def rand_next_time(t0, λfunc, λfunc_integral=None, λfunc_integral_inverse=None):
a = -math.log(random.random())
if λfunc_integral_inverse is None:
if λfunc_integral is None:
def L(t):
y, abserr = integrate.quad(λfunc, t0, t)
return y - a
else:
t0_integral = λfunc_integral(t0)
def L(t):
y = λfunc_integral(t) - t0_integral
return y - a
tol = 1e-4
try:
x = newtons_method(t0, L, λfunc, tol, 20)
except OverflowError: # can happen when we use the interpolation thing
inv_L = inversefunc(L, y_values=[0], accuracy=5)
x = inv_L[0]
else:
if abs(L(x)) > tol:
inv_L = inversefunc(L, y_values=[0], accuracy=5)
x = inv_L[0]
return x
else:
assert λfunc_integral is not None
return λfunc_integral_inverse(λfunc_integral(t0) + a)
def T0_bridge(l=2.0, g=9.8, rho=1.0, R=1.0, a=1.0, **kwargs):
integrand = lambda x, T0: np.sqrt(1.0 + inversefunc(B,
args=(T0, g, R, rho),
y_values=x,
domain=[0, 5],
image=[0, 10],
open_domain=False)**2)
l_fn = lambda T0: integrate.quad(integrand, 0, a, args=(T0, ))[0]
result = inversefunc(l_fn,
y_values=l,
domain=[0.0, 10**3],
image=[0, 10**3],
open_domain=True)
print('T0 bridge: ' + str(result))
return result
def main():
parser = argparse.ArgumentParser(
description='Percolation for a random cube')
parser.add_argument('n', type=int, help='number of rows')
parser.add_argument(
'p',
type=float,
help='probability for the cell be True in the matrix cube')
parser.add_argument('--estimate-threshold',
help='estimate the threshold of percolates',
action='store_true')
parser.add_argument(
'--nb-trials',
type=int,
help='number of times the experiment must be carried out')
args = parser.parse_args()
n = args.n
p = args.p
nb_trials = args.nb_trials
matr = rand_bool_matrix_3d(n, n, n, p)
# pprint(matr)
f = flow_hash(matr)
# pprint(f)
# print(percolates(matr))
# pprint(matr)
# res = flow_hash(matr)
# pprint(res)
if nb_trials is None:
nb_trials = 100
def perc_func(p):
success = experiment(n, p, nb_trials)
return success / nb_trials
NBINTERV = 11
prob_of_success = [0] * NBINTERV
probs = np.linspace(0, 1, NBINTERV)
for i, p in enumerate(probs):
success = experiment(n, p, nb_trials)
prob_of_success[i] = success / nb_trials
print(success, nb_trials, success / nb_trials)
print(prob_of_success)
fig, ax = plt.subplots()
ax.set_xlim(0, 1)
ax.set_ylim(0, 1)
plt.title('Probability of percolation nb_sites :' + str(n) + '³' +
' nb_trials: ' + str(nb_trials))
plt.xlabel('site vacancy probability')
plt.ylabel('percolation probability')
success_color = {True: 'green', False: 'red'}
colors = [success_color[p > 0.5] for p in prob_of_success]
plt.scatter(probs, prob_of_success, color=colors)
plt.show()
if args.estimate_threshold:
print('Estimating threshold value...')
