def T_Owen_int(h, a, jmax=50, cut_point=6):
"""
Return Owens T
==============
@param: h the h parameter of Owen's T
@param: a the a parameter of Owen's T (-1 <= a <= 1)
Python-numpy-scipy version for Owen's T translated from matlab version
T_owen.m of R module sn.T_int
"""
if type(h) in (float, float64):
h = array([h])
low = where(h <= cut_point)[0]
high = where(h > cut_point)[0]
n_low = low.size
n_high = high.size
irange = arange(0, jmax)
series = zeros(h.size)
if n_low > 0:
h_low = h[low].reshape(n_low, 1)
b = fui(h_low, irange)
cumb = b.cumsum(axis=1)
b1 = np_exp(-0.5 * h_low**2) * cumb
matr = ones((jmax, n_low)) - b1.transpose() # matlab ' means transpose
jk = kron(ones(jmax), [1.0, -1.0])
jk = jk[0:jmax] / (2 * irange + 1)
matr = inner((jk.reshape(jmax, 1) * matr).transpose(),
a**(2 * irange + 1))
series[low] = (np_arctan(a) - matr.flatten(1)) / (2 * pi)
if n_high > 0:
h_high = h[high]
atana = np_arctan(a)
series[high] = (atana * np_exp(-0.5 * (h_high**2) * a / atana) *
(1.0 + 0.00868 * (h_high**4) * a**4) / (2.0 * pi))
return series
def T_Owen_int(h, a, jmax=50, cut_point=6):
"""
Return Owens T
==============
@param: h the h parameter of Owen's T
@param: a the a parameter of Owen's T (-1 <= a <= 1)
Python-numpy-scipy version for Owen's T translated from matlab version
T_owen.m of R module sn.T_int
"""
if type(h) in (float, float64):
h = array([h])
low = where(h <= cut_point)[0]
high = where(h > cut_point)[0]
n_low = low.size
n_high = high.size
irange = arange(0, jmax)
series = zeros(h.size)
if n_low > 0:
h_low = h[low].reshape(n_low, 1)
b = fui(h_low, irange)
cumb = b.cumsum(axis=1)
b1 = np_exp(-0.5 * h_low ** 2) * cumb
matr = ones((jmax, n_low)) - b1.transpose() # matlab ' means transpose
jk = kron(ones(jmax), [1.0, -1.0])
jk = jk[0: jmax] / (2 * irange + 1)
matr = inner((jk.reshape(jmax, 1) * matr).transpose(),
a ** (2 * irange + 1))
series[low] = (np_arctan(a) - matr.flatten(1)) / (2 * pi)
if n_high > 0:
h_high = h[high]
atana = np_arctan(a)
series[high] = (atana * np_exp(-0.5 * (h_high ** 2) * a / atana) *
(1.0 + 0.00868 * (h_high ** 4) * a ** 4) / (2.0 * pi))
return series
def funbgh(s, a, b, R, df):
sqrt_df = np.sqrt(df+0.5)
ret = chi_logpdf(s,df)
ret += np_log(mvstdnormcdf(s*a/sqrt_df, s*b/sqrt_df, R,
maxpts=1000000, abseps=1e-6))
ret = np_exp(ret)
return ret
def funbgh2(s, a, b, R, df):
n = len(a)
sqrt_df = np.sqrt(df)
#np.power(s, df-1) * np_exp(-s*s*0.5)
return np_exp((df-1)*np_log(s)-s*s*0.5) \
* mvstdnormcdf(s*a/sqrt_df, s*b/sqrt_df, R[np.tril_indices(n, -1)],
maxpts=1000000, abseps=1e-4)
def ArrheniusRate(barrier):
#For now setting these here, Ideally we'd have a way to pass in this variable.
A = 1.0e12
T = 300
kb = 8.617e-5 # units of ev/K
from numpy import exp as np_exp
return A * np_exp(-barrier / (kb * T))
def plot_derivs(df, prms=False, n=6):
deriv = diff(df.y) / diff(df.x)
fig, ax = subplots(figsize=(15, 10))
ax.plot(df.x[:-1], deriv, 'k-', linewidth=1)
ax.set_xlabel('T/C')
ax.set_ylabel('Weight derivative/ % T$^{-1}$')
if prms:
pred_deriv = 0
for i in range(n):
A, k, s = prms[f'A{i}'], prms[f'k{i}'], prms[f's{i}']
expc = np_exp(k * (df.x - s)) #Exponential term
func_i = -A * k * expc / (expc + 1)**2
pred_deriv += func_i
ax.plot(df.x, func_i, '-.')
