{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "overhead-silly",
   "metadata": {},
   "source": [
    "# Series RLC Circuit\n",
    "\n",
    "Such a circuit is defined by the following equations:\n",
    "\n",
    "$$\\begin{align}\n",
    "\\text{R}&: V_R = I_R R \\\\\n",
    "\\text{L}&: V_L = L\\frac{dI_L}{dt} \\\\\n",
    "\\text{C}&: I_C = C\\frac{dV_C}{dt}\n",
    "\\end{align}$$\n",
    "\n",
    "Additionally, there are the Kirchhoff equations:\n",
    "\n",
    "$$I_R = I_L = I_C \\equiv I \\\\\n",
    "V_R + V_L + V_C = 0$$\n",
    "\n",
    "These equations may be written more succintly as\n",
    "\n",
    "$$\\begin{align}\n",
    "\\text{R}&: V_R = IR \\\\\n",
    "\\text{L}&: \\frac{dI}{dt} = - (V_R + V_C) / L \\\\\n",
    "\\text{C}&: \\frac{dV_C}{dt} = I / C\n",
    "\\end{align}$$\n",
    "\n",
    "Then the needed variables are clear: (VR, I, VC), Where 2 equations are differential and 1 is algebraic"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "sorted-strain",
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from matplotlib import rc\n",
    "\n",
    "rc(\"font\", family=\"serif\", size=15)\n",
    "rc(\"savefig\", dpi=600)\n",
    "rc(\"figure\", figsize=(8, 6))\n",
    "rc(\"mathtext\", fontset=\"dejavuserif\")\n",
    "rc(\"lines\", linewidth=3)\n",
    "from networkx import DiGraph\n",
    "\n",
    "from stream import Aggregator, Calculation, unpacked"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "alert-franklin",
   "metadata": {},
   "outputs": [],
   "source": [
    "class R(Calculation):\n",
    "    def __init__(self, R):\n",
    "        self.R = R\n",
    "        self.name = \"R\"\n",
    "\n",
    "    @unpacked\n",
    "    def calculate(self, VR, *, I):\n",
    "        return VR - I * self.R\n",
    "\n",
    "    @property\n",
    "    def mass_vector(self):\n",
    "        return (False,)\n",
    "\n",
    "    @property\n",
    "    def variables(self):\n",
    "        return {\"VR\": 0}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "congressional-token",
   "metadata": {},
   "outputs": [],
   "source": [
    "class L(Calculation):\n",
    "    def __init__(self, L):\n",
    "        self.L = L\n",
    "        self.name = \"L\"\n",
    "\n",
    "    @unpacked\n",
    "    def calculate(self, I, *, VR, VC):\n",
    "        return -(VR + VC) / self.L\n",
    "\n",
    "    @property\n",
    "    def mass_vector(self):\n",
    "        return (True,)\n",
    "\n",
    "    @property\n",
    "    def variables(self):\n",
    "        return {\"I\": 0}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "amended-auction",
   "metadata": {},
   "outputs": [],
   "source": [
    "class C(Calculation):\n",
    "    def __init__(self, C):\n",
    "        self.C = C\n",
    "        self.name = \"C\"\n",
    "\n",
    "    @unpacked\n",
    "    def calculate(self, VC, *, I):\n",
    "        return I / self.C\n",
    "\n",
    "    @property\n",
    "    def mass_vector(self):\n",
    "        return (True,)\n",
    "\n",
    "    @property\n",
    "    def variables(self):\n",
    "        return {\"VC\": 0}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "differential-triple",
   "metadata": {},
   "outputs": [],
   "source": [
    "r, l, c = R(1.0), L(1.0), C(1.0)\n",
    "\n",
    "g = DiGraph()\n",
    "g.add_edge(r, l, variables=(\"VR\",))\n",
    "g.add_edge(c, l, variables=(\"VC\",))\n",
    "g.add_edge(l, r, variables=(\"I\",))\n",
    "g.add_edge(l, c, variables=(\"I\",))\n",
    "\n",
    "agr = Aggregator(g)\n",
    "\n",
    "plt.figure(figsize=(12, 2))\n",
    "agr.draw(\n",
    "    node_options=dict(pos={r: (0, 0), l: (1, 0), c: (2, 0)}, node_size=2000, font_size=24),\n",
    "    edge_options=dict(label_pos=0.3, font_size=18),\n",
    ")\n",
    "plt.box()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "fitted-partnership",
   "metadata": {},
   "outputs": [],
   "source": [
    "from stream.analysis.report import report\n",
    "\n",
    "report(agr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "moved-liberty",
   "metadata": {},
   "outputs": [],
   "source": [
    "y0 = np.array([1, 1.0, -1])\n",
    "time = np.linspace(0, 10)\n",
    "\n",
    "sol = agr.solve(y0=y0, time=time, yp0=agr.compute(y0, 0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "photographic-settle",
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.figure(figsize=(8, 6))\n",
    "plt.plot(time, sol[:, 0], label=\"VR\")\n",
    "plt.plot(time, sol[:, 2], label=\"VC\")\n",
    "plt.legend()\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "96a64773",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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