def main():
#generate data
N=75
red = Mvn.rand(2)
blue = Matrix(red.sample(N))
red = Mvn.fromData(blue)
#create figure
fig = pylab.figure(1, figsize=(7, 7))
fig.suptitle('Mahalabois Distance')
ax = setupAxes(red.transform(-1))
# scatter plot of the origional data
scatter(ax[0,0],red,blue)
# scatter plot of the normalized data
scatter(ax[1,0],red/red,blue/red)
# draw the cumulative distribution
cumulative(ax[0,1],red,blue)
# draw the histogram
hist(red.mah().pdf,red.mah(blue),ax[1,1])
ax[0,1].set_xlim([0,None])
ax[1,1].set_ylim([0,None])
pylab.show()
def main():
#generate data
N = 75
red = Mvn.rand(2)
blue = Matrix(red.sample(N))
red = Mvn.fromData(blue)
#create figure
fig = pylab.figure(1, figsize=(7, 7))
fig.suptitle('Mahalabois Distance')
ax = setupAxes(red.transform(-1))
# scatter plot of the origional data
scatter(ax[0, 0], red, blue)
# scatter plot of the normalized data
scatter(ax[1, 0], red / red, blue / red)
# draw the cumulative distribution
cumulative(ax[0, 1], red, blue)
# draw the histogram
hist(red.mah().pdf, red.mah(blue), ax[1, 1])
ax[0, 1].set_xlim([0, None])
ax[1, 1].set_ylim([0, None])
pylab.show()
def makeObjects(flat=None, ndim=None, seed=None):
if seed is None:
seed = randint(1, 1e6)
numpy.random.seed(seed)
randn = numpy.random.randn
if ndim is None:
ndim = randint(0, 20)
shapes = {
None:lambda :max(randint(-ndim, ndim), 0),
True:lambda :randint(1, ndim),
False:lambda :0,
}
triple = lambda x:[x, x, x]
if flat in shapes:
flat = [item() for item in triple(shapes[flat])]
elif isinstance(flat, int):
flat = triple(flat)
assert all(f <= ndim for f in flat), "flatness can't be larger than ndim"
rvec = lambda n=1, ndim=ndim:Matrix(randn(n ,ndim))
A,B,C = [
Mvn.rand([ndim-F, ndim])
for F in flat
]
n = randint(1, 2*ndim)
M = rvec(n).H
M2 = rvec(n).H
E = Matrix.eye(ndim)
K1 = (numpy.random.randn())
K2 = (numpy.random.randn())
N = randint(-5, 5)
return {
'ndim' : ndim,
'A' : A,
'B' : B,
'C' : C,
'M' : M,
'M2' : M2,
'E' : E,
'K1' : K1,
'K2' : K2,
'N' : N,
}
def main():
"""
demonstrate the `covariance intersection algorithm
<http://en.wikipedia.org/wiki/Kalman_filter#Update>`_
"""
pylab.figure(1, figsize=(5,5))
red = Mvn.rand(shape=2)
blue = Mvn.rand(shape=2)
magenta = red & blue
red.plot( facecolor = 'r')
blue.plot( facecolor = 'b')
magenta.plot(facecolor = 'm')
pylab.xlabel('Magenta = Red & Blue')
pylab.show()
def main():
"""
demonstrate the `covariance intersection algorithm
<http://en.wikipedia.org/wiki/Kalman_filter#Update>`_
"""
pylab.figure(1, figsize=(5, 5))
red = Mvn.rand(shape=2)
blue = Mvn.rand(shape=2)
magenta = red & blue
red.plot(facecolor='r')
blue.plot(facecolor='b')
magenta.plot(facecolor='m')
pylab.xlabel('Magenta = Red & Blue')
pylab.show()
def makeObjects(flat=None, ndim=None, seed=None):
if seed is None:
seed = randint(1, 1e6)
numpy.random.seed(seed)
randn = numpy.random.randn
if ndim is None:
ndim = randint(0, 20)
shapes = {
None: lambda: max(randint(-ndim, ndim), 0),
True: lambda: randint(1, ndim),
False: lambda: 0,
}
triple = lambda x: [x, x, x]
if flat in shapes:
flat = [item() for item in triple(shapes[flat])]
elif isinstance(flat, int):
flat = triple(flat)
