def corr2cova(corr: _np.ndarray) -> _np.ndarray:
"""Converts sinex CORR matrix to COVA using the diagonal STD values"""
D = corr.diagonal() * corr.diagonal()[:, None]
_np.fill_diagonal(
corr,
1) # fill COVA diagonal with 1 so we only multiply with D to get COVA
return corr * D
def quantum_contrast(matrix: np.ndarray) -> float:
"""Calculate the quantum contrast from the diagonals
of a coincidence matrix.
The quantum contrast is the average of the diagonal divided by the average of the off-diagonal
The input should be a coincidence matrix
"""
off_diag_avg = (matrix.sum() -
matrix.diagonal().sum()) / (matrix.shape[0] *
(matrix.shape[1] - 1))
return np.average(matrix.diagonal()) / off_diag_avg
def _approx_permutation_2sided_1trans_normal1(a: np.ndarray) -> np.ndarray:
# This assumes that array_a has all positive entries, this guess does not match that found
# in the notes/paper because it doesn't include the sign function.
# build the empty target array
array_c = np.zeros(a.shape)
# Fill the first row of array_c with diagonal entries
array_c[0, :] = a.diagonal()
array_mask = ~np.eye(a.shape[0], dtype=bool)
# get all the non-diagonal element
array_c_non_diag = (a[array_mask]).T.reshape(a.shape[0], a.shape[1] - 1)
array_c_non_diag = array_c_non_diag[
np.arange(np.shape(array_c_non_diag)[0])[:, np.newaxis], np.argsort(abs(array_c_non_diag))
]
# form the right format in order to combine with matrix A
array_c_sorted = np.fliplr(array_c_non_diag).T
# fill the array_c with array_c_sorted
array_c[1:, :] = array_c_sorted
# the weight matrix
weight_c = np.zeros(a.shape)
weight_p = np.power(2, -0.5)
for weight in range(a.shape[0]):
weight_c[weight, :] = np.power(weight_p, weight)
# build the new matrix array_new
array_new = np.multiply(array_c, weight_c)
return array_new
def get_init_mat(P_1_0: np.ndarray) \
-> Tuple[int, np.ndarray, np.ndarray, np.ndarray]:
"""
Get information for diffuse initialization
Parameters:
----------
P_1_0 : initial state covariance. Diagonal value np.nan if diffuse
Returns:
----------
number_diffuse : number of diffuse state
A : selection matrix for diffuse states, equal to P_inf
Pi : selection matrix for stationary states
P_star : non-diffuse part of P_1_0
"""
is_diffuse = np.isnan(P_1_0.diagonal())
number_diffuse = np.count_nonzero(is_diffuse)
A = np.diag(is_diffuse.astype(float))
Pi = np.diag((~is_diffuse).astype(float))
P_clean = P_1_0.copy()
P_clean[np.isnan(P_clean)] = 0
P_star = Pi.dot(P_clean).dot(Pi.T)
return number_diffuse, A, Pi, P_star
def plot_var(fund_num: int, cov_mat: np.ndarray, highlight: list) -> None:
var = cov_mat.diagonal()
np.savetxt(os.path.join(os.getcwd(), 'tmp/group_var.csv'), var)
green_x = list()
for i in range(fund_num):
if i + 1 not in highlight:
green_x.append(i + 1)
green_y = list()
for i in green_x:
green_y.append(var[i - 1])
red_x = highlight
red_y = list()
for i in red_x:
red_y.append(var[i - 1])
f = plt.figure()
matplotlib.rc('xtick', labelsize=8)
matplotlib.rc('ytick', labelsize=10)
plt.bar(green_x, green_y, tick_label=green_x)
plt.bar(red_x, red_y, tick_label=red_x)
plt.xticks(rotation=270)
plt.xlabel('group')
plt.ylabel('variance')
plt.title("variance of each group")
f.savefig(os.path.join(os.getcwd(), 'figs/group_var.pdf'))
def cov_to_std(cov: np.ndarray) -> np.ndarray:
'''Compute standard deviation from co variance matrix
'''
diag = cov.diagonal()
std = np.sqrt(diag)
return std
def extendOneNode(X: np.ndarray, Y: np.ndarray):
# print(X,Y)
n = X.shape[0]
xLabelNodes = X.diagonal()#np.unique(X.diagonal())
extensions = []
for i,lNode in enumerate(xLabelNodes):
# print("node",lNode,"i",i)
indices = np.where(Y.diagonal() == lNode)[0]
for iY in indices:
for j in np.where(Y[iY] > 0)[0]:
if j != iY:
pad = np.zeros((1,n+1),dtype=int)
pad[0,-1] = Y[j,j]
pad[0,i] = Y[iY,j]
extensions.append(extend(X.copy(),pad))
return extensions
def visibility(matrix: np.ndarray) -> float:
"""Calculate the visibility of the state.
