def roots(self):
from numpy.lib.scimath import sqrt as csqrt
r1 = (-self.b - csqrt((self.b**2) -
(4 * self.a * self.c))) / (2 * self.a)
r2 = (-self.b + csqrt((self.b**2) -
(4 * self.a * self.c))) / (2 * self.a)
return r1, r2
def Mf(t0, t):
# define a function to compute the M matrix
Int_w1d = Id
for i in range(Ndim):
w1d = w1d_num[i](t)
w1d0 = w1d_num[i](t0)
dw1d0 = dw1d_num[i](t0)
g0 = gamma_num[i](t0)
Int_gamma = quad(gamma_num[i],
t0,
t,
args=(),
maxiter=quad_maxiter,
vec_func=False)[0]
Int_w1d = c_quad(w1d_num[i],
t0,
t,
ARGS=(),
MAXITER=quad_maxiter)
C = np.exp(-0.5 * Int_gamma) * np.cos(Int_w1d) * csqrt(
w1d0 / w1d)
S = np.exp(-0.5 * Int_gamma) * np.sin(Int_w1d) * csqrt(
w1d0 / w1d)
M11[i, i] = C + S * (g0 / (2 * w1d0) + dw1d0 / (2 * (w1d0)**2))
M12[i, i] = S / w1d0
M_ = (M11 + M12 @ A_num(t0))
return M_
def roots(a, b, c):
r1 = (-b + csqrt(b**2 - 4 * a * c)) / (2 * a)
r2 = (-b - csqrt(b**2 - 4 * a * c)) / (2 * a)
print(r1.imag, "imaginario")
print(r2.real, "real")
return r1, r2 #si no regreso nada no muestra nada
def i2(w, wp, k, v):
gv = g(w, wp)
e1 = csqrt((w + wp)**2 - 1)
e2 = csqrt(wp**2 - 1)
f_upper = f(k, np.real(e1 - e2), np.imag(e1 + e2) + 2 * v) * (gv + 1)
f_lower = f(k, np.real(e1 + e2), np.imag(e1 + e2) + 2 * v) * (gv - 1)
return f_upper + f_lower
def components(self):
"""list of ProjectiveCollection: The components of the degenerate quadrics."""
n = self.shape[-1]
indices = tuple(np.indices(self.shape[:-2]))
if n == 3:
b = adjugate(self.array)
i = np.argmax(np.abs(np.diagonal(b, axis1=-2, axis2=-1)), axis=-1)
beta = csqrt(-b[indices + (i, i)])
p = -b[indices +
(slice(None), i)] / np.where(beta != 0, beta, -1)[..., None]
else:
ind = np.indices((n, n))
ind = [
np.delete(np.delete(ind, i, axis=1), i, axis=2)
for i in combinations(range(n), n - 2)
]
ind = np.stack(ind, axis=1)
minors = det(self.array[..., ind[0], ind[1]])
p = csqrt(-minors)
# use the skew symmetric matrix m to get a matrix of rank 1 defining the same quadric
m = hat_matrix(p)
t = self.array + m
# components are in the non-zero rows and columns (up to scalar multiple)
i = np.unravel_index(
np.abs(t).reshape(t.shape[:-2] + (-1, )).argmax(axis=-1),
t.shape[-2:])
p, q = t[indices + i[:1]], t[indices + (slice(None), i[1])]
if self.dim > 2 and not np.all(
is_multiple(
q[..., None] * p[..., None, :],
t,
rtol=EQ_TOL_REL,
atol=EQ_TOL_ABS,
axis=(-2, -1),
)):
raise NotReducible("Quadric has no decomposition in 2 components.")
