def samples(d, n): # generate a sequence of unit length vector pairs
s = []
for i in range(0, n):
x1 = mat.randn((d, 1))
x2 = mat.randn((d, 1))
s.append((x1 / linalg.norm(x1), x2 / linalg.norm(x2)))
return s
def create_gaussian_particles(mean, std, N):
particles = np.empty((N, 5))
# angle
particles[:, 0] = mean[2] + (randn(N) * std[2])
# lv
particles[:, 1] = 11 + (randn(N) * 5.5)
# rv
particles[:, 2] = 11 + (randn(N) * 5.5)
# x
particles[:, 3] = mean[0] + (randn(N) * std[0])
# y
particles[:, 4] = mean[1] + (randn(N) * std[1])
particles[:, 0] %= 2 * np.pi
return particles
def init_subpopulations(self):
# Main excitatory subpopulation
self.e_size=int(self.params.network_group_size*.8)
self.group_e=self.subgroup(self.e_size)
self.group_e.C=self.pyr_params.C
self.group_e.gL=self.pyr_params.gL
self.group_e._refractory_time=self.pyr_params.refractory
# Main inhibitory subpopulation
self.i_size=int(self.params.network_group_size*.2)
self.group_i=self.subgroup(self.i_size)
self.group_i.C=self.inh_params.C
self.group_i.gL=self.inh_params.gL
self.group_i._refractory_time=self.inh_params.refractory
# Input-specific sub-subpopulations
self.groups_e=[]
for i in range(self.params.num_groups):
subgroup_e=self.group_e.subgroup(int(self.params.f*self.e_size))
self.groups_e.append(subgroup_e)
self.ns_e=self.group_e.subgroup(self.e_size-(self.params.num_groups*int(self.params.f*self.e_size)))
# Initialize state variables
self.vm = self.params.EL+randn(self.params.network_group_size)*mV
self.group_e.g_ampa_b = rand(self.e_size)*self.pyr_params.w_ampa_ext_correct*2.0
self.group_e.g_nmda = rand(self.e_size)*self.pyr_params.w_nmda*2.0
self.group_e.g_gaba_a = rand(self.e_size)*self.pyr_params.w_gaba*2.0
self.group_i.g_ampa_r = rand(self.i_size)*self.inh_params.w_ampa_rec*2.0
self.group_i.g_ampa_b = rand(self.i_size)*self.inh_params.w_ampa_bak*2.0
self.group_i.g_nmda = rand(self.i_size)*self.inh_params.w_nmda*2.0
self.group_i.g_gaba_a = rand(self.i_size)*self.inh_params.w_gaba*2.0
def testDownloadConsituentsGrabsData(self):
self.market.downloader.get = Mock()
self.market.downloader.get.return_value = DataFrame(randn(2, 1))
calls = [call(ticker + ".AX", self.start_date, self.end_date) for ticker in self.tickers]
self.market.download_data()
self.market.downloader.get.assert_has_calls(calls)
self.assertSetEqual(set(self.tickers), set(self.market.instruments.keys()))
def __init__(self, *args):
if len(args) < 2:
raise TypeError("__init__() missing 2 required positional arguments: 'n_X' and 'n_y'")
self._n = args
self._Theta = []
for i in range(len(args) - 1):
self._Theta.append(matlib.randn((args[i] + 1, args[i + 1])))
def __init__(self, dim):
self.num_tables = 2
self.hash_size = 8
if setup:
for i in range(self.num_tables):
projections = matlib.randn(self.hash_size, dim)
SQL.insert_table_data(db_conn, i, projections.tostring(), self.hash_size)
def awgn(image, sigma):
# image = cv2.cvtColor(image, cv2.COLOR_RGB2GRAY)
image = np.asarray(image).astype('double')
shape = image.shape
noise_map = randn(shape[0], shape[1])
noise = sigma * noise_map
noise_image = image + noise
return noise_image
def test_calc_correlation(self):
quotes = self.get_quotes()
rho = calc_correlation(quotes)
self.assertEqual(rho.shape, (1, 1))
self.assertEqual(list(rho.flat), [1])
return
rho = calc_correlation(quotes, quotes)
self.assertEqual(rho.shape, (2, 2))
self.assertEqual(list(rho.flat), [1, 1, 1, 1])
rho = calc_correlation(quotes, quotes, quotes)
self.assertEqual(rho.shape, (3, 3))
self.assertEqual(list(rho.flat), [1, 1, 1, 1, 1, 1, 1, 1, 1])
rho = calc_correlation(quotes, list(map(lambda x: -x, quotes)))
self.assertEqual(rho.shape, (2, 2))
self.assertEqual(list(rho.flat), [1, -1, -1, 1])
scipy.random.seed(12345)
a = list(randn(20000).flat)
b = list(randn(20000).flat)
c = list(randn(20000).flat)
rho = calc_correlation(a, b)
self.assertEqual(rho.shape, (2, 2))
self.assertAlmostEqual(rho[0][0], 1, places=1)
self.assertAlmostEqual(rho[0][1], 0, places=1)
self.assertAlmostEqual(rho[1][0], 0, places=1)
self.assertAlmostEqual(rho[1][1], 1, places=1)
rho = calc_correlation(a, b, c)
self.assertEqual(rho.shape, (3, 3))
self.assertAlmostEqual(rho[0][0], 1, places=1)
