def PCA(X, k):
"""
Compute PCA on the given matrix.
Args:
X - Matrix of dimesions (n,d). Where n is the number of sample points and d is the dimension of each sample.
For example, if we have 10 pictures and each picture is a vector of 100 pixels then the dimesion of the matrix would be (10,100).
k - number of eigenvectors to return
Returns:
U - Matrix with dimension (k,d). The matrix should be composed out of k eigenvectors corresponding to the largest k eigenvectors
of the covariance matrix.
S - k largest eigenvalues of the covariance matrix. vector of dimension (k, 1)
"""
cov_id_vaccine = np.matmul(mat.transpose(X), X)
w, v = lin.eig(cov_id_vaccine)
v = mat.transpose(v)
vec = []
d = len(w)
for i in range(d):
vec.append((w[i], v[i]))
vec.sort(key=lambda x: x[0], reverse=True)
U = np.stack([vec[i][1] for i in range(k)], axis=0)
#print(type(w))
w[::-1].sort()
w = w[:k]
S = np.array([w]).T
return U, S
def section_d():
lfw_people = load_data()
names = lfw_people.target_names
data, Y_values, h, w = get_pictures_by_names(names)
data = np.array(data)[:, :, 0]
standardize(data)
X_train, X_test, Y_train, Y_test = train_test_split(data,
Y_values,
test_size=0.25,
random_state=0)
k_vals = [1, 5, 10, 30, 50, 100, 150, 300, len(data[0])]
scores = []
for k in k_vals:
print("k is {}".format(k))
U, S = PCA(X_train, k)
A = np.matmul(X_train, mat.transpose(U))
X_test_newDim = mat.transpose(np.matmul(U,
np.matrix.transpose(X_test)))
res = svm.SVC(kernel='rbf', C=1000, gamma=10**-7).fit(A, Y_train)
scores.append(res.score(X_test_newDim, Y_test))
plt.plot(k_vals, scores, color='blue')
plt.xlabel('k values')
plt.ylabel('Accuracy')
plt.title('Accuracy through different dimensions')
plt.show()
def run():
error = 0
final_g = [0 for i in range(7)]
max_err = 100000000000000000000
for i in range(1000):
#error = 0
p = [(uniform(-1, 1), uniform(-1, 1)), (uniform(-1, 1), uniform(-1,
1))]
target = [
-p[0][0] + (p[0][0] - p[1][0]) * p[1][0] / (p[1][0] - p[1][1]), 1,
-(p[0][0] - p[1][0]) / (p[1][0] - p[1][1])
]
N = [(1, uniform(-1, 1), uniform(-1, 1)) for i in range(1000)]
classification = map(y_function,
[(x[1]**2 + x[2]**2 - 0.6) > 0 for x in N])
flipped_nums = []
for j in range(100):
flip = randrange(0, 1000)
while flip in flipped_nums:
flip = randrange(0, 1000)
flipped_nums.append(flip)
for f in flipped_nums:
classification[f] = -classification[f]
M = [(1, x[1], x[2], x[1] * x[2], x[1]**2, x[2]**2) for x in N]
g = matrix.transpose(
matrix(pinv([list(m)
for m in M])) * matrix([[float(c)]
for c in classification]))
N = [(1, uniform(-1, 1), uniform(-1, 1)) for i in range(1000)]
classification = map(y_function,
[(x[1]**2 + x[2]**2 - 0.6) > 0 for x in N])
flipped_nums = []
for j in range(100):
flip = randrange(0, 1000)
while flip in flipped_nums:
flip = randrange(0, 1000)
flipped_nums.append(flip)
for f in flipped_nums:
classification[f] = -classification[f]
M = [(1, x[1], x[2], x[1] * x[2], x[1]**2, x[2]**2) for x in N]
g_classification = matrix(
map(y_function2, [g * matrix.transpose(matrix(m)) for m in M]))
#final_g = [a + b for (a,b) in zip(final_g,[x/abs(g.tolist()[0][0]) for x in g.tolist()[0]])]
errors = [
x != t
for (x, t) in zip(g_classification.tolist()[0], classification)
]
for e in errors:
if e:
error += 1
#if error < max_err:
# max_err = error
# final_g = g
# print [x/abs(g.tolist()[0][0]) for x in g.tolist()[0]]
error /= 1000.0 * 1000.0
print error
def sample_z_i(self, i):
"""
Samples from distribution of i'th value of z-vector given other
parameters
:type i: int
:param i: number which indicates which feature's z value to sample
"""
if self.zs[i] == 1.0:
# This is all on page 48 (Appendix A) of group feature selection
# paper - pretty hard to explain without looking at that.
Theta = matrix(self.data)
Theta_t = matrix.transpose(Theta)
mult = np.zeros(self.d)
mult = mult + self.vs
mult[self.big_zeros] = 0.0
for j in range(self.multi_dim):
mult[i + j*self.g] = 0.0
A_minusg = mult*np.identity(self.d)
C_minusg = (self.sigma2*np.identity(self.size) +
Theta*A_minusg*Theta_t)
X_g = np.zeros([self.size, self.multi_dim])
for k in range(self.multi_dim):
X_g[:, k] = self.data[:, i + k*self.g]
X_g = matrix(X_g)
X_g_t = matrix.transpose(X_g)
C_inv = np.linalg.inv(C_minusg)
M = X_g_t*C_inv*X_g
eig_vals, eig_vecs = np.linalg.eigh(M)
y = matrix(self.y)
L = 0.0
for j in range(self.multi_dim):
s_j = eig_vals[j]
e_j = eig_vecs[:, j]
temp = y*C_inv*X_g
q_j = float(temp*e_j)
L = (L + 0.5*(q_j**2.0/((1.0/self.vs) + s_j)
- np.log(1.0 + self.vs*s_j)))
L_tot = np.exp(L)
else:
L_tot = 1.0
