Adds fixed dipole

pdme/model/fixed_dipole_model.py

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

pdme/model/fixed_magnitude_model.py

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

scripts/z-band-fixed-dipole-middle/all.py

@@ -0,0 +1,108 @@
+from pdme.model.fixed_dipole_model import FixedDipoleModel, FixedDipoleDiscretisation
+from pdme.measurement import OscillatingDipole, OscillatingDipoleArrangement
+import itertools
+import logging
+import multiprocessing
+import numpy
+import csv
+import random
+
+
+FILENAME = "z-band-fixed-dipole-middle-all-dots-square.csv"
+csv_fields = ["dipole_mom", "dipole_loc", "dipole_freq", "low_success", "low_count", "medium_success", "medium_count", "high_success", "high_count"]
+
+
+def get_pt():
+	return ((1, 1, 1), (random.uniform(-10, 10), random.uniform(-10, 10), random.uniform(3.5, 4.5)))
+
+
+def get_a_result(discretisation, dots, index):
+	return (index, discretisation.solve_for_index(dots, index))
+
+
+def main():
+	
+	with open(FILENAME, "a", newline="") as outfile:
+		# csv fields
+		writer = csv.DictWriter(outfile, fieldnames=csv_fields, dialect='unix')
+		writer.writeheader()
+	
+	for run in range(1, 101):
+		
+		p_pts, s_pts = get_pt()
+		dipoles = OscillatingDipoleArrangement([OscillatingDipole(p_pts, s_pts, run)])
+		logging.info(f"gonna work on point {(p_pts, s_pts, run)}")
+		dot_inputs = list(itertools.chain.from_iterable(
+			(([1, 2, 0], f), ([1, 1, 0], f), ([2, 1, 0], f), ([2, 2, 0], f)) for f in numpy.arange(1, 10, 2)
+		))
+		dots = dipoles.get_dot_measurements(dot_inputs)
+
+		model_low = FixedDipoleModel(-10, 10, -10, 10, 2.5, 3.5, numpy.array([1, 1, 1]), 1)
+		discretisation_low = FixedDipoleDiscretisation(model_low, 5, 5, 5)
+
+		model_medium = FixedDipoleModel(-10, 10, -10, 10, 3.5, 4.5, numpy.array([1, 1, 1]), 1)
+		discretisation_medium = FixedDipoleDiscretisation(model_medium, 5, 5, 5)
+
+		model_high = FixedDipoleModel(-10, 10, -10, 10, 4.5, 5.5, numpy.array([1, 1, 1]), 1)
+		discretisation_high = FixedDipoleDiscretisation(model_high, 5, 5, 5)
+		
+		with multiprocessing.Pool(multiprocessing.cpu_count()-1 or 1) as pool:
+			results_low = pool.starmap(get_a_result, zip(itertools.repeat(discretisation_low), itertools.repeat(dots), discretisation_low.all_indices()))
+
+		with multiprocessing.Pool(multiprocessing.cpu_count()-1 or 1) as pool:
+			results_medium = pool.starmap(get_a_result, zip(itertools.repeat(discretisation_medium), itertools.repeat(dots), discretisation_medium.all_indices()))
+
+		with multiprocessing.Pool(multiprocessing.cpu_count()-1 or 1) as pool:
+			results_high = pool.starmap(get_a_result, zip(itertools.repeat(discretisation_high), itertools.repeat(dots), discretisation_high.all_indices()))
+		
+		count_low = 0
+		success_low = 0
+		for idx, result in results_low:
+			count_low += 1
+			if result.success and result.cost <= 1e-10 and numpy.linalg.norm(result.x[0:3]) < 10:
+				answer = result.normalised_x
+				success_low += 1
+			else:
+				answer = None
+
+		count_medium = 0
+		success_medium = 0
+		for idx, result in results_medium:
+			count_medium += 1
+			if result.success and result.cost <= 1e-10 and numpy.linalg.norm(result.x[0:3]) < 10:
+				answer = result.normalised_x
+				success_medium += 1
+			else:
+				answer = None
+
+		count_high = 0
+		success_high = 0
+		for idx, result in results_high:
+			count_high += 1
+			if result.success and result.cost <= 1e-10 and numpy.linalg.norm(result.x[0:3]) < 10:
+				answer = result.normalised_x
+				success_high += 1
+			else:
+				answer = None
+
+		logging.info(f"Low   : Out of {count_low} cells, {success_low} were successful")
+		logging.info(f"Medium: Out of {count_medium} cells, {success_medium} were successful")
+		logging.info(f"High  : Out of {count_high} cells, {success_high} were successful")
+		
+		with open(FILENAME, "a", newline='') as outfile:
+			writer = csv.DictWriter(outfile, fieldnames=csv_fields, dialect='unix')
+			writer.writerow({
+				"dipole_mom": p_pts,
+				"dipole_loc": s_pts,
+				"dipole_freq": run,
+				"low_success": success_low,
+				"high_success": success_high,
+				"medium_success": success_medium,
+				"low_count": count_low,
+				"medium_count": count_medium,
+				"high_count": count_high
+			})
+
+if __name__ == "__main__":
+	logging.basicConfig(level=logging.INFO)
+	main()

