{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# How to compute a pointwise map from a functional map?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import geomstats.backend as gs\n",
    "\n",
    "from geomfum.convert import P2pFromFmConverter\n",
    "from geomfum.dataset import NotebooksDataset\n",
    "from geomfum.shape import TriangleMesh"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[Load meshes](00_load_mesh_from_file.ipynb)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(7207, 5000)"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dataset = NotebooksDataset()\n",
    "\n",
    "mesh_a = TriangleMesh.from_file(dataset.get_filename(\"cat-00\"))\n",
    "mesh_b = TriangleMesh.from_file(dataset.get_filename(\"lion-00\"))\n",
    "\n",
    "mesh_a.n_vertices, mesh_b.n_vertices"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[Set Laplace eigenbasis](./02_mesh_laplacian_spectrum.ipynb) for each mesh."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "mesh_a.laplacian.find_spectrum(spectrum_size=6, set_as_basis=True)\n",
    "mesh_b.laplacian.find_spectrum(spectrum_size=6, set_as_basis=True)\n",
    "\n",
    "mesh_b.basis.use_k = 5"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Assume we have a [valid functional map](./07_functional_map.ipynb) $C$ between `mesh_a` and `mesh_b` (which for demonstration purposes, we instantiate randomly)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(5, 6)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fmap_matrix = gs.random.uniform(\n",
    "    size=(mesh_b.basis.spectrum_size, mesh_a.basis.spectrum_size)\n",
    ")\n",
    "\n",
    "fmap_matrix.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Compute pointwise map."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(5000,)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p2p_converter = P2pFromFmConverter()\n",
    "\n",
    "p2p = p2p_converter(fmap_matrix, mesh_a.basis, mesh_b.basis)\n",
    "\n",
    "p2p.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The adjoint method can be used by setting `adjoint`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(5000,)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p2p_converter.adjoint = True\n",
    "\n",
    "p2p = p2p_converter(fmap_matrix, mesh_a.basis, mesh_b.basis)\n",
    "\n",
    "p2p.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The bijective method can be use by setting `bijective`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(7207,)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p2p_converter.bijective = True\n",
    "\n",
    "p2p = p2p_converter(fmap_matrix, mesh_a.basis, mesh_b.basis)\n",
    "\n",
    "p2p.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Further reading\n",
    "\n",
    "* [How to compute a functional map from a pointwise map?](./09_functional_from_pointwise.ipynb)\n",
    "\n",
    "* [How to compute a functional map?](./07_functional_map.ipynb)"
   ]
  }
 ],
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