assert all(f <= ndim
for f in flat), "flatness can't be larger than ndim"
rvec = lambda n=1, ndim=ndim: Matrix(randn(n, ndim))
A, B, C = [Mvn.rand([ndim - F, ndim]) for F in flat]
n = randint(1, 2 * ndim)
M = rvec(n).H
M2 = rvec(n).H
E = Matrix.eye(ndim)
K1 = (numpy.random.randn())
K2 = (numpy.random.randn())
N = randint(-5, 5)
return {
'ndim': ndim,
'A': A,
'B': B,
'C': C,
'M': M,
'M2': M2,
'E': E,
'K1': K1,
'K2': K2,
'N': N,
}
def main():
M1 = Mvn.rand(2)
M2 = Mvn.rand(2)
data1 = M1.sample(100)
data2 = M2.sample(100)
M1 = Mvn.fromData(data1)
M2 = Mvn.fromData(data2)
M3 = Mvn.fromData([M1, M2])
data3 = Matrix.stack([[data1], [data2]])
assert M3 == Mvn.fromData(data3)
A = pylab.gca()
M3.plot(A, facecolor='m', minalpha=0.1, zorder=-1)
M1.plot(A, facecolor='b', minalpha=0.1, zorder=0)
M2.plot(A, facecolor='r', minalpha=0.1, zorder=1)
pylab.scatter(data1[:, 0], data1[:, 1], facecolor='b', zorder=2)
pylab.scatter(data2[:, 0], data2[:, 1], facecolor='r', zorder=3)
pylab.show()
def main():
M1=Mvn.rand(2)
M2=Mvn.rand(2)
data1 = M1.sample(100)
data2 = M2.sample(100)
M1 = Mvn.fromData(data1)
M2 = Mvn.fromData(data2)
M3 = Mvn.fromData([M1,M2])
data3 = Matrix.stack([[data1],[data2]])
assert M3 == Mvn.fromData(data3)
A=pylab.gca()
M3.plot(A,facecolor='m',minalpha=0.1,zorder = -1)
M1.plot(A,facecolor='b',minalpha = 0.1,zorder = 0)
M2.plot(A,facecolor='r',minalpha = 0.1,zorder = 1)
pylab.scatter(data1[:,0],data1[:,1],facecolor='b',zorder = 2)
pylab.scatter(data2[:,0],data2[:,1],facecolor='r',zorder = 3)
pylab.show()
def main():
axes = triax()
N = int(10.0 ** (1 + 2 * numpy.random.rand()))
for dims in range(3):
ax = axes[dims]
ax.set_title("Mvn.rand((%s,2))" % dims)
for n in range(N):
M = Mvn.rand((dims, 2))
M.plot(ax, facecolor=numpy.random.rand(3))
pylab.tight_layout()
pylab.show()
def main():
axes = triax()
N = int(10.0**(1 + 2 * numpy.random.rand()))
for dims in range(3):
ax = axes[dims]
ax.set_title("Mvn.rand((%s,2))" % dims)
for n in range(N):
M = Mvn.rand((dims, 2))
M.plot(ax, facecolor=numpy.random.rand(3))
pylab.tight_layout()
pylab.show()
def main():
"""
demonstrate marginal distributions
"""
N = numpy.round(10.0**(1 + 2.5 * numpy.random.rand()))
#generate a random mvn
red = Mvn.rand(2)
#sample some data
blue = red.sample(N)
#create a figures of the apropriate size
pylab.figure(1, figsize=(6, 6))
#create axes for plotting
axes = triax()
mainax = axes[1, 0]
topax = axes[0, 0]
sideax = axes[1, 1]
#do the main plot
mainax.scatter(blue[:, 0], blue[:, 1], zorder=0, alpha=alpha)
red.plot(axis=mainax,
nstd=2,
zorder=1,
label=r'$\pm 2 \sigma$',
**plotParams)
mainax.legend()
#freeze the main axes
mainax.autoscale(False)
topax.set_autoscalex_on(False)
sideax.set_autoscaley_on(False)
#plot the histograms
hist(red[:, 0], blue[:, 0], topax, orientation='vertical')
hist(red[:, 1], blue[:, 1], sideax, orientation='horizontal')
#set the main title
font = {'size': 12}
mainax.set_xlabel('red', font)
topax.set_title('red[:,0]', font)
sideax.set_title('red[:,1]', font)
#draw the figure
pylab.show()
def main():
"""
demonstrate marginal distributions
"""
N=numpy.round(10.0**(1+2.5*numpy.random.rand()))
