Adds fixed dipole
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123
pdme/model/fixed_dipole_model.py
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123
pdme/model/fixed_dipole_model.py
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import numpy
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from dataclasses import dataclass
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from typing import Sequence, Tuple
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import scipy.optimize
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from pdme.model.model import Model
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from pdme.measurement import DotMeasurement
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class FixedDipoleModel(Model):
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'''
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Model of oscillating dipole with a fixed dipole moment.
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Parameters
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----------
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p : numpy.ndarray
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The fixed dipole moment.
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n : int
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The number of dipoles to assume.
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'''
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def __init__(self, xmin: float, xmax: float, ymin: float, ymax: float, zmin: float, zmax: float, p: numpy.ndarray, n: int) -> None:
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self.xmin = xmin
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self.xmax = xmax
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self.ymin = ymin
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self.ymax = ymax
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self.zmin = zmin
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self.zmax = zmax
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self.p = p
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self._n = n
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def __repr__(self) -> str:
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return f'FixedDipoleModel({self.xmin}, {self.xmax}, {self.ymin}, {self.ymax}, {self.zmin}, {self.zmax}, {self.p}, {self.n()})'
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def point_length(self) -> int:
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'''
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Dipole is constrained magnitude, but free orientation.
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Six degrees of freedom: (sx, sy, sz, w).
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'''
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return 4
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def n(self) -> int:
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return self._n
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def v_for_point_at_dot(self, dot: DotMeasurement, pt: numpy.ndarray) -> float:
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s = pt[0:3]
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w = pt[3]
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diff = dot.r - s
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alpha = self.p.dot(diff) / (numpy.linalg.norm(diff)**3)
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b = (1 / numpy.pi) * (w / (w**2 + dot.f**2))
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return alpha**2 * b
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def jac_for_point_at_dot(self, dot: DotMeasurement, pt: numpy.ndarray) -> numpy.ndarray:
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s = pt[0:3]
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w = pt[3]
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diff = dot.r - s
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alpha = self.p.dot(diff) / (numpy.linalg.norm(diff)**3)
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b = (1 / numpy.pi) * (w / (w**2 + dot.f**2))
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r_divs = (-self.p / (numpy.linalg.norm(diff)**3) + 3 * self.p.dot(diff) * diff / (numpy.linalg.norm(diff)**5)) * 2 * alpha * b
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f2 = dot.f**2
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w2 = w**2
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w_div = alpha**2 * (1 / numpy.pi) * ((f2 - w2) / ((f2 + w2)**2))
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return numpy.concatenate((r_divs, w_div), axis=None)
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@dataclass
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class FixedDipoleDiscretisation():
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'''
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Representation of a discretisation of a FixedDipoleDiscretisation.
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Also captures a rough maximum value of dipole.
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Parameters
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----------
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model : FixedDipoleModel
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The parent model of the discretisation.
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num_x : int
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The number of partitions of the x axis.
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num_y : int
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The number of partitions of the y axis.
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num_z : int
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The number of partitions of the z axis.
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'''
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model: FixedDipoleModel
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num_x: int
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num_y: int
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num_z: int
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def __post_init__(self):
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self.cell_count = self.num_x * self.num_y * self.num_z
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self.x_step = (self.model.xmax - self.model.xmin) / self.num_x
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self.y_step = (self.model.ymax - self.model.ymin) / self.num_y
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self.z_step = (self.model.zmax - self.model.zmin) / self.num_z
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def bounds(self, index: Tuple[float, float, float]) -> Tuple:
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xi, yi, zi = index
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# For this model, a point is (sx, sx, sy, w).
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# We want to keep w unbounded, restrict sx, sy, sz, px and py based on step.
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return (
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[
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xi * self.x_step + self.model.xmin, yi * self.y_step + self.model.ymin, zi * self.z_step + self.model.zmin,
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-numpy.inf
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],
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[
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(xi + 1) * self.x_step + self.model.xmin, (yi + 1) * self.y_step + self.model.ymin, (zi + 1) * self.z_step + self.model.zmin,
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numpy.inf
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]
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)
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def all_indices(self) -> numpy.ndindex:
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# see https://github.com/numpy/numpy/issues/20706 for why this is a mypy problem.
