def _calc_dist_2(words, w2v_model, distance_type, t):
l1_dist = 0
l2_dist = 0
cos_dist = 0
coord_dist = 0
t = float(t)
for word_id1 in range(len(words)):
for word_id2 in range(word_id1 + 1, len(words)):
# Calcular L1 w2v metric
l1_dist += (sci_dist.euclidean(w2v_model[words[word_id1]],
w2v_model[words[word_id2]]))
# Calcular L2 w2v metric
l2_dist += (sci_dist.sqeuclidean(w2v_model[words[word_id1]],
w2v_model[words[word_id2]]))
# Calcular cos w2v metric
cos_dist += (sci_dist.cosine(w2v_model[words[word_id1]],
w2v_model[words[word_id2]]))
# Calcular coordinate w2v metric
coord_dist += (sci_dist.sqeuclidean(
w2v_model[words[word_id1]], w2v_model[words[word_id2]]))
if distance_type == 'l1_dist':
return l1_dist / (t * (t - 1.0))
elif distance_type == 'l2_dist':
return l2_dist / (t * (t - 1.0))
elif distance_type == 'cos_dist':
return cos_dist / (t * (t - 1.0))
elif distance_type == 'coord_dist':
return coord_dist / (t * (t - 1.0))
return .0
def naive_set_right_view(comparable_views, current_view_list, key_list,
val_list, no_of_zoom, x, y):
if no_of_zoom == 1:
space = 1.0
elif no_of_zoom == 2:
space = 0.75
else:
space = 0.5
diff2 = 0
diff_1_2 = 0
heap = []
three_best_diff2 = [0 for i in range(10)]
view_list = [0 for i in range(10)]
space = 0
for view, scags in comparable_views.items():
window = view.split("; ")
window_x = ast.literal_eval(window[0])
window_y = ast.literal_eval(window[1])
if ((((left_view_x[0] - space) <= window_x[0] <=
(left_view_x[1] + space)) and
((left_view_x[0] - space) <= window_x[1] <=
(left_view_x[1] + space)))) or (((x[0] - space) <= window_x[0] <=
(x[1] + space)) and
((x[0] - space) <= window_x[1] <=
(x[1] + space))):
continue
view_diff = distance.sqeuclidean(np.asarray(scags),
np.asarray(current_view_list))
for ele in heap:
if (ele - 0.05) <= view_diff <= (ele + 0.05):
continue
if len(heap) < 10:
heappush(heap, view_diff)
else:
heappushpop(heap, view_diff)
if view_diff in heap:
three_best_diff2[heap.index(view_diff)] = scags
view_list[heap.index(view_diff)] = view
for ele in three_best_diff2:
if ele == 0:
continue
if distance.euclidean(np.asarray(ele),
np.asarray(diff1_scags)) > diff_1_2:
diff_1_2 = distance.sqeuclidean(np.asarray(ele),
np.asarray(diff1_scags))
diff2 = ele
view = key_list[val_list.index(diff2)]
right = view.split("; ")
right_view_x = ast.literal_eval(right[0])
right_view_y = ast.literal_eval(right[1])
def calcDisPosMin2(puntoEnX, centroides, data):
min = 0.0
aux = 0.0
pos = 0
min = distance.sqeuclidean(puntoEnX, centroides[0])
if len(centroides) > 1:
tam = len(centroides)
for i in range(1, tam):
aux = distance.sqeuclidean(puntoEnX, centroides[i])
if aux < min:
min = aux
pos = i
return min, pos
def topic_w2v(topic_words, word_embedding):
"""Word Embedding topic quality metric for a topic.
Calculates the Cosine Distance, L1 Distance, L2 Distance and Coordinate Distance topic quality metrics
for one individual topic based on the topic words.
Args:
topic_words: list
Words that compose one individual topic.
word_embedding: gensim.KeyedVectors
Mapping between words and vectors for the Word2Vec model. Generate with Gensim.
Returns:
cosine_distance: float
Resultant Cosine Distance for the topic.
l1_distance: float
Resultant L1 Distance metric for the topic.
l2_distance: float
Resultant L2 Distance metric for the topic.
coordinate_distance: float
Resultant Coordinate Distance metric for the topic.
"""
cosine_distance = 0.0
l1_distance = 0.0
l2_distance = 0.0
coordinate_distance = 0.0
n_top = len(topic_words)
t = float(n_top)
t = t * (t - 1.0)
for word_i_idx in range(n_top):
for word_j_idx in range(word_i_idx + 1, n_top):
try:
word_i = word_embedding[topic_words[word_i_idx]]
word_j = word_embedding[topic_words[word_j_idx]]
except KeyError:
continue
cosine_distance += (sci_dist.cosine(word_i, word_j))
l1_distance += (sci_dist.euclidean(word_i, word_j))
l2_distance += (sci_dist.sqeuclidean(word_i, word_j))
coordinate_distance += (sci_dist.sqeuclidean(word_i, word_j))
cosine_distance = cosine_distance / t
l1_distance = l1_distance / t
l2_distance = l2_distance / t
coordinate_distance = coordinate_distance / t
return cosine_distance, l1_distance, l2_distance, coordinate_distance
def getSigmaDerivKernelMat(self, FMat1, FMat2):
"""
Returns the derivative of the kernel matrix w.r.t. sigma where (kernelMat)_ij = kernel(FMat1[i],FMat2[j])
"""
kernelMat = self.getKernelMat(FMat1, FMat2)
distmat = np.array([[sqeuclidean(f1, f2) for f1 in FMat1]
for f2 in FMat2])
SDKernelMat = np.array([[
1 / self.sigma**3 * sqeuclidean(f1, f2) *
self.single_comparison(f1, f2, self.sigma)
for i, f1 in enumerate(FMat1)
] for f2 in FMat2])
# return 1/self.sigma**3 * distmat * kernelMat
return SDKernelMat
def getLshNN_op1(dataset, nnModel, thred_radius_dist, trained_num_probes,
thred_sameTweetDist):
ngIdxList = []
indexedInCluster = {}
clusters = []
for dataidx in range(dataset.shape[0]):
if dataidx in indexedInCluster:
nn_keys = None
else:
clusterIdx = len(clusters)
indexedInCluster[dataidx] = clusterIdx
clusters.append([dataidx])
nnModel.set_num_probes(trained_num_probes)
