def test_diff():
assert besselj(n, z).diff(z) == besselj(n - 1, z)/2 - besselj(n + 1, z)/2
assert bessely(n, z).diff(z) == bessely(n - 1, z)/2 - bessely(n + 1, z)/2
assert besseli(n, z).diff(z) == besseli(n - 1, z)/2 + besseli(n + 1, z)/2
assert besselk(n, z).diff(z) == -besselk(n - 1, z)/2 - besselk(n + 1, z)/2
assert hankel1(n, z).diff(z) == hankel1(n - 1, z)/2 - hankel1(n + 1, z)/2
assert hankel2(n, z).diff(z) == hankel2(n - 1, z)/2 - hankel2(n + 1, z)/2
def test_diff():
assert besselj(n, z).diff(z) == besselj(n - 1, z)/2 - besselj(n + 1, z)/2
assert bessely(n, z).diff(z) == bessely(n - 1, z)/2 - bessely(n + 1, z)/2
assert besseli(n, z).diff(z) == besseli(n - 1, z)/2 + besseli(n + 1, z)/2
assert besselk(n, z).diff(z) == -besselk(n - 1, z)/2 - besselk(n + 1, z)/2
assert hankel1(n, z).diff(z) == hankel1(n - 1, z)/2 - hankel1(n + 1, z)/2
assert hankel2(n, z).diff(z) == hankel2(n - 1, z)/2 - hankel2(n + 1, z)/2
def test_bessel_rand():
assert td(besselj(randcplx(), z), z)
assert td(bessely(randcplx(), z), z)
assert td(besseli(randcplx(), z), z)
assert td(besselk(randcplx(), z), z)
assert td(hankel1(randcplx(), z), z)
assert td(hankel2(randcplx(), z), z)
assert td(jn(randcplx(), z), z)
assert td(yn(randcplx(), z), z)
def test_bessel_rand():
assert td(besselj(randcplx(), z), z)
assert td(bessely(randcplx(), z), z)
assert td(besseli(randcplx(), z), z)
assert td(besselk(randcplx(), z), z)
assert td(hankel1(randcplx(), z), z)
assert td(hankel2(randcplx(), z), z)
assert td(jn(randcplx(), z), z)
assert td(yn(randcplx(), z), z)
def __init__(self, intens=None, puls=None, phas=None):
# Célérité des ondes ; à modifier en fonction du milieu
self.cel = 3e8
# Composante du potentiel vecteur associée à la pulsation omega
self.A_component = sp.I * mu * Ic / 4 * sp.hankel2(0, k * r) * sp.exp(
sp.I * omega * t)
# Composante du champ magnétique associée à la pulsation omega
self.B_component = -sp.diff(self.A_component, r).simplify()
# Conversion de fonctions formelles à fonctions numériques
self.impl_modules = ['numpy', {"hankel2": spec.hankel2}]
if intens is not None:
if phas is not None:
intens = np.asarray(intens) * np.exp(1j * np.asarray(phas))
self.pulsations = np.array(puls)
self.frequences = puls / (2 * np.pi)
c0 = self.cel
mu0_v = 4e-7 * np.pi
spectral_data = zip(intens, puls)
cmp = sp.re(self.B_component).subs({c: c0, mu: mu0_v})
orthExpr = sum(
cmp.subs({Ic: cur, omega:om}) \
for (cur,om) in spectral_data if (cur!=0 and om!=0))
orthFunc = sp.lambdify((r, t), orthExpr, modules=self.impl_modules)
self.orthExpr = orthExpr
self.orthFunc = orthFunc
self.vorthFunc = np.vectorize(orthFunc)
# Fonctions en cartésien
rxy = sp.sqrt(x**2 + y**2)
self.orthFuncCart = sp.lambdify((x, y, t),
orthExpr.subs({r: rxy}),
modules=self.impl_modules)
self.vorthFuncCart = np.vectorize(self.orthFuncCart)
self.fieldExpr = (-y * Cart.i + x * Cart.j) * orthExpr.subs(
{r: rxy}) / rxy
self.fieldFunc = sp.lambdify((x, y, t),
self.fieldExpr.to_matrix(Cart),
modules=self.impl_modules)
def test_meromorphic():
assert besselj(2, x).is_meromorphic(x, 1) == True