test = np.random.uniform()
if (test < (self.p0*L_tot)/(self.p0*L_tot + (1.0 - self.p0))
or L_tot > 1000000000000.0):
self.zs[i] = 1.0
else:
self.zs[i] = 0.0
self.zeros, self.ones = find_zero(self.zs)
self.big_zeros = np.zeros(len(self.zeros)*self.multi_dim, dtype = int)
self.big_ones = np.zeros(len(self.ones)*self.multi_dim, dtype = int)
self.fill_in_binary()
return
def utility_kalman_filter_ball(ball):
if (t==0): # initialize filter
ball.xhat = matlib.zeros((8,1))
ball.xhat_delayed = ball.xhat
ball.S = np.diag([\
globals.field_width/2, # initial variance of x-position of ball
globals.field_width/2, # initial variance of y-position of ball
.01, # initial variance of x-velocity of ball
.01, # initial variance of y-velocity of ball
.001, # initial variance of x-acceleration of ball
.001, # initial variance of y-acceleration of ball
.0001, # initial variance of x-jerk of ball
.0001, # initial variance of y-jerk of ball
]);
ball.S_delayed=ball.S
# prediction step between measurements
N = 10;
for i in range(1,N):
xhat = xhat + (globals.loop_rate/N)*globals.A_ball*xhat;
ball.S = ball.S + (globals.loop_rate/N)*(globals.A_ball*ball.S+ball.S*matrix.transpose(globals.A_ball)+globals.Q_ball)
# correction step at measurement
# only update when the camera flag is one indicating a new measurement
# case 1 does not compensate for camera delay
# case 2 compensates for fixed camera delay
if ball.camera_flag == 1:
y = ball.position_camera; # actual measurement
y_pred = globals.C_ball*xhat; # predicted measurement
L = S*matrix.transpose(globals.C_ball)/(globals.R_ball+globals.C_ball*S*matrix.transpose(globals.C_ball))
S = (np.eye(8)-L*globals.C_ball)*S;
xhat = xhat + L*(y-y_pred);
elif ball.camera_flag == 2:
y = ball.position_camera; # actual measuremnt
y_pred = globals.C_ball*ball.xhat_delayed; # predicted measurement
L = ball.S_delayed*matrix.transpose(globals.C_ball)/(globals.R_ball+globals.C_ball*ball.S_delayed*matrix.transpose(globals.C_ball))
ball.S_delayed = (np.eye(8)-L*globals.C_ball)*ball.S_delayed
ball.xhat_delayed = ball.xhat_delayed + L*(y-y_pred);
for i in range(1,N*(globals.camera_sample_rate/globals.loop_rate)):
ball.xhat_delayed = ball.xhat_delayed + (globals.loop_rate/N)*(globals.A_ball*ball.xhat_delayed);
ball.S_delayed = ball.S_delayed + (globals.loop_rate/N)*(globals.A_ball*ball.S_delayed+ball.S_delayed*matrix.transpose(globals.A_ball)+globals.Q_ball)
ball.xhat = ball.xhat_delayed
ball.S = ball.S_delayed
# output current estimate of state
ball.position = xhat[0:1];
ball.velocity = xhat[2:3];
ball.acceleration = xhat[4:5];
ball.jerk = xhat[6:7];
ball.S = globals.S_ball;
def draw_object():
glVertexAttribPointer(locations[b"vertex"], 3, GL_FLOAT, False, record_len,
vertex_offset)
glVertexAttribPointer(locations[b"tex_coord"], 3, GL_FLOAT, False,
record_len, tex_coord_offset)
glVertexAttribPointer(locations[b"normal"], 3, GL_FLOAT, False, record_len,
normal_offset)
glVertexAttribPointer(locations[b"color"], 3, GL_FLOAT, False, record_len,
color_offset)
modelview = m.identity()
modelview = m.mul(modelview, m.scale(scale, scale, scale))
modelview = m.mul(modelview, q.matrix(rotation))
glUniformMatrix4fv(locations[b"modelview_matrix"], 1, GL_FALSE,
c_matrix(modelview))
normal = m.transpose(m.inverse(m.top_left(modelview)))
glUniformMatrix3fv(locations[b"normal_matrix"], 1, GL_FALSE,
c_matrix(normal))
offset = 0
for size in sizes:
glDrawElements(GL_TRIANGLE_STRIP, size, GL_UNSIGNED_INT,
c_void_p(offset))
offset += size * uint_size
def greedyBipartite(cls, cost_matrix):
"""
Greedy algorithm for bipartite matching of two tracks.
Takes in a len(track1) x len(track2) matrix, where the cells are weights between the nodes in
the tracks.
Finds a, b and c for the tracks, as defined above.
"""
from numpy import zeros, shape, max, argmax, unravel_index, matrix
dimensions = shape(cost_matrix)
cost = {'a': 0.0, 'b': 0.0, 'c': 0.0, 'd': -1}
cost['b'] += cls.getZeroOccurrences(cost_matrix)
cost['c'] += cls.getZeroOccurrences(matrix.transpose(cost_matrix))
while max(cost_matrix) > 0:
pos = argmax(cost_matrix)
row, col = unravel_index([pos], dimensions)
dimensions = list(dimensions)
val = max(cost_matrix)
cost_matrix[row[0], :] = zeros(dimensions[1])
cost_matrix[:, col[0]] = zeros(dimensions[0])
cost['a'] += val
return cost
def lapjvBipartite(cls, cost_matrix):
"""
Optimal algorithm for bipartite matching of two tracks.
Takes in len(track1) x len(track2) matrix, where the cells are weights between the nodes in
the tracks.
Finds a, b and c for the tracks, as defined above.