#generate a random mvn
red=Mvn.rand(2)
#sample some data
blue = red.sample(N)
#create a figures of the apropriate size
pylab.figure(1, figsize=(6,6))
#create axes for plotting
axes = triax()
mainax = axes[1,0]
topax = axes[0,0]
sideax = axes[1,1]
#do the main plot
mainax.scatter(blue[:,0],blue[:,1],zorder = 0,alpha = alpha);
red.plot(axis = mainax, nstd=2, zorder = 1,label=r'$\pm 2 \sigma$',**plotParams)
mainax.legend()
#freeze the main axes
mainax.autoscale(False)
topax.set_autoscalex_on(False)
sideax.set_autoscaley_on(False)
#plot the histograms
hist(red[:,0],blue[:,0],topax,orientation = 'vertical')
hist(red[:,1],blue[:,1],sideax,orientation = 'horizontal')
#set the main title
font = {'size':12}
mainax.set_xlabel('red',font)
topax.set_title('red[:,0]',font)
sideax.set_title('red[:,1]',font)
#draw the figure
pylab.show()
def main():
#get axis
ax0 = pylab.subplot(1, 2, 1)
ax1 = pylab.subplot(1, 2, 2)
#get data
A = Mvn.rand(2)
data = A.sample(10000)
#squish the data to spherical variance
deltas = ((data - A.mean) / A).array()
#calculate the errors in the squished space
errors = (deltas**2).sum(1)
print errors
hist(A.dist2(), errors, ax0)
pylab.show()
def main():
#get axis
ax0 = pylab.subplot(1,2,1)
ax1 = pylab.subplot(1,2,2)
#get data
A = Mvn.rand(2)
data = A.sample(10000)
#squish the data to spherical variance
deltas = ((data-A.mean)/A).array()
#calculate the errors in the squished space
errors = (deltas**2).sum(1)
print errors
hist(A.dist2(),errors,ax0)
pylab.show()
path = 'kalman'
#seed the rng so results are reproducible.
seed(path)
#create publisher
P = Publisher(path)
#create figure
fig = pylab.figure(figsize = (6, 6))
## kalman filter parameters
#the actual, hidden state
actual = numpy.array([[0, 5]])
#the sensor
sensor = Mvn(vectors = [[1, 0], [0, 1]],var = [1, numpy.inf])
#the system noise
noise = Mvn(vectors = [[1, 0], [0, 1]], var = numpy.array([0.5, 1])**2)
#the shear transform to move the system forward
transform = Matrix([[1, 0], [0.5, 1]])
filtered = sensor.measure(actual)
## initial plot
ax = newAx(fig)
#plot the initial actual position
#! /usr/bin/env python
import numpy
from mvn import Mvn
from mvn.matrix import Matrix
from mvn.mixture import Mixture
import pylab
pylab.ion()
source = Mixture([
Mvn.rand(2),
Mvn.rand(2),
])
data = source.sample(200)
W1, R1 = [1e7], Mvn(mean=[10.0, 10.0], var=numpy.array([10.0, 10.0])**2)
W2, R2 = [1e7], Mvn(mean=[-10.0, -10.0], var=numpy.array([10.0, 10.0])**2)
old_p = numpy.inf
for N in range(10):
pylab.gcf().clear()
pi1 = sum(W1)
pi2 = sum(W2)
(pi1, pi2) = [pi1 / (pi1 + pi2), pi2 / (pi1 + pi2)]
#! /usr/bin/env python
import numpy
from mvn import Mvn
from mvn.matrix import Matrix
from mvn.mixture import Mixture
import pylab;
pylab.ion()
source = Mixture([
Mvn.rand(2),
Mvn.rand(2),
])
data = source.sample(200)
W1,R1 = [1e7],Mvn(mean=[ 10.0, 10.0],var=numpy.array([10.0,10.0])**2)
W2,R2 = [1e7],Mvn(mean=[-10.0,-10.0],var=numpy.array([10.0,10.0])**2)
old_p = numpy.inf
for N in range(10):
pylab.gcf().clear()
pi1 = sum(W1)
pi2 = sum(W2)
(pi1,pi2) = [
#directory for resulting figures
path = 'kalman'
#seed the rng so results are reproducible.
