def _arc_cosine_hypothesis_test(ac_output, X, W, b, s):
"""
Runs hypothesis test for Arc Cosine layer.
Inputs:
ac_output -- output of net after running arc cosine layer
X -- input data
W -- weight parameter from train_init_net
b -- bias parameter from train_init_net
s -- degree parameter
"""
# Get output from net
net_output = workspace.FetchBlob(ac_output)
# Computing output directly
x_rand = np.matmul(X, np.transpose(W)) + b
x_pow = np.power(x_rand, s)
if s > 0:
h_rand_features = np.piecewise(x_rand,
[x_rand <= 0, x_rand > 0],
[0, 1])
else:
h_rand_features = np.piecewise(x_rand,
[x_rand <= 0, x_rand > 0],
[0, lambda x: x / (1 + x)])
output_ref = np.multiply(x_pow, h_rand_features)
# Comparing net output and computed output
npt.assert_allclose(net_output, output_ref, rtol=1e-3, atol=1e-3)
def EpEvo(t,eta,j,Gamma0,q):
#
# For now I'm going to set a few params at good values
# Adjust later
z=2.332
#q=power(10.,q)
#q=1.E-3
#E0 = 1.E54
E0 = 1.97E55
#E0 = power(10.,E0)
g = (j+1.-eta)*0.5
n0 = 1.E2
#xd = ((3.-eta)*E0 / ( 4.*pi*n0*Gamma0**2. * mp ) )**(1./3.)
xd = 1.8E16*((1.+j-eta)*(E0/1.E54)/((n0/100.)*(Gamma0/300.)))**(1./3.)
#td = (1.+z)*xd / (Gamma0**2. * c)
td = 6.7*(1.+z)*((1.+j-eta)*(E0/1.E54)/((n0/100.)*(Gamma0/300.)**8.))**(1./3.)
### Calculate X(t) ###
test = td/(2. * g + 1.) *( Gamma0**(2.+1./g) + 2.*g)
condition1 = t<td
condition2 = logical_and(td<=t, t<=test)
X = piecewise(t, [condition1, condition2],\
[lambda t: t/td, \
lambda t: ((2.*g+1.)*(t/td) - 2.*g)**(1./(2.*g+1.)) ])
### Calculate X(t) ###
### Calculate Gamma(X) ###
condition3 = X<1.
condition4 = logical_and(1.<=X, X<=Gamma0**(1./g))
Gamma = piecewise(X, [condition3, condition4],\
[lambda X: Gamma0, \
lambda X: Gamma0*X**(-g) ])
### Calculate Gamma(X) ###
eE0 = 3.E-8 * (1E-3) * n0**(.5)*q*Gamma0**4. /(1.+z)
result = 511.8 * eE0*(Gamma/Gamma0)**4. * (X)**(-eta/2.)
return result
def makewdnoise(f,wdstyle,obs='X'):
if wdstyle == 'mldc':
x = 2.0 * math.pi * model.lisaL * f
t = 4 * x**2 * N.sin(x)**2 * (1.0 if obs == 'X' else 1.5)
return t * ( N.piecewise(f,(f >= 1.0e-4 ) & (f < 1.0e-3 ),[lambda f: 10**-44.62 * f**-2.3, 0]) + \
N.piecewise(f,(f >= 1.0e-3 ) & (f < 10**-2.7),[lambda f: 10**-50.92 * f**-4.4, 0]) + \
N.piecewise(f,(f >= 10**-2.7) & (f < 10**-2.4),[lambda f: 10**-62.8 * f**-8.8, 0]) + \
N.piecewise(f,(f >= 10**-2.4) & (f < 10**-2.0),[lambda f: 10**-89.68 * f**-20.0,0]) )
elif wdstyle in wdnoise:
mod, p = wdnoise[wdstyle]
p = p[0] if obs == 'X' else p[1] # assume AE if not X
y = N.log10(f)
if mod == 'rat42':
return 10.0**( (p[0]*y**4+p[1]*y**3+p[2]*y**2+p[3]*y+p[4])/(y**2+p[5]*y+p[6]) )
elif mod == 'poly4':
return 10.0**( p[0]*y**4+p[1]*y**3+p[2]*y**2+p[3]*y+p[4] )
else:
raise NotImplementedError
else:
if '.txt' in wdstyle:
conf = N.loadtxt(wdstyle)
conf[N.isnan(conf[:,1]),1] = 0
return N.interp(f,conf[:,0],conf[:,1])
else:
raise NotImplementedError
def EpEvo(t,eta,g,Gamma0,q):
#
# For now I'm going to set a few params at good values
# Adjust later
z=2.332
# q=1.E-4
# q=1E-3
E0 = 9.1E53
n0 = 1.E2
#n0 = power(10,n0)
#xd = ((3.-eta)*E0 / ( 4.*pi*n0*Gamma0**2. * mp ) )**(1./3.)
xd = 2.6E16*((1.-eta/3.)*(E0/1.E54)/((n0/100.)*(Gamma0/300.)))**(1./3.)
#td = (1.+z)*xd / (Gamma0**2. * c)
td = 9.7*(1.+z)*((1.-eta/3.)*(E0/1.E54)/((n0/100.)*(Gamma0/300.)**8.))**(1./3.)
### Calculate X(t) ###
test = td/(2. * g + 1.) *( Gamma0**(2.+1./g) + 2.*g)
#frac = t/td
condition1 = t<td
condition2 = logical_and(td<=t, t<=test)
X = piecewise(t, [condition1, condition2],\
[lambda t: t/td, \
lambda t: ((2.*g+1.)*(t/td) - 2.*g)**(1./(2.*g+1.)) ])
### Calculate X(t) ###
### Calculate Gamma(X) ###
condition3 = X<1.
condition4 = logical_and(1.<=X, X<=Gamma0**(1./g))
Gamma = piecewise(X, [condition3, condition4],\
[lambda X: Gamma0, \
lambda X: Gamma0*X**(-g) ])
### Calculate Gamma(X) ###
eE0 = 3.E-8 * (1E-3) * n0**(.5)*q *Gamma0**4. /(1.+z)
# eE0 = 3.E-8 * n0**(.5)*q*Gamma0**4. /(1.+z)
return 511. * eE0*(Gamma/Gamma0)**4. * (X/xd)**(-eta/2.)
def __init__(self, Ymax, Y0, mumax, lag, x):
# x is x data
a1 = np.piecewise(x, [x < lag, x >= lag], [0.0, 1.0])
tc = (Ymax-Y0)/mumax+lag
a2 = np.piecewise(x, [x < tc, x >= tc], [0.0, 1.0])
self.Buchanan = Y0*(1.0-a1)+(Y0 + mumax*(x-lag))*a1*(1.0-a2) + Ymax*a2
print x, self.Buchanan
def _get_solution(self):
"""Get the solution from the solver output
Fills the dictionary self.sol with the information:
* 's': The optimal s as a function of time
* 't': The time vector
* 'states': Numerical values of the states defined in self.sys
TODO: perform accurate integration to determine time
TODO: Do exact interpolation
"""
solver = self.prob['solver']
N = self.options['N']
x_opt = np.array(solver.getOutput("x")).ravel()
b_opt = np.reshape(x_opt, (N + 1, -1), order='F')
self.sol['b'] = b_opt
# Determine time on a sufficiently fine spatial grid
s0 = np.linspace(0, 1, 1001)
delta = s0[1] - s0[0]
pieces = [lambda s, b=b_opt, ss=ss, j=j:
sum([bb * (s - ss) ** i / fact[i]
for i, bb in enumerate(b[j])])
for j, ss in enumerate(self.prob['s'][:-1])]
conds = lambda s0: [np.logical_and(self.prob['s'][i] <= s0,
s0 <= self.prob['s'][i+1])
for i in range(N)]
b0_opt = np.piecewise(s0, conds(s0), pieces)
b0_opt[b0_opt < 0] = 0
time = np.cumsum(np.hstack([0, 2 * delta / (np.sqrt(b0_opt[:-1]) +
np.sqrt(b0_opt[1:]))]))
# Resample to constant time-grid
t = np.arange(time[0], time[-1], self.options['Ts'])
st = np.interp(t, time, s0)
# Evaluate solution on equidistant time grid
b_opt = np.c_[[np.piecewise(st, conds(st), pieces, b=b_opt[:, i:])
for i in range(self.sys.order)]].T
st = np.matrix(st)
# Determine s and derivatives from b_opt
b, Ds = self._make_path()[1:]
Ds_f = cas.SXFunction([b], [Ds]) # derivatives of s wrt b
Ds_f.init()
s_opt = np.hstack((st.T, np.array([evalf(Ds_f, bb).toArray().ravel()
for bb in b_opt])))
self.sol['s'] = np.asarray(s_opt)
self.sol['t'] = t
# Evaluate the states
f = cas.SXFunction([self.s], [cas.substitute(cas.vertcat(self.sys.x.values()),
self.sys.y, self.path)])
f_val = np.array([evalf(f, s.T).toArray().ravel() for s in s_opt])
self.sol['states'] = dict([(k, f_val[:, i]) for i, k in
enumerate(self.sys.x.keys())])
def EpEvo(t,A,eta,g,E0,Gamma0,n0,q):
#c = 2.99E10 #cm/s
c=1.