# nn_keys: (id1, id2, ...)
nn_keys = nnModel.find_near_neighbors(dataset[dataidx, :],
thred_radius_dist)
nn_dists = [(idx, key) for idx, key in enumerate(nn_keys)
if key > dataidx - 130000 and key < dataidx +
130000 and sqeuclidean(dataset[dataidx, :], dataset[
key, :]) < thred_sameTweetDist]
#nn_dists = [(idx, key) for idx, key in enumerate(nn_keys) if sqeuclidean(dataset[dataidx,:], dataset[key,:]) < 0.2]
#print len(nn_keys), len(nn_dists), nn_dists[:min(10, len(nn_dists))], nn_dists[-min(10, len(nn_dists)):]
for idx, key in nn_dists:
indexedInCluster[key] = clusterIdx
ngIdxList.append(nn_keys)
if (dataidx + 1) % 10000 == 0:
print "## completed", dataidx + 1, len(clusters), time.asctime()
ngIdxList = np.asarray(ngIdxList)
return ngIdxList, indexedInCluster, clusters
def Dist(array1, array2, dist):
if dist == 'braycurtis':
return distance.braycurtis(array1, array2)
elif dist == 'correlation':
return distance.correlation(array1, array2)
elif dist == 'mahalanobis':
return distance.mahalanobis(array1, array2)
elif dist == 'minkowski':
return distance.minkowski(array1, array2)
elif dist == 'seuclidean':
return distance.seuclidean(array1, array2)
elif dist == 'sqeuclidean':
return distance.sqeuclidean(array1, array2)
elif dist == 'pearsonp':
r, p = pearsonr(array1, array2)
return p
elif dist == 'pearsonr':
r, p = pearsonr(array1, array2)
return r
elif dist == 'spearmanp':
r, p = spearmanr(array1, array2)
return p
elif dist == 'spearmanr':
r, p = spearmanr(array1, array2)
return r
def random_walk_matrix(matrix, startVector, R, maxIterations, normThreshold):
"""
Runs Random Walk with Restart using a matrix implementation
@param matrix: numpy array, normalized adjancency matrix of entire PPI network
@param startVector: numpy array, contains weighted start probabilities
@param R: float, probability of restart parameter
@param maxInterations: integer, maximum number of iterations to run
@param normThreshold: integer, threshold at which the algorithm stops running if the difference between two steps is less than it
@returns numpy array, final vector containing ranked proteins
"""
print("STARTING RANDOM WALK")
previousVector = np.copy(startVector)
iterations = 0
diff = float('inf')
while diff > normThreshold and iterations < maxIterations:
print("iteration:", iterations)
# Perform one step of the walk
newVector = (1 - R) * np.matmul(matrix, previousVector)
newVector = np.add(newVector, R * startVector)
diff = distance.sqeuclidean(newVector, previousVector)
previousVector = newVector
iterations += 1
return newVector
def rbfKernel_Inst(x1, x2, gamma):
"""
The rbf kernel between two instances
"""
norm = sqeuclidean(x1, x2) # returns the squared euclidean norm
k = np.exp(-gamma * norm)
return k
def recommend(time, user_features, choices):
global recommended, last_user_features, hits, articles_all
last_user_features = user_features
# scaler = StandardScaler()
# Exploit
if hits > 0: # and np.random.uniform() > 1/t:
# Predict article features for user features
features = []
for i in range(6):
# uf = scaler.fit_transform([user_features])
pred = models[i].predict([user_features])
features.append(pred[0])
# Get nearest choice and recommend it
dist = 1e99
for choice in choices:
d = sqeuclidean(features, articles_all[choice])
if d < dist:
dist = d
recommended = choice
# Explore
if recommended is None:
recommended = np.random.choice(choices)
# Always needs to return an article
return recommended
def distance(S,T):
"""
Calculates the Euclidean distance between two sequences of varying
lengths, using early abandon if possible.
"""
n, m = len(S), len(T)
if n > m:
n,m = m,n
S,T = T,S
min_distance = np.inf
for i in range(0, m - n + 1):
stop = False
sum_distance = 0.0
for j,x in enumerate(S):
y = T[i+j]
sum_distance += sqeuclidean(x, y)
# Abandon calculations as soon as the best distance (so far) has
# been surpassed---adding more values will only increase it.
if sum_distance >= min_distance:
stop = True
break
if not stop:
min_distance = sum_distance
return min_distance
def euclidian_distance(dataset, sim_dataset):
sq_error = 0
from scipy.spatial.distance import sqeuclidean
for i in range(dataset.shape[1]):
sq_error += sqeuclidean(sim_dataset[:, i], dataset[:, i])
return sq_error
def rrt(self, max_iterations=1000000):
def pick_random_state():
x = random.uniform(-1.2, 0.6)
y = random.uniform(-0.07, 0.076)
return (x, y)
self.snapshot_buffer = []
observation = self.envs[0].reset()
self.state_buffer = [observation]
for iteration in range(max_iterations):
rand_state = pick_random_state()
closest_state = min(
self.state_buffer,
key=lambda i: distance.sqeuclidean(i, rand_state))
self.envs[0].unwrapped.state = closest_state
random_action = self.envs[0].action_space.sample()
print(iteration)
for _ in range(1):
observation, reward, done, info = self.envs[0].step(
random_action)
if observation[0] > 0.5:
print("DAMN!")
exit()
# self.envs[0].unwrapped.render()
self.state_buffer.append(observation)
if done:
observation = self.envs[0].reset()
def compute_distance(query_channel, channel, mean_vec, distance_type='eucos'):
""" Compute the specified distance type between chanels of mean vector and query image.
In caffe library, FC8 layer consists of 10 channels. Here, we compute distance
of distance of each channel (from query image) with respective channel of
Mean Activation Vector. In the paper, we considered a hybrid distance eucos which
combines euclidean and cosine distance for bouding open space. Alternatively,
other distances such as euclidean or cosine can also be used.
Input:
--------
query_channel: Particular FC8 channel of query image
channel: channel number under consideration
mean_vec: mean activation vector
Output:
--------
query_distance : Distance between respective channels
"""
if distance_type == 'eucos':
query_distance = spd.euclidean(mean_vec[channel, :],
query_channel) / 200. + spd.cosine(
mean_vec[channel, :], query_channel)
elif distance_type == 'euclidean':
query_distance = spd.euclidean(mean_vec[channel, :],
query_channel) / 200.
elif distance_type == 'cosine':
query_distance = spd.cosine(mean_vec[channel, :], query_channel)
elif distance_type == DistanceType.squeuclidean():
query_distance = spd.sqeuclidean(mean_vec[channel, :], query_channel)
else:
print(
"distance type not known: enter either of eucos, euclidean or cosine"
)
return query_distance
def distance_between_rows(X):
"""Compute euclidean distance between rows of data matrix.
Parameters
----------
X : array_like or ndarray.
Input data.
Returns
-------
dist : ndarray (2D).
Simmetric matrix of computed distance between rows.