# TODO: make order of components reproducible
p, q = np.real_if_close(p), np.real_if_close(q)
if self.is_dual:
return [
PointCollection(p, copy=False),
PointCollection(q, copy=False)
]
elif n == 3:
return [
LineCollection(p, copy=False),
LineCollection(q, copy=False)
]
return [PlaneCollection(p, copy=False), PlaneCollection(q, copy=False)]
def Mf(t0, t): # define a function to compute the M matrix w1 = w1_num[i](t) w10 = w1_num[i](t0) dw10 = dw1_num[i](t0) Int_w1 = c_quad(w1_num[i], t0, t, ARGS=(), MAXITER=quad_maxiter) C = np.cos(Int_w1)*csqrt(w10/w1) S = np.sin(Int_w1)*csqrt(w10/w1) M11[i,i] = C + S*dw10/(2*(w10)**2) M12[i,i] = S/w10
def Mf(t0, t): # define a function to compute the M matrix for i in range(Ndim): w1 = w1_num[i](t) w10 = w1_num[i](t0) dw10 = dw1_num[i](t0) Int_w1 = c_quad(w1_num[i], t0, t, ARGS=(), MAXITER=quad_maxiter) C = np.cos(Int_w1)*csqrt(w10/w1) S = np.sin(Int_w1)*csqrt(w10/w1) M11[i,i] = C + S*dw10/(2*(w10)**2) M12[i,i] = S/w10 M_ = P_num(t) @ (M11 @ Pinv_num(t0) + M12 @ (dPinv_num(t0) + Pinv_num(t0) @ A_num(t0))) return M_
def Mf(t0, t): # define a function to compute the M matrix for i in range(Ndim): w1 = w1_num[i](t) w10 = w1_num[i](t0) dw10 = dw1_num[i](t0) Int_w1 = c_quad(w1_num[i], t0, t, ARGS=()) C = np.cos(Int_w1)*csqrt(w10/w1) S = np.sin(Int_w1)*csqrt(w10/w1) M11[i,i] = C + S*dw10/(2*(w10)**2) M12[i,i] = S/w10 M_ = (M11 + M12 @ A_num(t0)) return M_
def components(self):
""":obj:`list` of :obj:`ProjectiveElement`: The components of a degenerate conic."""
a = csqrt(-np.linalg.det(self.array[[[1], [2]], [1, 2]]))
b = csqrt(-np.linalg.det(self.array[[[0], [2]], [0, 2]]))
c = csqrt(-np.linalg.det(self.array[[[0], [1]], [0, 1]]))
m = np.array([[0, c, -b],
[-c, 0, a],
[b, -a, 0]])
t = self.array + m
i = np.unravel_index(np.abs(t).argmax(), t.shape)
if self.is_dual:
return [Point(t[i[0]]), Point(t[:, i[1]])]
return [Line(t[i[0]]), Line(t[:, i[1]])]
def Mf(t0, t): # define a function to compute the M matrix w1 = w1_vec(t) w10 = w1_vec(t0) dw10 = dw1(t0) for i in range(Ndim): Int_w1 = c_quad(w1_sing, t0, t, ARGS=(i)) C = np.cos(Int_w1)*csqrt(w10[i]/w1[i]) S = np.sin(Int_w1)*csqrt(w10[i]/w1[i]) M11[i,i] = C + S*dw10[i]/(2*(w10[i])**2) M12[i,i] = S/w10[i] Pinvt0 = dPinv_num(t0) M_ = P_num(t) @ (M11 @ Pinvt0 + M12 @ () + Pinvt0 @ A_num(t0)) return M_
def Mf(t0, t):
# define a function to compute the M matrix
w1 = w1_vec(t)
w10 = w1_vec(t0)
dw10 = dw1(t0)
Int_w1 = Id
for i in range(Ndim):
Int_w1 = c_quad(w1_sing, t0, t, ARGS=(i), MAXITER=quad_maxiter)
C = np.cos(Int_w1) * csqrt(w10[i] / w1[i])
S = np.sin(Int_w1) * csqrt(w10[i] / w1[i])
M11[i, i] = C + S * dw10[i] / (2 * (w10[i])**2)
M12[i, i] = S / w10[i]
M_ = (M11 + M12 @ A_num(t0))
return M_
def omega(s, s_0, alpha):
"""A conformal variable.
