def poly_E(eps, eps_R, F, P):
r"""
Function to obtain the polynomial E and its roots in the s-domain.
:param eps: Constant term associated with S21
:param eps_R: Constant term associated with S11
:param F: Polynomial F, i.e., numerator of S11 (in s-domain)
:param P: Polynomial P, i.e., numerator of S21 (in s-domain)
For further explanation, see "filter theory notes" by the author.
:rtype: [polynomial_E, roots_E] ... where polynomial E is the
denominator of S11 and S21
"""
N = len(F)
nfz = len(P)
if ((N + nfz) % 2 == 0) and (abs(eps.real) > 0):
warnings.warn("'eps' value should be pure imaginary when (N+nfz) is an even number")
elif ((N + nfz + 1) % 2 == 0) and (abs(eps.imag) > 0):
warnings.warn("'eps' value should be pure real when (N+nfz) is an odd number")
s = sp.Symbol("s")
poly_P = sp.Poly(P.ravel().tolist(), s)
poly_F = sp.Poly(F.ravel().tolist(), s)
poly_E = eps_R * poly_P + eps * poly_F
roots_E = I_to_i(sp.nroots(poly_E))
roots_E = np.reshape(roots_E, (len(roots_E), -1))
roots_E = -abs(roots_E.real) + 1j * roots_E.imag # all roots to the LHS
# create the polynomial from the obtained LHS roots
poly_E = np.poly(roots_E.ravel().tolist())
poly_E = np.reshape(poly_E, (len(poly_E), -1))
return poly_E, roots_E
def risco_root_sanity(self):
r, chi = spy.symbols("r, chi")
p = (r * (r - 6))**2 - self.s_bh**2 * (2 * r *
(3 * r + 14) - 9 * self.s_bh**2)
p2 = (r * (r - 6))**2 - chi**2 * (2 * r * (3 * r + 14) - 9 * chi**2)
return p2.as_poly(), spy.nroots(p)
def solve_poly_inequality_numerically(expr, b, strict):
poly = expr - b
symX = get_poly_symbol(expr)
# Obtain numerical roots.
roots = sympy.nroots(poly)
zeros = sorted([r for r in roots if r.is_real])
if not zeros:
return sympy.EmptySet
# Construct intervals around roots.
mk_intvl = lambda a, b: \
Interval(a, b, left_open=strict, right_open=strict)
intervals = list(
chain([mk_intvl(-oo, zeros[0])],
[mk_intvl(x, y) for x, y in zip(zeros, zeros[1:])],
[mk_intvl(zeros[-1], oo)]))
# Define probe points.
xs_probe = list(
chain([zeros[0] - 1 / 2],
[(i.left + i.right) / 2
for i in intervals[1:-1] if isinstance(i, Interval)],
[zeros[-1] + 1 / 2]))
# Evaluate poly at the probe points.
f_xs_probe = [poly.subs(symX, x) for x in xs_probe]
# Return intervals where poly is less than zero.
idxs = [i for i, fx in enumerate(f_xs_probe) if fx < 0]
return make_union(*[intervals[i] for i in idxs])
def poly_E(eps, eps_R, F, P):
r"""
Function to obtain the polynomial E and its roots in the s-domain.
:param eps: Constant term associated with S21
:param eps_R: Constant term associated with S11
:param F: Polynomial F, i.e., numerator of S11 (in s-domain)
:param P: Polynomial P, i.e., numerator of S21 (in s-domain)
For further explanation, see "filter theory notes" by the author.
:rtype: [polynomial_E, roots_E] ... where polynomial E is the
denominator of S11 and S21
"""
N = len(F);
nfz = len(P)
if (((N + nfz) % 2 == 0) and (abs(eps.real) > 0)):
warnings.warn("'eps' value should be pure imaginary when (N+nfz) is an even number")
elif (((N + nfz + 1) % 2 == 0) and (abs(eps.imag) > 0)):
warnings.warn("'eps' value should be pure real when (N+nfz) is an odd number")
s = sp.Symbol('s')
poly_P = sp.Poly(P.ravel().tolist(), s)
poly_F = sp.Poly(F.ravel().tolist(), s)
poly_E = eps_R * poly_P + eps * poly_F
roots_E = I_to_i(sp.nroots(poly_E))
roots_E = np.reshape(roots_E, (len(roots_E), -1))
roots_E = -abs(roots_E.real) + 1j * roots_E.imag # all roots to the LHS
# create the polynomial from the obtained LHS roots
poly_E = np.poly(roots_E.ravel().tolist())
poly_E = np.reshape(poly_E, (len(poly_E), -1))
return poly_E, roots_E
def atten_coeff(disp, solve_mode=0):
k = Symbol('k')
if solve_mode == 0:
# Solve mode for transverse dispersion relation
ksol = list(solveset(disp, k))[0]
else:
# Solve mode for longitudinal dispersion relation
ksol = list(nroots(disp, maxsteps=100))[2]
alpha = abs(im(ksol))
return alpha
def risso_polar_sanity(self):
r, chi = spy.symbols("r, chi")
p2 = r**3 * (r**2 * (r - 6) + chi**2 *
(3 * r + 4)) + chi**4 * (3 * r * (r - 2) + chi**2)
print(p2.as_poly())
p = r**3 * (r**2 * (r - 6) + self.s_bh**2 *
(3 * r + 4)) + self.s_bh**4 * (3 * r *
(r - 2) + self.s_bh**2)
return spy.nroots(p)
def CiLP(self):
x = sp.symbols('x')
eq1 = self.legendreP(self.s, False, True)
eq2 = self.legendreP(self.s - 1, False, True)
eq3 = sp.Mul(sp.Integer(-1), eq2)
eq4 = sp.Add(eq1, eq3)
P = sp.Poly(eq4, x)
Pc = P.all_coeffs()
roots = list(np.roots(Pc))[::-1]
listeq = sp.nroots(sp.Poly(eq4, x), self.nd)
return roots, listeq
def poly_E(eps, eps_R, F, P):
"""Function to obtain the polynomial E and its roots in the s-domain."""
s = sp.Symbol('s')
poly_P = sp.Poly(P.ravel().tolist(), s)
poly_F = sp.Poly(F.ravel().tolist(), s)
poly_E = eps_R * poly_P + eps * poly_F
roots_E = I_to_i(sp.nroots(poly_E))
roots_E = np.reshape(roots_E, (len(roots_E), -1))
roots_E = -abs(roots_E.real) + 1j * roots_E.imag # all roots to the LHS
# create the polynomial from the obtained LHS roots
poly_E = np.poly(roots_E.ravel().tolist())
poly_E = np.reshape(poly_E, (len(poly_E), -1))
return poly_E, roots_E
def find_dzdx_poly_root(
dzdx_poly_: Poly,
xhat_: float,
xivhat0_: float,
guess: float = 0.1,
eta_: Optional[Rational] = None,
method: str = "brentq",
bracket: Tuple[float, float] = (0, 1e3),
) -> Any:
"""
TODO.
Args:
TODO
"""
if eta_ is not None and eta_ == Rational(1, 4):
poly_eqn_ = dzdx_poly_.subs({xhat: xhat_, xivhat_0: xivhat0_})
poly_lambda: Callable = lambdify([dzdx], poly_eqn_.as_expr())
# return poly_eqn_
dpoly_lambda: Optional[Callable] = lambdify(
[dzdx],
diff(poly_eqn_.as_expr(), dzdx) if method == "newton" else None,
)
bracket_: Optional[Tuple[float, float]] = (bracket if method
== "brentq" else None)
for guess_ in [0, guess]:
root_search = root_scalar(
poly_lambda,
fprime=dpoly_lambda,
method=method,
bracket=bracket_,
x0=guess_,
)
if root_search.converged:
break
dzdx_poly_root: float = root_search.root
else:
dzdx_poly_roots = nroots(
dzdx_poly_.subs({
xhat: xhat_,
xivhat_0: xivhat0_
}))
dzdx_poly_root = [
root_ for root_ in dzdx_poly_roots
if Abs(im(root_)) < 1e-10 and re(root_) > 0
][0]
return dzdx_poly_root
def px_value(
x_: float,
pz_: float,
px_poly_eqn: Eq,
px_var_: Symbol = px,
pz_var_: Symbol = pz,
) -> float:
"""
TODO.
