Module traceon.interpolation
Classes
class FieldAxial (z, electrostatic_coeffs=None, magnetostatic_coeffs=None)-
An electrostatic field resulting from a radial series expansion around the optical axis. You should not initialize this class yourself, but it is used as a base class for the fields returned by the
axial_derivative_interpolationmethods. This base class overloads the +,*,- operators so it is very easy to take a superposition of different fields.Expand source code
class FieldAxial(S.Field, ABC): """An electrostatic field resulting from a radial series expansion around the optical axis. You should not initialize this class yourself, but it is used as a base class for the fields returned by the `axial_derivative_interpolation` methods. This base class overloads the +,*,- operators so it is very easy to take a superposition of different fields.""" def __init__(self, z, electrostatic_coeffs=None, magnetostatic_coeffs=None): N = len(z) assert z.shape == (N,) assert electrostatic_coeffs is None or len(electrostatic_coeffs)== N-1 assert magnetostatic_coeffs is None or len(magnetostatic_coeffs) == N-1 assert electrostatic_coeffs is not None or magnetostatic_coeffs is not None assert z[0] < z[-1], "z values in axial interpolation should be ascending" self.z = z self.electrostatic_coeffs = electrostatic_coeffs if electrostatic_coeffs is not None else np.zeros_like(magnetostatic_coeffs) self.magnetostatic_coeffs = magnetostatic_coeffs if magnetostatic_coeffs is not None else np.zeros_like(electrostatic_coeffs) self.has_electrostatic = np.any(self.electrostatic_coeffs != 0.) self.has_magnetostatic = np.any(self.magnetostatic_coeffs != 0.) def is_electrostatic(self): return self.has_electrostatic def is_magnetostatic(self): return self.has_magnetostatic def __str__(self): name = self.__class__.__name__ return f'<Traceon {name}, zmin={self.z[0]} mm, zmax={self.z[-1]} mm,\n\tNumber of samples on optical axis: {len(self.z)}>' def __add__(self, other): if isinstance(other, FieldAxial): assert np.array_equal(self.z, other.z), "Cannot add FieldAxial if optical axis sampling is different." assert self.electrostatic_coeffs.shape == other.electrostatic_coeffs.shape, "Cannot add FieldAxial if shape of axial coefficients is unequal." assert self.magnetostatic_coeffs.shape == other.magnetostatic_coeffs.shape, "Cannot add FieldAxial if shape of axial coefficients is unequal." return self.__class__(self.z, self.electrostatic_coeffs+other.electrostatic_coeffs, self.magnetostatic_coeffs + other.magnetostatic_coeffs) return NotImplemented def __sub__(self, other): return self.__add__(-other) def __radd__(self, other): return self.__add__(other) def __mul__(self, other): if isinstance(other, int) or isinstance(other, float): return self.__class__(self.z, other*self.electrostatic_coeffs, other*self.magnetostatic_coeffs) return NotImplemented def __neg__(self): return -1*self def __rmul__(self, other): return self.__mul__(other)Ancestors
- Field
- abc.ABC
Subclasses
Methods
def is_electrostatic(self)def is_magnetostatic(self)
Inherited members
class FieldRadialAxial (field, zmin, zmax, N=None)-
Expand source code
class FieldRadialAxial(FieldAxial): """ """ def __init__(self, field, zmin, zmax, N=None): assert isinstance(field, S.FieldRadialBEM) z, electrostatic_coeffs, magnetostatic_coeffs = FieldRadialAxial._get_interpolation_coefficients(field, zmin, zmax, N=N) super().