{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# **hkl_soleil** E6C test of calculations\n",
    "\n",
    "Non-exhaustive tests of *hkl_soleil* {ref}`E6C <geometries-hkl_soleil-e6c>` computations of orientation, U, UB,\n",
    "and rotation directions, with the aid of Yong Chu's mental math.\n",
    "\n",
    "[TL;DR](https://www.merriam-webster.com/dictionary/TL%3BDR) E6C appears to function\n",
    "as documented and as expected."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Create a simulated diffractometer for calculations\n",
    "\n",
    "These tests use a simulated diffractometer to test the solver's calculation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "import hklpy2\n",
    "\n",
    "e6c = hklpy2.creator(name=\"e6c\", geometry=\"E6C\")\n",
    "e6c.core.solver.mode = 'constant_chi_vertical'\n",
    "e6c.wavelength.put(1.)  # Angstrom"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Setup the crystal lattice\n",
    "\n",
    "Use the default `sample`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "e6c.sample=Sample(name='sample', lattice=Lattice(a=1, system='cubic'))\n",
      "h=0, k=0, l=0\n",
      "wavelength=1.0\n",
      "mu=0, omega=0, chi=0, phi=0, gamma=0, delta=0\n"
     ]
    }
   ],
   "source": [
    "print(f\"{e6c.sample=}\")\n",
    "e6c.wh()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Compute the **UB** matrix from two reflections"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[[6.283183866345, 2.367192e-06, 0.0],\n",
       " [0.0, 6.28318625087, 0.0],\n",
       " [2.66395e-07, -1.611768e-06, 6.283184307075]]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# checking orientation of delta\n",
    "r1p = dict(mu=0.0, omega=30.0, chi=0.0, phi=0.0, gamma=0., delta=60.)\n",
    "r1 = e6c.add_reflection((0, 0, 1), r1p)\n",
    "r2p = dict(mu=0.0, omega=120.0, chi=0.0, phi=0.0, gamma=0, delta=60.)\n",
    "r2 = e6c.add_reflection((1, 0, 0), r2p)\n",
    "e6c.core.calc_UB(r1, r2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Show the computed **U** matrix\n",
    "\n",
    "**Note**:  Here, $U=I$, where $I$ is the identity matrix."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[[1.0, 0.0, -4.2398e-08],\n",
       " [0.0, 1.0, 2.56521e-07],\n",
       " [4.2398e-08, -2.56521e-07, 1.0]]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "e6c.sample.U"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Show the computed **UB** matrix\n",
    "\n",
    "**Note**:  Here, $UB=2\\pi\\cdot I$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[[6.283183866345, 2.367192e-06, 0.0],\n",
       " [0.0, 6.28318625087, 0.0],\n",
       " [2.66395e-07, -1.611768e-06, 6.283184307075]]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "e6c.sample.UB"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Calculate various (_hkl_) given motor positions\n",
    "\n",
    "This is the `inverse()` transformation.\n",
    "\n",
    "### (010)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "expecting (0,1,0)= Hklpy2DiffractometerPseudoPos(h=-3.7675e-07, k=0.999999849807, l=2.56521e-07)\n"
     ]
    }
   ],
   "source": [
    "pos = e6c.inverse(dict(mu=0.0, omega=30.0, chi=90.0, phi=0.0, gamma=0, delta=60.))\n",
    "print('expecting (0,1,0)=', pos)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "expecting (0,1,0)= Hklpy2DiffractometerPseudoPos(h=-3.7675e-07, k=0.999999849807, l=2.56521e-07)\n"
     ]
    }
   ],
   "source": [
    "# alternate settings for same reflection\n",