assert besselj(2, x).is_meromorphic(x, 0) == True
assert besselj(2, x).is_meromorphic(x, oo) == False
assert besselj(S(2) / 3, x).is_meromorphic(x, 1) == True
assert besselj(S(2) / 3, x).is_meromorphic(x, 0) == False
assert besselj(S(2) / 3, x).is_meromorphic(x, oo) == False
assert besselj(x, 2 * x).is_meromorphic(x, 2) == False
assert besselk(0, x).is_meromorphic(x, 1) == True
assert besselk(2, x).is_meromorphic(x, 0) == True
assert besseli(0, x).is_meromorphic(x, 1) == True
assert besseli(2, x).is_meromorphic(x, 0) == True
assert bessely(0, x).is_meromorphic(x, 1) == True
assert bessely(0, x).is_meromorphic(x, 0) == False
assert bessely(2, x).is_meromorphic(x, 0) == True
assert hankel1(3, x**2 + 2 * x).is_meromorphic(x, 1) == True
assert hankel1(0, x).is_meromorphic(x, 0) == False
assert hankel2(11, 4).is_meromorphic(x, 5) == True
assert hn1(6, 7 * x**3 + 4).is_meromorphic(x, 7) == True
assert hn2(3, 2 * x).is_meromorphic(x, 9) == True
assert jn(5, 2 * x + 7).is_meromorphic(x, 4) == True
assert yn(8, x**2 + 11).is_meromorphic(x, 6) == True
numerator = 2*besselj(1, ka_sintheta).evalf()#2*bessel_firstkind(1, ka_sintheta)
try:
rp_theta = np.abs(numerator/ka_sintheta)
except:
rp_theta = 0
return rp_theta
##### Vibrating cap on sphere
Wn, Pn, h2n, h2n_prime, theta, w0, n, theta0, k, R, H_theta, kR = symbols(
'Wn Pn h2n h2n_prime theta w0 n theta0 k R H_theta kR')
# take equation 6 to define Wn now
Wn = 0.5 * w0 * (legendre(n - 1, cos(theta0)) - legendre(n + 1, cos(theta0)))
h2n = hankel2(n, kR)
# h2n_prime_term = diff(hankel2(n, k*R), k*R)
h2n_prime_term = diff(h2n, kR)
# equation 23
common_term = ((I ** n) * Wn) / h2n_prime_term
denominator = summation(common_term, (n, 0, 20))
numerator_term = common_term * legendre(n, cos(theta))
numerator = summation(numerator_term, (n, 0, 20))
H_theta = Abs(numerator / denominator)
calc_H_theta = lambdify((theta, k, R, theta0, kR,w0), H_theta)
def vibrating_cap_of_sphere(theta, k, **kwargs):
def dispeq_gyrotropic_cylindersArrayFull(N_max, w_01, a_0, ee, cylXY, k, p, EE, GG, HH, c, ):
m = list(range(-N_max, N_max + 1, 1))
if N_max == 0:
m = 0
nu = m
w = w_01
k0 = w / c
q = cmath.sqrt(1 - p **2)
# q = q * (2 * ((q.imag) <= 0) - 1)
Q = k0 * a_0 * q
# вычисляем элементы матрицы рассеяния для внутренней области цилиндра
mainq = EE ** 2 - GG ** 2 + EE * HH - (HH + EE) * p ** 2
F=cmath.sqrt(EE*GG**2*HH*(GG**2-(HH-EE)**2))
Pb=cmath.sqrt(EE-(HH+EE)*GG**2/(HH-EE)**2-2*F/(HH-EE)**2)
Pc=cmath.sqrt(EE-(HH+EE)*GG**2/(HH-EE)**2+2*F/(HH-EE)**2)
#radq = math.sqrt((HH - EE) ** 2 * p **4 + 2 * ((GG ** 2)*(HH + EE) - EE * (HH - EE) **2) * p **2 +(EE ** 2 - GG ** 2 - EE * HH) ** 2)
radq = -(HH-EE)*cmath.sqrt((p**2-Pb**2)*(p**2-Pc**2))
q1 = cmath.sqrt(0.5 * (mainq - radq) / EE)
q2 = cmath.sqrt(0.5 * (mainq + radq) / EE)
n1 = -(EE / (p * GG) ) * (p ** 2 + q1 ** 2 + (GG ** 2)/EE - EE)
n2 = -(EE / (p * GG) ) * (p ** 2 + q2 ** 2 + (GG ** 2)/EE - EE)
alp1 = -1 + (p ** 2 + q1 ** 2 - EE) / GG
alp2 = -1 + (p ** 2 + q2 ** 2 - EE) / GG
bet1 = 1 + p / n1
bet2 = 1 + p / n2
#что делать с Q она мнимая, брать действительную или мнимую часть?
