<commit_before>{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# The Helmert transform\n",
    "$\n",
    "\\begin{bmatrix}\n",
    "    x\\\\\n",
    "    y\\\\\n",
    "    z\\\\\n",
    "\\end{bmatrix}^B\n",
    "=\n",
    "\\begin{bmatrix}\n",
    "    t_X\\\\\n",
    "    t_Y\\\\\n",
    "    t_Z\\\\\n",
    "\\end{bmatrix}\n",
    "+\n",
    "\\begin{bmatrix}\n",
    "    1+S  & -r_Z & r_Y\\\\\n",
    "    r_Z  & 1+s  & -r_X\\\\\n",
    "    -r_Y & r_X  & 1+S\\\\\n",
    "\\end{bmatrix}\n",
    "\\cdot\n",
    "\\begin{bmatrix}\n",
    "    x\\\\\n",
    "    y\\\\\n",
    "    z\\\\\n",
    "\\end{bmatrix}^A\n",
    "$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def helmert(x, y, z=0):\n",
    "    \"\"\" Example implementation of Helmert transform \"\"\"\n",<commit_msg>I can't remember what I did to this workbook. It's fine.<commit_after>{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# The Helmert transform\n",
    "$\n",
    "\\begin{bmatrix}\n",
    "    x\\\\\n",
    "    y\\\\\n",
    "    z\\\\\n",
    "\\end{bmatrix}^B\n",
    "=\n",
    "\\begin{bmatrix}\n",
    "    t_X\\\\\n",
    "    t_Y\\\\\n",
    "    t_Z\\\\\n",
    "\\end{bmatrix}\n",
    "+\n",
    "\\begin{bmatrix}\n",
    "    1+s  & -r_Z & r_Y\\\\\n",
    "    r_Z  & 1+s  & -r_X\\\\\n",
    "    -r_Y & r_X  & 1+s\\\\\n",
    "\\end{bmatrix}\n",
    "\\cdot\n",
    "\\begin{bmatrix}\n",
    "    x\\\\\n",
    "    y\\\\\n",
    "    z\\\\\n",
    "\\end{bmatrix}^A\n",
    "$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def helmert(x, y, z=0):\n",
    "    \"\"\" Example implementation of Helmert transform \"\"\"\n",
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{'dir': 'git-commits-cleaned', 'id': '5236551', 'n_tokens_mistral': 889, 'n_tokens_neox': 834, 'n_words': 125}