self.assertAlmostEqual(rho[0][1], 0, places=1)
self.assertAlmostEqual(rho[0][2], 0, places=1)
self.assertAlmostEqual(rho[1][0], 0, places=1)
self.assertAlmostEqual(rho[1][1], 1, places=1)
self.assertAlmostEqual(rho[1][2], 0, places=1)
self.assertAlmostEqual(rho[2][0], 0, places=1)
self.assertAlmostEqual(rho[2][1], 0, places=1)
self.assertAlmostEqual(rho[2][2], 1, places=1)
def testDownloadConsituentsGrabsData(self):
self.market.downloader.get = Mock()
self.market.downloader.get.return_value = DataFrame(randn(2, 1))
calls = [
call(ticker + ".AX", self.start_date, self.end_date)
for ticker in self.tickers
]
self.market.download_data()
self.market.downloader.get.assert_has_calls(calls)
self.assertSetEqual(set(self.tickers),
set(self.market.instruments.keys()))
def gaussian_orthogonal_kernel(deg):
n = 2**deg
rows = []
for i in range(0, n):
x = mat.randn(n, 1)
x = x / linalg.norm(x)
p = mat.zeros((1, n))
for r in rows:
p += (r * x) * r
y = np.transpose(x) - p
y = y / linalg.norm(y)
rows.append(y)
return np.concatenate(rows)
def predict(particles, u, std, dt):
""" move according to control input u (heading change, velocity)
with noise Q (std heading change, std velocity)`"""
(vl, vr) = u
R = wheel_base_half * (vl + vr) / (vr - vl)
wt = (vr - vl) / (wheel_base_half * 2) * dt
ICCx = particles[:, 3] - R * np.sin(particles[:, 0])
ICCy = particles[:, 4] + R * np.cos(particles[:, 0])
particles[:, 3] = np.cos(wt) * (particles[:, 3] - ICCx) - np.sin(wt) * (
particles[:, 4] - ICCy) + ICCx
particles[:, 4] = np.sin(wt) * (particles[:, 3] - ICCx) + np.cos(wt) * (
particles[:, 4] - ICCy) + ICCy
N = len(particles)
# update heading
particles[:, 0] += wt
# particles[:, 0] %= 2 * np.pi
# TODO
# move in the (noisy) commanded direction
particles[:, 1] = vr + (randn(N) * 5)
particles[:, 2] = vl + (randn(N) * 5)
def Path(self, timeline, nb_path):
dsigmas = 0.5 * self.Vol**2
adjused_drift = (self.Drift - dsigmas)
T = len(timeline)
L = zeros([nb_path, T])
W = array(randn((nb_path, T)))
L[:, 0] = log(
self.InitialValue) + adjused_drift * timeline[0] + self.Vol * sqrt(
timeline[0]) * W[:, 0]
for t in range(1, T):
delta = timeline[t] - timeline[t - 1]
L[:,
t] = L[:, t -
1] + adjused_drift * delta + self.Vol * sqrt(delta) * W[:,
t]
return exp(L)
def init_subpopulations(self):
# Main excitatory subpopulation
self.e_size = int(self.params.network_group_size * .8)
self.group_e = self.subgroup(self.e_size)
self.group_e.C = self.pyr_params.C
self.group_e.gL = self.pyr_params.gL
self.group_e._refractory_time = self.pyr_params.refractory
# Main inhibitory subpopulation
self.i_size = int(self.params.network_group_size * .2)
self.group_i = self.subgroup(self.i_size)
self.group_i.C = self.inh_params.C
self.group_i.gL = self.inh_params.gL
self.group_i._refractory_time = self.inh_params.refractory
# Input-specific sub-subpopulations
self.groups_e = []
for i in range(self.params.num_groups):
subgroup_e = self.group_e.subgroup(int(self.params.f *
self.e_size))
self.groups_e.append(subgroup_e)
# Initialize state variables
self.vm = self.params.EL + randn(self.params.network_group_size) * mV
self.group_e.g_ampa_b = rand(
self.e_size) * self.pyr_params.w_ampa_ext_correct * 2.0
self.group_e.g_nmda = rand(self.e_size) * self.pyr_params.w_nmda * 2.0
self.group_e.g_gaba_a = rand(
self.e_size) * self.pyr_params.w_gaba * 2.0
self.group_i.g_ampa_r = rand(
self.i_size) * self.inh_params.w_ampa_rec * 2.0
self.group_i.g_ampa_b = rand(
self.i_size) * self.inh_params.w_ampa_ext * 2.0
#self.group_i.g_nmda = self.inh_params.w_nmda*100.0+10.0*nS*randn(self.i_size)
self.group_i.g_nmda = rand(self.i_size) * self.inh_params.w_nmda * 2.0
self.group_i.g_gaba_a = rand(
self.i_size) * self.inh_params.w_gaba * 2.0
arr = np.arange(32).reshape((8, 4))
print("np.arange(32).reshape((8, 4)):")
print(arr)
print(arr[[1, 5, 7, 2], [0, 3, 1, 2]]) #[ 4 23 29 10]
print(" 输出矩阵转置: ")
arr = np.arange(15).reshape((3, 5))
print(arr.T)
print("输出np.arange(10)：")
arr = np.arange(10)
print(arr)
print("输出np.sqrt(arr)：")
print(np.sqrt(arr)) #仍是一维数组，求数组中的每个元素求平方根
print("输出np.exp(arr))：")
print(np.exp(arr)) #仍是一维数组，求以e为底，数组中的每个元素作为指数的值
print("randn(8):")
x = randn(8) #生成8个随机数
print(x)
print("randn(8):")
y = randn(8)
