{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# UB matrix : calculate from 2 reflections.\n",
    "\n",
    "$UB$ is the 3x3 orientation matrix used to transform coordinates between\n",
    "reciprocal space directions (of the crystal lattice planes) and the rotational\n",
    "axes of the diffractometer."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Create a diffractometer object\n",
    "\n",
    "First, create a diffractometer object that uses the `\"hkl_soleil\"` solver with\n",
    "the `\"hkl\"` computation engine.  This solver provides support for many\n",
    "diffractometer geometries.  This example will use the simulated 4-circle\n",
    "geometry from the solver's `\"E4CV\"`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from hklpy2 import SimulatedE4CV\n",
    "\n",
    "diffractometer = SimulatedE4CV(name=\"diffractometer\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Defaults\n",
    "\n",
    "The diffractometer object starts with a default sample.  The structure is cubic ($a=b=c$, 90 degree corners)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Sample(name='sample', lattice=Lattice(a=1, system='cubic'))"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "diffractometer.sample"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Add 2 reflections\n",
    "\n",
    "Two reflections are needed to calculate $UB$.  Since we do not specify the wavelength, the support assumes the diffractometer's current wavelength."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "diffractometer.wavelength.get()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Add two non-parallel reflections.  Here, just the values of the pseudos and\n",
    "reals are specified as Python tuples, in the exact order expected by the\n",
    "*solver* geometry."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "r100 = diffractometer.add_reflection((1, 0, 0), (-145.451, 5, -5, 69.0966), name=\"(100)\")\n",
    "r010 = diffractometer.add_reflection((0, 1, 0), (-145.451, 5, 85, 69.0966), name=\"(010)\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Compute UB\n",
    "\n",
    "Compute $UB$ with these two reflections:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "diffractometer.operator.calcUB(r100, r010)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Show the calculated $UB$ matrix:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[[0.545455367746, -6.239787515781, -0.495931249329],\n",
       " [-0.547615682228, -0.543471605558, 6.235637359796],\n",
       " [-6.235464145574, -0.498104382852, -0.591013127949]]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "diffractometer.operator.solver.UB"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Try it out\n",
    "\n",
    " corresponding to the $(1,0,0)$ reflection:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "SimulatedE4CVRealPos(omega=-149.999999959667, chi=4.999999963097, phi=-4.999297295242, tth=60.000000080666)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "diffractometer.forward(1, 0, 0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Show the (first set of computed) angles corresponding to the $(1 \\bar1 1)$ reflection:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "SimulatedE4CVRealPos(omega=-119.999999996665, chi=-34.931758281633, phi=-44.822626886902, tth=120.00000000667)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "diffractometer.forward(1, -1, 1)"
   ]
  }
 ],
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