a = inversefunc(perc_func, y_values=0.5, domain=[0.3, 0.8])
b = inverse(perc_func, 0.5, 0.3, 0.8)
print('Threshold value using pynverse', a)
print('Threshold value is', b)
def prob(ball_r, balls_dist, angle_1, angle_2, cue_ball_angle, omega):
min_in_angle = min(angle_1, angle_2)
max_in_angle = max(angle_1, angle_2)
def f(t):
try:
return asin(balls_dist * sin(t) /
(2 * ball_r)) - abs(t) + cue_ball_angle
except:
pass
def pdf(x):
var = 0.1 #* exp(-(balls_dist-ball_r*2))
return pow(2 * pi * var, -0.5) * exp(-((x - omega)**2) / (2 * var))
try:
bound = asin(2 * ball_r / balls_dist)
except:
return 0
f_image = [min_in_angle, max_in_angle]
inv_f = inversefunc(f, domain=[-1 * bound, bound], image=f_image)
return integrate.quad(pdf, inv_f(f_image[0]), inv_f(f_image[1]))[0]
def test_inversefunc_vminclosedvmaxclosed():
accuracy = 2
cos = (lambda x: np.cos(x))
invfunc = inversefunc(cos, domain=[0, np.pi])
yval = [1, 0, -1]
xvalexpected = [0., np.pi / 2, np.pi]
assert_array_almost_equal(invfunc(yval), xvalexpected, accuracy)
def test_inversefunc_with_y_values():
accuracy = 2
cube = (lambda x: x**3)
yval = [-27, -8, -1, 0, 1, 8, 27]
xvalexpected = [-3, -2, -1, 0, 1, 2, 3]
xval = inversefunc(cube, y_values=yval)
assert_array_almost_equal(xval, xvalexpected, accuracy)
def test_inversefunc_vmaxclosed():
accuracy = 2
square = (lambda x: x**2)
invfunc = inversefunc(square, domain=[None, 0])
yval = [4, 16, 64]
xvalexpected = [-2, -4, -8]
assert_array_almost_equal(invfunc(yval), xvalexpected, accuracy)
def test_inversefunc_vminclosed():
accuracy = 2
square = (lambda x: x**2)
invfunc = inversefunc(square, domain=0)
yval = [4, 16, 64]
xvalexpected = [2, 4, 8]
assert_array_almost_equal(invfunc(yval), xvalexpected, accuracy)
class CPP_nBRW:
# INPUT the number N
def __init__(self, N):
self.N = N
self.currPos = [0]*N
self.history = [self.currPos[:]]
# INPUT nGen, the number of generations to run the N-BRW for.
# OUTPUT stores the N-BRW in the array self.history
def run(self, nGen):
for gen in range(nGen):
print('Currently in generation {0}'.format(gen))
self.currPos = self.branch_and_select()
self.history += [self.currPos]
# The rest of the class is made up of internal methods
# required to do the calculations
def unnormalized_cdf(self, x, lower_bound):
return self.primitive(x) - self.primitive(lower_bound)
def primitive(self, x):
if x == np.inf:
return np.real(self.N * (np.exp(1j) + np.exp(-1j)) / 2)
return np.real(sum([1j * np.exp(-1j) * (np.exp(2j)*expi(-(x-x0)-1j)
- expi(1j - (x-x0))) / (2*np.pi) for x0 in self.currPos]))
def inverse_sample(self, lower_bound, upper_bound, normalizing_constant):
cdf = lambda x: self.unnormalized_cdf(x, lower_bound)
/ normalizing_constant
return inversefunc(cdf, stat.uniform.rvs(),
domain=[lower_bound,
min(upper_bound, lower_bound + 20)],
image=[0,1])
def test_inversefunc_with_multargs():
accuracy = 2
func = (lambda x, y, z: x**3 + y + z)
invfunc = inversefunc(func, args=(1, 2))
yval = [-24, -5, 2, 3, 4, 11, 30]
xvalexpected = [-3, -2, -1, 0, 1, 2, 3]
assert_array_almost_equal(invfunc(yval), xvalexpected, accuracy)
def invertedFit(params, tval, vval):
"""
Inverts the fit (from given parameters), and returns the times used for
the fit.
"""
k = params[0]
phi = params[1] #phase
A = params[2] #amplitude
T = 1 / (k) #period
#print(T,v_off,phi,k,A)
sine = (lambda t: A * np.sin(2 * np.pi * k * t - phi)
) #define sin as a function of time.
t_list = np.linspace(tval - T / 2, tval + T / 2, 100)
sine_vals = sine(t_list)
a_max = np.argmax(sine_vals)
a_min = np.argmin(sine_vals)
t_max = t_list[a_max]
t_min = t_list[a_min]
if (t_min > t_max):
minval = t_max
t_max = t_min
t_min = minval
try:
t_close = inversefunc(sine, y_values=vval, domain=[t_min, t_max])
except ValueError:
print(t_max, t_min, vval, tval)
print(params)
return (t_close - tval) #used to be t_close-tval
def test_inversefunc_infinite():
accuracy = 2
cube = (lambda x: x**3)
invfunc = inversefunc(cube)
yval = [-27, -8, -1, 0, 1, 8, 27]
xvalexpected = [-3, -2, -1, 0, 1, 2, 3]
assert_array_almost_equal(invfunc(yval), xvalexpected, accuracy)
def test_inversefunc_vminclosedvmaxopen():
accuracy = 2
cos = (lambda x: np.cos(x))
invfunc = inversefunc(cos, domain=[0, np.pi], open_domain=[False, True])
yval = [1 / np.sqrt(2), 0, -1 / np.sqrt(2)]
xvalexpected = [np.pi / 4, np.pi / 2, 3 * np.pi / 4]
assert_array_almost_equal(invfunc(yval), xvalexpected, accuracy)
def delay_mean_empiric(lmr, overhead=1.1, d_tot=None, n=100):
'''return the simulated mean delay of the map phase, i.e., the average
delay until d droplets have been computed and wait_for servers
have become available. assumes that droplets are computed in
optimal order.
