def logdotexp(logA, logB):
"""
Given the log of two matrices A and B as logA and logB, carries out A * B in log space
"""
maxA = np.max(logA)
maxB = np.max(logB)
if np.abs(maxA) == np.Inf:
sortA = np.sort(logA.reshape(-1))
if np.sum(np.abs(sortA) != np.Inf) == 0:
C = np.zeros([logA.shape[0], logB.shape[1]],
dtype='complex128') - np.Inf
return C
else:
maxA = sortA[np.sum(np.abs(sortA) != np.Inf) - 1]
if np.abs(maxB) == np.Inf:
sortB = np.sort(logB.reshape(-1))
if np.sum(np.abs(sortB) != np.Inf) == 0:
C = np.zeros([logA.shape[0], logB.shape[1]],
dtype='complex128') - np.Inf
return C
else:
maxB = sortB[np.sum(np.abs(sortB) != np.Inf)]
expA = np.exp(logA - maxA)
expB = np.exp(logB - maxB)
C = np.log(np.dot(expA, expB)) + maxA + maxB
return C
def G4(positions, cell, numbers, elements, params):
cutoff_radius = params['cutoff_radius']
eta = params['eta']
zeta = params['zeta']
lbda = params['lbda']
cos, Rij, Rik, Rjk, i, jk = atomsAngle(positions, cell, cutoff_radius)
g4 = (1 + lbda * cos)**zeta * np.exp(
-eta * (Rij**2 + Rik**2 + Rjk**2) / cutoff_radius**2)
g4 = g4 * cutoff(cutoff_radius, Rij) * cutoff(cutoff_radius, Rik) * cutoff(
cutoff_radius, Rjk)
g4 *= 2**(1 - zeta)
atoms_mask = np.arange(len(positions))[:, None] == i[None, :]
# the shape of g4 will become (#atoms, len(g4)) and multiply atoms_mask to get the corresponding center atom's fingerprints
g4 = np.repeat(g4[None, :], len(positions), axis=0)
g4 *= atoms_mask
index = np.indices((len(elements), len(elements))).reshape(2, -1)
mask = index[1] >= index[0]
index = index[:, mask].T
pairs = np.repeat(np.sort(numbers[jk])[:, None], len(index), axis=1)
elements = np.sort(elements)[index]
pairs_mask = np.sum(pairs == elements, axis=2)
pairs_mask = np.where(pairs_mask == 2, 1, 0)
g4 = np.dot(g4, pairs_mask)
return g4
def mle_batch_euclidean(self, data, k):
"""
Calculates LID values of data w.r.t batch
Args:
data: samples to calculate LIDs of
batch: samples to calculate LIDs against
k: the number of nearest neighbors to consider
Returns: the calculated LID values
"""
batch = self.training_data_ndarray
f = lambda v: -k / np.sum(np.log((v / v[-1]) + 1e-9))
gamma = self.classifier.kernel.gamma
if gamma is None:
gamma = 1.0 / self.training_data_ndarray.shape[1]
K = rbf_kernel(data, Y=batch, gamma=gamma)
K = np.reciprocal(K)
# K = cdist(data, batch)
# get the closest k neighbours
if self.xc is not None and self.xc.shape[0] == 1:
# only one attack sample
sorted_distances = np.sort(K)[0, 1:1 + k]
else:
sorted_distances = np.sort(K)[0, 0:k]
a = np.apply_along_axis(f, axis=0, arr=sorted_distances)
return np.nan_to_num(a)
def reduce_grid(x):
"""
Undoes expand_grid to take (nx, 2) array to two vectors containing unique values of each col.
