def get_u(self):
points = npmat.hstack([s.center_position for s in self.solids])
center = npmat.asmatrix(npmat.average(points, axis = 1)).T
centered_points = points - center
correlation_matrix = (centered_points * centered_points.T)/self.nb_solids
u = iterate(correlation_matrix, self.NB_ITERATIONS)
return u
def calc_phi_points(points, laserpos, lasertheta):
"""Given an array of triples points that should be in the plane generated by a
laser at laserpos with theta lasertheta, calculate the inclination of the laser
plane's normal vector."""
plane_line = ddd.coord(-np.sin(lasertheta), np.cos(lasertheta), 0)
normals = np.cross(np.array(plane_line.T)[0], points - np.array(laserpos.T)[0])
return calc_phi_norm(np.average((normals.T / npl.norm(normals, axis = 1)).T, axis = 0), lasertheta)
def colliding_boxes(self):
nb_solids = self.nb_solids
points = npmat.hstack([s.center_position for s in self.solids])
center = npmat.asmatrix(npmat.average(points, axis = 1)).T
centered_points = points - center
correlation_matrix = (centered_points * centered_points.T) / nb_solids
u = iterate(correlation_matrix, self.NB_ITERATIONS)
if self.projected_bounds is None:
self.projected_bounds = []
for i in range(nb_solids):
self.projected_bounds.append((i, 0, 0.))
self.projected_bounds.append((i, 1, 0.))
min_max_projections = npmat.empty((nb_solids, 2))
for solid_id in range(nb_solids):
solid_AABB_corners = self.solids[solid_id].AABB_corners()
corners_projections = u.T * solid_AABB_corners
min_max_projections[solid_id, 0] = np.min(corners_projections)
min_max_projections[solid_id, 1] = np.max(corners_projections)
for i in range(2 * nb_solids):
solid_id, begin_or_end_id, value = self.projected_bounds[i]
new_value = min_max_projections[solid_id, begin_or_end_id]
self.projected_bounds[i] = (solid_id, begin_or_end_id, new_value)
# TODO: linear sorting
self.projected_bounds.sort(key = lambda x : x[2])
output = []
active_solids = []
for i in range(2 * nb_solids):
solid_id, begin_or_end_id, value = self.projected_bounds[i]
if begin_or_end_id == 0:
for active_solid_id in active_solids:
if self.solids[active_solid_id].AABB_intersect_with(self.solids[solid_id]):
output.append((active_solid_id, solid_id))
active_solids.append(solid_id)
else:
active_solids.remove(solid_id)
return output
def calc_phi(xys, ref_half_plane, view, cameraposor, laserpos, lasertheta):
"""Given an array of pixel pairs xys from a camera with view and cameraposor and
laser with laserpos and lasertheta, calculate the laser inclination based on a
known half-plane ref_half_plane. Throws a NoReferenceException if no pixels are
in the reference half-plane."""
cref_pos = ddd.unrotate(ref_half_plane.pos - cameraposor.pos, cameraposor)
cref_side = ddd.unrotate(ref_half_plane.side, cameraposor)
cref_line = np.cross(cref_side, ddd.unrotate(ref_half_plane.normal, cameraposor), axis = 0)
# TODO less copy-pasta
cpos = np.array([cref_pos[1, 0], -cref_pos[2, 0]]) / cref_pos[0, 0] * ddd.view_number(view) \
+ np.array([view.centerx, view.centery])
cline_ = cref_pos / cref_pos[0, 0] - cref_line / cref_line[0, 0]
cside_ = np.array([cref_side[1, 0], -cref_side[2, 0]])
cside = np.array([cline_[2, 0], cline_[1, 0]])
if np.dot(cside, cside_) < 0:
cside = - cside
dxys = xys - cpos
dot_products = np.array(np.mat([cside]) * np.mat(dxys).T)[0]
good_xys = xys[dot_products >= 0]
print("say "+str(np.average(good_xys[:,1])))
if len(good_xys) == 0:
raise NoReferenceException()
threepoints = ddd.threedize_plane(good_xys, view, cameraposor, ref_half_plane)
return calc_phi_points(threepoints, laserpos, lasertheta)
def signal(prices, index):
"""
Signals to buy/sell stocks.
Returns tuple (X1, X2, ..., Xn), where n is amount of stocks,
Xi is one of the ('sell', 'buy', None).
:param prices: list of price lists of stocks, in time ascending order
:param index: list of k(!) price lists of benchmark values for k last
periods, in time ascending order, with same time frame as stocks.
"""
def betas(prices_m):
"""
Count beta parameters for all stocks, described in 'prices_m' matrix,
according to 'index' benchmark.
:param prices_m: matrix of prices. Each column represents a stock.
