{
    "cells": [
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "# How to compute the mesh Laplacian?"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 1,
            "metadata": {},
            "outputs": [],
            "source": [
                "from geomfum.dataset import NotebooksDataset\n",
                "from geomfum.laplacian import LaplacianFinder\n",
                "from geomfum.shape import TriangleMesh"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "[Load a mesh](00_load_mesh_from_file.ipynb)."
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 2,
            "metadata": {},
            "outputs": [],
            "source": [
                "dataset = NotebooksDataset()\n",
                "mesh = TriangleMesh.from_file(dataset.get_filename(\"cat-00\"))"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "Find Laplacian."
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 6,
            "metadata": {},
            "outputs": [],
            "source": [
                "laplacian_finder = LaplacianFinder()"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 7,
            "metadata": {},
            "outputs": [
                {
                    "data": {
                        "text/plain": [
                            "((7207, 7207), (7207, 7207))"
                        ]
                    },
                    "execution_count": 7,
                    "metadata": {},
                    "output_type": "execute_result"
                }
            ],
            "source": [
                "stiffness_matrix, mass_matrix = laplacian_finder(mesh)\n",
                "\n",
                "(stiffness_matrix.shape, mass_matrix.shape)"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "Tip: different algorithms can be used by changing `which` (check docs for possibilities)."
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "Syntax sugar:"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 8,
            "metadata": {},
            "outputs": [
                {
                    "data": {
                        "text/plain": [
                            "((7207, 7207), (7207, 7207))"
                        ]
                    },
                    "execution_count": 8,
                    "metadata": {},
                    "output_type": "execute_result"
                }
            ],
            "source": [
                "mesh.laplacian.find(laplacian_finder=laplacian_finder, recompute=False)\n",
                "\n",
                "(mesh.laplacian.stiffness_matrix.shape, mesh.laplacian.mass_matrix.shape)"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "## Further reading\n",
                "\n",
                "* [How to compute the mesh Laplacian spectrum?](./02_mesh_laplacian_spectrum.ipynb)"
            ]
        }
    ],
    "metadata": {
        "kernelspec": {
            "display_name": "venv",
            "language": "python",
            "name": "python3"
        },
        "language_info": {
            "codemirror_mode": {
                "name": "ipython",
                "version": 3
            },
            "file_extension": ".py",
            "mimetype": "text/x-python",
            "name": "python",
            "nbconvert_exporter": "python",
            "pygments_lexer": "ipython3",
            "version": "3.11.8"
        }
    },
    "nbformat": 4,
    "nbformat_minor": 2
}