The visibility is the sum of the diagonal divided by the sum over the whole coincidence matrix
The input should be a coincidence matrix
"""
return matrix.diagonal().sum() / matrix.sum()
def diagonals(arr: np.ndarray) -> Lines:
if arr.ndim == 1:
diags.append(arr)
else:
diagonals(arr.diagonal())
diagonals(np.flip(arr, 0).diagonal())
return diags
def evaluate(self, state: np.ndarray):
tic = time()
situations = self.situations
to_str = lambda array: ''.join(map(str, array))
size = len(state)
# the opponent state 1 --> 2, 2 --> 1
opponent_state = state.copy()
opponent_state[opponent_state == 1] = 3
opponent_state[opponent_state == 2] = 1
opponent_state[opponent_state == 3] = 2
opponent_reverse_state = opponent_state[::-1]
my_record = defaultdict(int)
opponent_record = defaultdict(int)
reverse_state = state[::-1]
my_horizontal, my_vertical = [to_str(x) for x in state], [
to_str(state[..., x]) for x in range(size)
]
my_lr_diag, my_rl_diag = [], []
op_horizontal, op_vertical = [to_str(x) for x in opponent_state], [
to_str(opponent_state[..., x]) for x in range(size)
]
op_lr_diag, op_rl_diag = [], []
for i in range(-size, size):
my_lr_diag.append(to_str(state.diagonal(i)))
my_rl_diag.append(to_str(reverse_state.diagonal(i)))
op_lr_diag.append(to_str(opponent_state.diagonal(i)))
op_rl_diag.append(to_str(opponent_reverse_state.diagonal(i)))
# pprint(my_horizontal)
# pprint(my_vertical)
# pprint(my_lr_diag)
# pprint(my_rl_diag)
my_record = self._check_lines(my_record, *my_horizontal, *my_vertical,
*my_lr_diag, *my_rl_diag)
opponent_record = self._check_lines(opponent_record, *op_horizontal,
*op_vertical, *op_lr_diag,
*op_rl_diag)
my_mark = sum(
map(lambda situ: situations[situ] * my_record[situ],
my_record.keys()))
opponent_mark = sum(
map(lambda situ: situations[situ] * opponent_record[situ],
opponent_record.keys()))
self.evaluate_time += (time() - tic)
self.evaluate_num += 1
# print('evaluate:', self.evaluate_num)
return (my_mark -
1.1 * opponent_mark) if self.color == 1 else (opponent_mark -
1.1 * my_mark)
def recall(matrix: np.ndarray) -> np.ndarray:
"""
Calculate recall of prediction
:param matrix: Confusion matrix
:return: Recall for every class
"""
return np.divide(matrix.diagonal(), matrix.sum(axis=0))
def precision(matrix: np.ndarray) -> np.ndarray:
"""
Calculate precision of prediction
:param matrix: Confusion matrix
:return: Precision for every class
"""
return np.divide(matrix.diagonal(), matrix.sum(axis=1))
def accuracy(matrix: np.ndarray) -> float:
"""
Calculate accuracy of prediction
:param matrix: Confusion matrix calculated
:return: Accuracy
"""
return matrix.diagonal().sum() / matrix.sum()
def non_diag(a: np.ndarray):
"""
Remove the Diagonal Entries from a matrix
:param a: 2D Numpy Array to operate on
:return: A copy of the matrix with diagonal elements zeroed out
"""
return a - np.diagflat(a.diagonal())
def gaussian_predictions(
model: GPModel,
x_test: torch.Tensor,
expected_mu: np.ndarray,
expected_s: np.ndarray,
):
"""
Every GP model with a gaussian likelihood needs the same set of tests run on
its ._predict() method.