scripts/z-band-fixed-dipole-middle/narrowersquare.py

@@ -0,0 +1,108 @@
+from pdme.model.fixed_dipole_model import FixedDipoleModel, FixedDipoleDiscretisation
+from pdme.measurement import OscillatingDipole, OscillatingDipoleArrangement
+import itertools
+import logging
+import multiprocessing
+import numpy
+import csv
+import random
+
+
+FILENAME = "z-band-fixed-dipole-middle-all-dots-narrower-square.csv"
+csv_fields = ["dipole_mom", "dipole_loc", "dipole_freq", "low_success", "low_count", "medium_success", "medium_count", "high_success", "high_count"]
+
+
+def get_pt():
+	return ((1, 1, 1), (random.uniform(-10, 10), random.uniform(-10, 10), random.uniform(3.5, 4.5)))
+
+
+def get_a_result(discretisation, dots, index):
+	return (index, discretisation.solve_for_index(dots, index))
+
+
+def main():
+	
+	with open(FILENAME, "a", newline="") as outfile:
+		# csv fields
+		writer = csv.DictWriter(outfile, fieldnames=csv_fields, dialect='unix')
+		writer.writeheader()
+	
+	for run in range(1, 101):
+		
+		p_pts, s_pts = get_pt()
+		dipoles = OscillatingDipoleArrangement([OscillatingDipole(p_pts, s_pts, run)])
+		logging.info(f"gonna work on point {(p_pts, s_pts, run)}")
+		dot_inputs = list(itertools.chain.from_iterable(
+			(([-.25, .25, 0], f), ([-.25, -.25, 0], f), ([.25, -.25, 0], f), ([.25, .25, 0], f)) for f in numpy.arange(1, 10, 2)
+		))
+		dots = dipoles.get_dot_measurements(dot_inputs)
+
+		model_low = FixedDipoleModel(-10, 10, -10, 10, 2.5, 3.5, numpy.array([1, 1, 1]), 1)
+		discretisation_low = FixedDipoleDiscretisation(model_low, 5, 5, 5)
+
+		model_medium = FixedDipoleModel(-10, 10, -10, 10, 3.5, 4.5, numpy.array([1, 1, 1]), 1)
+		discretisation_medium = FixedDipoleDiscretisation(model_medium, 5, 5, 5)
+
+		model_high = FixedDipoleModel(-10, 10, -10, 10, 4.5, 5.5, numpy.array([1, 1, 1]), 1)
+		discretisation_high = FixedDipoleDiscretisation(model_high, 5, 5, 5)
+		
+		with multiprocessing.Pool(multiprocessing.cpu_count()-1 or 1) as pool:
+			results_low = pool.starmap(get_a_result, zip(itertools.repeat(discretisation_low), itertools.repeat(dots), discretisation_low.all_indices()))
+
+		with multiprocessing.Pool(multiprocessing.cpu_count()-1 or 1) as pool:
+			results_medium = pool.starmap(get_a_result, zip(itertools.repeat(discretisation_medium), itertools.repeat(dots), discretisation_medium.all_indices()))
+
+		with multiprocessing.Pool(multiprocessing.cpu_count()-1 or 1) as pool:
+			results_high = pool.starmap(get_a_result, zip(itertools.repeat(discretisation_high), itertools.repeat(dots), discretisation_high.all_indices()))
+		
+		count_low = 0
+		success_low = 0
+		for idx, result in results_low:
+			count_low += 1
+			if result.success and result.cost <= 1e-10 and numpy.linalg.norm(result.x[0:3]) < 10:
+				answer = result.normalised_x
+				success_low += 1
+			else:
+				answer = None
+
+		count_medium = 0
+		success_medium = 0
+		for idx, result in results_medium:
+			count_medium += 1
+			if result.success and result.cost <= 1e-10 and numpy.linalg.norm(result.x[0:3]) < 10:
+				answer = result.normalised_x
+				success_medium += 1
+			else:
+				answer = None
+
+		count_high = 0
+		success_high = 0
+		for idx, result in results_high:
+			count_high += 1
+			if result.success and result.cost <= 1e-10 and numpy.linalg.norm(result.x[0:3]) < 10:
+				answer = result.normalised_x
+				success_high += 1
+			else:
+				answer = None
+
+		logging.info(f"Low   : Out of {count_low} cells, {success_low} were successful")
+		logging.info(f"Medium: Out of {count_medium} cells, {success_medium} were successful")
+		logging.info(f"High  : Out of {count_high} cells, {success_high} were successful")
+		
+		with open(FILENAME, "a", newline='') as outfile:
+			writer = csv.DictWriter(outfile, fieldnames=csv_fields, dialect='unix')
+			writer.writerow({
+				"dipole_mom": p_pts,
+				"dipole_loc": s_pts,
+				"dipole_freq": run,
+				"low_success": success_low,
+				"high_success": success_high,
+				"medium_success": success_medium,
+				"low_count": count_low,
+				"medium_count": count_medium,
+				"high_count": count_high
+			})
+
+if __name__ == "__main__":
+	logging.basicConfig(level=logging.INFO)
+	main()