Parameters
----------
s
the Mandelstam variable `s`
s_0
usually non-negative. Above `s_0`, the conformal variable is complex.
alpha
the center of the conformal expansion
"""
sqrt_s = csqrt(s)
diff = alpha * csqrt(s_0 - s)
return (sqrt_s - diff) / (sqrt_s + diff)
def Mf(t0, t): # define a function to compute the M matrix w1 = w1_vec(t) w10 = w1_vec(t0) dw10 = dw1(t0) Int_w1 = Id for i in range(Ndim): Int_w1 = quad(w1_sing, t0, t, args=(i, True), maxiter=10)[0] + 1j*quad(w1_sing, t0, t, args=(i, False), maxiter=10)[0] C = np.cos(Int_w1)*csqrt(w10[i]/w1[i]) S = np.sin(Int_w1)*csqrt(w10[i]/w1[i]) M11[i,i] = C + S*dw10[i]/(2*(w10[i])**2) M12[i,i] = S/w1[i] Pinv = np.linalg.inv(P(t)) M_ = Pinv @ (M11 @ P(t0) + M12 @ (dP(t0) + P(t0) @ A_num(t0))) return M_
def diagonalize_isotropic(permittivity, settings): # pylint: disable=too-many-locals
"""Diagonalizes propagation matrix for a homogeneous pattern. The
diagonalization is done by hand to ensure appropriate ordering of s and p
polarizations. The ith (i + g_num)th eigenvector and eigenvalue correspond
to the s- (p-) polarization of the ith diffraction order.
The input and output arguments are the same as for diagonalize_structured
except for the first input argument, which is a 3-element list of
permittivities instead of a pattern.
"""
g_num = settings['g_num']
frequency = settings['frequency']
kx_vec = settings['kx_vec']
ky_vec = settings['ky_vec']
k_perp_mat = np.vstack((-np.diag(ky_vec), np.diag(kx_vec)))
k_norm = np.sqrt(kx_vec**2 + ky_vec**2)
eig_vals_s = permittivity[0] * frequency**2 - k_norm**2
eig_vals_s = csqrt(eig_vals_s)
eig_vals_s[np.imag(eig_vals_s) < 0] *= -1
eig_vals_p = permittivity[0] * (frequency**2 - k_norm**2 / permittivity[2])
eig_vals_p = csqrt(eig_vals_p)
eig_vals_p[np.imag(eig_vals_p) < 0] *= -1
eig_vals = np.hstack((eig_vals_s, eig_vals_p))
if np.any(abs(eig_vals) / frequency < config.TOL):
raise RuntimeError("Encountered a mode that does not propagate "
"out of plane (q = 0). The current implementation "
"of pyPho is incapable of handling this situation "
":(")
ind = (k_norm / frequency < config.TOL)
ind = np.where(ind)[0]
k_norm[ind] = 1
eig_vecs_s = k_perp_mat / k_norm
eig_vecs_s[:, ind] = 0
eig_vecs_s[g_num + ind, ind] = 1
eig_vecs_p = np.vstack((np.diag(kx_vec), np.diag(ky_vec))) / k_norm
eig_vecs_p[:, ind] = 0
eig_vecs_p[ind, ind] = 1
eig_vecs_p = eig_vecs_p * eig_vals_p / (csqrt(permittivity[0] * frequency))
eig_vecs_e = np.hstack((eig_vecs_s, eig_vecs_p))
eig_vecs_h = -(permittivity[0] * frequency**2 * np.eye(2 * g_num) -
k_perp_mat @ k_perp_mat.T) @ eig_vecs_e / (frequency *
eig_vals)
return eig_vals, eig_vecs_e, eig_vecs_h
def w1_sing(t, n):
Ap2_ = Aprime2_num(t)
w2 = -J_[n, n]
if w2.size > 1:
w2 = w2[0]
w1_ = np.asscalar(csqrt(w2))
return w1_