"""
# Predictions without full covariance
mu_diag, s_diag = model._predict(x_test, diag=True)
assert isinstance(mu_diag, torch.Tensor)
assert isinstance(s_diag, torch.Tensor)
assert mu_diag.shape[0] == x_test.shape[0]
assert mu_diag.shape[1] == model.Y.shape[1]
assert all([ss == ms for ss, ms in zip(mu_diag.shape, s_diag.shape)])
assert all(
[
a == pytest.approx(e)
for a, e in zip(mu_diag.detach().numpy().flatten(), expected_mu.flatten())
]
)
assert all(
[
a == pytest.approx(e)
for a, e in zip(
s_diag.detach().numpy().flatten(), expected_s.diagonal().flatten()
)
]
)
# Predictions with full covariance
mu_full, s_full = model._predict(x_test, diag=False)
assert isinstance(mu_full, torch.Tensor)
assert isinstance(s_full, torch.Tensor)
assert mu_full.shape[0] == x_test.shape[0]
assert mu_full.shape[1] == model.Y.shape[1]
assert all([ss == x_test.shape[0] for ss in s_full.shape])
assert all(
[
a == pytest.approx(e)
for a, e in zip(mu_full.detach().numpy().flatten(), expected_mu.flatten())
]
)
assert all(
[
a == pytest.approx(e)
for a, e in zip(s_full.detach().numpy().flatten(), expected_s.flatten())
]
)
def diagonal(m: np.ndarray) -> np.ndarray:
"""
Get the diagonal of the `feature x feature` matrix for each output.
:param m: array of shape `(n_outputs, n_features, n_features)`
:return: array of shape `(n_outputs, n_features)`, with the diagonals of arg ``m``
"""
assert m.ndim == 3
assert m.shape[1] == m.shape[2]
return m.diagonal(axis1=1, axis2=2)
def recall_per_class(matrix: np.ndarray) -> np.ndarray:
"""
Compute the recall per class based on the confusion matrix.
:param matrix: the computed confusion matrix
:return: the recall (per class), defined as TP/(TP+FN)
"""
tp_per_class = matrix.diagonal()
sum_tp_fn_per_class = matrix.sum(1)
return divide_arrays_with_possible_zeros(tp_per_class, sum_tp_fn_per_class)
def cm_to_accuracies(cm: np.ndarray) -> np.ndarray:
"""
Convert confusion matrix to an array with accuracy for each class.
:param cm: the confusion matrix.
:return: Accuracy for each class
"""
# Divide confusion matrix row's values with their sums.
cm = cm.astype('float') / cm.sum(axis=1)[:, np.newaxis]
# Return the diagonal, which is the accuracy of each class.
return cm.diagonal()
def apply_along_diags(func: Callable,
mat: np.ndarray,
offsets: Iterable,
filter_fn: Callable = None) -> Generator:
"""Apply a function to a cetain set of diagonals.
:param func: Callable. Function applied to each diagonal.
:param mat: np.ndarray. 2d ndarray.
:param offsets: list. List of diagonal offsets.
:param filter_fn: Callable. Function applied to each daigonal, should return a mask.
:return: Generator. Yielding the result of applying func to each diagonal.
"""
max_len = mat.shape[0]
offsets = tuple(offsets)
if filter_fn is None:
for offset in offsets:
if offset >= max_len:
break
diag = mat.diagonal(offset)
yield func(diag)
else:
diag = mat.diagonal(offsets[len(offsets) - 1])
res = func(diag)
if isinstance(res, np.ndarray):
for offset in offsets:
if offset >= max_len:
break
diag = mat.diagonal(offset)
mask = filter_fn(diag)
zeros = np.zeros_like(diag)
zeros[mask] = func(diag[mask])
yield zeros, mask
else:
for offset in offsets:
if offset >= max_len:
break
diag = mat.diagonal(offset)
yield func(diag[filter_fn(diag)])
def get_inductances(L: np.ndarray, length: float = 1.0):
'''Returns Le and Ke matrices of inductor values and coupling coefficients
Input is per unit inductance matrix, size N x N
Le are individual inductor values, size N
Ke are coupling coefficients, size N x N'''
assert L.ndim == 2
Le = L.diagonal() * length
N = L.shape[0]