ax.grid()
#ax.set_xlim(300,1000)
#ax.set_ylim(-1,0.3)
#ax.plot(df.x,pred_deriv,'-',color='lime')
#savefig('Deriv.png',dpi=300)
show()
def approach_goal(y, dy, goal):
# based on Hoffmann (2009) but instead of
# avoiding obstacles, we approach a goal
gamma = 10 # 1/5
beta = 1 / np.pi
p = np.zeros(2)
if np_norm(dy) > 1e-5:
# calculate current heading
phi_dy = np.arctan2(dy[1], dy[0])
# calc vector to goal
goal_vec = goal - y
phi_goal = np.arctan2(goal_vec[1], goal_vec[0])
# angle diff
phi = phi_goal - phi_dy
# tuned inverse sigmoid to create force towards goal
dphi = gamma * phi * np_exp(-beta * np_abs(phi))
pval = goal_vec * dphi
# print("force vector:", pval, dy)
p += pval
return p
def funbgh2(s, a, b, R, df):
n = len(a)
sqrt_df = np.sqrt(df)
#np.power(s, df-1) * np_exp(-s*s*0.5)
return np_exp((df-1)*np_log(s)-s*s*0.5) \
* mvstdnormcdf(s*a/sqrt_df, s*b/sqrt_df, R[np.tril_indices(n, -1)],
maxpts=1000000, abseps=1e-4)
def funbgh(s, a, b, R, df):
sqrt_df = np.sqrt(df + 0.5)
ret = chi_logpdf(s, df)
ret += np_log(
mvstdnormcdf(s * a / sqrt_df,
s * b / sqrt_df,
R,
maxpts=1000000,
abseps=1e-6))
ret = np_exp(ret)
return ret
def image_gaussian(kernel_sig_x=None,kernel_sig_y=None,l_mesh=None,m_mesh=None,cell_reso=None):
'''Takes desired properties for a kernel in u,v space (in pixel coords),
and creates FT of this'''
fiddle = 2*pi
sig_l, sig_m = 1.0/(fiddle*cell_reso*kernel_sig_x), 1.0/(fiddle*cell_reso*kernel_sig_y)
l_bit = l_mesh*l_mesh / (2*sig_l*sig_l)
m_bit = m_mesh*m_mesh / (2*sig_m*sig_m)
return np_exp(-(l_bit + m_bit))
def derivs(f, x, params):
# Electrostatic potential.
phi = f[0]
# Electric field.
e = f[1]
# Calculate vi.
vi = np_sqrt(params[0]**2 - 2*phi)
# Derivatives (d2phidx2 is actually de/dx which is the negative of d^2phi/dx^2).
dphidx = -e
d2phidx2 = params[0]/vi - np_exp(phi)
# Result of the function in the order f is given.
return [dphidx, d2phidx2]
def gaussian(sig_x=None,sig_y=None,gridsize=KERNEL_SIZE,x_offset=0,y_offset=0):
'''Creates a gaussian array of a specified gridsize, with the
the gaussian peak centred at an offset from the centre of the grid'''
x_cent = int(gridsize / 2.0) + x_offset
y_cent = int(gridsize / 2.0) + y_offset
x = arange(gridsize)
y = arange(gridsize)
x_mesh, y_mesh = meshgrid(x,y)
x_bit = (x_mesh - x_cent)*(x_mesh - x_cent) / (2*sig_x*sig_x)
y_bit = (y_mesh - y_cent)*(y_mesh - y_cent) / (2*sig_y*sig_y)
amp = 1 / (2*pi*sig_x*sig_y)
gaussian = amp*np_exp(-(x_bit + y_bit))
return gaussian
def selfUpdate(self):
'''First run the self-update function of superclass,
then convert unit-value to actuator value,
then operate actuator on the unit value scaled
to the actuator range'''
super(HomeoUnitNewtonianActuator, self).selfUpdate()
#=======================================================================
# 'write value to file, if needed'
# if self._fileOut is not None:
# self._fileOut.write(str(self.criticalDeviation))
# self._fileOut.flush()
#=======================================================================
#=======================================================================
# '''For testing'''
# if self.actuator._wheel == 'right':
# self.rightSpeed = scaleTo([-self.maxDeviation,self.maxDeviation],self.transducer.range(),self.criticalDeviation)
# else:
# self.leftSpeed = scaleTo([-self.maxDeviation,self.maxDeviation],self.transducer.range(),self.criticalDeviation)
# delta = self.leftSpeed - self.rightSpeed
# if abs(delta) > self.maxDelta:
# self.maxDelta = abs(delta)
# hDebug('unit', ("The unit value is %f and its scaled value is %f. The delta b/w wheels is %f and maxDelta is %f" % (self.criticalDeviation,
# scaleTo([-self.maxDeviation,self.maxDeviation],self.transducer.range(),self.criticalDeviation),
# delta,
# self.maxDelta))
# 'end testing'
#=======================================================================