Q1 = (q1 * a_0) * k0
Q2 = (q2 * a_0) * k0
mMax = 2 * N_max + 1
JM = np.zeros(((3, 31)), dtype=np.complex)
n=0
for per in range(-N_max,N_max+1,1):
JM[n][0] = besselj(per + 1, Q1) #JM1
JM[n][1] = besselj(per + 1, Q2) #JM2
JM[n][2]= besselj(per, Q1) #Jm1
JM[n][3]= besselj(per, Q2) #Jm2
JM[n][4]= JM[n][per + 2] / Q1 #Jm1_Q1
JM[n][5]= JM[n][per + 3]/ Q2 #Jm2_Q2
JM[n][6]= (((1j / HH) * n1) * q1) * JM[n][per + 2] #Ez1
JM[n][7] = (((1j / HH) * n2) * q2) * JM[n][per + 3] #Ez2
JM[n][8] = 1j * (JM[n][per] + (alp1 * per) * JM[n][per + 4]) #Ephi1
JM[n][9]= 1j * (JM[n][per+1] + (alp2 * per) *JM[n][per + 5] ) #Ephi2
JM[n][10]= - q1 * JM[n][per + 2] #Hz1
JM[n][11]= - q2 * JM[n][per + 3] #Hz2
JM[n][12] = - n1 * (JM[n][per] - (bet1 * per) * JM[n][per + 4]) #Hphi1
JM[n][13]= - n2 * (JM[n][per+1] - (bet2 * per) * JM[n][per + 5]) #Hphi2
# вычисляем элементы матрицы рассеяния для внешней области цилиндра
JM[n][14] = hankel2(per, Q) #H2m
JM[n][15]= -(JM[n][per + 14]/ Q)* per + hankel2(per + 1, Q) #dH2m
#Jm_out = besselj(m, Q)
#dJm_out = Jm_out * m / Q - besselj(m + 1, Q)
JM[n][16] =-1j * q * JM[n][per + 14] #Ez_sct
JM[n][17]= q * JM[n][per + 14] #Hz_sct
A = 1 / (k0 * (1 - p ^ 2))
JM[n][18] = -1j*q * (A * ((p * (per / a_0)) * JM[n][per + 14])) #Ephi_sctE
JM[n][19]= 1j*q * (A * (k0 * q * JM[n][per + 15])) #Ephi_sctH
JM[n][20]= q * (A * ((p * (per / a_0)) * JM[n][per + 14])) #Hphi_sctH
JM[n][21] = -q * (A * (k0 * q * JM[n][per + 15])) #Hphi_sctE
n = n + 1
matrixGS = np.zeros(((mMax*4*2, mMax*4*2)), dtype=np.complex)
for jj in range(0, 2):
for jm in range(1, 4, 1):
for ll in range(0, 2):
for jnu in range(1, 4, 1):
jmmm = (jm - 1) * 4+1
jnunu = (jnu - 1) * 4+1
# спросить про проход ведь будет совпадение номеров
if jj == ll:
if jm == jnu:
matrixGS[jmmm + jj * 4 * mMax, jnunu + ll * 4 * mMax] = JM[jm + 1][6] # Ez1
matrixGS[jmmm + jj * 4 * mMax, jnunu + ll * 4 * mMax + 1] = JM[jm + 1][7] # Ez2(jm)
matrixGS[jmmm + jj * 4 * mMax, jnunu + ll * 4 * mMax + 2] = JM[jm + 1][16] # Ez_sct(jm)
