Cartans.ipynb

CartansTest.ipynb

{
  "cells": [
    {
      "metadata": {
        "trusted": true
      },
      "cell_type": "code",
      "source": "from clifford.tools import orthoFrames2Verser as cartan\nfrom clifford.tools.g3c import * \nfrom clifford.tools.g3 import generate_rotation_rotor\nfrom scipy import e,rand\nimport numpy as np",
      "execution_count": 1,
      "outputs": []
    },
    {
      "metadata": {
        "trusted": true
      },
      "cell_type": "code",
      "source": "def cartans_lines(line_list_a, line_list_b):\n    V_found,rs = cartan(A=line_list_a,B=line_list_b)\n    e123inf =e123*einf \n    theta = ((V_found*~V_found)*e1234)(0)\n    V_found = e**(-theta/2*e123inf)*V_found\n    return V_found",
      "execution_count": 2,
      "outputs": []
    },
    {
      "metadata": {
        "trusted": true
      },
      "cell_type": "code",
      "source": "n_objects_used = 5\n\ncomponent_errors = []\nfor i in range(1000):\n\n    line_list_a = [random_line() for i in range(n_objects_used)]\n    r = generate_translation_rotor(random_euc_mv())*generate_rotation_rotor(np.random.randn(),random_euc_mv().normal(), random_euc_mv().normal())\n    line_list_b = [(r*l*~r).normal() for l in line_list_a]\n    V_found = cartans_lines(line_list_a, line_list_b)\n    line_list_c = [(V_found*l*~V_found).normal() for l in line_list_a]\n    for b,c in zip(line_list_b,line_list_c):\n        component_errors.append(np.max(np.abs(b.value - c.value)))",
      "execution_count": 36,
      "outputs": []
    },
    {
      "metadata": {
        "trusted": true
      },
      "cell_type": "code",
      "source": "print(max(component_errors))\nprint(np.mean(component_errors))",
      "execution_count": 37,
      "outputs": [
        {
          "output_type": "stream",
          "text": "0.5888467065055061\n0.002065627867944979\n",
          "name": "stdout"
        }
      ]
    },
    {
      "metadata": {
        "trusted": true
      },
      "cell_type": "code",
      "source": "",
      "execution_count": 19,
      "outputs": [
        {
          "output_type": "stream",
          "text": "0\n0\n",
          "name": "stdout"
        }
      ]
    },
    {
      "metadata": {
        "trusted": true
      },
      "cell_type": "code",
      "source": "%%prun -s cumulative\nfor i in range(10000):\n    cartans_lines(line_list_a, line_list_b)",
      "execution_count": 38,
      "outputs": [
        {
          "output_type": "stream",
          "text": " ",
          "name": "stdout"
        }
      ]
    },
    {
      "metadata": {
        "trusted": true
      },
      "cell_type": "code",
      "source": "",
      "execution_count": null,
      "outputs": []
    }
  ],
  "metadata": {
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3",
      "language": "python"
    },
    "language_info": {
      "name": "python",
      "pygments_lexer": "ipython3",
      "codemirror_mode": {
        "name": "ipython",
        "version": 3
      },
      "version": "3.5.2",
      "mimetype": "text/x-python",
      "nbconvert_exporter": "python",
      "file_extension": ".py"
    },
    "gist": {
      "id": "7577011e2e73250edd59e4e836c9d6cc",
      "data": {
        "description": "Cartans.ipynb",
        "public": true
      }
    },
    "_draft": {
      "nbviewer_url": "https://gist.github.com/7577011e2e73250edd59e4e836c9d6cc"
    }
  },
  "nbformat": 4,
  "nbformat_minor": 2
}