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return numpy.ndindex((self.num_x, self.num_y, self.num_z)) # type:ignore
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def solve_for_index(self, dots: Sequence[DotMeasurement], index: Tuple[float, float, float]) -> scipy.optimize.OptimizeResult:
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bounds = self.bounds(index)
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sx_mean = (bounds[0][0] + bounds[1][0]) / 2
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sy_mean = (bounds[0][1] + bounds[1][1]) / 2
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sz_mean = (bounds[0][2] + bounds[1][2]) / 2
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return self.model.solve(dots, initial_pt=numpy.array([sx_mean, sy_mean, sz_mean, .1]), bounds=bounds)
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162
pdme/model/fixed_magnitude_model.py
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162
pdme/model/fixed_magnitude_model.py
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import numpy
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from dataclasses import dataclass
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from typing import Sequence, Tuple
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import scipy.optimize
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from pdme.model.model import Model
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from pdme.measurement import DotMeasurement
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class FixedMagnitudeModel(Model):
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'''
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Model of oscillating dipole with a fixed magnitude, but free rotation.
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Parameters
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----------
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pfixed : float
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The fixed dipole magnitude.
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n : int
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The number of dipoles to assume.
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'''
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def __init__(self, xmin: float, xmax: float, ymin: float, ymax: float, zmin: float, zmax: float, pfixed: float, n: int) -> None:
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self.xmin = xmin
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self.xmax = xmax
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self.ymin = ymin
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self.ymax = ymax
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self.zmin = zmin
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self.zmax = zmax
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self.pfixed = pfixed
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self._n = n
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def __repr__(self) -> str:
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return f'FixedMagnitudeModel({self.xmin}, {self.xmax}, {self.ymin}, {self.ymax}, {self.zmin}, {self.zmax}, {self.n()})'
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def point_length(self) -> int:
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'''
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Dipole is constrained magnitude, but free orientation.
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Six degrees of freedom: (p_theta, p_phi, sx, sy, sz, w).
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'''
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return 6
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def n(self) -> int:
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return self._n
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def v_for_point_at_dot(self, dot: DotMeasurement, pt: numpy.ndarray) -> float:
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p_theta = pt[0]
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p_phi = pt[1]
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s = pt[2:5]
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w = pt[5]
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p = numpy.array([
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self.pfixed * numpy.sin(p_theta) * numpy.cos(p_phi),
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self.pfixed * numpy.sin(p_theta) * numpy.sin(p_phi),
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self.pfixed * numpy.cos(p_theta)
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])
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diff = dot.r - s
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alpha = p.dot(diff) / (numpy.linalg.norm(diff)**3)
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b = (1 / numpy.pi) * (w / (w**2 + dot.f**2))
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return alpha**2 * b
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def jac_for_point_at_dot(self, dot: DotMeasurement, pt: numpy.ndarray) -> numpy.ndarray:
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p_theta = pt[0]
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p_phi = pt[1]
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s = pt[2:5]
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w = pt[5]
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p = numpy.array([
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self.pfixed * numpy.sin(p_theta) * numpy.cos(p_phi),
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self.pfixed * numpy.sin(p_theta) * numpy.sin(p_phi),
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self.pfixed * numpy.cos(p_theta)
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])
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diff = dot.r - s
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alpha = p.dot(diff) / (numpy.linalg.norm(diff)**3)
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b = (1 / numpy.pi) * (w / (w**2 + dot.f**2))
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theta_div_middle = self.pfixed * (
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diff[0] * numpy.cos(p_phi) * numpy.cos(p_theta)
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+ diff[1] * numpy.sin(p_phi) * numpy.cos(p_theta)
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- diff[2] * numpy.sin(p_theta)
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)
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theta_div = 2 * alpha * (theta_div_middle) / (numpy.linalg.norm(diff)**3) * b
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phi_div_middle = self.pfixed * (
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diff[1] * numpy.sin(p_theta) * numpy.cos(p_phi)
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- diff[0] * numpy.sin(p_theta) * numpy.sin(p_phi)
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)
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phi_div = 2 * alpha * (phi_div_middle) / (numpy.linalg.norm(diff)**3) * b
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r_divs = (-p / (numpy.linalg.norm(diff)**3) + 3 * p.dot(diff) * diff / (numpy.linalg.norm(diff)**5)) * 2 * alpha * b
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f2 = dot.f**2
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w2 = w**2
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w_div = alpha**2 * (1 / numpy.pi) * ((f2 - w2) / ((f2 + w2)**2))
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return numpy.concatenate((theta_div, phi_div, r_divs, w_div), axis=None)
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@dataclass
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class FixedMagnitudeDiscretisation():
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'''
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Representation of a discretisation of a FixedMagnitudeDiscretisation.