matrixGS[jmmm + jj * 4 * mMax, jnunu + ll * 4 * mMax + 3] = 0
matrixGS[jmmm + jj * 4 * mMax + 1, jnunu + ll * 4 * mMax] = JM[jm + 1][10] # Hz1
matrixGS[jmmm + jj * 4 * mMax + 1, jnunu + ll * 4 * mMax + 1] = JM[jm + 1][11] # Hz2
matrixGS[jmmm + jj * 4 * mMax + 1, jnunu + ll * 4 * mMax + 2] = 0
matrixGS[jmmm + jj * 4 * mMax + 1, jnunu + ll * 4 * mMax + 3] = - JM[jm + 1][17] # -Hz_sct
matrixGS[jmmm + jj * 4 * mMax + 2, jnunu + ll * 4 * mMax] = JM[jm + 1][8] # Ephi1
matrixGS[jmmm + jj * 4 * mMax + 2, jnunu + ll * 4 * mMax + 1] = JM[jm + 1][9] # Ephi2
matrixGS[jmmm + jj * 4 * mMax + 2, jnunu + ll * 4 * mMax + 2] = -JM[jm + 1][18] # -Ephi_sctE
matrixGS[jmmm + jj * 4 * mMax + 2, jnunu + ll * 4 * mMax + 3] = -JM[jm + 1][19] # -Ephi_sctH
matrixGS[jmmm + jj * 4 * mMax + 3, jnunu + ll * 4 * mMax] = JM[jm + 1][12] # Hphi1
matrixGS[jmmm + jj * 4 * mMax + 3, jnunu + ll * 4 * mMax + 1] = JM[jm + 1][13] # Hphi2
matrixGS[jmmm + jj * 4 * mMax + 3, jnunu + ll * 4 * mMax + 2] = -JM[jm + 1][21] # -Hphi_sctE
matrixGS[jmmm + jj * 4 * mMax + 3, jnunu + ll * 4 * mMax + 3] = -JM[jm + 1][20] # -Hphi_sctH
else:
Ljl = float(math.sqrt((cylXY[jj , 0] - cylXY[ll , 0]) ** 2 + (cylXY[jj , 1] - cylXY[ll , 1]) ** 2))
thetaIJ =float(math.atan(abs(cylXY[jj , 1] - cylXY[ll , 1]) / abs(cylXY[jj , 0] - cylXY[ll , 0])))
if ((cylXY[jj , 0] - cylXY[ll , 0]) <= 0 and (cylXY[jj , 1] - cylXY[ll , 1]) > 0):
thetaIJ = cmath.pi - thetaIJ
elif ((cylXY[jj , 0] - cylXY[ll , 0]) <= 0 and (cylXY[jj, 1] - cylXY[ll , 1]) <= 0):
thetaIJ = cmath.pi + thetaIJ
elif ((cylXY[jj , 1] - cylXY[ll , 1]) <= 0 and (cylXY[jj, 0] - cylXY[ll , 0]) > 0):
thetaIJ = 2 * cmath.pi - thetaIJ
JM[jnu - 1][22] = -cmath.exp(-1j * (nu[jnu - 1] - m[jm - 1]) * thetaIJ) ** hankel2((m[jm - 1] - nu[jnu - 1]), k0 * q * Ljl)
JM[jnu - 1][23] = besselj(m[jnu - 1], Q) # Jm_out
JM[jnu - 1][24] = -JM[jnu - 1][23] * m[jnu - 1] / Q + besselj(m[jnu - 1] + 1, Q) # dJm_out