"""
from quick.webtools.clustering.JonkerVolgenant import JonkerVolgenant
from numpy import matrix
matches = JonkerVolgenant.findJonkerVolgenant(cost_matrix)
cost = {'a': 0, 'b': 0, 'c': 0, 'd': -1}
track1Length = len(cost_matrix)
track2Length = len(cost_matrix[0])
cost['b'] += cls.getZeroOccurrences(cost_matrix)
cost['c'] += cls.getZeroOccurrences(matrix.transpose(cost_matrix))
if track1Length < track2Length:
for matchID in range(0, track1Length):
val = cost_matrix[matchID, matches[matchID]]
cost['a'] += val
else:
for matchID in range(0, track2Length):
val = cost_matrix[matches[matchID], matchID]
cost['a'] += val
return cost
def SqrtCorrel(self):
(w,v) = linalg.eig(self.Sigma)
wreal = []
for i in range(self.N):
wreal += [sqrt(w[i].real)]
wdiag = diag(wreal)
self.Sqrt = wdiag.dot(matrix.transpose(v))
def _inversion(self, P_mat_t, fft_v, m):
b = np.zeros([self.L - m, 1], dtype = complex)
for el in range(m, self.L, 1):
b[el-m] = fft_v[m + el**2][0]
P = P_mat_t[:, m:]
flmt_t = np.linalg.lstsq(npmtrx.transpose(P),b)[0]
return flmt_t
def draw_object(): glVertexAttribPointer(locations[b"vertex"], 3, GL_FLOAT, False, record_len, vertex_offset) glVertexAttribPointer(locations[b"tex_coord"], 3, GL_FLOAT, False, record_len, tex_coord_offset) glVertexAttribPointer(locations[b"normal"], 3, GL_FLOAT, False, record_len, normal_offset) glVertexAttribPointer(locations[b"color"], 3, GL_FLOAT, False, record_len, color_offset) modelview = m.identity() modelview = m.mul(modelview, m.scale(scale, scale, scale)) modelview = m.mul(modelview, q.matrix(rotation)) glUniformMatrix4fv(locations[b"modelview_matrix"], 1, GL_FALSE, c_matrix(modelview)) normal = m.transpose(m.inverse(m.top_left(modelview))) glUniformMatrix3fv(locations[b"normal_matrix"], 1, GL_FALSE, c_matrix(normal)) offset = 0 for size in sizes: glDrawElements(GL_TRIANGLE_STRIP, size, GL_UNSIGNED_INT, c_void_p(offset)) offset += size*uint_size
def brkga_mutation(runsize, num_col=4):
'''Here we will create random mutant solutions of randomly chosen levels and number of factors,
Also no mutation rate is required as we always have to generate a particular number of mutant,
solutions based on the size of population. Call this function recursively to generate more than one mutant'''
lev = find_levels(runsize)
new_matrix = []
temp_fact = []
for l in range(num_col):
lev_selected = lev[random.randint(0, len(lev)-1)]
temp_fact.append(lev_selected)
new_col = []
for i in range(lev_selected):
for j in range(int(runsize/lev_selected)):
new_col.append(i)
random.shuffle(new_col)
new_matrix.append(new_col)
new_matrix = matrix(new_matrix).reshape(num_col, runsize)
new_matrix = matrix.transpose(new_matrix)
temp = str(runsize)
for i in list(remove_duplicates(temp_fact)):
temp += ',' + str(i) + '^' + str(temp_fact.count(i))
new_oa = OA(temp, new_matrix)
return new_oa
def brkga_mutation(runsize, num_col=4):
'''Here we will create random mutant solutions of randomly chosen levels and number of factors,
Also no mutation rate is required as we always have to generate a particular number of mutant,
solutions based on the size of population. Call this function recursively to generate more than one mutant'''
lev = find_levels(runsize)
new_matrix = []
temp_fact = []
for l in range(num_col):
lev_selected = lev[random.randint(0, len(lev) - 1)]
temp_fact.append(lev_selected)
new_col = []
for i in range(lev_selected):
for j in range(int(runsize / lev_selected)):
new_col.append(i)
random.shuffle(new_col)
new_matrix.append(new_col)
new_matrix = matrix(new_matrix).reshape(num_col, runsize)
new_matrix = matrix.transpose(new_matrix)
temp = str(runsize)
for i in list(remove_duplicates(temp_fact)):
temp += ',' + str(i) + '^' + str(temp_fact.count(i))
new_oa = OA(temp, new_matrix)
return new_oa
def regression_weights(x_t, head, exponential=False):
"""does needed matrix calculations for regression weights
Args:
x_t (nd arr): X transpose matrix
head (md arr): Y(training data) matrix
exponential (bool, optional): if a simple exponential regression is about to do. Defaults to False.
Returns:
pd arr: calculated weights
"""
product = np.copy(x_t)
product = np.matmul(product, mt.transpose(product))
product = la.inv(product)
product = np.matmul(product, x_t)
product = np.matmul(product,(np.log(mt.transpose(head)) if (exponential) else mt.transpose(head))) # exponential must fit the logarithm of records
return product
def to_compositions(self):
'''
Return corresponding compositional data object
'''
from Compositions import CompData
matrix, row_labels, col_labels = self.to_matrix()
f_mat = CompData(matrix.transpose(), dtype=float)
return f_mat, row_labels, col_labels
def to_compositions(self):
'''
Return corresponding compositional data object
'''
from Compositions import CompData
matrix, row_labels, col_labels = self.to_matrix()
f_mat = CompData(matrix.transpose(), dtype=float)
return f_mat, row_labels, col_labels
def run():
error = 0
final_g = [0 for i in range(7)]
max_err = 100000000000000000000
for i in range(1000):
#error = 0
p = [(uniform(-1,1), uniform(-1,1)), (uniform(-1,1), uniform(-1,1))]
target = [-p[0][0]+(p[0][0]-p[1][0])*p[1][0]/(p[1][0]-p[1][1]), 1, -(p[0][0]-p[1][0])/(p[1][0]-p[1][1])]
N = [(1,uniform(-1,1),uniform(-1,1)) for i in range(1000)]
classification = map(y_function, [(x[1]**2 + x[2]**2 - 0.6) > 0 for x in N])
flipped_nums = []
for j in range(100):
flip = randrange(0,1000)
while flip in flipped_nums:
flip = randrange(0,1000)
flipped_nums.append(flip)
for f in flipped_nums:
classification[f] = -classification[f]
M = [(1, x[1], x[2], x[1]*x[2], x[1]**2, x[2]**2) for x in N]
g = matrix.transpose(matrix(pinv([list(m) for m in M]))*matrix([[float(c)] for c in classification]))
N = [(1,uniform(-1,1),uniform(-1,1)) for i in range(1000)]
classification = map(y_function, [(x[1]**2 + x[2]**2 - 0.6) > 0 for x in N])
flipped_nums = []
for j in range(100):
flip = randrange(0,1000)
while flip in flipped_nums:
flip = randrange(0,1000)
flipped_nums.append(flip)
for f in flipped_nums:
classification[f] = -classification[f]
M = [(1, x[1], x[2], x[1]*x[2], x[1]**2, x[2]**2) for x in N]
g_classification = matrix(map(y_function2, [g*matrix.transpose(matrix(m)) for m in M]))
#final_g = [a + b for (a,b) in zip(final_g,[x/abs(g.tolist()[0][0]) for x in g.tolist()[0]])]
errors = [x != t for (x,t) in zip(g_classification.tolist()[0], classification)]
for e in errors:
if e:
error += 1
#if error < max_err:
# max_err = error
# final_g = g
# print [x/abs(g.tolist()[0][0]) for x in g.tolist()[0]]
error /= 1000.0 * 1000.0
print error
def Example():
C = Copula([Currency.XBT,Currency.ETH, Currency.BCH, Currency.LTC, Currency.XRP])
#C = Copula([Currency.BCH])
C.ComputeCorrelation()
print(C.Sigma)
tab = C.Simulate(10000)
cov = matrix.transpose(tab).dot(tab)/10000
print(cov)
def sample_sigma2(self, k, sigma2_hat):
"""
Samples from distribution of the error given other parameters.
