def drho_coulombg_rescaled(angL, eta, rho, hvalue, dirvalue):
return fp.mpf(
mp.diff(lambda x: mp.coulombg(angL, eta, x),
rho,
1,
h=hvalue,
direction=dirvalue)) * fp.mpf(mp.coulombc(angL,
eta)) / eta**angL
def test_division(self):
expr = DivisionExpression(
SimpleSinExpression(),
OffsetExpression(SimpleCoshExpression(), 2),
)
with mp.workdps(30):
f = expr.evaluator(use_mp=True)
space = mp.linspace(0, mp.pi, 10)
for n in range(1, 5):
self.assertListAlmostEqual(
[f.diff(x, n) for x in space],
[mp.diff(f, x, n) for x in space],
delta=1e-28,
)
def mycoulfg_mix(angL, eta, rho, hvalue, dirvalue):
if rho > (eta + np.sqrt(eta**2 + angL * (angL + 1))):
f, df, g, dg, IFAIL = mycoulfg(angL, eta, rho)
if (IFAIL != 0):
print(IFAIL)
else:
f = fp.mpf(mp.coulombf(angL, eta, rho))
g = fp.mpf(mp.coulombg(angL, eta, rho))
df = fp.mpf(
mp.diff(lambda x: mp.coulombf(angL, eta, x),
rho,
1,
h=hvalue,
direction=dirvalue))
dg = fp.mpf(
mp.diff(lambda x: mp.coulombg(angL, eta, x),
rho,
1,
h=hvalue,
direction=dirvalue))
# print(f,df,g,dg)
return f, df, g, dg
def c1(p):
return (-1 / (96 * mp.pi() * mp.pi())) * mp.diff(lambda x: c0(x), p, 3)
coulombf_ufunc = np.frompyfunc(
lambda angL, eta, rho: fp.mpf(mp.coulombf(angL, eta, rho)), 3,
1) # argment: angL, eta, rho=k*r
coulombg_ufunc = np.frompyfunc(
lambda angL, eta, rho: fp.mpf(mp.coulombg(angL, eta, rho)), 3,
1) # argment: angL, eta, rho=k*r
coulombw_ufunc = np.frompyfunc(
lambda angL, eta, rho: fp.mpf(mp.whitw(eta, angL + 0.5, 2 * rho)), 3,
1) # argment: angL, eta, rho=k*r
# argment: angL, eta, rho=k*r, note this order is different from whitw's argument, i
#and there is a factor of 2 for the 3rd argument
drho_coulombf_ufunc = np.frompyfunc(
lambda angL, eta, rho, hvalue, dirvalue: fp.mpf(
mp.diff(lambda x: mp.coulombf(angL, eta, x),
rho,
1,
h=hvalue,
direction=dirvalue)), 5, 1)
drho_coulombg_ufunc = np.frompyfunc(
lambda angL, eta, rho, hvalue, dirvalue: fp.mpf(
mp.diff(lambda x: mp.coulombg(angL, eta, x),
rho,
1,
h=hvalue,
direction=dirvalue)), 5, 1)
drho_coulombw_ufunc = np.frompyfunc(
lambda angL, eta, rho, hvalue, dirvalue: fp.mpf(
mp.diff(lambda x: mp.whitw(eta, angL + 0.5, 2 * x),
rho,
1,
h=hvalue,
def __init__(self, npts):
# Legendre poly
lp = lambda x: mp.legendre(npts, x)
self.points = mp.polyroots(mp.taylor(lp, 0, npts)[::-1])
self.weights = [2/((1 - p*p)*mp.diff(lp, p)**2) for p in self.points]
def c1(p): return (-1/(96*PI*PI))*mp.diff(lambda x: c0(x), p, 3)