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Also captures a rough maximum value of dipole.
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Parameters
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----------
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model : FixedMagnitudeModel
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The parent model of the discretisation.
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num_ptheta: int
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The number of partitions of ptheta.
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num_pphi: int
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The number of partitions of pphi.
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num_x : int
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The number of partitions of the x axis.
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num_y : int
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The number of partitions of the y axis.
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num_z : int
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The number of partitions of the z axis.
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'''
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model: FixedMagnitudeModel
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num_ptheta: int
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num_pphi: int
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num_x: int
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num_y: int
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num_z: int
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def __post_init__(self):
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self.cell_count = self.num_x * self.num_y * self.num_z
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self.x_step = (self.model.xmax - self.model.xmin) / self.num_x
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self.y_step = (self.model.ymax - self.model.ymin) / self.num_y
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self.z_step = (self.model.zmax - self.model.zmin) / self.num_z
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self.h_step = 2 / self.num_ptheta
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self.phi_step = 2 * numpy.pi / self.num_pphi
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def bounds(self, index: Tuple[float, float, float, float, float]) -> Tuple:
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pthetai, pphii, xi, yi, zi = index
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# For this model, a point is (p_theta, p_phi, sx, sx, sy, w).
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# We want to keep w unbounded, restrict sx, sy, sz, px and py based on step.
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return (
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[
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numpy.arccos(1 - pthetai * self.h_step), pphii * self.phi_step,
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xi * self.x_step + self.model.xmin, yi * self.y_step + self.model.ymin, zi * self.z_step + self.model.zmin,
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-numpy.inf
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],
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[
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numpy.arccos(1 - (pthetai + 1) * self.h_step), (pphii + 1) * self.phi_step,
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(xi + 1) * self.x_step + self.model.xmin, (yi + 1) * self.y_step + self.model.ymin, (zi + 1) * self.z_step + self.model.zmin,
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numpy.inf
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]
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)
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def all_indices(self) -> numpy.ndindex:
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# see https://github.com/numpy/numpy/issues/20706 for why this is a mypy problem.
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return numpy.ndindex((self.num_ptheta, self.num_pphi, self.num_x, self.num_y, self.num_z)) # type:ignore
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def solve_for_index(self, dots: Sequence[DotMeasurement], index: Tuple[float, float, float, float, float]) -> scipy.optimize.OptimizeResult:
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bounds = self.bounds(index)
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ptheta_mean = (bounds[0][0] + bounds[1][0]) / 2
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pphi_mean = (bounds[0][1] + bounds[1][1]) / 2
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sx_mean = (bounds[0][2] + bounds[1][2]) / 2
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sy_mean = (bounds[0][3] + bounds[1][3]) / 2
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sz_mean = (bounds[0][4] + bounds[1][4]) / 2
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return self.model.solve(dots, initial_pt=numpy.array([ptheta_mean, pphi_mean, sx_mean, sy_mean, sz_mean, .1]), bounds=bounds)
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