"""
alpha0 = k/2.0
beta0 = k*sigma2_hat/2.0
alpha = alpha0 + self.size/2.0
data = np.copy(self.data)
y = np.copy(self.y)
w = np.copy(self.w)
data = matrix(data)
y = matrix.transpose(matrix(y))
w = matrix.transpose(matrix(w))
beta = beta0 + 0.5*matrix.transpose(y - data*w)*(y - data*w)
self.sigma2 = invgamma.rvs(alpha, scale = beta)
return
def sample_w(self):
"""
Samples from distribution of weights given other parameters.
"""
nothing, eta_rem = self.regcalc()
eta_rem = np.delete(eta_rem, self.big_zeros, 0)
eta_rem = np.delete(eta_rem, self.big_zeros, 1)
X = self.data
X = np.delete(X, self.big_zeros, 1)
y = matrix.transpose(matrix(self.y))
mean_rem = (1.0/(self.sigma2))*eta_rem*matrix.transpose(matrix(X))*y
mean_simp = np.zeros(len(self.big_ones))
for i in range(len(self.big_ones)):
mean_simp[i] = float(mean_rem[i])
if len(mean_simp) > 0:
self.w[self.big_ones] = multivariate_normal.rvs(mean_simp, eta_rem)
self.w[self.big_zeros] = 0.0
return
def plot_dist_mat(self, metric ='euclidean', file = None, transpose = True, show_labels = False, **kwargs):
import distances
from heatmap_clust import clust_data, heatmap_clust
matrix, row_labels, col_labels = self.to_matrix()
if transpose:
mat = matrix.transpose()
labels = map(lambda s: s.split('_')[-1], col_labels)
else:
mat = matrix
labels = map(lambda s: s.split('_')[-1], row_labels)
D = distances.pdist(mat, metric)
if show_labels: heatmap_clust(D, file = file, labels =labels, **kwargs)
else: heatmap_clust(D, file = file, **kwargs)
def plot_dist_mat(self, metric ='euclidean', file = None, transpose = True, show_labels = False, **kwargs):
import distances
from heatmap_clust import clust_data, heatmap_clust
matrix, row_labels, col_labels = self.to_matrix()
if transpose:
mat = matrix.transpose()
labels = map(lambda s: s.split('_')[-1], col_labels)
else:
mat = matrix
labels = map(lambda s: s.split('_')[-1], row_labels)
D = distances.pdist(mat, metric)
if show_labels: heatmap_clust(D, file = file, labels =labels, **kwargs)
else: heatmap_clust(D, file = file, **kwargs)
def ComputeCorrelation(self):
A = zeros(shape = (self.N, self.T))
for i in range(self.N):
A[i] = self.Densities[self.CurrencyList[i]].StdReturns
temp = DataFrame(A)
Sigma = A.dot(matrix.transpose(A))
Sigma /= float(self.T)
std = []
for i in range(self.N):
std += [sqrt(Sigma[i,i])]
for i in range(self.N):
for j in range(self.N):
Sigma[i,j] /= std[i] * std[j]
self.Sigma = Sigma
def nmf_div(V, k, n_max_iterations=1000, random_seed=RANDOM_SEED):
"""
Non-negative matrix factorize matrix with k from ks using divergence.
:param V: numpy array or pandas DataFrame; (n_samples, n_features); the matrix to be factorized by NMF
:param k: int; number of components
:param n_max_iterations: int;
:param random_seed:
:return:
"""
eps = finfo(float).eps
N = V.shape[0]
M = V.shape[1]
V = matrix(V)
seed(random_seed)
W = rand(N, k)
H = rand(k, M)
for t in range(n_max_iterations):
VP = dot(W, H)
W_t = matrix.transpose(W)
H = multiply(H, dot(W_t, divide(V, VP))) + eps
for i in range(k):
W_sum = 0
for j in range(N):
W_sum += W[j, i]
for j in range(M):
H[i, j] = H[i, j] / W_sum
VP = dot(W, H)
H_t = matrix.transpose(H)
W = multiply(W, dot(divide(V, VP + eps), H_t)) + eps
W = divide(W, ndarray.sum(H, axis=1, keepdims=False))
err = sum(multiply(V, log(divide(V + eps, VP + eps))) - V + VP) / (M * N)
return W, H, err
def MLE(X, y):
"""
Maximum likelihood estimate of weights
:type X: array of size #data points*4 by #dimensions*4 containing floats
:param X: matrix containing features for each data point
:type y: array of size #data points*4 containing floats
:param y: vector filled with target variables
"""
Theta = np.matrix(X)
Theta_t = np.matrix.transpose(Theta)
inv = np.linalg.inv(Theta_t * Theta)
return inv * Theta_t * matrix.transpose(matrix(y))
def GaussNewton(steps, X, Y, B):
print('Running Gauss-Newton method for B =', B)
J = linalg.norm(f(X, Y, B))**2
Jo = J
histB = [B]
for i in range(steps):
Jac = buildJ(X, Y, B)
JacT = matrix.transpose(Jac)
B = B - np.matmul(np.linalg.inv(np.matmul(JacT, Jac)),
np.matmul(JacT, f(X, Y, B)))
J = linalg.norm(f(X, Y, B))**2
histB.append(B)
histB = np.matrix(histB)
if (J > Jo):
print("Diverged!")
else:
print("Converged to", B)
return histB
def regcalc(self):
"""
Calculates the estimates for mean and covariance matrix of weights
given a particular z-vector.