Args:
TODO
"""
px_poly_eqn_: Poly = poly(px_poly_eqn.subs({rx: x_, x: x_, pz_var_: pz_}))
px_poly_roots: List[float] = nroots(px_poly_eqn_)
pxgen: float = [
root_ for root_ in px_poly_roots
if Abs(im(root_)) < 1e-10 and re(root_) > 0
][0]
return solve(Eq(px_poly_eqn_.gens[0], pxgen), px_var_)[0]
def max_rE_gains_3d(order, numeric=True):
"""max rE for a given order is the largest root of the order+1 Legendre
polynomial"""
x = sp.symbols('x')
lp = sp.legendre_poly(order + 1, x)
# there are more efficient methods to find the roots of the Legendre
# polynomials, but this is good enough for our purposes
# See discussion at:
# https://math.stackexchange.com/questions/12160/roots-of-legendre-polynomial
if order < 5 and not numeric:
roots = sp.roots(lp)
else:
roots = sp.nroots(lp)
# the roots can be in the keys of a dictionary or in a list,
# this works for either one
max_rE = np.max([*roots])
return [sp.legendre(n, max_rE) for n in range(order + 1)]
def poleres2pz(poles,residues,offset,slope, maxsteps=500):
"""
Convert a pole-resiude representation of a TF --
f(s) = Sum [r/(s-p)] + k + s * h
to a pole zero representation
f(s) = Sum[s-z] / Sum[s-p]
"""
from sympy import Symbol, together, expand, numer, denom, nroots
x = Symbol('x')
f = sum([r/(x-p) for p,r in zip(poles, residues)])
f += offset + slope*x
ft = together(f)
nf = expand(numer(ft))
zeros = nroots(nf,maxsteps=maxsteps)
return np.array([complex(xx) for xx in poles]), np.array([complex(xx) for
xx in zeros])
def risso(self, tol=1e-5):
r = spy.symbols("r")
c = np.cos(self.s_bh_tilt)
x1 = self.s_bh**2 * (3 * self.s_bh**2 + 4 * r *
(2 * r - 3)) + r**2 * (15 * r * (r - 4) + 28)
x2 = 6 * r**4 * (r**2 - 4)
x = self.s_bh**2 * x1 - x2
y1 = self.s_bh**4 * (self.s_bh**4 + r**2 * (7 * r * (3 * r - 4) + 36))
y2 = 6 * r * (r - 2) * (self.s_bh**6 + 2 * r**3 *
(self.s_bh**2 * (3 * r + 2) + 3 * r**2 *
(r - 2)))
y = y1 + y2
z = (r * (r - 6))**2 - self.s_bh**2 * (2 * r *
(3 * r + 14) - 9 * self.s_bh**2)
p = r**8 * z + self.s_bh**2 * (1 -
c**2) * (self.s_bh**2 *
(1 - c**2) * y - 2 * r**4 * x)
roots = np.array(spy.nroots(p, maxsteps=int(1e4)), dtype="complex128")
a = self.risso_polar()
b = self.risco()
R = [
r.real for r in roots if r.real - tol <= max(a, b) and r.real +
tol >= min(a, b) and r.imag < tol
]
try:
assert len(R) == 1
except AssertionError:
print(R)
return R[0]
def forecast_typhoon(userlocation, forecast, wind_7_r, wind_10_r):
nearlocation = np.empty([2, 2])
time_goin_10 = 0
time_goout_10 = 0
time_goin_10_first = 0
time_goout_10_first = 0
time_goin_10_second = 0
time_goout_10_second = 0
time_goin_7 = np.zeros([2])
time_goout_7 = np.zeros([2])
time_goin_7_first = 0
time_goout_7_first = 0
time_goin_7_second = 0
time_goout_7_second = 0
nearlat = 0
nearlon = 0
neartm = 0
dist = np.sqrt((forecast[1, :] - userlocation[0]) ** 2 + (forecast[2, :] - userlocation[1]) ** 2)
idx_near = np.argmin(dist)
###
###
if idx_near == 0:
idx_near_after = idx_near + 1
a2 = (forecast[2, idx_near] - forecast[2, idx_near_after]) / (
forecast[1, idx_near] - forecast[1, idx_near_after]
)
b2 = forecast[2, idx_near] - a2 * forecast[1, idx_near]
dist2 = abs(a2 * userlocation[0] + b2 - userlocation[1]) * np.sqrt(a2 ** 2 + 1)
nearlocation[0, 0] = -(a2 * b2 - a2 * userlocation[1] - userlocation[0]) / (a2 * a2 + 1)
nearlocation[0, 1] = a2 * nearlocation[0, 0] + b2
neardist = dist2
if nearlocation[1, 0] < min(forecast[1, idx_near], forecast[1, idx_near_after]) or nearlocation[1, 0] > max(
forecast[1, idx_near], forecast[1, idx_near_after]
):
time_near = (forecast[0, idx_near_after] - forecast[0, idx_near]) * (dist2 - dist[idx_near]) / (
dist[idx_near_after] - dist[idx_near]
) + forecast[0, idx_near]
else:
time_near = (forecast[0, idx_near_after] - forecast[0, idx_near]) * (dist[idx_near] - dist2) / (
dist[idx_near_after] - dist[idx_near]
) + forecast[0, idx_near]
if dist2 <= wind_10_r / 111:
if time_near < forecast[0, idx_near] and dist[idx_near] <= wind_10_r / 111:
# print('10 level wind influence me11')
time_goout_10 = (forecast[0, idx_near_after] - forecast[0, idx_near]) * (
wind_10_r / 111 - dist[idx_near]
) / (dist[idx_near_after] - dist[idx_near]) + forecast[0, idx_near]
time_goin_10 = -(time_goout_10 - time_near) + time_near
nearlat = forecast[1, idx_near]
nearlon = forecast[2, idx_near]
neartm = forecast[0, idx_near]
if time_near < forecast[0, idx_near] and dist[idx_near] > wind_10_r / 111:
pass
# print('10 level wind not influence me11')
if time_near >= forecast[0, idx_near] and dist[idx_near] <= wind_10_r / 111:
pass
# print('10 level wind influence me12')
time_goout_10 = (forecast[0, idx_near_after] - forecast[0, idx_near]) * (
wind_10_r / 111 - dist[idx_near]
) / (dist[idx_near_after] - dist[idx_near]) + forecast[0, idx_near]
time_goin_10 = -(time_goout_10 - time_near) + time_near
nearlat = nearlocation[0, 0]
nearlon = nearlocation[0, 1]
neartm = time_near
if time_near >= forecast[0, idx_near] and dist[idx_near] > wind_10_r / 111:
# print('10 level wind influence me13')
time_goin_10 = (forecast[0, idx_near_after] - forecast[0, idx_near]) * (
-wind_10_r / 111 + dist[idx_near]
) / (dist[idx_near_after] - dist[idx_near]) + forecast[0, idx_near]
time_goout_10 = (time_near - time_goin_10) + time_near
nearlat = nearlocation[0, 0]
nearlon = nearlocation[0, 1]
neartm = time_near
else:
pass
# print('10 level wind not influence me12')
if dist2 <= wind_7_r / 111:
if time_near < forecast[0, idx_near] and dist[idx_near] <= wind_7_r / 111:
# print('7 level wind influence me11')
time_goout_7 = (forecast[0, idx_near_after] - forecast[0, idx_near]) * (
wind_7_r / 111 - dist[idx_near]
) / (dist[idx_near_after] - dist[idx_near]) + forecast[0, idx_near]
time_goin_7 = (time_goout_7 - time_near) + time_near
nearlat = forecast[1, idx_near]
nearlon = forecast[2, idx_near]
neartm = forecast[0, idx_near]
if time_near < forecast[0, idx_near] and dist[idx_near] > wind_7_r / 111:
pass
# print('7 level wind not influence me11')
if time_near >= forecast[0, idx_near] and dist[idx_near] <= wind_7_r / 111:
# print('7 level wind influence me12')
time_goout_7 = (forecast[0, idx_near_after] - forecast[0, idx_near]) * (
wind_7_r / 111 - dist[idx_near]
) / (dist[idx_near_after] - dist[idx_near]) + forecast[0, idx_near]
time_goin_7 = (time_goout_7 - time_near) + time_near
nearlat = nearlocation[0, 0]
nearlon = nearlocation[0, 1]
neartm = time_near
if time_near >= forecast[0, idx_near] and dist[idx_near] > wind_7_r / 111:
# print('7 level wind influence me13')
time_goin_7 = (forecast[0, idx_near_after] - forecast[0, idx_near]) * (
-wind_7_r / 111 + dist[idx_near]
) / (dist[idx_near_after] - dist[idx_near]) + forecast[0, idx_near]
time_goout_7 = (time_near - time_goin_7) + time_near
nearlat = nearlocation[0, 0]
nearlon = nearlocation[0, 1]
neartm = time_near
else:
pass
# print('7 level wind not influence me12')
time_goin_10 = time_goin_10_first
time_goout_10 = time_goout_10_first
time_goin_7 = time_goin_7_first
time_goout_7 = time_goout_7_first
###
###
if idx_near == np.size(dist) - 1:
idx_near_before = idx_near - 1
a1 = (forecast[2, idx_near] - forecast[2, idx_near_before]) / (
forecast[1, idx_near] - forecast[1, idx_near_before]
)
b1 = forecast[2, idx_near] - a1 * forecast[1, idx_near]
dist1 = abs(a1 * userlocation[0] + b1 - userlocation[1]) * np.sqrt(a1 ** 2 + 1)
nearlocation[1, 0] = -(a1 * b1 - a1 * userlocation[1] - userlocation[0]) / (a1 * a1 + 1)
nearlocation[1, 1] = a1 * nearlocation[1, 0] + b1
neardist = dist1
if nearlocation[1, 0] < min(forecast[1, idx_near], forecast[1, idx_near_before]) or nearlocation[1, 0] > max(
forecast[1, idx_near], forecast[1, idx_near_before]
):
time_near = (forecast[0, idx_near] - forecast[0, idx_near_before]) * (dist[idx_near] - dist1) / (
dist[idx_near_before] - dist[idx_near]
) + forecast[0, idx_near]
else:
time_near = (forecast[0, idx_near] - forecast[0, idx_near_before]) * (dist1 - dist[idx_near]) / (
dist[idx_near_before] - dist[idx_near]
) + forecast[0, idx_near]
if dist1 <= wind_10_r / 111:
if time_near < forecast[0, idx_near] and dist[idx_near] <= wind_10_r / 111:
# print('10 level wind influence me21')
time_goout_10_first = (forecast[0, idx_near] - forecast[0, idx_near_before]) * (
wind_10_r / 111 - dist[idx_near]
) / (dist[idx_near_before] - dist[idx_near]) + forecast[0, idx_near]
time_goin_10_first = (time_goout_10_first - time_near) + time_near
nearlat = nearlocation[1, 0]
nearlon = nearlocation[1, 1]
neartm = time_near
if time_near < forecast[0, idx_near] and dist[idx_near] > wind_10_r / 111:
# print('10 level wind influence me22')
time_goout_10_first = (forecast[0, idx_near] - forecast[0, idx_near_before]) * (
dist[idx_near] - wind_10_r / 111
) / (dist[idx_near_before] - dist[idx_near]) + forecast[0, idx_near]
time_goin_10_first = (time_goout_10_first - time_near) + time_near
nearlat = nearlocation[1, 0]
nearlon = nearlocation[1, 1]
neartm = time_near
if time_near >= forecast[0, idx_near] and dist[idx_near] <= wind_10_r / 111:
# print('10 level wind influence me23')
time_goin_10_first = (forecast[0, idx_near] - forecast[0, idx_near_before]) * (
dist[idx_near] - wind_10_r / 111
) / (dist[idx_near_before] - dist[idx_near]) + forecast[0, idx_near]
time_goout_10_first = (time_near - time_goin_10_first) + time_near
nearlat = nearlocation[1, 0]
nearlon = nearlocation[1, 1]
neartm = time_near
if time_near >= forecast[0, idx_near] and dist[idx_near] > wind_10_r / 111:
# print('10 level wind influence me24')
time_goin_10_first = (forecast[0, idx_near] - forecast[0, idx_near_before]) * (
dist[idx_near] - wind_10_r / 111
) / (dist[idx_near_before] - dist[idx_near]) + forecast[0, idx_near]
time_goout_10_first = (time_near - time_goin_10_first) + time_near
nearlat = nearlocation[1, 0]
nearlon = nearlocation[1, 1]
neartm = time_near
else:
pass
# print('10 level wind not influence me21')
if dist1 <= wind_7_r / 111:
if time_near < forecast[0, idx_near] and dist[idx_near] <= wind_7_r / 111:
# print('7 level wind influence me21')
time_goout_7_first = (forecast[0, idx_near] - forecast[0, idx_near_before]) * (
wind_7_r / 111 - dist[idx_near]
) / (dist[idx_near_before] - dist[idx_near]) + forecast[0, idx_near]
time_goin_7_first = (time_goout_7_first - time_near) + time_near
nearlat = nearlocation[1, 0]
nearlon = nearlocation[1, 1]
neartm = time_near
if time_near < forecast[0, idx_near] and dist[idx_near] > wind_7_r / 111:
# print('7 level wind influence me22')
time_goout_7_first = (forecast[0, idx_near] - forecast[0, idx_near_before]) * (
dist[idx_near] - wind_7_r / 111
) / (dist[idx_near_before] - dist[idx_near]) + forecast[0, idx_near]
time_goin_7_first = (time_goout_7_first - time_near) + time_near
nearlat = nearlocation[1, 0]
nearlon = nearlocation[1, 1]
neartm = time_near
if time_near >= forecast[0, idx_near] and dist[idx_near] <= wind_7_r / 111:
# print('7 level wind influence me23')
time_goin_7_first = (forecast[0, idx_near] - forecast[0, idx_near_before]) * (
dist[idx_near] - wind_7_r / 111
) / (dist[idx_near_before] - dist[idx_near]) + forecast[0, idx_near]
time_goout_7_first = (time_near - time_goin_7_first) + time_near
nearlat = nearlocation[1, 0]
nearlon = nearlocation[1, 1]
neartm = time_near
if time_near >= forecast[0, idx_near] and dist[idx_near] > wind_7_r / 111:
# print('7 level wind influence me24')
time_goin_7_first = (forecast[0, idx_near] - forecast[0, idx_near_before]) * (
dist[idx_near] - wind_7_r / 111
) / (dist[idx_near_before] - dist[idx_near]) + forecast[0, idx_near]
time_goout_7_first = (time_near - time_goin_7_first) + time_near
nearlat = nearlocation[1, 0]
nearlon = nearlocation[1, 1]
neartm = time_near
else:
pass
# print('7 level wind not influence me22')
time_goin_10 = time_goin_10_first
time_goout_10 = time_goout_10_first
time_goin_7 = time_goin_7_first
time_goout_7 = time_goout_7_first
nearlat = nearlocation[1, 0]
nearlon = nearlocation[1, 1]
neartm = time_near
###
###
if idx_near < np.size(dist) - 1 and idx_near > 0:
idx_near_before = idx_near - 1
idx_near_after = idx_near + 1
xf = np.empty([3, 3])
xf[0, 0] = forecast[1, idx_near] ** 2
xf[1, 0] = forecast[1, idx_near_before] ** 2
xf[2, 0] = forecast[1, idx_near_after] ** 2
xf[0, 1] = forecast[1, idx_near]
xf[1, 1] = forecast[1, idx_near_before]
xf[2, 1] = forecast[1, idx_near_after]
xf[0, 2] = 1
xf[1, 2] = 1
xf[2, 2] = 1
y = [forecast[2, idx_near], forecast[2, idx_near_before], forecast[2, idx_near_after]]
bounds_lat_min = min(forecast[1, idx_near_before : idx_near_after + 1])
bounds_lat_max = max(forecast[1, idx_near_before : idx_near_after + 1])
fac = np.linalg.solve(xf, y)
from scipy.optimize import minimize_scalar
f = lambda x: np.sqrt(
(x - userlocation[0]) ** 2 + (fac[0] * x ** 2 + fac[1] * x + fac[2] - userlocation[1]) ** 2
)
rslt = minimize_scalar(f, bounds=(bounds_lat_min, bounds_lat_max))
nearlat = rslt.x
nearlon = fac[0] * nearlat ** 2 + fac[1] * nearlat + fac[2]
neardist = f(nearlat)
if nearlat < max(forecast[1, idx_near], forecast[1, idx_near_before]) and nearlat > min(
