mckee
perm = reverse_cuthill_mckee(A)
else:
from Florence.Tensor import symrcm
perm = symrcm(A)
return perm
vtkexport("Poisson_fe_H20_mesh", fes, geom)
print('Mesh generation', time.time() - start)
bfes = mesh_boundary(fes)
cn = connected_nodes(bfes)
temp = NodalField(nfens=fens.count(), dim=1)
for j in cn:
temp.set_ebc([j],
val=boundaryf(fens.xyz[j, 0], fens.xyz[j, 1], fens.xyz[j, 2]))
temp.apply_ebc()
femm = FEMMHeatDiff(material=m,
fes=fes,
integration_rule=GaussRule(dim=3, order=3))
S = femm.connection_matrix(geom)
perm = reverse_cuthill_mckee(S, symmetric_mode=True)
temp.numberdofs(node_perm=perm)
# temp.numberdofs()
start = time.time()
fi = ForceIntensity(magn=lambda x, J: Q)
F = femm.distrib_loads(geom, temp, fi, 3)
print('Heat generation load', time.time() - start)
start = time.time()
F += femm.nz_ebc_loads_conductivity(geom, temp)
print('NZ EBC load', time.time() - start)
start = time.time()
K = femm.conductivity(geom, temp)
print('Matrix assembly', time.time() - start)
start = time.time()
# lu = splu(K)
# T = lu.solve(F)
#
# Note that `i_start` is the index of the adjacency matrix.
# Thus, even though we have indexed our nodes starting at 1, in the adjacency matrix the indices start from 0 (as they always do in Python).
# + pycharm={"name": "#%%\n"}
import scipy.sparse.csgraph as csgraph
csgraph.breadth_first_order(gm.adjacency_matrix(G),
i_start=0,
return_predecessors=False)
# + [markdown] pycharm={"name": "#%% md\n"}
# ### 4. Reverse Cuthill McKee
# + pycharm={"name": "#%%\n"}
csgraph.reverse_cuthill_mckee(gm.adjacency_matrix(G))
# + [markdown] pycharm={"name": "#%% md\n"}
# # Grids
#
# ## 450. Triangular grid
# + pycharm={"name": "#%%\n"}
from scipy.spatial import Delaunay
import matplotlib.pyplot as plt
points = np.array([[0, 0], [1, 0], [0, 1], [1, 1]])
triangles = np.array([[0, 1, 2], [1, 2, 3]])
plt.triplot(points[:, 0], points[:, 1], triangles)
# + pycharm={"name": "#%%\n"}
def compute_band_matrix(self,
dim_finale=1000,
QID_columns=None,
lista_sensibili_column=None,
lista_sensibili_r=None,
density=0.03,
plot=True,
withRCM=True):
"""
Metodo per la lettura da file del dataframe e
per la creazione di una matrice bandizzata
tramite algoritmo reverse_cuthill_mckee
"""
density = math.sqrt(density)
# lettura file e dimensionamento matrice
original_dataset = self.dataframe
if original_dataset is not None and lista_sensibili_r is not None and lista_sensibili_column is not None and QID_columns is not None:
if len(original_dataset.columns
) < dim_finale + len(lista_sensibili_column):
choose = input(
"Non ci sono abbastanza colonne, vuoi cambiare il numero di colonne da %d a %d? [s/n] "
% (dim_finale, len(original_dataset.columns) -
len(lista_sensibili_column)))
if choose == "s":
dim_finale = len(
original_dataset.columns) - len(lista_sensibili_column)
else:
return
if len(original_dataset) < dim_finale:
choose = input(
"Non ci sono abbastanza righe, vuoi cambiare il numero di righe da %d a %d? [y/N] "
% (dim_finale, len(original_dataset)))
if choose == "y":
dim_finale = len(original_dataset)
else:
return
self.size_after_RCM = dim_finale
# permutazione randomica valori da inserire nella matrice banda
lista_sensibili_row = list()
indice_righe = 0