# спросить почему они одинаковые?
JM[jnu - 1][25] = JM[jnu - 1][22] * JM[jnu - 1][23] # Ez_inc
JM[jnu - 1][26] = JM[jnu - 1][22] * JM[jnu - 1][23] # Hz_inc
A = 1 / (k0 * (1 - p ** 2))
JM[jnu - 1][27] = - JM[jnu - 1][22] * (
A * ((p * (m[jnu - 1] / a_0)) * JM[jnu - 1][23])) # Ephi_incE
JM[jnu - 1][28] = - JM[jnu - 1][22] * (A * (- 1j * k0 * q * JM[jnu - 1][24])) # Ephi_incH
JM[jnu - 1][29] = - JM[jnu - 1][22] * (A * (1j * k0 * q * JM[jnu - 1][24])) # Hphi_incE
JM[jnu - 1][30] = -JM[jnu - 1][22] * (A * ((p * (m[jnu - 1] / a_0)) * JM[jnu - 1][23]))
matrixGS[jmmm + jj * 4 * mMax, jnunu + ll * 4 * mMax] = 0
matrixGS[jmmm + jj * 4 * mMax, jnunu + ll * 4 * mMax + 1] = 0
matrixGS[jmmm + jj * 4 * mMax, jnunu + ll * 4 * mMax + 2] = JM[jm + 1][25] # Ez_inc
matrixGS[jmmm + jj * 4 * mMax, jnunu + ll * 4 * mMax + 3] = 0
matrixGS[jmmm + jj * 4 * mMax + 1, jnunu + ll * 4 * mMax] = 0
matrixGS[jmmm + jj * 4 * mMax + 1, jnunu + ll * 4 * mMax + 1] = 0
matrixGS[jmmm + jj * 4 * mMax + 1, jnunu + ll * 4 * mMax + 2] = 0
matrixGS[jmmm + jj * 4 * mMax + 1, jnunu + ll * 4 * mMax + 3] = JM[jm + 1][25] # Hz_inc
matrixGS[jmmm + jj * 4 * mMax + 2, jnunu + ll * 4 * mMax] = 0
matrixGS[jmmm + jj * 4 * mMax + 2, jnunu + ll * 4 * mMax + 1] = 0
matrixGS[jmmm + jj * 4 * mMax + 2, jnunu + ll * 4 * mMax + 2] = JM[jm + 1][ 27] # Ephi_incE
matrixGS[jmmm + jj * 4 * mMax + 2, jnunu + ll * 4 * mMax + 3] = JM[jm + 1][28] # Ephi_incH
matrixGS[jmmm + jj * 4 * mMax + 3, jnunu + ll * 4 * mMax] = 0
matrixGS[jmmm + jj * 4 * mMax + 3, jnunu + ll * 4 * mMax + 1] = 0
matrixGS[jmmm + jj * 4 * mMax + 3, jnunu + ll * 4 * mMax + 2] = JM[jm + 1][29] # Hphi_incE
matrixGS[jmmm + jj * 4 * mMax + 3, jnunu + ll * 4 * mMax + 3] = JM[jm + 1][30] # Hphi_incH
return abs(np.linalg.det(matrixGS))
def test_conjugate():
n = Symbol('n')
z = Symbol('z', extended_real=False)
x = Symbol('x', extended_real=True)
y = Symbol('y', real=True, positive=True)
t = Symbol('t', negative=True)
for f in [besseli, besselj, besselk, bessely, hankel1, hankel2]:
assert f(n, -1).conjugate() != f(conjugate(n), -1)
assert f(n, x).conjugate() != f(conjugate(n), x)
assert f(n, t).conjugate() != f(conjugate(n), t)
rz = randcplx(b=0.5)
for f in [besseli, besselj, besselk, bessely]:
assert f(n, 1 + I).conjugate() == f(conjugate(n), 1 - I)
assert f(n, 0).conjugate() == f(conjugate(n), 0)
assert f(n, 1).conjugate() == f(conjugate(n), 1)
assert f(n, z).conjugate() == f(conjugate(n), conjugate(z))
assert f(n, y).conjugate() == f(conjugate(n), y)
assert tn(f(n, rz).conjugate(), f(conjugate(n), conjugate(rz)))
assert hankel1(n, 1 + I).conjugate() == hankel2(conjugate(n), 1 - I)
assert hankel1(n, 0).conjugate() == hankel2(conjugate(n), 0)
assert hankel1(n, 1).conjugate() == hankel2(conjugate(n), 1)
assert hankel1(n, y).conjugate() == hankel2(conjugate(n), y)