:param x: (nx, 2) points
:return: x1, x2 each vectors
"""
x1 = np.sort(np.unique(x[:, 0]))
x2 = np.sort(np.unique(x[:, 1]))
return x1, x2
def other_r_selection(rl1_select, z2_z1s):
''' Chose the meaningful dimensions from the second layer to the end of the network
rl1_select (list): The dimension kept over the first layer
z2_z1s (list of ndarrays): z^{(l + 1)}| z^{(l)}, s
--------------------------------------------------------------------------
return (list of int): The dimensions to keep from the second layer of the network
'''
S = [zz.shape[2] for zz in z2_z1s] + [1]
CORR_THRESHOLD = 0.20
L = len(z2_z1s)
M = np.array([zz.shape[0] for zz in z2_z1s] + [z2_z1s[-1].shape[1]])
prev_new_r = [len(rl1_select)]
dims_to_keep = []
for l in range(L):
# Will not keep the following layers if one of the previous layer is of dim 1
if prev_new_r[l] <= 1:
dims_to_keep.append([])
prev_new_r.append(0)
else:
old_rl = z2_z1s[l].shape[-1]
corr = np.zeros(old_rl)
for s in range(S[l]):
for m1 in range(M[l + 1]):
pca = PCA(n_components=1)
pca.fit_transform(z2_z1s[l][m1, :, s])
corr += np.abs(pca.components_[0])
average_corr = corr / (S[l] * M[l + 1])
new_rl = np.sum(average_corr > CORR_THRESHOLD)
if prev_new_r[l] > new_rl: # Respect r1 > r2 > r3 ....
wanted_dims = np.where(
average_corr > CORR_THRESHOLD)[0].tolist()
wanted_dims = np.sort(wanted_dims)
dims_to_keep.append(wanted_dims)
else: # Have to delete other dimensions to match r1 > r2 > r3 ....
nb_dims_to_remove = old_rl - prev_new_r[l] + 1
unwanted_dims = np.argpartition(
average_corr, nb_dims_to_remove)[:nb_dims_to_remove]
wanted_dims = list(set(range(old_rl)) - set(unwanted_dims))
wanted_dims = np.sort(wanted_dims)
dims_to_keep.append(wanted_dims)
new_rl = len(wanted_dims)
prev_new_r.append(new_rl)
return dims_to_keep
def step_generator(t, **kwargs):
'''
Makes a random piecewise constant step frequency input. Note
that the steps always take on integer values.
'''
# lets make random piecewise frequency
num_steps = 2
if 'num_steps' in kwargs:
num_steps = kwargs['num_steps'] - 1
# pick num_pieces random locations for step ledges
r = np.random.permutation(len(t))[:num_steps]
r = np.sort(r)
# generate random level per step
levels = np.round(5 * np.random.rand(num_steps + 1)) + 1
f = np.ones((t.size, 1))
# set each chunk to appropriate level
f[:r[0]] *= levels[0] # set first chunk to appropriate level
for n in range(1, len(r) - 1):
f[r[n - 1]:r[n]] *= levels[n]
f[r[-1]:] *= levels[-1]
return f
def run(backend=SUPPORTED_BACKENDS[0], quiet=True):
num_rows = 10
rank = 3
matrix = np.random.normal(size=(num_rows, num_rows))
matrix = 0.5 * (matrix + matrix.T)
# Solve the problem with pymanopt.
manifold = Oblique(rank, num_rows)
cost, euclidean_gradient, euclidean_hessian = create_cost_and_derivates(
manifold, matrix, backend
)
problem = pymanopt.Problem(
manifold,
cost,
euclidean_gradient=euclidean_gradient,
euclidean_hessian=euclidean_hessian,
)
optimizer = TrustRegions(verbosity=2 * int(not quiet))
X = optimizer.run(problem).point
if quiet:
return
C = X.T @ X
print("Diagonal elements:", np.diag(C))
print("Eigenvalues:", np.sort(np.linalg.eig(C)[0].real)[::-1])
def train(self, subsample_idcs=None, ridge=1e-9, max_storage=1e8):
self.idcs = np.sort(subsample_idcs)
self.X_ind = self.X[self.idcs, :]
self.chunk_size = int(max_storage / float(self.idcs.shape[0]))
if self.chunk_size == 0:
self.chunk_size = 1
csz = self.chunk_size
#can handle len(idcs)**2 memory, len(idcs)**3 time cost
Kxx = self.k(self.X[self.idcs, :])
Ysum = np.zeros((self.idcs.shape[0], self.Y.shape[1]))
Ksum = np.zeros((self.idcs.shape[0], self.idcs.shape[0]))