Examples
--------
>>> x = np.array(([2, 4, 3], [1, 5, 7], [8, 6, 9])).T
>>> distance_between_rows(x)
[[ 0. 4.89897949 6.164414 ]
[ 4.89897949 0. 3.74165739]
[ 6.164414 3.74165739 0. ]]
"""
X = check_array(X)
dist = np.zeros((X.shape[0], X.shape[0]))
for i in range(X.shape[0] - 1):
for j in range(i + 1, X.shape[0]):
dist[i, j] = dist[j, i] = np.sqrt(sqeuclidean(X[i], X[j]))
return dist
def getDistMat(self, FMat1, FMat2):
"""
"""
distmat = np.array([[sqeuclidean(f1, f2) for f1 in FMat1]
for f2 in FMat2])
return distmat
def c_kmeanspp(self):
start=time.time()
centroides=np.zeros((self.k,self.X[0].shape[0]))
ri=np.random.randint(0, high=self.X.shape[0])
centroides[0] = self.X[ri]
distancias_cuadradas=np.zeros((self.X.shape[0],1))
current=1
for i in range(1,self.k):
for j in range(self.X.shape[0]):
templ=[]
for l in range(current):
templ.append(distance.sqeuclidean(self.X[j],centroides[l]))
distancias_cuadradas[j]=np.min(templ)
total=np.sum(distancias_cuadradas)
distancias_cuadradas=distancias_cuadradas/total
distancias_cuadradas=np.cumsum(distancias_cuadradas)
ran=np.random.rand()
for m in range(distancias_cuadradas.shape[0]):
if ran<distancias_cuadradas[m]:
centroides[i]=self.X[m]
current+=1
break
end=time.time()
#print("inicializacion kmeans++ en :",(end-start)," s")
return centroides
def match_person(path, person, threshold=0.0):
"""
Finds the match for the person among people in the DB
:param df:
:param person:
:param threshold: maximum distance for which person if matched. if Min distance > threshold, None is returned
:return: name of the match or None
"""
df = pd.read_csv(path)
df.set_index(['Unnamed: 0'], inplace=True)
if 'Unnamed: 0.1' in df.columns:
del df['Unnamed: 0.1']
person = person.set_index([ID])
distances = {}
if df.empty:
return None, None
for row in df.iterrows():
name, value = row
distances[name] = sqeuclidean(person, value)
best = sorted(distances, key=distances.get)[0]
if distances[best] < threshold:
return None, None
diff = abs(person - value)
feature = diff.idxmin(axis=1)[0]
return best, feature
def get_belief_given_observation(image_path, encoder, aspect_nodes_path):
belief_time = time.time()
aspect_nodes = np.load(aspect_nodes_path)['aspect_nodes']
num_aspect_nodes = len(aspect_nodes)
image = Image.open(image_path)
image = image_to_tensor(image)
image_tensor = to_var(image)
encoder_feat = encoder(image_tensor).view(-1).data.numpy()
belief_inverse_dist = np.zeros(num_aspect_nodes)
belief_negative_dist = np.zeros(num_aspect_nodes)
belief_squared_dist = np.zeros(num_aspect_nodes)
for i, aspect_node in enumerate(aspect_nodes):
belief_inverse_dist[i] = 1./(1e-8 + distance.euclidean(encoder_feat, aspect_node))
belief_negative_dist[i] = -distance.euclidean(encoder_feat, aspect_node)
belief_squared_dist[i] = 1./(1e-8 + distance.sqeuclidean(encoder_feat, aspect_node))
belief_inverse_dist /= belief_inverse_dist.sum()
belief_squared_dist /= belief_squared_dist.sum()
belief_negative_dist -= (belief_negative_dist.min() + belief_negative_dist.max())
belief_negative_dist /= belief_negative_dist.sum()
print('getting belief took %.2f secs'%(time.time()-belief_time))
return belief_inverse_dist, belief_squared_dist, belief_negative_dist
def intersects(self, src, dest=None):
'''
It dest is None then it returns true if src is inside the region,
otherwise it returns true if the line segment intersects the region.
.. math ::
w = x_{center} - x_0
u = (x_1 - x_0)/norm(x_1 - x_0)
d = norm(w - (w \cdot u) u)
return \ d <= radius
'''
if isinstance(src, Point):
src = src.coords
if dest:
if isinstance(dest, Point):
dest = dest.coords
w = self.center - src
u = (dest - src)
lambd = dot(w, u) / sqeuclidean(u, 0)
lambd = min(max(lambd, 0), 1)
dist = euclidean(w - lambd * u, 0)
return dist <= self.radius
return euclidean(self.center, src) <= self.radius
def _transformcellrbf(packet):
group_df = packet[0]
minpipeend = packet[1]
samplevec_list = packet[2]
radius_list = packet[3]
learconst_list = packet[4]
irr_list = packet[5]
paramlist = packet[6]
plotpipe = packet[7]
shouldplot = packet[8]
selfpid = os.getpid()
gamma = 1/len(paramlist)
for irr in irr_list:
samplevec = samplevec_list[irr]
try:
#find min section
func = lambda row: abs(1 - np.exp(gamma *sqeuclidean(row.as_matrix(columns=paramlist), samplevec)**2))
rbf_df = group_df.apply(func, axis=1)
mindiff = rbf_df.min(skipna=True)
minindex = rbf_df.argmin(skipna=True)
minposition = group_df.loc[minindex, ['x_position', 'y_position']].as_matrix()
except Exception, msg:
print 'Msg: ', msg
print 'samplevec', samplevec
print 'irr: ', irr
print 'rfb_df: ', rbf_df
print 'mindiff', mindiff
print 'argmin: ', rbf_df.argmin(skipna=True)
#giveresult to main process adn wait respond
minpipeend.send({'job': 'min', 'mindiff': mindiff, 'position': minposition, 'pid': selfpid})
if minpipeend.poll(600):
letter = minpipeend.recv()
#perturb the cellmap
minposition, minpid = letter
if minpid == selfpid:
group_df.loc[minindex, 'pick_count'] += 1
output_df = pnd.DataFrame(columns=paramlist)
for index in group_df.index.values:
distance = np.linalg.norm(group_df.loc[index, ['x_position', 'y_position']].as_matrix() - minposition)
if distance < radius_list[irr]:
smoothkernel = (radius_list[irr]-distance)/radius_list[irr]
cellvec = group_df.loc[index].as_matrix(columns=paramlist)
learnconstant = learconst_list[irr]
#SOM Equation here
output = cellvec + learnconstant * smoothkernel * (samplevec - cellvec)
output_df.loc[index] = output
for index in output_df.index.values:
group_df.loc[index, paramlist] = output_df.loc[index, paramlist]
#sending group_df back to main to be plotted
if shouldplot:
plotpipe.send({'job' :'plot', 'groupdf': group_df, 'pid':selfpid})
def euclidean(self, x, y):
"""
:param x: is the 1D detector or training/test array (i.e normal python array) to be compared to y
:param y: is the 1D training/test or detector array (i.e normal python array) to be compared to x
:return:
"""
output = math.sqrt(dist.sqeuclidean(x, y))
return output
def weight(self, angOrg, angTarg, pOrg, pTarg, b):
#pOrg.append(angOrg)
#pTarg.append(angTarg)
dist = distance.sqeuclidean(pOrg, pTarg)
return (1 / (2 * b)) * np.exp(-1 * (dist / b))
def _signals_distance(real_signal, model_signal):
"""
Computes distance as 1 - R_squared statistic
"""
residuals = distance.sqeuclidean(real_signal, model_signal)
mean = float(sum(real_signal)) / len(real_signal)
variance = sum((x - mean) ** 2 for x in real_signal)
return residuals / variance
def squared_exp_cov(x_p, x_q):
"""Calculates the squared exponential covariance function between the
outputs f(x_p) and f(x_q) given the input vectors x_p and x_q, as per Eq. 2.16 of
R&W.