assert hankel1(n, z).conjugate() == hankel2(conjugate(n), conjugate(z))
assert tn(hankel1(n, rz).conjugate(), hankel2(conjugate(n), conjugate(rz)))
assert hankel2(n, 1 + I).conjugate() == hankel1(conjugate(n), 1 - I)
assert hankel2(n, 0).conjugate() == hankel1(conjugate(n), 0)
assert hankel2(n, 1).conjugate() == hankel1(conjugate(n), 1)
assert hankel2(n, y).conjugate() == hankel1(conjugate(n), y)
assert hankel2(n, z).conjugate() == hankel1(conjugate(n), conjugate(z))
assert tn(hankel2(n, rz).conjugate(), hankel1(conjugate(n), conjugate(rz)))
def test_conjugate():
from sympy import conjugate, I, Symbol
n, z, x = Symbol('n'), Symbol('z', real=False), Symbol('x', real=True)
y, t = Symbol('y', real=True, positive=True), Symbol('t', negative=True)
for f in [besseli, besselj, besselk, bessely, hankel1, hankel2]:
assert f(n, -1).conjugate() != f(conjugate(n), -1)
assert f(n, x).conjugate() != f(conjugate(n), x)
assert f(n, t).conjugate() != f(conjugate(n), t)
rz = randcplx(b=0.5)
for f in [besseli, besselj, besselk, bessely]:
assert f(n, 1 + I).conjugate() == f(conjugate(n), 1 - I)
assert f(n, 0).conjugate() == f(conjugate(n), 0)
assert f(n, 1).conjugate() == f(conjugate(n), 1)
assert f(n, z).conjugate() == f(conjugate(n), conjugate(z))
assert f(n, y).conjugate() == f(conjugate(n), y)
assert tn(f(n, rz).conjugate(), f(conjugate(n), conjugate(rz)))
assert hankel1(n, 1 + I).conjugate() == hankel2(conjugate(n), 1 - I)
assert hankel1(n, 0).conjugate() == hankel2(conjugate(n), 0)
assert hankel1(n, 1).conjugate() == hankel2(conjugate(n), 1)
assert hankel1(n, y).conjugate() == hankel2(conjugate(n), y)
assert hankel1(n, z).conjugate() == hankel2(conjugate(n), conjugate(z))
assert tn(hankel1(n, rz).conjugate(), hankel2(conjugate(n), conjugate(rz)))
assert hankel2(n, 1 + I).conjugate() == hankel1(conjugate(n), 1 - I)
assert hankel2(n, 0).conjugate() == hankel1(conjugate(n), 0)
assert hankel2(n, 1).conjugate() == hankel1(conjugate(n), 1)
assert hankel2(n, y).conjugate() == hankel1(conjugate(n), y)
assert hankel2(n, z).conjugate() == hankel1(conjugate(n), conjugate(z))
assert tn(hankel2(n, rz).conjugate(), hankel1(conjugate(n), conjugate(rz)))
def test_conjugate():
from sympy import conjugate, I, Symbol
n = Symbol("n")
z = Symbol("z", extended_real=False)
x = Symbol("x", extended_real=True)
y = Symbol("y", real=True, positive=True)
t = Symbol("t", negative=True)
for f in [besseli, besselj, besselk, bessely, hankel1, hankel2]:
assert f(n, -1).conjugate() != f(conjugate(n), -1)
assert f(n, x).conjugate() != f(conjugate(n), x)
assert f(n, t).conjugate() != f(conjugate(n), t)
rz = randcplx(b=0.5)
for f in [besseli, besselj, besselk, bessely]:
assert f(n, 1 + I).conjugate() == f(conjugate(n), 1 - I)
assert f(n, 0).conjugate() == f(conjugate(n), 0)