"""
Theta = np.matrix(self.data)
Theta_t = np.matrix.transpose(Theta)
mult = np.zeros(self.d)
mult = mult + 1.0/self.vs
mult[self.big_zeros] = 10000000.0
I_vs = mult*np.identity(self.d)
Eta_z = np.linalg.inv((1.0/self.sigma2)*Theta_t*Theta + I_vs)
ys = matrix.transpose(matrix(self.y))
prelim = Theta_t * ys
M_N = (1/self.sigma2) * Eta_z * prelim
return M_N, Eta_z
def _spatial_elimination(self, P_mat_t, f_t, flm_t, m):
P_mat = npmtrx.transpose(P_mat_t[:, :m])
gm = np.dot(P_mat, flm_t)
gm_neg = np.conj(gm)
phi_weights = np.reshape(self._phi_weights[m][:m ** 2], [m ** 2, 1])
phi_weights_neg =np.reshape(self._phi_weights_neg[m][:m ** 2], [m ** 2, 1])
f_temp = np.zeros_like(phi_weights)
f_temp_neg = np.zeros_like(phi_weights_neg)
for ii in range(m):
f_temp[ii**2 : (ii+1)**2, :] = gm[ii]
f_temp_neg[ii ** 2 : (ii + 1) ** 2, :] = gm_neg[ii]
f_temp= np.multiply(f_temp, phi_weights)
f_temp_neg = np.multiply(f_temp_neg, phi_weights_neg)
f_t = f_t - f_temp - f_temp_neg
return f_t
def section_c(k_vals=[1, 5, 10, 30, 50, 100, 150, 300]):
selected_images, h, w = get_pictures_by_name()
data = np.array(selected_images)[:, :, 0]
n = len(data)
standardize(data)
k_vals.append(len(data[0]))
dist = []
for k in k_vals:
#print("k= "+str(k))
l2 = 0
U, S = PCA(data, k)
V = np.matmul(data, np.matrix.transpose(U))
xPrime = mat.transpose(np.matmul(np.transpose(U), np.transpose(V)))
for i in range(5):
rand_number = np.random.randint(0, n - 1)
#plot_vectors(np.array([data[rand_number], xPrime[rand_number]]), h, w, 1, 2)
l2 += lin.norm(data[rand_number] - xPrime[rand_number])
dist.append(l2)
plt.plot(k_vals, dist, color='r', marker='o')
plt.xlabel('dim')
plt.ylabel('L2 norms')
plt.title('L2_distances after changing dimensions')
plt.show()
def LS(self, abscissa, observations, PARAM, x_fix, x_ini):
# The initial parameters are the ones from DLT but where the radio button is set as free
x = []
for i in range(9):
if (PARAM[i] == 1) or (PARAM[i] == 2):
#Free or apriori values
x.append(x_ini[i])
x = array(x)
# 2D coordinates are understood as observations
observations = array(observations)
# 3D coordinates are understood as the abscissas
abscissa = array(abscissa)
npoints = size(observations[:, 1])
l_x = size(
x
) #9-size(nonzero(PARAM==0)[0])#int(sum(PARAM))#Number of free parameters
sigmaobservationservation = 1
Kl = zeros(shape=(2 * npoints, 2 * npoints))
# A error of "sigmaobservationservation" pixels is a priori set
for i in range(npoints):
Kl[2 * i - 1, 2 * i - 1] = sigmaobservationservation**2
Kl[2 * i, 2 * i] = sigmaobservationservation**2
# The P matrix is a weight matrix, useless if equal to identity (but can be used in some special cases)
P = linalg.pinv(Kl)
# A is the Jacobian matrix
A = zeros(shape=(2 * npoints, l_x))
# H is the hessian matrix
H = zeros(shape=(l_x, l_x))
# b is a transition matrix
b = zeros(shape=(l_x))
# v contains the residual errors between observations and predictions
v = zeros(shape=(2 * npoints))
# v_test contain the residual errors between observations and predictions after an update of H
v_test = zeros(shape=(2 * npoints))
# x_test is the updated parameters after an update of H
x_test = zeros(shape=(l_x))
# dx is the update vector of x and x_test
dx = array([0.] * l_x)
it = -1
maxit = 1000
# At least one iteration, dx > inc
dx[0] = 1
# Lambda is the weightage parameter in Levenberg-marquart between the gradient and the gauss-newton parts.
Lambda = 0.01
# increment used for Jacobian and for convergence criterium
inc = 0.001
while (max(abs(dx)) > inc) & (it < maxit):
#new iteration, parameters updates are greater than the convergence criterium
it = it + 1
# For each observations, we compute the derivative with respect to each parameter
# We form therefore the Jacobian matrix
for i in range(npoints):
#ubul and vbul are the prediction with current parameters
ubul, vbul = self.dircal(x, abscissa[i, :], x_fix, PARAM)
# The difference between the observation and prediction is used for parameters update
v[2 * i - 1] = observations[i, 0] - ubul
v[2 * i] = observations[i, 1] - vbul
for j in range(l_x):
x_temp = copy(x)
x_temp[j] = x[j] + inc
u2, v2 = self.dircal(x_temp, abscissa[i, :], x_fix, PARAM)
A[2 * i - 1, j] = (u2 - ubul) / inc
A[2 * i, j] = (v2 - vbul) / inc
# The sum of the square of residual (S0) must be as little as possible.
# That's why we speak of "least square"... tadadam !
S0 = sum(v**2)
H = dot(dot(matrix.transpose(A), P), A)
b = dot(dot(matrix.transpose(A), P), v)
try:
dx = dot(linalg.pinv(H + Lambda * diag(diag(H))), b)
x_test = x + dx
except:
# The matrix is not always reversal.
# In this case, we don't accept the update and go for another iteration
S2 = S0
else:
for i in range(npoints):
# We check that the update has brought some good stuff in the pocket
# In other words, we check that the sum of square of less than before (better least square!)
utest, vtest = self.dircal(x_test, abscissa[i, :], x_fix,
PARAM)
v_test[2 * i - 1] = observations[i, 0] - utest
v_test[2 * i] = observations[i, 1] - vtest
S2 = sum(v_test**2)
# Check if sum of square is less
if S2 < S0:
Lambda = Lambda / 10
x = x + dx
else:
Lambda = Lambda * 10
# Covariance matrix of parameters
self.Qxx = sqrt(diag(linalg.inv(dot(dot(matrix.transpose(A), P), A))))
p = zeros(shape=(len(PARAM)))
m = 0
#n = 0
for k in range(len(PARAM)):
if (PARAM[k] == 1) or (PARAM[k] == 2):
p[k] = x[m]
m = m + 1
else:
p[k] = x_fix[k]
#n = n+1
L1p = self.CoeftoMatrixProjection(p)
x0 = p[0]
y0 = p[1]
z0 = p[2]
tilt = p[3]
azimuth = p[4]
swing = p[5]
focal = p[6]
u0 = p[7]
v0 = p[8]
R = zeros((3, 3))
R[0, 0] = -cos(azimuth) * cos(swing) - sin(azimuth) * cos(tilt) * sin(
swing)
R[0, 1] = sin(azimuth) * cos(swing) - cos(azimuth) * cos(tilt) * sin(
swing)
R[0, 2] = -sin(tilt) * sin(swing)
R[1, 0] = cos(azimuth) * sin(swing) - sin(azimuth) * cos(tilt) * cos(
