trajectory_derivate.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "interpreter": {
      "hash": "fd9f199d7ce166a1e1fc959fbadba5c69a2231f0d3ee56353deab5bb56021a27"
    },
    "kernelspec": {
      "display_name": "Python 3.6.8 64-bit ('ML': virtualenv)",
      "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": "3.6.8"
    },
    "orig_nbformat": 4,
    "colab": {
      "name": "trajectory_derivate.ipynb",
      "provenance": [],
      "include_colab_link": true
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/giuliovv/trajectory_planning/blob/master/trajectory_derivate.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ORIKdryYUPY2"
      },
      "source": [
        "import sympy\n",
        "from sympy import Symbol, Sum, IndexedBase\n",
        "from sympy.parsing.sympy_parser import parse_expr"
      ],
      "execution_count": 55,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "hNvsgveTUPZD"
      },
      "source": [
        "a = IndexedBase(\"alpha\", \"i\")\n",
        "xr = IndexedBase(\"x_r\", \"i\")\n",
        "yr = IndexedBase(\"y_r\", \"i\")\n",
        "xl = IndexedBase(\"x_l\", \"i\")\n",
        "yl = IndexedBase(\"y_l\", \"i\")\n",
        "\n",
        "x = IndexedBase(\"x\", \"i\")\n",
        "y = IndexedBase(\"y\", \"i\")\n",
        "\n",
        "kp = Symbol(\"k_p\")\n",
        "kl = Symbol(\"k_l\")\n",
        "\n",
        "i = Symbol(\"i\")\n",
        "N = Symbol(\"N\")\n",
        "\n",
        "g = Symbol(\"gamma\")"
      ],
      "execution_count": 56,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Tc3N7dgfW1wy"
      },
      "source": [
        "def print_latex(text, title=\"\", fontsize=40):\n",
        "  lat = sympy.latex(text)\n",
        "\n",
        "  #add text                                                                       \n",
        "  plt.text(0, 0.5, r\"$%s = %s$\" % (title, lat), fontsize=fontsize)                                  \n",
        "\n",
        "  # #hide axes                                                                      \n",
        "  fig = plt.gca()\n",
        "  fig.axis('off')\n",
        "  plt.draw()"
      ],
      "execution_count": 57,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5AHsQUe5UPZG"
      },
      "source": [
        "## Formulation"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "2BAEzA_5WWFC"
      },
      "source": [
        "import matplotlib.pyplot as plt"
      ],
      "execution_count": 58,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 248
        },
        "id": "nyHtI__sUPZI",
        "outputId": "f3489bda-e8da-4b47-a41a-74ce550528ce"
      },
      "source": [
        "ds = sympy.sqrt((x[i+1]-x[i])**2+(y[i+1]-y[i])**2)\n",
        "print_latex(ds, title=r\"\\Delta{s_i}\")"
      ],
      "execution_count": 59,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 248
        },
        "id": "j0NBv73dUPZO",
        "outputId": "674e01d3-3ba0-42d4-b407-a81568a34adf"
      },
      "source": [
        "Jl = ds**2\n",
        "print_latex(Sum(Jl, (\"i\", 0, N)), title=\"J_l\")"
      ],
      "execution_count": 60,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 248
        },
        "id": "51Kly4d-UPZR",
        "outputId": "aa934b7a-9f94-4383-c8e9-f6eeff9d7e0e"
      },
      "source": [
        "Jp = (sympy.atan((y[i+1]-y[i])/(x[i+1]-x[i]))-sympy.atan((y[i]-y[i-1])/(x[i]-x[i-1])))/(ds)\n",
        "print_latex(Sum(Jp, (\"i\", 1, N)), title=\"J_p\")"
      ],
      "execution_count": 61,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "jBQUUROAUPZT"
      },
      "source": [
        "## Substitutions"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 223
        },
        "id": "SJTx7EayUPZU",
        "outputId": "8b3f73e9-8bc8-4602-c3b6-3dba2aa7c1f4"
      },
      "source": [
        "Jl = Jl \\\n",
        "    .subs(x[i+1], xr[i+1]+a[i+1]*(xl[i+1]-xr[i+1])) \\\n",
        "    .subs(x[i], xr[i]+a[i]*(xl[i]-xr[i])) \\\n",
        "    .subs(y[i], yr[i]+a[i]*(yl[i]-yr[i])) \\\n",
        "    .subs(y[i+1], yr[i+1]+a[i+1]*(yl[i+1]-yr[i+1])) \\\n",
        "    + g*sympy.Max(0, a[i]-1) + g*sympy.Min(0, a[i]) # Constraint\n",
        "\n",
        "print_latex(Sum(Jl, (\"i\", 0, N-1)), title=\"J_l\")"
      ],
      "execution_count": 62,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 248
        },
        "id": "cXWKLDnkUPZY",
        "outputId": "3686eb36-25ce-405d-df56-ba960bfb750b"
      },
      "source": [
        "Jp = Jp \\\n",
        "    .subs(x[i+1], xr[i+1]+a[i+1]*(xl[i+1]-xr[i+1])) \\\n",
        "    .subs(x[i], xr[i]+a[i]*(xl[i]-xr[i])) \\\n",
        "    .subs(x[i-1], xr[i-1]+a[i-1]*(xl[i-1]-xr[i-1])) \\\n",
        "    .subs(y[i], yr[i]+a[i]*(yl[i]-yr[i])) \\\n",
        "    .subs(y[i+1], yr[i+1]+a[i+1]*(yl[i+1]-yr[i+1])) \\\n",
        "    .subs(y[i-1], yr[i-1]+a[i-1]*(yl[i-1]-yr[i-1])) \\\n",
        "    + g*sympy.Max(0, a[i]-1) + g*sympy.Min(0, a[i]) # Constraint\n",
        "\n",
        "\n",