pbar = ProgressBar('Chunk sum', 0, self.X.shape[0])
j = 0
csz = self.idcs.shape[0]
while j * csz < self.X.shape[0]:
pbar.update(j * csz)
Kchunk = self.k(self.X[j * csz:(j + 1) * csz, :],
self.X[self.idcs, :])
Ychunk = self.Y[j * csz:(j + 1) * csz, :]
Ysum += Kchunk.T.dot(Ychunk)
Ksum += Kchunk.T.dot(Kchunk)
j += 1
pbar.finish()
self.V = Ksum + self.lvar * Kxx
self.V += ridge * np.fabs(self.V).max() * np.eye(self.V.shape[0])
self.alpha = np.linalg.solve(self.V, Ysum)
self.V /= self.lvar
def generate_random_features_1d(data, num_feat):
'''
This functions generates random features for a set of paired inputs, such as times and observations
Inputs:
- data: (n x d) array
- num_feat: number of random features to be generated
Output:
- features in fixed dimensional space (n x num_feat) array
'''
# find length-scale for random features using median heuristic
if isinstance(data, list):
mean_obs = int(np.mean([len(row) for row in data]))
data_sig = np.array([
x[np.sort(np.random.choice(range(len(x)), mean_obs,
replace=False))] for x in data
if len(x) >= mean_obs
])
sig = meddistance(np.concatenate(data_sig)[:, np.newaxis],
subsample=1000)
else:
sig = meddistance(data, subsample=1000)
return np.array(
[f1(row[:, np.newaxis], rp(num_feat, sig, 1)) for row in data])
def specified_task(problem):
"""Given a problem, return parameters for running a topology optimization."""
fixdofs = np.flatnonzero(problem.normals.ravel())
alldofs = np.arange(2 * (problem.width + 1) * (problem.height + 1))
freedofs = np.sort(list(set(alldofs) - set(fixdofs)))
params = {
# material properties
'young': 1,
'young_min': 1e-9,
'poisson': 0.3,
'g': 0,
# constraints
'volfrac': problem.density,
'xmin': 0.001,
'xmax': 1.0,
# input parameters
'nelx': problem.width,
'nely': problem.height,
'mask': problem.mask,
'freedofs': freedofs,
'fixdofs': fixdofs,
'forces': problem.forces.ravel(),
'penal': 3.0,
'filter_width': 2,
}
return params
def summarize_res(sname, datasize):
print(sname)
res = []
times = []
for i in range(100):
PATH = ROOT_PATH + "/MMR_IVs/results/zoo/" + sname + "/"
filename = os.path.join(
PATH, str(date.today()),
'LMO_errs_{}_nystr_prodkern_{}.npy'.format(i, datasize))
if os.path.exists(filename):
tmp_res = np.load(filename, allow_pickle=True)
if tmp_res[-1] is not None:
res += [tmp_res[-1]]
time_path = os.path.join(
PATH, str(date.today()),
'/LMO_errs_{}_nystr_prodkern_{}_time.npy'.format(i, datasize))
if os.path.exists(time_path):
t = np.load(time_path)
times += [t]
res = np.array(res)
times = np.array(times)
res = remove_outliers(res)
times = np.sort(times)[:80]
print(times)
print('mean, std: ', np.mean(res), np.std(res))
print('time: ', np.mean(times), np.std(times))
def __init__(self,
breakpoints,
alpha=0.05,
penalizer=0.0,
fit_intercept=True,
*args,
**kwargs):
super(PiecewiseExponentialRegressionFitter, self).__init__(alpha=alpha)
breakpoints = np.sort(breakpoints)
if len(breakpoints) and not (breakpoints[-1] < np.inf):
raise ValueError("Do not add inf to the breakpoints.")
if len(breakpoints) and breakpoints[0] < 0:
raise ValueError("First breakpoint must be greater than 0.")
self.breakpoints = np.append(breakpoints, [np.inf])
self.n_breakpoints = len(self.breakpoints)
self._hazard = egrad(self._cumulative_hazard, argnum=1) # pylint: disable=unexpected-keyword-arg
self.penalizer = penalizer
self.fit_intercept = fit_intercept
self._fitted_parameter_names = [
"lambda_%d_" % i for i in range(self.n_breakpoints)
]
def interpolate(t, y, num_obs=50):
"""
Interpolates each trajectory such that observation times coincide for each one.