# setSpeed = scaleTo([-self.maxDeviation,self.maxDeviation],self.transducer.range(),self.criticalDeviation)
# setSpeed = self.criticalDeviation
''' Use logistic function to normalize speed to [-1,1]'''
if self._maxSpeed is None:
try:
self._maxSpeed = self._transducer.range()[1]* self._maxSpeedFraction
except:
raise HomeoUnitError("Cannot get max speed from Transducer")
hDebug('unit', ("critDev for unit: %s is %.3f" % (self.name, self.criticalDeviation)))
setSpeed = float(-self._maxSpeed) + ((2 * self._maxSpeed)/ (1+np_exp(- self._switchingRate * self.criticalDeviation)))
setSpeed = round(setSpeed,3)
hDebug('unit', ("Speed set by %s is %f with critDev: %.3f " % (self.name, setSpeed, self.criticalDeviation)))
self.transducer.funcParameters = setSpeed
self.transducer.act()
def plot_f(df, prms, pts):
def f(prms, X, n):
func = prms['B']
for i in range(n):
A, k, s = prms[f'A{i}'], prms[f'k{i}'], prms[f's{i}']
func += A / (1 + np_exp(k * (X - s)))
return func
n = pts.shape[1]
pred = f(prms, array(df.x), n).flatten()
fig, ax = subplots(figsize=(15, 10))
ax.plot(df.x, pred, 'r-')
ax.plot(df.x, df.y, 'k--')
for i in range(n):
A, k, s = prms[f'A{i}'], prms[f'k{i}'], prms[f's{i}']
func_i = A / (1 + np_exp(k * (df.x - s))) + pts[1, i]
#The last term moves the funtion up or down to match the chosen center
ax.plot(df.x, func_i, '--')
show()
def image2kernel(image=None,cell_reso=None,u_off=0.0,v_off=0.0,l_mesh=None,m_mesh=None):
'''Takes an input image array, and FTs to create a kernel
Uses the u_off and v_off (given in pixels values), cell resolution
and l and m coords to phase shift the image, to create a kernel
with the given u,v offset'''
##TODO WARNING - if you want to use a complex image for the kernel,
##may need to either take the complex conjugate, or flip the sign in
##the phase shift, or reverse the indicies in l_mesh, m_mesh. Or some
##combo of all!! J. Line 20-07-2016
phase_shift_image = image * np_exp(2.0j * pi*(u_off*cell_reso*l_mesh + v_off*cell_reso*m_mesh))
#phase_shift_image = image * np_exp(2j * pi*(u_off*l_mesh + v_off*m_mesh))
##FFT shift the image ready for FFT
phase_shift_image = fft.ifftshift(phase_shift_image)
##Do the forward FFT as we define the inverse FFT for u,v -> l,m.
##Scale the output correctly for the way that numpy does it, and remove FFT shift
recovered_kernel = fft.fft2(phase_shift_image) / (image.shape[0] * image.shape[1])
recovered_kernel = fft.fftshift(recovered_kernel)
#return recovered_kernel
return recovered_kernel
def gaussian(x, mu, sig):
""" Not normally distributed!
"""
diff = np.array([x - mu])
return np_exp((-np_sqrt(np_dot(diff, diff))**2.) / (2. * sig**2.))
# Plot electrostatic potential and electric field. ax1.plot(x,y[:, 0], label = r"Electrostatic Potential, $\phi$", linestyle = "-") ax1.plot(x,y[:, 1], label = r"Electric Field, $E$", linestyle = "-") ax1.set_xlabel(r"Debye Lengths") ax1.set_ylabel(r"Normalised Potential \& Electric Field") ax1.grid(b = True, which = "major", linestyle = "--", alpha = 0.6) # Minor ticks option. #ax1.grid(b = True, which = "minor", linestyle = "-.", alpha = 0.05) #ax1.minorticks_on() ax1.legend(loc = 3) # Plot current. mi = 1840 me = 1 j = np_sqrt(mi/(2*np_pi*me)) * np_exp(y[:,0]) - 1 ax2.plot(x, j, label = r"Current, $J$") ax2.set_xlabel(r"Debye Lengths") ax2.set_ylabel(r"Normalised Current") ax2.grid(b = True, which = "major", linestyle = "--", alpha = 0.6) # Minor ticks option. #ax2.grid(b = True, which = "minor", linestyle = "-.", alpha = 0.05) #ax2.minorticks_on() ax2.legend(loc = 0) # Tighten layout. plt.tight_layout() # Show figure. plt.show() # Save figure.