'''
if d_tot is None:
d_tot = lmr['nrows'] * lmr['nvectors'] / lmr['droplet_size'] * overhead
result = 0.0
max_drops = lmr['droplets_per_server'] * lmr['nvectors']
if max_drops * lmr['nservers'] < d_tot:
return math.inf
dropletc = lmr['dropletc'] # cache this value
a = np.zeros(lmr['nservers'])
for _ in range(n):
delays(0, lmr, out=a)
t_servers = a[lmr['wait_for'] - 1] # a is sorted
f = lambda x: np.floor(
np.minimum(np.maximum((x - a) / dropletc, 0), max_drops)).sum()
t_droplets = inversefunc(f, y_values=d_tot)[0]
result += max(t_servers, t_droplets)
# average and add decoding delay
result /= n
result += lmr['decodingc']
return result
def ej8():
f, fda, e, v = exp_dist(0.01386)
d = math.sqrt(v)
print("a) P(X < 100) =","%.3f"%fda(100))
print(" P(X < 100) =","%.3f"%fda(200))
print(" P(100 < X < 200) =","%.3f"%(fda(200)-fda(100)))
print("b) P(e+d*2 < X) =", "%.3f"%(1 - fda(e+d*2)))
print("c) mediana(X) =", "%.3f"%(inversefunc(fda,0.5)))
def pressure_old(mu,T):
'''Pressure at SVP in Pa as a function of chemical potential (in K) and
temperature.
'''
P0 = pressure_SVP(T)
Pmu = pynverse.inversefunc(chemical_potential, args=(T),domain=[1E-200,None],
accuracy=8)
return Pmu(mu)
def get_time_at_height_boost(y, theta, boost_amount):
f = lambda x: get_height_at_time_boost(x, theta, boost_amount)
f_max = min(scipy.optimize.fmin(lambda x: -f(x), 0, disp=False)[0], 1.4)
f_inverse = inversefunc(f, domain=[0, f_max])
if y < f(f_max):
return f_inverse(y)
else:
return f_max
def get_time_at_height(y):
f = lambda x: get_height_at_time(x)
f_max = min(scipy.optimize.fmin(lambda x: -f(x), 0, disp=False), 1.4)
f_inverse = inversefunc(f, domain=[0, f_max])
if y < f_max:
return f_inverse(y)
else:
return f_max
def f_dp(x, alpha_aa, alpha_c, a_aa0, b_aa0, a_c0, b_c0, a_aa1, b_aa1, a_c1,
b_c1):
f_c = (lambda x_c: alpha_c * beta.cdf(x_c, a_c1, b_c1, 0, 1) +
(1 - alpha_c) * beta.cdf(x_c, a_c0, b_c0, 0, 1))
inv_f_c = inversefunc(f_c, domain=[0, 1], open_domain=[False, False])
return float(
inv_f_c(alpha_aa * beta.cdf(x, a_aa1, b_aa1) +
(1 - alpha_aa) * beta.cdf(x, a_aa0, b_aa0)))
def inverse_sample(self, lower_bound, upper_bound, normalizing_constant):
cdf = lambda x: self.unnormalized_cdf(x, lower_bound
) / normalizing_constant
return inversefunc(
cdf,
stat.uniform.rvs(),
domain=[lower_bound,
min(upper_bound, lower_bound + 20)],
image=[0, 1])
def int_conf(x, d, n, conf):
a = (1 + conf) / 2
invz = inversefunc(auxz)
z = invz(a)
izq = "%.3f" % (x - z * d / math.sqrt(n))
der = "%.3f" % (x + z * d / math.sqrt(n))
ic = (float(izq), float(der))
lon = ic[1] - ic[0]
return ic, lon
def ppf(self, x: Union[float, np.ndarray]) -> Union[float, np.ndarray]:
"""The ppf (percent point function - the inverse of the cdf) evaluated at x.
Since this is not analytically available, compute it with an inversefunc module.
:param x: x values, where the ppf should be evaluated.
:return: Corresponding value of ppf at x.