Note: initially cubic interpolation gave great power, but this happens as an artifact of the interpolation,
as both trajectories have the same number of observations. Type I error was increased as a result. To avoid
this we settled for a linear interpolation between observations.
Splines were also tried but gave very bad interpolations.
"""
t = np.array([np.sort(row) for row in t])
t = np.insert(t, 0, 0, axis=1)
t = np.insert(t, len(t[0]), 1, axis=1)
y = np.insert(y, 0, y[:, 0], axis=1)
y = np.insert(y, len(y[0]), y[:, -1], axis=1)
new_t = np.zeros(num_obs)
new_y = np.zeros(num_obs)
for i in range(len(t)):
f = interp1d(t[i], y[i], kind='linear')
#f = splrep(t[i], y[i])
t_temp = np.random.uniform(low=0.0, high=1.0,
size=num_obs) #np.linspace(0.1,0.9,num_obs)
y_temp = f(t_temp)
#y_temp = splev(t_temp, f, der=0)
new_y = np.vstack((new_y, y_temp))
new_t = np.vstack((new_t, t_temp))
return new_t[1:], new_y[1:]
def train(self, subsample_idcs=None, ridge=1e-9):
self.idcs = np.sort(subsample_idcs)
self.X_ind = self.X[self.idcs, :]
Kxx = self.k(self.X[self.idcs, :])
self.alpha = np.linalg.solve(
Kxx + self.lvar * np.eye(self.idcs.shape[0]), self.Y[self.idcs, :])
self.V = Kxx + self.lvar * np.eye(self.idcs.shape[0])
def permute(self, perm):
"""
Permute the discrete latent states.
"""
assert np.all(np.sort(perm) == np.arange(self.K))
self.init_state_distn.permute(perm)
self.transitions.permute(perm)
self.observations.permute(perm)
def _simplex_projection(x):
u = np.sort(x)[::-1]
idcs = np.arange(1, u.shape[0] + 1)
rho_nz = u + 1. / idcs * (1. - np.cumsum(u)) > 0
rho = idcs[rho_nz].max()
lmb = 1. / rho * (1. - u[:rho].sum())
out = np.maximum(x + lmb, 0.)
return out / out.sum()
def pretrain(self, subsample_idcs, ridge=1e-9):
self.sridcs = np.sort(subsample_idcs)
#get matrices necessary to compute khat(x,x') and muhat(x)
#using subset of regressors
srgp = SubsetRegressorsGP(self.X, self.Y, self.k, self.lvar)
srgp.train(self.sridcs, ridge)
self.pre_alpha = srgp.alpha
self.V = srgp.V
self.V += ridge * np.fabs(self.V).max() * np.eye(self.sridcs.shape[0])
def compute_khat_iterates(iterate_chains,
warmup=0.85,
param_idx=0,
increasing=True):
"""
Compute the khat over iterates for a variational parameter after removing warmup.