print(y)
print(np.maximum(x, y)) #仍是一维数组，每个元素为数组x和y对应元素最大的那个；
print("-------------------------------------")
xarr = np.array([1.1, 1.2, 1.3, 1.4, 1.5])
yarr = np.array([2.1, 2.2, 2.3, 2.4, 2.5])
cond = np.array([True, False, True, True, False])
result = np.where(cond, xarr, yarr)
print(result) #输出：[1.1 2.2 1.3 1.4 2.5]
print("-------------------------------------")
arr = randn(4, 4)
print(arr)
print(np.where(arr > 0, 2, -2))
def buildNumericDataFrame(columns, length):
index = date_range("1/1/2010", periods = length, freq = "D")
return DataFrame(randn(length, len(columns)), index = index, columns = columns)
import math
import numpy as np
import numpy.matlib as nm
import matplotlib.pyplot as plt
n = 100
u = nm.randn(n, 1) / 4 + 2
x = nm.randn(n, 1) / 2 + 1
w = 2 * nm.exp(-8 * np.power((x - 2), 2) + 2 * np.power((x - 1), 2))
y = nm.sin(nm.pi * x) / (nm.pi * x) + 0.1 * nm.randn(n, 1)
x2 = np.ones(len(x)).reshape(len(x), 1) # 生成一个维度为（n，1），元素全是1的数组
x = np.c_[x, x2] # x(:,2)=1;加第二行为1
t1 = np.multiply(nm.repmat(w, 1, 2), x) # np.multiply为矩阵对应元素相乘
t = np.linalg.inv(x.T * t1) * (x.T *
(np.multiply(w, y))) # np.linalg.inv(.)求逆矩阵
X = nm.linspace(-1, 3, 100) # 生成数据节点
Y = nm.sin(nm.pi * X) / (nm.pi * X) # 根据节点计算Y
u = np.c_[u, x2]
v = u * t
print(u.shape)
plt.figure()
plt.plot(x[:, 0], y, 'bo', label='xi,yi') # 绘制原始数据点
plt.plot(X, Y, 'r-', label='f(x)') # 绘制重要度加权的最小二乘曲线
plt.plot(u[:, 0], v, 'kx', label='xi1,yi1') # 绘制最小二乘曲线
plt.legend() # 显示绘制的legend
plt.show() # 显示绘制的画布
def run_pf1(N,
sensor_std_err=1,
do_plot=True,
plot_particles=False,
xlim=(-10, 40),
ylim=(0, 140),
initial_x=None,
vl=None,
vr=None,
t=None,
angle=None,
dist=None):
landmarks = np.array([[0, 10, 10], [0.1, 5, 15], [-0.1, 15, 5],
[0.3, 10, 15], [-1, 15, 15]])
NL = len(landmarks)
iters = len(t)
plt.figure()
# create particles and weights
if initial_x is not None:
particles = create_gaussian_particles(mean=initial_x,
std=(5, 5, np.pi / 4),
N=N)
else:
particles = create_uniform_particles((0, 20), (0, 20), (0, 6.28), N)
weights = np.zeros(N)
if plot_particles:
alpha = .20
if N > 5000:
alpha *= np.sqrt(5000) / np.sqrt(N)
plt.scatter(particles[:, 3], particles[:, 4], alpha=alpha, color='g')
xs = []
robot_pos = np.array([0., 0., 13.8])
x = 0
y = 0
for i in range(1, iters):
# TODO
# robot_pos += (1, 1)
dt = t[i] - t[i - 1]
robot_pos = (angle[i - 1], vl[i - 1], vr[i - 1])
# landmarks = np.array([robot_pos])
# distance from robot to each landmark
zs = (norm(landmarks - robot_pos) + (randn(NL) * sensor_std_err))
# move diagonally forward to (x+1, x+1)
predict(particles, u=(0.00, 1.414), std=(.2, .05), dt=dt)
# incorporate measurements
update(particles, weights, z=zs, R=sensor_std_err, landmarks=landmarks)
# resample if too few effective particles
if neff(weights) < N / 2:
indexes = systematic_resample(weights)
resample_from_index(particles, weights, indexes)
mu, var = estimate(particles, weights)
xs.append(mu)
if plot_particles:
plt.scatter(particles[:, 0],
particles[:, 2],
color='k',
marker=',',
s=1)
p1 = plt.scatter(robot_pos[1],
robot_pos[2],
marker='',
color='k',
s=180,
lw=3)
p2 = plt.scatter(mu[0], mu[1], marker='s', color='r')
# xs = np.array(xs)
# plt.plot(xs[:, 0], xs[:, 1])
plt.legend([p1, p2], ['Actual', 'PF'], loc=4, numpoints=1)
# plt.xlim(*xlim)
# plt.ylim(*ylim)
# print('final position error, variance:\n\t', mu - np.array([iters, iters]), var)
plt.show()
def __init__(self, n_X, n_RBF, n_y):
self._n_X = n_X
self._n_RBF = n_RBF
self._n_y = n_y
self._Theta1 = matlib.randn((n_RBF, n_X))
self._Theta2 = matlib.randn((n_RBF + 1, n_y))
# -*- encoding: utf-8 -*-
"""
4.6.1 创建矩阵
"""
import numpy as np
import numpy.matlib as mat
print(np.mat([[1, 2, 3], [4, 5, 6]], dtype=np.int)) # 使用列表创建矩阵
print(np.mat(np.arange(6).reshape((2, 3)))) # 使用数组创建矩阵
print(np.mat('1 4 7; 2 5 8; 3 6 9')) # 使用Matlab风格的字符串创建矩阵
print(mat.zeros((2, 3))) # 全0矩阵
print(mat.ones((2, 3))) # 全1矩阵
print(mat.eye(3)) # 单位矩阵
print(mat.empty((2, 3))) # 空矩阵
print(mat.rand((2, 3))) # [0,1)区间随机数矩阵
print(mat.randn((2, 3))) # 均值0方差1的高斯（正态）分布矩阵
def buildNumericDataFrame(columns, length):
index = date_range("1/1/2010", periods=length, freq="D")
return DataFrame(randn(length, len(columns)), index=index, columns=columns)