mp = 1.67E-26 # keV ??
z=1.
#q=1.E-3
#Gamma0 = 300.
#g = (3.-eta)/2.
#n0 = 1.E2
#xd = ((3.-eta)*E0 / ( 4.*pi*n0*Gamma0**2. * mp ) )**(1./3.)
xd = 2.6E16*((1.-eta/3.)*(E0/1.E54)/((n0/100.)*(Gamma0/300.)))**(1./3.)
#td = (1.+z)*xd / (Gamma0**2. * c)
td = 9.7*(1.+z)*((1.-eta/3.)*(E0/1.E54)/((n0/100.)*(Gamma0/300.)**8.))**(1./3.)
### Calculate X(t) ###
test = (td/(2. * g + 1.) * Gamma0**(2.+1./g) + 2.*g)
#frac = t/td
condition1 = t<td
condition2 = logical_and(td<=t, t<=test)
X = piecewise(t, [condition1, condition2],\
[lambda t: t/td, \
lambda t: ((2.*g+1.)*(t/td) - 2.*g)**(1./(2.*g+1.)) ])
### Calculate X(t) ###
### Calculate Gamma(X) ###
condition3 = X<1.
condition4 = logical_and(1.<=X, X<=Gamma0**(1./g))
Gamma = piecewise(X, [condition3, condition4],\
[lambda X: Gamma0, \
lambda X: Gamma0*X**(-g) ])
### Calculate Gamma(X) ###
eE0 = 3.E-8 * n0**(.5)*q*Gamma0**4. /(1.+z)
return A*eE0*(Gamma/Gamma0)**4. * (X/xd)**(-eta/2.)
def I(w, wa, wb, wc):
wa,wb,wc = float(wa), float(wb), float(wc)
f = (wb - wa) / (wc - wa)
eps = (wc-wa)/1e3
if (wb-wa)>eps and (wc-wb)>eps:
w1 = wa+eps
w2 = wb-eps
w3 = wc-eps
return np.piecewise(w,
[(w <= wa-eps),
(wa-eps < w) & (w <= wa+eps),
(wa+eps < w) & (w < wb-eps),
(wb-eps <= w) & (w <= wb+eps),
(wb+eps < w) & (w < wc-eps),
(wc-eps <= w) & (w < wc+eps),
(wc+eps <= w)],
[0,
4/np.sqrt(f*(1-((w1 - wa) / (wc - wa)))) * K([(1-f)*((w1 - wa) / (wc - wa)) / (f*(1-((w1 - wa) / (wc - wa))))]),
lambda w: 4/np.sqrt(f*(1-((w - wa) / (wc - wa)))) * K((1-f)*((w - wa) / (wc - wa)) / (f*(1-((w - wa) / (wc - wa))))),
4/np.sqrt(f*(1-((w2 - wa) / (wc - wa)))) * K([(1-f)*((w2 - wa) / (wc - wa)) / (f*(1-((w2 - wa) / (wc - wa))))]),
lambda w: 4/np.sqrt(((w - wa) / (wc - wa))*(1-f)) * K((1-((w - wa) / (wc - wa)))*f / (((w - wa) / (wc - wa))*(1-f))),
4/np.sqrt(((w3 - wa) / (wc - wa))*(1-f)) * K([(1-((w3 - wa) / (wc - wa)))*f / (((w3 - wa) / (wc - wa))*(1-f))]),
0])
elif (wb-wa)<=eps:
w2 = wb+eps
w3 = wc-eps
return np.piecewise(w,
[(w <= wa-eps),
(wa-eps < w) & (w <= wb+eps),
(wb+eps < w) & (w < wc-eps),
(wc-eps <= w) & (w < wc+eps),
(wc+eps <= w)],
[0,
4/np.sqrt(((w2 - wa) / (wc - wa))*(1-f)) * K([(1-((w2 - wa) / (wc - wa)))*f / (((w2 - wa) / (wc - wa))*(1-f))]),
lambda w: 4/np.sqrt(((w - wa) / (wc - wa))*(1-f)) * K((1-((w - wa) / (wc - wa)))*f / (((w - wa) / (wc - wa))*(1-f))),
4/np.sqrt(((w3 - wa) / (wc - wa))*(1-f)) * K([(1-((w3 - wa) / (wc - wa)))*f / (((w3 - wa) / (wc - wa))*(1-f))]),
0])
elif (wc-wb)<=eps:
w1 = wa+eps
w2 = wb-eps
return np.piecewise(w,
[(w <= wa-eps),
(wa-eps < w) & (w <= wa+eps),
(wa+eps < w) & (w < wb-eps),
(wb-eps <= w) & (w <= wc+eps),
(wc+eps <= w)],
[0,
4/np.sqrt(f*(1-((w1 - wa) / (wc - wa)))) * K([(1-f)*((w1 - wa) / (wc - wa)) / (f*(1-((w1 - wa) / (wc - wa))))]),
lambda w: 4/np.sqrt(f*(1-((w - wa) / (wc - wa)))) * K((1-f)*((w - wa) / (wc - wa)) / (f*(1-((w - wa) / (wc - wa))))),
4/np.sqrt(f*(1-((w2 - wa) / (wc - wa)))) * K([(1-f)*((w2 - wa) / (wc - wa)) / (f*(1-((w2 - wa) / (wc - wa))))]),
0])
def phi(xs, Z):
"""Evaluate phi(x) on a numpy list.
This uses invibro.phi.phi0_cache to interpolate values."""