NOTE: In contrast to sqeuclidean used below, the sq_dist function from the
code accompanying the book calculates ALL pairwise distances between column
vectors of two matrices."""
return np.exp(-0.5 * sqeuclidean(x_p, x_q))
def rgb(self, value=PAD()):
"""
RGB values for discrete features
:param value: mood value wrapped in a PAD object
:return: numpy array containing r, g and b values between 0 and 1
"""
similarities = np.array([1-sqeuclidean(f, value.state) for f in self.f_vec])
strongest = min(enumerate(1-similarities/np.linalg.norm(similarities, 1)), key=itemgetter(1))
return self.rgb_vec[strongest[0]]
def euclidean(self, x, y):
"""
:param x: is the 1D detector or training/test array (i.e normal python array) to be compared to y
:param y: is the 1D training/test or detector array (i.e normal python array) to be compared to x
:return:
"""
print "getting euclidean distance between {0} and {1}".format(x, y)
output = math.sqrt(dist.sqeuclidean(x, y))
return output
def rgb_alt(self, value=PAD()):
"""
Averaged RGB values between all measured features
:param value: mood value wrapped in a PAD object
:return: numpy array containing r, g and b values between 0 and 1
"""
similarities = np.array([1-sqeuclidean(f, value.state) for f in self.f_vec])
weights = 1-similarities/np.linalg.norm(similarities, 1)
return np.average(self.rgb_vec, axis=0, weights=weights)
def squared_exp_cov(x_p, x_q):
"""Calculates the squared exponential covariance function between the
outputs f(x_p) and f(x_q) given the input vectors x_p and x_q, as per Eq. 2.16 of
R&W.
NOTE: In contrast to sqeuclidean used below, the sq_dist function from the
code accompanying the book calculates ALL pairwise distances between column
vectors of two matrices."""
return np.exp(-0.5 * sqeuclidean(x_p, x_q))
def riot(M, num_anchor=30, num_random=1000):
"""
check out IEEE CLOUD18 paper
:param M:
:param num_anchor:
:param num_random:
:return:
"""
logging.debug("Working on model " + M.name + " @ div_conv.py::riot")
anchors = M.init_random_pop(num_anchor)
# add some diagonals also
d = M.decNum
for i in range(d):
diag = M.init_random_pop(1, default_value=i / (d - 1))
anchors = pd.merge(anchors, diag, how='outer')
M.eval_pd_df(anchors)
logging.debug("Evaluating %d anchors done" % anchors.shape[0])
randoms = M.init_random_pop(num_random)
DIST_MTX = pd.DataFrame(index=anchors.index, columns=randoms.index)
for a in anchors.index:
for r in randoms.index:
DIST_MTX.loc[a, r] = distance.sqeuclidean(randoms.loc[r, M.decs],
anchors.loc[a, M.decs])
logging.debug("Distance in configuration spaces calc done.")
# guessing the objectives. see JC oral slides final.pdf P44 at jianfeng.us
for r in randoms.index:
n, f = np.argmin(DIST_MTX[r].tolist()), np.argmax(DIST_MTX[r].tolist())
nf = (anchors.loc[n] - anchors.loc[f])[M.decs].values
nr = (anchors.loc[n] - randoms.loc[r])[M.decs].values
rf = (randoms.loc[r] - anchors.loc[f])[M.decs].values
pQ = np.dot(nf, nr) / np.dot(nf, rf)
randoms.loc[r, M.objs] = anchors.loc[n, M.objs] + (pQ / (pQ + 1)) * (
anchors.loc[f, M.objs] - anchors.loc[n, M.objs])
# Hypothesis showing
# randoms_cp = randoms.copy(deep=True)
# randoms_cp[M.objs] = -1
# M.eval_pd_df(randoms_cp)
# logging.debug('The avg absolute guessing error is:')
# error = np.average(np.abs(randoms[M.objs] - randoms_cp[M.objs]), axis=0)
# logging.debug(error)
# collecting and returning
all_configs = pd.merge(anchors, randoms, how='outer')
cleared, dominated = cull(all_configs[M.objs])
res = all_configs.loc[cleared]
M.eval_pd_df(res, force_eval_all=True)
cleared, dominated = cull(res)
return res.loc[cleared]
def f(x_t_p, x_t, sigma):
diff = np.abs(np.subtract(x_t_p, x_t))
if (diff >= sigma * 2).any():
return 0.
if f_cache[diff[0], diff[1]] != -1:
return f_cache[diff[0], diff[1]]
else:
distance = (1/(2*np.pi*(sigma ** 2))) * np.exp((-sd.sqeuclidean(x_t_p, x_t))/(2 * (sigma ** 2)))
f_cache[diff[0], diff[1]] = distance
return distance
def label_im(im):
"""Assigns each pixel to a region label."""
nrow = im.shape[0]
ncol = im.shape[1]
lab = np.empty([nrow, ncol], dtype=int)
for irow in range(0, nrow):
for icol in range(0, ncol):
elem = im[irow, icol, :]
min_dist2 = distance.sqeuclidean(elem, RGB_LST[0])
min_ix = 0
for imin in range(1, len(RGB_LST)):
dist2 = distance.sqeuclidean(elem, RGB_LST[imin])
if (dist2 < min_dist2):
min_dist2 = dist2
min_ix = imin
lab[irow, icol] = RGB_LAB[min_ix]
return lab
def _holt__(x, xi, p, y, l, b, s, m, n, max_seen):
"""
Simple Exponential Smoothing
Minimization Function
(,)
"""
alpha, beta, phi, alphac, betac, y_alpha = _holt_init(x, xi, p, y, l, b)
for i in range(1, n):
l[i] = (y_alpha[i - 1]) + (alphac * (l[i - 1]))
return sqeuclidean(l, y)
def getSigmaDerivSigmaVecKernelMat(self, FMat1, FMat2, sigmaVec):
"""
Returns the derivative of the kernel matrix w.r.t. sigma.