def ci_bootstrapping_method(self):
print("-------2.2.2 Use Bootstrap method--------")
B = 1000
sigma = 0.05
print("Using confidance level: ", sigma)
lower_bound_rate = sigma / 2
higher_bound_rate = 1 - lower_bound_rate
lower_bound = int(lower_bound_rate * B)
higher_bound = int(higher_bound_rate * B)
beta_set = []
alpha_set = []
beta_t_set = []
alpha_t_set = []
ret_len = len(self.cc_return_index)
y = list(self.cc_return_single_stock)
X = np.array(self.cc_return_index).reshape(ret_len, 1)
alpha = self.alpha
beta = self.beta
y_mean = np.mean(y)
y_var = np.var(y)
y_std = np.std(y)
sample_mean = np.mean(X)
sample_var = np.var(X)
sample_std = np.std(X)
se_alpha = y_var * ((1 / ret_len) + (sample_mean**2) /
(ret_len * sample_var))
se_beta = y_var * (1 / (ret_len * sample_var))
# Non-parametric bootstrap
print("-------2.2.2.1 Use Non-parametric Bootstrap method--------")
beta_set.clear()
alpha_set.clear()
beta_t_set.clear()
alpha_t_set.clear()
for i in range(B):
rs_idx = [random.randint(0, ret_len - 1) for _ in range(ret_len)]
rs_X = X[rs_idx]
rs_y = np.array(y)[rs_idx]
rs_y_var = np.var(rs_y)
rs_model = linear_model.LinearRegression()
rs_model.fit(rs_X, rs_y)
rs_beta = rs_model.coef_
rs_alpha = rs_model.intercept_
rs_mean = np.mean(rs_X)
rs_var = np.var(rs_X)
rs_se_alpha = rs_y_var * ((1 / ret_len) + ((rs_mean**2) /
(ret_len * rs_var)))
rs_se_beta = rs_y_var * (1 / (ret_len * rs_var))
rs_alpha_t = (rs_alpha - alpha) / rs_se_alpha
rs_beta_t = (rs_beta - beta) / rs_se_beta
beta_set.append(rs_beta)
alpha_set.append(rs_alpha)
alpha_t_set.append(rs_alpha_t)
beta_t_set.append(rs_beta_t)
beta_set.sort()
alpha_t_set.sort()
beta_t_set.sort()
# non-parametric bootstrap percentile method
print(
"------2.2.2.1.1 Use non-parametric bootstrap percentile method-------"
)
print("Alpha CI:")
print(alpha_set[lower_bound], alpha_set[higher_bound])
print("Beta CI:")
print(beta_set[lower_bound], beta_set[higher_bound])
self.ci_non_para_bs_percentile_alpha_l = alpha_set[lower_bound]
self.ci_non_para_bs_percentile_alpha_h = alpha_set[higher_bound]
self.ci_non_para_bs_percentile_beta_l = beta_set[lower_bound]
self.ci_non_para_bs_percentile_beta_h = beta_set[higher_bound]
# non-parametric bootstrap t method
print("------2.2.2.1.2 Use non-parametric bootstrap t method-------")
print("Alpha CI:")
print(alpha - alpha_t_set[higher_bound] * se_alpha,
alpha - alpha_t_set[lower_bound] * se_alpha)
print("Beta CI:")
print(beta - beta_t_set[higher_bound] * se_beta,
beta - beta_t_set[lower_bound] * se_beta)
self.ci_non_para_bs_t_alpha_l = alpha - alpha_t_set[
higher_bound] * se_alpha
self.ci_non_para_bs_t_alpha_h = alpha - alpha_t_set[
lower_bound] * se_alpha
self.ci_non_para_bs_t_beta_l = beta - beta_t_set[higher_bound] * se_beta
self.ci_non_para_bs_t_beta_h = beta - beta_t_set[lower_bound] * se_beta
# Parameter bootstrap
print("----------2.2.2.2 Use parametric bootstrap method-----------")
beta_set.clear()
alpha_set.clear()
beta_t_set.clear()
alpha_t_set.clear()
para_x_samples = sample_std * matlib.randn((B, ret_len)) + sample_mean
para_eps_samples = y_std * matlib.randn((B, ret_len)) + y_mean
para_y_samples = beta[0] * para_x_samples + alpha + para_eps_samples
for i in range(B):
rs_y = para_y_samples[i].reshape((-1, 1))
rs_X = np.array(para_x_samples[i]).reshape(ret_len, 1)
rs_y_var = np.var(rs_y)
rs_model = linear_model.LinearRegression()
rs_model.fit(rs_X, rs_y)
rs_beta = rs_model.coef_
rs_alpha = rs_model.intercept_
rs_mean = np.mean(rs_X)
rs_std = np.std(rs_X)
rs_var = np.var(rs_X)
rs_se_alpha = rs_y_var * ((1 / ret_len) + ((rs_mean**2) /
(ret_len * rs_var)))
rs_se_beta = rs_y_var * (1 / (ret_len * rs_var))
rs_alpha_t = (rs_alpha - alpha) / rs_se_alpha
rs_beta_t = (rs_beta - beta) / rs_se_beta
beta_set.append(rs_beta)
alpha_set.append(rs_alpha)
alpha_t_set.append(rs_alpha_t)
beta_t_set.append(rs_beta_t)
alpha_set.sort()
beta_set.sort()
alpha_t_set.sort()
beta_t_set.sort()
# Parametric bootstrap method - percentile method
print(
"--------2.2.2.2.1 Use parametric bootstrap method - percentile method----------"
)
print("Alpha CI:")
print(alpha_set[lower_bound], alpha_set[higher_bound])
print("Beta CI:")
print(beta_set[lower_bound], beta_set[higher_bound])