"""
return inversefunc(self.cdf)(x)
def T0_catenary(l=2.0, g=9.8, rho=1.0, a=1.0, **kwargs):
l_fn = lambda T0: (T0 / (g * rho)) * np.sinh(((g * rho) / T0) * a)
result = inversefunc(l_fn,
y_values=l,
domain=[0, 10**9],
image=[0, 10**9],
open_domain=True)
print(result)
return result
def to_points(self, num):
def arclength(s):
d_arc = lambda x: np.sqrt(1 + self.poly.grad_at(x)**2)
return quad(d_arc, 0, s)[0]
s1 = inversefunc(arclength, self.length).tolist()
points = [(s, self.poly.eval_at(s), arclength(s))
for s in np.linspace(0, s1, num=num)]
return self.rel_to_abs(points)
def test_inversefunc_vminopenvmaxopen():
accuracy = 2
tan = (lambda x: np.tan(x))
invfunc = inversefunc(tan,
domain=[-np.pi / 2, np.pi / 2],
open_domain=True)
yval = [1, 0, -1]
xvalexpected = [np.pi / 4, 0., -np.pi / 4]
assert_array_almost_equal(invfunc(yval), xvalexpected, accuracy)
def fp_lmfit(params, x, data, dt, I0, I_max, iter_step):
# Gathering parameters
k = params["k"]
I_star = params["I_star"]
#print("k={}, I_star={}".format(k, I_star))
# Declaring the engine
engine_nk = nk.cn_nekhoroshev(I_max, 1.0, I_star, 1 / (k * 2), 0, I0, dt)
multiplier = 0.01 / integrate.simps(engine_nk.diffusion,
np.linspace(0, I_max, len(I0)))
while True:
engine_nk = nk.cn_nekhoroshev(I_max, multiplier, I_star, 1 / (k * 2),
0, I0, dt)
# Allocating lists and counter
t = []
survival = []
# Starting while loop for fitting procedure
step = 0
reached = True
while (1.0 - engine_nk.get_particle_loss() >= data[-1]):
# Append the data
t.append(step * iter_step * dt * multiplier)
survival.append(1.0 - engine_nk.get_particle_loss())
# Iterate
engine_nk.iterate(iter_step)
# Evolve counter
step += 1
if step == 10000:
#print("End not reached!")
reached = False
break
# Append one last time
t.append(step * iter_step * dt * multiplier)
survival.append(1.0 - engine_nk.get_particle_loss())
if len(t) > 10:
break
else:
#print("decrease multiplier")
multiplier /= 10
# Post processing
if reached:
f = interp1d(t, survival, kind="cubic")
inv_f = inversefunc(f,
domain=(t[0], t[-1]),
image=(survival[-1], survival[0]))
point_t = inv_f(data[-1])
point_s = inv_f(data[0])
points_t = np.linspace(point_s, point_t, len(x))
values_f = f(points_t)
else:
f = interp1d(t, survival, kind="cubic")
points_t = np.linspace(0, t[-1], len(x))
values_f = f(points_t) * 10
return values_f - data
def test_inversefunc_vmaxopen():
accuracy = 2
log = (lambda x: np.log10(-x))
invfunc = inversefunc(log,
domain=[None, 0],
open_domain=True,
image=[-np.inf, None])
yval = [-2., -3.]
xvalexpected = [-0.01, -0.001]
assert_array_almost_equal(invfunc(yval), xvalexpected, accuracy)
def pressure_fit(μ_,T):
'''Pressure at SVP in Pa as a function of chemical potential (in K) and
temperature.
'''
import pynverse
P0 = pressure_SVP(T)
Pμ = pynverse.inversefunc(chemical_potential, args=(T),domain=[1E-200,None],
accuracy=8)
return Pμ(μ_)
def inv(value):
if value >= Limit(bound):
function = (lambda m: Limit(m))
z = inversefunc(function, y_values=value)
else:
z = 0
L = value
while L - Limit(z) >= 10**(-4):
z = z + 0.001
return z
def simple_resonant_frequency(L, C, Ic, beta_RF, fDC):
# first, need to get dDC from fDC.
fDC_func = (lambda x: (x + beta_RF * math.sin(x)) / (2 * math.pi))
fDC_inv = inversefunc(fDC_func) # function that goes from fDC to dDC
dDC = fDC_inv(fDC) # use that inverted function to get dDC value
# dDC = fDC*2*math.pi
Ljj = (2.068 * 1.e-15) / (2 * math.pi * Ic * math.cos(dDC))
Ltot = (1 / L + 1 / Ljj)**(-1) # parallel inductances
resonant_frequency = (1 / (2 * math.pi)) * (Ltot * C)**(-.5)
return np.real(resonant_frequency)
def transform_non_affine(self, a):
inverseCumLogLaplaceVectorized = np.vectorize(inversefunc(cumLogLaplaceMaker(self.mu, \
self.sigma), domain=[1e-5, float("Inf")]))
return inverseCumLogLaplaceVectorized(a)