Z0, x_bound = phi0_cache['Z0'], phi0_cache['xs'][0]
c1 = pi ** 2 /6; c2 = 7 * pi ** 4 / 60.0
neg = lambda x: log((Z - x) / (Z + x))
interp = lambda x: phi0_cache['interp'](x) + log((Z + x) / (Z0 + x))
large = lambda x: log(1 + Z / x) + c1 / x ** 2 + c2 / x ** 4
return (
piecewise(xs, [xs < 0], [neg, 0.0]) +
piecewise(abs(xs), [abs(xs) < x_bound], [interp, large]) +
complex(0, -0.5) * n(xs)
)
def _evaluate(self, t):
if self.direction == 1:
kernel = np.piecewise(
t, [t < 0, t >= 0], [
lambda t: 0,
lambda t: (1.0 / self._sigma_scaled.magnitude) * np.exp(
(-t / self._sigma_scaled).magnitude)]) / t.units
elif self.direction == -1:
kernel = np.piecewise(
t, [t < 0, t >= 0], [
lambda t: (1.0 / self._sigma_scaled.magnitude) * np.exp(
(t / self._sigma_scaled).magnitude),
lambda t: 0]) / t.units
return kernel
def loadExampleData():
data = pd.DataFrame({'Seconds': np.arange(0,15,1/200)})
t = data.loc[:,'Seconds'].values
data.loc[:,'T ACP'] = \
np.piecewise(t, [t < 4, 4 <= t], [1,0]) * (1800/4*t) + \
np.piecewise(t, [t < 4,(4<=t)*(t<=12)], [0,1]) * (1800 + (1200-1800)/8*(t-4)) + \
np.piecewise(t, [12 < t, 20 < t], [1,0]) * (1500 + -400/8*(t-12))
data.loc[:,'time'] = t
self.data = data
self.initExampleData()
self.camera = 'rad'
self.times = [4,7,12]
def reposition(coords, box_size):
com = compute_com_pbc(coords, box_size)
cob = box_size / 2.0
coords_recenter = coords - com + cob
coords_recenter_x = coords_recenter[:,0]
coords_recenter_y = coords_recenter[:,1]
coords_recenter_z = coords_recenter[:,2]
#print coords_recenter
coords_recenter_x = np.piecewise(coords_recenter_x, [coords_recenter_x < 0.0, (coords_recenter_x >= 0.0) * (coords_recenter_x <= box_size[0]), coords_recenter_x > box_size[0]], \
[lambda coords_recenter_x: coords_recenter_x + box_size[0], lambda coords_recenter_x: coords_recenter_x, lambda coords_recenter_x: coords_recenter_x - box_size[0]])
coords_recenter_y = np.piecewise(coords_recenter_y, [coords_recenter_y < 0.0, (coords_recenter_y >= 0.0) * (coords_recenter_y <= box_size[1]), coords_recenter_y > box_size[1]], \
[lambda coords_recenter_y: coords_recenter_y + box_size[1], lambda coords_recenter_y: coords_recenter_y, lambda coords_recenter_y: coords_recenter_y - box_size[1]])
coords_recenter_z = np.piecewise(coords_recenter_z, [coords_recenter_z < 0.0, (coords_recenter_z >= 0.0) * (coords_recenter_z <= box_size[2]), coords_recenter_z > box_size[2]], \
[lambda coords_recenter_z: coords_recenter_z + box_size[2], lambda coords_recenter_z: coords_recenter_z, lambda coords_recenter_z: coords_recenter_z - box_size[2]])
return np.array(zip(coords_recenter_x,coords_recenter_y,coords_recenter_z))
def I_axial(w, wa, wc):
if wc > wa:
return np.piecewise(w, [(w <= wa),
(wa < w) & (w < wc),
(wc <= w)],
[0,
lambda w: 1 / (2*np.sqrt((w - wa) / (wc - wa))),
0])
elif wa > wc:
return np.piecewise(w, [(w <= wc),
(wc < w) & (w < wa),
(wa <= w)],
[0,
lambda w: 1 / (2*np.sqrt((w - wa) / (wc - wa))),
0])
def f(x, a1, b1, c1, d1, b2, c2, v0):
a2_calculated = a2(a1, b1, c1, d1, b2, c2, v0)
d2_calculated = d2(a1, b1, c1, d1, b2, c2, v0)
return np.piecewise(
x,
[x < v0, x >= v0],
[lambda x: p(x, a1, b1, c1, d1), lambda x: p(x, a2_calculated, b2, c2, d2_calculated)])
def B_012(x):
""" A linear B-spline function B(x | 0, 1, 2)."""
x = np.atleast_1d(x)
return np.piecewise(x, [(x < 0) | (x > 2),
(x >= 0) & (x < 1),
(x >= 1) & (x <= 2)],
[lambda x: 0., lambda x: x, lambda x: 2.-x])
def fermi_poly3(x):
"""fermi_poly3(x), equal to -Li_3(-e^x)"""
def f0(x):
return np.exp(x)
def f1(x):
ex = np.exp(x)
return (1 + (-0.125 + (0.037037037037037035 + (-0.015625 + (0.008 - 0.004629629629629629*ex)*ex)*ex)*ex)*ex)*ex
def f2(x):
x2 = x**2
return 0.9015426773696955 + (0.8224670334241131 + (0.34657359027997264 + (0.08333333333333333 + (0.010416666666666666 +(-0.00017361111111111112 + (6.200396825396825e-6 +(-2.927965167548501e-7 + (1.6179486665597777e-8 + (-9.90785651003905e-10 + (6.525181428041877e-11 +(-4.5372283133067906e-12 + 3.290608283068484e-13*x2)*x2)*x2)*x2)*x2)*x2)*x2)*x2)*x)*x)*x)*x
def f3(x):
invex = np.exp(-x)
return (((((0.008*invex - 0.015625)*invex + 0.037037037037037035)*invex) - 0.125)*invex + 1)*invex + 1.6449340668482262*x + 0.16666666666666666*x**3
def f4(x):
return 1.6449340668482262*x + 0.16666666666666666*x**3
# fix for bug in piecewise, fixed in more recent numpy
if np.isscalar(x):
x = np.array([x], dtype=float)
# define piecewise function and evaluate
ans = np.piecewise(x, [x<=-20, np.logical_and(x>-20, x<=-2), \
np.logical_and(x>-2, x<=2), np.logical_and(x>2, x<=20)],\
[f0, f1, f2, f3, f4])
return ans
def fermi_poly2(x):
"""fermi_poly2(x), equal to -Li_2(-e^x)"""
def f0(x):
return np.exp(x)
def f1(x):
ex = np.exp(x)
return (1.+( -0.25+( 0.111111+( -0.0625+( 0.04+( -0.0277778+( 0.0204082+( -0.015625+( 0.0123457+( -0.01+( 0.00826446+( -0.00694444+( 0.00591716+( -0.00510204+( 0.00444444+( -0.00390625+( 0.00346021+( -0.00308642+( 0.00277008+ -0.0025*ex)*ex)*ex)*ex)*ex)*ex)*ex)*ex)*ex)*ex)*ex)*ex)*ex)*ex)*ex)*ex)*ex)*ex)*ex)*ex
def f2(x):
ex = x**2
return 0.822467+(0.6931471805599453+( 0.25+( 0.04166666666666666+( -0.0010416666666666534+( 0.00004960317460316857+( -2.927965167558005e-6+(1.9415383998507108e-7+( -1.3870999148454729e-8+(1.0440288911003276e-9+(-8.167040926799743e-11+6.5806618711692295e-12*ex)*ex)*ex)*ex)*ex)*ex)*ex)*ex)*x)*x)*x
def f3(x):
ex = np.exp(-x)
return 1.6449340668482262 + 0.5*x**2 - (1.+( -0.25+( 0.111111+( -0.0625+( 0.04+( -0.0277778+( 0.0204082+( -0.015625+( 0.0123457+( -0.01+( 0.00826446+( -0.00694444+( 0.00591716+( -0.00510204+( 0.00444444+( -0.00390625+( 0.00346021+( -0.00308642+( 0.00277008 -0.0025*ex)*ex)*ex)*ex)*ex)*ex)*ex)*ex)*ex)*ex)*ex)*ex)*ex)*ex)*ex)*ex)*ex)*ex)*ex)*ex
def f4(x):
return 1.6449340668482262 + 0.5*x**2
# fix for bug in piecewise, fixed in more recent numpy
if np.isscalar(x):
x = np.array([x], dtype=float)
# define piecewise function and evaluate
ans = np.piecewise(x, [x<=-20, np.logical_and(x>-20, x<=-1), \
np.logical_and(x>-1, x<=1), np.logical_and(x>1, x<=20)],\
[f0, f1, f2, f3, f4])
return ans
def fermi_poly5half(x):
"""fermi_poly5half(x), equal to -Li_{5/2}(-e^x)
FAILS TESTS (COMPARING TO LERCH), DO NOT USE WITHOUT INVESTIGATING MORE
"""
def f0(x):
return np.exp(x)
def f1(x):
ex = np.exp(x)
return (1 + (-0.17677669529663687 + (0.06415002990995843 - (0.03125 + (0.01788854381999832 - (0.011340230290662863 + (0.007713560673657698 - (0.005524271728019902 + (0.00411522633744856 - 0.0031622776601683794*ex)*ex)*ex)*ex)*ex)*ex)*ex)*ex)*ex)*ex