Parameters
----------
iterate_chains : multi-dimensional array, shape=(n_chains, n_iters, n_var_params)
warmup : warmup iterates
param_idx : index of the variational parameter
increasing : boolean sort array in increasing order: TRUE or decreasing order:FALSE
fraction: the fraction of iterates
Returns
-------
maximum of khat over all chains for the variational parameter param_idx
"""
chains = iterate_chains[:, :, param_idx]
n_iters = chains.shape[1]
n_chains = chains.shape[0]
k_hat_values = np.zeros(n_chains)
for i in range(n_chains):
if increasing:
sorted_chain = np.sort(chains[i, :])
else:
sorted_chain = np.sort(-chains[i, :])
ind_last = int(n_iters * warmup)
filtered_chain = sorted_chain[ind_last:]
if increasing:
filtered_chain = filtered_chain - np.min(filtered_chain)
else:
filtered_chain = filtered_chain - np.min(filtered_chain)
k_post, _ = gpdfit(filtered_chain)
k_hat_values[i] = k_post
return np.nanmax(k_hat_values)
def sample_inputs(type, ndata, range):
low, high = range
if type == 'gridbox':
x = np.linspace(low, high, ndata).reshape(ndata, 1)
elif type == "uniform":
x = np.random.uniform(low, high, size=(ndata, 1))
elif type == 'normal':
x = np.random.randn(ndata, 1)
return np.sort(x, axis=0)
def load_data(path='datasets/plays.tsv'):
raw_data = pd.read_table('datasets/plays.tsv')
raw_data = raw_data.drop(raw_data.columns[1], axis=1)
raw_data.columns = ['user', 'artist', 'plays']
data = raw_data.dropna().sample(frac=1)[:70]
data['user_id'] = data['user'].astype("category").cat.codes
data['artist_id'] = data['artist'].astype("category").cat.codes
data = data.drop(['user', 'artist'], axis=1)
data = data.loc[data.plays != 0]
users = list(np.sort(data.user_id.unique()))
artists = list(np.sort(data.artist_id.unique()))
plays = list(data.plays)
rows = data.user_id.astype(int)
cols = data.artist_id.astype(int)
return sparse.csr_matrix((plays, (rows, cols)),
shape=(len(users), len(artists)))
def generate_synthetic_data(self, theta, Ndata):
"""
Generate a synthetic dataset from parameters theta.
:param theta: ChangepointParams instance
:param Ndata: number of data points
:return: (x, y) pairs corresponding to synthetic dataset
"""
L = self.xmax - self.xmin
x = np.sort(self.xmin + L * np.random.uniform(size=(Ndata, )))
epsilon = np.random.normal(size=x.shape)
y = self.predict(theta, x) + theta.sig * epsilon
return x, y
def k_select(w_s, k, new_L, clustering_layer):
''' Automatic choice of the number of components by layer
w_s (list): The path probabilities for all s in [1,S]
k (dict): The number of component on each layer
new_L (int): The selected total number of layers.
clustering_layer (int): The index of the clustering layer
--------------------------------------------------------------------------
returns (dict): The components kept for all the layers of the network
'''
L = len(k)
n_clusters = k[clustering_layer]
# If the clustering layer (cl) is deleted, define the last existing layer as cl
last_layer_idx = new_L - 1
if last_layer_idx < clustering_layer:
clustering_layer = last_layer_idx
components_to_keep = []
w = w_s.reshape(*k, order='C')
for l in range(new_L):
PROBA_THRESHOLD = 1 / (k[l] * 4)
other_layers_indices = tuple(set(range(L)) - set([l]))
components_proba = w.sum(other_layers_indices)
#print(components_proba)
if l == clustering_layer:
biggest_lik_comp = np.sort(
components_proba.argsort()[::-1][:n_clusters])
components_to_keep.append(biggest_lik_comp)
else:
comp_kept = np.where(components_proba > PROBA_THRESHOLD)[0]
comp_kept = np.sort(comp_kept)
components_to_keep.append(comp_kept)
return components_to_keep
def _update_clipping_parameter(self, impt_smplg_weight):
""" Updates the clipping parameter for Bottou's heuristic
Args:
impt_smplg_weight (np.array): importance sampling weights
"""
if self.hyperparams['M'] == 'auto':
sorted_copy = np.sort(impt_smplg_weight.copy())
self.hyperparams['M'] = sorted_copy[-5]
elif self.hyperparams['M'] == 'None':
pass
else:
self.hyperparams['M'] = float(self.hyperparams['M'])
