def func(self, X, V):
k = self.C.TFdata.k
v1 = self.C.TFdata.v1
w1 = self.C.TFdata.w1
if k >=0:
J_coords = self.F.sysfunc.J_coords
w = sqrt(k)
q = v1 - (1j/w)*matrixmultiply(self.F.sysfunc.J_coords,v1)
p = w1 + (1j/w)*matrixmultiply(transpose(self.F.sysfunc.J_coords),w1)
p /= linalg.norm(p)
q /= linalg.norm(q)
p = reshape(p,(p.shape[0],))
q = reshape(q,(q.shape[0],))
direc = conjugate(1/matrixmultiply(transpose(conjugate(p)),q))
p = direc*p
l1 = firstlyapunov(X, self.F.sysfunc, w, J_coords=J_coords, p=p, q=q)
return array([l1])
else:
return array([1])
def sem(im, direction='X'):
r"""
Simulates an SEM photograph looking into the porous material in the
specified direction. Features are colored according to their depth into
the image, so darker features are further away.
Parameters
----------
im : array_like
ND-image of the porous material with the solid phase marked as 1 or
True
direction : string
Specify the axis along which the camera will point. Options are
'X', 'Y', and 'Z'.
Returns
-------
A 2D greyscale image suitable for use in matplotlib\'s ```imshow```
function.
"""
im = sp.array(~im, dtype=int)
if direction in ['Y', 'y']:
im = sp.transpose(im, axes=[1, 0, 2])
if direction in ['Z', 'z']:
im = sp.transpose(im, axes=[2, 1, 0])
t = im.shape[0]
depth = sp.reshape(sp.arange(0, t), [t, 1, 1])
im = im * depth
im = sp.amax(im, axis=0)
return im
def xray(im, direction='X'):
r"""
Simulates an X-ray radiograph looking through the porouls material in the
specfied direction. The resulting image is colored according to the amount
of attenuation an X-ray would experience, so regions with more solid will
appear darker.
Parameters
----------
im : array_like
ND-image of the porous material with the solid phase marked as 1 or
True
direction : string
Specify the axis along which the camera will point. Options are
'X', 'Y', and 'Z'.
Returns
-------
A 2D greyscale image suitable for use in matplotlib\'s ```imshow```
function.
"""
im = sp.array(~im, dtype=int)
if direction in ['Y', 'y']:
im = sp.transpose(im, axes=[1, 0, 2])
if direction in ['Z', 'z']:
im = sp.transpose(im, axes=[2, 1, 0])
im = sp.sum(im, axis=0)
return im
def LonVsLatArray(self):
""" """
self.glatbins = arange(self.glatlim[0], self.glatlim[1] + self.glatstp,
self.glatstp)
for glat in self.glatbins:
hwm14Obj = HWM14(alt=self.alt,
ap=self.ap,
glat=glat,
glonlim=self.glonlim,
glonstp=self.glonstp,
option=4,
verbose=self.verbose,
ut=self.ut)
Uwind = reshape(hwm14Obj.Uwind, (len(hwm14Obj.Uwind), 1))
Vwind = reshape(hwm14Obj.Vwind, (len(hwm14Obj.Vwind), 1))
self.Uwind = Uwind if glat == self.glatlim[0] else append(
self.Uwind, Uwind, axis=1)
self.Vwind = Vwind if glat == self.glatlim[0] else append(
self.Vwind, Vwind, axis=1)
self.glonbins = hwm14Obj.glonbins
self.Uwind = transpose(self.Uwind)
self.Vwind = transpose(self.Vwind)
def func(self, X, V):
H = self.F.sysfunc.hess(X, self.F.coords, self.F.coords)
q = self.F.testfunc.data.v/linalg.norm(self.F.testfunc.data.v)
p = self.F.testfunc.data.w/matrixmultiply(transpose(self.F.testfunc.data.w),q)
return array(0.5*matrixmultiply(transpose(p), reshape([bilinearform(H[i,:,:], q, q) \
for i in range(H.shape[0])],(H.shape[0],1)))[0])
def Problem3Real():
beta = 0.9
N = 1000
u = lambda c: sp.sqrt(c)
W = sp.linspace(0,1,N)
X, Y = sp.meshgrid(W,W)
Wdiff = sp.transpose(X-Y)
index = Wdiff <0
Wdiff[index] = 0
util_grid = u(Wdiff)
util_grid[index] = -10**10
Vprime = sp.zeros((N,1))
psi = sp.zeros((N,1))
delta = 1.0
tol = 10**-9
it = 0
max_iter = 500
while (delta >= tol) and (it < max_iter):
V = Vprime
it += 1;
#print(it)
val = util_grid + beta*sp.transpose(V)
Vprime = sp.amax(val, axis = 1)
Vprime = Vprime.reshape((N,1))
psi_ind = sp.argmax(val,axis = 1)
psi = W[psi_ind]
delta = sp.dot(sp.transpose(Vprime - V),Vprime-V)
return psi
def get_data(**kwargs):
data_file_name = kwargs['file_name'] + '.input'
true_file_name = kwargs['file_name'] + '.true'
reads_matrix = pd.DataFrame.from_csv(data_file_name, sep="\t").as_matrix()
var_reads = [scipy.transpose(reads_matrix[:,1])]
ref_reads = [scipy.transpose(reads_matrix[:,0])]
# Initialize the VAF_matrix, so skip the first two columns
VAF_matrix = scipy.transpose( reads_matrix[:,1]/ map(float, reads_matrix[:,0]))
# Iterate over columns minus the first two
reads_matrix = reads_matrix.T[2:]
for i, column in enumerate(reads_matrix):
# Skip every other column
if i % 2 != 0:
continue
var_reads.append(reads_matrix[i+1])
ref_reads.append(reads_matrix[i])
VAF_matrix = scipy.vstack((VAF_matrix, reads_matrix[i+1]/map(float, reads_matrix[i])))
var_reads = map(scipy.ndarray.tolist, var_reads)
ref_reads = map(scipy.ndarray.tolist, ref_reads)
true_VAFs, true_clusters = read_true_file(true_file_name)
Data = bnpy.data.XData(X=scipy.transpose(scipy.matrix(VAF_matrix)))
return (Data, var_reads, ref_reads, true_clusters, true_VAFs)
def mlr(x,y,order):
"""Multiple linear regression fit of the columns of matrix x
(dependent variables) to constituent vector y (independent variables)
order - order of a smoothing polynomial, which can be included
in the set of independent variables. If order is
not specified, no background will be included.
