charged-shells/rotational_path.py

import numpy as np
from dataclasses import dataclass, field
import quaternionic
import expansion
from parameters import ModelParams
import interactions
import matplotlib.pyplot as plt
from pathlib import Path


Quaternion = quaternionic.array
Array = np.ndarray
Expansion = expansion.Expansion


@dataclass
class PairRotationalPath:

    rotations1: list[Quaternion] = field(default_factory=list)
    rotations2: list[Quaternion] = field(default_factory=list)
    x_axis: list[Array] = field(default_factory=list)
    overlapping_last: bool = True
    _default_x_axis: Array = None

    def add(self, rotation1: Quaternion, rotation2: Quaternion, x_axis: Array = None):
        rotation1, rotation2 = np.broadcast_arrays(rotation1, rotation2)
        self.rotations1.append(Quaternion(rotation1))
        self.rotations2.append(Quaternion(rotation2))
        if x_axis is None:
            x_axis = np.arange(len(rotation1)) if self._default_x_axis is None else self._default_x_axis
        self.add_x_axis(x_axis)

    def add_x_axis(self, x_axis: Array):
        try:
            last_x_val = self.x_axis[-1][-1]
        except IndexError:
            last_x_val = 0
        if self.overlapping_last:
            self.x_axis.append(x_axis + last_x_val)
        else:
            raise NotImplementedError('Currently only overlapping end points for x-axes are supported.')

    def set_default_x_axis(self, default_x_axis: Array):
        self._default_x_axis = default_x_axis

    def add_euler(self, *, alpha1: Array = 0, beta1: Array = 0, gamma1: Array = 0,
                  alpha2: Array = 0, beta2: Array = 0, gamma2: Array = 0,
                  x_axis: Array = None):
        R1_euler = quaternionic.array.from_euler_angles(alpha1, beta1, gamma1)
        R2_euler = quaternionic.array.from_euler_angles(alpha2, beta2, gamma2)
        self.add(Quaternion(R1_euler), Quaternion(R2_euler), x_axis)

    def stack_rotations(self) -> (Quaternion, Quaternion):
        return Quaternion(np.vstack(self.rotations1)), Quaternion(np.vstack(self.rotations2))

    def stack_x_axes(self) -> Array:
        return np.hstack(self.x_axis)


@dataclass
class PathEnergyPlot:
    """Path comparison for a pair of charge distributions, possibly at different parameter values."""

    expansion1: Expansion
    expansion2: Expansion
    rot_path: PairRotationalPath
    dist: float | Array
    params: ModelParams

    def __post_init__(self):
        if not isinstance(self.dist, Array):
            self.dist = np.array([self.dist])

    def evaluate_energy(self):
        energy = []
        for dist in self.dist:
            for params in self.params.unravel():
                energy.append(interactions.charged_shell_energy(self.expansion1, self.expansion2, dist, params))
        return np.squeeze(np.stack(energy, axis=-1))

    def path_energy(self):
        rotations1, rotations2 = self.rot_path.stack_rotations()
        self.expansion1.rotate(rotations1)
        self.expansion2.rotate(rotations2)
        return self.evaluate_energy()

    def section_energies(self):
        energy_list = []
        for rot1, rot2 in zip(self.rot_path.rotations1, self.rot_path.rotations2):
            self.expansion1.rotate(rot1)
            self.expansion2.rotate(rot2)
            energy_list.append(self.evaluate_energy())
        return energy_list

    def normalization(self, norm_euler_angles: dict):
        if norm_euler_angles is None:
            return np.array([1.])
        self.expansion1.rotate_euler(alpha=norm_euler_angles.get('alpha1', 0),
                                     beta=norm_euler_angles.get('beta1', 0),
                                     gamma=norm_euler_angles.get('gamma1', 0))
        self.expansion2.rotate_euler(alpha=norm_euler_angles.get('alpha2', 0),
                                     beta=norm_euler_angles.get('beta2', 0),
                                     gamma=norm_euler_angles.get('gamma2', 0))
        return np.abs(self.evaluate_energy())

    def evaluate_path(self, norm_euler_angles: dict = None):
        energy = self.path_energy()
        normalization = self.normalization(norm_euler_angles)
        energy = energy / normalization[None, ...]
        energy = energy.reshape(energy.shape[0], -1)
        return np.squeeze(energy)

    def plot(self, labels: list[str] = None, norm_euler_angles: dict = None, save_as: Path = None):
        energy = self.evaluate_path(norm_euler_angles=norm_euler_angles)
        x_axis = self.rot_path.stack_x_axes()

        fig, ax = plt.subplots()
        ax.axhline(y=0, c='k', linestyle=':')
        ax.plot(x_axis, np.squeeze(energy), label=labels)
        ax.legend(fontsize=12)
        ax.tick_params(which='both', direction='in', top=True, right=True, labelsize=12)
        ax.set_xlabel('angle', fontsize=13)
        ax.set_ylabel('U', fontsize=13)
        plt.tight_layout()
        if save_as is not None:
            plt.savefig(save_as, dpi=600)
        plt.show()

    def plot_sections(self, norm_euler_angles: dict = None, save_as: Path = None):
        energy_list = self.section_energies()
        normalization = self.normalization(norm_euler_angles)

        fig, ax = plt.subplots()
        ax.axhline(y=0, c='k', linestyle=':')
        for x_axis, energy in zip(self.rot_path.x_axis, energy_list):
            energy, norm = np.broadcast_arrays(energy, normalization)
            ax.plot(x_axis, energy / norm)
        # ax.legend(fontsize=12)
        ax.tick_params(which='both', direction='in', top=True, right=True, labelsize=12)
        ax.set_xlabel('angle', fontsize=13)
        ax.set_ylabel('U', fontsize=13)
        if save_as is not None:
            plt.savefig(save_as, dpi=600)
        plt.show()


@dataclass
class PathExpansionComparison:
    """Path comparison for different charge distribution models."""

    ex_list: list[Expansion]
    rot_path: PairRotationalPath
    dist: float
    params: ModelParams
    path_list: list[PathEnergyPlot] = field(default_factory=list)

    def __post_init__(self):
        for ex in self.ex_list:
            self.path_list.append(PathEnergyPlot(ex, ex.clone(), self.rot_path, self.dist, self.params))

    def evaluate_path(self, norm_euler_angles: dict = None):
        path_vals = []
        for path in self.path_list:
            path_vals.append(path.evaluate_path(norm_euler_angles))
        return np.stack(path_vals)

    def plot(self, labels: list[str] = None, norm_euler_angles: dict = None, save_as: Path = None):
        energy = self.evaluate_path(norm_euler_angles=norm_euler_angles)
        x_axis = self.rot_path.stack_x_axes()

        fig, ax = plt.subplots()
        ax.axhline(y=0, c='k', linestyle=':')
        ax.plot(x_axis, np.squeeze(energy).T, label=labels)
        ax.legend(fontsize=12)
        ax.tick_params(which='both', direction='in', top=True, right=True, labelsize=12)
        ax.set_xlabel('angle', fontsize=13)
        ax.set_ylabel('U', fontsize=13)
        plt.tight_layout()
        if save_as is not None:
            plt.savefig(save_as, dpi=600)
        plt.show()