{
  "cells": [
    {
      "cell_type": "markdown",
      "id": "9284b7ba-a0eb-444d-b72c-6231e6c70ebb",
      "metadata": {},
      "source": [
        "# PN vs QN\n",
        "\n",
        "Copyright (C) 2026 Andreas Kloeckner\n",
        "\n",
        "<details>\n",
        "<summary>MIT License</summary>\n",
        "Permission is hereby granted, free of charge, to any person obtaining a copy\n",
        "of this software and associated documentation files (the \"Software\"), to deal\n",
        "in the Software without restriction, including without limitation the rights\n",
        "to use, copy, modify, merge, publish, distribute, sublicense, and/or sell\n",
        "copies of the Software, and to permit persons to whom the Software is\n",
        "furnished to do so, subject to the following conditions:\n",
        "\n",
        "The above copyright notice and this permission notice shall be included in\n",
        "all copies or substantial portions of the Software.\n",
        "\n",
        "THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n",
        "IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n",
        "FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE\n",
        "AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n",
        "LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,\n",
        "OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN\n",
        "THE SOFTWARE.\n",
        "</details>\n",
        "\n",
        "---\n",
        "\n",
        "Based on [Cubature, Approximation, and Isotropy in the Hypercube](https://10.1137/16M1066312). (Trefethen)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 19,
      "metadata": {},
      "outputs": [],
      "source": [
        "import numpy as np\n",
        "import numpy.linalg as la\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "import modepy as mp\n",
        "import modepy.tools as mp_tools"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 32,
      "metadata": {},
      "outputs": [
        {
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7f2816c50c20>]"
            ]
          },
          "execution_count": 32,
          "metadata": {},
          "output_type": "execute_result"
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "shape = mp.Hypercube(2)\n",
        "space = mp.QN(2, 60)\n",
        "\n",
        "nodes = mp.edge_clustered_nodes_for_space(space, shape)\n",
        "basis = mp.basis_for_space(space, shape)\n",
        "\n",
        "plt.plot(nodes[0], nodes[1], \"o\")"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 52,
      "metadata": {},
      "outputs": [],
      "source": [
        "vdm = mp.vandermonde(basis.functions, nodes)\n",
        "\n",
        "r = la.norm(nodes, 2, axis=0)\n",
        "gauss_coeffs = la.solve(vdm, np.exp(-(r/0.2)**2))"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 53,
      "metadata": {},
      "outputs": [],
      "source": [
        "coeffs_reshaped = mp_tools.reshape_array_for_tensor_product_space(space, gauss_coeffs, axis=0)\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 54,
      "metadata": {},
      "outputs": [
        {
          "data": {
            "text/plain": [
              "<matplotlib.colorbar.Colorbar at 0x7f281657d160>"
            ]
          },
          "execution_count": 54,
          "metadata": {},
          "output_type": "execute_result"
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 640x480 with 2 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "plt.imshow(np.log10(1e-15+np.abs(coeffs_reshaped)))\n",
        "plt.colorbar()\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 55,
      "metadata": {},
      "outputs": [
        {
          "data": {
            "text/plain": [
              "<matplotlib.colorbar.Colorbar at 0x7f28166252b0>"
            ]
          },
          "execution_count": 55,
          "metadata": {},
          "output_type": "execute_result"
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 640x480 with 2 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "plt.imshow(np.log10(1e-15+np.abs(coeffs_reshaped[::2, ::2])))\n",
        "plt.colorbar()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": []
    }
  ],
  "metadata": {
    "kernelspec": {
      "display_name": "Python 3 (ipykernel)",
      "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": "3.14.7"
    }
  },
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