Each row represents price at successive time stamp
:return: matrix with betas. Each column represents a stock. Each row
represents beta at successive time period
"""
returns_m = ml.divide(ml.subtract(prices_m[1:], prices_m[:-1]),
prices_m[:-1])
index_m = ml.matrix(index).T
index_returns_m = ml.divide(ml.subtract(index_m[1:], index_m[:-1]),
index_m[:-1])
result = ml.empty((k, prices_m.shape[1]))
for i in range(k):
for j in range(stock_amount):
x = returns_m[:, j]
y = index_returns_m[:, i]
result[i, j] = np.cov(x, y, rowvar=0)[0][1]/np.var(y)
return result
def regime(reduced_returns_m):
"""
Make a regime switch based on PCA standard deviation acceleration.
:param reduced_returns_m: matrix of PCA. Each column represents a
stock. Each row represents price at successive time stamp
:return: one of the strings, 'momentum' - if trend is ment to
continue its movement, 'mean_reversion' - otherwise
"""
cross_sect_vol = np.std(reduced_returns_m, axis=1)
changes = cross_sect_vol[1:] - cross_sect_vol[:-1]
squared_changes = np.square(changes)
distance_times = reduced_returns_m.shape[0] - 1 # because there is
# T - 1 changes
distance = np.zeros(distance_times)
for t in range(distance_times):
sum_amount = min(t + 1, H)
for i in range(sum_amount):
distance[t] += squared_changes[t - i, 0]
distance[t] = np.sqrt(distance[t])
signal = distance[1:] - distance[:-1]
if np.max(signal) > 0:
return 'momentum'
else:
return 'mean_reversion'
prices_m = ml.matrix(prices).T
# Preparing main matrices for further computations
try:
log_returns_m = np.log(ml.divide(prices_m[1:], prices_m[:-1]))
except TypeError as e:
raise WrongPricesError(prices_m)
time_period, stock_amount = log_returns_m.shape
mean_log_returns_m = ml.average(log_returns_m, axis=0)
demeaned_log_returns_m = log_returns_m - mean_log_returns_m
covariation_m = demeaned_log_returns_m.T * demeaned_log_returns_m
# Count eigenvectors of covariation matrix and compose PCA matrix from them
e_values, e_vectors = eig(covariation_m)
abs_e_values = np.absolute(e_values)
# TODO: np.absolute(e_vectors) or something like that
indexed_abs_e_values = [(i, v) for i, v in enumerate(abs_e_values)]
w = sorted(indexed_abs_e_values, reverse=False,
key=lambda x: x[1])
e_vectors_m = ml.empty((stock_amount, k))
for j in range(k):
e_vectors_m[:, j] = e_vectors[:, w[j][0]]
# Main part: project returns on PCA universe
reduced_returns_m = (e_vectors_m.T * demeaned_log_returns_m.T).T
# Count beta parameters with respect to given benchmark index
betas_m = betas(prices_m)
time = time_period - time_shift
if time < H:
raise WrongParameterException("time_shift should be less than H")
# Collect data from returns in one vector
accumulated_reduced_returns = ml.zeros((1, k))
for i in range(H):
accumulated_reduced_returns += reduced_returns_m[time - 1 - i]
# Make a prediction about further returns behaviour
estimation = accumulated_reduced_returns * betas_m + \
mean_log_returns_m
if regime_switcher:
regime = regime(reduced_returns_m)
else:
regime = 'mean_reversion'
# Finally, decide for each stock, whether we need to sell it as
# overvalued or buy as undervalued. Other way around for momentum switch
max_recent_log_returns = log_returns_m[-H:].max(0)
result = []
for i in range(stock_amount):
if max_recent_log_returns[0, i] > estimation[0, i] + epsilon:
if regime == 'mean_reversion':
result.append('sell')
else:
result.append('buy')
elif max_recent_log_returns[0, i] < estimation[0, i] - epsilon:
if regime == 'mean_reversion':
result.append('buy')
else:
result.append('sell')
else:
result.append(None)
return result
with open('uk_players_positions.pkl', 'rb') as p:
pos = pickle.load(p)
with open('uk_players_avg_ratings.pkl', 'rb') as p:
ratings = pickle.load(p)
# TRANSFORM LABELS 'POSITIONS' INTO NUMERIC
le = preprocessing.LabelEncoder()
y = le.fit_transform(pos)
print("LABEL DECODING")
for i in range(0, 16, 1):
print(str(i) + '\t' + str(le.inverse_transform([i])))
v = DictVectorizer(sparse=False)
X = v.fit_transform(players)
# CLASSIFY FOR POSITION
classifiers = [MultinomialNB(), LinearSVC(), LogisticRegression()]
for clf in classifiers:
clf.fit(X, y)
predicted = cross_val_predict(clf, X, y, cv=10)
print(str(metrics.classification_report(y, predicted)))
# REGRESSION FOR MATCH RATING
y = ratings
regression = [LinearRegression(), Lasso()]
for clf in regression:
score = cross_val_score(clf, X, y, scoring='neg_mean_squared_error', cv=10)
print(average(score))