def _integrand(self, k_y):
"""..."""
if self.x == 0:
xi = k_y
return _cexp(1.0j * (-(xi**3) / 3 + (xi * self._ry / self._W_y)))
else:
# next line needs _integrand declared cpdef without nogil attribute,
# and will execute slower than repeating the super class integration
# routine function here
#return super(IncAiry2d, self)._integrand(k_y)
return self.spectrum(k_y) * _cexp(
1j * self._phase(k_y, self.x, self._ry))
def _f_Laguerre_Gauss_spherical(self, sin_theta, theta, phi, W_y, k, m):
"""Laguerre-Gaussian spectrum amplitude.
Implementation for spherical coordinates.
"""
return self._f_Gauss_spherical(sin_theta, W_y, k) * theta**_abs(m) * \
_cexp(1j*m*phi)
def _f_Laguerre_Gauss_cartesian(self, k_y, k_z, W_y, k, m):
"""Laguerre-Gaussian spectrum amplitude.
Impementation for Cartesian coordinates.
"""
return self._f_Gauss_cartesian(k_y, k_z, W_y) * \
_cexp(1j*m*self._phi(k_y, k_z)) * self._theta(k_y, k_z, k)**_abs(m)
def _integrand(self, theta, phi):
"""Integrand function."""
sin_theta = _sin(theta)
cos_theta = _cos(theta)
return sin_theta * cos_theta * self.spectrum(sin_theta, theta, phi) * \
_cexp(1j*self._phase(sin_theta, cos_theta,
phi, self.x, self._ry, self._rz))
def _integrand(self, k_y, k_z):
"""Integrand function."""
return self.spectrum(k_y, k_z) * \
_cexp(1j*self._phase(k_y, k_z, self.x, self._ry, self._rz))
def _integrand(self, k_y):
"""Integrand function."""
return self.spectrum(k_y) * _cexp(
1j * self._phase(k_y, self.x, self._ry))
def _f_Airy(self, k_y, W_y, M, W):
"""Airy spectrum amplitude."""
return W_y * _cexp(1.0j*(-1/3)*(k_y*W_y)**3) \
* self._heaviside(W_y * k_y - (M - W)) \
* self._heaviside((M + W) - W_y * k_y)