{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# How to compute a functional map from a pointwise map?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import geomstats.backend as gs\n",
    "import numpy as np\n",
    "\n",
    "from geomfum.convert import FmFromP2pBijectiveConverter, FmFromP2pConverter\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 pointwise map](./10_pointwise_from_functional.ipynb) between `mesh_a` and `mesh_b` (which for demonstration purposes, we instantiate randomly)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(5000,)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p2p_12 = gs.from_numpy(np.random.choice(mesh_a.n_vertices, size=mesh_b.n_vertices))\n",
    "\n",
    "p2p_12.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Compute functional map."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(5, 6)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fm_converter = FmFromP2pConverter()\n",
    "\n",
    "fmap_matrix = fm_converter(p2p_12, mesh_a.basis, mesh_b.basis)\n",
    "\n",
    "fmap_matrix.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The `pseudo_inverse` can be used instead."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(5, 6)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fm_converter.pseudo_inverse = True\n",
    "\n",
    "fmap_matrix = fm_converter(p2p_12, mesh_a.basis, mesh_b.basis)\n",
    "\n",
    "fmap_matrix.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The bijective method can be used using a different converter."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(7207,)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p2p_21 = gs.from_numpy(np.random.choice(mesh_b.n_vertices, size=mesh_a.n_vertices))\n",
    "\n",
    "p2p_21.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(5, 6)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fm_bij_converter = FmFromP2pBijectiveConverter()\n",
    "\n",
    "fmap_matrix = fm_bij_converter(p2p_21, mesh_a.basis, mesh_b.basis)\n",
    "\n",
    "fmap_matrix.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Further reading\n",
    "\n",
    "* [How to compute a pointwise map from a functional map?](./10_pointwise_from_functional.ipynb)\n",
    "\n",
    "* [How to compute a functional map?](./07_functional_map.ipynb)"
   ]
  }
 ],
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