"""
SDSVkernelMat = np.array([[
1 / (sigmaVec[i]**3) * sqeuclidean(f1, f2) *
self.single_comparison(f1, f2, sigmaVec[i])
for i, f1 in enumerate(FMat1)
] for f2 in FMat2])
return SDSVkernelMat
def cls_ctd(point, ctd):
min_distance = float('inf')
belongs_to_cluster = None
for j, centroid in enumerate(ctd):
dist = distance.sqeuclidean(point, centroid)
if dist < min_distance:
min_distance = dist
belongs_to_cluster = j
return belongs_to_cluster
def closest_centroid(point, centroids):
min_distance = float('inf')
belongs_to_cluster = None
for j, centroid in enumerate(centroids):
dist = distance.sqeuclidean(point, centroid)
if dist < min_distance:
min_distance = dist
belongs_to_cluster = j
return belongs_to_cluster
def _holt__(x, xi, p, y, l, b, s, m, n, max_seen):
"""
Simple Exponential Smoothing
Minimization Function
(,)
"""
alpha, beta, phi, alphac, betac, y_alpha = _holt_init(x, xi, p, y, l, b)
for i in range(1, n):
l[i] = (y_alpha[i - 1]) + (alphac * (l[i - 1]))
return sqeuclidean(l, y)
def closest_centroid(point, centroids, k):
min_distance = float('inf')
belongs_to_cluster = None
for i in range(k):
dist = distance.sqeuclidean(point, centroids[i])
if dist < min_distance:
min_distance = dist
belongs_to_cluster = i
return belongs_to_cluster
def multiquadric(x, y, c=0):
"""Compute a multiquadric kernel.
The Multiquadric kernel can be used in the same situations as the Rational
Quadratic kernel. As is the case with the Sigmoid kernel, it is also an
example of an non-positive definite kernel:
K(x, y) = sqrt(||x - y||^2 + c^2)
where `x` and `y` are vectors in the input space (i.e., vectors of
features computed from training or test samples), ||x - y||^2 is the
squared Euclidean norm, and `c` ≥ 0 is a free parameter (default=0).
"""
return sqrt(dist.sqeuclidean(x, y) + c**2)
def get_pert_sigma(prev_population, sim_theta):
M = (int) (len(prev_population) * 0.2)
from scipy.spatial.distance import sqeuclidean
distances = []
for p in prev_population:
distances.append(sqeuclidean(p, sim_theta))
nearest = []
indices = [i[0] for i in sorted(enumerate(distances), key=lambda x:x[1])]
for index in indices[:M]:
nearest.append(prev_population[index])
return np.cov(np.vstack(nearest).T)
def rational_quadratic(x, y, c=0):
"""Compute a rational quadratic kernel.
The Rational Quadratic kernel is less computationally intensive than the
Gaussian kernel and can be used as an alternative when using the Gaussian
becomes too expensive:
K(x, y) = 1 - (||x - y||^2 / (||x - y||^2 + c))
where `x` and `y` are vectors in the input space (i.e., vectors of
features computed from training or test samples), ||x - y||^2 is the
squared Euclidean norm, and `c` ≥ 0 is a free parameter (default=0).
"""
d = dist.sqeuclidean(x, y)
return 1 - d / (d + c)
def cal_matrix_euc(list_word, dict_word_vec):
"""
sqe_euclid類似度で単語間の距離を計算
list_word: 単語のリスト
dict_word_vec: 単語がkey, 分散表現がvalueのdict
return: cos_matrix: 各単語間の類似度を計算したmatrix
"""
euc_matrix = np.zeros((len(list_word), len(list_word)))
for i, word1 in enumerate(list_word):
for j, word2 in enumerate(list_word):
euc_matrix[i][j] = sqeuclidean(dict_word_vec[word1], dict_word_vec[word2])
return euc_matrix
def _holt_add_dam(x, xi, p, y, l, b, s, m, n, max_seen):
"""
Additive and Additive Damped
Minimization Function
(A,) & (Ad,)
"""
alpha, beta, phi, alphac, betac, y_alpha = _holt_init(x, xi, p, y, l, b)
if alpha == 0.0:
return max_seen
if beta > alpha:
return max_seen
for i in range(1, n):
l[i] = (y_alpha[i - 1]) + (alphac * (l[i - 1] + phi * b[i - 1]))
b[i] = (beta * (l[i] - l[i - 1])) + (betac * phi * b[i - 1])
return sqeuclidean(l + phi * b, y)
def _holt_mul_dam(x, xi, p, y, l, b, s, m, n, max_seen):
"""
Multiplicative and Multiplicative Damped
Minimization Function
(M,) & (Md,)
"""
alpha, beta, phi, alphac, betac, y_alpha = _holt_init(x, xi, p, y, l, b)
if alpha == 0.0:
return max_seen
if beta > alpha:
return max_seen
for i in range(1, n):
l[i] = (y_alpha[i - 1]) + (alphac * (l[i - 1] * b[i - 1]**phi))
b[i] = (beta * (l[i] / l[i - 1])) + (betac * b[i - 1]**phi)
return sqeuclidean(l * b**phi, y)
def _holt_win__add(x, xi, p, y, l, b, s, m, n, max_seen):
"""
Additive Seasonal
Minimization Function
(,A)
"""
alpha, beta, gamma, phi, alphac, betac, gammac, y_alpha, y_gamma = _holt_win_init(
x, xi, p, y, l, b, s, m)
if alpha == 0.0:
return max_seen
if gamma > 1 - alpha:
return max_seen
for i in range(1, n):
l[i] = (y_alpha[i - 1]) - (alpha * s[i - 1]) + (alphac * (l[i - 1]))
s[i + m - 1] = y_gamma[i - 1] - (gamma * (l[i - 1])) + (gammac * s[i - 1])
return sqeuclidean(l + s[:-(m - 1)], y)
def gaussian(x, y, sigma=1):
"""Compute a Gaussian kernel.
The Gaussian kernel is an example of radial basis function kernel. It can
be define as:
K(x, y) = exp(-||x - y||^2 / 2σ^2)
where `x` and `y` are vectors in the input space (i.e., vectors of
features computed from training or test samples), ``||x - y||^2` is the
squared Euclidean norm, and the adjustable parameter `sigma`
plays a major role in the performance of the kernel, and should be
carefully tuned to the problem at hand. If overestimated, the exponential
will behave almost linearly and the higher-dimensional projection will
start to lose its non-linear power. In the other hand, if underestimated,
the function will lack regularization and the decision boundary will be
highly sensitive to noise in training data.