b - fit coeffs
f - fit result (m x 1 column vector)
r - residual (m x 1 column vector)
"""
if order > 0:
s=scipy.ones((len(y),1))
for j in range(order):
s=scipy.concatenate((s,(scipy.arange(0,1+(1.0/(len(y)-1)),1.0/(len(y)-1))**j)[:,nA]),1)
X=scipy.concatenate((x, s),1)
else:
X = x
#calc fit b=fit coefficients
b = scipy.dot(scipy.dot(scipy.linalg.pinv(scipy.dot(scipy.transpose(X),X)),scipy.transpose(X)),y)
f = scipy.dot(X,b)
r = y - f
return b,f,r
def plot_disc_policy():
#First compute policy function...==========================================
N = 500
w = sp.linspace(0,100,N)
w = w.reshape(N,1)
u = lambda c: sp.sqrt(c)
util_vec = u(w)
alpha = 0.5
alpha_util = u(alpha*w)
alpha_util_grid = sp.repeat(alpha_util,N,1)
m = 20
v = 200
f = discretelognorm(w,m,v)
VEprime = sp.zeros((N,1))
VUprime = sp.zeros((N,N))
EVUprime = sp.zeros((N,1))
psiprime = sp.ones((N,1))
gamma = 0.1
beta = 0.9
m = 15
tol = 10**-9
delta = 1+tol
it = 0
while (delta >= tol):
it += 1
psi = psiprime.copy()
arg1 = sp.repeat(sp.transpose(VEprime),N,0)
arg2 = sp.repeat(EVUprime,N,1)
arg = sp.array([arg2,arg1])
psiprime = sp.argmax(arg,axis = 0)
for j in sp.arange(0,m):
VE = VEprime.copy()
VU = VUprime.copy()
EVU = EVUprime.copy()
VEprime = util_vec + beta*((1-gamma)*VE + gamma*EVU)
arg1 = sp.repeat(sp.transpose(VE),N,0)*psiprime
arg2 = sp.repeat(EVU,N,1)*(1-psiprime)
arg = arg1+arg2
VUprime = alpha_util_grid + beta*arg
EVUprime = sp.dot(VUprime,f)
delta = sp.linalg.norm(psiprime -psi)
wr_ind = sp.argmax(sp.diff(psiprime), axis = 1)
wr = w[wr_ind]
print w[250],wr[250]
#Then plot=================================================================
plt.plot(w,psiprime[250,:])
plt.ylim([-.5,1.5])
plt.xlabel(r'$w\prime$')
plt.yticks([0,1])
plt.savefig('disc_policy.pdf')
def updatedata(self, A):
if self.update:
if self.corr:
self.data.B = self.data.w*(linalg.norm(A,1)/linalg.norm(self.data.w,1))
self.data.C = self.data.v*(linalg.norm(A,Inf)/linalg.norm(self.data.v,1))
else:
# Note: Problem when singular vectors switch smallest singular value (See NewLorenz).
# To overcome this, I have implemented a 1e-8 random nudge.
try:
ALU = linalg.lu_factor(A)
BC = linalg.lu_solve(ALU, c_[linalg.lu_solve(ALU, self.data.B + 1e-8*self.data.Brand), \
self.data.C + 1e-8*self.data.Crand], trans=1)
C = linalg.lu_solve(ALU, BC[:,-1*self.data.q:])
B = BC[:,0:self.data.p]
except:
if self.C.verbosity >= 1:
print 'Warning: Problem updating border vectors. Using svd...'
U, S, Vh = linalg.svd(A)
B = U[:,-1*self.data.p:]
C = num_transpose(Vh)[:,-1*self.data.q:]
bmult = cmult = 1
if matrixmultiply(transpose(self.data.B), B) < 0:
bmult = -1
if matrixmultiply(transpose(self.data.C), C) < 0:
cmult = -1
self.data.B = bmult*B*(linalg.norm(A,1)/linalg.norm(B))
self.data.C = cmult*C*(linalg.norm(A,Inf)/linalg.norm(C))
def Problem3Real():
beta = 0.9
N = 1000
u = lambda c: sp.sqrt(c)
W = sp.linspace(0, 1, N)
X, Y = sp.meshgrid(W, W)
Wdiff = sp.transpose(X - Y)
index = Wdiff < 0
Wdiff[index] = 0
util_grid = u(Wdiff)
util_grid[index] = -10**10
Vprime = sp.zeros((N, 1))
psi = sp.zeros((N, 1))
delta = 1.0
tol = 10**-9
it = 0
max_iter = 500
while (delta >= tol) and (it < max_iter):
V = Vprime
it += 1
#print(it)
val = util_grid + beta * sp.transpose(V)
Vprime = sp.amax(val, axis=1)
Vprime = Vprime.reshape((N, 1))
psi_ind = sp.argmax(val, axis=1)
psi = W[psi_ind]
delta = sp.dot(sp.transpose(Vprime - V), Vprime - V)
return psi
def updatedata(self, A):
# Update b, c
try:
ALU = linalg.lu_factor(A)
BC = linalg.lu_solve(ALU, c_[linalg.lu_solve(ALU, self.data.b + 1e-8*self.data.Brand[:,:1]), \
self.data.c + 1e-8*self.data.Crand[:,:1]], trans=1)
C = linalg.lu_solve(ALU, BC[:,-1:])
B = BC[:,:1]
except:
if self.C.verbosity >= 1:
print 'Warning: Problem updating border vectors. Using svd...'