    "pos = e6c.inverse(dict(mu=30.0, omega=0.0, chi=0.0, phi=0.0, gamma=60., delta=0.))\n",
    "print('expecting (0,1,0)=', pos)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### (0 -1 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "expecting (0,-1,0)= Hklpy2DiffractometerPseudoPos(h=3.7675e-07, k=-0.999999849807, l=-2.56521e-07)\n"
     ]
    }
   ],
   "source": [
    "pos = e6c.inverse(dict(mu=0, omega=30., chi=-90.0, phi=0.0, gamma=0., delta=60.))\n",
    "print('expecting (0,-1,0)=', pos)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### (-1 0 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "expecting (-1,0,0)= Hklpy2DiffractometerPseudoPos(h=-1.000000229316, k=0, l=4.2398e-08)\n"
     ]
    }
   ],
   "source": [
    "pos = e6c.inverse(dict(mu=0.0, omega=-60.0, chi=0.0, phi=0.0, gamma=0, delta=60.))\n",
    "print('expecting (-1,0,0)=', pos)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Diffracting upside-down now\n",
    "\n",
    "Note that omega and phi only need to sum to +/-120\n",
    "($\\omega+\\varphi = \\pm |120|$), which reflects what\n",
    "the inverse calculations from the library give."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### (100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "expecting (1,0,0)= Hklpy2DiffractometerPseudoPos(h=1.000000229316, k=0, l=-4.2398e-08)\n",
      "expecting (1,0,0)= Hklpy2DiffractometerPseudoPos(h=1.000000229316, k=0, l=-4.2398e-08)\n",
      "expecting (1,0,0)= Hklpy2DiffractometerPseudoPos(h=1.000000229316, k=0, l=-4.2398e-08)\n"
     ]
    }
   ],
   "source": [
    "pos = e6c.inverse(dict(mu=0.0, omega=-50.0, chi=0.0, phi=-70.0, gamma=0, delta=-60.))\n",
    "print('expecting (1,0,0)=', pos)\n",
    "\n",
    "pos = e6c.inverse(dict(mu=0.0, omega=-100.0, chi=0.0, phi=-20.0, gamma=0, delta=-60.))\n",
    "print('expecting (1,0,0)=', pos)\n",
    "\n",
    "pos = e6c.inverse(dict(mu=0.0, omega=100.0, chi=0.0, phi=-220.0, gamma=0, delta=-60.))\n",
    "print('expecting (1,0,0)=', pos)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### (011)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "expecting (0,1,1)= Hklpy2DiffractometerPseudoPos(h=-3.7675e-07, k=0.999999849807, l=1.000000415693)\n"
     ]
    }
   ],
   "source": [
    "pos = e6c.inverse(dict(mu=0.0, omega=45.0, chi=45.0, phi=0.0, gamma=0, delta=90.))\n",
    "print('expecting (0,1,1)=', pos)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Verify that $\\omega+\\varphi = \\pm 120$ is kept.\n",
    "\n",
    "Calculate all allowed combinations of motor positions, given $hkl$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "expecting either omega+phi = 120 or -120 (approximately)\n",
      "0 Hklpy2DiffractometerRealPos(mu=0, omega=119.999992124449, chi=45.0, phi=-2.429236e-06, gamma=0, delta=59.999984419525)\n",
      "1 Hklpy2DiffractometerRealPos(mu=0, omega=-119.999992124449, chi=45.0, phi=-2.429236e-06, gamma=0, delta=-59.999984419525)\n",
      "2 Hklpy2DiffractometerRealPos(mu=0, omega=-60.000007875551, chi=45.0, phi=-179.999997570764, gamma=0, delta=59.999984419525)\n",
      "3 Hklpy2DiffractometerRealPos(mu=0, omega=60.000007875551, chi=45.0, phi=-179.999997570764, gamma=0, delta=-59.999984419525)\n"
     ]
    }
   ],
   "source": [
    "print(\"expecting either omega+phi = 120 or -120 (approximately)\")\n",
    "solutions = e6c.core.forward([1, 0, 0])\n",
    "for i, sol in enumerate(solutions):\n",
    "    print(i, sol)"
   ]
  }
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