__init__(z, electrostatic_coeffs, magnetostatic_coeffs) assert self.electrostatic_coeffs.shape == (len(z)-1, backend.DERIV_2D_MAX, 6) assert self.magnetostatic_coeffs.shape == (len(z)-1, backend.DERIV_2D_MAX, 6) @staticmethod def _get_interpolation_coefficients(field: S.FieldRadialBEM, zmin, zmax, N=None): assert zmax > zmin, "zmax should be bigger than zmin" N_charges = max(len(field.electrostatic_point_charges.charges), len(field.magnetostatic_point_charges.charges)) N = N if N is not None else int(FACTOR_AXIAL_DERIV_SAMPLING_2D*N_charges) z = np.linspace(zmin, zmax, N) st = time.time() elec_derivs = np.concatenate(util.split_collect(field.get_electrostatic_axial_potential_derivatives, z), axis=0) elec_coeffs = _quintic_spline_coefficients(z, elec_derivs.T) mag_derivs = np.concatenate(util.split_collect(field.get_magnetostatic_axial_potential_derivatives, z), axis=0) mag_coeffs = _quintic_spline_coefficients(z, mag_derivs.T) logging.log_info(f'Computing derivative interpolation took {(time.time()-st)*1000:.2f} ms ({len(z)} items)') return z, elec_coeffs, mag_coeffs def electrostatic_field_at_point(self, point_): """ Compute the electric field, \\( \\vec{E} = -\\nabla \\phi \\) Parameters ---------- point: (2,) array of float64 Position at which to compute the field. Returns ------- Numpy array containing the field strengths (in units of V/mm) in the r and z directions. """ point = np.array(point_) assert point.shape == (3,), "Please supply a three dimensional point" return backend.field_radial_derivs(point, self.z, self.electrostatic_coeffs) def magnetostatic_field_at_point(self, point_): """ Compute the magnetic field \\( \\vec{H} \\) Parameters ---------- point: (2,) array of float64 Position at which to compute the field. Returns ------- (2,) np.ndarray of float64 containing the field strength (in units of A/m) in the x, y and z directions. """ point = np.array(point_) assert point.shape == (3,), "Please supply a three dimensional point" return backend.field_radial_derivs(point, self.z, self.magnetostatic_coeffs) def electrostatic_potential_at_point(self, point_): """ Compute the electrostatic potential (close to the axis). Parameters ---------- point: (2,) array of float64 Position at which to compute the potential. Returns ------- Potential as a float value (in units of V). """ point = np.array(point_) assert point.shape == (3,), "Please supply a three dimensional point" return backend.potential_radial_derivs(point, self.z, self.electrostatic_coeffs) def magnetostatic_potential_at_point(self, point_): """ Compute the magnetostatic scalar potential (satisfying \\(\\vec{H} = -\\nabla \\phi \\)) close to the axis Parameters ---------- point: (2,) array of float64 Position at which to compute the field. Returns ------- Potential as a float value (in units of A). """ point = np.array(point_) assert point.shape == (3,), "Please supply a three dimensional point" return backend.potential_radial_derivs(point, self.z, self.magnetostatic_coeffs) def get_tracer(self, bounds): return T.TracerRadialAxial(self, bounds)Ancestors
- FieldAxial
- Field
- abc.ABC
Methods
def electrostatic_field_at_point(self, point_)-
Compute the electric field, \vec{E} = -\nabla \phi
Parameters
point:(2,) arrayoffloat64- Position at which to compute the field.
Returns
Numpy array containing the field strengths (in units of V/mm) in the r and z directions.
def electrostatic_potential_at_point(self, point_)-
Compute the electrostatic potential (close to the axis).
Parameters
point:(2,) arrayoffloat64- Position at which to compute the potential.
Returns
Potential as a float value (in units of V).
def get_tracer(self, bounds)def magnetostatic_field_at_point(self, point_)-
Compute the magnetic field \vec{H}
Parameters
point:(2,) arrayoffloat64- Position at which to compute the field.
Returns
(2,) np.ndarray of float64 containing the field strength (in units of A/m) in the x, y and z directions.
def magnetostatic_potential_at_point(self, point_)-
Compute the magnetostatic scalar potential (satisfying \vec{H} = -\nabla \phi ) close to the axis
Parameters
point:(2,) arrayoffloat64- Position at which to compute the field.
Returns
Potential as a float value (in units of A).
Inherited members