assert f(n, 1).conjugate() == f(conjugate(n), 1)
assert f(n, z).conjugate() == f(conjugate(n), conjugate(z))
assert f(n, y).conjugate() == f(conjugate(n), y)
assert tn(f(n, rz).conjugate(), f(conjugate(n), conjugate(rz)))
assert hankel1(n, 1 + I).conjugate() == hankel2(conjugate(n), 1 - I)
assert hankel1(n, 0).conjugate() == hankel2(conjugate(n), 0)
assert hankel1(n, 1).conjugate() == hankel2(conjugate(n), 1)
assert hankel1(n, y).conjugate() == hankel2(conjugate(n), y)
assert hankel1(n, z).conjugate() == hankel2(conjugate(n), conjugate(z))
assert tn(hankel1(n, rz).conjugate(), hankel2(conjugate(n), conjugate(rz)))
assert hankel2(n, 1 + I).conjugate() == hankel1(conjugate(n), 1 - I)
assert hankel2(n, 0).conjugate() == hankel1(conjugate(n), 0)
assert hankel2(n, 1).conjugate() == hankel1(conjugate(n), 1)
assert hankel2(n, y).conjugate() == hankel1(conjugate(n), y)
assert hankel2(n, z).conjugate() == hankel1(conjugate(n), conjugate(z))
assert tn(hankel2(n, rz).conjugate(), hankel1(conjugate(n), conjugate(rz)))
def test_conjugate():
from sympy import conjugate, I, Symbol
n, z, x = Symbol('n'), Symbol('z', real=False), Symbol('x', real=True)
y, t = Symbol('y', real=True, positive=True), Symbol('t', negative=True)
for f in [besseli, besselj, besselk, bessely, jn, yn, hankel1, hankel2]:
assert f(n, -1).conjugate() != f(conjugate(n), -1)
assert f(n, x).conjugate() != f(conjugate(n), x)
assert f(n, t).conjugate() != f(conjugate(n), t)
rz = randcplx(b=0.5)
for f in [besseli, besselj, besselk, bessely, jn, yn]:
assert f(n, 1 + I).conjugate() == f(conjugate(n), 1 - I)
assert f(n, 0).conjugate() == f(conjugate(n), 0)
assert f(n, 1).conjugate() == f(conjugate(n), 1)
assert f(n, z).conjugate() == f(conjugate(n), conjugate(z))
assert f(n, y).conjugate() == f(conjugate(n), y)
assert tn(f(n, rz).conjugate(), f(conjugate(n), conjugate(rz)))
assert hankel1(n, 1 + I).conjugate() == hankel2(conjugate(n), 1 - I)
assert hankel1(n, 0).conjugate() == hankel2(conjugate(n), 0)
assert hankel1(n, 1).conjugate() == hankel2(conjugate(n), 1)
assert hankel1(n, y).conjugate() == hankel2(conjugate(n), y)
assert hankel1(n, z).conjugate() == hankel2(conjugate(n), conjugate(z))
assert tn(hankel1(n, rz).conjugate(), hankel2(conjugate(n), conjugate(rz)))
assert hankel2(n, 1 + I).conjugate() == hankel1(conjugate(n), 1 - I)
assert hankel2(n, 0).conjugate() == hankel1(conjugate(n), 0)
assert hankel2(n, 1).conjugate() == hankel1(conjugate(n), 1)
assert hankel2(n, y).conjugate() == hankel1(conjugate(n), y)
assert hankel2(n, z).conjugate() == hankel1(conjugate(n), conjugate(z))
assert tn(hankel2(n, rz).conjugate(), hankel1(conjugate(n), conjugate(rz)))
def GetScalarGreen2D(rho=Symbol(r'\rho'), k=Symbol('k')):
## (del_T^2 + k^2)G= -delta(rho)
G = 1 / (4 * I) * hankel2(0, k * rho)
return G