while len(lista_sensibili_row) < dim_finale and len(
lista_sensibili_row) < len(lista_sensibili_r):
lista_sensibili_row.append(lista_sensibili_r[indice_righe])
indice_righe += 1
lista_QID_column = list()
indice_righe = 0
while len(lista_QID_column) < dim_finale and len(
lista_QID_column) < len(QID_columns):
lista_QID_column.append(QID_columns[indice_righe])
indice_righe += 1
total_col = list()
for pip in lista_QID_column:
total_col.append(pip)
for pip in lista_sensibili_column:
total_col.append(pip)
items_final = dict(zip(total_col, total_col))
df_sensitive = original_dataset.iloc[lista_sensibili_row][
lista_sensibili_column]
df_square = original_dataset.iloc[lista_sensibili_row][
lista_QID_column]
sum_for_columns = df_square[lista_QID_column].sum()
sum_total = 0
for sum_column in sum_for_columns:
sum_total += sum_column
density_before = sum_total / (dim_finale * dim_finale)
"""
df1 = df_square.sample(frac=density, axis=0)
df2 = df1.sample(frac=density, axis=1)
df3 = pd.DataFrame(1, index=df2.index, columns=df2.columns)
df_square.update(df3)
"""
num_rows = int(density * dim_finale)
random_column = np.random.permutation(QID_columns)[:num_rows]
random_row = np.random.permutation(lista_sensibili_row)[:num_rows]
df_square.update(
pd.DataFrame(1, index=random_row, columns=random_column))
sum_for_columns = df_square[lista_QID_column].sum()
sum_total = 0
for sum_column in sum_for_columns:
sum_total += sum_column
self.density = sum_total / (dim_finale * dim_finale)
print("Density before : %s -- %s -- %s" %
(density_before, self.density, density * density))
if withRCM:
# creazione matrice banda tramite riordine della matrice iniziale
sparse = csr_matrix(df_square)
order = reverse_cuthill_mckee(sparse)
column_reordered = [df_square.columns[i] for i in order]
df_square_band = df_square.iloc[order][column_reordered]
df_sensitive_band = df_sensitive.iloc[order]
final_df = pd.concat([df_square_band, df_sensitive_band],
axis=1,
join='inner')
# calcolo larghezze di banda pre e post processing
[i, j] = np.where(df_square == 1)
bw = max(i - j) + max(j - i) + 1
self.original_band = bw
[i, j] = np.where(df_square_band == 1)
bw1 = max(i - j) + max(j - i) + 1
self.band_after_rcm = bw1
# parametri per il plot delle matrici
if plot:
f, (ax1, ax2) = pltt.subplots(1, 2, sharey=True)
ax1.spy(df_square, marker='.', markersize='3')
ax2.spy(df_square_band, marker='.', markersize='3')
pltt.show()
print("Bandwidth before RCM: ", bw)
print("Bandwidth after RCM", bw1)
self.dataframe_bandizzato = final_df
self.items_final = items_final
self.lista_sensibili = lista_sensibili_column
else:
final_df = pd.concat([df_square, df_sensitive],
axis=1,
join='inner')
[i, j] = np.where(self.df_square_complete == 1)
bw = max(i - j) + max(j - i) + 1
self.original_band = bw
self.band_after_rcm = bw
if plot:
print("Bandwidth before RCM: ", bw)
self.dataframe_bandizzato = final_df
self.items_final = items_final
self.lista_sensibili = lista_sensibili_column
else:
print("Error 404: Dataset not found or file not found.")
def _best_subset(self, num_qubits):
"""Computes the qubit mapping with the best connectivity.
Args:
num_qubits (int): Number of subset qubits to consider.
Returns:
ndarray: Array of qubits to use for best connectivity mapping.