def f2(x):
res = (7.999472242952045e-8 + (2.015789875039643e-8 + (-5.182488893752819e-9 + (-1.3550552937770878e-9 + (3.5944104666022113e-10 + (9.653703483078106e-11 + (-2.6209625544677692e-11 + (-7.185930974961928e-12 + (1.9812061650792594e-12 + 5.447084984800099e-13*x)*x)*x)*x)*x)*x)*x)*x)*x)*x
return 0.8671998890121841+(0.7651470246254081+(0.30244932171081546+(0.06335080210161399+(0.0049450362799933825+(-0.0007320093393446121+(-0.00013339945006254949 + (0.000027147085179903566+(5.930588304137955e-6+(-1.3626304577484817e-6 + (-3.252451788607287e-7 + res*x)*x)*x)*x)*x)*x)*x)*x)*x)*x)*x
def f3(x):
res = 5.992860912139351e-7 + (-6.083668666935579e-8 + (5.041252634789406e-9 + (-3.386896134140133e-10 + (1.8196669171414837e-11 + (-7.642990316874879e-13 + (2.4202106712129105e-14 + (-5.437364923509245e-16 + (7.72925401611516e-18 -5.228771407811986e-20*x)*x)*x)*x)*x)*x)*x)*x)*x
return 0.869416215427492 + (0.7603408345815055 + (0.30606614629176887 + (0.06361411550944529 + (0.002145410757189772 + (0.002020072416997651 + (-0.0017045762862650151 + (0.0006382881546811445 + (- 0.00016246851298525836 + (0.00003140383144730955 + (-4.819813947314412e-6+res*x)*x)*x)*x)*x)*x)*x)*x)*x)*x)*x
def f4(x):
x2 = x**2
invex = np.sqrt(x)
return (-2.0851412241155116/x/x - 0.5343060576801043)/x/invex + 1.8561093322772355*invex + 0.30090111122547003*x2*invex
def f5(x):
x2 = x**2
invex = np.sqrt(x)
return 1.8561093322772355*invex + 0.30090111122547003*x2*invex
# fix for bug in piecewise, fixed in more recent numpy
if np.isscalar(x):
x = np.array([x], dtype=float)
# define piecewise function and evaluate
ans = np.piecewise(x, [x<=-20, np.logical_and(x>-20, x<=-2), \
np.logical_and(x>-2, x<=2), np.logical_and(x>2, x<=12), \
np.logical_and(x>12, x<=20)], [f0, f1, f2, f3, f4, f5])
return ans
def de_sitter_form_testing(x,s,A,C,N3,num_slices):
"""
The functional form for de Sitter Space. x is position, s, A, C
are all fit parameters. N3 is the total number of 3-simplices in
the spacetime. num_slices is the number of time slices in the spacetime.
"""
# A normalized cosine. used for clarity.
n_cos = lambda y: np.cos(y/(s * N3**(1/3.)))
# The full width/half-max of the spacetime
fwhm = np.arccos(np.sqrt((np.pi * A/2.)*(s * N3**(1/3.)/N3)))
# The conditional functions
# for -num_slices/2.0 <= (x - C) < -s * N3**(1/3.) * fwhm
# or
# s * N3**(1/3.) * fwhm < (x-C) <= num_slices/2.0
stem = lambda x: float(A)
# for -s * N3**(1/3.) * fwhm <= (x - C) <= s * N3**(1/3.) * fwhm
bulk = lambda x: (2/np.pi) * (N3/(s * N3**(1/3.))) * n_cos(x-C)**2
# List of conditions for the piecewise function
conds = [(-num_slices/2.0 <= (x-C))&((x-C) < -s * N3**(1/3.) * fwhm),
(-s * N3**(1/3.) * fwhm <= (x-C))&((x-C) <= s * N3**(1/3.) * fwhm),
(s * N3**(1/3.) * fwhm < (x-C))&((x-C) <= num_slices/2.0)]
# List of return functions for the piecewise function
returnfuncs = [stem,bulk,stem]
return np.piecewise(x,conds,returnfuncs)
def _ale(self):
"""ale algorithm in SubSection 3.1 of the paper.
Basically just the implementation of the following formula:
In_prime = f(In, z)
Calculates In and z, then return In_prime
:return In_prime:
"""
# Calculate In
In = self.img_gray / 255.0 # 2d array, equation 2
# Calculate z
cdf = cv2.calcHist([self.img_gray], [0], None, [256], [0, 256]).cumsum()
L = np.searchsorted(cdf, 0.1 * self.img_gray.shape[0] * self.img_gray.shape[1], side='right')
L_as_array = np.array([L]) # L as array, for np.piecewise
z_as_array = np.piecewise(L_as_array,
[L_as_array <= 50,
50 < L_as_array <= 150,
L_as_array > 150
],
[0, (L-50) / 100.0, 1]
)
z = z_as_array[0] # take the value out of array
self.z = z
# Result In_prime = f(In, z)
In_prime = 0.5 * (In**(0.75*z+0.25) + (1-In)*0.4*(1-z) + In**(2-z))
return In_prime
def invert_or_zero(x):
'''Calculate 1 / x unless x is zero, in which case zero is returned.'''
return numpy.piecewise(
x,
[x == 0, x != 0],
[lambda x: 0, lambda x: 1 / x],
)
def ptx_temperature(r0, r, standard=ptxITS90, poly=None) -> Quantity("°C"):
"""
Compute the PTx temperature at a given temperature.
Accepts an additive correction polynomial that is applied to the resistance.
If the poly kwarg is None, the polynom is automatically selected.
noCorrection is used for other r0 values. In this case, use a
custom polynomial (numpy poly1d object) as the poly kwarg.
See http://www.thermometricscorp.com/pt1000 for reference
"""
r = normalize_numeric(r)
A, B = standard.a, standard.b
# Select
if poly is None:
if abs(r0 - 1000.0) < 1e-3: poly = pt1000Correction
elif abs(r0 - 100.0) < 1e-3: poly = pt100Correction
else: poly = noCorrection
t = ((-r0 * A + np.sqrt(r0 * r0 * A * A - 4 * r0 * B * (r0 - r))) /
(2.0 * r0 * B))
# For subzero-temperature refine the computation by the correction polynomial
if isinstance(r, numbers.Number):
if r < r0:
t += poly(r)
else: # Treated like a numpy array
t += poly(r) * np.piecewise(r, [r < r0, r >= r0], [1.0, 0.0])
return t
def intgl_simp38(f,a,b,steps=-1,h=1):
if steps>0:
xis = np.linspace(a,b,steps+1)
h = xis[1]-xis[0]
fxis = f(xis)
wis = np.zeros(steps+1)
pcs = []; fpcs = []
for i in xrange(0,steps-2,3):
wis[i:i+4] += [1,3,3,1]
pcs.append(xis[i:i+4])
fpcs.append(fxis[i:i+4])
wis *= 3*h/8
if steps%3==2:
wis[-3:] += [h/3,4*h/3,h/3]
pcs.append(xis[-3:])
fpcs.append(fxis[-3:])
elif steps%3==1:
wis[-2:] += [h/2,h/2]
pcs.append(xis[-2:])
fpcs.append(fxis[-2:])
fapprox = lambda x: np.piecewise(x,
[np.logical_and(p[0]<=x,x<=p[-1]) for p in pcs],
[lagrange(pcs[i],fpcs[i]) for i in xrange(len(pcs))])# np.interp(x,xis,fxis)
# fapprox = lambda x: np.interp(x,xis,fxis)
return (sum(fxis*wis),xis,fxis,wis,fapprox) # h/2 * sum(np.array([f(x) for x in xs]) * np.array([1]+[2]*(len(xs)-2)+[1]))
def phiPrime(self,t):
"""
derivative of the double exponential transform
"""
if N.isscalar(t):
t = M.array([t])
return N.piecewise(t,[M.fabs(t)>5.0],[self.phiPrime1,self.phiPrime2])
def crystalball(x,s,a,n,xbar,sigma):
A = np.power(n/np.absolute(a),n)*np.exp(-np.absolute(a)**2/2)
B = n/np.absolute(a)-np.absolute(a)
C = n/np.absolute(a)*(1/(n-1))*np.exp(-np.absolute(a)**2/2)
D = np.sqrt(np.pi/2)*(1+erf(np.absolute(a)/np.sqrt(2)))
N = 1/(sigma*(C+D))
return np.piecewise(x, [(x-xbar)/sigma > -a], [lambda x:s*N*np.exp(-np.power(x-xbar,2)/(2*sigma**2)), lambda x:s*N*A*np.power((B-(x-xbar)/sigma),-n)])
def BorueErukhimovich_Powerlaw(q, C, r0, s, t, nu):
"""Borue-Erukhimovich model ending in a power-law.