swing)
R[1, 1] = -sin(azimuth) * sin(swing) - cos(azimuth) * cos(tilt) * cos(
swing)
R[1, 2] = -sin(tilt) * cos(swing)
R[2, 0] = -sin(azimuth) * sin(tilt)
R[2, 1] = -cos(azimuth) * sin(tilt)
R[2, 2] = cos(tilt)
# Get "look at" vector for openGL pose
######################################
#Generate vectors in camera system
dirCam = array([0, 0, -focal])
upCam = array([0, -1, 0])
downCam = array([0, 1, 0])
#Rotate in the world system
dirWorld = dot(linalg.inv(R), dirCam.T)
lookat = array(dirWorld) + array([x0, y0, z0])
upWorld = dot(linalg.inv(R), upCam.T)
#not_awesome_vector = array([0,0,-focal])
#almost_awesome_vector = dot(linalg.inv(R),not_awesome_vector.T)
#awesome_vector = array(almost_awesome_vector)+array([x0,y0,z0])
return x, L1p, lookat, upWorld #awesome_vector
#!/usr/bin/env python3
from numpy import linalg
from numpy import matlib
from numpy import random
from numpy import matmul
from numpy import matrix
random.seed(1543)
amat = matlib.rand(10, 10)
bmat = linalg.inv(amat)
dmat = matrix.transpose(bmat)
cmat = matmul(amat, bmat)
def printmat(mat):
rows = mat.shape[0]
columns = mat.shape[1]
print(rows, columns)
for i in range(rows):
for j in range(columns):
print(mat.item((i, j)), end=" ")
print()
printmat(amat)
printmat(dmat)
import librosa
from python_speech_features import mfcc
import scipy.io.wavfile as wav
from pydub import AudioSegment
from numpy import matrix
from scipy.fftpack import dct
# Loading the audio from 30 to 35 secs in the 'y'
y, sr = librosa.load("./Tutorials/sample.wav", offset=30, duration=5.0)
onset_frames = librosa.onset.onset_detect(y=y, sr=sr)
actual_frames = librosa.frames_to_time(onset_frames, sr=sr)
# For getting the first onset from the audio
t1 = 30 * 1000 # start time
t2 = (30 + actual_frames[0]) * 1000 # end time
newAudio = AudioSegment.from_wav("./Tutorials/sample.wav")
newAudio = newAudio[t1:t2]
newAudio.export('./Tutorials/newSample.wav', format="wav")
# Getting the MFCC
(rate, sig) = wav.read("./Tutorials/newSample.wav")
mfcc_feat = matrix.transpose(
mfcc(signal=sig, samplerate=rate, nfft=2048, ceplifter=4))
# for getting the first 4 dct of the mfcc we obtained
# TODO: In paper it said that we get 52 dimensional vector. Check that???
mfcc_feat_dct = []
for mfcc_coeff in mfcc_feat:
mfcc_feat_dct.append(dct(x=mfcc_coeff, n=4))
iterations = 0
error = 0
for i in range(10000):
p = [(uniform(-1, 1), uniform(-1, 1)), (uniform(-1, 1), uniform(-1, 1))]
target = [
1, -(p[0][0] - p[1][0]) / (p[1][0] - p[1][1]),
-p[0][0] + (p[0][0] - p[1][0]) * p[1][0] / (p[1][0] - p[1][1])
]
N = [(uniform(-1, 1), uniform(-1, 1), 1) for i in range(10)]
classification = map(
y_function,
[(x[0] * target[0] + x[1] * target[1] + x[2] * target[2]) > 0
for x in N])
g = matrix.transpose(
matrix(pinv([list(n) for n in N])) *
matrix([[float(c)] for c in classification])).tolist()[0]
g_classification = map(y_function,
[(x[0] * g[0] + x[1] * g[1] + x[2] * g[2]) > 0
for x in N])
while g_classification != classification:
#print g
incorrect = [
p for p in N
if classification[N.index(p)] != g_classification[N.index(p)]
]
#print len(incorrect)
index = randrange(0, len(incorrect))
#print [classification[N.index(incorrect[index])] * x for x in incorrect[index]]
def LS(self,abscissa,observations,PARAM,x_fix,x_ini):
# The initial parameters are the ones from DLT but where the radio button is set as free
x = []
for i in range(9):
if PARAM[i]:
x.append(x_ini[i])
x = array(x)
# 2D coordinates are understood as observations
observations = array(observations)
# 3D coordinates are understood as the abscissas
abscissa = array(abscissa)
npoints = size(observations[:,1])
l_x = int(sum(PARAM));
sigmaobservationservation = 1
Kl = zeros(shape=(2*npoints,2*npoints))
# A error of "sigmaobservationservation" pixels is a priori set
for i in range (npoints):
Kl[2*i-1,2*i-1]=sigmaobservationservation**2
Kl[2*i,2*i]=sigmaobservationservation**2
# The P matrix is a weight matrix, useless if equal to identity (but can be used in some special cases)
P=linalg.pinv(Kl);
# A is the Jacobian matrix
A = zeros(shape=(2*npoints,l_x))
# H is the hessian matrix
H = zeros(shape=(l_x,l_x))
# b is a transition matrix
b = zeros(shape=(l_x))
# v contains the residual errors between observations and predictions
v = zeros(shape=(2*npoints))
# v_test contain the residual errors between observations and predictions after an update of H
v_test = zeros(shape=(2*npoints))
# x_test is the updated parameters after an update of H
x_test = zeros(shape=(l_x))
# dx is the update vector of x and x_test
dx = array([0.]*l_x)
it=-1;
maxit=1000;
# At least one iteration, dx > inc
dx[0]=1
# Lambda is the weightage parameter in Levenberg-marquart between the gradient and the gauss-newton parts.
Lambda = 0.01
# increment used for Jacobian and for convergence criterium
inc = 0.001
while (max(abs(dx))> inc) & (it<maxit):
#new iteration, parameters updates are greater than the convergence criterium
it=it+1;
# For each observations, we compute the derivative with respect to each parameter
# We form therefore the Jacobian matrix
for i in range(npoints):
#ubul and vbul are the prediction with current parameters
ubul, vbul = self.dircal(x,abscissa[i,:],x_fix,PARAM)
# The difference between the observation and prediction is used for parameters update
v[2*i-1]=observations[i,0]-ubul
v[2*i]=observations[i,1]-vbul
for j in range(l_x):
x_temp = copy(x);
x_temp[j] = x[j]+inc
u2, v2 = self.dircal(x_temp,abscissa[i,:],x_fix,PARAM)
A[2*i-1,j]= (u2-ubul)/inc
A[2*i,j]= (v2-vbul)/inc
# The sum of the square of residual (S0) must be as little as possible.
# That's why we speak of "least square"... tadadam !
S0 = sum(v**2);
H = dot(dot(matrix.transpose(A),P),A);
b = dot(dot(matrix.transpose(A),P),v);
try:
dx = dot(linalg.pinv(H+Lambda*diag(diag(H))),b);
x_test = x+dx;
except:
# The matrix is not always reversal.
# In this case, we don't accept the update and go for another iteration
S2 = S0
else:
for i in range(npoints):
# We check that the update has brought some good stuff in the pocket
# In other words, we check that the sum of square of less than before (better least square!)
utest, vtest = self.dircal(x_test,abscissa[i,:],x_fix,PARAM);
v_test[2*i-1]=observations[i,0]-utest;
v_test[2*i]=observations[i,1]-vtest;
S2 = sum(v_test**2);
# Check if sum of square is less
if S2<S0:
Lambda = Lambda/10
x = x + dx
else:
Lambda = Lambda*10
# Covariance matrix of parameters
self.Qxx = sqrt(diag(linalg.inv(dot(dot(matrix.transpose(A),P),A))))
p = zeros(shape=(len(PARAM)))
m = 0
n = 0
for k in range(len(PARAM)):
if PARAM[k]:
p[k] = x[m]
m = m+1
else:
p[k] = x_fix[n]
n = n+1
L1p = self.CoeftoMatrixProjection(p)
x0 = p[0];
y0 = p[1];
z0 = p[2];
tilt = p[3];
azimuth = p[4];
swing = p[5];
focal = p[6];
u0 = p[7];
v0 = p[8];
R = zeros((3,3))
R[0,0] = -cos(azimuth)*cos(swing)-sin(azimuth)*cos(tilt)*sin(swing)
R[0,1] = sin(azimuth)*cos(swing)-cos(azimuth)*cos(tilt)*sin(swing)
R[0,2] = -sin(tilt)*sin(swing)
R[1,0] = cos(azimuth)*sin(swing)-sin(azimuth)*cos(tilt)*cos(swing)
R[1,1] = -sin(azimuth)*sin(swing)-cos(azimuth)*cos(tilt)*cos(swing)
R[1,2] = -sin(tilt)*cos(swing)
R[2,0] = -sin(azimuth)*sin(tilt)
R[2,1] = -cos(azimuth)*sin(tilt)
R[2,2] = cos(tilt)
# Get "look at" vector for openGL pose
not_awesome_vector = array([0,0,-focal])
almost_awesome_vector = dot(linalg.inv(R),not_awesome_vector.T)
awesome_vector = array(almost_awesome_vector)+array([x0,y0,z0])
return x, L1p, awesome_vector
usecols = [0, 1],
dtype = {0: 'S30', 1: 'int'},
names = ['word', document],
header = None)
# merge with previous ones
y = pd.merge(y, y_i, on = 'word', how = 'outer')
# kill NaNs
y = y.fillna(0)
# choose prior
print ''
priorChoice = int(input('Uninformative (1) or informative (2) prior? '))
if priorChoice == 1:
alpha_i = m.transpose(m([0.01] * len(y)))
elif priorChoice == 2:
priors = pd.read_csv(rpath + 'corpus.csv', # load global frequencies
usecols = [0, 1],
names = ['word', 'gfreq'],
header = None)
y = pd.merge(y, priors, on = 'word', how = 'left') # merge w/ y
y = y.fillna(y['gfreq'].min()) # replace missing by argmin(alphas)
alpha_i = m.transpose(m(y.gfreq)) # extract alphas
del y['gfreq'] # clean up y
else:
sys.exit('Invalid choice')
# estimate p_i
yword = m.transpose(m(np.hstack((['word'], np.array(y.word))))) # word list
y_i = m(y.iloc[:, 1:])
def EoM(t,x):
'''
FLIGHT Equations of Motion
'''
global m
global Ixx
global Iyy
global Izz
global Ixz
global S
global b
global cBar
global CONHIS
global u
global tuHis
global deluHis
global uInc
global MODEL
global RUNNING
MODEL = 2
CONHIS = 1
RUNNING = 1
tuHis = array([0, 33, 67, 100])
deluHis = array(zeros(28)).reshape((4,7))
u = array([0,0,0,0,0,0,0]).reshape((7,1)).ravel()
print(f'tuHis = {tuHis}')
print(f'deluHis = {deluHis}')
print(f'u = {u}')
print(f'x = {x}')
if MODEL == 0:
from AeroModelAlpha import AeroModelAlpha as AeroModel
elif MODEL == 1:
from AeroModelMach import AeroModelMach as AeroModel
else:
from AeroModelUser import AeroModelUser as AeroModel
##### Event Function ####### ????????????????
############################
# Earth-to-Body-Axis Transformation Matrix
HEB = DCM(x[9],x[10],x[11])
# Atmospheric States
x[5] = min(x[5], 0) #Limit x[5] to <=0
(airDens,airPres,temp,soundSpeed) = Atoms(-x[5])
# Body-Axis Wind Field
windb = WindField(-x[5],x[9],x[10],x[11])
# Body-Axis Gravity Components
gb = matmul(HEB, array([0,0,9.80665]).reshape((3,1))).ravel()
print(f'windb = {windb}')
# Air-Relative Velocity Vector
x[0] = max(x[0],0) # Limit axial velocity to >= 0 m/s
Va = array([[x[0],x[1],x[2]]]).reshape(3,1).ravel() + windb
print(f'Va 1st part = {array([[x[0],x[1],x[2]]]).reshape(3,1).ravel()}')
print(f'windb.T = {matrix.transpose(windb)}')
print(f'Va = {Va}')
V = sqrt(matmul(matrix.transpose(Va), Va))
print(f'V = {V}')
alphar = arctan(Va[2]/abs(Va[0]))
#alphar = min(alphar, (pi/2 - 1e-6)) # Limit angle of attack to <= 90 deg
#alpha = 57.2957795 * float(alphar)
alpha = 57.2957795 * alphar
betar = arcsin(Va[1] / V)
beta = 57.2957795 * betar
Mach = V / soundSpeed
qbar = 0.5 * airDens * V**2
print(f'Mach = {Mach}')
# Incremental Flight Control Effects
if CONHIS >=1 and RUNNING ==1:
## uInc = array([])
uInc = interp(t, tuHis,deluHis[:, 0])
uInc = matrix.transpose(array(uInc)) # Transpose
uTotal = u + uInc
else:
uTotal = u
# Force and Moment Coefficients; Thrust
(CD,CL,CY,Cl,Cm,Cn,Thrust) = AeroModel(x,uTotal,Mach,alphar,betar,V)
print(f'CD = {CD}')
m = 4800
Ixx = 20950
Iyy=49675
Izz = 62525
Ixz = -1710
cBar = 3.03
b = 10
S = 27.77
lHT = 5.2
lVT = 3.9
StaticThrust = 49000