        "print_latex(Sum(Jp, (\"i\", 1, N-1)), title=\"J_p\")"
      ],
      "execution_count": 63,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 130
        },
        "id": "RhmQG0b2UPZa",
        "outputId": "074cbf22-0ada-4782-bd41-753ce44b9329"
      },
      "source": [
        "J = kl*Sum(Jl, (\"i\", 0, N-1)) + kp * Sum(Jp, (\"i\", 1, N-1))\n",
        "print_latex(J, title=\"J\")"
      ],
      "execution_count": 64,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "x4XnI7UNUPZc"
      },
      "source": [
        "## Gradient"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "bc-NjQkyCo0u"
      },
      "source": [
        "NB d/dx min(x,const) = 0 if min(x, const) = const else 1"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "UFiXehSagMMt"
      },
      "source": [
        "def to_matlab(der):\n",
        "  return sympy.ccode(der) \\\n",
        "    .replace(\"x_l[i]\", \"leftpoints(idx, 1)\") \\\n",
        "    .replace(\"x_l[i + 1]\", \"leftpoints(idx+1, 1)\") \\\n",
        "    .replace(\"x_r[i]\", \"rightpoints(idx, 1)\") \\\n",
        "    .replace(\"x_r[i + 1]\", \"rightpoints(idx+1, 1)\") \\\n",
        "    .replace(\"y_l[i]\", \"leftpoints(idx, 2)\") \\\n",
        "    .replace(\"y_l[i + 1]\", \"leftpoints(idx+1, 2)\") \\\n",
        "    .replace(\"y_r[i]\", \"rightpoints(idx, 2)\") \\\n",
        "    .replace(\"y_r[i + 1]\", \"rightpoints(idx+1, 2)\") \\\n",
        "    .replace(\"x_l[i - 1]\", \"leftpoints(idx-1, 1)\") \\\n",
        "    .replace(\"y_l[i - 1]\", \"leftpoints(idx-1, 2)\") \\\n",
        "    .replace(\"x_r[i - 1]\", \"rightpoints(idx-1, 1)\") \\\n",
        "    .replace(\"y_r[i - 1]\", \"rightpoints(idx-1, 2)\") \\\n",
        "    .replace(\"alpha[i]\", \"alpha(idx)\") \\\n",
        "    .replace(\"alpha[i + 1]\", \"alpha(idx+1)\") \\\n",
        "    .replace(\"alpha[i - 1]\", \"alpha(idx-1)\") \\\n",
        "    .replace(\"pow\", \"power\")"
      ],
      "execution_count": 65,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 90
        },
        "id": "O4Qyc7LRUPZe",
        "outputId": "f21fe5d7-55f9-4c0f-e15c-f1873edf569e"
      },
      "source": [
        "gradient = J.diff(a[i])\n",
        "print_latex(gradient, title=r\"\\frac{dj}{d\\alpha_i}\")"
      ],
      "execution_count": 66,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 53
        },
        "id": "rcpzmpDdUPZf",
        "outputId": "a4e6f3ca-dc6d-476d-8368-e101d0ef5a65"
      },
      "source": [
        "# d/a\n",
        "gradient_jl = Jl.diff(a[i])\n",
        "gradient_code_jl = to_matlab(gradient_jl)\n",
        "gradient_code_jl"
      ],
      "execution_count": 67,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "string"
            },
            "text/plain": [
              "'// Not supported in C:\\n// Heaviside\\n// Heaviside\\ngamma*Heaviside(alpha(idx) - 1) + gamma*Heaviside(-alpha(idx)) + (-2*leftpoints(idx, 1) + 2*rightpoints(idx, 1))*((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) - (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx+1, 1) - rightpoints(idx, 1)) + (-2*leftpoints(idx, 2) + 2*rightpoints(idx, 2))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) - (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx+1, 2) - rightpoints(idx, 2))'"
            ]
          },
          "metadata": {},
          "execution_count": 67
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 53
        },
        "id": "fdhRjJBcf12W",
        "outputId": "f9f5a3ad-1ac8-48ce-d248-c34d04e8af69"
      },
      "source": [
        "# d/a+1\n",
        "gradient_jl_ap1 = Jl.diff(a[i+1])\n",
        "gradient_code_jl_plus1 = to_matlab(gradient_jl_ap1)\n",
        "gradient_code_jl_plus1"
      ],
      "execution_count": 68,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "string"
            },
            "text/plain": [
              "'(2*leftpoints(idx+1, 1) - 2*rightpoints(idx+1, 1))*((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) - (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx+1, 1) - rightpoints(idx, 1)) + (2*leftpoints(idx+1, 2) - 2*rightpoints(idx+1, 2))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) - (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx+1, 2) - rightpoints(idx, 2))'"
            ]
          },
          "metadata": {},
          "execution_count": 68
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 87
        },
        "id": "KhdCo0RnU92t",
        "outputId": "cf85e52b-b71c-45c5-d2d8-4595019ddbfe"
      },
      "source": [
        "gradient_jp_a = Jp.diff(a[i])\n",
        "gradient_code_jp = to_matlab(gradient_jp_a)\n",
        "gradient_code_jp"
      ],
      "execution_count": 69,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "string"
            },
            "text/plain": [