Inputs:
-------
``q``: independent variable
``C``: scaling factor
``r0``: typical el.stat. screening length
``s``: dimensionless charge concentration
``t``: dimensionless temperature
``nu``: excluded volume parameter
Formula:
--------
``C*(x^2+s)/((x^2+s)(x^2+t)+1)`` where ``x=q*r0`` if ``q<qsep``
``A*q^(-1/nu)``if ``q>qsep``
``A`` and ``qsep`` are determined from conditions of smoothness at the
cross-over.
"""
def get_xsep(alpha, s, t):
A = alpha + 2
B = 2 * s * alpha + t * alpha + 4 * s
C = s * t * alpha + alpha + alpha * s ** 2 + alpha * s * t - 2 + 2 * s ** 2
D = alpha * s ** 2 * t + alpha * s
r = np.roots([A, B, C, D])
#print "get_xsep: ", alpha, s, t, r
return r[r > 0][0] ** 0.5
get_B = lambda C, xsep, s, t, nu:C * (xsep ** 2 + s) / ((xsep ** 2 + s) * (xsep ** 2 + t) + 1) * xsep ** (1.0 / nu)
x = q * r0
xsep = np.real_if_close(get_xsep(-1.0 / nu, s, t))
A = get_B(C, xsep, s, t, nu)
return np.piecewise(q, (x < xsep, x >= xsep),
(lambda a:BorueErukhimovich(a, C, r0, s, t),
lambda a:A * (a * r0) ** (-1.0 / nu)))
def _apply(self, imls):
"""
Given IML values, interpolate the corresponding loss ratio
value(s) on the curve.
Input IML value(s) is/are clipped to IML range defined for this
vulnerability function.
:param float array iml: IML value
:returns: :py:class:`numpy.ndarray` containing a number of interpolated
values equal to the size of the input (1 or many)
"""
# for imls < min(iml) we return a loss of 0 (default)
ret = numpy.zeros(len(imls))
# imls are clipped to max(iml)
imls_curve = numpy.piecewise(
imls,
[imls > self.imls[-1]],
[self.imls[-1], lambda x: x])
# for imls such that iml > min(iml) we get a mean loss ratio
# by interpolation and sample the distribution
idxs, = numpy.where(imls_curve >= self.imls[0])
imls_curve = numpy.array(imls_curve)[idxs]
means = self._mlr_i1d(imls_curve)
# apply uncertainty
covs = self._cov_for(imls_curve)
ret[idxs] = self.distribution.sample(means, covs, covs * imls_curve)
return ret
def phi(self,t):
"""
double exponential transformation
"""
if N.isscalar(t):
t = M.array([t])
return N.piecewise(t,[M.fabs(t)>5.0],[self.phi1,self.phi2])
def spherical_variogram_model(m, d):
"""Spherical model, m is [psill, range, nugget]"""
psill = float(m[0])
range_ = float(m[1])
nugget = float(m[2])
return np.piecewise(d, [d <= range_, d > range_],
[lambda x: psill * ((3.*x)/(2.*range_) - (x**3.)/(2.*range_**3.)) + nugget, psill + nugget])
def get_LUT_value(data, window, level):
"""Apply the RGB Look-Up Table for the given data and window/level value."""
f = lambda data: ((data - (level - 0.5)) / (window - 1) + 0.5) * (255 - 0)
return np.piecewise(data, [
data <= (level - 0.5 - (window - 1) / 2),
data > (level - 0.5 + (window - 1) / 2)
], [0, 255, f])
n = 8
pos.findEnergies(n)
# Plot some of the stationary states
V0 = pos.V0
b = pos.b
x = np.linspace(-b, b, 200 * b)
for i in range(0, n):
plt.plot(x, energy(i) + psi_n(i, x), label="E: " + str(energy(i)))
xW = np.linspace(-b - 0.1, b + 0.1, 200 * b)
plt.plot(
xW,
np.piecewise(xW, [
xW > b,
np.logical_and(xW <= b, xW > 1),
np.logical_and(1 >= xW, xW >= -1),
np.logical_and(-1 > xW, xW >= -b), -b > xW
], [10 + energy(n), 0, -V0, 0, 10 + energy(n)]))
plt.ylim(-V0 - 1, energy(n - 1) + 1)
plt.xlabel("$x/a$")
plt.ylabel("$\psi(x)$")
#plt.legend()
#plt.show()
plt.savefig("WiW_stationarySolutions.png")
def psi_n_odd(n, x): k = np.sqrt(-2*energies["odd"][n]) l = np.sqrt(2*(energies["odd"][n] + V0)) A = np.exp(k)*1/(np.sqrt(1/k+1/(np.sin(l))**2 - 1/np.tan(l))) return np.piecewise(x, [x > 1, np.logical_and(1 >= x, x >= -1), -1 > x], [lambda x: A*np.exp(-k*x), lambda x: A*np.exp(-k)/(np.sin(l))*np.sin(l*x), lambda x: -A*np.exp(k*x)])
"Small": lambda dwt: 0.831 * dwt - 0.2,
"Handy": lambda dwt: 1.05 * (0.153 - 0.00000158 * dwt),
"Handymax": lambda dwt: 1.05 * (0.151 - 0.00000127 * dwt),
"Panamax": lambda dwt: 1.05 * 0.079,
"Capesize": lambda dwt: 0.0817 - 0.0000000486 * dwt,
"VLBC": lambda dwt: 1.05 * (0.076 - 0.0000000261 * dwt)
}
# Derived DWT regression formulas (with 5 significant digits)
SMALL_DWT = lambda L, B: 0.0029893 * L**3.0395 - 366.02 * np.sqrt(1737. - 67. *
B) + 11575.0
HANDY_DWT = lambda L, B: 0.00030717 * L**3.0441 + 1894.9 * B - 28158.0
HANDYMAX_DWT = lambda L, B: 7.0187e-09 * L**5.5157 + 1841.0 * B - 34850.0
PANAMAX_DWT = lambda L, B: np.piecewise(
L,
[(L < 201.05) * (L >= 193.68), (L <= 226.32) * (L >= 201.05),
(L > 226.32) * (L <= 233.68)],
[(L - 107.00) / 0.0014, (L - 31.00) / 0.00267, (L - 180.50) / 0.0005],
)
CAPESIZE_DWT = lambda L, B: 0.0030344 * L**3.1056 + np.piecewise(
B, [(B < 41) * (B >= 38), (B <= 47) *
(B >= 41)], [1979.8 * B - 55038.1, 3167.7 * B - 103740.0])
VLBC_DWT = lambda L, B: 1602.29 * L - 279210.0
DERIVED_DWT = [
SMALL_DWT,
HANDY_DWT,
HANDYMAX_DWT,
PANAMAX_DWT,
CAPESIZE_DWT,
def safe_inverse_root(d):
if (d < 0).any():
raise ValueError
return np.piecewise(d, [d > 0, d == 0], [lambda x: x**(-0.5), lambda x: x])
def fu():
return lambda x: np.piecewise(x, [x == 0, x > 0],
[0, lambda x: x**2 * np.log(x)])
def generate_pin_bandstructure(mat, Lp,Aname,Na,d, Ln,Dname,Nd, Va):
# The Material class will find the bulk energy levels
mp=Material(mat,{Aname:Na})
mn=Material(mat,{Dname:Nd})
# Band edges far on the p and n side
Ecp=mp.Ec-mp.EBulk-Va/2
Evp=mp.Ev-mp.EBulk-Va/2
Ecn=mn.Ec-mn.EBulk+Va/2
Evn=mn.Ev-mn.EBulk+Va/2
# Depletion edges, assuming depletion fully within device.
# Note, these are locations in x (with appropriate signs), where depletion ends
# ...not the absolute widths of the respective regions!
xn= (-Na*d+np.sqrt(Na**2*d**2+2*mn.eps*(Ecp-Ecn)/q*Na/Nd*(Na+Nd)))/(Na+Nd) + d/2
xp=-(-Nd*d+np.sqrt(Nd**2*d**2+2*mn.eps*(Ecp-Ecn)/q*Nd/Na*(Na+Nd)))/(Na+Nd) - d/2
# P-side depletion should stay within the device
assert (xp > -Lp-d/2), "p-side depletion region extends outside device!"