qbarS = qbar * S
CX = -CD * cos(alphar) + CL * sin(alphar) # Body-axis X coefficient
CZ = -CD * sin(alphar) - CL * cos(alphar) # Body-axis Z coefficient
# State Accelerations
Xb = (CX * qbarS + Thrust) / m
print(f'CX = {CX}')
print(f'qbarS = {qbarS}')
print(f'Thrust = {Thrust}')
Yb = CY * qbarS / m
Zb = CZ * qbarS / m
Lb = Cl * qbarS * b
Mb = Cm * qbarS * cBar
Nb = Cn * qbarS * b
nz = -Zb / 9.80665 # Normal load factor
# Dynamic Equations
xd1 = Xb + gb[0] + x[8] * x[1] - x[7] * x[2]
xd2 = Yb + gb[1] - x[8] * x[0] + x[6] * x[2]
xd3 = Zb + gb[2] + x[7] * x[0] - x[6] * x[1]
print(f'Xb = {Xb}')
print(f'gb[0] = {gb[0]}')
print(f'xd1 = {xd1}')
# xd1 = xd1[0][0]
# xd2 = xd2[0][0]
# xd3 = xd3[0][0]
HEB_T = matrix.transpose(HEB)
y = matmul(HEB_T, array([x[0], x[1], x[2]]))
#HEB_T = matrix.transpose(HEB)
#y = matmul(HEB_T, (array(x[0],x[1],x[2]))
xd4 = y[0]
xd5 = y[1]
xd6 = y[2]
xd7 = ((Izz * Lb + Ixz * Nb - (Ixz * (Iyy - Ixx - Izz) * x[6] + (Ixz**2 + Izz * (Izz - Iyy)) * x[8]) * x[7]) / (Ixx * Izz - Ixz**2))
xd8 = ((Mb - (Ixx - Izz) * x[6] * x[8] - Ixz * (x[6]**2 - x[8]**2)) / Iyy)
xd9 = ((Ixz * Lb + Ixx * Nb + (Ixz * (Iyy - Ixx - Izz) * x[8] + (Ixz**2 + Ixx * (Ixx - Iyy)) * x[6]) * x[7]) / (Ixx * Izz - Ixz**2))
# xd7 = xd7[0][0]
# xd8 = xd8[0][0]
# xd9 = xd9[0][0]
cosPitch = cos(x[10])
if abs(cosPitch) <= 0.00001:
cosPitch = 0.00001 * (abs(cosPitch)/cosPitch) # sign(cosPitch) == (abs(cosPitch)/cosPitch) for python
tanPitch = sin(x[10]) / cosPitch
xd10 = x[6] + (sin(x[9]) * x[7] + cos(x[9]) * x[8]) * tanPitch
xd11 = cos(x[9]) * x[7] - sin(x[9]) * x[8]
xd12 = (sin(x[9]) * x[7] + cos(x[9]) * x[8]) / cosPitch
xdot = array([xd1,xd2,xd3,xd4,xd5,xd6,xd7,xd8,xd9,xd10,xd11,xd12])
for i in range(1,13):
print(f'xd{str(i)} = {xdot[i-1]} ')
return xdot
I = []
for i in range(len(M[0])):
row = []
for j in range(len(M[0])):
if i == j:
row.append(1.0)
else:
row.append(0.0)
I.append(row)
I = matrix(I)
print (M.transpose()*M).diagonal(0)
print (M.transpose()*M+(float(10**k)*I)).diagonal(0)
g = (pinv(M.transpose()*M+(float(10**k)*I))*M.transpose()*matrix([[float(c)] for c in classification])).transpose()
print g
g_classification = matrix(map(y_function2, [g*matrix.transpose(matrix(m)) for m in M]))
errors = [x != t for (x,t) in zip(g_classification.tolist()[0], classification)]
for e in errors:
if e:
in_error += 1
in_error /= float(len(errors))
print in_error
N = []
classification = []
for line in out_sample:
x1,x2,y = map(lambda x: float(x), line.split())
N.append([1,x1,x2])
2: "linear-sinusoidal regression",
3: "exponential regression"
}
##
x_t = np.arange(1, train + 1, 1)
x_t = [x_t, np.copy(x_t), np.copy(x_t), np.copy(x_t)]
##
x_t[0] = np.array([np.ones(train), x_t[0]])
x_t[1] = np.array([np.ones(train), x_t[1], x_t[1]**2])
x_t[2] = np.array([np.ones(train), x_t[2], np.sin(2 * ma.pi / 500 * x_t[2])])
x_t[3] = np.array([np.ones(train), x_t[3]])
## calculation
product = [np.ones(train), np.ones(train), np.ones(train), np.ones(train)]
for i in range(4):
product[i] = np.copy(x_t[i])
product[i] = np.matmul(product[i], mt.transpose(product[i]))
product[i] = la.inv(product[i])
product[i] = np.matmul(product[i], x_t[i])
product[i] = np.matmul(
product[i],
(np.log(mt.transpose(head)) if (i == 3) else
mt.transpose(head))) # exponential must fit the logarithm of records
# %%
product
# %% [markdown]
# ### plotting whole records and regression points through whole domain
# %%
domain = np.arange(1., train + 11, 1)
def y_function(b):
if b:
return 1
else:
return -1
iterations = 0
error = 0
for i in range(10000):
p = [(uniform(-1,1), uniform(-1,1)), (uniform(-1,1), uniform(-1,1))]
target = [1, -(p[0][0]-p[1][0])/(p[1][0]-p[1][1]), -p[0][0]+(p[0][0]-p[1][0])*p[1][0]/(p[1][0]-p[1][1])]
N = [(uniform(-1,1),uniform(-1,1),1) for i in range(10)]
classification = map(y_function, [(x[0]*target[0] + x[1]*target[1] + x[2]*target[2]) > 0 for x in N])
g = matrix.transpose(matrix(pinv([list(n) for n in N]))*matrix([[float(c)] for c in classification])).tolist()[0]
g_classification = map(y_function, [(x[0]*g[0] + x[1]*g[1] + x[2]*g[2]) > 0 for x in N])
while g_classification != classification:
#print g
incorrect = [p for p in N if classification[N.index(p)] != g_classification[N.index(p)]]
#print len(incorrect)
index = randrange(0,len(incorrect))
#print [classification[N.index(incorrect[index])] * x for x in incorrect[index]]
g = [p[0] + p[1] for p in zip(g, [classification[N.index(incorrect[index])] * x for x in incorrect[index]])]
g_classification = map(y_function, [(x[0]*g[0] + x[1]*g[1] + x[2]*g[2]) > 0 for x in N])
iterations += 1
#print classification[N.index(incorrect[index])]
#print incorrect[index], N.index(incorrect[index])
#print classification, g_classification