U, S, Vh = linalg.svd(A)
B = U[:,-1:]
C = num_transpose(Vh)[:,-1:]
bmult = cmult = 1
if matrixmultiply(transpose(self.data.b), B) < 0:
bmult = -1
if matrixmultiply(transpose(self.data.c), C) < 0:
cmult = -1
self.data.b = bmult*B*(linalg.norm(A,1)/linalg.norm(B))
self.data.c = cmult*C*(linalg.norm(A,Inf)/linalg.norm(C))
# Update
if self.update:
self.data.B[:,0] = self.data.b*(linalg.norm(A,1)/linalg.norm(self.data.b))
self.data.C[:,0] = self.data.c*(linalg.norm(A,Inf)/linalg.norm(self.data.c))
self.data.B[:,1] = self.data.w[:,2]*(linalg.norm(A,1)/linalg.norm(self.data.w,1))
self.data.C[:,1] = self.data.v[:,2]*(linalg.norm(A,Inf)/linalg.norm(self.data.v,1))
self.data.D[0,1] = self.data.g[0,1]
self.data.D[1,0] = self.data.g[1,0]
def update_image(original_im, ci_red, ci_green, ci_blue):
# diagnostics = dict()
original_im = scipy.transpose(original_im)
# diagnostics['original_im'] = original_im
# diagnostics['ci_red'] = ci_red
# diagnostics['ci_green'] = ci_green
# diagnostics['ci_blue'] = ci_blue
new_r = scipy.multiply(original_im[0], original_im[0] > ci_red)
new_g = scipy.multiply(original_im[1], original_im[1] > ci_green)
new_b = scipy.multiply(original_im[2], original_im[2] > ci_blue)
new_im = (new_r, new_g, new_b)
new_im = scipy.transpose(new_im)
# diagnostics['new_im'] = new_im
# with open('/Users/lages/Documents/sauceda/pictures_processed/diagnostics'
# '.p', 'wb') as f:
# pickle.dump(diagnostics, f)
return new_im
def baseline1(myarray):
"""Set first bin of each row to zero
"""
size = myarray.shape
take_array = scipy.transpose(
scipy.resize(scipy.transpose(myarray[:, 0]), (size[1], size[0])))
return myarray - take_array
def _padarray(myarray, frame, type):
"""Used in a number of funcs to pad out array cols at start and
end so that the original shape of the array is maintained
following processing"""
(div, mod) = divmod(frame,
2) #pad array to keep original shape after averaging
if mod <> 0:
pad = (frame - 1) / 2
else:
pad = frame / 2
size = myarray.shape
if type == 'av':
start = scipy.transpose(
scipy.resize(scipy.transpose(scipy.mean(myarray[:, 0:pad], 1)),
(pad, size[0])))
end = scipy.transpose(
scipy.resize(
scipy.transpose(
scipy.mean(myarray[:, size[1] - pad:size[1]], 1)),
(pad, size[0])))
elif type == 'zero':
start = end = scipy.transpose(
scipy.resize(scipy.zeros((size[0], 1)), (pad, size[0])))
padarray = scipy.concatenate((start, myarray, end), 1)
return padarray, size
def hyperplane_equation_by_nullspace_from_points(points, t_equivalence='True'):
t_ = []
if t_equivalence == True:
debug("original points:\n", points)
for point in points:
t_.append(eT(point))
points = t_
debug("points:\n", points)
try:
debug("determinant of points:", scipy.linalg.det(points))
except:
pass
homogeneous_points = []
for point in points:
homogeneous_points.append(scipy.append(point, [1]))
debug("homogeneous points:", homogeneous_points)
nullspace = scipy.linalg.null_space(homogeneous_points)
nullspace = scipy.ndarray.flatten(nullspace[:-1])
debug("nullspace from homogeneous points:", nullspace)
constant_term = scipy.dot(scipy.transpose(nullspace), points[0])
debug("constant_term:", constant_term)
norm = scipy.linalg.norm(nullspace)
debug("norm:", norm)
unit_normal = scipy.divide(nullspace, norm)
print("unit normal vector:", unit_normal)
constant_term = scipy.dot(scipy.transpose(unit_normal), points[0])
print("constant_term:", constant_term)
return unit_normal, constant_term
def simplicial_grid_2d(n):
"""
Create an NxN 2d grid in the unit square
The number of vertices along each axis is (N+1) for a total of (N+1)x(N+1) vertices
A tuple (vertices,indices) of arrays is returned
"""
vertices = zeros(((n + 1)**2, 2))
vertices[:, 0] = ravel(resize(arange(n + 1), (n + 1, n + 1)))
vertices[:, 1] = ravel(transpose(resize(arange(n + 1), (n + 1, n + 1))))
vertices /= n
indices = zeros((2 * (n**2), 3), scipy.int32)
t1 = transpose(
concatenate((matrix(arange(n)), matrix(arange(
1, n + 1)), matrix(arange(n + 2, 2 * n + 2))),
axis=0))
t2 = transpose(
concatenate((matrix(arange(n)), matrix(arange(
n + 2, 2 * n + 2)), matrix(arange(n + 1, 2 * n + 1))),
axis=0))
first_row = concatenate((t1, t2))
for i in xrange(n):
indices[(2 * n * i):(2 * n * (i + 1)), :] = first_row + i * (n + 1)
return (vertices, indices)
def sqcover(A,n):
edge = sp.sqrt(A) # the length of an edge
d = edge/n # the distance between two adjacent points
r = d/2 # the "radius of "
end = edge - r # end point
base = sp.linspace(r, end, n)
first_line = sp.transpose(sp.vstack((base, r*sp.ones(n))))
increment = sp.transpose(sp.vstack((sp.zeros(n), d*sp.ones(n))))
pts = first_line
y_diff = increment
for i in range(n-1):
pts = sp.vstack((pts, first_line + y_diff))
y_diff = y_diff + increment
# Color matter
colors = []
for p in pts:
cval = n*p[0] + p[1] # the x-coord has a higher weight
cval = colormap.Spectral(cval/((n+1)*end)) # normalize by the max value that cval can take.
colors.append(cval)
colors = sp.array(colors)
cover = (pts, r, colors)
return cover
def plot_delta():
beta = 0.99
N = 1000
u = lambda c: sp.sqrt(c)
W = sp.linspace(0,1,N)
X, Y = sp.meshgrid(W,W)
Wdiff = sp.transpose(X-Y)
index = Wdiff <0
Wdiff[index] = 0
util_grid = u(Wdiff)
util_grid[index] = -10**10
Vprime = sp.zeros((N,1))
delta = sp.ones(1)
tol = 10**-9
it = 0
max_iter = 500
while (delta[-1] >= tol) and (it < max_iter):
V = Vprime
it += 1;
print(it)
val = util_grid + beta*sp.transpose(V)
Vprime = sp.amax(val, axis = 1)
Vprime = Vprime.reshape((N,1))
delta = sp.append(delta,sp.dot(sp.transpose(Vprime - V),Vprime-V))
plt.figure()
plt.plot(delta[1:])
plt.ylabel(r'$\delta_k$')
plt.xlabel('iteration')
plt.savefig('convergence.pdf')
def plot_delta():
beta = 0.99
N = 1000
u = lambda c: sp.sqrt(c)
W = sp.linspace(0,1,N)
X, Y = sp.meshgrid(W,W)
Wdiff = sp.transpose(X-Y)
index = Wdiff <0
Wdiff[index] = 0
util_grid = u(Wdiff)
util_grid[index] = -10**10
Vprime = sp.zeros((N,1))
delta = sp.ones(1)
tol = 10**-9
it = 0
max_iter = 500
while (delta[-1] >= tol) and (it < max_iter):
V = Vprime
it += 1;
print(it)
val = util_grid + beta*sp.transpose(V)
Vprime = sp.amax(val, axis = 1)
Vprime = Vprime.reshape((N,1))