def Mf(t0, t): # define a function to compute the M matrix Int_w1d = Id for i in range(Ndim): w1d = w1d_num[i](t) w1d0 = w1d_num[i](t0) dw1d0 = dw1d_num[i](t0) g0 = gamma_num[i](t0) Int_gamma = c_quad(gamma_num[i], t0, t) Int_w1d = c_quad(w1d_num[i], t0, t) C = np.exp(-0.5*Int_gamma)*np.cos(Int_w1d)*csqrt(w1d0/w1d) S = np.exp(-0.5*Int_gamma)*np.sin(Int_w1d)*csqrt(w1d0/w1d) M11[i,i] = C + S*(g0/(2*w1d0) + dw1d0/(2*(w1d0)**2)) M12[i,i] = S/w1d0 M_ = (M11 + M12 @ A_num(t0)) return M_
def w1_sing(t, n):
A_ = Ap(t)
w2 = -A_[n, n]
if w2.size > 1:
w2 = w2[0]
w1_ = np.asscalar(csqrt(w2))
return w1_
def q_resonator(M):
A = M[0, 0]
B = M[0, 1]
C = M[1, 0]
D = M[1, 1]
q = (-(D - A) + csqrt((D - A)**2 + 4 * B * C)) / (2 * np.abs(C))
return q
def ForwardModel(resistivities, thicknesses, frequency):
MU = 4*np.pi*10**(-7)
w = 2*np.pi * frequency
n = len(resistivities)
impedances = np.zeros(n, dtype='complex_')
# print('================================================================')
# print(n)
# print(resistivities)
# print(thicknesses)
# print('================================================================')
impedances[n-1] = csqrt( csqrt(-1) * w * MU * float(resistivities[n-1]) )
if n > 1:
for j in range(n-2,-1,-1):
resistivity = float(resistivities[j])
thickness = float(thicknesses[j])
dj = csqrt(csqrt(-1) * (w * MU / resistivity ))
wj = dj * resistivity
ej = np.exp(-2 * thickness * dj)
belowImpedance = impedances[j+1]
rj = (wj - belowImpedance) / (wj + belowImpedance)
re = rj * ej
Zj = wj * ((1 - re) / (1 + re))
impedances[j] = Zj
Z = impedances[0]
absZ = abs(Z)
apparentResistivity = absZ * absZ / (MU * w)
phase = np.rad2deg( np.arctan2(np.imag(Z), np.real(Z)) )
return apparentResistivity, phase
def from_tangent(cls, tangent, a, b, c, d):
"""Construct a conic through four points and tangent to a line.
Parameters
----------
tangent : Line
a, b, c, d : Point
The points lying on the conic.
Returns
-------
Conic
The resulting conic.
"""
if any(tangent.contains(p) for p in [a, b, c, d]):
raise ValueError(
"The supplied points cannot lie on the supplied tangent!")
a1, a2 = (
Line(a, c).meet(tangent).normalized_array,
Line(b, d).meet(tangent).normalized_array,
)
b1, b2 = (
Line(a, b).meet(tangent).normalized_array,
Line(c, d).meet(tangent).normalized_array,
)
o = tangent.general_point.array
a2b1 = det([o, a2, b1])
a2b2 = det([o, a2, b2])
a1b1 = det([o, a1, b1])
a1b2 = det([o, a1, b2])
c1 = csqrt(a2b1 * a2b2)
c2 = csqrt(a1b1 * a1b2)
x = Point(c1 * a1 + c2 * a2, copy=False)
y = Point(c1 * a1 - c2 * a2, copy=False)
conic = cls.from_points(a, b, c, d, x)
if np.all(np.isreal(conic.array)):
return conic
return cls.from_points(a, b, c, d, y)
def w1_vec(t):
A_ = Ap(t)
w1_ = np.ones(Ndim).astype(np.complex64)
for n in range(Ndim):
w2 = -A_[n, n]
if w2.size > 1:
w2 = w2[0]
w1_[n] = np.asscalar(csqrt(w2))
return w1_
def components(self):
""":obj:`list` of :obj:`ProjectiveElement`: The components of a degenerate conic."""