scripts/z-band-fixed-dipole-middle/widesquare.py

@@ -0,0 +1,108 @@
+from pdme.model.fixed_dipole_model import FixedDipoleModel, FixedDipoleDiscretisation
+from pdme.measurement import OscillatingDipole, OscillatingDipoleArrangement
+import itertools
+import logging
+import multiprocessing
+import numpy
+import csv
+import random
+
+
+FILENAME = "z-band-fixed-dipole-middle-all-dots-wide-square.csv"
+csv_fields = ["dipole_mom", "dipole_loc", "dipole_freq", "low_success", "low_count", "medium_success", "medium_count", "high_success", "high_count"]
+
+
+def get_pt():
+	return ((1, 1, 1), (random.uniform(-10, 10), random.uniform(-10, 10), random.uniform(3.5, 4.5)))
+
+
+def get_a_result(discretisation, dots, index):
+	return (index, discretisation.solve_for_index(dots, index))
+
+
+def main():
+	
+	with open(FILENAME, "a", newline="") as outfile:
+		# csv fields
+		writer = csv.DictWriter(outfile, fieldnames=csv_fields, dialect='unix')
+		writer.writeheader()
+	
+	for run in range(1, 101):
+		
+		p_pts, s_pts = get_pt()
+		dipoles = OscillatingDipoleArrangement([OscillatingDipole(p_pts, s_pts, run)])
+		logging.info(f"gonna work on point {(p_pts, s_pts, run)}")
+		dot_inputs = list(itertools.chain.from_iterable(
+			(([1, 2, 0], f), ([1, 1, 0], f), ([2, 1, 0], f), ([2, 2, 0], f)) for f in numpy.arange(1, 10, 2)
+		))
+		dots = dipoles.get_dot_measurements(dot_inputs)
+
+		model_low = FixedDipoleModel(-10, 10, -10, 10, 2.5, 3.5, numpy.array([1, 1, 1]), 1)
+		discretisation_low = FixedDipoleDiscretisation(model_low, 5, 5, 5)
+
+		model_medium = FixedDipoleModel(-10, 10, -10, 10, 3.5, 4.5, numpy.array([1, 1, 1]), 1)
+		discretisation_medium = FixedDipoleDiscretisation(model_medium, 5, 5, 5)
+
+		model_high = FixedDipoleModel(-10, 10, -10, 10, 4.5, 5.5, numpy.array([1, 1, 1]), 1)
+		discretisation_high = FixedDipoleDiscretisation(model_high, 5, 5, 5)
+		
+		with multiprocessing.Pool(multiprocessing.cpu_count()-1 or 1) as pool:
+			results_low = pool.starmap(get_a_result, zip(itertools.repeat(discretisation_low), itertools.repeat(dots), discretisation_low.all_indices()))
+
+		with multiprocessing.Pool(multiprocessing.cpu_count()-1 or 1) as pool:
+			results_medium = pool.starmap(get_a_result, zip(itertools.repeat(discretisation_medium), itertools.repeat(dots), discretisation_medium.all_indices()))
+
+		with multiprocessing.Pool(multiprocessing.cpu_count()-1 or 1) as pool:
+			results_high = pool.starmap(get_a_result, zip(itertools.repeat(discretisation_high), itertools.repeat(dots), discretisation_high.all_indices()))
+		
+		count_low = 0
+		success_low = 0
+		for idx, result in results_low:
+			count_low += 1
+			if result.success and result.cost <= 1e-10 and numpy.linalg.norm(result.x[0:3]) < 10:
+				answer = result.normalised_x
+				success_low += 1
+			else:
+				answer = None
+
+		count_medium = 0
+		success_medium = 0
+		for idx, result in results_medium:
+			count_medium += 1
+			if result.success and result.cost <= 1e-10 and numpy.linalg.norm(result.x[0:3]) < 10:
+				answer = result.normalised_x
+				success_medium += 1
+			else:
+				answer = None
+
+		count_high = 0
+		success_high = 0
+		for idx, result in results_high:
+			count_high += 1
+			if result.success and result.cost <= 1e-10 and numpy.linalg.norm(result.x[0:3]) < 10:
+				answer = result.normalised_x
+				success_high += 1
+			else:
+				answer = None
+
+		logging.info(f"Low   : Out of {count_low} cells, {success_low} were successful")
+		logging.info(f"Medium: Out of {count_medium} cells, {success_medium} were successful")
+		logging.info(f"High  : Out of {count_high} cells, {success_high} were successful")
+		
+		with open(FILENAME, "a", newline='') as outfile:
+			writer = csv.DictWriter(outfile, fieldnames=csv_fields, dialect='unix')
+			writer.writerow({
+				"dipole_mom": p_pts,
+				"dipole_loc": s_pts,
+				"dipole_freq": run,
+				"low_success": success_low,
+				"high_success": success_high,
+				"medium_success": success_medium,
+				"low_count": count_low,
+				"medium_count": count_medium,
+				"high_count": count_high
+			})
+
+if __name__ == "__main__":
+	logging.basicConfig(level=logging.INFO)
+	main()