Ke = np.zeros_like(L)
for i in range(N):
for j in range(N):
Ke[i, j] = L[i, j] / np.sqrt(L[i, i] * L[j, j])
return Le, Ke
def canonicalForm(graph: np.ndarray,embeddings=None):
labelNodes = graph.diagonal()
start = np.zeros((1,1),dtype=int)
maxNodes = np.where(labelNodes == np.max(labelNodes))[0]
start[0,0] = np.max(labelNodes)
canonical = {
"code" : ''
}
for idStart in maxNodes:
S = {
"tree" : start,
"index" : np.array([idStart]),
"code" : encodeGraph(start)
}
while (len(S["index"]) < len(labelNodes)):
# trees = []
newCandidates = {}
for i in range(graph.shape[0]):
if i in S["index"]:
continue
Q = []
t = S["tree"]
for id,j in enumerate(S["index"]):
if graph[i,j] == 0:
continue
rowExpand = np.zeros((1,t.shape[0]),dtype=int)
rowExpand[0,id] = graph[i,j]
tree = np.r_[t,rowExpand]
colExpand = np.zeros((tree.shape[0],1),dtype=int)
colExpand[id,0] = graph[i,j]
colExpand[tree.shape[0]-1,0] = graph[i,i]
tree = np.c_[tree,colExpand]
indexTree = np.concatenate([S["index"],np.array([i])])
codeTree = encodeGraph(tree)
newCandidates[codeTree] = {
"tree" : tree,
"index" : indexTree,
"code" : codeTree
}
S = newCandidates[max(newCandidates.keys())]
canonical = S if canonical["code"] < S["code"] else canonical
if embeddings is not None:
for k in embeddings.keys():
topo = []
for subNodes in embeddings[k]:
reindexedNodes = np.array([subNodes[idNode] for idNode in canonical['index']])
topo.append(reindexedNodes)
embeddings[k] = topo
return canonical
def solve_linear_system_sparse(
A: np.ndarray,
u: np.ndarray
) -> np.ndarray:
'''
funcao que resolve um sistema linear da forma Ax = u para A matriz
trigonal simétrica esparsa, retornando o vetor x
@parameters:
- A: dim = ((N-1)x(N-1)), matriz quadrada de entrada do sistema
- u: dim = ((N-1)x1), vetor de saida da equacao
@output:
- x: dim = ((N-1)x1), vetor de incognitas
'''
# A.x = L.D.Lt.x
a = np.asarray(A.diagonal(0)).ravel()
N = a.shape[0] + 1
b = np.concatenate((np.array([0]), np.asarray(A.diagonal(1)).ravel()))
d, l = perform_ldlt_transformation_sparse(a, b)
# Como explicado no relatorio, resolvemos o problema atraves da reso-
# lucao de 3 loops: primeiro resolvemos em z, depois em y e ai sim em
# x
#Loop em z:
z = np.zeros(N-1)
z[0] = u[0]
for i in range(1, N-1):
z[i] = u[i] - z[i-1]*l[i]
#Loop em y:
y = np.zeros(N-1)
for i in range(N-1):
y[i] = z[i]/d[i]
#Loop em x:
x = np.zeros(N-1)
x[-1] = y[-1]
for i in range(N-3, -1, -1):
x[i] = y[i] - x[i+1]*l[i+1]
return x
def search(mat: np.ndarray, row: int) -> Generator[np.ndarray, None, None]:
assert row >= 0
if row == N:
yield mat
for col in [
i for i in range(N)
if np.all(mat[:row, i] == 0) # not occupied horizontally
and np.all(mat.diagonal(i - row) ==
0) # not occupied on the main diagonal
and np.all(np.fliplr(mat).diagonal(N - 1 - i - row) ==
0) # not occupied on the opposite diagonal
]:
mat[row, col] = 1
yield from search(mat, row + 1)
mat[row, col] = 0
def terminal_test_great(self, state: np.ndarray, action):
continuity_test = lambda string: '11111' in string or '22222' in string
x, y = action
board_size = len(state)
horizontal = ''.join(map(str, state[x, max(0, y - 4): min(board_size, y + 5)]))
vertical = ''.join(map(str, state[max(0, x - 4): min(board_size, x + 5), y]))
lr_diag = ''.join(map(str, state.diagonal(y - x)))
rl_diag = ''.join(map(str, state[:, ::-1].diagonal(14 - x - y)))
if continuity_test(horizontal) or continuity_test(vertical) or continuity_test(lr_diag) or continuity_test(rl_diag):
return True
return False
def precision_per_class(matrix: np.ndarray) -> np.ndarray:
"""
Compute the precision per class based on the confusion matrix.