self.ci_para_bs_percentile_alpha_l = alpha_set[lower_bound]
self.ci_para_bs_percentile_alpha_h = alpha_set[higher_bound]
self.ci_para_bs_percentile_beta_l = beta_set[lower_bound]
self.ci_para_bs_percentile_beta_h = beta_set[higher_bound]
# Parametric bootstrap method - t method
print(
"---------2.2.2.2.2 Use parametric bootstrap method - t method----------"
)
print("Alpha CI:")
print(alpha - alpha_t_set[higher_bound] * se_alpha,\
alpha - alpha_t_set[lower_bound] * se_alpha)
print("Beta CI:")
print(beta - beta_t_set[higher_bound] * se_beta,\
beta - beta_t_set[lower_bound] * se_beta)
self.ci_para_bs_t_alpha_l = alpha - alpha_t_set[higher_bound] * se_alpha
self.ci_para_bs_t_alpha_h = alpha - alpha_t_set[lower_bound] * se_alpha
self.ci_para_bs_t_beta_l = beta - beta_t_set[higher_bound] * se_beta
self.ci_para_bs_t_beta_h = beta - beta_t_set[lower_bound] * se_beta
# parametric bootstrap method - SEboot method
# calculate SEboot using resampling
print(
"---------2.2.2.2.3 Use parametric bootstrap method - SEboot method----------"
)
se_boot_alpha = (sum([(i - np.mean(alpha_set))**2
for i in alpha_set]) / (B - 1))**0.5
se_boot_beta = (sum([(i - np.mean(beta_set))**2
for i in beta_set]) / (B - 1))**0.5
print("----置信区间 95% using +/- 2 * SE")
print("Alpha CI:")
print(alpha - 2 * se_boot_alpha, alpha + 2 * se_boot_alpha)
print("Beta CI:")
print(beta - 2 * se_boot_beta, beta + 2 * se_boot_beta)
self.ci_para_bs_se_alpha_l = alpha - 2 * se_boot_alpha
self.ci_para_bs_se_alpha_h = alpha + 2 * se_boot_alpha
self.ci_para_bs_se_beta_l = beta - 2 * se_boot_beta
self.ci_para_bs_se_beta_h = beta + 2 * se_boot_beta
#Indexing with slices print(arr[1:6]) print(arr2d) print(arr2d[:2]) print(arr2d[:2, 1:]) print(arr2d[1, :2]) print(arr2d[2, :1]) print(arr2d[:, :1]) #Boolean Indexing names = np.array(['Bob', 'Joe', 'Will', 'Bob', 'Will', 'Joe', 'Joe']) data = randn(7, 4) print(names == 'Bob') print(data[names == 'Bob']) print(data[names == 'Bob', 2:]) print(data[names == 'Bob', 3]) print(names != 'Bob') print(data[-(names == 'Bob')]) mask = (names == 'Bob') | (names == 'Will') print(mask) print(data[mask])
def test_suite_1():
n1 = 100
n2 = 100
n = n1+n2
d = 5
eta = .1
degree = 3
iterations = 1
results = mat.zeros((8,5))
times = mat.zeros((1,5))
sigma = 2
# 1st col is non-kernelized
# 2nd col is poly-kernel
for itr in xrange(iterations):
X = mat.randn(n1,d)
Phi_X = poly.phi(X, degree)
D0 = X + mat.rand(n2,d) / 1000
# Verify identity K(X,X) = 1
D1 = mat.randn(n2,d)
# How does kernel perform iid data
D2 = mat.rand(n2,d)
# Uniform rather than normal distribution
D3 = mat.randn(n2,d) * 2 + 2
# Linear transformation
D4 = mat.power(mat.randn(n2,d) + 1 ,3)
#Non-linear transformation
D5 = mat.power(X+1,3)
#non-linear transformation of the D0 dataset;
D6 = mat.rand(n2,d)/100 + mat.eye(n2,d)
#Totally different data - should have low similarity
D7 = mat.rand(n2,d)/100 + mat.eye(n2,d)*5
# Scaled version of D7
Data = [D0, D1, D2, D3, D4, D5, D6, D7]
for idx in xrange(8):
D = Data[idx]
start = time.time()
results[idx, 0] += nk_bhatta(X, D, 0)
nk = time.time()
emp = time.time()
results[idx, 1] += Bhattacharrya(X,D,gaussk(sigma),eta,5)
e5 = time.time()
results[idx, 2] += Bhattacharrya(X,D,gaussk(sigma),eta,15)
e15 = time.time()
results[idx, 3] += Bhattacharrya(X,D,gaussk(sigma),eta,25)
e25 = time.time()
nktime = nk-start
emptime = emp-nk
e5time = e5-emp
e15time = e15-e5
e25time = e25-e15
print "nk: {:.1f}, emp: {:.1f}, e5: {:.1f}, e15: {:.1f}, e25: {:.1f}".format(nktime, emptime, e5time, e15time, e25time)
times[0,0]+= nktime
times[0,4]+= emptime
times[0,1]+= e5time
times[0,2]+= e15time
times[0,3]+= e25time
np.save('some_array',arr)
arr = np.load('some_array.npy')
print(arr)
###############################################################
np.savez('array_archive.npz', a=arr, b=arr)
arch = np.load('array_archive.npz')
print(arch['b'])
print('\n')
###############################################################
arr = randn(100)
np.savetxt('array_ex.txt',arr, delimiter=',')
arrtxt = np.loadtxt('array_ex.txt',delimiter=',')
print(arrtxt)
print('\n')
###############################################################
x = np.array([[1.,2.,3.],[4.,5.,6.]])