scripts/z-band-fixed-magnitude-middle/all.py

@@ -0,0 +1,117 @@
+from pdme.model.fixed_magnitude_model import FixedMagnitudeModel, FixedMagnitudeDiscretisation
+from pdme.measurement import OscillatingDipole, OscillatingDipoleArrangement
+import itertools
+import logging
+import multiprocessing
+import numpy
+import csv
+import random
+
+
+FILENAME = "z-band-fixed-magnitude-middle-all-dots-square.csv"
+csv_fields = ["dipole_mom", "dipole_loc", "dipole_freq", "low_success", "low_count", "medium_success", "medium_count", "high_success", "high_count"]
+
+
+def get_uniform_sphere():
+	r = 6
+	a = random.uniform(-10, 10)
+	b = random.uniform(-10, 10)
+	c = random.uniform(-10, 10)
+	f = (a**2 + b**2 + c**2)**.5
+	return (a * r / f, b * r / f, c * r / f)
+
+
+def get_pt():
+	return (get_uniform_sphere(), (random.uniform(-10, 10), random.uniform(-10, 10), random.uniform(3.5, 4.5)))
+
+
+def get_a_result(discretisation, dots, index):
+	return (index, discretisation.solve_for_index(dots, index))
+
+
+def main():
+	
+	with open(FILENAME, "a", newline="") as outfile:
+		# csv fields
+		writer = csv.DictWriter(outfile, fieldnames=csv_fields, dialect='unix')
+		writer.writeheader()
+	
+	for run in range(1, 101):
+		
+		p_pts, s_pts = get_pt()
+		dipoles = OscillatingDipoleArrangement([OscillatingDipole(p_pts, s_pts, run)])
+		logging.info(f"gonna work on point {(p_pts, s_pts, run)}")
+		dot_inputs = list(itertools.chain.from_iterable(
+			(([1, 2, 0], f), ([1, 1, 0], f), ([2, 1, 0], f), ([2, 2, 0], f)) for f in numpy.arange(1, 10, 2)
+		))
+		dots = dipoles.get_dot_measurements(dot_inputs)
+
+		model_low = FixedMagnitudeModel(-10, 10, -10, 10, 2.5, 3.5, 6, 1)
+		discretisation_low = FixedMagnitudeDiscretisation(model_low, 6, 6, 5, 5, 5)
+
+		model_medium = FixedMagnitudeModel(-10, 10, -10, 10, 3.5, 4.5, 6, 1)
+		discretisation_medium = FixedMagnitudeDiscretisation(model_medium, 6, 6, 5, 5, 5)
+
+		model_high = FixedMagnitudeModel(-10, 10, -10, 10, 4.5, 5.5, 6, 1)
+		discretisation_high = FixedMagnitudeDiscretisation(model_high, 6, 6, 5, 5, 5)
+		
+		with multiprocessing.Pool(multiprocessing.cpu_count()-1 or 1) as pool:
+			results_low = pool.starmap(get_a_result, zip(itertools.repeat(discretisation_low), itertools.repeat(dots), discretisation_low.all_indices()))
+
+		with multiprocessing.Pool(multiprocessing.cpu_count()-1 or 1) as pool:
+			results_medium = pool.starmap(get_a_result, zip(itertools.repeat(discretisation_medium), itertools.repeat(dots), discretisation_medium.all_indices()))
+
+		with multiprocessing.Pool(multiprocessing.cpu_count()-1 or 1) as pool:
+			results_high = pool.starmap(get_a_result, zip(itertools.repeat(discretisation_high), itertools.repeat(dots), discretisation_high.all_indices()))
+		
+		count_low = 0
+		success_low = 0
+		for idx, result in results_low:
+			count_low += 1
+			if result.success and result.cost <= 1e-10 and numpy.linalg.norm(result.x[0:3]) < 10:
+				answer = result.normalised_x
+				success_low += 1
+			else:
+				answer = None
+
+		count_medium = 0
+		success_medium = 0
+		for idx, result in results_medium:
+			count_medium += 1
+			if result.success and result.cost <= 1e-10 and numpy.linalg.norm(result.x[0:3]) < 10:
+				answer = result.normalised_x
+				success_medium += 1
+			else:
+				answer = None
+
+		count_high = 0
+		success_high = 0
+		for idx, result in results_high:
+			count_high += 1
+			if result.success and result.cost <= 1e-10 and numpy.linalg.norm(result.x[0:3]) < 10:
+				answer = result.normalised_x
+				success_high += 1
+			else:
+				answer = None
+
+		logging.info(f"Low   : Out of {count_low} cells, {success_low} were successful")
+		logging.info(f"Medium: Out of {count_medium} cells, {success_medium} were successful")
+		logging.info(f"High  : Out of {count_high} cells, {success_high} were successful")
+		
+		with open(FILENAME, "a", newline='') as outfile:
+			writer = csv.DictWriter(outfile, fieldnames=csv_fields, dialect='unix')
+			writer.writerow({
+				"dipole_mom": p_pts,
+				"dipole_loc": s_pts,
+				"dipole_freq": run,
+				"low_success": success_low,
+				"high_success": success_high,
+				"medium_success": success_medium,
+				"low_count": count_low,
+				"medium_count": count_medium,
+				"high_count": count_high
+			})
+
+if __name__ == "__main__":
+	logging.basicConfig(level=logging.INFO)
+	main()