"""
if num_qubits == 1:
return np.array([0])
if num_qubits == 0:
return []
device_qubits = self.coupling_map.size()
cmap = np.asarray(self.coupling_map.get_edges())
data = np.ones_like(cmap[:, 0])
sp_cmap = sp.coo_matrix(
(data, (cmap[:, 0], cmap[:, 1])), shape=(device_qubits, device_qubits)
).tocsr()
best = 0
best_map = None
best_error = np.inf
best_sub = None
# do bfs with each node as starting point
for k in range(sp_cmap.shape[0]):
bfs = cs.breadth_first_order(
sp_cmap, i_start=k, directed=False, return_predecessors=False
)
connection_count = 0
sub_graph = []
for i in range(num_qubits):
node_idx = bfs[i]
for j in range(sp_cmap.indptr[node_idx], sp_cmap.indptr[node_idx + 1]):
node = sp_cmap.indices[j]
for counter in range(num_qubits):
if node == bfs[counter]:
connection_count += 1
sub_graph.append([node_idx, node])
break
if self.backend_prop:
curr_error = 0
# compute meas error for subset
avg_meas_err = np.mean(self.meas_arr)
meas_diff = np.mean(self.meas_arr[bfs[0:num_qubits]]) - avg_meas_err
if meas_diff > 0:
curr_error += self.num_meas * meas_diff
cx_err = np.mean([self.cx_mat[edge[0], edge[1]] for edge in sub_graph])
if self.coupling_map.is_symmetric:
cx_err /= 2
curr_error += self.num_cx * cx_err
if connection_count >= best and curr_error < best_error:
best = connection_count
best_error = curr_error
best_map = bfs[0:num_qubits]
best_sub = sub_graph
else:
if connection_count > best:
best = connection_count
best_map = bfs[0:num_qubits]
best_sub = sub_graph
# Return a best mapping that has reduced bandwidth
mapping = {}
for edge in range(best_map.shape[0]):
mapping[best_map[edge]] = edge
new_cmap = [[mapping[c[0]], mapping[c[1]]] for c in best_sub]
rows = [edge[0] for edge in new_cmap]
cols = [edge[1] for edge in new_cmap]
data = [1] * len(rows)
sp_sub_graph = sp.coo_matrix((data, (rows, cols)), shape=(num_qubits, num_qubits)).tocsr()
perm = cs.reverse_cuthill_mckee(sp_sub_graph)
best_map = best_map[perm]
return best_map
def rcm(A: spmatrix, b: ndarray) -> Tuple[spmatrix, ndarray, ndarray]:
p = spg.reverse_cuthill_mckee(A, symmetric_mode=False)
return A[p].T[p].T, b[p], p
def delta_buildmatrices():
cols = []
kappa = 5
its = 24
ind = []
# run simulations
print("===================")
print("RUNNING SIMULATIONS")
print("===================")
if count:
nsl = 0
sl = 0
for j in tqdm(indices):
edgelist = list(graphs[int(j)].edges)
colorlist = coloring[j][0]
net = ColorNNetwork(colorlist.tolist(), edgelist)
coldyn = simulate_Kuramoto(net,
K=2,
timesec=60,
verbose=0,
intrinsic=0)[0]
s = dataout[int(j)]
if count:
if s:
if sl >= 100:
pass
else:
cols.append(coldyn)
ind.append(int(j))
sl += 1
else:
if nsl >= 100:
pass
else:
cols.append(coldyn)
ind.append(int(j))
nsl += 1
if sl >= 100 and nsl >= 100:
break
print(len(cols), len(ind))
adjmatsnsl = []
adjmatssl = []
n = 30
dataynsl = []
dataysl = []
# create adjacency matrices
print("==================")
print("ADJACENCY MATRICES")
print("==================")
if count:
nsl = 0
sl = 0
for i, j in enumerate(tqdm(ind)):
# index from the graphs
graph = graphs[int(j)]
# compute rcm
rcm = np.asarray(reverse_cuthill_mckee(csr_matrix(\
nx.adjacency_matrix(graph).todense())
)
)
adjdyn = []
# assigning colors
for col in cols[i]:
for x in range(n):
for y in range(x + 1):
if graph.has_edge(x, y):
widthcol = width([col[x], col[y]], kappa)
graph.add_weighted_edges_from([(x, y, widthcol)])
frame = nx.adjacency_matrix(graph).todense()[:,rcm][rcm,:] + \
np.diag(np.asarray(col)[rcm])
adjdyn.append(frame)
# pad iterations to uniform length
frameseq = np.stack(np.asarray(adjdyn + [adjdyn[-1]] *
((its + 1) - len(cols[i]))),
axis=0)
if count:
s = dataout[int(j)]
if s:
sl += 1
else:
nsl += 1
print("SYNC:", len(dataysl), "NONSYNC:", len(dataynsl))
if sl > 100:
pass
else:
adjmatssl.append(frameseq)
dataysl.append(s)
if nsl > 100:
pass
else:
adjmatsnsl.append(frameseq)
dataynsl.append(s)
if sl > 100 and nsl > 100:
break
print(len(adjmatssl), len(dataynsl))
print(len(adjmatsnsl), len(dataysl))
#datain = np.stack(adjmats, axis=0)
# save results
with open(path + 'delta.npy', 'wb') as f:
np.save(f, adjmatssl)
np.save(f, dataysl)
np.save(f, adjmatsnsl)
np.save(f, dataynsl)
def cuthill_mckee(G): sG = G.matrix(csr=True) order = ssc.reverse_cuthill_mckee(sG, symmetric_mode=True) return permute_graph(G, order)