def _zetaInv(self, taup, lam):
'''Invert C{zeta} using Newton's method.
@return: 2-Tuple C{(u, v)}.
@see: C{void TMExact::zetainv(real taup, real lam,
real &u, real &v)}.
@raise EllipticError: No convergence.
'''
psi = asinh(taup)
sca = 1.0 / hypot1(taup)
u, v, trip = self._zetaInv0(psi, lam)
if not trip:
stol2 = _TOL_10 / max(psi, 1.0)**2
U, V = Fsum(u), Fsum(v)
# min iterations = 2, max = 6, mean = 4.0
for _ in range(self._trips_): # GEOGRAPHICLIB_PANIC
snu, cnu, dnu = self._Eu.sncndn(u)
snv, cnv, dnv = self._Ev.sncndn(v)
T, L, _ = self._zeta3( snu, cnu, dnu, snv, cnv, dnv)
dw, dv = self._zetaDwd(snu, cnu, dnu, snv, cnv, dnv)
T = (taup - T) * sca
L -= lam
u, du = U.fsum2_(T * dw, L * dv)
v, dv = V.fsum2_(T * dv, -L * dw)
if trip:
break
trip = (du**2 + dv**2) < stol2
else:
raise EllipticError('no %s convergence' % ('zetaInv',))
return u, v
def _sigmaInv(self, xi, eta):
'''Invert C{sigma} using Newton's method.
@return: 2-Tuple C{(u, v)}.
@see: C{void TMExact::sigmainv(real xi, real eta,
real &u, real &v)}.
@raise EllipticError: No convergence.
'''
u, v, trip = self._sigmaInv0(xi, eta)
if not trip:
U, V = Fsum(u), Fsum(v)
# min iterations = 2, max = 7, mean = 3.9
for _ in range(self._trips_): # GEOGRAPHICLIB_PANIC
snu, cnu, dnu = self._Eu.sncndn(u)
snv, cnv, dnv = self._Ev.sncndn(v)
X, E, _ = self._sigma3(v, snu, cnu, dnu, snv, cnv, dnv)
dw, dv = self._sigmaDwd( snu, cnu, dnu, snv, cnv, dnv)
X = xi - X
E -= eta
u, du = U.fsum2_(X * dw, E * dv)
v, dv = V.fsum2_(X * dv, -E * dw)
if trip:
break
trip = (du**2 + dv**2) < _TOL_10
else:
raise EllipticError('no %s convergence' % ('sigmaInv',))
return u, v
def _sigmaInv(self, xi, eta):
'''(INTERNAL) Invert C{sigma} using Newton's method.
@return: 2-Tuple C{(u, v)}.
@see: C{void TMExact::sigmainv(real xi, real eta,
real &u, real &v)}.
@raise EllipticError: No convergence.
'''
u, v, trip = self._sigmaInv0(xi, eta)
if trip:
self._iteration = 0
else:
U, V = Fsum(u), Fsum(v)
# min iterations = 2, max = 7, mean = 3.9
for self._iteration in range(1, _TRIPS): # GEOGRAPHICLIB_PANIC
sncndn6 = self._sncndn6(u, v)
X, E, _ = self._sigma3(v, *sncndn6)
dw, dv = self._sigmaDwd( *sncndn6)
X = xi - X
E -= eta
u, du = U.fsum2_(X * dw, E * dv)
v, dv = V.fsum2_(X * dv, -E * dw)
if trip:
break
trip = hypot2(du, dv) < _TOL_10
else:
t = unstr(self._sigmaInv.__name__, xi, eta)
raise EllipticError(_no_convergence_, txt=t)
return u, v
def _zetaInv(self, taup, lam):
'''(INTERNAL) Invert C{zeta} using Newton's method.
@return: 2-Tuple C{(u, v)}.
@see: C{void TMExact::zetainv(real taup, real lam,
real &u, real &v)}.
@raise EllipticError: No convergence.
'''
psi = asinh(taup)
sca = 1.0 / hypot1(taup)
u, v, trip = self._zetaInv0(psi, lam)
if trip:
self._iteration = 0
else:
stol2 = _TOL_10 / max(psi**2, 1.0)
U, V = Fsum(u), Fsum(v)
# min iterations = 2, max = 6, mean = 4.0
for self._iteration in range(1, _TRIPS): # GEOGRAPHICLIB_PANIC
sncndn6 = self._sncndn6(u, v)
T, L, _ = self._zeta3( *sncndn6)
dw, dv = self._zetaDwd(*sncndn6)
T = (taup - T) * sca
L -= lam
u, du = U.fsum2_(T * dw, L * dv)
v, dv = V.fsum2_(T * dv, -L * dw)
if trip:
break
trip = hypot2(du, dv) < stol2
else:
t = unstr(self._zetaInv.__name__, taup, lam)
raise EllipticError(_no_convergence_, txt=t)
return u, v
def _sigmaInv(self, xi, eta):
'''(INTERNAL) Invert C{sigma} using Newton's method.
@return: 2-Tuple C{(u, v)}.
@see: C{void TMExact::sigmainv(real xi, real eta,
real &u, real &v)}.
@raise EllipticError: No convergence.
'''
u, v, trip = self._sigmaInv0(xi, eta)
if not trip:
U, V = Fsum(u), Fsum(v)
# min iterations = 2, max = 7, mean = 3.9
for _ in range(self._trips_): # GEOGRAPHICLIB_PANIC
sncndn6 = self._sncndn6(u, v)
X, E, _ = self._sigma3(v, *sncndn6)
dw, dv = self._sigmaDwd( *sncndn6)
X = xi - X
E -= eta
u, du = U.fsum2_(X * dw, E * dv)
v, dv = V.fsum2_(X * dv, -E * dw)
if trip:
break
trip = hypot2(du, dv) < _TOL_10
else:
raise EllipticError('no %s%r convergence' %
('_sigmaInv', (xi, eta)))
return u, v