              "'// Not supported in C:\\n// Heaviside\\n// Heaviside\\ngamma*Heaviside(alpha(idx) - 1) + gamma*Heaviside(-alpha(idx)) + (-((-leftpoints(idx, 1) + rightpoints(idx, 1))*(-(leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) - rightpoints(idx-1, 2) + rightpoints(idx, 2))/power(-(leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) - rightpoints(idx-1, 1) + rightpoints(idx, 1), 2) + (leftpoints(idx, 2) - rightpoints(idx, 2))/(-(leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) - rightpoints(idx-1, 1) + rightpoints(idx, 1)))/(1 + power(-(leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) - rightpoints(idx-1, 2) + rightpoints(idx, 2), 2)/power(-(leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) - rightpoints(idx-1, 1) + rightpoints(idx, 1), 2)) + ((leftpoints(idx, 1) - rightpoints(idx, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) - (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx+1, 2) - rightpoints(idx, 2))/power((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) - (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx+1, 1) - rightpoints(idx, 1), 2) + (-leftpoints(idx, 2) + rightpoints(idx, 2))/((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) - (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx+1, 1) - rightpoints(idx, 1)))/(1 + power((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) - (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx+1, 2) - rightpoints(idx, 2), 2)/power((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) - (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx+1, 1) - rightpoints(idx, 1), 2)))/sqrt(power((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) - (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx+1, 1) - rightpoints(idx, 1), 2) + power((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) - (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx+1, 2) - rightpoints(idx, 2), 2)) + (-1.0/2.0*(-2*leftpoints(idx, 1) + 2*rightpoints(idx, 1))*((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) - (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx+1, 1) - rightpoints(idx, 1)) - 1.0/2.0*(-2*leftpoints(idx, 2) + 2*rightpoints(idx, 2))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) - (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx+1, 2) - rightpoints(idx, 2)))*(atan(((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) - (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx+1, 2) - rightpoints(idx, 2))/((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) - (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx+1, 1) - rightpoints(idx, 1))) - atan((-(leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) - rightpoints(idx-1, 2) + rightpoints(idx, 2))/(-(leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) - rightpoints(idx-1, 1) + rightpoints(idx, 1))))/power(power((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) - (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx+1, 1) - rightpoints(idx, 1), 2) + power((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) - (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx+1, 2) - rightpoints(idx, 2), 2), 3.0/2.0)'"
            ]
          },
          "metadata": {},
          "execution_count": 69
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 87
        },
        "id": "hsGMp1r1gqkk",
        "outputId": "c4eac406-40d8-45a3-c3ef-a51a0f1f21d8"
      },
      "source": [
        "gradient_jp_ap1 = Jp.diff(a[i+1])\n",
        "gradient_code_jp_plus_1 = to_matlab(gradient_jp_ap1)\n",
        "gradient_code_jp_plus_1"
      ],
      "execution_count": 70,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "string"
            },
            "text/plain": [
              "'(-1.0/2.0*(2*leftpoints(idx+1, 1) - 2*rightpoints(idx+1, 1))*((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) - (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx+1, 1) - rightpoints(idx, 1)) - 1.0/2.0*(2*leftpoints(idx+1, 2) - 2*rightpoints(idx+1, 2))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) - (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx+1, 2) - rightpoints(idx, 2)))*(atan(((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) - (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx+1, 2) - rightpoints(idx, 2))/((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) - (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx+1, 1) - rightpoints(idx, 1))) - atan((-(leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) - rightpoints(idx-1, 2) + rightpoints(idx, 2))/(-(leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) - rightpoints(idx-1, 1) + rightpoints(idx, 1))))/power(power((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) - (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx+1, 1) - rightpoints(idx, 1), 2) + power((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) - (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx+1, 2) - rightpoints(idx, 2), 2), 3.0/2.0) + ((-leftpoints(idx+1, 1) + rightpoints(idx+1, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) - (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx+1, 