if not self.is_degenerate:
return [self]
a = csqrt(-np.linalg.det(self.matrix[np.array([1,2])[:, np.newaxis], np.array([1,2])]))
b = csqrt(-np.linalg.det(self.matrix[np.array([0,2])[:, np.newaxis], np.array([0,2])]))
c = csqrt(-np.linalg.det(self.matrix[np.array([0,1])[:, np.newaxis], np.array([0,1])]))
m = np.array([[0, c, -b],
[-c, 0, a],
[b, -a, 0]])
t = self.matrix + m
x, y = np.nonzero(t)
result = []
for a in np.concatenate((t[x,:], t[:,y].T)):
l = Point(a) if self.is_dual else Line(a)
if l not in result:
result.append(l)
return result
def w1_sing(t, n): if Use_Aprime2_or_J: W2 = -Aprime2_num(t) elif not Use_Aprime2_or_J: W2 = -J_num(t) w2 = W2[n, n] if w2.size > 1: w2 = w2[0] w1_ = np.asscalar(csqrt(w2)) return w1_
def w1_sing(t, n, real): J_ = J(t) w2 = -J_[n,n] if w2.size > 1: w2 = w2[0] w1_ = np.asscalar(csqrt(w2)) if real: w1_ = np.real(w1_) elif not real: w1_ = np.imag(w1_) return w1_
def calc_anomalies(a, phi0):
khat = np.array([np.cos(phi0), np.sin(phi0)])
x1 = (h*khat[0] + (h*khat[1])[:, np.newaxis]) / a
# print(x1)
x2 = (h/a)**2
x3 = x1**2 - (x2 + x2[:, np.newaxis]) + 1
# mask = np.where(x3 > 0, True, False)
minuspart = -x1 - csqrt(x3)
pluspart = -x1 + csqrt(x3)
# print(sin_theta0)
anomaly_theta0 = []
for item in minuspart.flatten():
if item.imag == 0 and 0 < item.real < np.pi/2:
anomaly_theta0.append(item)
for item in pluspart.flatten():
if item.imag == 0 and 0 < item.real < np.pi/2:
anomaly_theta0.append(item)
return np.arcsin(np.array(anomaly_theta0)) * 180 / np.pi
def twoloop(self, z, p):
s = p[0]
g = p[1:]
r_in, a, b = np.array(g, dtype=np.complex128) * mm
r = r_in + a / 2
Rsq = r + a**2 / 24 / r
c = csqrt((b**2 - a**2) / 12)
pterm = (Rsq + c)**2 / (z**2 + (Rsq + c)**2)**(1.5)
mterm = (Rsq - c)**2 / (z**2 + (Rsq - c)**2)**(1.5)
B = 1 / 4 * const.mu_0 * s * (pterm + mterm)
return np.real(B) # complex part is 0 anyways
def w1_vec(t): if Use_Aprime2_or_J: W2 = -Aprime2_num(t) elif not Use_Aprime2_or_J: W2 = -J_num(t) w1_ = np.ones(Ndim).astype(np.complex64) for n in range(Ndim): w2 = W2[n,n] if w2.size > 1: w2 = w2[0] w1_[n] = np.asscalar(csqrt(w2)) return w1_
def components(self):
"""list of ProjectiveElement: The components of a degenerate quadric."""
