def rbm_grad_exact(W, x, vis_gauss=False):
batch_size = float(len(x))
v, h = W.v, W.h
G = 0 * W
H = sigmoid(W*x)
G += 1./batch_size * W.outp(x, H)
if not vis_gauss:
Z = brute_force_Z(W)
def prob(V):
return exp( free_energy(W, V)[0] - Z )
for i in xrange(2**v):
V = int_to_bin(i, v)
H = sigmoid(W* V)
G -= prob(V) * W.outp(V, H)
loss = - ( free_energy(W, x).mean(0) - Z )
if vis_gauss:
Z = brute_force_Z_vis_gauss(W)
def prob(H):
b = W.T() * H
z = .5*dot(b,b.T) + dot(H,W[2])
return float(exp(z-Z) )
for i in xrange(2**h):
H = int_to_bin(i, h)
b = W.T()*H
G -= prob(H) * W.outp(b,H)
loss = - (-.5*amap(dot,x,x).mean() + free_energy(W, x).mean(0) - Z)
return batch_size * G, dict(loss=batch_size * loss)
def processData(self):
print self.magSampleList
#plot(array(self.magSampleList))
#show()
self.mags = array(self.magSampleList)
xs = self.mags[:,0]
ys = self.mags[:,1]
zs = self.mags[:,2]
cxs, x_offset, x_scale = self.applyCalibration(xs)
cys, y_offset, y_scale = self.applyCalibration(ys)
czs, z_offset, z_scale = self.applyCalibration(zs)
def residuals(params,x,y,z):
xo = params[0]
xs = params[1]
yo = params[2]
ys = params[3]
zo = params[4]
zs = params[5]
xc = empty(shape(x))
for i in range(len(x)):
xc[i] = (x[i] - xo) * xs
yc = empty(shape(y))
for i in range(len(y)):
yc[i] = (y[i] - yo) * ys
zc = empty(shape(z))
for i in range(len(z)):
zc[i] = (z[i] - zo) * zs
res = []
for i in range(len(xc)):
norm = l2norm(array([xc[i],yc[i],zc[i]])) - 1.0
res.append(norm)
return array(res)
p0 = [x_offset, x_scale, y_offset, y_scale, z_offset, z_scale]
ls = leastsq(residuals, p0, args=(xs,ys,zs))
x_offset = ls[0][0]
x_scale = ls[0][1]
y_offset = ls[0][2]
y_scale = ls[0][3]
z_offset = ls[0][4]
z_scale = ls[0][5]
cxs = self.applyCalibration(xs, calibration=(x_offset,x_scale))[0]
cys = self.applyCalibration(ys, calibration=(y_offset,y_scale))[0]
czs = self.applyCalibration(zs, calibration=(z_offset,z_scale))[0]
calibratedMag = empty((len(cxs),3))
calibratedMag[:,0] = cxs
calibratedMag[:,1] = cys
calibratedMag[:,2] = czs
magnitudes = amap(lambda v: l2norm(v), calibratedMag)
self.calibratedMag = calibratedMag
mlab.points3d(cxs,cys,czs, scale_mode='none', scale_factor=0.02)
#mlab.points3d(array([-1.0,1.0]),array([0.0,0.0]),array([0.0,0.0]), scale_mode='none', scale_factor=0.02)
sphere = mlab.points3d(0,0,0, opacity=0.5, resolution=100, color=(1.0,0.0,0.0), scale_mode='none', scale_factor=2.0)
sphere.actor.property.backface_culling = True
mlab.show()
figure()
plot(magnitudes)
show()
# write calibration to a file
f = open(self.filename,mode='w')
f.write("id,x_offset,x_scale,y_offset,y_scale,z_offset,z_scale\n")
f.write("%d,%f,%f,%f,%f,%f,%f\n"%(self.id,x_offset,x_scale,y_offset,y_scale,z_offset,z_scale))
f.write("\n")
for l in self.magSampleList:
f.write("%d,%d,%d\n"%(l[0],l[1],l[2]))
f.close()
resError = []
for i in range(len(cxs)):
resError.append(self.calculateResidualError(cxs[i],cys[i],czs[i]))
print len(resError)
print mean(resError)
# Ft_per_Fs = -TQFe/(TQb + TQc + TQf)
######################
# Moment arm for proximal
PP1 = twoDmag_ang( rp, qp1 )
AB1 = AB + twoDmag_ang( rb, qb1 )
PB1 = PA + AB1
dirB1P1 = (PP1 - PB1)/p.norm(PP1 - PB1)
mF = p.cross( AB1, dirB1P1 )
return (t,q,g, mF)
aa = (p.arange(83.0)+20.0) * D2R
u = p.amap(q2tg,aa)
ut = u[:,0]
uq = u[:,1]; uqd = uq*R2D
ug = u[:,2]
ufma= u[:,3]
dt0 = ut[1]-ut[0]
dt1 = ut[-1]-ut[-2]
dg0 = ug[1]-ug[0]
dg1 = ug[-1]-ug[-2]
##############
# label Skeleton Plot
p.figure(10); p.grid(True)
p.title('Skeleton of Important Points')
def make_V_O_M(self):
from numpy import zeros, ones
V = zeros((self.T, self.batch_size, self.V))
O = zeros((self.T, self.batch_size, self.O))
M = zeros((self.T, self.batch_size, 1))
from pylab import rand, randn
for b in range(self.batch_size):
from pylab import randint
if self.batch_size < self.char_size**self.num_chars:
# our minibatch is too small and requires random
# sampling
data = randint(self.char_size, size=self.num_chars)
elif self.batch_size == self.char_size**self.num_chars:
# our minibatch is large enoguh to contain all possible
# sequences, so each possible sequence will appear precisely
# once in the batch.
from pylab import base_repr, amap
data = amap(int,
base_repr(
b,
base=self.char_size,
padding=self.num_chars))[-self.num_chars:]
else:
raise TypeError("self.batch_size (%s) is bigger than %s" %
(self.batch_size, self.char_size**self.num_chars))
# input
V[:, b, -1] = 1
V[:self.num_chars, b, :] = 0
V[:self.num_chars, b, :self.char_size] = \
expand(data,
self.char_size)
if self.teacher_force:
# I'll admit I haven't tested teacher_force.
V[-self.num_chars:, b, :] = 0
V[-self.num_chars:, b, :self.char_size] = \
expand(data,
self.char_size)
# a pre signal. Cool.
V[-self.num_chars-1, b, :] = 0
V[-self.num_chars-1, b, -2] = 1
# output:
O[:, b, -1] = 1
O[-self.num_chars:, b, :] = 0
O[-self.num_chars:, b, :self.char_size] = \
expand(data,
self.char_size)
if self.only_predict_the_memory_bits:
M[:, b, :] = 0
M[-self.num_chars:, b, :] = 1
else:
M[:, b, :] = 1
return V, O, M
def softmax_slow(a):
def softmax_1(a):
e=exp(a-a.max())
return e/e.sum()
return amap(softmax_1,a)
def import_letter(filename):
if not re.search('\.png$', filename):
filename += '.png'
arr = imread(filename)
f_rev = lambda a: float32(not aa)
return amap(lambda y: map(f_rev, y), arr[:,:,0]).flatten()
def plot_locatables(locatables, style='kx', **kwargs):
get_x = lambda l: l.position.x
get_y = lambda l: l.position.y
pylab.plot(pylab.amap(get_x, locatables), pylab.amap(get_y, locatables),
style, **kwargs)
def int_to_bin(i, v):
assert(0 <= i < 2**v)
return (amap(int,list(binary_repr(i).zfill(v)))[newaxis,:]).astype('f')
