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():
#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()
pylab.gcf().clear()
pi1 = sum(W1)
pi2 = sum(W2)
(pi1, pi2) = [pi1 / (pi1 + pi2), pi2 / (pi1 + pi2)]
d1 = R1.density(data) * pi1
d2 = R2.density(data) * pi2
(W1, W2) = [
d1 / (d1 + d2),
d2 / (d1 + d2),
]
R1 = Mvn.fromData(data=data, weights=W1, bias=True)
R2 = Mvn.fromData(data=data, weights=W2, bias=True)
#print 'W1=%s' % sum(W1)
#print 'W2=%s' % sum(W2)
pylab.scatter(data[:, 0], data[:, 1], c='r', alpha=0.5, zorder=3)
R1.plot(zorder=2)
R2.plot(zorder=1)
# pylab.gca().add_artist(R1.patch())
# pylab.gca().add_artist(R2.patch())
pylab.draw()
p = sum(pi1 * W1 * pi2 * W2)
print 'p=%s' % p
# if abs(p-old_p) <0.0000001:
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()
pi2 = sum(W2)
(pi1,pi2) = [
pi1/(pi1+pi2),
pi2/(pi1+pi2)
]
d1 = R1.density(data)*pi1
d2 = R2.density(data)*pi2
(W1,W2) = [
d1/(d1+d2),
d2/(d1+d2),
]
R1 = Mvn.fromData(data = data,weights = W1,bias=True)
R2 = Mvn.fromData(data = data,weights = W2,bias=True)
#print 'W1=%s' % sum(W1)
#print 'W2=%s' % sum(W2)
pylab.scatter(data[:,0],data[:,1],c='r',alpha=0.5, zorder = 3)
R1.plot(zorder = 2)
R2.plot(zorder = 1)
# pylab.gca().add_artist(R1.patch())
# pylab.gca().add_artist(R2.patch())
pylab.draw()
p=sum(pi1*W1*pi2*W2)
print 'p=%s' % p
# if abs(p-old_p) <0.0000001:
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()