# Algorithm adapted from Perspectives on Projective Geometry, Section 11.1
n = self.shape[0]
if n == 3:
b = adjugate(self.array)
i = np.argmax(np.abs(np.diag(b)))
beta = csqrt(-b[i, i])
p = -b[:, i] / beta if beta != 0 else b[:, i]
else:
p = []
for ind in combinations(range(n), n - 2):
# calculate all principal minors of order 2
row_ind = [[j] for j in range(n) if j not in ind]
col_ind = [j for j in range(n) if j not in ind]
p.append(csqrt(-det(self.array[row_ind, col_ind])))
# use the skew symmetric matrix m to get a matrix of rank 1 defining the same quadric
m = hat_matrix(p)
t = self.array + m
# components are in the non-zero rows and columns (up to scalar multiple)
i = np.unravel_index(np.abs(t).argmax(), t.shape)
p, q = t[i[0]], t[:, i[1]]
if self.dim > 2 and not is_multiple(
np.outer(q, p), t, rtol=EQ_TOL_REL, atol=EQ_TOL_ABS):
raise NotReducible("Quadric has no decomposition in 2 components.")
p, q = np.real_if_close(p), np.real_if_close(q)
if self.is_dual:
return [Point(p, copy=False), Point(q, copy=False)]
elif n == 3:
return [Line(p, copy=False), Line(q, copy=False)]
return [Plane(p, copy=False), Plane(q, copy=False)]
def spemiss(f, tk, theta, ssw):
'''
* returns the specular emissivity of sea water for given freq. (GHz),
* temperature T (K), incidence angle theta (degrees), salinity (permil)
*
* Returned values verified against data in Klein and Swift (1977) and
* against Table 3.8 in Olson (1987, Ph.D. Thesis)
*
'''
from numpy.lib.scimath import sqrt as csqrt
#implicit none
#real*4 f,tk,theta,ssw,ev,eh
#real*4 fold,tkold,sswold,epsr,epsi,epsrold,epsiold
#save fold,tkold,sswold,epsrold,epsiold
#*
#real*4 tc,costh,sinth,rthet
#complex*8 etav,etah,eps,cterm1v,cterm1h,cterm2,cterm3v,cterm3h
#*
# <------------ !!! This section has been modified
#if ((f != fold) | (tk != tkold) | (ssw < sswold)):
# tc = tk - 273.15
# fold = f
# tkold = tk
# sswold = ssw
tc = tk - 273.15
epsr, epsi = epsalt(f, tc, ssw)
epsrold = epsr
epsiold = epsi
#else:
#epsr = epsrold
#epsi = epsiold
eps = epsr + 1.0j * epsi #cmplx(epsr,epsi)
etav = eps
etah = 1.0 + 1.0j * 0.0 #(1.0, 0.0)
rthet = theta * 0.017453292
costh = np.cos(rthet)
sinth = np.sin(rthet)
sinth = sinth * sinth
cterm1v = etav * costh
cterm1h = etah * costh
eps = eps - sinth
cterm2 = csqrt(eps) # <---------- csqrt
cterm3v = (cterm1v - cterm2) / (cterm1v + cterm2)
cterm3h = (cterm1h - cterm2) / (cterm1h + cterm2)
#print('cterm3v: {}, cterm3h: {}'.format(cterm3v, cterm3h))
ev = 1.0 - np.abs(cterm3v)**2 #cabs(cterm3v)**2
eh = 1.0 - np.abs(cterm3h)**2 #cabs(cterm3h)**2
return ev, eh
def calculate(self, parameters):
A = parameters["A"]
b = parameters["b"]
A, b = process_params(A, b)
response = self.init_response()
if no_es_invertible(A):
response["error"] = "La matriz no es invertible"
return response
if not es_definida_positiva(A):
response["error"] = "La matriz no definida positiva"
return response
n = len(A)
# L = np.zeros((n, n))
# U = np.zeros((n, n))
# Utilizar estas si se quiere trabajar con complejos
L = np.zeros((n, n), dtype="complex")
U = np.zeros((n, n), dtype="complex")
for k in range(n):
suma1 = np.sum([L[k, p] * U[p, k] for p in range(0, k)])
L[k, k] = U[k, k] = csqrt(A[k, k] - suma1)