delta = sp.append(delta,sp.dot(sp.transpose(Vprime - V),Vprime-V))
plt.figure()
plt.plot(delta[1:])
plt.ylabel(r'$\delta_k$')
plt.xlabel('iteration')
plt.savefig('convergence.pdf')
def load(self):
self.load_images()
self.load_logfile()
self.times = set()
for ts in self.timestamp_to_image.keys():
self.times.add(ts)
for ts in self.timestamp_to_fread.keys():
self.times.add(ts)
for ts in self.timestamp_to_odom.keys():
self.times.add(ts)
self.times = list(self.times)
self.times.sort()
self.times = array(self.times)
#get freadings XY representation
t_to_f = self.timestamp_to_fread
self.freadings_XY = transpose(
[[t_to_f[i].location.x, t_to_f[i].location.y]
for i in sorted(self.timestamp_to_fread.keys())])
self.freadings_Th = transpose([
t_to_f[i].location.theta
for i in sorted(self.timestamp_to_fread.keys())
])
def getHessFull(gammas=None, amounts=None, numExps=3):
if gammas is None:
gammas = getGammas(numExps)
if amounts is None:
amounts = getAmounts(numExps)
numExps = scipy.size(gammas)
hessgg = getHessGG(gammas)
hessAA = getHessAA(amounts, gammas)
numerAg1 = -scipy.outer(amounts, amounts * gammas)
denomAg1 = scipy.outer(scipy.ones(numExps), gammas)
denomAg2 = scipy.transpose(denomAg1) + denomAg1
denomAg3 = denomAg2 * denomAg2
hessAg = old_div(numerAg1, denomAg3)
numergA1 = -scipy.outer(amounts * gammas, amounts)
denomgA1 = scipy.outer(gammas, scipy.ones(numExps))
denomgA2 = scipy.transpose(denomgA1) + denomgA1
denomgA3 = denomgA2 * denomgA2
hessgA = old_div(numergA1, denomgA3)
hessFull = scipy.bmat([[hessAA, hessAg], [hessgA, hessgg]])
return hessFull
def calc_BB_Y_2s_ham_3s(A_m1, A_p2, C, C_m1, Vlh, Vrh_p1, l_m2, r_p2, l_s_m1,
l_si_m1, r_s_p1, r_si_p1):
Vr_p1 = sp.transpose(Vrh_p1, axes=(0, 2, 1)).conj()
Vrri_p1 = sp.zeros_like(Vr_p1)
try:
for s in xrange(Vrri_p1.shape[0]):
Vrri_p1[s] = r_si_p1.dot_left(Vr_p1[s])
except AttributeError:
for s in xrange(Vrri_p1.shape[0]):
Vrri_p1[s] = Vr_p1[s].dot(r_si_p1)
Vl = sp.transpose(Vlh, axes=(0, 2, 1)).conj()
liVl = sp.zeros_like(Vl)
for s in xrange(liVl.shape[0]):
liVl[s] = l_si_m1.dot(Vl[s])
Y = sp.zeros((Vlh.shape[1], Vrh_p1.shape[2]), dtype=Vrh_p1.dtype)
if not A_p2 is None:
for s in xrange(C.shape[0]):
Y += Vlh[s].dot(
l_s_m1.dot(eps_r_op_2s_C12(r_p2, C[s], Vrri_p1, A_p2)))
if not A_m1 is None:
for u in xrange(C_m1.shape[2]):
Y += eps_l_op_2s_A1_A2_C34(l_m2, A_m1, liVl,
C_m1[:, :,
u]).dot(r_s_p1.dot(Vrh_p1[u]))
etaBB_sq = mm.adot(Y, Y)
return Y, etaBB_sq
def trueFeatureStats(T, R, fMap, discountFactor, stateProp=1, MAT_LIMIT=1e8):
""" Gather the statistics needed for LSTD,
assuming infinite data (true probabilities).
Option: if stateProp is < 1, then only a proportion of all
states will be seen as starting state for transitions """
dim = len(fMap)
numStates = len(T)
statMatrix = zeros((dim, dim))
statResidual = zeros(dim)
ss = range(numStates)
repVersion = False
if stateProp < 1:
ss = random.sample(ss, int(numStates * stateProp))
elif dim * numStates**2 < MAT_LIMIT:
repVersion = True
# two variants, depending on how large we can afford our matrices to become.
if repVersion:
tmp1 = tile(fMap, (numStates,1,1))
tmp2 = transpose(tmp1, (2,1,0))
tmp3 = tmp2 - discountFactor * tmp1
tmp4 = tile(T, (dim,1,1))
tmp4 *= transpose(tmp1, (1,2,0))
statMatrix = tensordot(tmp3, tmp4, axes=[[0,2], [1,2]]).T
statResidual = dot(R, dot(fMap, T).T)
else:
for sto in ss:
tmp = fMap - discountFactor * repmat(fMap[:, sto], numStates, 1).T
tmp2 = fMap * repmat(T[:, sto], dim, 1)
statMatrix += dot(tmp2, tmp.T)
statResidual += R[sto] * dot(fMap, T[:, sto])
return statMatrix, statResidual
def LonVsHeiArray(self):
""" """
self.altbins = arange(self.altlim[0], self.altlim[1] + self.altstp,
self.altstp)
for alt in self.altbins:
if True:
hwm14Obj = HWM14(alt=alt,
ap=self.ap,
glat=self.glat,
glonlim=self.glonlim,
glonstp=self.glonstp,
option=self.option,
verbose=self.verbose,
ut=self.ut)
else:
pass
Uwind = reshape(hwm14Obj.Uwind, (len(hwm14Obj.Uwind), 1))
Vwind = reshape(hwm14Obj.Vwind, (len(hwm14Obj.Vwind), 1))
self.Uwind = Uwind if alt == self.altlim[0] else append(
self.Uwind, Uwind, axis=1)
self.Vwind = Vwind if alt == self.altlim[0] else append(
self.Vwind, Vwind, axis=1)
self.glonbins = hwm14Obj.glonbins
self.Uwind = transpose(self.Uwind)
self.Vwind = transpose(self.Vwind)
def read_input_data(self):
"""
On init, read the data file.
"""
true_file_name = self.data_dir + ".input"
reads_matrix = pd.DataFrame.from_csv(true_file_name,
sep="\t").as_matrix()
var_reads = [scipy.transpose(reads_matrix[:, 1])]
ref_reads = [scipy.transpose(reads_matrix[:, 0])]
# Initialize the VAF_matrix, so skip the first two columns
VAF_matrix = scipy.transpose(reads_matrix[:, 1] /
map(float, reads_matrix[:, 0]))
# Iterate over columns minus the first two
reads_matrix = reads_matrix.T[2:]
for i, column in enumerate(reads_matrix):
# Skip every other column
if i % 2 != 0:
continue
var_reads.append(reads_matrix[i + 1])
ref_reads.append(reads_matrix[i])
VAF_matrix = scipy.vstack(
(VAF_matrix,
reads_matrix[i + 1] / map(float, reads_matrix[i])))
var_reads = map(scipy.ndarray.tolist, var_reads)
ref_reads = map(scipy.ndarray.tolist, ref_reads)
self.VAFs = VAF_matrix
self.reads_matrix = reads_matrix
self.var_reads = var_reads
self.ref_reads = ref_reads
def mlr(self, x, y):
"""Multiple linear regression fit of the columns of matrix x
(dependent variables) to constituent vector y (independent variables)
order - order of a smoothing polynomial, which can be included
in the set of independent variables. If order is
not specified, no background will be included.
b - fit coeffs
f - fit result (m x 1 column vector)
r - residual (m x 1 column vector)
"""
if self.order > 0:
s = scipy.ones((len(y), 1))
for j in range(self.order):
s = scipy.concatenate(
(s, (scipy.arange(0, 1 + (1.0 / (len(y) - 1)), 1.0 /
(len(y) - 1))**j)[:, nA]), 1)
X = scipy.concatenate((x, s), 1)
else:
X = x
#calc fit b=fit coefficients
b = scipy.dot(
scipy.dot(scipy.linalg.pinv(scipy.dot(scipy.transpose(X), X)),
scipy.transpose(X)), y)
f = scipy.dot(X, b)
r = y - f
return b, f, r
def sdc_to_distributions(self, mysdc):
"""
Convert the SDC to distributions used in the inference.