:param matrix: the computed confusion matrix
:return: the precision (per class), defined as TP/(TP+FP)
"""
if not matrix.shape[0] == matrix.shape[1]:
# If the matrix is not square (there is a column for "other" label), the "other" column is deleted.
# Otherwise, there will be 3 elements in TP and 4 in TP+FP meaning they can't be divided.
matrix = np.delete(matrix, -1, 1)
tp_per_class = matrix.diagonal()
sum_tp_fp_per_class = matrix.sum(0)
return divide_arrays_with_possible_zeros(tp_per_class, sum_tp_fp_per_class)
def evaluate(self, state: np.ndarray):
tic = time()
situations = self.situations
to_str = lambda array: ''.join(map(str, array))
# the opponent state 1 --> 2, 2 --> 1
opponent_state = state.copy()
opponent_state[opponent_state == 1] = 3
opponent_state[opponent_state == 2] = 1
opponent_state[opponent_state == 3] = 2
print(state)
print(opponent_state)
my_record = defaultdict(int)
opponent_record = defaultdict(int)
reverse_state = state[::-1]
for i in range(len(state)):
horizontal = to_str(state[i])
vertical = to_str(state[..., i])
lr_diag = to_str(state.diagonal(i))
rl_diag = to_str(reverse_state.diagonal(-i))
my_record = self._check_lines(my_record, horizontal, vertical,
lr_diag, rl_diag)
horizontal = to_str(opponent_state[i])
vertical = to_str(opponent_state[..., i])
lr_diag = to_str(opponent_state.diagonal(i))
rl_diag = to_str(opponent_state.diagonal(-i))
opponent_record = self._check_lines(opponent_record, horizontal,
vertical, lr_diag, rl_diag)
my_mark = sum(
map(lambda situ: situations[situ] * my_record[situ],
my_record.keys()))
opponent_mark = sum(
map(lambda situ: situations[situ] * opponent_record[situ],
opponent_record.keys()))
self.evaluate_time += (time() - tic)
self.evaluate_num += 1
return (my_mark -
opponent_mark) if self.color == 1 else (opponent_mark -
my_mark)
def extendFFSM(self, X: np.ndarray, Y: np.ndarray):
pos = np.where(Y.diagonal() == X[-1, -1])[0]
n = X.shape[0]
extensions = []
for p in pos:
if p < n - 1:
indices = np.where(Y[p, p + 1:] > 0)[0]
# indices = np.where(Y[p] > 0)[0]
for i in indices:
# if i!=p:
pad = np.zeros((1, n + 1), dtype=int)
# pad[0,-1] = Y[i,i]
# pad[0,-2] = Y[p,i]
pad[0, -1] = Y[p + i + 1, p + i + 1]
pad[0, -2] = Y[p, p + i + 1]
extensions.append(self.extend(X, pad))
return extensions
def logit_tpm(tpm: _np.ndarray) -> _np.ndarray:
"""Transform tpm to logit space for unconstrained optimization.
Note: There must be no zeros on the main diagonal.
Args:
tpm (np.ndarray) Transition probability matrix.
Returns:
(np.nadarray) lg_tpm of shape (1, m**2-m).
"""
assert_st_matrix(tpm)
logits = _np.log(tpm / tpm.diagonal()[:, None])
lg_tpm = get_off_diag(logits)
return lg_tpm
def diagonalWinCheck(board: np.ndarray) -> int:
diags = [
board[::-1, :].diagonal(i)
for i in range(-board.shape[0] + 1, board.shape[1])
]
diags.extend(
board.diagonal(i)
for i in range(board.shape[1] - 1, -board.shape[0], -1))
for i in diags:
if any(
sum(1 for _ in islice(g, 4)) == 4 for k, g in groupby(i)
if k == 1):
return 1
elif any(
sum(1 for _ in islice(g, 4)) == 4 for k, g in groupby(i)
if k == 2):
return 2
return 0
def pauli_twirl_chi_matrix(chi_matrix: np.ndarray) -> np.ndarray:
r"""
Implements a Pauli twirl of a chi matrix (aka a process matrix).
See the folloiwng reference for more details
[SPICC] Scalable protocol for identification of correctable codes
Silva et al.,
PRA 78, 012347 2008
http://dx.doi.org/10.1103/PhysRevA.78.012347
https://arxiv.org/abs/0710.1900
Note: Pauli twirling a quantum channel can give rise to a channel that is less noisy; use with
care.
:param chi_matrix: a dim**2 by dim**2 chi or process matrix
:return: dim**2 by dim**2 chi or process matrix
"""
return np.diag(chi_matrix.diagonal())
def _mutual_proximity_gaussi_sparse(
S: np.ndarray, sample_size: int = 0, test_set_ind: np.ndarray = None, verbose: int = 0, log=None
):
"""MP gaussi for sparse similarity matrices.