seed(path)
#create publisher
P = Publisher(path)
#create figure
fig = pylab.figure(figsize=(6, 6))
## kalman filter parameters
#the actual, hidden state
actual = numpy.array([[0, 5]])
#the sensor
sensor = Mvn(vectors=[[1, 0], [0, 1]], var=[1, numpy.inf])
#the system noise
noise = Mvn(vectors=[[1, 0], [0, 1]], var=numpy.array([0.5, 1])**2)
#the shear transform to move the system forward
transform = Matrix([[1, 0], [0.5, 1]])
filtered = sensor.measure(actual)
## initial plot
ax = newAx(fig)
#plot the initial actual position
ax.plot(actual[:, 0], actual[:, 1], **actualParams)
def main():
N = 75 #numpy.round(10.0**(1.5+1*numpy.random.rand()))
#generate data
red = Mvn.rand(2)
blue = red.sample(N)
red = Mvn.fromData(blue)
#create figure
fig = pylab.figure(1, figsize=(7, 7))
fig.suptitle('Mahalabois Distance')
axgrid = GridSpec(2, 2)
ax = numpy.empty([2, 2], dtype=object)
#get axes
ax[0, 0] = subplot(axgrid[0, 0])
ax[0, 0].axis('equal')
ax[0, 0].grid('on')
ax[0, 0].set_title('red')
@curry
def forewardTransform(center, M, x, y):
center = center.squeeze()
x = Matrix(x)
y = Matrix(y)
xy = numpy.hstack([x.T, y.T])
xy = xy - center[None, :]
xy = numpy.array(xy * M)
mags = (numpy.array(xy)**2).sum(1)[:, None]**0.5
dirs = xy / mags
xy = dirs * mags**2
return xy[:, 0].squeeze(), xy[:, 1].squeeze()
@curry
def reverseTransform(center, M, x, y):
center = center.squeeze()
x = Matrix(x)
y = Matrix(y)
xy = numpy.hstack([x.T, y.T])
xy = xy - center[None, :]
xy = numpy.array(xy * M)
mags = (numpy.array(xy)**2).sum(1)[:, None]**0.5
dirs = xy / mags
xy = dirs * mags**0.5 + center
return xy[:, 0].squeeze(), xy[:, 1].squeeze()
foreward = forewardTransform(red.mean, red.transform(-1))
reverse = reverseTransform(red.mean, red.transform(1))
grid_helper = GridHelperCurveLinear([foreward, reverse])
ax[1, 0] = subplot(axgrid[1, 0],
projection='custom',
transform=grid_helper)
ax[1, 0].axis('equal')
ax[1, 0].grid('on')
ax[1, 0].set_title('red/red')
ax[0, 1] = subplot(axgrid[0, 1])
ax[0, 1].grid('on')
ax[0, 1].set_title('red.mah2().cdf()')
ax[0, 1].set_ylim([0, 1])
ax[1, 1] = pylab.subplot(axgrid[1, 1], sharex=ax[0, 1]) #,sharey=ax[0,1])
ax[1, 1].grid('on')
ax[1, 1].set_title('red.mah2().pdf()')
scatter(ax[0, 0], red, blue)
# blue0 = Matrix(blue)/red
# blue0 = blue0.array()
red0 = red / red
blue0 = foreward(blue[:, 0], blue[:, 1])
blue0 = numpy.hstack([blue0[0][:, None], blue0[1][:, None]])
scatter(ax[1, 0], red0, blue0)
mah2 = red.mah2(blue)
mah2.sort()
ax[0, 1].hlines(numpy.arange(mah2.size, dtype=float) / mah2.size,
0,
mah2,
color='b',
alpha=alpha)
ax[0, 1].scatter(mah2,
numpy.arange(mah2.size, dtype=float) / mah2.size,