"""
print "*******************************"
if "right" in mysdc["verb"]:
D_mat = transpose(self.T_mat_right)
elif "left" in mysdc["verb"]:
D_mat = transpose(self.T_mat_left)
elif "turn_around" in mysdc["verb"]:
D_mat = transpose(self.T_mat_back * self.T_mat_face)
elif "face" in mysdc["verb"]:
print "using face"
D_mat = transpose(self.T_mat_face)
else:
D_mat = transpose(self.T_mat_str)
D_mat = ones(self.T_mat_str.shape)
print "before vertical"
print_tmat(transpose(D_mat), 40, 42)
if "up" in mysdc["verb"]:
print "using up"
D_mat = D_mat * transpose(self.T_mat_up)
elif "down" in mysdc["verb"]:
D_mat = D_mat * transpose(self.T_mat_down)
else:
print "using stay"
D_mat = D_mat * transpose(self.T_mat_stay)
print "dmat final"
print_tmat(transpose(D_mat), 40, 42)
T_mat = ones([len(D_mat), len(D_mat[0])]) * 1.0
if mysdc["sr"] != None and len(
mysdc["landmarks"]) > 0 and self.use_spatial_relations:
sr_i = self.sr_class.engineToIdx(mysdc["sr"])
SR_mat = self.srel_mat[sr_i, :, :, :]
L_mat = self.get_prob_landmark_given_sdc_modifiers(mysdc)
else:
SR_mat = None
L_mat = None
if mysdc["landmark"] != None:
landmark_i = self.names_to_index[mysdc["landmark"]]
O_mat_oriented = self.O_mat_oriented[:, landmark_i]
O_mat_topo = self.O_mat[:, landmark_i]
if "face" in mysdc["verb"]:
print "using O_mat_oriented"
O_mat = O_mat_oriented
else:
O_mat = O_mat_topo
print "shape", O_mat_topo.shape
print "O_mat_topo", O_mat_topo[18]
print "O_mat_oriented", O_mat_oriented[18]
else:
O_mat = None
return O_mat, T_mat, SR_mat, L_mat, D_mat
def calc_BB_Y_2s_ham_3s(A_m1, A_p2, C, C_m1, Vlh, Vrh_p1, l_m2, r_p2, l_s_m1, l_si_m1, r_s_p1, r_si_p1):
Vr_p1 = sp.transpose(Vrh_p1, axes=(0, 2, 1)).conj()
Vrri_p1 = sp.zeros_like(Vr_p1)
try:
for s in xrange(Vrri_p1.shape[0]):
Vrri_p1[s] = r_si_p1.dot_left(Vr_p1[s])
except AttributeError:
for s in xrange(Vrri_p1.shape[0]):
Vrri_p1[s] = Vr_p1[s].dot(r_si_p1)
Vl = sp.transpose(Vlh, axes=(0, 2, 1)).conj()
liVl = sp.zeros_like(Vl)
for s in xrange(liVl.shape[0]):
liVl[s] = l_si_m1.dot(Vl[s])
Y = sp.zeros((Vlh.shape[1], Vrh_p1.shape[2]), dtype=Vrh_p1.dtype)
if not A_p2 is None:
for s in xrange(C.shape[0]):
Y += Vlh[s].dot(l_s_m1.dot(eps_r_op_2s_C12(r_p2, C[s], Vrri_p1, A_p2)))
if not A_m1 is None:
for u in xrange(C_m1.shape[2]):
Y += eps_l_op_2s_A1_A2_C34(l_m2, A_m1, liVl, C_m1[:, :, u]).dot(r_s_p1.dot(Vrh_p1[u]))
etaBB_sq = mm.adot(Y, Y)
return Y, etaBB_sq
def plot_resid(d, savename='resfig1.png'):
"""
Plots the residual frequency after the first wipe using the TLE velocity.
"""
flim = [-2.e3, 2.e3]
t = d['tvec']
dates = [dt.datetime.fromtimestamp(ts) for ts in t]
datenums = md.date2num(dates)
xfmt = md.DateFormatter('%Y-%m-%d %H:%M:%S')
fig1 = plt.figure(figsize=(7, 9))
doppler_residual = sp.interpolate.interp1d(d['tvec'], d['dopfit'])
fvec = d["fvec"]
res0 = d["res0"]
res1 = d["res1"]
plt.subplot(211)
mesh = plt.pcolormesh(datenums,
fvec,
sp.transpose(10. * sp.log10(res0 + 1e-12)),
vmin=-5,
vmax=25)
plt.plot(datenums, (150.0 / 400.0) * doppler_residual(t),
"r--",
label="doppler resid")
ax = plt.gca()
ax.xaxis.set_major_formatter(xfmt)
plt.ylim(flim)
plt.subplots_adjust(bottom=0.2)
plt.xticks(rotation=25)
plt.xlabel("UTC")
plt.ylabel("Frequency (Hz)")
plt.title("Power ch0 (dB) %1.2f MHz" % (150.012))
plt.legend()
plt.colorbar(mesh, ax=ax)
# quicklook spectra of residuals spectra along with measured Doppler residual from second channel.
plt.subplot(212)
mesh = plt.pcolormesh(datenums,
fvec,
sp.transpose(10. * sp.log10(res1 + 1e-12)),
vmin=-5,
vmax=25)
plt.plot(datenums, doppler_residual(t), "r--", label="doppler resid")
ax = plt.gca()
ax.xaxis.set_major_formatter(xfmt)
plt.ylim(flim)
plt.xlabel("UTC")
plt.ylabel("Frequency (Hz)")
plt.title("Power ch1 (dB), %1.2f MHz" % (400.032))
plt.subplots_adjust(bottom=0.2)
plt.xticks(rotation=25)
plt.legend()
plt.colorbar(mesh, ax=ax)
plt.tight_layout()
print('Saving residual plots: ' + savename)
plt.savefig(savename, dpi=300)
plt.close(fig1)
def __interpolateBetweenBinaryObjects(obj1, obj2, slices):
"""
Takes two binary objects and puts slices slices in-between them, each of which
contains a smooth binary transition between the objects.