forecast[1, idx_near], forecast[1, idx_near_before]
):
neartm = (forecast[0, idx_near] - forecast[0, idx_near_before]) * (neardist - dist[idx_near]) / (
dist[idx_near_before] - dist[idx_near]
) + forecast[0, idx_near]
else:
neartm = (forecast[0, idx_near_after] - forecast[0, idx_near]) * (dist[idx_near] - neardist) / (
dist[idx_near_after] - dist[idx_near]
) + forecast[0, idx_near]
lat = smy.Symbol("lat")
lat_goinout_10raw = smy.nroots(
(lat - userlocation[0]) ** 2
+ (fac[0] * lat ** 2 + fac[1] * lat + fac[1] - userlocation[1]) ** 2
- (wind_10_r / 111) ** 2,
n=6,
)
lat_goinout_7raw = smy.nroots(
(lat - userlocation[0]) ** 2
+ (fac[0] * lat ** 2 + fac[1] * lat + fac[1] - userlocation[1]) ** 2
- (wind_10_r / 111) ** 2,
n=6,
)
lat_goinout_10 = [complex(flag).real for flag in lat_goinout_10raw]
lat_goinout_7 = [complex(flag).real for flag in lat_goinout_7raw]
lon_goinout_10 = [
fac[0] * complex(flag).real ** 2 + fac[1] * complex(flag).real + fac[2] for flag in lat_goinout_10raw
]
lon_goinout_7 = [
fac[0] * complex(flag).real ** 2 + fac[1] * complex(flag).real + fac[2] for flag in lat_goinout_7raw
]
if dist[idx_near] <= wind_10_r / 111:
# print('10 level wind influence me31')
if dist[idx_near_before] >= wind_10_r / 111:
idx_in = idx_near_before
else:
idx_in = 0
if dist[idx_near_after] >= wind_10_r / 111:
idx_out = idx_near_after
else:
idx_out = np.size(dist) - 1
a2 = (forecast[2, idx_near] - forecast[2, idx_out]) / (forecast[1, idx_near] - forecast[1, idx_out])
b2 = forecast[2, idx_near] - a2 * forecast[1, idx_near]
dist2 = abs(a2 * userlocation[0] + b2 - userlocation[1]) * np.sqrt(a2 ** 2 + 1)
nearlocation[1, 0] = -(a2 * b2 - a2 * userlocation[1] - userlocation[0]) / (a2 * a2 + 1)
nearlocation[1, 1] = a2 * nearlocation[1, 0] + b2
a1 = (forecast[2, idx_near] - forecast[2, idx_in]) / (forecast[1, idx_near] - forecast[1, idx_in])
b1 = forecast[2, idx_near] - a1 * forecast[1, idx_near]
dist1 = abs(a1 * userlocation[0] + b1 - userlocation[1]) * np.sqrt(a1 ** 2 + 1)
nearlocation[0, 0] = -(a1 * b1 - a1 * userlocation[1] - userlocation[0]) / (a1 * a1 + 1)
nearlocation[0, 1] = a1 * nearlocation[0, 0] + b1
neardist = min(dist1, dist2)
if dist[idx_in] > wind_10_r / 111 and dist[idx_in + 1] <= wind_10_r / 111:
time_goin_10_first = (forecast[0, idx_near] - forecast[0, idx_in]) * (
dist[idx_in] - (wind_10_r / 111)
) / (dist[idx_in] - dist[idx_near]) + forecast[0, idx_in]
else:
time_goin_10_first = (forecast[0, idx_near] - forecast[0, idx_in]) * (
dist[idx_in] - (wind_10_r / 111)
) / (dist[idx_in] - dist[idx_near]) + forecast[0, idx_in]
if dist[idx_out] < wind_10_r / 111 and dist[idx_out + 1] >= wind_10_r / 111:
time_goout_10_first = (-forecast[0, idx_near] + forecast[0, idx_out]) * (
-dist[idx_out] + (wind_10_r / 111)
) / (dist[idx_out] - dist[idx_near]) + forecast[0, idx_out]
# print "311"
else:
time_goout_10_first = (-forecast[0, idx_near] + forecast[0, idx_out]) * (
-dist[idx_out] + (wind_10_r / 111)
) / (dist[idx_out] - dist[idx_near]) + forecast[0, idx_out]
# print "312"
time_goin_10_second = 0
time_goout_10_second = 0
else:
if neardist > wind_10_r / 111:
pass
# print('10 level wind not influence me31')
else:
# print('10 level wind influence me32')
dist_from_before = min(
np.sqrt(
(lat_goinout_10 - forecast[1, idx_near_before]) ** 2
+ (lon_goinout_10 - forecast[2, idx_near_before]) ** 2
)
)
dist_from_after = min(
np.sqrt(
(lat_goinout_10 - forecast[1, idx_near_after]) ** 2
+ (lon_goinout_10 - forecast[2, idx_near_after]) ** 2
)
)
dist_near_from_before = np.sqrt(
(nearlat - forecast[1, idx_near_before]) ** 2 + (nearlon - forecast[2, idx_near_before]) ** 2
)
dist_near_from_after = np.sqrt(
(nearlat - forecast[1, idx_near_after]) ** 2 + (nearlon - forecast[2, idx_near_after]) ** 2
)
time_goin_10_first = (
neartm - forecast[0, idx_near_before]
) * dist_from_before / dist_near_from_before + forecast[0, idx_near_before]
time_goout_10_first = neartm - time_goin_10_first + neartm
time_goout_10_second = (
neartm - forecast[0, idx_near_after]
) * dist_from_after / dist_near_from_after + forecast[0, idx_near_after]
time_goin_10_second = -time_goout_10_second + neartm + neartm
if time_goin_10_first != 0 and time_goin_10_second != 0:
time_goin_10 = min(time_goin_10_first, time_goin_10_second)
else:
if time_goin_10_first == 0:
time_goin_10 = time_goin_10_second
if time_goin_10_second == 0:
time_goin_10 = time_goin_10_first
if time_goout_10_first != 0 and time_goout_10_second != 0:
time_goin_10 = max(time_goout_10_first, time_goout_10_second)
else:
if time_goout_10_first == 0:
time_goout_10 = time_goout_10_second
if time_goout_10_second == 0:
time_goout_10 = time_goout_10_first
if dist[idx_near] <= wind_7_r / 111:
# print('7 level wind influence me31')
if dist[idx_near_before] >= wind_7_r / 111:
idx_in = idx_near_before
else:
idx_in = 0
if dist[idx_near_after] >= wind_7_r / 111:
idx_out = idx_near_after
else:
idx_out = np.size(dist) - 1
a2 = (forecast[2, idx_near] - forecast[2, idx_out]) / (forecast[1, idx_near] - forecast[1, idx_out])
b2 = forecast[2, idx_near] - a2 * forecast[1, idx_near]
dist2 = abs(a2 * userlocation[0] + b2 - userlocation[1]) * np.sqrt(a2 ** 2 + 1)
nearlocation[1, 0] = -(a2 * b2 - a2 * userlocation[1] - userlocation[0]) / (a2 * a2 + 1)
nearlocation[1, 1] = a2 * nearlocation[1, 0] + b2
a1 = (forecast[2, idx_near] - forecast[2, idx_in]) / (forecast[1, idx_near] - forecast[1, idx_in])
b1 = forecast[2, idx_near] - a1 * forecast[1, idx_near]
dist1 = abs(a1 * userlocation[0] + b1 - userlocation[1]) * np.sqrt(a1 ** 2 + 1)
nearlocation[0, 0] = -(a1 * b1 - a1 * userlocation[1] - userlocation[0]) / (a1 * a1 + 1)
nearlocation[0, 1] = a1 * nearlocation[0, 0] + b1
neardist = min(dist1, dist2)
if dist[idx_in] > wind_7_r / 111 and dist[idx_in + 1] <= wind_7_r / 111:
time_goin_7_first = (forecast[0, idx_near] - forecast[0, idx_in]) * (
dist[idx_in] - (wind_7_r / 111)
) / (dist[idx_in] - dist[idx_near]) + forecast[0, idx_in]
else:
time_goin_7_first = (forecast[0, idx_near] - forecast[0, idx_in]) * (
dist[idx_in] - (wind_7_r / 111)
) / (dist[idx_in] - dist[idx_near]) + forecast[0, idx_in]
if dist[idx_out] < wind_7_r / 111 and dist[idx_out + 1] >= wind_7_r / 111:
time_goout_7_first = (-forecast[0, idx_near] + forecast[0, idx_out]) * (
-dist[idx_out] + (wind_7_r / 111)
) / (dist[idx_out] - dist[idx_near]) + forecast[0, idx_out]
else:
time_goout_7_first = (-forecast[0, idx_near] + forecast[0, idx_out]) * (
-dist[idx_out] + (wind_7_r / 111)
) / (dist[idx_out] - dist[idx_near]) + forecast[0, idx_out]