def init_multicomponent_source(sky_coord, frame, observation, bg_rms, flux_percentiles=None,
thresh=1., symmetric=True, monotonic=True):
"""Initialize multiple components
See `MultiComponentSource` for a description of the parameters
"""
if flux_percentiles is None:
flux_percentiles = [25]
# Initialize the first component as an extended source
sed, morph = init_extended_source(sky_coord, frame, observation, bg_rms,
thresh, symmetric, monotonic)
# create a list of components from base morph by layering them on top of
# each other so that they sum up to morph
K = len(flux_percentiles) + 1
Ny, Nx = morph.shape
morphs = np.zeros((K, Ny, Nx), dtype=morph.dtype)
morphs[0, :, :] = morph[:, :]
max_flux = morph.max()
percentiles_ = np.sort(flux_percentiles)
last_thresh = 0
for k in range(1, K):
perc = percentiles_[k - 1]
flux_thresh = perc * max_flux / 100
mask_ = morph > flux_thresh
morphs[k - 1][mask_] = flux_thresh - last_thresh
morphs[k][mask_] = morph[mask_] - flux_thresh
last_thresh = flux_thresh
# renormalize morphs: initially Smax
for k in range(K):
if np.all(morphs[k] <= 0):
msg = "Zero or negative morphology for component {} at y={}, x={}"
logger.warning(msg.format(k, *skycoords))
morphs[k] /= morphs[k].max()
# optimal SEDs given the morphologies, assuming img only has that source
seds = get_best_fit_seds(morphs, frame, observation)
for k in range(K):
if np.any(seds[k] <= 0):
# If the flux in all channels is <=0,
# the new sed will be filled with NaN values,
# which will cause the code to crash later
msg = "Zero or negative SED {} for component {} at y={}, x={}".format(seds[k], k, *sky_coord)
if np.all(sed <= 0):
logger.warning(msg)
else:
logger.info(msg)
return seds, morphs
def __init__(self, breakpoints, *args, **kwargs):
breakpoints = np.sort(breakpoints)
if not (breakpoints[-1] < np.inf):
raise ValueError("Do not add inf to the breakpoints.")
if breakpoints[0] < 0:
raise ValueError("First breakpoint must be greater than 0.")
self.breakpoints = np.append(breakpoints, [np.inf])
n_breakpoints = len(self.breakpoints)
self._fitted_parameter_names = ["lambda_%d_" % i for i in range(n_breakpoints)]
super(PiecewiseExponentialFitter, self).__init__(*args, **kwargs)
def plot_train_fits(W, axarr):
params = pred_fun(W, train_images)
means = params[:, :8]
variances = np.exp(params[:,-8:]) # axis aligned variances
# plot 5 random data points and 4 random marginals
idx = np.sort(np.random.permutation(train_images.shape[0])[:axarr.shape[0]])
dims = np.sort(np.random.permutation(samps.shape[-1])[:axarr.shape[1]])
for r, i in enumerate(idx):
for c, d in enumerate(dims):
axarr[r, c].cla()
n, bins, patches = axarr[r, c].hist(samps[i, :, d],
bins=20, normed=True)
axarr[r, c].plot( [means[i, d], means[i, d]], [0, n.max()] )
thgrid = np.linspace(min(bins[0], means[i,d]),
max(bins[-1], means[i,d]), 50)
axarr[r, c].plot(thgrid,
np.exp(gu.mog_logmarglike(thgrid,
means = np.array([ means[i] ]),
covs = np.array([ np.diag(variances[i]) ]),
pis = np.array([1.]),
ind = d)))
axarr[r, c].set_title("Idx = %d, dim = %d"%(i, d))
plt.draw()
def list_simulate_spectral(cov, J, n_simulate=1000, seed=82):
"""
Simulate the null distribution using the spectrums of the covariance
matrix. This is intended to be used to approximate the null
distribution.
Return (a numpy array of simulated n*FSSD values, eigenvalues of cov)
"""
# eigen decompose
eigs, _ = np.linalg.eig(cov)
eigs = np.real(eigs)
# sort in decreasing order
eigs = -np.sort(-eigs)
sim_fssds = FSSD.simulate_null_dist(eigs, J, n_simulate=n_simulate, seed=seed)
return sim_fssds, eigs
def __init__(self, breakpoints, alpha=0.05, penalizer=0.0):
super(PiecewiseExponentialRegressionFitter, self).__init__(alpha=alpha)
breakpoints = np.sort(breakpoints)
if len(breakpoints) and not (breakpoints[-1] < np.inf):
raise ValueError("Do not add inf to the breakpoints.")
if len(breakpoints) and breakpoints[0] < 0:
raise ValueError("First breakpoint must be greater than 0.")