@note private inner function
"""
if not obj1.shape == obj2.shape:
raise AttributeError(
"The two supplied objects have to be of the same shape, not {} and {}.".format(obj1.shape, obj2.shape)
)
# constant
offset = 0.5 # must be a value smaller than the minimal distance possible
temporal_dimension = 3
# get all voxel position
obj1_voxel = scipy.nonzero(obj1)
obj2_voxel = scipy.nonzero(obj2)
# get smallest pairwise distances between all object voxels
distances = cdist(scipy.transpose(obj1_voxel), scipy.transpose(obj2_voxel))
# keep for each True voxel of obj1 only the smallest distance to a True voxel in obj2
min_distances = distances.min(1)
# test if all seems to work
if len(min_distances) != len(obj1_voxel[0]):
raise Exception("Invalid number of minimal distances received.")
# replace True voxels in obj1 with their respective distances to the True voxels in obj2
thr_obj = obj1.copy()
thr_obj = thr_obj.astype(scipy.float_)
thr_obj[obj1_voxel] = min_distances
thr_obj[obj1_voxel] += offset # previous steps distances include zeros, therefore this is required
# compute the step size for each slice that is added
maximum = min_distances.max()
step = maximum / float(slices + 1)
threshold = maximum
# control step: see if thr_obj really corresponds to obj1
if not scipy.all(thr_obj.astype(scipy.bool_) == obj1.astype(scipy.bool_)):
raise Exception("First created object does not correspond to obj1.")
# assemble return volume
return_volume = [thr_obj.astype(scipy.bool_)] # corresponds to obj1
for _ in range(slices):
threshold -= step
# remove all value higher than the threshold
thr_obj[thr_obj > threshold] = 0
# add binary volume to list /makes a copy)
return_volume.append(thr_obj.astype(scipy.bool_))
# add last slice (corresponds to es obj2 slice)
thr_obj[thr_obj > offset] = 0
return_volume.append(thr_obj.astype(scipy.bool_))
# return binary scipy array
return scipy.rollaxis(scipy.asarray(return_volume, dtype=scipy.bool_), 0, temporal_dimension + 1)
def disc_policy():
#First compute policy function...==========================================
N = 500
w = sp.linspace(0, 100, N)
w = w.reshape(N, 1)
u = lambda c: sp.sqrt(c)
util_vec = u(w)
alpha = 0.5
alpha_util = u(alpha * w)
alpha_util_grid = sp.repeat(alpha_util, N, 1)
m = 20
v = 200
f = discretelognorm(w, m, v)
VEprime = sp.zeros((N, 1))
VUprime = sp.zeros((N, N))
EVUprime = sp.zeros((N, 1))
psiprime = sp.ones((N, 1))
gamma = 0.1
beta = 0.9
m = 15
tol = 10**-9
delta = 1 + tol
it = 0
while (delta >= tol):
it += 1
psi = psiprime.copy()
arg1 = sp.repeat(sp.transpose(VEprime), N, 0)
arg2 = sp.repeat(EVUprime, N, 1)
arg = sp.array([arg2, arg1])
psiprime = sp.argmax(arg, axis=0)
for j in sp.arange(0, m):
VE = VEprime.copy()
VU = VUprime.copy()
EVU = EVUprime.copy()
VEprime = util_vec + beta * ((1 - gamma) * VE + gamma * EVU)
arg1 = sp.repeat(sp.transpose(VE), N, 0) * psiprime
arg2 = sp.repeat(EVU, N, 1) * (1 - psiprime)
arg = arg1 + arg2
VUprime = alpha_util_grid + beta * arg
EVUprime = sp.dot(VUprime, f)
delta = sp.linalg.norm(psiprime - psi)
wr_ind = sp.argmax(sp.diff(psiprime), axis=1)
wr = w[wr_ind]
print w[250], wr[250]
#Then plot=================================================================
plt.plot(w, psiprime[250, :])
plt.ylim([-.5, 1.5])
plt.xlabel(r'$w\prime$')
plt.yticks([0, 1])
plt.savefig('disc_policy.pdf')
plt.clf()
def calculate_ld(snps):
#filter non binary snps
snps_t = scipy.transpose(snps)
snps_stand = scipy.transpose((snps_t - scipy.mean(snps, 1)) / scipy.std(snps, 1))
r2_values =scipy.dot(snps_stand, scipy.transpose(snps_stand))
r2_values *= (1.0 / snps.shape[1])
r2_values **= 2
return r2_values
def baseline2(myarray):
"""Subtract average of the first and last bin from each bin
"""
size = myarray.shape
take_array = scipy.transpose(
scipy.resize(scipy.transpose((myarray[:, 0] + myarray[:, size[1] - 1]) / 2), (size[1], size[0]))
)
return myarray - take_array
def calculate_ld(snps):
#filter non binary snps
snps_t = scipy.transpose(snps)
snps_stand = scipy.transpose((snps_t - scipy.mean(snps, 1)) / scipy.std(snps, 1))
r2_values =scipy.dot(snps_stand, scipy.transpose(snps_stand))
r2_values *= (1.0 / snps.shape[1])
r2_values **= 2
return r2_values
def __interpolateBetweenBinaryObjects(obj1, obj2, slices):
"""
Takes two binary objects and puts slices slices in-between them, each of which
contains a smooth binary transition between the objects.
@note private inner function
"""
if not obj1.shape == obj2.shape:
raise AttributeError('The two supplied objects have to be of the same shape, not {} and {}.'.format(obj1.shape, obj2.shape))
# constant
offset = 0.5 # must be a value smaller than the minimal distance possible
temporal_dimension = 3
# get all voxel position
obj1_voxel = scipy.nonzero(obj1)
obj2_voxel = scipy.nonzero(obj2)
# get smallest pairwise distances between all object voxels
distances = cdist(scipy.transpose(obj1_voxel),
scipy.transpose(obj2_voxel))
# keep for each True voxel of obj1 only the smallest distance to a True voxel in obj2
min_distances = distances.min(1)
# test if all seems to work
if len(min_distances) != len(obj1_voxel[0]):
raise Exception('Invalid number of minimal distances received.')
# replace True voxels in obj1 with their respective distances to the True voxels in obj2
thr_obj = obj1.copy()
thr_obj = thr_obj.astype(scipy.float_)
thr_obj[obj1_voxel] = min_distances
thr_obj[obj1_voxel] += offset # previous steps distances include zeros, therefore this is required
# compute the step size for each slice that is added
maximum = min_distances.max()
step = maximum / float(slices + 1)
threshold = maximum
# control step: see if thr_obj really corresponds to obj1
if not scipy.all(thr_obj.astype(scipy.bool_) == obj1.astype(scipy.bool_)):
raise Exception('First created object does not correspond to obj1.')