Please do not directly use this function, but invoke via
mutual_proximity_gaussi()
"""
n = S.shape[0]
self_value = 1 # similarity matrix
if test_set_ind is None:
train_set_ind = slice(0, n)
else:
train_set_ind = np.setdiff1d(np.arange(n), test_set_ind)
# ===========================================================================
# from sklearn.utils.sparsefuncs_fast import csr_mean_variance_axis0 # @UnresolvedImport
# mu, var = csr_mean_variance_axis0(S[train_set_ind])
# sd = np.sqrt(var)
# del var
# ===========================================================================
# mean, variance WITHOUT zero values (missing values), ddof=0
if S.diagonal().max() != 1.0 or S.diagonal().min() != 1.0:
raise ValueError("Self similarities must be 1.")
S_param = S[train_set_ind]
# the -1 accounts for self similarities that must be excluded from the calc
mu = np.array((S_param.sum(0) - 1.0) / (S_param.getnnz(0) - 1)).ravel()
X = S_param
X.data **= 2
E1 = np.array((X.sum(0) - 1.0) / (X.getnnz(0) - 1)).ravel()
del X, S_param
E2 = mu ** 2
va = E1 - E2
del E1, E2
sd = np.sqrt(va)
del va
S_mp = lil_matrix(S.shape)
for i in range(n):
if verbose and log and ((i + 1) % 1000 == 0 or i + 1 == n):
log.message("MP_gaussi: {} of {}.".format(i + 1, n), flush=True)
j_idx = slice(i + 1, n)
S_ij = S[i, j_idx].toarray().ravel() # Extract dense rows temporarily
S_ji = S[j_idx, i].toarray().ravel() # for vectorization below.
p1 = norm.cdf(S_ij, mu[i], sd[i]) # mu, sd broadcasted
p1[S_ij == 0] = 0
del S_ij
p2 = norm.cdf(S_ji, mu[j_idx], sd[j_idx])
p2[S_ji == 0] = 0
del S_ji
tmp = np.empty(n - i)
tmp[0] = self_value / 2.0
tmp[1:] = (p1 * p2).ravel()
S_mp[i, i:] = tmp
del tmp, j_idx
S_mp += S_mp.T
return S_mp.tocsr()
def _mutual_proximity_gammai_sparse(S: np.ndarray, test_set_ind: np.ndarray = None, verbose: int = 0, log=None):
"""MP gammai for sparse similarity matrices.
Please do not directly use this function, but invoke via
mutual_proximity_gammai()
"""
n = S.shape[0]
self_value = 1.0
if test_set_ind is None:
train_set_ind = slice(0, n)
else:
train_set_ind = np.setdiff1d(np.arange(n), test_set_ind)
# mean, variance WITH zero values
# =======================================================================
# from sklearn.utils.sparsefuncs_fast import csr_mean_variance_axis0
# mu, va = csr_mean_variance_axis0(self.S[train_set_mask])
# =======================================================================
# mean, variance WITHOUT zero values (missing values), ddof=1
if S.diagonal().max() != 1.0 or S.diagonal().min() != 1.0:
raise ValueError("Self similarities must be 1.")
S_param = S[train_set_ind]
# the -1 accounts for self similarities that must be excluded from the calc
mu = np.array((S_param.sum(0) - 1) / (S_param.getnnz(0) - 1)).ravel()
E2 = mu ** 2
X = S_param.copy()
X.data **= 2
n_x = X.getnnz(0) - 1
E1 = np.array((X.sum(0) - 1) / (n_x)).ravel()
del X
# for an unbiased sample variance
va = n_x / (n_x - 1) * (E1 - E2)
del E1
A = E2 / va
B = va / mu
del mu, va, E2
A[A < 0] = np.nan
B[B <= 0] = np.nan
S_mp = lil_matrix(S.shape, dtype=np.float32)
for i in range(n):
if verbose and log and ((i + 1) % 1000 == 0 or i + 1 == n):
log.message("MP_gammai: {} of {}".format(i + 1, n), flush=True)
j_idx = slice(i + 1, n)
Dij = S[i, j_idx].toarray().ravel() # Extract dense rows temporarily
p1 = _local_gamcdf(Dij, A[i], B[i])
del Dij
Dji = S[j_idx, i].toarray().ravel() # for vectorization below.
p2 = _local_gamcdf(Dji, A[j_idx], B[j_idx])
del Dji
tmp = np.empty(n - i)
tmp[0] = self_value / 2.0
tmp[1:] = (p1 * p2).ravel()
S_mp[i, i:] = tmp
del tmp, j_idx
S_mp += S_mp.T
return S_mp.tocsr()