def chi_pdf(x, df):
tmp = (df-1.)*np_log(x) + (-x*x*0.5) - (df*0.5-1)*np_log(2.0) \
- sps_gammaln(df*0.5)
return np_exp(tmp)
def f(prms, X, n):
func = prms['B']
for i in range(n):
A, k, s = prms[f'A{i}'], prms[f'k{i}'], prms[f's{i}']
func += A / (1 + np_exp(k * (X - s)))
return func
def exponentiate(self):
result_df = np_exp(self._df)
return Curve("", self._df.X, result_df.Y)
def rate(diff):
J = 1.0
kbT = 1.0
from numpy import exp as np_exp
return min(1.0, np_exp(-diff * J / kbT))
def BoltzmannP(self, Enew):
'''Given a new value of the energy, return the Boltzmann factor'''
return np_exp(-(Enew - self.E) / self.T)
def gaussian(x, mu, sig):
return np_exp(-np_power(x - mu, 2.) / (2 * np_power(sig, 2.)))
def soft_max(distribution):
""" Calculate softmax for given distribution
"""
sum_exps = np_sum(np_exp(distribution[:, 0]), axis=0)
distribution[:, 0] = np_exp(distribution[:, 0]) / sum_exps
return distribution
def search_isa(
seed_node, scaler, par_inputs_fn
): # Picks out of a subset of its neighbors and adds the best node
with open(par_inputs_fn, 'rb') as f:
inputs = pickle_load(f)
with open(inputs['modelfname'], 'rb') as f:
model = pickle_load(f)
folNm = inputs['folNm']
folNm_out = inputs['folNm_out']
score_prev = 0
cd, g1 = starting_edge(folNm, seed_node)
if cd == 0:
return
max_nodes = inputs["max_size"] - len(g1)
num_iter = 1
last_iter_imp = 0
thres_neig = inputs["thres_neig"]
T = inputs["T0"] # T0 value
alpha = inputs["alpha"]
while num_iter < max_nodes: # Limiting number of iteration rounds
logging_debug("Adding next node")
# neig_list_old = neig_list
# g1, cc, node_to_add, score_curr, comp_bool, rand_flag, neig_list = add_top_neig(g1, thres_neig, folNm, inputs, model, scaler, neig_list)
g1, cc, node_to_add, score_curr, comp_bool, rand_flag = add_top_neig(
g1, thres_neig, folNm, inputs, model, scaler)
if (score_curr is None) or (comp_bool is None):
score_curr, comp_bool = get_score(g1, model, scaler,
inputs['model_type'])
if cc == 0:
break
if score_curr < inputs["classi_thresh"]:
logging_debug("Complex found")
# Remove the node last added
g1.remove_node(node_to_add)
break
cur_trial = rand_uniform(low=0.0, high=1.0)
if score_curr < score_prev:
prob_isa = np_exp((score_curr - score_prev) / T)
if cur_trial > prob_isa:
# Remove the node last added
g1.remove_node(node_to_add)
# neig_list = neig_list_old
else:
logging_debug("Accepting with low probability")
rand_flag = 1
elif score_curr > score_prev:
last_iter_imp = num_iter
if (num_iter - last_iter_imp
) > 10: # Has been a long time since a score improvement
logging_debug("Long time since score improvement")
break
score_prev = score_curr
num_iter += 1
T = float(T) / alpha
# If number of nodes is less than 2, don't write.
with open(folNm_out + "/" + seed_node, 'wb') as f:
pickle_dump((frozenset(g1.nodes()), score_prev), f)
def rate(diff):
J = 1.0
kbT = 1.0
from numpy import exp as np_exp
return min(1.0, np_exp(-diff*J/kbT))
def chi_pdf(x, df):
tmp = (df-1.)*np_log(x) + (-x*x*0.5) - (df*0.5-1)*np_log(2.0) \
- sps_gammaln(df*0.5)
return np_exp(tmp)