# assemble return volume
return_volume = [thr_obj.astype(scipy.bool_)] # corresponds to obj1
for _ in range(slices):
threshold -= step
# remove all value higher than the threshold
thr_obj[thr_obj > threshold] = 0
# add binary volume to list /makes a copy)
return_volume.append(thr_obj.astype(scipy.bool_))
# add last slice (corresponds to es obj2 slice)
thr_obj[thr_obj > offset] = 0
return_volume.append(thr_obj.astype(scipy.bool_))
# return binary scipy array
return scipy.rollaxis(scipy.asarray(return_volume, dtype=scipy.bool_), 0, temporal_dimension + 1)
def nb_vals(matrix, indices):
matrix = scipy.array(matrix)
indices = tuple(scipy.transpose(scipy.atleast_2d(indices)))
arr_shape = scipy.shape(matrix)
dist = scipy.ones(arr_shape)
dist[indices] = 0
dist = scipy.ndimage.distance_transform_cdt(dist, metric='chessboard')
nb_indices = scipy.transpose(scipy.nonzero(dist == 1))
return [matrix[tuple(ind)] for ind in nb_indices]
def least_squares_interpolant(x, y):
xmat = sp.zeros((len(x), 2))
for i in range(len(x)):
for j in range(2):
xmat[i][j] = x[i] ** j
a = sp.matmul(sp.transpose(xmat), xmat)
b = sp.matmul(sp.transpose(xmat), y)
ans = numpy.linalg.solve(a, b)
return ans, xmat
def to_minimize_fidelity(theta):
temp_z_gate = np.matmul(
sp.linalg.expm(-2 * np.pi * 1j * theta * self.H_zeeman),
U_ideal)
temp_m = np.matmul(sp.conjugate(sp.transpose(target)),
temp_z_gate)
return np.real(1. - (sp.trace(
np.matmul(temp_m, sp.conjugate(sp.transpose(temp_m)))) +
np.abs(sp.trace(temp_m))**2.) / 20.)
def baseline2(myarray):
"""Subtract average of the first and last bin from each bin
"""
size = myarray.shape
take_array = scipy.transpose(
scipy.resize(
scipy.transpose((myarray[:, 0] + myarray[:, size[1] - 1]) / 2),
(size[1], size[0])))
return myarray - take_array
def mls(p):
data = ascii.read("datos.dat")
x=data["col1"]
y=data["col2"]
z=data["col3"]
sig=30*(10**(-6))
Y=sy.subtract(y,1)
A=[]
for m in x:
pol=[]
for i in range(p+1):
pol.append(m**i)
if m <0.4 or m>0.7:
pol.append(0)
A.append(pol)
else:
pol.append(-1)
A.append(pol)
theta= sy.dot( sy.linalg.inv(sy.dot( sy.transpose(A),A )) , sy.dot(sy.transpose(A),Y) )
modelo=[]
for i in x:
poli=1
for s in range(p+1):
poli+=(theta[s]*(i**s))
e=sy.random.normal(0,sig)
if i <0.4 or i>0.7:
modelo.append(poli)
else:
modelo.append(poli - theta[len(theta)-1])
chi2=0
for h in range(len(x)):
chi2+= ((y[h]-modelo[h]) / (sig) ) **2
return modelo, theta , len(x) ,sig ,chi2
def trim(image): # 255 - white
tr_image = transpose(image)
start = 0
while sum(tr_image[start]) == 255 * len(tr_image[start]):
# condition on i is not needed, because of the balance between white and black
start += 1
finish = len(tr_image) - 1
while sum(tr_image[finish]) == 255 * len(tr_image[finish]):
finish -= 1
return transpose(tr_image[start: finish + 1])
def Problem6Real():
N = 500
w = sp.linspace(0,100,N)
w = w.reshape(N,1)
u = lambda c: sp.sqrt(c)
util_vec = u(w)
alpha = 0.5
alpha_util = u(alpha*w)
alpha_util_grid = sp.repeat(alpha_util,N,1)
m = 20
v = 200
f = discretelognorm(w,m,v)
VEprime = sp.zeros((N,1))
VUprime = sp.zeros((N,N))
EVUprime = sp.zeros((N,1))
psiprime = sp.ones((N,1))
gamma = 0.1
beta = 0.9
m = 15
tol = 10**-9
delta = 1+tol
it = 0
while (delta >= tol):
it += 1
psi = psiprime.copy()
arg1 = sp.repeat(sp.transpose(VEprime),N,0)
arg2 = sp.repeat(EVUprime,N,1)
arg = sp.array([arg2,arg1])
psiprime = sp.argmax(arg,axis = 0)
for j in sp.arange(0,m):
VE = VEprime.copy()
VU = VUprime.copy()
EVU = EVUprime.copy()
VEprime = util_vec + beta*((1-gamma)*VE + gamma*EVU)
arg1 = sp.repeat(sp.transpose(VE),N,0)*psiprime
arg2 = sp.repeat(EVU,N,1)*(1-psiprime)
arg = arg1+arg2
VUprime = alpha_util_grid + beta*arg
EVUprime = sp.dot(VUprime,f)
delta = sp.linalg.norm(psiprime -psi)
#print(delta)
wr_ind = sp.argmax(sp.diff(psiprime), axis = 1)
wr = w[wr_ind]
plt.plot(w,wr)
plt.show()
return wr
def calc_BB_Y_2s_tp(C_tp, Vlh, Vrh_p1, l_s_m1, r_s_p1):
Vl = sp.transpose(Vlh, axes=(0, 2, 1)).conj().copy()
Vr_p1 = sp.transpose(Vrh_p1, axes=(0, 2, 1)).conj().copy()
Y = 0
for al in xrange(len(C_tp)):
Y += eps_l_noop(l_s_m1, Vl, C_tp[al][0]).dot(eps_r_noop(r_s_p1, C_tp[al][1], Vr_p1))
etaBB_sq = mm.adot(Y, Y)
return Y, etaBB_sq
def param(y):
Y=sy.subtract(y,1)
A=[]
for m in x:
A.append([1,m,m**2,m**3,m**4,m**5])
theta= sy.dot( sy.linalg.inv(sy.dot( sy.transpose(A),A )) , sy.dot(sy.transpose(A),Y) )
return theta
def shift_back_front(x,phi,neq,dx): n = len(x)/neq u = scipy.reshape(x,(neq,n)) u_left = scipy.transpose([u[:,0]]) u_right = scipy.transpose([u[:,-1]]) u_ext = scipy.c_[u_left,u,u_right] dudx = 1./(2*dx)*(u_ext[:,2:]-u_ext[:,:-2]) #u_ext = scipy.c_[u_left,u_left,u,u_right,u_right] #dudx = 1./(12*dx)*(-u_ext[:,4:]+8*u_ext[:,3:-1]-8*u_ext[:,1:-3]+u_ext[:,:-4]) x_shifted=scipy.reshape(u+phi*dudx,(neq*n,)) return x_shifted
def shplot3d(self):
fig = plt.figure()
space = axs.Axes3D(fig)
# plot the wall
points = self.xyzxyz()
top = sp.transpose(points[0])
space.scatter(top[0],top[1],top[2])
