def show_sigmas_for_2_kappas():
# generate the Gaussian data
xs = np.arange(-4, 4, 0.1)
mean = 0
sigma = 1.5
ys = [stats.gaussian(x, mean, sigma * sigma) for x in xs]
#generate our samples
kappa = 2
x0, x1, x2 = _sigma_points(mean, sigma, kappa)
samples = [x0, x1, x2]
for x in samples:
p1 = plt.scatter([x], [stats.gaussian(x, mean, sigma * sigma)],
s=80,
color='k')
kappa = -.5
x0, x1, x2 = _sigma_points(mean, sigma, kappa)
samples = [x0, x1, x2]
for x in samples:
p2 = plt.scatter([x], [stats.gaussian(x, mean, sigma * sigma)],
s=80,
color='b')
plt.legend([p1, p2], ['$kappa$=2', '$kappa$=-0.5'])
plt.plot(xs, ys)
plt.show()
def show_sigmas_for_2_kappas():
# generate the Gaussian data
xs = np.arange(-4, 4, 0.1)
mean = 0
sigma = 1.5
ys = [stats.gaussian(x, mean, sigma*sigma) for x in xs]
#generate our samples
kappa = 2
x0,x1,x2 = _sigma_points(mean, sigma, kappa)
samples = [x0,x1,x2]
for x in samples:
p1 = plt.scatter([x], [stats.gaussian(x, mean, sigma*sigma)], s=80, color='k')
kappa = -.5
x0,x1,x2 = _sigma_points(mean, sigma, kappa)
samples = [x0,x1,x2]
for x in samples:
p2 = plt.scatter([x], [stats.gaussian(x, mean, sigma*sigma)], s=80, color='b')
plt.legend([p1,p2], ['$kappa$=2', '$kappa$=-0.5'])
plt.plot(xs, ys)
plt.show()
def show_3_sigma_points():
xs = np.arange(-4, 4, 0.1)
var = 1.5
ys = [stats.gaussian(x, 0, var) for x in xs]
samples = [0, 1.2, -1.2]
for x in samples:
plt.scatter ([x], [stats.gaussian(x, 0, var)], s=80)
plt.plot(xs, ys)
plt.show()
def show_3_sigma_points():
xs = np.arange(-4, 4, 0.1)
var = 1.5
ys = [stats.gaussian(x, 0, var) for x in xs]
samples = [0, 1.2, -1.2]
for x in samples:
plt.scatter([x], [stats.gaussian(x, 0, var)], s=80)
plt.plot(xs, ys)
plt.show()
def plot_gaussian_multiply():
xs = np.arange(-5, 10, 0.1)
mean1, var1 = 0, 5
mean2, var2 = 5, 1
mean, var = stats.mul(mean1, var1, mean2, var2)
ys = [stats.gaussian(x, mean1, var1) for x in xs]
plt.plot(xs, ys, label='M1')
ys = [stats.gaussian(x, mean2, var2) for x in xs]
plt.plot(xs, ys, label='M2')
ys = [stats.gaussian(x, mean, var) for x in xs]
plt.plot(xs, ys, label='M1 x M2')
plt.legend()
plt.show()
def plot_gaussian_multiply():
xs = np.arange(-5, 10, 0.1)
mean1, var1 = 0, 5
mean2, var2 = 5, 1
mean, var = stats.mul(mean1, var1, mean2, var2)
ys = [stats.gaussian(x, mean1, var1) for x in xs]
plt.plot(xs, ys, label='M1')
ys = [stats.gaussian(x, mean2, var2) for x in xs]
plt.plot(xs, ys, label='M2')
ys = [stats.gaussian(x, mean, var) for x in xs]
plt.plot(xs, ys, label='M1 x M2')
plt.legend()
plt.show()
def display_stddev_plot():
xs = np.arange(10, 30, 0.1)
var = 8
stddev = math.sqrt(var)
p2, = plt.plot(xs, [stats.gaussian(x, 20, var) for x in xs])
x = 20 + stddev
y = stats.gaussian(x, 20, var)
plt.plot([x, x], [0, y], "g")
plt.plot([20 - stddev, 20 - stddev], [0, y], "g")
y = stats.gaussian(20, 20, var)
plt.plot([20, 20], [0, y], "b")
ax = plt.axes()
ax.annotate("68%", xy=(20.3, 0.045))
ax.annotate(
"", xy=(20 - stddev, 0.04), xytext=(x, 0.04), arrowprops=dict(arrowstyle="<->", ec="r", shrinkA=2, shrinkB=2)
)
ax.xaxis.set_ticks([20 - stddev, 20, 20 + stddev])
ax.xaxis.set_ticklabels(["$-\sigma$", "$\mu$", "$\sigma$"])
ax.yaxis.set_ticks([])
plt.show()
def test_gaussian():
import scipy.stats
mean = 3.