"""
return exp(-(dist.sqeuclidean(x, y)/2*sigma**2))
def _holt_win_add_add_dam(x, xi, p, y, l, b, s, m, n, max_seen):
"""
Additive and Additive Damped with Additive Seasonal
Minimization Function
(A,A) & (Ad,A)
"""
alpha, beta, gamma, phi, alphac, betac, gammac, y_alpha, y_gamma = _holt_win_init(
x, xi, p, y, l, b, s, m)
if alpha * beta == 0.0:
return max_seen
if beta > alpha or gamma > 1 - alpha:
return max_seen
for i in range(1, n):
l[i] = (y_alpha[i - 1]) - (alpha * s[i - 1]) + \
(alphac * (l[i - 1] + phi * b[i - 1]))
b[i] = (beta * (l[i] - l[i - 1])) + (betac * phi * b[i - 1])
s[i + m - 1] = y_gamma[i - 1] - (gamma * (l[i - 1] + phi * b[i - 1])) + (gammac * s[i - 1])
return sqeuclidean((l + phi * b) + s[:-(m - 1)], y)
def _holt_win_mul_mul_dam(x, xi, p, y, l, b, s, m, n, max_seen):
"""
Multiplicative and Multiplicative Damped with Multiplicative Seasonal
Minimization Function
(M,M) & (Md,M)
"""
alpha, beta, gamma, phi, alphac, betac, gammac, y_alpha, y_gamma = _holt_win_init(
x, xi, p, y, l, b, s, m)
if alpha * beta == 0.0:
return max_seen
if beta > alpha or gamma > 1 - alpha:
return max_seen
for i in range(1, n):
l[i] = (y_alpha[i - 1] / s[i - 1]) + \
(alphac * (l[i - 1] * b[i - 1]**phi))
b[i] = (beta * (l[i] / l[i - 1])) + (betac * b[i - 1]**phi)
s[i + m - 1] = (y_gamma[i - 1] / (l[i - 1] *
b[i - 1]**phi)) + (gammac * s[i - 1])
return sqeuclidean((l * b**phi) * s[:-(m - 1)], y)
def _maptosmllestrbf(jobpacket):
cellmap_df = jobpacket[0]
paramlist = jobpacket[1]
mainsource_df = jobpacket[2]
gamma = 1/len(paramlist)
defvec = array([1.0 for i in xrange(len(paramlist))])
resultlist = []
for sourceindex in mainsource_df.index.values:
sourceid = mainsource_df.ix[sourceindex]['id']
sourcelabel = mainsource_df.ix[sourceindex]['label']
sourcevec = mainsource_df.ix[sourceindex].as_matrix(columns=paramlist)
func =lambda row: abs(1 - exp(gamma *sqeuclidean(row.as_matrix(columns=paramlist), sourcevec)**2))
result_df = cellmap_df.apply(func, axis=1)
minindex = result_df.argmin()
resultlist.append([minindex, sourceid, sourcelabel])
return resultlist
def euclidean_metric(w, X, y):
return sqeuclidean(X.dot(w), y)
def get_distance_scipy(a, b):
"""Get the squared Euclidean distance between two Points using scipy"""
return sqeuclidean(a.coords, b.coords)
def _predict(self, h=None, smoothing_level=None, smoothing_slope=None,
smoothing_seasonal=None, initial_level=None, initial_slope=None,
damping_slope=None, initial_seasons=None, use_boxcox=None, lamda=None, remove_bias=None):
"""
Helper prediction function
Parameters
----------
h : int, optional
The number of time steps to forecast ahead.
"""
# Variable renames to alpha,beta, etc as this helps with following the
# mathematical notation in general
alpha = smoothing_level
beta = smoothing_slope
gamma = smoothing_seasonal
phi = damping_slope
# Start in sample and out of sample predictions
data = self.endog
damped = self.damped
seasoning = self.seasoning
trending = self.trending
trend = self.trend
seasonal = self.seasonal
m = self.seasonal_periods
phi = phi if damped else 1.0
if use_boxcox == 'log':
lamda = 0.0
y = boxcox(data, 0.0)
elif isinstance(use_boxcox, float):
lamda = use_boxcox
y = boxcox(data, lamda)
elif use_boxcox:
y, lamda = boxcox(data)
else:
lamda = None
y = data.squeeze()
if np.ndim(y) != 1:
raise NotImplementedError('Only 1 dimensional data supported')
y_alpha = np.zeros((self.nobs,))
y_gamma = np.zeros((self.nobs,))
alphac = 1 - alpha
y_alpha[:] = alpha * y
if trending:
betac = 1 - beta
if seasoning:
gammac = 1 - gamma
y_gamma[:] = gamma * y
l = np.zeros((self.nobs + h + 1,))
b = np.zeros((self.nobs + h + 1,))
s = np.zeros((self.nobs + h + m + 1,))
l[0] = initial_level
b[0] = initial_slope
s[:m] = initial_seasons
phi_h = np.cumsum(np.repeat(phi, h + 1)**np.arange(1, h + 1 + 1)
) if damped else np.arange(1, h + 1 + 1)
trended = {'mul': np.multiply,
'add': np.add,
None: lambda l, b: l
}[trend]
detrend = {'mul': np.divide,
'add': np.subtract,
None: lambda l, b: 0
}[trend]
dampen = {'mul': np.power,
'add': np.multiply,
None: lambda b, phi: 0
}[trend]
if seasonal == 'mul':
for i in range(1, self.nobs + 1):
l[i] = y_alpha[i - 1] / s[i - 1] + \
(alphac * trended(l[i - 1], dampen(b[i - 1], phi)))
if trending:
b[i] = (beta * detrend(l[i], l[i - 1])) + \
(betac * dampen(b[i - 1], phi))
s[i + m - 1] = y_gamma[i - 1] / \
trended(l[i - 1], dampen(b[i - 1], phi)) + \
(gammac * s[i - 1])
slope = b[1:i + 1].copy()
season = s[m:i + m].copy()
l[i:] = l[i]
if trending:
b[:i] = dampen(b[:i], phi)
b[i:] = dampen(b[i], phi_h)
trend = trended(l, b)
s[i + m - 1:] = [s[(i - 1) + j % m] for j in range(h + 1 + 1)]
fitted = trend * s[:-m]
elif seasonal == 'add':
for i in range(1, self.nobs + 1):
l[i] = y_alpha[i - 1] - (alpha * s[i - 1]) + \
(alphac * trended(l[i - 1], dampen(b[i - 1], phi)))
if trending:
b[i] = (beta * detrend(l[i], l[i - 1])) + \
(betac * dampen(b[i - 1], phi))
s[i + m - 1] = y_gamma[i - 1] - \
(gamma * trended(l[i - 1],
dampen(b[i - 1], phi))) + (gammac * s[i - 1])
slope = b[1:i + 1].copy()
season = s[m:i + m].copy()
l[i:] = l[i]
if trending:
b[:i] = dampen(b[:i], phi)