# x-grid for calculation
x=np.linspace(-Lp-d/2,Ln+d/2,50000)
# If the n-side depletion region is fully within the device
if (xn<Ln+d/2):
# Return np.piecewise band diagram from depletion approximation
return {"x":x,\
"Ec":np.piecewise(x,
[x<xp, (x>=xp)&(x<-d/2), (x>=-d/2)&(x<d/2), (x>=d/2)&(x<xn), x>=xn],
[lambda x: Ecp, lambda x: Ecp-.5*q*Na/mp.eps*(x-xp)**2,
lambda x: Ecp-.5*q*Na/mp.eps*(-d/2-xp)**2-q*Na/mp.eps*(-d/2-xp)*(x+d/2),
lambda x: Ecn+.5*q*Nd/mn.eps*(xn-x)**2, lambda x: Ecn]),\
"Ev":np.piecewise(x,
[x<xp, (x>=xp)&(x<-d/2), (x>=-d/2)&(x<d/2), (x>=d/2)&(x<xn), x>=xn],
[lambda x: Evp, lambda x: Evp-.5*q*Na/mp.eps*(x-xp)**2,
lambda x: Evp-.5*q*Na/mp.eps*(-d/2-xp)**2-q*Na/mp.eps*(-d/2-xp)*(x+d/2),
lambda x: Evn+.5*q*Nd/mn.eps*(xn-x)**2, lambda x: Evn]),\
"EB": np.piecewise(x,
[x<xp, (x>=xp)&(x<xn), (x>=xn)],
[lambda x: -Va/2, lambda x: np.NaN, lambda x: Va/2]),\
"Vr": -Va,\
"material": mp}
# If the n-side depletion region hits the device edge
else:
# Assume a sheet charge after the n-side to rebalance charge
# Recalculate xp, and the sheet charge.
xp=-(-(d+Ln)+np.sqrt((d+Ln)**2+(Nd/Na*Ln**2+2*mp.eps*(Ecp-Ecn)/(q*Na))))-d/2
sigma_n=Na*(-d/2-xp)-Nd*Ln
# Again, make sure the p-side depletion is still inside the device
assert (xp > -Lp), "p-side depletion region extends outside device!"
# Return a np.piecewise bandstructure given our maxed out depletion
return {"x":x,\
"Ec":np.piecewise(x,
[x<xp, (x>=xp)&(x<-d/2), (x>=-d/2)&(x<d/2), (x>=d/2)&(x<Ln+d/2), x>=Ln+d/2],
[lambda x: Ecp, lambda x: Ecp-.5*q*Na/mp.eps*(x-xp)**2,
lambda x: Ecp-.5*q*Na/mp.eps*(-d/2-xp)**2-q*Na/mp.eps*(-d/2-xp)*(x+d/2),
lambda x: Ecn+.5*q*Nd/mn.eps*(Ln+d/2-x)**2+q*sigma_n*(Ln+d/2-x)/mn.eps, lambda x: Ecn]),\
"Ev":np.piecewise(x,
[x<xp, (x>=xp)&(x<-d/2), (x>=-d/2)&(x<d/2), (x>=d/2)&(x<Ln+d/2), x>=Ln+d/2],
[lambda x: Evp, lambda x: Evp-.5*q*Na/mp.eps*(x-xp)**2,
lambda x: Evp-.5*q*Na/mp.eps*(-d/2-xp)**2-q*Na/mp.eps*(-d/2-xp)*(x+d/2),
lambda x: Evn+.5*q*Nd/mn.eps*(Ln+d/2-x)**2+q*sigma_n*(Ln+d/2-x)/mn.eps, lambda x: Evn]),\
"EB": np.piecewise(x,
[x<xp, (x>=xp)&(x<xn), (x>=Ln+d/2)],
[lambda x: -Va/2, lambda x: np.NaN, lambda x: Va/2]),\
"Vr": -Va,\
"material": mn}
def ReLU_derivative(x):
y = x
np.piecewise(y, [ReLU(y) == 0, ReLU(y) == y], [0, 1])
return y
out : ndarray
!!! The output is the same shape and type as `x` !!!
and is found by calling the functions in `funclist` on the appropriate portions of `x`,
as defined by the boolean arrays in `condlist`.
Portions not covered by any condition have a default value of 0.
See also: choose, select (Indexing routines), where (Sorting, searching, and counting)
Notes
This is similar to `choose` or `select`,
except that functions are evaluated on elements of `x` that satisfy the corresponding condition from `condlist`.
"""
x = np.linspace(-2.5, 2.5, 6)
x
np.piecewise(x, [x < 0, x >= 0],
[-1, 1]) # array([-1., -1., -1., 1., 1., 1.])
# Define the absolute value, which is -x for x <0 and x for x >= 0.
np.piecewise(
x, [x < 0, x >= 0],
[lambda x: -x, lambda x: x]) # array([2.5, 1.5, 0.5, 0.5, 1.5, 2.5])
# Apply the same function to a scalar value.
y = -2
np.piecewise(y, [y < 0, y >= 0], [lambda x: -x, lambda x: x]) # array(2)
#%%
xx = np.arange(100)
import matplotlib.pyplot as plt
def inc_tophat(x):
J = x.size
q = np.piecewise(x,[x < -0.25,x >= -0.25],[0.0,1.0])*np.piecewise(x,[x <= 0.25, x > 0.25],[1.0,0.0])
return q
import matplotlib.pyplot as plt
import numpy as np
import scipy.constants as sc
from matplotlib.widgets import Slider, Button, RadioButtons
fig, ax = plt.subplots(figsize=(20, 10))
plt.subplots_adjust(left=0.15, bottom=0.30)
po = 0.000002
a = 20
x = np.arange(0.01, 40, 0.01)
H1 = lambda x: np.piecewise(x, [x < 20.0, x >= 20], [1, 0])
H2 = lambda x: np.piecewise(x, [x < 20.0, x >= 20], [0, 1])
K = H1(x) * (po / sc.epsilon_0) * ((x / 3) - (x**3) / (5 * a**2)) + H2(x) * (
(a**3) / x**2) * (po / sc.epsilon_0) * (0.133333333)
k1 = H2(x) * ((a**3) / x**2) * (po / sc.epsilon_0) * (0.133333333)
plt.plot(x,
K,
"blue",
linewidth=2,
label="Campo Electrico Interno",
color="blue")
plt.plot(x, k1, linewidth=2, label="Campo Electrico Externo", color="green")
plt.legend(loc=1)
font1 = {"family": "century", "color": "black", "weight": "normal", "size": 1}
font2 = {"family": "century", "color": "black", "weight": "normal", "size": 1}
def k(x, theta):
return np.piecewise(x, [
x < 0.25,
np.logical_and(x >= 0.25, x < 0.5),
np.logical_and(x < 0.75, x >= 0.5), (x >= 0.75)
], theta)
def generate_spikedpn_bandstructure(mat, Lp,Aname,Na, sigmaD, Ln,Dname,Nd, Va):
# The Material class will find the bulk energy levels
mp=Material(mat,{Aname:Na})
mn=Material(mat,{Dname:Nd})
# Band edges far on the p and n side
Ecp=mp.Ec-mp.EBulk-Va/2
Evp=mp.Ev-mp.EBulk-Va/2
Ecn=mn.Ec-mn.EBulk+Va/2
Evn=mn.Ev-mn.EBulk+Va/2
# x-grid for calculation
x=np.linspace(-Lp,Ln,50000)
# Depletion edges, assuming spike is undepleted
sigma=np.sqrt(2*mp.eps*Na*(Ecp-Ecn)/q)
print ("Va",Va," sigma", sigma)
xp=-sigma/Na
# If the spike is not fully depleted
if(sigma<sigmaD):
print ("not dep")
# P-side depletion should stay within the device
assert (xp > -Lp), "p-side depletion region extends outside device!"