# plot the pan bottom
bottom = sp.transpose(points[1])
space.scatter(bottom[0],bottom[1],bottom[2])
plt.show()
def __locate_newton(self, X, C):
"""x[0:self.dim] = (x,alpha)
x[self.dim] = beta
x[self.dim+1:2*self.dim] = p
"""
J_coords = C.CorrFunc.jac(X[0:C.dim], C.coords)
J_params = C.CorrFunc.jac(X[0:C.dim], C.params)
return r_[C.CorrFunc(X[0:C.dim]) + X[C.dim]*X[C.dim+1:], \
matrixmultiply(transpose(J_coords),X[C.dim+1:]), \
matrixmultiply(transpose(X[C.dim+1:]),J_params), \
matrixmultiply(transpose(X[C.dim+1:]),X[C.dim+1:]) - 1]
def param(y):
#Y=sy.subtract(y,1)
Y=y
A=[]
for m in x:
A.append([1,m,m**2,m**3,m**4,m**5,m**6,m**7,m**8,m**9,m**10,m**11,m**12,m**13,m**14,m**15])
theta= sy.dot( sy.linalg.inv(sy.dot( sy.transpose(A),A )) , sy.dot(sy.transpose(A),Y) )
return theta
def get_chords(self, direction, spacing=10, trim_edges=True):
if direction == 'x':
swap_axes = [0, 1, 2]
elif direction == 'y':
swap_axes = [1, 0, 2]
elif direction == 'z':
swap_axes = [2, 1, 0]
image = sp.transpose(self.image, swap_axes)
image = self._apply_chords(image=image,
spacing=spacing,
trim_edges=trim_edges)
image = sp.transpose(image, swap_axes)
return image
def struct_dropout(xx, pivots):
lam = 1
xfreq = xx[pivots,:]
P = xfreq * transpose(xx)
print('finish computing P')
normvec = np.squeeze(np.asarray(xx.sum(1)))
normvec = normvec.astype(float)
d = len(normvec)
for i in xrange(d): normvec[i] = 1 / (normvec[i] + lam)
Q = spdiags([normvec],[0],d,d)
print('finish computing Q')
W = P * Q
print('finish computing W')
return transpose(csc_matrix(W * xx).tanh().todense())
def _sampling_matrix(hessian, cutoff=None, diag = None, temperature=1, step_scale=1):
# basically need SVD of hessian - singular values and eigenvectors
# hessian = u * diag(singVals) * vh
#u, sing_vals, vh = scipy.linalg.svd(hessian)
# scroll through the singular values and find the ones whose inverses will
# be huge and set them to zero also, load up the array of singular values
# that we store
# cutoff = (1.0/_.singVals[0])*1.0e03
# double cutoff = _.singVals[0]*1.0e-02
# when cutoff is set to zero it means that all values are included
# cutoff*(sloppiest eigenvalue)
if cutoff:
u, sing_vals, vh = scipy.linalg.svd(hessian)
cutoff_sing_val = cutoff * max(sing_vals)
#when cutoff is set to zero it means that all values are included
D = 1.0/scipy.maximum(sing_vals, cutoff_sing_val)
samp_mat = scipy.transpose(vh)*scipy.sqrt(D)
# instead of cutoff use another method, adding diagonal term to hessian
elif diag is not None:
u, sing_vals, vh = scipy.linalg.svd(hessian+diag)
D = 1.0/sing_vals
samp_mat = scipy.transpose(vh)*scipy.sqrt(D)
cutoff_sing_val = diag[0,0]
else:
u, sing_vals, vh = scipy.linalg.svd(hessian)
D = 1.0/sing_vals
samp_mat = scipy.transpose(vh)*scipy.sqrt(D)
cutoff_sing_val = 0
## now fill in the sampling matrix ("square root" of the Hessian)
## note that sqrt(D[i]) is taken here whereas Kevin took sqrt(D[j])
## this is because vh is the transpose of his PT -JJW
#samp_mat = scipy.transpose(vh) * scipy.sqrt(D)
# Divide the sampling matrix by an additional factor such
# that the expected quadratic increase in cost will be about 1.
cutoff_vals = scipy.compress(sing_vals < cutoff_sing_val, sing_vals)
if len(cutoff_vals):
scale = scipy.sqrt(len(sing_vals) - len(cutoff_vals)
+ sum(cutoff_vals)/cutoff_sing_val)
else:
scale = scipy.sqrt(len(sing_vals))
samp_mat /= scale
samp_mat *= step_scale
samp_mat *= scipy.sqrt(temperature)
return samp_mat
def param(y):
Y=sy.subtract(y,1)
A=[]
for m in x:
if m <0.4 or m>0.7:
A.append([1,m,m**2,m**3,m**4,m**5,0])
else:
A.append([1,m,m**2,m**3,m**4,m**5,-1])
theta= sy.dot( sy.linalg.inv(sy.dot( sy.transpose(A),A )) , sy.dot(sy.transpose(A),Y) )
return theta
def bialttoeig(q, p, n, A): v1, v2 = invwedge(q, n) w1, w2 = invwedge(p, n) A11 = bilinearform(A,v1,v1) A22 = bilinearform(A,v2,v2) A12 = bilinearform(A,v1,v2) A21 = bilinearform(A,v2,v1) v11 = matrixmultiply(transpose(v1),v1) v22 = matrixmultiply(transpose(v2),v2) v12 = matrixmultiply(transpose(v1),v2) D = v11*v22 - v12*v12 k = (A11*A22 - A12*A21)/D return k[0][0], v1, w1
def setdata(self, X, V):
A = self.bialtprodeye(2*self.F.J_coords)
"""Note: p, q <= min(n,m)"""
self.data.Brand = 2*(random((A.shape[0],self.data.p))-0.5)
self.data.Crand = 2*(random((A.shape[1],self.data.q))-0.5)
self.data.B = zeros((A.shape[0],self.data.p), Float)
self.data.C = zeros((A.shape[1],self.data.q), Float)
self.data.D = zeros((self.data.q,self.data.p), Float)
U, S, Vh = linalg.svd(A)
self.data.b = U[:,-1:]
self.data.c = num_transpose(Vh)[:,-1:]
if self.update:
self.data.B[:,1] = self.data.b
self.data.C[:,1] = self.data.c
U2, S2, Vh2 = linalg.svd(c_[r_[A, transpose(self.data.C[:,1])], r_[self.data.B[:,1], [[0]]]])
self.data.B[:,2] = U2[0:A.shape[0],-1:]
self.data.C[:,2] = num_transpose(Vh2)[0:A.shape[1],-1:]
self.data.D[0,1] = U2[A.shape[0],-1]
self.data.D[1,0] = num_transpose(Vh2)[A.shape[1],-1]
else:
self.data.B = self.data.Brand
self.data.C = self.data.Crand