b[i:] = dampen(b[i], phi_h)
trend = trended(l, b)
s[i + m - 1:] = [s[(i - 1) + j % m] for j in range(h + 1 + 1)]
fitted = trend + s[:-m]
else:
for i in range(1, self.nobs + 1):
l[i] = y_alpha[i - 1] + \
(alphac * trended(l[i - 1], dampen(b[i - 1], phi)))
if trending:
b[i] = (beta * detrend(l[i], l[i - 1])) + \
(betac * dampen(b[i - 1], phi))
slope = b[1:i + 1].copy()
season = s[m:i + m].copy()
l[i:] = l[i]
if trending:
b[:i] = dampen(b[:i], phi)
b[i:] = dampen(b[i], phi_h)
trend = trended(l, b)
fitted = trend
level = l[1:i + 1].copy()
if use_boxcox or use_boxcox == 'log' or isinstance(use_boxcox, float):
fitted = inv_boxcox(fitted, lamda)
level = inv_boxcox(level, lamda)
slope = detrend(trend[:i], level)
if seasonal == 'add':
season = (fitted - inv_boxcox(trend, lamda))[:i]
elif seasonal == 'mul':
season = (fitted / inv_boxcox(trend, lamda))[:i]
else:
pass
sse = sqeuclidean(fitted[:-h - 1], data)
# (s0 + gamma) + (b0 + beta) + (l0 + alpha) + phi
k = m * seasoning + 2 * trending + 2 + 1 * damped
aic = self.nobs * np.log(sse / self.nobs) + (k) * 2
aicc = aic + (2 * (k + 2) * (k + 3)) / (self.nobs - k - 3)
bic = self.nobs * np.log(sse / self.nobs) + (k) * np.log(self.nobs)
resid = data - fitted[:-h - 1]
if remove_bias:
fitted += resid.mean()
if not damped:
phi = np.NaN
self.params = {'smoothing_level': alpha,
'smoothing_slope': beta,
'smoothing_seasonal': gamma,
'damping_slope': phi,
'initial_level': l[0],
'initial_slope': b[0],
'initial_seasons': s[:m],
'use_boxcox': use_boxcox,
'lamda': lamda,
'remove_bias': remove_bias}
hwfit = HoltWintersResults(self, self.params, fittedfcast=fitted, fittedvalues=fitted[:-h - 1],
fcastvalues=fitted[-h - 1:], sse=sse, level=level,
slope=slope, season=season, aic=aic, bic=bic,
aicc=aicc, resid=resid, k=k)
return HoltWintersResultsWrapper(hwfit)
from scipy.sparse import *
from scipy.sparse.linalg import *
import numpy
import matplotlib.pyplot as plt
text_data = [line.strip() for line in open('data\\reduced-data.txt')]
data = [[float(value) for value in line.rstrip(',').split(',')] for line in text_data]
labels = [line.strip() for line in open('data\\artistList.txt')]
artist_name = sys.argv[1]
num_neighbors = int(sys.argv[2])
artist_vec = []
for i in range(0, len(labels)):
if (artist_name == labels[i]):
artist_vec = data[i]
if (len(artist_vec) == 0):
print "Artist not found"
sys.exit()
distances = [(labels[i], sqeuclidean(numpy.array(data[i]), numpy.array(artist_vec))) for i in range(0, len(labels))]
similar = sorted(distances, key=lambda pair: pair[1])
for i in range(0, num_neighbors):
print similar[i][0]
u, unique_idx = np.unique(nearest_idxs, return_index=True)
# calculate error of transformation
# and select if better than previous
sum_dist = 0
for i in range(0, len(nearest_idxs)):
if nearest_idxs[i] == kd_osm.n:
# distance higher than threshold (ie no next neighbor found)
# break
sum_dist = prev_distance + 1
break
if i not in unique_idx:
# same point matches twice, -> punish
sum_dist += 400
else:
sum_dist += sqeuclidean(osm_corners[nearest_idxs[i], 0:2], transformed_img[i, 0:2])
if abs(sum_dist) < prev_distance:
print(sum_dist)
best_trafo = trafo
prev_distance = abs(sum_dist)
plt.hold(False)
plt.scatter(osm_corners[:, 0], osm_corners[:, 1], color=(1,0,0))
plt.hold(True)
plt.scatter(transformed_img[:, 0], transformed_img[:, 1], color=(0,1,0))
plt.scatter(src[:, 0], src[:, 1], color=(0,0,1), s=30)
plt.show()
print("\n\n\nBest Result: ")
print(best_trafo)
print("DISTANCE: ", prev_distance)
def rbf_kernel(x_i, x_t, gamma) :
return math.exp(- gamma * distance.sqeuclidean(x_i, x_t) )
def getLshNN_op1(dataset, nnModel, thred_radius_dist, trained_num_probes, thred_sameTweetDist):
ngIdxList= []
indexedInCluster = {}
clusters = []
for dataidx in range(dataset.shape[0]):
if dataidx in indexedInCluster:
nn_keys = None
else:
clusterIdx = len(clusters)
indexedInCluster[dataidx] = clusterIdx
clusters.append([dataidx])
nnModel.set_num_probes(trained_num_probes)
# nn_keys: (id1, id2, ...)
nn_keys = nnModel.find_near_neighbors(dataset[dataidx,:], thred_radius_dist)
nn_dists = [(idx, key) for idx, key in enumerate(nn_keys) if key > dataidx-130000 and key < dataidx+130000 and sqeuclidean(dataset[dataidx,:], dataset[key,:]) < thred_sameTweetDist]
#nn_dists = [(idx, key) for idx, key in enumerate(nn_keys) if sqeuclidean(dataset[dataidx,:], dataset[key,:]) < 0.2]
#print len(nn_keys), len(nn_dists), nn_dists[:min(10, len(nn_dists))], nn_dists[-min(10, len(nn_dists)):]
for idx, key in nn_dists:
indexedInCluster[key] = clusterIdx
ngIdxList.append(nn_keys)
if (dataidx+1) % 10000 == 0:
print "## completed", dataidx+1, len(clusters), time.asctime()
ngIdxList = np.asarray(ngIdxList)
return ngIdxList, indexedInCluster, clusters
def _predict(self, h=None, smoothing_level=None, smoothing_slope=None,
smoothing_seasonal=None, initial_level=None, initial_slope=None,
damping_slope=None, initial_seasons=None, use_boxcox=None, lamda=None,
remove_bias=None, is_optimized=None):
"""
Helper prediction function
Parameters
----------
h : int, optional
The number of time steps to forecast ahead.