color='b',
alpha=alpha)
x = numpy.linspace(*ax[0, 1].get_xlim(), num=500)
ax[0, 1].plot(x, red.mah2().cdf(x), color='r', linewidth=2, alpha=alpha)
hist(red.mah2().pdf, red.mah2(blue), ax[1, 1])
ax[0, 1].set_xlim([0, None])
ax[1, 1].set_ylim([0, None])
pylab.show()
def main():
N=75#numpy.round(10.0**(1.5+1*numpy.random.rand()))
#generate data
red = Mvn.rand(2)
blue = red.sample(N)
red = Mvn.fromData(blue)
#create figure
fig = pylab.figure(1, figsize=(7, 7))
fig.suptitle('Mahalabois Distance')
axgrid = GridSpec(2, 2)
ax = numpy.empty([2, 2],dtype = object)
#get axes
ax[0, 0] = subplot(axgrid[0, 0])
ax[0, 0].axis('equal')
ax[0, 0].grid('on')
ax[0, 0].set_title('red')
@curry
def forewardTransform(center, M, x, y):
center = center.squeeze()
x = Matrix(x)
y = Matrix(y)
xy = numpy.hstack([x.T, y.T])
xy = xy - center[None, :]
xy = numpy.array(xy*M)
mags = (numpy.array(xy)**2).sum(1)[:, None]**0.5
dirs = xy/mags
xy = dirs*mags**2
return xy[:, 0].squeeze(), xy[:, 1].squeeze()
@curry
def reverseTransform(center, M, x, y):
center = center.squeeze()
x = Matrix(x)
y = Matrix(y)
xy = numpy.hstack([x.T, y.T])
xy = xy - center[None, :]
xy = numpy.array(xy*M)
mags = (numpy.array(xy)**2).sum(1)[:, None]**0.5
dirs = xy/mags
xy = dirs*mags**0.5 + center
return xy[:, 0].squeeze(), xy[:, 1].squeeze()
foreward = forewardTransform(red.mean, red.transform(-1))
reverse = reverseTransform(red.mean, red.transform(1))
grid_helper = GridHelperCurveLinear([
foreward,
reverse
])
ax[1, 0] = subplot(axgrid[1, 0],
projection = 'custom',
transform = grid_helper
)
ax[1, 0].axis('equal')
ax[1, 0].grid('on')
ax[1, 0].set_title('red/red')
ax[0, 1] = subplot(axgrid[0, 1])
ax[0, 1].grid('on')
ax[0, 1].set_title('red.mah2().cdf()')
ax[0, 1].set_ylim([0, 1])
ax[1, 1] = pylab.subplot(axgrid[1, 1], sharex=ax[0, 1])#,sharey=ax[0,1])
ax[1, 1].grid('on')
ax[1,1].set_title('red.mah2().pdf()')
scatter(ax[0, 0], red, blue)
# blue0 = Matrix(blue)/red
# blue0 = blue0.array()
red0 = red/red
blue0 = foreward(blue[:, 0], blue[:, 1])
blue0 = numpy.hstack([blue0[0][:, None], blue0[1][:, None]])
scatter(ax[1, 0], red0, blue0)
mah2 = red.mah2(blue)
mah2.sort()
ax[0, 1].hlines(numpy.arange(mah2.size, dtype = float)/mah2.size, 0,mah2, color = 'b', alpha = alpha)
ax[0, 1].scatter(mah2, numpy.arange(mah2.size, dtype = float)/mah2.size, color = 'b', alpha = alpha)
x = numpy.linspace(*ax[0, 1].get_xlim(), num=500)
ax[0, 1].plot(x, red.mah2().cdf(x), color = 'r', linewidth = 2, alpha = alpha)
hist(red.mah2().pdf, red.mah2(blue), ax[1, 1])
ax[0, 1].set_xlim([0, None])
ax[1, 1].set_ylim([0, None])
pylab.show()