time_goin_7_second = 0
time_goout_7_second = 0
else:
if neardist > wind_7_r / 111:
pass
# print('7 level wind not influence me31')
else:
# print('7 level wind influence me32')
dist_from_before = min(
np.sqrt(
(lat_goinout_7 - forecast[1, idx_near_before]) ** 2
+ (lon_goinout_7 - forecast[2, idx_near_before]) ** 2
)
)
dist_from_after = min(
np.sqrt(
(lat_goinout_7 - forecast[1, idx_near_after]) ** 2
+ (lon_goinout_7 - forecast[2, idx_near_after]) ** 2
)
)
dist_near_from_before = np.sqrt(
(nearlat - forecast[1, idx_near_before]) ** 2 + (nearlon - forecast[2, idx_near_before]) ** 2
)
dist_near_from_after = np.sqrt(
(nearlat - forecast[1, idx_near_after]) ** 2 + (nearlon - forecast[2, idx_near_after]) ** 2
)
time_goin_7_first = (
neartm - forecast[0, idx_near_before]
) * dist_from_before / dist_near_from_before + forecast[0, idx_near_before]
time_goout_7_first = neartm - time_goin_7_first + neartm
time_goout_7_second = (
neartm - forecast[0, idx_near_after]
) * dist_from_after / dist_near_from_after + forecast[0, idx_near_after]
time_goin_7_second = -time_goout_7_second + neartm + neartm
if time_goin_7_first != 0 and time_goin_7_second != 0:
time_goin_7 = min(time_goin_7_first, time_goin_7_second)
else:
if time_goin_7_first == 0:
time_goin_7 = time_goin_7_second
if time_goin_7_second == 0:
time_goin_7 = time_goin_7_first
if time_goout_7_first != 0 and time_goout_7_second != 0:
time_goin_7 = max(time_goout_7_first, time_goout_7_second)
else:
if time_goout_7_first == 0:
time_goout_7 = time_goout_7_second
if time_goout_7_second == 0:
time_goout_7 = time_goout_7_first
# print time_goin_7_first,time_goin_10_first,time_goin_7_second,time_goin_10_second
# print time_goout_7_first,time_goout_10_first,time_goout_7_second,time_goout_10_second
return (
time_goin_10,
time_goout_10,
time_goin_7,
time_goout_7,
nearlat,
nearlon,
neartm,
neardist * 111,
neardist * 111 - wind_10_r,
neardist * 111 - wind_7_r,
)
r2 = lambdify(t, e_2, 'numpy')
print [i for i in r2(1)]
mpm.mp.dps = 15
x1, x2, x3, x4, x5, x6, x7, x8 = symbols('x1, x2, x3, x4, x5, x6, x7, x8')
e_3 = Poly(x1*x2 + x3*(x1**2) + x4*(x1**3) + x5*(x1**4) + x6*(x1**5) +
x7*(x1**6), (x1, x2, x3, x4, x5, x6, x7))
#Bien, un punto singular!
#r3 = nsolve((e_3 - 863, e_3 - 538, e_3 - 778, e_3 - 638, e_3 - 430, e_3 - 644,
# e_3 - 740), (x1, x2, x3, x4, x5, x6, x7), (-0.23, 110, 230, 440,
# 330, 50, -10))
p2 = Poly(q**5 +2*q +1, q)
r4 = nroots(Poly(p2, q), 15)
r5 = newton_method(0, w, 5)
r6 = newton_method(0, m, 12)
r7 = chi2(p_reader)
r8 = integrate(L(p_reader), (j, -100, 100))
print L(p_reader, 0.00000000001)
f10= (x**3)*y**4 + 4*x**2*y**2 + 2*x**3*y - 1
f = f9
n = sympy.degree(f,y)
coeffs = coeff_functions(sympy.poly(f,y),x)
# compute the path parameterization around a given branch point
bpt = 3
G = monodromy_graph(f,x,y)
path_segments = path_around_branch_point(G,bpt,1)
nseg = len(path_segments)
# select a root at the base_point
a = G.nodes[0]['basepoint']
fibre = map(numpy.complex,sympy.nroots(f.subs(x,a),n=15))
# analytically continue
ypath = []
for k in range(nseg):
# print("=== segment %k ===")
# print("fibre (start) =")
# for yj in fibre: print(yj)
ypath += analytically_continue(df,coeffs,n,fibre,1,path_segments[k][0])
fibre = [yij for yij in ypath[-1]]
# print("fibre (end) =")
# for yj in fibre: print(yj)
# parse out yroots data: right now it's of the form
# Choose non-wetting material
# 0 - Air
# 1 - Oil
# 2 - Gas
material_mode = 2
S0 = np.linspace(epsilon, 0.9, N)
w_array = [10, 100, 500, 1000, 5000]
w_label = [str(i) for i in w_array]
k = Symbol('k')
for i in range(len(w_array)):
w = w_array[i]
print('Progress: ' + str(int(100 * (i + 1) / 5)) + '%')
disp_rel = longitudinal_disp(S0, w, material_mode)
k_array = [list(nroots(d, maxsteps=100))[0:3] for d in disp_rel]
for j in range(3):
speed_array = [w / abs(re(e[j])) for e in k_array]
attenuation_array = [abs(im(e[j])) for e in k_array]
plt.figure(j)
if j == 2:
plt.plot(S0, speed_array, label=w_label[i])
else:
plt.semilogy(S0, speed_array, label=w_label[i])
plt.figure(j + 3)
plt.semilogy(S0, attenuation_array, label=w_label[i])
for j in range(3):
plt.figure(j)
from sympy.abc import x from sympy import roots, nroots f = 4 * x**3 + 2 * x - 3 roots(f) nroots(f)
def solve_poly_equality_numerically(expr, b):
roots = sympy.nroots(expr - b)
zeros = [r for r in roots if r.is_real]
return FiniteReal(*zeros)
def pade(A):
X = np.subtract.outer(A[1:, 0], A[:, 0]).T
column_size = np.size(A, 0)
M = (A[0, 1] / (A[1:, 1])) - 1
Z = np.zeros((column_size, column_size - 1))
Z[0, 0] = M[0] / X[0, 0]
Z[0, 1:] = (Z[0, 0] * X[0, 1:] / M[1:]) - 1
for i in range(1, column_size - 1):
Z[i, i] = Z[i - 1, i] / X[i, i]
Z[i, i + 1:] = (Z[i, i] * X[i, i + 1:] / Z[i - 1, i + 1:]) - 1
diag_z = Z.diagonal()
def build_frac(a, z, size):
plus_one = Rational(str(
z[size - 2])) * (t - Rational(str(a[size - 2, 0]))) + Rational(1)
frac = None
for i in reversed(range(size - 1)):
if i == 0:
frac = Rational(str(a[0, 1])) / plus_one
else:
frac = (Rational(str(z[i - 1])) *
(t - Rational(str(a[i - 1, 0])))) / plus_one
frac = frac.ratsimp()
plus_one = Rational(1) + frac
return frac
eqa = build_frac(A, diag_z, column_size)
diag_z = list(diag_z)
diag_z[-1] = 0
eqa_minus1 = build_frac(A, diag_z, column_size)
eqa_der = eqa.diff(t)
eqa_der = eqa_der.ratsimp()
numerator, denominator = fraction(eqa_der)
try:
sol = nroots(numerator, n=15, maxsteps=100)
except:
try:
sol = nroots(numerator, n=15, maxsteps=150)
except:
return None
sol = np.array(sol, dtype=complex)
num = len(sol)
eqa_solve = np.empty(num, dtype=complex)
eqa_der_solve = np.empty(num, dtype=complex)
eqa_minus1_solve = np.empty(num, dtype=complex)
for i in range(num):
eqa_solve[i] = eqa.evalf(subs={t: sol[i]})
eqa_der_solve[i] = eqa_der.evalf(subs={t: sol[i]})
eqa_minus1_solve[i] = eqa_minus1.evalf(subs={t: sol[i]})
df = pd.DataFrame()
df['alpha'] = np.abs(sol)
df['theta'] = np.angle(sol)
df['real'] = eqa_solve.real
df['imag'] = eqa_solve.imag
df['real_der'] = eqa_der_solve.real
df['imag_der'] = eqa_der_solve.imag
df['abs_der'] = np.abs(eqa_der_solve)
pade_error = eqa_solve - eqa_minus1_solve
df['real_err'] = pade_error.real
df['imag_err'] = pade_error.imag
df = df.loc[df['theta'] > 0].reset_index()
return df
def forecast_typhoon(userlocation, forecast, wind_7_r, wind_10_r):
nearlocation = np.empty([2, 2])
time_goin_10 = 0
time_goout_10 = 0
time_goin_10_first = 0
time_goout_10_first = 0
time_goin_10_second = 0
time_goout_10_second = 0