y = np.array([[6.,23.],[-1,7],[8,9]])
print(x)
print(y)
print('\n')
import numpy as np
from numpy.matlib import randn
arr = randn(4, 4)
print(arr)
# 将>0的数赋为2，否则 = -2
print(np.where(arr > 0, 2, -2))
# 将>0的数赋为2，否则 为原值
print(np.where(arr > 0, 2, arr))
if __name__ == '__main__':
pass
import numpy as np
import numpy.matlib as matlib
from numpy import *
import matplotlib.pyplot as plt
import random
Num = 100
x_data = np.linspace(-3, 3, Num)
x_datawithPi = x_data * pi
s = matlib.randn(Num)
print(x_data.shape)
newb = s.flatten()
s = np.ravel(newb)
Y_data = np.sin(x_datawithPi) / x_datawithPi + 0.1 * x_data + 0.05 * s
print(Y_data)
plt.scatter(x_data, Y_data, color="black", linewidth=2)
plt.xlim(-3, 3)
plt.ylim(-2, 2)
plt.show()
data = vstack((x_data, Y_data))
savetxt("Validation\LinearModeValidation\eye.txt", data.transpose())
def testDownloadsConstituentsUpdatesStatus(self):
self.market.downloader.get = Mock()
self.market.downloader.get.return_value = DataFrame(randn(2, 1))
self.market.download_data()
expected_status = dict(zip(self.tickers, [True] * len(self.tickers)))
self.assertEqual(self.market.status, expected_status)
def learn_perceptron(neg_examples_nobias, pos_examples_nobias, w_init,
w_gen_feas):
"""
%%
% Learns the weights of a perceptron for a 2-dimensional dataset and plots
% the perceptron at each iteration where an iteration is defined as one
% full pass through the data. If a generously feasible weight vector
% is provided then the visualization will also show the distance
% of the learned weight vectors to the generously feasible weight vector.
% Required Inputs:
% neg_examples_nobias - The num_neg_examples x 2 matrix for the examples with target 0.
% num_neg_examples is the number of examples for the negative class.
% pos_examples_nobias - The num_pos_examples x 2 matrix for the examples with target 1.
% num_pos_examples is the number of examples for the positive class.
% w_init - A 3-dimensional initial weight vector. The last element is the bias.
% w_gen_feas - A generously feasible weight vector.
% Returns:
% w - The learned weight vector.
%%
"""
#%Bookkeeping
#% Size(vector, [dimension requried]) - get size of first dimension (rows)
#num_neg_examples = size(neg_examples_nobias,1);
num_neg_examples = neg_examples_nobias.shape[0]
#num_pos_examples = size(pos_examples_nobias,1);
num_pos_examples = pos_examples_nobias.shape[0]
num_err_history = []
# should be array?
w_dist_history = []
# should be array?
#%Here we add a column of ones to the examples in order to allow us to learn
#%bias parameters
#% Ones(rows, cols)
#neg_examples = [neg_examples_nobias,ones(num_neg_examples,1)];
neg_examples = c_[neg_examples_nobias,
ones(num_neg_examples)].astype(float32)
#pos_examples = [pos_examples_nobias,ones(num_pos_examples,1)];
pos_examples = c_[pos_examples_nobias,
ones(num_pos_examples)].astype(float32)
#%If weight vectors have not been provided, initialize them appropriately
#% exist(name, type)
#% || is short circuit boolean or (stops when overall value determined)
#% randn(rows, cols) - random matrix with zero mean and variance one
#if (~exist('w_init','var') || isempty(w_init))
if 'w_init' not in locals() or w_init.size == 0:
# w = randn(3,1);
w = randn((3, 1))
#else
else:
w = w_init.astype(float32)
#end
#if (~exist('w_gen_feas','var'))
if 'w_gen_feas' not in locals():
w_gen_feas = []
# should be array?
#end
#%Find the data points that the perceptron has incorrectly classified
#%and record the number of errors it makes.
iter_ = 0
[mistakes0, mistakes1] = eval_perceptron(neg_examples, pos_examples, w)
#num_errs = size(mistakes0,1) + size(mistakes1,1);
num_errs = mistakes0.shape[0] + mistakes1.shape[0]
#% (..., end, ...) end index is last entry for a particular dimension
#num_err_history(end+1) = num_errs;
num_err_history.append(num_errs)
#fprintf('Number of errors in iteration %d:\t%d\n',iter,num_errs);
print('Number of errors in iteration %d:\t%d\n' % (iter_, num_errs))
#fprintf(['weights:\t', mat2str(w), '\n']);
print('weights:\n', w, '\n')
plot_perceptron(neg_examples, pos_examples, mistakes0, mistakes1,
num_err_history, w, w_dist_history)
#key = input('<Press enter to continue, q to quit.>', 's');
key = input('<Press enter to continue, q to quit.>')
#if (key == 'q')
if (key == 'q'):
return
#end
#%If a generously feasible weight vector exists, record the distance
#%to it from the initial weight vector.
#if (length(w_gen_feas) ~= 0)
if w_gen_feas.size != 0:
#% (..., end, ...) end index is last entry for a particular dimension
#% norm(x1 - x2) is Euclidean distance between two vectors
#w_dist_history(end+1) = norm(w - w_gen_feas);
w_dist_history.append(norm(w - w_gen_feas))
#end
#%Iterate until the perceptron has correctly classified all points.