for i in range(k + 1, n):
suma2 = np.sum(L[i, p] * U[p, k] for p in range(0, k))
L[i, k] = (A[i, k] - suma2) / U[k, k]
for j in range(k + 1, n):
suma3 = np.sum(L[k, p] * U[p, j] for p in range(0, k))
U[k, j] = (A[k, j] - suma3) / L[k, k]
z = self.sustitucion_progresiva(L, b)
x = self.sustitucion_regresiva(U, z)
L = np.real(L)
U = np.real(U)
response["L"] = np.round(L, 4).tolist()
response["U"] = np.round(U, 4).tolist()
response["z"] = np.round(np.real(z), 4).tolist()
response["x"] = np.round(np.real(x), 4).tolist()
return response
def get_target(self):
""" Build a reflectance image of the target and calculate surface normals at every pixel
"""
# Set up pixel relative x-coodinates
x = np.linspace(-1.0, 1.0, self.n_pix * self.anti_aliasing)
# Meshgrid the x and y coordinates as the same
x, y = np.meshgrid(x, x)
# Calculate the polar coordinate theta of each pixel
theta = np.arctan2(y, x)
# Produce a siemens star target with the given number of spokes/sectors
siemans_star = np.cos(self.Nsector_pairs * theta)
# Create an array that will become a target mask
mask = np.ones(siemans_star.shape)
# Make the mask binary by taking the sign of the siemens star
siemans_star = np.sign(siemans_star)/2.0 + 0.5
# Set all value outside the unit circle to the new value
circle = np.sqrt(x**2 + y**2) > 1.0
mask[circle] = 0.0
# downsample if aliasing requested
if self.anti_aliasing > 1.0:
the_filter = np.ones((self.anti_aliasing, self.anti_aliasing)) / self.anti_aliasing**2
# Apply 2D filter convolution
siemans_star = sg.convolve2d(siemans_star, the_filter, mode = 'full')
# Convole the mask as well
mask = sg.convolve2d(mask, the_filter, mode = 'full')
siemans_star = siemans_star[0.0::self.anti_aliasing, ::self.anti_aliasing]
mask = mask[0.0::self.anti_aliasing, ::self.anti_aliasing]
x = np.linspace(-1.0, 1.0, siemans_star.shape[0])
y = np.linspace(-1.0, 1.0, siemans_star.shape[1])
x, y = np.meshgrid(x, y)
# Create blank list of normal vector components
normal_vector_list = [[],[],[]]
normal_vector_list[0] = x
normal_vector_list[1] = y
normal_vector_list[2] = (csqrt(1.0 - x**2 - y**2)).real
# Save reflectance map, normal vectors and mask in self
self.normal_vector_list = normal_vector_list
self.siemens_star = siemans_star
self.mask = mask
return normal_vector_list, mask, siemans_star
def get_supercritical_velocity_array(self):
"""Calculate the supercritical velocity for the given temperature or pressure range."""
v_array_calculation = csqrt(2 * 1000 * (self.get_enthalpy_column() - self.get_mean_enthalpy_at_tp()))
v_array = np.where(np.iscomplex(v_array_calculation), 0, v_array_calculation).astype(float)
return v_array
# Raised Cosine
z = np.linspace(-Length/2,Length/2,no_sections)
delta_n = 0.5*d_n_max*(1+np.cos(np.pi*(z/(0.1*Length))))
for i in range(0,lambda_points):
MAT = np.eye(2)
for m in range(no_sections-1,0,-1):
kapadc = 4*np.pi*delta_n[m]/wavelength[i]
kapaac = kapadc/2
delta = kapadc+0.5*(2*ko[i]*n_eff[i]-2*np.pi/period)
alpha = csqrt(kapaac**2-delta**2)
T = TMM(period, dz, delta_n[m], delta, alpha,dz)
MAT =np.dot(MAT,T)
R[i] = np.abs(MAT[0,1]/MAT[0,0])
plt.figure(2)
plt.plot(wavelength,R)
plt.figure(3)
plt.plot(z,delta_n)
plt.show()