time_goin_7 = np.zeros([2])
time_goout_7 = np.zeros([2])
time_goin_7_first = 0
time_goout_7_first = 0
time_goin_7_second = 0
time_goout_7_second = 0
nearlat = 0
nearlon = 0
neartm = 0
dist = np.sqrt((forecast[1, :] - userlocation[0])**2 +
(forecast[2, :] - userlocation[1])**2)
idx_near = np.argmin(dist)
###
###
if idx_near == 0:
idx_near_after = idx_near + 1
a2 = (forecast[2, idx_near] - forecast[2, idx_near_after]) / (
forecast[1, idx_near] - forecast[1, idx_near_after])
b2 = forecast[2, idx_near] - a2 * forecast[1, idx_near]
dist2 = abs(a2 * userlocation[0] + b2 -
userlocation[1]) * np.sqrt(a2**2 + 1)
nearlocation[0, 0] = -(a2 * b2 - a2 * userlocation[1] -
userlocation[0]) / (a2 * a2 + 1)
nearlocation[0, 1] = a2 * nearlocation[0, 0] + b2
neardist = dist2
if nearlocation[1, 0] < min(
forecast[1, idx_near],
forecast[1, idx_near_after]) or nearlocation[1, 0] > max(
forecast[1, idx_near], forecast[1, idx_near_after]):
time_near = (forecast[0, idx_near_after] -
forecast[0, idx_near]) * (dist2 - dist[idx_near]) / (
dist[idx_near_after] -
dist[idx_near]) + forecast[0, idx_near]
else:
time_near = (forecast[0, idx_near_after] -
forecast[0, idx_near]) * (dist[idx_near] - dist2) / (
dist[idx_near_after] -
dist[idx_near]) + forecast[0, idx_near]
if dist2 <= wind_10_r / 111:
if time_near < forecast[
0, idx_near] and dist[idx_near] <= wind_10_r / 111:
#print('10 level wind influence me11')
time_goout_10 = (forecast[0, idx_near_after] - forecast[
0, idx_near]) * (wind_10_r / 111 - dist[idx_near]) / (
dist[idx_near_after] -
dist[idx_near]) + forecast[0, idx_near]
time_goin_10 = -(time_goout_10 - time_near) + time_near
nearlat = forecast[1, idx_near]
nearlon = forecast[2, idx_near]
neartm = forecast[0, idx_near]
if time_near < forecast[
0, idx_near] and dist[idx_near] > wind_10_r / 111:
pass
#print('10 level wind not influence me11')
if time_near >= forecast[
0, idx_near] and dist[idx_near] <= wind_10_r / 111:
pass
#print('10 level wind influence me12')
time_goout_10 = (forecast[0, idx_near_after] - forecast[
0, idx_near]) * (wind_10_r / 111 - dist[idx_near]) / (
dist[idx_near_after] -
dist[idx_near]) + forecast[0, idx_near]
time_goin_10 = -(time_goout_10 - time_near) + time_near
nearlat = nearlocation[0, 0]
nearlon = nearlocation[0, 1]
neartm = time_near
if time_near >= forecast[
0, idx_near] and dist[idx_near] > wind_10_r / 111:
#print('10 level wind influence me13')
time_goin_10 = (forecast[0, idx_near_after] - forecast[
0, idx_near]) * (-wind_10_r / 111 + dist[idx_near]) / (
dist[idx_near_after] -
dist[idx_near]) + forecast[0, idx_near]
time_goout_10 = (time_near - time_goin_10) + time_near
nearlat = nearlocation[0, 0]
nearlon = nearlocation[0, 1]
neartm = time_near
else:
pass
#print('10 level wind not influence me12')
if dist2 <= wind_7_r / 111:
if time_near < forecast[
0, idx_near] and dist[idx_near] <= wind_7_r / 111:
#print('7 level wind influence me11')
time_goout_7 = (forecast[0, idx_near_after] - forecast[
0, idx_near]) * (wind_7_r / 111 - dist[idx_near]) / (
dist[idx_near_after] -
dist[idx_near]) + forecast[0, idx_near]
time_goin_7 = (time_goout_7 - time_near) + time_near
nearlat = forecast[1, idx_near]
nearlon = forecast[2, idx_near]
neartm = forecast[0, idx_near]
if time_near < forecast[
0, idx_near] and dist[idx_near] > wind_7_r / 111:
pass
#print('7 level wind not influence me11')
if time_near >= forecast[
0, idx_near] and dist[idx_near] <= wind_7_r / 111:
#print('7 level wind influence me12')
time_goout_7 = (forecast[0, idx_near_after] - forecast[
0, idx_near]) * (wind_7_r / 111 - dist[idx_near]) / (
dist[idx_near_after] -
dist[idx_near]) + forecast[0, idx_near]
time_goin_7 = (time_goout_7 - time_near) + time_near
nearlat = nearlocation[0, 0]
nearlon = nearlocation[0, 1]
neartm = time_near
if time_near >= forecast[
0, idx_near] and dist[idx_near] > wind_7_r / 111:
#print('7 level wind influence me13')
time_goin_7 = (forecast[0, idx_near_after] - forecast[
0, idx_near]) * (-wind_7_r / 111 + dist[idx_near]) / (
dist[idx_near_after] -
dist[idx_near]) + forecast[0, idx_near]
time_goout_7 = (time_near - time_goin_7) + time_near
nearlat = nearlocation[0, 0]
nearlon = nearlocation[0, 1]
neartm = time_near
else:
pass
#print('7 level wind not influence me12')
time_goin_10 = time_goin_10_first
time_goout_10 = time_goout_10_first
time_goin_7 = time_goin_7_first
time_goout_7 = time_goout_7_first
###
###
if idx_near == np.size(dist) - 1:
idx_near_before = idx_near - 1
a1 = (forecast[2, idx_near] - forecast[2, idx_near_before]) / (
forecast[1, idx_near] - forecast[1, idx_near_before])
b1 = forecast[2, idx_near] - a1 * forecast[1, idx_near]
dist1 = abs(a1 * userlocation[0] + b1 -
userlocation[1]) * np.sqrt(a1**2 + 1)
nearlocation[1, 0] = -(a1 * b1 - a1 * userlocation[1] -
userlocation[0]) / (a1 * a1 + 1)
nearlocation[1, 1] = a1 * nearlocation[1, 0] + b1
neardist = dist1
if nearlocation[1, 0] < min(
forecast[1, idx_near],
forecast[1, idx_near_before]) or nearlocation[1, 0] > max(
forecast[1, idx_near], forecast[1, idx_near_before]):
time_near = (forecast[0, idx_near] - forecast[0, idx_near_before]
) * (dist[idx_near] -
dist1) / (dist[idx_near_before] -
dist[idx_near]) + forecast[0, idx_near]
else:
time_near = (forecast[0, idx_near] - forecast[0, idx_near_before]
) * (dist1 - dist[idx_near]) / (
dist[idx_near_before] -
dist[idx_near]) + forecast[0, idx_near]
if dist1 <= wind_10_r / 111:
if time_near < forecast[
0, idx_near] and dist[idx_near] <= wind_10_r / 111:
#print('10 level wind influence me21')
time_goout_10_first = (
forecast[0, idx_near] - forecast[0, idx_near_before]
) * (wind_10_r / 111 -
dist[idx_near]) / (dist[idx_near_before] -
dist[idx_near]) + forecast[0, idx_near]
time_goin_10_first = (time_goout_10_first -
time_near) + time_near
nearlat = nearlocation[1, 0]
nearlon = nearlocation[1, 1]
neartm = time_near
if time_near < forecast[
0, idx_near] and dist[idx_near] > wind_10_r / 111:
#print('10 level wind influence me22')
time_goout_10_first = (
forecast[0, idx_near] - forecast[0, idx_near_before]) * (
dist[idx_near] - wind_10_r / 111) / (
dist[idx_near_before] -
dist[idx_near]) + forecast[0, idx_near]
time_goin_10_first = (time_goout_10_first -
time_near) + time_near
nearlat = nearlocation[1, 0]
nearlon = nearlocation[1, 1]
neartm = time_near
if time_near >= forecast[
0, idx_near] and dist[idx_near] <= wind_10_r / 111:
#print('10 level wind influence me23')
time_goin_10_first = (
forecast[0, idx_near] - forecast[0, idx_near_before]) * (
dist[idx_near] - wind_10_r / 111) / (