#while (num_errs > 0)
while num_errs > 0:
iter_ = iter_ + 1
#%Update the weights of the perceptron.
w = update_weights(neg_examples, pos_examples, w)
#%If a generously feasible weight vector exists, record the distance
#%to it from the current weight vector.
#if (length(w_gen_feas) ~= 0)
if w_gen_feas.size != 0:
#w_dist_history(end+1) = norm(w - w_gen_feas);
w_dist_history.append(norm(w - w_gen_feas))
#end
#%Find the data points that the perceptron has incorrectly classified.
#%and record the number of errors it makes.
[mistakes0, mistakes1] = eval_perceptron(neg_examples, pos_examples, w)
#num_errs = size(mistakes0,1) + size(mistakes1,1);
num_errs = mistakes0.shape[0] + mistakes1.shape[0]
#num_err_history(end+1) = num_errs;
num_err_history.append(num_errs)
#fprintf('Number of errors in iteration %d:\t%d\n',iter,num_errs);
print('Number of errors in iteration %d:\t%d\n' % (iter_, num_errs))
#fprintf(['weights:\t', mat2str(w), '\n']);
print('weights:\n', w, '\n')
plot_perceptron(neg_examples, pos_examples, mistakes0, mistakes1,
num_err_history, w, w_dist_history)
#key = input('<Press enter to continue, q to quit.>', 's');
key = input('<Press enter to continue, q to quit.>')
#if (key == 'q')
if (key == 'q'):
break
import math
import numpy as np
import numpy.matlib as nm
import matplotlib.pyplot as plt
np.seterr(divide='ignore', invalid='ignore')
n = 200
a = nm.linspace(0, nm.pi, n / 2)
x_u = np.c_[nm.cos(a) + 0.5, nm.cos(a) - 0.5].reshape(n, 1)
u = -10 * x_u + nm.randn(n, 1)
x_v = np.c_[nm.sin(a), -nm.sin(a)].reshape(n, 1)
v = 10 * x_v + nm.randn(n, 1)
x = np.c_[u, v]
y = np.zeros((n, 1))
y[0] = 1
y[n - 1] = -1
x2 = np.sum(np.power(x, 2), 1)
hh = 2 * 1**2
k = nm.exp(-(nm.repmat(x2, 1, n) + nm.repmat(x2.T, n, 1) - 2 * x * x.T) / hh)
w = k
t_tmp1 = k**2 + 1 * np.eye(n) + 10 * k * (nm.diag(sum(w)) - w) * k
t = np.linalg.inv(t_tmp1) * (k * y)
m = 100
X = nm.linspace(-20, 20, m).T
X2 = np.power(X, 2)
U = nm.exp(
-(nm.repmat(np.power(u, 2), 1, m) + nm.repmat(X2.T, n, 1) - 2 * u * X.T) /
hh)
V = nm.exp(
import numpy as np
import matplotlib.pyplot as plt
from numpy.matlib import randn
import pylab
###############################################################
arr = np.arange(10)
print(np.sqrt(arr))
print("\n")
print(np.exp(arr))
print("\n")
###############################################################
x = randn(8)
y = randn(8)
print(x)
print(y)
print("\n")
print(np.maximum(x, y))
print("\n")
###############################################################
points = np.arange(-5, 5, 0.01)
xs, ys = np.meshgrid(points, points)
print(ys)
print("\n")
###############################################################
# -*- coding: utf-8 -*-
"""
Created on Mon Mar 12 16:01:13 2018
@author: Administrator
@description： numpy库中的数组排序(sort)函数
"""
import numpy as np
from numpy.matlib import randn
arr = randn(8)
print("排序前：")
print(arr)
print("排序后：")
print(np.sort(arr))
S = np.array([[1, 0], [0, 1], [1, 1]])
sigma_n = 0.2
M, K = S.shape
N = 6
num_problem = 500
CD_homo_P = dict()
SVD_homo_P = dict()
QP_homo_P = dict()
U_true_set = dict()
for each in range(num_problem):
Z_true = 1 + np.array([random.expovariate(1) for rand in range(M)])
U_true = np.random.rand(K, N)
X_clean = np.diag(Z_true).dot(S).dot(U_true)
X = X_clean + (X_clean * sigma_n) * np.array(mtl.randn(M, N))
U_true_set[str(each)] = U_true
prot_sub = dict()
prot_sub['S'] = S
prot_sub['X'] = X
hf.null_sp_dim(prot_sub)
# SVD sovler
SVD_solution = Solvers.SVD(prot_sub)
SVD_protein, SVD_opt = SVD_solution
SVD_homo_P[str(each)] = SVD_protein
# QP solver
QP_solution = Solvers.QP(prot_sub)
QP_protein, QP_opt = QP_solution
QP_homo_P[str(each)] = QP_protein
def testDownloadsConstituentsUpdatesStatus(self):
self.market.downloader.get = Mock()
self.market.downloader.get.return_value = DataFrame(randn(2, 1))
self.market.download_data()
expected_status = dict(zip(self.tickers, [True] * len(self.tickers)))
self.assertEqual(self.market.status, expected_status)
def generate_latent_points(latent_dim, n_samples):
# generate points in the latent space
x_input = randn(latent_dim * n_samples)
# reshape into a batch of inputs for the network
x_input = x_input.reshape(n_samples, latent_dim)
return x_input
print(arr * arr)
print(arr - arr)
arr2d = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
print(arr2d[2])
arr3d = np.array([[[1, 2, 3], [4, 5, 6]], [[7, 8, 9], [10, 11, 12]]])
old_values = arr3d[0].copy()
print('------------')
arr3d[0] = 42
print(arr3d)
arr3d[0] = old_values
print(arr3d)
names = np.array(['Bob', 'Joe', 'Will', 'Bob', 'Will', 'Joe', 'Joe'])
print(names)
data = randn(7, 4)
print(data)
# Boolean Indexing
# Suppose each name corresponds to a row in the data array. If we wanted to select all
# the rows with corresponding name 'Bob'. Like arithmetic operations, comparisons
# (such as ==) with arrays are also vectorized. Thus, comparing names with the string
# 'Bob' yields a boolean array:
print(names == 'Bob')
print(data[names == 'Bob'])
print(data[names == 'Bob', 2:],)
print(data[names == 'Bob', 3])
print(data[((names == 'Bob') | (names == 'Will'))])
