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  {
   "cell_type": "markdown",
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   "source": [
    "# Refine lattice from 3 reflections\n",
    "\n",
    "**NOTE**: work-in-progress\n",
    "\n",
    "The lattice parameters of a sample can be computed from a set of 3 or more\n",
    "reflections if the **solver** provides such a method.  The hkl_soleil solver\n",
    "uses a simplex.  The computed lattice is likely the lowest symmetry since the\n",
    "parameters are refined to meet best the observed reflections."
   ]
  },
  {
   "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 3 reflections\n",
    "\n",
    "At least three reflections are needed to refine the lattice parameters.  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 three non-parallel reflections.  Here, just the values of the pseudos and reals are\n",
    "specified as Python tuples, in the exact order expected by the *solver*\n",
    "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)\")\n",
    "r001 = diffractometer.add_reflection((0, 0, 1), (-145.451, -85, -95, 69.0966), name=\"(001)\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Compute refined lattice\n",
    "\n",
    "Compute the lattice refined with these three reflections.  Notice that the refined lattice is triclinic and not the original cubic symmetry."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Lattice(a=0.885, b=0.8953, c=0.8987, alpha=79.9999, beta=85.0196, gamma=89.5632, system='triclinic')"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lattice = diffractometer.operator.refine_lattice([r100, r010, r001])\n",
    "lattice"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The `refine_lattice()` method returns the refined lattice but does not actually change the sample lattice:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Lattice(a=1, system='cubic')"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "diffractometer.sample.lattice"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Change the sample lattice\n",
    "\n",
    "The sample lattice can be changed with the refined lattice:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Lattice(a=0.885, b=0.8953, c=0.8987, alpha=79.9999, beta=85.0196, gamma=89.5632, system='triclinic')"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "diffractometer.sample.lattice = lattice\n",
    "diffractometer.sample.lattice"
   ]
  }
 ],
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