var = 1.5
std = var**0.5
for i in np.arange(-5,5,0.1):
p0 = scipy.stats.norm(mean, std).pdf(i)
p1 = gaussian(i, mean, var)
assert near_equal(p0, p1)
def test_gaussian():
import scipy.stats
mean = 3.
var = 1.5
std = var**0.5
for i in np.arange(-5,5,0.1):
p0 = scipy.stats.norm(mean, std).pdf(i)
p1 = gaussian(i, mean, var)
assert near_equal(p0, p1)
def display_stddev_plot():
xs = np.arange(10, 30, 0.1)
var = 8
stddev = math.sqrt(var)
p2, = plt.plot(xs, [stats.gaussian(x, 20, var) for x in xs])
x = 20 + stddev
y = stats.gaussian(x, 20, var)
plt.plot([x, x], [0, y], 'g')
plt.plot([20 - stddev, 20 - stddev], [0, y], 'g')
y = stats.gaussian(20, 20, var)
plt.plot([20, 20], [0, y], 'b')
ax = plt.axes()
ax.annotate('68%', xy=(20.3, 0.045))
ax.annotate('',
xy=(20 - stddev, 0.04),
xytext=(x, 0.04),
arrowprops=dict(arrowstyle="<->", ec="r", shrinkA=2,
shrinkB=2))
ax.xaxis.set_ticks([20 - stddev, 20, 20 + stddev])
ax.xaxis.set_ticklabels(['$-\sigma$', '$\mu$', '$\sigma$'])
ax.yaxis.set_ticks([])
plt.show()
def display_stddev_plot():
figsize = pylab.rcParams['figure.figsize']
pylab.rcParams['figure.figsize'] = 12,6
xs = np.arange(10,30,0.1)
var = 8; stddev = math.sqrt(var)
p2, = plt.plot (xs,[stats.gaussian(x, 20, var) for x in xs])
x = 20+stddev
y = stats.gaussian(x, 20, var)
plt.plot ([x,x], [0,y],'g')
plt.plot ([20-stddev, 20-stddev], [0,y], 'g')
y = stats.gaussian(20,20,var)
plt.plot ([20,20],[0,y],'b')
ax = plt.axes()
ax.annotate('68%', xy=(20.3, 0.045))
ax.annotate('', xy=(20-stddev,0.04), xytext=(x,0.04),
arrowprops=dict(arrowstyle="<->",
ec="r",
shrinkA=2, shrinkB=2))
ax.xaxis.set_ticks ([20-stddev, 20, 20+stddev])
ax.xaxis.set_ticklabels(['$-\sigma$','$\mu$','$\sigma$'])
ax.yaxis.set_ticks([])
plt.show()
def plot_gaussian(mu, variance, mu_line=False, xlim=None, xlabel=None, ylabel=None):
xs = np.arange(mu - variance * 2, mu + variance * 2, 0.1)
ys = [stats.gaussian(x, mu, variance) * 100 for x in xs]
plt.plot(xs, ys)
if mu_line:
plt.axvline(mu)
if xlim:
plt.xlim(xlim)
if xlabel:
plt.xlabel(xlabel)
if ylabel:
plt.ylabel(ylabel)
plt.show()
def plot_gaussian(mu,
variance,
mu_line=False,
xlim=None,
xlabel=None,
ylabel=None):
xs = np.arange(mu - variance * 2, mu + variance * 2, 0.1)
ys = [stats.gaussian(x, mu, variance) * 100 for x in xs]
plt.plot(xs, ys)
if mu_line:
plt.axvline(mu)
if xlim:
plt.xlim(xlim)
if xlabel:
plt.xlabel(xlabel)
if ylabel:
plt.ylabel(ylabel)
plt.show()