dist[idx_near_before] -
dist[idx_near]) + forecast[0, idx_near]
time_goout_10_first = (time_near -
time_goin_10_first) + time_near
nearlat = nearlocation[1, 0]
nearlon = nearlocation[1, 1]
neartm = time_near
if time_near >= forecast[
0, idx_near] and dist[idx_near] > wind_10_r / 111:
#print('10 level wind influence me24')
time_goin_10_first = (
forecast[0, idx_near] - forecast[0, idx_near_before]) * (
dist[idx_near] - wind_10_r / 111) / (
dist[idx_near_before] -
dist[idx_near]) + forecast[0, idx_near]
time_goout_10_first = (time_near -
time_goin_10_first) + time_near
nearlat = nearlocation[1, 0]
nearlon = nearlocation[1, 1]
neartm = time_near
else:
pass
#print('10 level wind not influence me21')
if dist1 <= wind_7_r / 111:
if time_near < forecast[
0, idx_near] and dist[idx_near] <= wind_7_r / 111:
#print('7 level wind influence me21')
time_goout_7_first = (
forecast[0, idx_near] - forecast[0, idx_near_before]
) * (wind_7_r / 111 -
dist[idx_near]) / (dist[idx_near_before] -
dist[idx_near]) + forecast[0, idx_near]
time_goin_7_first = (time_goout_7_first -
time_near) + time_near
nearlat = nearlocation[1, 0]
nearlon = nearlocation[1, 1]
neartm = time_near
if time_near < forecast[
0, idx_near] and dist[idx_near] > wind_7_r / 111:
#print('7 level wind influence me22')
time_goout_7_first = (
forecast[0, idx_near] - forecast[0, idx_near_before]
) * (dist[idx_near] -
wind_7_r / 111) / (dist[idx_near_before] -
dist[idx_near]) + forecast[0, idx_near]
time_goin_7_first = (time_goout_7_first -
time_near) + time_near
nearlat = nearlocation[1, 0]
nearlon = nearlocation[1, 1]
neartm = time_near
if time_near >= forecast[
0, idx_near] and dist[idx_near] <= wind_7_r / 111:
#print('7 level wind influence me23')
time_goin_7_first = (
forecast[0, idx_near] - forecast[0, idx_near_before]
) * (dist[idx_near] -
wind_7_r / 111) / (dist[idx_near_before] -
dist[idx_near]) + forecast[0, idx_near]
time_goout_7_first = (time_near -
time_goin_7_first) + time_near
nearlat = nearlocation[1, 0]
nearlon = nearlocation[1, 1]
neartm = time_near
if time_near >= forecast[
0, idx_near] and dist[idx_near] > wind_7_r / 111:
#print('7 level wind influence me24')
time_goin_7_first = (
forecast[0, idx_near] - forecast[0, idx_near_before]
) * (dist[idx_near] -
wind_7_r / 111) / (dist[idx_near_before] -
dist[idx_near]) + forecast[0, idx_near]
time_goout_7_first = (time_near -
time_goin_7_first) + time_near
nearlat = nearlocation[1, 0]
nearlon = nearlocation[1, 1]
neartm = time_near
else:
pass
#print('7 level wind not influence me22')
time_goin_10 = time_goin_10_first
time_goout_10 = time_goout_10_first
time_goin_7 = time_goin_7_first
time_goout_7 = time_goout_7_first
nearlat = nearlocation[1, 0]
nearlon = nearlocation[1, 1]
neartm = time_near
###
###
if idx_near < np.size(dist) - 1 and idx_near > 0:
idx_near_before = idx_near - 1
idx_near_after = idx_near + 1
xf = np.empty([3, 3])
xf[0, 0] = forecast[1, idx_near]**2
xf[1, 0] = forecast[1, idx_near_before]**2
xf[2, 0] = forecast[1, idx_near_after]**2
xf[0, 1] = forecast[1, idx_near]
xf[1, 1] = forecast[1, idx_near_before]
xf[2, 1] = forecast[1, idx_near_after]
xf[0, 2] = 1
xf[1, 2] = 1
xf[2, 2] = 1
y = [
forecast[2, idx_near], forecast[2, idx_near_before],
forecast[2, idx_near_after]
]
bounds_lat_min = min(forecast[1, idx_near_before:idx_near_after + 1])
bounds_lat_max = max(forecast[1, idx_near_before:idx_near_after + 1])
fac = np.linalg.solve(xf, y)
from scipy.optimize import minimize_scalar
f = lambda x: np.sqrt(
(x - userlocation[0])**2 +
(fac[0] * x**2 + fac[1] * x + fac[2] - userlocation[1])**2)
rslt = minimize_scalar(f, bounds=(bounds_lat_min, bounds_lat_max))
nearlat = rslt.x
nearlon = fac[0] * nearlat**2 + fac[1] * nearlat + fac[2]
neardist = f(nearlat)
if nearlat < max(forecast[1, idx_near],
forecast[1, idx_near_before]) and nearlat > min(
forecast[1, idx_near], forecast[1,
idx_near_before]):
neartm = (forecast[0, idx_near] - forecast[0, idx_near_before]) * (
neardist - dist[idx_near]
) / (dist[idx_near_before] - dist[idx_near]) + forecast[0,
idx_near]
else:
neartm = (forecast[0, idx_near_after] - forecast[0, idx_near]) * (
dist[idx_near] - neardist
) / (dist[idx_near_after] - dist[idx_near]) + forecast[0, idx_near]
lat = smy.Symbol('lat')
lat_goinout_10raw = smy.nroots(
(lat - userlocation[0])**2 +
(fac[0] * lat**2 + fac[1] * lat + fac[1] - userlocation[1])**2 -
(wind_10_r / 111)**2,
n=6)
lat_goinout_7raw = smy.nroots(
(lat - userlocation[0])**2 +
(fac[0] * lat**2 + fac[1] * lat + fac[1] - userlocation[1])**2 -
(wind_10_r / 111)**2,
n=6)
lat_goinout_10 = [complex(flag).real for flag in lat_goinout_10raw]
lat_goinout_7 = [complex(flag).real for flag in lat_goinout_7raw]
lon_goinout_10 = [
fac[0] * complex(flag).real**2 + fac[1] * complex(flag).real +
fac[2] for flag in lat_goinout_10raw
]
lon_goinout_7 = [
fac[0] * complex(flag).real**2 + fac[1] * complex(flag).real +
fac[2] for flag in lat_goinout_7raw
]
if dist[idx_near] <= wind_10_r / 111:
#print('10 level wind influence me31')
if dist[idx_near_before] >= wind_10_r / 111:
idx_in = idx_near_before
else:
idx_in = 0
if dist[idx_near_after] >= wind_10_r / 111:
idx_out = idx_near_after
else:
idx_out = np.size(dist) - 1
a2 = (forecast[2, idx_near] - forecast[2, idx_out]) / (
forecast[1, idx_near] - forecast[1, idx_out])
b2 = forecast[2, idx_near] - a2 * forecast[1, idx_near]
dist2 = abs(a2 * userlocation[0] + b2 -
userlocation[1]) * np.sqrt(a2**2 + 1)
nearlocation[1, 0] = -(a2 * b2 - a2 * userlocation[1] -
userlocation[0]) / (a2 * a2 + 1)
nearlocation[1, 1] = a2 * nearlocation[1, 0] + b2
a1 = (forecast[2, idx_near] - forecast[2, idx_in]) / (
forecast[1, idx_near] - forecast[1, idx_in])
b1 = forecast[2, idx_near] - a1 * forecast[1, idx_near]
dist1 = abs(a1 * userlocation[0] + b1 -
userlocation[1]) * np.sqrt(a1**2 + 1)
nearlocation[0, 0] = -(a1 * b1 - a1 * userlocation[1] -
userlocation[0]) / (a1 * a1 + 1)
nearlocation[0, 1] = a1 * nearlocation[0, 0] + b1
neardist = min(dist1, dist2)
if dist[idx_in] > wind_10_r / 111 and dist[idx_in +
1] <= wind_10_r / 111:
time_goin_10_first = (forecast[0, idx_near] - forecast[
0, idx_in]) * (dist[idx_in] - (wind_10_r / 111)) / (
dist[idx_in] - dist[idx_near]) + forecast[0, idx_in]
else:
time_goin_10_first = (forecast[0, idx_near] - forecast[
0, idx_in]) * (dist[idx_in] - (wind_10_r / 111)) / (
dist[idx_in] - dist[idx_near]) + forecast[0, idx_in]
if dist[idx_out] < wind_10_r / 111 and dist[idx_out +
1] >= wind_10_r / 111:
time_goout_10_first = (-forecast[0, idx_near] + forecast[
0, idx_out]) * (-dist[idx_out] + (wind_10_r / 111)) / (
dist[idx_out] - dist[idx_near]) + forecast[0, idx_out]
#print "311"
else:
time_goout_10_first = (-forecast[0, idx_near] + forecast[
0, idx_out]) * (-dist[idx_out] + (wind_10_r / 111)) / (
dist[idx_out] - dist[idx_near]) + forecast[0, idx_out]
#print "312"
time_goin_10_second = 0
time_goout_10_second = 0
else:
if neardist > wind_10_r / 111:
pass
#print('10 level wind not influence me31')
else:
#print('10 level wind influence me32')
dist_from_before = min(
np.sqrt(
(lat_goinout_10 - forecast[1, idx_near_before])**2 +
(lon_goinout_10 - forecast[2, idx_near_before])**2))
dist_from_after = min(
np.sqrt((lat_goinout_10 - forecast[1, idx_near_after])**2 +
(lon_goinout_10 - forecast[2, idx_near_after])**2))
dist_near_from_before = np.sqrt(
(nearlat - forecast[1, idx_near_before])**2 +
(nearlon - forecast[2, idx_near_before])**2)
dist_near_from_after = np.sqrt(
(nearlat - forecast[1, idx_near_after])**2 +
(nearlon - forecast[2, idx_near_after])**2)
time_goin_10_first = (
neartm - forecast[0, idx_near_before]
) * dist_from_before / dist_near_from_before + forecast[
0, idx_near_before]
time_goout_10_first = neartm - time_goin_10_first + neartm
time_goout_10_second = (
neartm - forecast[0, idx_near_after]
) * dist_from_after / dist_near_from_after + forecast[
0, idx_near_after]
time_goin_10_second = -time_goout_10_second + neartm + neartm
if time_goin_10_first != 0 and time_goin_10_second != 0:
time_goin_10 = min(time_goin_10_first, time_goin_10_second)
else:
if time_goin_10_first == 0:
time_goin_10 = time_goin_10_second
if time_goin_10_second == 0:
time_goin_10 = time_goin_10_first
if time_goout_10_first != 0 and time_goout_10_second != 0:
time_goin_10 = max(time_goout_10_first, time_goout_10_second)
else:
if time_goout_10_first == 0:
time_goout_10 = time_goout_10_second
if time_goout_10_second == 0:
time_goout_10 = time_goout_10_first
if dist[idx_near] <= wind_7_r / 111:
#print('7 level wind influence me31')
if dist[idx_near_before] >= wind_7_r / 111:
idx_in = idx_near_before
else:
idx_in = 0
if dist[idx_near_after] >= wind_7_r / 111:
idx_out = idx_near_after
else:
idx_out = np.size(dist) - 1
a2 = (forecast[2, idx_near] - forecast[2, idx_out]) / (
forecast[1, idx_near] - forecast[1, idx_out])
b2 = forecast[2, idx_near] - a2 * forecast[1, idx_near]
dist2 = abs(a2 * userlocation[0] + b2 -
userlocation[1]) * np.sqrt(a2**2 + 1)
nearlocation[1, 0] = -(a2 * b2 - a2 * userlocation[1] -
userlocation[0]) / (a2 * a2 + 1)
nearlocation[1, 1] = a2 * nearlocation[1, 0] + b2
a1 = (forecast[2, idx_near] - forecast[2, idx_in]) / (
forecast[1, idx_near] - forecast[1, idx_in])
b1 = forecast[2, idx_near] - a1 * forecast[1, idx_near]
dist1 = abs(a1 * userlocation[0] + b1 -
userlocation[1]) * np.sqrt(a1**2 + 1)
nearlocation[0, 0] = -(a1 * b1 - a1 * userlocation[1] -
userlocation[0]) / (a1 * a1 + 1)
nearlocation[0, 1] = a1 * nearlocation[0, 0] + b1
neardist = min(dist1, dist2)
if dist[idx_in] > wind_7_r / 111 and dist[idx_in +
1] <= wind_7_r / 111:
time_goin_7_first = (forecast[0, idx_near] - forecast[
0, idx_in]) * (dist[idx_in] - (wind_7_r / 111)) / (
dist[idx_in] - dist[idx_near]) + forecast[0, idx_in]
else:
time_goin_7_first = (forecast[0, idx_near] - forecast[
0, idx_in]) * (dist[idx_in] - (wind_7_r / 111)) / (
dist[idx_in] - dist[idx_near]) + forecast[0, idx_in]
if dist[idx_out] < wind_7_r / 111 and dist[idx_out +
1] >= wind_7_r / 111:
time_goout_7_first = (-forecast[0, idx_near] + forecast[
0, idx_out]) * (-dist[idx_out] + (wind_7_r / 111)) / (
dist[idx_out] - dist[idx_near]) + forecast[0, idx_out]
else:
time_goout_7_first = (-forecast[0, idx_near] + forecast[
0, idx_out]) * (-dist[idx_out] + (wind_7_r / 111)) / (
dist[idx_out] - dist[idx_near]) + forecast[0, idx_out]
time_goin_7_second = 0
time_goout_7_second = 0
else:
if neardist > wind_7_r / 111:
pass
#print('7 level wind not influence me31')
else:
#print('7 level wind influence me32')
dist_from_before = min(
np.sqrt((lat_goinout_7 - forecast[1, idx_near_before])**2 +
(lon_goinout_7 - forecast[2, idx_near_before])**2))
dist_from_after = min(
np.sqrt((lat_goinout_7 - forecast[1, idx_near_after])**2 +
(lon_goinout_7 - forecast[2, idx_near_after])**2))
dist_near_from_before = np.sqrt(
(nearlat - forecast[1, idx_near_before])**2 +
(nearlon - forecast[2, idx_near_before])**2)
dist_near_from_after = np.sqrt(
(nearlat - forecast[1, idx_near_after])**2 +
(nearlon - forecast[2, idx_near_after])**2)
time_goin_7_first = (
neartm - forecast[0, idx_near_before]
) * dist_from_before / dist_near_from_before + forecast[
0, idx_near_before]
time_goout_7_first = neartm - time_goin_7_first + neartm
time_goout_7_second = (
neartm - forecast[0, idx_near_after]
) * dist_from_after / dist_near_from_after + forecast[
0, idx_near_after]
time_goin_7_second = -time_goout_7_second + neartm + neartm
if time_goin_7_first != 0 and time_goin_7_second != 0:
time_goin_7 = min(time_goin_7_first, time_goin_7_second)
else:
if time_goin_7_first == 0:
time_goin_7 = time_goin_7_second
if time_goin_7_second == 0:
time_goin_7 = time_goin_7_first
if time_goout_7_first != 0 and time_goout_7_second != 0:
time_goin_7 = max(time_goout_7_first, time_goout_7_second)
else:
if time_goout_7_first == 0:
time_goout_7 = time_goout_7_second
if time_goout_7_second == 0:
time_goout_7 = time_goout_7_first
#print time_goin_7_first,time_goin_10_first,time_goin_7_second,time_goin_10_second
#print time_goout_7_first,time_goout_10_first,time_goout_7_second,time_goout_10_second
return (time_goin_10, time_goout_10, time_goin_7, time_goout_7, nearlat,
nearlon, neartm, neardist * 111, neardist * 111 - wind_10_r,
neardist * 111 - wind_7_r)
f10= (x**3)*y**4 + 4*x**2*y**2 + 2*x**3*y - 1
f = f9
n = sympy.degree(f,y)
coeffs = coeff_functions(sympy.poly(f,y),x)
# compute the path parameterization around a given branch point
bpt = 3
G = monodromy_graph(f,x,y)
path_segments = path_around_branch_point(G,bpt,1)
nseg = len(path_segments)
# select a root at the base_point
a = G.node[0]['basepoint']
fibre = map(numpy.complex,sympy.nroots(f.subs(x,a),n=15))
# analytically continue
ypath = []
for k in xrange(nseg):
# print "=== segment %k ==="
# print "fibre (start) ="
# for yj in fibre: print yj
ypath += analytically_continue(df,coeffs,n,fibre,1,path_segments[k][0])
fibre = [yij for yij in ypath[-1]]
# print "fibre (end) ="
# for yj in fibre: print yj
# parse out yroots data: right now it's of the form