# Depletion edges, assuming depletion fully within device.
# Note, these are locations in x (with appropriate signs), where depletion ends
# ...not the absolute widths of the respective regions!
return {"x":x,\
"Ec":np.piecewise(x,
[x<xp,(x>=xp)&(x<0),(x>=0)],
[lambda x: Ecp, lambda x: Ecp-.5*q*Na/mp.eps*(x-xp)**2,lambda x: Ecn]),\
"Ev":np.piecewise(x,
[x<xp,(x>=xp)&(x<0),(x>=0)],
[lambda x: Evp, lambda x: Evp-.5*q*Na/mp.eps*(x-xp)**2,lambda x: Evn]),\
"EB": np.piecewise(x,
[x<xp, (x>=xp)&(x<0), (x>=0)],
[lambda x: -Va/2, lambda x: np.NaN, lambda x: Va/2]),\
"Vr": -Va,\
"material": mp}
# If the spike is fully depleted, we actually have to solve for xn
else:
xn=-sigmaD/(Nd+Na)+np.sqrt(sigmaD**2/(Nd+Na)**2-2/(Nd+Na)*(sigmaD**2/(2*Nd)-Na*mn.eps*(Ecp-Ecn)/(q*Nd)))
xp=-(Nd/Na*xn+sigmaD/Na)
# N-side depletion should stay within the device, because I haven't considered full depletion
assert (xn < Ln), "n-side depletion region extends outside device, and I haven't coded that"
# Return np.piecewise band diagram from depletion approximation
return {"x":x,\
"Ec":np.piecewise(x,
[x<xp, (x>=xp)&(x<0), (x>=0)&(x<xn), x>=xn],
[lambda x: Ecp, lambda x: Ecp-.5*q*Na/mp.eps*(x-xp)**2,
lambda x:Ecn+.5*q*Nd/mn.eps*(xn-x)**2, Ecn]),\
"Ev":np.piecewise(x,
[x<xp, (x>=xp)&(x<0), (x>=0)&(x<xn), x>=xn],
[lambda x: Evp, lambda x: Evp-.5*q*Na/mp.eps*(x-xp)**2,
lambda x:Evn+.5*q*Nd/mn.eps*(xn-x)**2, Evn]),\
"EB": np.piecewise(x,
[x<xp, (x>=xp)&(x<xn), (x>=xn)],
[lambda x: -Va/2, lambda x: np.NaN, lambda x: Va/2]),\
"Vr": -Va,\
"material": mp}
def _int_piecewise(x, *condlist, **kwargs):
return np.piecewise(x, list(condlist), kwargs["funclist"],
*kwargs["func_args"], **kwargs["func_kw"])
def inner(x, deg=2):
return np.piecewise(
x, [x < a, x > b],
[lambda x: (a - x)**deg, lambda x: (x - b)**deg])
def psi_n_even(n, x): k = np.sqrt(-2*energies["even"][n]) l = np.sqrt(2*(energies["even"][n] + V0)) A = np.exp(k)*1/(np.sqrt(1/k+1/(np.cos(l))**2 + np.tan(l))) return np.piecewise(x, [x > 1, 1 >= x, -1 > x], [lambda x: A*np.exp(-k*x), lambda x: A*np.exp(-k)/(np.cos(l))*np.cos(l*x), lambda x: A*np.exp(k*x)])
apply_fit(freqs, p_lambertian, quartic_fit, "cyan", plt)
apply_fit(freqs, p_specular, quartic_fit, "r", plt)
def lambertian(f):
return -2.98e-11 * (f**4) + 1.71e-8 * (f**3) - 2.47e-6 * (
f**2) + 7.83e-4 * f + 5.88e-2
def total_diff(f):
return -2.9e-13 * f**4 - 3.1e-9 * f**3 + 3.21e-6 * f**2 + 2.03e-4 * f + 7.16e-2
plt.plot(freqs,
np.piecewise(freqs, [freqs < 366.2, freqs >= 366.2], [
lambda f: -2.98e-11 * (f**4) + 1.71e-8 * (f**3) - 2.47e-6 *
(f**2) + 7.83e-4 * f + 5.88e-2, 0.318
]),
label='Physical Lambertian Probability',
c='cyan')
plt.plot(
freqs,
np.piecewise(freqs, [freqs < 366.2, freqs >= 366.2],
[lambda f: total_diff(f), lambda f: 0.318 + 1.51e-14 * f**5]),
c='g',
label='Physical Total Diffusive Probability')
plt.plot(
freqs,
np.piecewise(
freqs, [freqs < 366.2, freqs >= 366.2],
[lambda f: 1 - total_diff(f), lambda f: 1 -
(0.318 + 1.51e-14 * f**5)]),
def trailer_profile(z):
n = np.piecewise(z, [z<1.8558, z>2.8689],\
[ 0., 0., lambda z: 0.4+0.6/1.0131*(z-1.8558)])
# the last value is the default value, when no condition is satisfied
return (n)
def init_progressive_mask(mask, bounds):
random_nums = np.random.uniform(0, bounds, mask.shape)
conds = [mask == 1, mask == -1]
funcs = [lambda x: bounds - x, lambda x: x - bounds]
return np.piecewise(random_nums, conds,
funcs) # return initialised random numbers
import numpy as np
import matplotlib.pyplot as mp
ary = np.array([60, 50, 70, 32, 65, 28, 73, 93])
r = np.piecewise(ary, [np.all([ary <= 100, ary >= 60], axis=0), ary < 60],
[1, 0])
print(r)
def Huber_loss(a, delta):
# a=y-t
# H=np.where(abs(a)<=delta,1/2*a**2,delta*(abs(a)-delta/2))
dH = np.piecewise(a, [abs(a) <= delta, a > delta, -a < delta], [a, delta, -delta])
return dH
def piecewise_linear_2(x, x0, y0, a1, a2):
condlist = [x <= x0]
funclist = [lambda x: a1*x + y0 - a1*x0, lambda x: a2*x + y0 - a2*x0]
return np.piecewise(x, condlist, funclist)
x = np.array([
[3, 1],
[2, 5],
[1, 8],
[6, 4],
[5, 2],
[3, 5],
[4, 7],
[4, -1]])
y = np.array([0, 1, 1, 0, 0, 1, 1, 0])
# 把整个空间分为500*500的网格化矩阵
l, r = x[:,0].min()-1, x[:,0].max()+1
b, t = x[:,1].min()-1, x[:,1].max()+1
grid_x, grid_y = np.meshgrid(
np.linspace(l, r, 500),
np.linspace(b, t, 500))
# grid_z存储了网格化矩阵中每个坐标点的类别标签：0 / 1
grid_z = np.piecewise(grid_x,
[grid_x>grid_y, grid_x<grid_y] ,
[0, 1])
# 绘制散点图
mp.figure('Simple Classification', facecolor='lightgray')
mp.title('Simple Classification', fontsize=20)
mp.xlabel('x', fontsize=14)
mp.ylabel('y', fontsize=14)
mp.tick_params(labelsize=10)
# 为网格化矩阵中的每个元素填充背景颜色
mp.pcolormesh(grid_x, grid_y, grid_z, cmap='gray')
mp.scatter(x[:, 0], x[:, 1], c=y, cmap='brg', s=80)
mp.show()
def E_gsf(self, **kwargs):
"""
Returns values for generalized stacking fault energy interpolated from
the raw data. Values can be obtained relative to a1, a2 fractional
coordinates, x, y plotting coordinates, or pos Cartesian coordinates.