self.breakpoints = np.append(breakpoints, [np.inf])
self.n_breakpoints = len(self.breakpoints)
self.penalizer = penalizer
self._fitted_parameter_names = ["lambda_%d_" % i for i in range(self.n_breakpoints)]
def generate_random_features(t, y, num_feat):
'''
This functions generates random features for a set of paired inputs, such as times and observations
Inputs:
- t: first dimension of data, (n x d) array
- y: second dimension of data, (n x d) array
- num_feat: number of random features to be generated
Output:
- features in fixed dimensional space (n x num_feat) array
'''
# if different sizes do interpolation and coerce to equal number of dimensions
if isinstance(t, list):
# find length-scale for random features using median heuristic
mean_obs = int(np.mean([len(row) for row in t]))
np.random.seed(0)
t_sig = np.array([
x[np.sort(np.random.choice(range(len(x)), mean_obs,
replace=False))] for x in t
if len(x) > mean_obs
])
y_sig = np.array([
x[np.sort(np.random.choice(range(len(x)), mean_obs,
replace=False))] for x in y
if len(x) > mean_obs
])
sig = meddistance(np.hstack((t_sig, y_sig)), subsample=1000)
np.random.seed()
else:
sig = meddistance(np.hstack((t, y)), subsample=1000)
return np.array([
f1(np.hstack((t[:, np.newaxis], y[:, np.newaxis])),
rp(num_feat, sig, 2)) for (t, y) in zip(t, y)
])
def init_multicomponent_source(sky_coord,
scene,
observations,
bg_rms,
flux_percentiles=None,
obs_idx=0,
thresh=1.,
symmetric=True,
monotonic=True):
"""Initialize multiple components
See `MultiComponentSource` for a description of the parameters
"""
try:
iter(observations)
except TypeError:
observations = [observations]
if flux_percentiles is None:
flux_percentiles = [25]
# Initialize the first component as an extended source
sed, morph = init_extended_source(sky_coord, scene, observations, bg_rms,
obs_idx, thresh, symmetric, monotonic)
# create a list of components from base morph by layering them on top of
# each other so that they sum up to morph
K = len(flux_percentiles) + 1
Ny, Nx = morph.shape
morphs = np.zeros((K, Ny, Nx), dtype=morph.dtype)
morphs[0, :, :] = morph[:, :]
max_flux = morph.max()
percentiles_ = np.sort(flux_percentiles)
last_thresh = 0
for k in range(1, K):
perc = percentiles_[k - 1]
flux_thresh = perc * max_flux / 100
mask_ = morph > flux_thresh
morphs[k - 1][mask_] = flux_thresh - last_thresh
morphs[k][mask_] = morph[mask_] - flux_thresh
last_thresh = flux_thresh
# renormalize morphs: initially Smax
for k in range(K):
morphs[k] /= morphs[k].max()
# optimal SEDs given the morphologies, assuming img only has that source
seds = get_best_fit_seds(morphs, scene, observations)
return seds, morphs
def projectSimplex(mat):
""" project each row vector to the simplex
"""
nPoints, nVars = mat.shape
mu = np.fliplr(np.sort(mat, axis=1))
sum_hist = np.cumsum(mu, axis=1)
flag = (mu - 1./np.tile(np.arange(1,nVars+1),(nPoints,1))*(sum_hist-1) > 0)
f_flag = lambda flagPoint: len(flagPoint) - 1 - \
flagPoint[::-1].argmax()
lastTrue = map(f_flag, flag)
sm_row = sum_hist[np.arange(nPoints), lastTrue]
theta = (sm_row - 1)*1./(np.array(lastTrue)+1.)
w = np.maximum(mat - np.tile(theta, (nVars,1)).T, 0.)
return w
def projectSimplex_vec(v):
""" project vector v onto the probability simplex
Parameter
---------
v: shape(nVars,)
input vector
Returns
-------
w: shape(nVars,)
projection of v onto the probability simplex
"""
nVars = v.shape[0]
mu = np.sort(v,kind='quicksort')[::-1]
sm_hist = np.cumsum(mu)
flag = (mu - 1./np.arange(1,nVars+1)*(sm_hist-1) > 0)
lastTrue = len(flag) - 1 - flag[::-1].argmax()
sm_row = sm_hist[lastTrue]
theta = 1./(lastTrue+1) * (sm_row - 1)
w = np.maximum(v-theta, 0.)
return w