alxtz · January 7, 2026 11:07
diff --git a/metro_modeling.ipynb b/metro_modeling.ipynb
 {
 "cells": [
  {
   "cell_type": "markdown",
   "id": "dcec6df6",
   "metadata": {},
   "source": [
    "### 基礎依賴"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "c3c85e6e",
   "metadata": {},
   "outputs": [],
   "source": [
    "import sympy as sp  # pyright: ignore[reportMissingImports]\n",
    "t = sp.symbols('t')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7712e22c",
   "metadata": {},
   "source": [
    "### 要考慮的 metro function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "b4acb4d9",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "分段函數為 Piecewise((0.6*t**2, (t >= 0) & (t <= 30)), (36*t - 540, (t <= 90) & (t > 30)), (36*t - 0.6*(t - 90)**2 - 540, (t <= 120) & (t > 90)))\n"
     ]
    }
   ],
   "source": [
    "d = sp.Piecewise(\n",
    "    (0.6 * (t**2), (0<=t) & (t<=30)),\n",
    "    ((36*t - 540), (30<t) & (t<=90)),\n",
    "    ((\n",
    "        2700 +\n",
    "        -0.6 * ((t-90)**2) +\n",
    "        36 * (t-90)\n",
    "    ), (90<t) & (t<=120)),\n",
    ")\n",
    "print(\"分段函數為\", d)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "1548b900",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np  # pyright: ignore[reportMissingImports]\n",
    "import matplotlib.pyplot as plt  # pyright: ignore[reportMissingImports]\n",
    "\n",
    "d_num = sp.lambdify(t, d, modules=['numpy'])\n",
    "\n",
    "def plot_d_func():\n",
    "  t_values = np.linspace(0, 150, 150)\n",
    "  y_values = d_num(t_values)\n",
    "\n",
    "  plt.plot(t_values, y_values, label=r\"$d(x)$\")\n",
    "  plt.title(f\"...\")\n",
    "  plt.legend()\n",
    "  plt.grid(True)\n",
    "  plt.show()\n",
    "plot_d_func()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "d26a6bb8",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "在 t=0 時, d(0) 為 0.0\n",
      "在 t=30 時, d(30) 為 540.0\n",
      "在 t=90 時, d(90) 為 2700.0\n",
      "在 t=120 時, d(120) 為 3240.0\n"
     ]
    }
   ],
   "source": [
    "print(\"在 t=0 時, d(0) 為\", d_num(0))\n",
    "print(\"在 t=30 時, d(30) 為\", d_num(30))\n",
    "print(\"在 t=90 時, d(90) 為\", d_num(90))\n",
    "print(\"在 t=120 時, d(120) 為\", d_num(120))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "c4a37f8d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "v 函式為 Piecewise((1.2*t, (t >= 0) & (t <= 30)), (36, (t <= 90) & (t > 30)), (144.0 - 1.2*t, (t <= 120) & (t > 90)))\n"
     ]
    }
   ],
   "source": [
    "d_derivative = v = sp.diff(d, t)\n",
    "v_num = sp.lambdify(t, v, modules=['numpy'])\n",
    "\n",
    "print(\"v 函式為\", v)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "47aa3cad",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np  # pyright: ignore[reportMissingImports]\n",
    "import matplotlib.pyplot as plt  # pyright: ignore[reportMissingImports]\n",
    "\n",
    "def plot_v_func():\n",
    "  t_values = np.linspace(0, 150, 150)\n",
    "  y_values = v_num(t_values)\n",
    "\n",
    "  plt.plot(t_values, y_values, label=r\"$v(x)$\")\n",
    "  plt.title(f\"...\")\n",
    "  plt.legend()\n",
    "  plt.grid(True)\n",
    "  plt.show()\n",
    "plot_v_func()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "87b52622",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "在 t=0 時, v(0) 為 0.0\n",
      "在 t=30 時, v(30) 為 36.0\n",
      "在 t=90 時, v(90) 為 36.0\n",
      "在 t=120 時, v(120) 為 0.0\n"
     ]
    }
   ],
   "source": [
    "print(\"在 t=0 時, v(0) 為\", v_num(0))\n",
    "print(\"在 t=30 時, v(30) 為\", v_num(30))\n",
    "print(\"在 t=90 時, v(90) 為\", v_num(90))\n",
    "print(\"在 t=120 時, v(120) 為\", v_num(120))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "a7baca77",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "a 函式為 Piecewise((1.2, (t >= 0) & (t <= 30)), (0, (t <= 90) & (t > 30)), (-1.2, (t <= 120) & (t > 90)))\n"
     ]
    }
   ],
   "source": [
    "v_derivative = a = sp.diff(v, t)\n",
    "a_num = sp.lambdify(t, a, modules=['numpy'])\n",
    "\n",
    "print(\"a 函式為\", a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "624f94e9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np  # pyright: ignore[reportMissingImports]\n",
    "import matplotlib.pyplot as plt  # pyright: ignore[reportMissingImports]\n",
    "\n",
    "def plot_a_func():\n",
    "  t_values = np.linspace(0, 150, 150)\n",
    "  y_values = a_num(t_values)\n",
    "\n",
    "  plt.plot(t_values, y_values, label=r\"$a(x)$\")\n",
    "  plt.title(f\"...\")\n",
    "  plt.legend()\n",
    "  plt.grid(True)\n",
    "  plt.show()\n",
    "plot_a_func()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "c9c67779",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "在 t=0 時, a(0) 為 1.2\n",
      "在 t=30 時, a(30) 為 1.2\n",
      "在 t=90 時, a(90) 為 0.0\n",
      "在 t=120 時, a(120) 為 -1.2\n"
     ]
    }
   ],
   "source": [
    "print(\"在 t=0 時, a(0) 為\", a_num(0))\n",
    "print(\"在 t=30 時, a(30) 為\", a_num(30))\n",
    "print(\"在 t=90 時, a(90) 為\", a_num(90))\n",
    "print(\"在 t=120 時, a(120) 為\", a_num(120))"
   ]
  }
 ],
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