scripts/z-band-fixed-magnitude-middle/narrowersquare.py

@@ -0,0 +1,117 @@
+from pdme.model.fixed_magnitude_model import FixedMagnitudeModel, FixedMagnitudeDiscretisation
+from pdme.measurement import OscillatingDipole, OscillatingDipoleArrangement
+import itertools
+import logging
+import multiprocessing
+import numpy
+import csv
+import random
+
+
+FILENAME = "z-band-fixed-magnitude-middle-all-dots-narrower-square.csv"
+csv_fields = ["dipole_mom", "dipole_loc", "dipole_freq", "low_success", "low_count", "medium_success", "medium_count", "high_success", "high_count"]
+
+
+def get_uniform_sphere():
+	r = 6
+	a = random.uniform(-10, 10)
+	b = random.uniform(-10, 10)
+	c = random.uniform(-10, 10)
+	f = (a**2 + b**2 + c**2)**.5
+	return (a * r / f, b * r / f, c * r / f)
+
+
+def get_pt():
+	return (get_uniform_sphere(), (random.uniform(-10, 10), random.uniform(-10, 10), random.uniform(3.5, 4.5)))
+
+
+def get_a_result(discretisation, dots, index):
+	return (index, discretisation.solve_for_index(dots, index))
+
+
+def main():
+	
+	with open(FILENAME, "a", newline="") as outfile:
+		# csv fields
+		writer = csv.DictWriter(outfile, fieldnames=csv_fields, dialect='unix')
+		writer.writeheader()
+	
+	for run in range(1, 101):
+		
+		p_pts, s_pts = get_pt()
+		dipoles = OscillatingDipoleArrangement([OscillatingDipole(p_pts, s_pts, run)])
+		logging.info(f"gonna work on point {(p_pts, s_pts, run)}")
+		dot_inputs = list(itertools.chain.from_iterable(
+			(([-.25, .25, 0], f), ([-.25, -.25, 0], f), ([.25, -.25, 0], f), ([.25, .25, 0], f)) for f in numpy.arange(1, 10, 2)
+		))
+		dots = dipoles.get_dot_measurements(dot_inputs)
+
+		model_low = FixedMagnitudeModel(-10, 10, -10, 10, 2.5, 3.5, 6, 1)
+		discretisation_low = FixedMagnitudeDiscretisation(model_low, 6, 6, 5, 5, 5)
+
+		model_medium = FixedMagnitudeModel(-10, 10, -10, 10, 3.5, 4.5, 6, 1)
+		discretisation_medium = FixedMagnitudeDiscretisation(model_medium, 6, 6, 5, 5, 5)
+
+		model_high = FixedMagnitudeModel(-10, 10, -10, 10, 4.5, 5.5, 6, 1)
+		discretisation_high = FixedMagnitudeDiscretisation(model_high, 6, 6, 5, 5, 5)
+		
+		with multiprocessing.Pool(multiprocessing.cpu_count()-1 or 1) as pool:
+			results_low = pool.starmap(get_a_result, zip(itertools.repeat(discretisation_low), itertools.repeat(dots), discretisation_low.all_indices()))
+
+		with multiprocessing.Pool(multiprocessing.cpu_count()-1 or 1) as pool:
+			results_medium = pool.starmap(get_a_result, zip(itertools.repeat(discretisation_medium), itertools.repeat(dots), discretisation_medium.all_indices()))
+
+		with multiprocessing.Pool(multiprocessing.cpu_count()-1 or 1) as pool:
+			results_high = pool.starmap(get_a_result, zip(itertools.repeat(discretisation_high), itertools.repeat(dots), discretisation_high.all_indices()))
+		
+		count_low = 0
+		success_low = 0
+		for idx, result in results_low:
+			count_low += 1
+			if result.success and result.cost <= 1e-10 and numpy.linalg.norm(result.x[0:3]) < 10:
+				answer = result.normalised_x
+				success_low += 1
+			else:
+				answer = None
+
+		count_medium = 0
+		success_medium = 0
+		for idx, result in results_medium:
+			count_medium += 1
+			if result.success and result.cost <= 1e-10 and numpy.linalg.norm(result.x[0:3]) < 10:
+				answer = result.normalised_x
+				success_medium += 1
+			else:
+				answer = None
+
+		count_high = 0
+		success_high = 0
+		for idx, result in results_high:
+			count_high += 1
+			if result.success and result.cost <= 1e-10 and numpy.linalg.norm(result.x[0:3]) < 10:
+				answer = result.normalised_x
+				success_high += 1
+			else:
+				answer = None
+
+		logging.info(f"Low   : Out of {count_low} cells, {success_low} were successful")
+		logging.info(f"Medium: Out of {count_medium} cells, {success_medium} were successful")
+		logging.info(f"High  : Out of {count_high} cells, {success_high} were successful")
+		
+		with open(FILENAME, "a", newline='') as outfile:
+			writer = csv.DictWriter(outfile, fieldnames=csv_fields, dialect='unix')
+			writer.writerow({
+				"dipole_mom": p_pts,
+				"dipole_loc": s_pts,
+				"dipole_freq": run,
+				"low_success": success_low,
+				"high_success": success_high,
+				"medium_success": success_medium,
+				"low_count": count_low,
+				"medium_count": count_medium,
+				"high_count": count_high
+			})
+
+if __name__ == "__main__":
+	logging.basicConfig(level=logging.INFO)
+	main()