Parameters
----------
a1 : float(s), optional
Fractional coordinate(s) along a1vect.
a2 : float(s), optional
Fractional coordinate(s) along a2vect.
pos : np.array, optional
3D Cartesian position vector(s).
x : float(s), optional
Plotting x coordinate(s).
y : float(s), optional
Plotting y coordinate(s).
a1vect : np.array, optional
Vector for the a1 fractional coordinates. Default value of None
uses the saved a1vect.
a2vect : np.array, optional
Vector for the a2 fractional coordinates. Default value of None
uses the saved a2vect.
xvect : np.array, optional
Cartesian vector corresponding to the plotting x-axis. If None
(default), this is taken as the Cartesian of a1vect.
smooth : bool, optional
If True (default) the returned values are smoothed using a RBF fit.
If False, the closest measured values are returned.
"""
if not self.__hasdata:
raise AttributeError('gamma surface data not set')
smooth = kwargs.pop('smooth', True)
# Convert x, y to a1, a2
if 'x' in kwargs:
x = kwargs.pop('x')
y = kwargs.pop('y')
a1vect = kwargs.pop('a1vect', None)
a2vect = kwargs.pop('a2vect', None)
xvect = kwargs.pop('xvect', None)
assert len(kwargs) == 0, 'Unknown/incompatible arguments given'
a1, a2 = self.xy_to_a12(x, y, a1vect=a1vect, a2vect=a2vect, xvect=xvect)
# Convert pos to a1, a2
elif 'pos' in kwargs:
pos = kwargs.pop('pos')
a1vect = kwargs.pop('a1vect', None)
a2vect = kwargs.pop('a2vect', None)
assert len(kwargs) == 0, 'Unknown/incompatible arguments given'
a1, a2 = self.pos_to_a12(pos, a1vect=a1vect, a2vect=a2vect)
# Get a1, a2 from kwargs
else:
a1 = np.array(kwargs.pop('a1'))
a2 = np.array(kwargs.pop('a2'))
a1vect = kwargs.pop('a1vect', None)
a2vect = kwargs.pop('a2vect', None)
assert len(kwargs) == 0, 'Unknown/incompatible arguments given'
if a1vect is not None or a2vect is not None:
shape = a1.shape
# Convert into pos using given a1vect, a2vect, then back into a1, a2
pos = self.a12_to_pos(a1, a2, a1vect=a1vect, a2vect=a2vect)
a1, a2 = self.pos_to_a12(pos)
a1 = a1.reshape(shape)
a2 = a2.reshape(shape)
# Return interpolated values
if smooth:
cushion = (1 - self.data.a1.max()) / 2
# Wrap all a1, a2 values within [-cushion, 1.0 - cushion)
while np.any(a1 >= 1.0 - cushion):
a1[a1 >= 1.0 - cushion] -= 1.0
while np.any(a1 < -cushion):
a1[a1 < -cushion] += 1.0
while np.any(a2 >= 1.0 - cushion):
a2[a2 >= 1.0 - cushion] -= 1.0
while np.any(a2 < -cushion):
a2[a2 < -cushion] += 1.0
# Compute weighting factors
def zone1(x):
return (x + cushion) / (2 * cushion)
def zone2(x):
return np.ones_like(x)
x = np.piecewise(a1, [a1 < cushion, a1>= cushion], [zone1, zone2])
y = np.piecewise(a2, [a2 < cushion, a2>= cushion], [zone1, zone2])
# Linear smoothing across boundaries
return ( x * y * self.__E_gsf_fit(a1, a2)
+ x * (1 - y) * self.__E_gsf_fit(a1, a2 + 1)
+ (1 - x) * y * self.__E_gsf_fit(a1 + 1, a2)
+ (1 - x) * (1 - y) * self.__E_gsf_fit(a1 + 1, a2 + 1))
# Return nearest values
else:
# Wrap all values within 0.0 < a1, a2 < 1.0
while np.any(a1 > 1.0):
a1[a1 > 1.0] -= 1.0
while np.any(a1 < 0.0):
a1[a1 < 0.0] += 1.0
while np.any(a2 > 1.0):
a2[a2 > 1.0] -= 1.0
while np.any(a2 < 0.0):
a2[a2 < 0.0] += 1.0
return self.__E_gsf_nearest(np.array([a1.flatten(), a2.flatten()]).T).reshape(a1.shape)
def piecewise_linear_3(x, x0, x1, y0, a1, a2, a3):
condlist = [x <= x0, x <= x1, x1 < x]
funclist = [lambda x: a1*x + y0, lambda x: a2*x + (a1*x0 + y0 - a2*x0), lambda x: a3*x + (a2*(x1-x0) + a1*x0 + y0) - a3*x1, lambda x: 0]
print(len(condlist), len(funclist))
return np.piecewise(x, condlist, funclist)
def piecewise_linear(x, x0, y0, k1, k2):
return np.piecewise(
x, [x < x0],
[lambda x: k1 * x + y0 - k1 * x0, lambda x: k2 * x + y0 - k2 * x0])
import matplotlib.pyplot as plt
import numpy as np
import pdb
x = np.linspace(-1, 1, 1000)
cutoff = 0.3
satslope = 10
y = np.piecewise(
x, [x < -cutoff,
np.logical_and(x >= -cutoff, x < cutoff), x >= cutoff], [
lambda x: x * satslope +
(satslope - 1) * cutoff, lambda x: x, lambda x: x * satslope -
(satslope - 1) * cutoff
])
plt.plot(x, y)
plt.show()
def f(x, b):
return np.piecewise(x, [x < -b, x > b], [0, 1, 5])
from scipy.sparse import diags
import scipy.linalg as la
import numpy as np
import matplotlib.pyplot as plt
import scipy as sp
import scipy.constants as sc
l = 1e-9 # Lengde på boksen
Dx = 1.0E-11 # Steglengden
x = np.arange(0, l, Dx) # x-kooridnatene
size = len(x) # Størrelsen på matrisa
V = np.zeros(size) # Potensialet, som et array
# konstanter, definert ved hjelp av scipy - biblioteket
h = sc.h
hbar = sc.hbar
m = sc.m_e
c = sc.c
def analy(i):
E = (i**2 * sc.pi**2 * hbar**2) / (2 * m * l**2)
return E / sc.eV
n = np.arange(1, (size + 1), 1)
V = np.piecewise(x, [x < 0, x > l], [np.inf, np.inf, 0])
energi_funk = np.sqrt(2 / l) - np.sin((n * np.pi * x) / l)
engeri_verdi = (n * np.pi * hbar) / (2 * m * l)
def Vpot(x): # Pozo de potencial
y=np.piecewise(x, [x < -1, x >= 1],[lambda x:20, lambda x:20])
return y
x_train, x_valid, y_train, y_valid, ids_train, ids_valid = train_test_split(
X_train,
Y_train,
np.array(datamanager.train_ids),
test_size=0.08,
stratify=coverage[:, 1],
random_state=RANDOM_STATE[FOLD_NUMBER])
x_train_, y_train_ = augment_images(x_train, y_train)
if PRED_ON_TRAIN:
x_valid = x_train_
y_valid = y_train_
ids_valid = ids_train
y_train_ = np.piecewise(y_train_, [y_train_ > 127.5, y_train_ < 127.5],
[1, 0])
y_valid = np.piecewise(y_valid, [y_valid > 127.5, y_valid < 127.5], [1, 0])
assert x_train_.shape[1:] == x_valid.shape[1:]
time_delta = datetime.datetime.now() - start_time
print('Loading time', time_delta)
if MODEL:
amodel = create_model((datamanager.img_size_input,
datamanager.img_size_input, datamanager.im_chan))
if LOAD_PREV_MODEL:
print('Loading weights')
amodel.load_weights('base_model.h5')
if TRAIN:
print('Start training')
#