{
  "cells": [
    {
      "cell_type": "markdown",
      "id": "5e003b6c-bd72-4460-9c2c-67d4771e11c0",
      "metadata": {},
      "source": [
        "# Kernel in the Source and Target Variables (\"Anterpolation and Interpolation\")\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>"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 52,
      "metadata": {},
      "outputs": [],
      "source": [
        "import numpy as np\n",
        "import numpy.linalg as la\n",
        "import matplotlib.pyplot as plt"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "362ce8f8-a607-4820-ab61-e85a6b9ec3c6",
      "metadata": {},
      "source": [
        "Some Chebyshev utilities up front:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 53,
      "metadata": {},
      "outputs": [
        {
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7fd6564a63c0>]"
            ]
          },
          "execution_count": 53,
          "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": [
        "def Tk(k, x):\n",
        "    return np.cos(k*np.arccos(x))\n",
        "\n",
        "nnodes = 20\n",
        "k = nnodes-1\n",
        "nodes = np.cos(np.arange(k+1)/k*np.pi)\n",
        "\n",
        "xplot = np.linspace(-1, 1, 1000)\n",
        "plt.plot(xplot, Tk(k, xplot))\n",
        "plt.plot(nodes, Tk(k, nodes), \"x\")\n"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "fcd40508-caed-4d46-9166-6477d1715e0f",
      "metadata": {},
      "source": [
        "Now construct an interpolation toolkit with `vdm(targets)` and `interp_to_targets(targets, nodes)`, and test it:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 73,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "1.330113796882415e-11\n"
          ]
        }
      ],
      "source": [
        "def vdm(targets):\n",
        "    return Tk(np.arange(k+1), targets[:, None])\n",
        "        \n",
        "def interp_to_targets(targets, nodes):\n",
        "    return vdm(targets) @ la.inv(vdm(nodes))\n",
        "\n",
        "print(la.norm(np.sin(5*xplot) - interp_to_targets(xplot, nodes)@np.sin(5*nodes), np.inf))"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 74,
      "metadata": {},
      "outputs": [],
      "source": [
        "N = 1000\n",
        "sources = np.random.rand(N) * 2 - 1\n",
        "charges = np.random.randn(N)\n",
        "\n",
        "targets = np.random.rand(N)*2 - 1 - 4\n",
        "\n",
        "def interaction_mat(targets, sources):\n",
        "    return np.log(np.abs(targets[:, None] - sources))"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "271569f8-7542-4528-9b52-cf377e08b196",
      "metadata": {},
      "source": [
        "Try out target-space interpolation as a matrix identity:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 75,
      "metadata": {},
      "outputs": [
        {
          "data": {
            "text/plain": [
              "np.float64(6.222583118946094e-13)"
            ]
          },
          "execution_count": 75,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "tgt_nodes = nodes - 4\n",
        "la.norm(\n",
        "    interp_to_targets(targets+4, tgt_nodes+4) @ interaction_mat(tgt_nodes, sources)\n",
        "    -\n",
        "    interaction_mat(targets, sources),\n",
        "    2\n",
        ")"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "fb96a61c-8864-4b90-8d26-355bc2678b95",
      "metadata": {},
      "source": [
        "Now try out source interpolation (\"anterpolation\") as a matrix identity:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 76,
      "metadata": {},
      "outputs": [
        {
          "data": {
            "text/plain": [
              "np.float64(6.806409517866512e-13)"
            ]
          },
          "execution_count": 76,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "la.norm(\n",
        "    interaction_mat(targets, nodes) @ interp_to_targets(sources, nodes).T\n",
        "    -\n",
        "    interaction_mat(targets, sources), \n",
        "    2)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": []
    }
  ],
  "metadata": {
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      "codemirror_mode": {
        "name": "ipython",
        "version": 3
      },
      "file_extension": ".py",
      "mimetype": "text/x-python",
      "name": "python",
      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
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