scripts/z-band-fixed-magnitude-middle/widesquare.py

@@ -0,0 +1,117 @@
+from pdme.model.fixed_magnitude_model import FixedMagnitudeModel, FixedMagnitudeDiscretisation
+from pdme.measurement import OscillatingDipole, OscillatingDipoleArrangement
+import itertools
+import logging
+import multiprocessing
+import numpy
+import csv
+import random
+
+
+FILENAME = "z-band-fixed-magnitude-middle-all-dots-wide-square.csv"
+csv_fields = ["dipole_mom", "dipole_loc", "dipole_freq", "low_success", "low_count", "medium_success", "medium_count", "high_success", "high_count"]
+
+
+def get_uniform_sphere():
+	r = 6
+	a = random.uniform(-10, 10)
+	b = random.uniform(-10, 10)
+	c = random.uniform(-10, 10)
+	f = (a**2 + b**2 + c**2)**.5
+	return (a * r / f, b * r / f, c * r / f)
+
+
+def get_pt():
+	return (get_uniform_sphere(), (random.uniform(-10, 10), random.uniform(-10, 10), random.uniform(3.5, 4.5)))
+
+
+def get_a_result(discretisation, dots, index):
+	return (index, discretisation.solve_for_index(dots, index))
+
+
+def main():
+	
+	with open(FILENAME, "a", newline="") as outfile:
+		# csv fields
+		writer = csv.DictWriter(outfile, fieldnames=csv_fields, dialect='unix')
+		writer.writeheader()
+	
+	for run in range(1, 101):
+		
+		p_pts, s_pts = get_pt()
+		dipoles = OscillatingDipoleArrangement([OscillatingDipole(p_pts, s_pts, run)])
+		logging.info(f"gonna work on point {(p_pts, s_pts, run)}")
+		dot_inputs = list(itertools.chain.from_iterable(
+			(([-2, 2, 0], f), ([-2, -2, 0], f), ([2, -2, 0], f), ([2, 2, 0], f)) for f in numpy.arange(1, 10, 2)
+		))
+		dots = dipoles.get_dot_measurements(dot_inputs)
+
+		model_low = FixedMagnitudeModel(-10, 10, -10, 10, 2.5, 3.5, 6, 1)
+		discretisation_low = FixedMagnitudeDiscretisation(model_low, 6, 6, 5, 5, 5)
+
+		model_medium = FixedMagnitudeModel(-10, 10, -10, 10, 3.5, 4.5, 6, 1)
+		discretisation_medium = FixedMagnitudeDiscretisation(model_medium, 6, 6, 5, 5, 5)
+
+		model_high = FixedMagnitudeModel(-10, 10, -10, 10, 4.5, 5.5, 6, 1)
+		discretisation_high = FixedMagnitudeDiscretisation(model_high, 6, 6, 5, 5, 5)
+		
+		with multiprocessing.Pool(multiprocessing.cpu_count()-1 or 1) as pool:
+			results_low = pool.starmap(get_a_result, zip(itertools.repeat(discretisation_low), itertools.repeat(dots), discretisation_low.all_indices()))
+
+		with multiprocessing.Pool(multiprocessing.cpu_count()-1 or 1) as pool:
+			results_medium = pool.starmap(get_a_result, zip(itertools.repeat(discretisation_medium), itertools.repeat(dots), discretisation_medium.all_indices()))
+
+		with multiprocessing.Pool(multiprocessing.cpu_count()-1 or 1) as pool:
+			results_high = pool.starmap(get_a_result, zip(itertools.repeat(discretisation_high), itertools.repeat(dots), discretisation_high.all_indices()))
+		
+		count_low = 0
+		success_low = 0
+		for idx, result in results_low:
+			count_low += 1
+			if result.success and result.cost <= 1e-10 and numpy.linalg.norm(result.x[0:3]) < 10:
+				answer = result.normalised_x
+				success_low += 1
+			else:
+				answer = None
+
+		count_medium = 0
+		success_medium = 0
+		for idx, result in results_medium:
+			count_medium += 1
+			if result.success and result.cost <= 1e-10 and numpy.linalg.norm(result.x[0:3]) < 10:
+				answer = result.normalised_x
+				success_medium += 1
+			else:
+				answer = None
+
+		count_high = 0
+		success_high = 0
+		for idx, result in results_high:
+			count_high += 1
+			if result.success and result.cost <= 1e-10 and numpy.linalg.norm(result.x[0:3]) < 10:
+				answer = result.normalised_x
+				success_high += 1
+			else:
+				answer = None
+
+		logging.info(f"Low   : Out of {count_low} cells, {success_low} were successful")
+		logging.info(f"Medium: Out of {count_medium} cells, {success_medium} were successful")
+		logging.info(f"High  : Out of {count_high} cells, {success_high} were successful")
+		
+		with open(FILENAME, "a", newline='') as outfile:
+			writer = csv.DictWriter(outfile, fieldnames=csv_fields, dialect='unix')
+			writer.writerow({
+				"dipole_mom": p_pts,
+				"dipole_loc": s_pts,
+				"dipole_freq": run,
+				"low_success": success_low,
+				"high_success": success_high,
+				"medium_success": success_medium,
+				"low_count": count_low,
+				"medium_count": count_medium,
+				"high_count": count_high
+			})
+
+if __name__ == "__main__":
+	logging.basicConfig(level=logging.INFO)
+	main()