# Fancy Indexing
# Fancy indexing is a term adopted by NumPy to describe indexing using integer arrays.
# -*- coding: utf-8 -*-
"""
Created on Mon Mar 12 16:07:17 2018
@author: Administrator
@description： any和all函数
"""
import numpy as np
from numpy.matlib import randn
print(
'Boolean values are coerced to 1 (True) and 0 (False) in the above methods. Thus, sum is often used as a means of counting True values in a boolean array:'
)
arr = randn(100)
print("输出生成的随机数数组中数值大于0的个数：")
print((arr > 0).sum())
bools = np.array([False, False, True, False])
print(bools)
print("只要有一个为true就输出true:")
print(bools.any()) # true
print("全部才输出true：")
print(bools.all()) #false
bools2 = np.array([True, True, True, True])
print(bools2.all()) #true
#两个数组之间
# any():a数组与b数组有一个元素对应相等就输出true
#all():a数组与b数组每个元素都对应相等才输出true
a = np.array([1, 2, 3])
b = np.array([2, 2, 3])
boolean = (a == b).all()
boolean2 = (a == b).any()
# coding:utf-8 from matplotlib.pyplot import plot, show, figure from numpy.matlib import randn, array, vstack, where from scipy.cluster.vq import kmeans, vq # 生成正态分布的二维数据 class1 = 1.5 * randn(100, 2) class2 = randn(100, 2) + array([5, 5]) features = vstack((class1, class2)) # 用k=2对这些数据进行聚类 centroids, variance = kmeans(features, 2) # 通过矢量化函数对每个数据点进行归类: code, distance = vq(features, centroids) figure() ndx = where(code == 0)[0] plot(features[ndx, 0], features[ndx, 1], '*') ndx = where(code == 1)[0] plot(features[ndx, 0], features[ndx, 1], 'r.') plot(features[:, 0], features[:, 1], 'go') show()
print('\n')
print(arr2d[:, :1])
print('\n')
arr2d[:2, 1:]=0
print(arr2d)
print('\n')
###############################################################
#Page 92
#Boolean Indexing
###############################################################
names = np.array(['Bob', 'Joe', 'Will', 'Bob', 'Will', 'Joe', 'Joe'])
data = randn(7,4)
print(names)
print(data)
print('\n')
print(names == 'Bob')
print('\n')
print(data[names == 'Bob'])
print('\n')
print(data[names == 'Bob',2:])
print('\n')
print(data[names == 'Bob',3])
print('\n')
print(names != 'Bob')
print('\n')
print(data[-(names == 'Bob')])
arr_slice[1] = 10 arr[:] # n-d arrays arr2d = np.array([[1,2,3], [4,5,6], [7,8,9]]) arr3d = np.array([[[1,2,3], [4,5,6]], [[7,8,9], [10,11,12]]]) # demo copying on 3d array old_values = arr3d[0].copy() arr3d[0] = 42 arr3d[0] = old_values # Boolean indices names = np.array(['Bob', 'Joe', 'Will', 'Bob', 'Will', 'Joe', 'Joe']) from numpy.matlib import randn data = randn(7,4) bob_index = names == 'Bob' names[bob_index] data[bob_index] data[bob_index, :2] data[bob_index, :10] data[:, bob_index] not_bob = names != 'Bob' data[not_bob] data[bob_index] data[~bob_index] data[~not_bob] data[data < 0] = 0 data[names != 'Joe'] = 7
def sample(self, x):
m = self.inf(x, meanonly=True)
return m + np.exp(self.kernel.lik) * np.randn(m.shape)
"""
import numpy as np
from numpy.matlib import randn
print("创建一维数组：")
data1 = [3, 3.3, 9, 5, 6]
arr1 = np.array(data1)
print(arr1)
print("创建二维数组:")
data2 = [[1, 2, 3, 4], [5, 6, 7, 8]]
arr2 = np.array(data2)
print(arr2)
# Type of data in array.
print("输出第一个数组的数据类型:", arr1.dtype)
print("输出第二个数组的维数:", arr2.ndim)
print("输出第三个数组的形状:", arr2.shape)
#用zeros函数创建数组
print("np.zeros(10)创建10个元素都是0的一维数组： ")
print(np.zeros(10))
print("np.zeros((3, 6))创建3行6列都是0的二维数组：")
print(np.zeros((3, 6)))
#用Empty函数创建数组，其初始值为乱值
print("np.empty((3,6))创建3行6列都是0的二维数组：")
print(np.empty((3, 6)))
#用arrange函数创建数组
print("np.arange(9)创建一维数组：")
print(np.arange(9))
#用随机函数randn创建二维数组，7行4列
print("randn(7, 4))创建数字随机的一维数组：")
data = randn(7, 4)
print(data)