"""
# Variable renames to alpha, beta, etc as this helps with following the
# mathematical notation in general
alpha = smoothing_level
beta = smoothing_slope
gamma = smoothing_seasonal
phi = damping_slope
# Start in sample and out of sample predictions
data = self.endog
damped = self.damped
seasoning = self.seasoning
trending = self.trending
trend = self.trend
seasonal = self.seasonal
m = self.seasonal_periods
phi = phi if damped else 1.0
if use_boxcox == 'log':
lamda = 0.0
y = boxcox(data, 0.0)
elif isinstance(use_boxcox, float):
lamda = use_boxcox
y = boxcox(data, lamda)
elif use_boxcox:
y, lamda = boxcox(data)
else:
lamda = None
y = data.squeeze()
if np.ndim(y) != 1:
raise NotImplementedError('Only 1 dimensional data supported')
y_alpha = np.zeros((self.nobs,))
y_gamma = np.zeros((self.nobs,))
alphac = 1 - alpha
y_alpha[:] = alpha * y
if trending:
betac = 1 - beta
if seasoning:
gammac = 1 - gamma
y_gamma[:] = gamma * y
l = np.zeros((self.nobs + h + 1,))
b = np.zeros((self.nobs + h + 1,))
s = np.zeros((self.nobs + h + m + 1,))
l[0] = initial_level
b[0] = initial_slope
s[:m] = initial_seasons
phi_h = np.cumsum(np.repeat(phi, h + 1)**np.arange(1, h + 1 + 1)
) if damped else np.arange(1, h + 1 + 1)
trended = {'mul': np.multiply,
'add': np.add,
None: lambda l, b: l
}[trend]
detrend = {'mul': np.divide,
'add': np.subtract,
None: lambda l, b: 0
}[trend]
dampen = {'mul': np.power,
'add': np.multiply,
None: lambda b, phi: 0
}[trend]
nobs = self.nobs
if seasonal == 'mul':
for i in range(1, nobs + 1):
l[i] = y_alpha[i - 1] / s[i - 1] + \
(alphac * trended(l[i - 1], dampen(b[i - 1], phi)))
if trending:
b[i] = (beta * detrend(l[i], l[i - 1])) + \
(betac * dampen(b[i - 1], phi))
s[i + m - 1] = y_gamma[i - 1] / trended(l[i - 1], dampen(b[i - 1], phi)) + \
(gammac * s[i - 1])
slope = b[1:nobs + 1].copy()
season = s[m:nobs + m].copy()
l[nobs:] = l[nobs]
if trending:
b[:nobs] = dampen(b[:nobs], phi)
b[nobs:] = dampen(b[nobs], phi_h)
trend = trended(l, b)
s[nobs + m - 1:] = [s[(nobs - 1) + j % m] for j in range(h + 1 + 1)]
fitted = trend * s[:-m]
elif seasonal == 'add':
for i in range(1, nobs + 1):
l[i] = y_alpha[i - 1] - (alpha * s[i - 1]) + \
(alphac * trended(l[i - 1], dampen(b[i - 1], phi)))
if trending:
b[i] = (beta * detrend(l[i], l[i - 1])) + \
(betac * dampen(b[i - 1], phi))
s[i + m - 1] = y_gamma[i - 1] - \
(gamma * trended(l[i - 1], dampen(b[i - 1], phi))) + \
(gammac * s[i - 1])
slope = b[1:nobs + 1].copy()
season = s[m:nobs + m].copy()
l[nobs:] = l[nobs]
if trending:
b[:nobs] = dampen(b[:nobs], phi)
b[nobs:] = dampen(b[nobs], phi_h)
trend = trended(l, b)
s[nobs + m - 1:] = [s[(nobs - 1) + j % m] for j in range(h + 1 + 1)]
fitted = trend + s[:-m]
else:
for i in range(1, nobs + 1):
l[i] = y_alpha[i - 1] + \
(alphac * trended(l[i - 1], dampen(b[i - 1], phi)))
if trending:
b[i] = (beta * detrend(l[i], l[i - 1])) + \
(betac * dampen(b[i - 1], phi))
slope = b[1:nobs + 1].copy()
season = s[m:nobs + m].copy()
l[nobs:] = l[nobs]
if trending:
b[:nobs] = dampen(b[:nobs], phi)
b[nobs:] = dampen(b[nobs], phi_h)
trend = trended(l, b)
fitted = trend
level = l[1:nobs + 1].copy()
if use_boxcox or use_boxcox == 'log' or isinstance(use_boxcox, float):
fitted = inv_boxcox(fitted, lamda)
level = inv_boxcox(level, lamda)
slope = detrend(trend[:nobs], level)
if seasonal == 'add':
season = (fitted - inv_boxcox(trend, lamda))[:nobs]
else: # seasonal == 'mul':
season = (fitted / inv_boxcox(trend, lamda))[:nobs]
sse = sqeuclidean(fitted[:-h - 1], data)
# (s0 + gamma) + (b0 + beta) + (l0 + alpha) + phi
k = m * seasoning + 2 * trending + 2 + 1 * damped
aic = self.nobs * np.log(sse / self.nobs) + k * 2
if self.nobs - k - 3 > 0:
aicc_penalty = (2 * (k + 2) * (k + 3)) / (self.nobs - k - 3)
else:
aicc_penalty = np.inf
aicc = aic + aicc_penalty
bic = self.nobs * np.log(sse / self.nobs) + k * np.log(self.nobs)
resid = data - fitted[:-h - 1]
if remove_bias:
fitted += resid.mean()
if not damped:
phi = np.NaN
self.params = {'smoothing_level': alpha,
'smoothing_slope': beta,
'smoothing_seasonal': gamma,
'damping_slope': phi,
'initial_level': l[0],
'initial_slope': b[0],
'initial_seasons': s[:m],
'use_boxcox': use_boxcox,
'lamda': lamda,
'remove_bias': remove_bias}
# Format parameters into a DataFrame
codes = ['alpha', 'beta', 'gamma', 'l.0', 'b.0', 'phi']
codes += ['s.{0}'.format(i) for i in range(m)]
idx = ['smoothing_level', 'smoothing_slope', 'smoothing_seasonal',
'initial_level', 'initial_slope', 'damping_slope']
idx += ['initial_seasons.{0}'.format(i) for i in range(m)]
formatted = [alpha, beta, gamma, l[0], b[0], phi]
formatted += s[:m].tolist()
formatted = list(map(lambda v: np.nan if v is None else v, formatted))
formatted = np.array(formatted)
if is_optimized is None:
optimized = np.zeros(len(codes), dtype=np.bool)
else:
optimized = is_optimized.astype(np.bool)
included = [True, trending, seasoning, True, trending, damped]
included += [True] * m
formatted = pd.DataFrame([[c, f, o] for c, f, o in zip(codes, formatted, optimized)],
columns=['name', 'param', 'optimized'],
index=idx)
formatted = formatted.loc[included]
hwfit = HoltWintersResults(self, self.params, fittedfcast=fitted,
fittedvalues=fitted[:-h - 1], fcastvalues=fitted[-h - 1:],
sse=sse, level=level, slope=slope, season=season, aic=aic,
bic=bic, aicc=aicc, resid=resid, k=k,
params_formatted=formatted, optimized=optimized)
return HoltWintersResultsWrapper(hwfit)
def sqeuclidean((x, y)):
return distance.sqeuclidean(x, y)
def probability(self, x):
return cmath.exp(
-0.5 * self.precision * distance.sqeuclidean(x, self.mean)
).real