z-band-fixed-dipole-middle-all-dots-narrower-square.csv

@@ -0,0 +1,102 @@
+"dipole_mom","dipole_loc","dipole_freq","low_success","low_count","medium_success","medium_count","high_success","high_count"
+"dipole_mom","dipole_loc","dipole_freq","low_success","low_count","medium_success","medium_count","high_success","high_count"
+"(1, 1, 1)","(-1.3071476997121163, -6.700249117765953, 4.395652427243794)","1","65","125","68","125","73","125"
+"(1, 1, 1)","(7.218372433770103, -5.4783551032463755, 3.5820519422486634)","2","75","125","71","125","63","125"
+"(1, 1, 1)","(2.670117263667258, -9.627026891446988, 4.003539768646438)","3","77","125","81","125","76","125"
+"(1, 1, 1)","(2.3513316333181518, -8.402829356877447, 4.419760582254243)","4","87","125","98","125","90","125"
+"(1, 1, 1)","(-2.9839225924046575, -6.141574546943785, 4.1041288625417485)","5","73","125","87","125","76","125"
+"(1, 1, 1)","(-4.204110846621358, 2.5303736517209057, 4.048769088470612)","6","95","125","98","125","97","125"
+"(1, 1, 1)","(2.3951582053250107, -3.806262247740051, 3.52835893773293)","7","42","125","53","125","51","125"
+"(1, 1, 1)","(4.614882297991274, -8.808238152984519, 3.7824650173104026)","8","90","125","97","125","92","125"
+"(1, 1, 1)","(9.855038420690349, -5.756988885735215, 4.02622426234394)","9","63","125","63","125","60","125"
+"(1, 1, 1)","(-1.975488734839292, 1.1919182845159497, 3.6993525693957134)","10","5","125","5","125","1","125"
+"(1, 1, 1)","(4.392293449091486, 8.928201833428023, 4.054857054102779)","11","39","125","47","125","51","125"
+"(1, 1, 1)","(-0.8851390479842447, -8.799158377226185, 4.401733682923287)","12","67","125","66","125","66","125"
+"(1, 1, 1)","(0.42620076797180495, -1.6572190172596173, 4.26833391853475)","13","4","125","9","125","8","125"
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z-band-fixed-dipole-middle-all-dots-square.csv

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z-band-fixed-magnitude-middle-all-dots-narrower-square.csv

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z-band-fixed-magnitude-middle-all-dots-square.csv

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z-band-fixed-magnitude-middle-all-dots-wide-square.csv

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