2) - rightpoints(idx, 2))/power((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) - (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx+1, 1) - rightpoints(idx, 1), 2) + (leftpoints(idx+1, 2) - rightpoints(idx+1, 2))/((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) - (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx+1, 1) - rightpoints(idx, 1)))/((1 + power((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) - (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx+1, 2) - rightpoints(idx, 2), 2)/power((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) - (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx+1, 1) - rightpoints(idx, 1), 2))*sqrt(power((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) - (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx+1, 1) - rightpoints(idx, 1), 2) + power((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) - (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx+1, 2) - rightpoints(idx, 2), 2)))'"
            ]
          },
          "metadata": {},
          "execution_count": 70
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 87
        },
        "id": "f3_WotMCg2Ys",
        "outputId": "d20eac07-ca99-4fce-e4a2-d4c7c1b1520c"
      },
      "source": [
        "gradient_jp_am1 = Jp.diff(a[i-1])\n",
        "gradient_code_jp_minus_1 = to_matlab(gradient_jp_am1)\n",
        "gradient_code_jp_minus_1"
      ],
      "execution_count": 71,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "string"
            },
            "text/plain": [
              "'-((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*(-(leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) - rightpoints(idx-1, 2) + rightpoints(idx, 2))/power(-(leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) - rightpoints(idx-1, 1) + rightpoints(idx, 1), 2) + (-leftpoints(idx-1, 2) + rightpoints(idx-1, 2))/(-(leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) - rightpoints(idx-1, 1) + rightpoints(idx, 1)))/((1 + power(-(leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) - rightpoints(idx-1, 2) + rightpoints(idx, 2), 2)/power(-(leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) - rightpoints(idx-1, 1) + rightpoints(idx, 1), 2))*sqrt(power((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) - (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx+1, 1) - rightpoints(idx, 1), 2) + power((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) - (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx+1, 2) - rightpoints(idx, 2), 2)))'"
            ]
          },
          "metadata": {},
          "execution_count": 71
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "tmsG0EkkUPZh"
      },
      "source": [
        "## Hessian"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 53
        },
        "id": "Bg-UzAYeUPZh",
        "outputId": "cac8b4ec-e3ec-4750-b913-8cf05008b8c2"
      },
      "source": [
        "hessian = gradient.diff(a[i])\n",
        "print_latex(hessian, title=r\"\\frac{dj}{d^2\\alpha_i}\")"
      ],
      "execution_count": 72,
      "outputs": [
        {
          "output_type": "display_data",
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            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 53
        },
        "id": "H1jm02eKUPZj",
        "outputId": "af9b0db4-85fc-4917-e4c0-d1fd4072bbc5"
      },
      "source": [
        "# Jl /a^2\n",
        "hessian_jl = gradient_jl.diff(a[i])\n",
        "hessian_code_jl = to_matlab(hessian_jl)\n",
        "hessian_code_jl"
      ],
      "execution_count": 73,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "string"
            },
            "text/plain": [
              "'// Not supported in C:\\n// DiracDelta\\n// DiracDelta\\ngamma*DiracDelta(alpha(idx) - 1) - gamma*DiracDelta(alpha(idx)) + (-2*leftpoints(idx, 1) + 2*rightpoints(idx, 1))*(-leftpoints(idx, 1) + rightpoints(idx, 1)) + (-2*leftpoints(idx, 2) + 2*rightpoints(idx, 2))*(-leftpoints(idx, 2) + rightpoints(idx, 2))'"
            ]
          },
          "metadata": {},
          "execution_count": 73
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        },
        "id": "E7NyyuV8hYhu",
        "outputId": "871d4149-102c-4278-c04c-1de04ed46144"
      },
      "source": [
        "# Jl /a*ai+1\n",
        "hessian_jl_a_ap1 = gradient_jl.diff(a[i+1])\n",
        "hessian_code_jl_a_ap1 = to_matlab(hessian_jl_a_ap1)\n",
        "hessian_code_jl_a_ap1"
      ],
      "execution_count": 74,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "string"
            },
            "text/plain": [
              "'(leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*(-2*leftpoints(idx, 1) + 2*rightpoints(idx, 1)) + (leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*(-2*leftpoints(idx, 2) + 2*rightpoints(idx, 2))'"
            ]
          },
          "metadata": {},
          "execution_count": 74
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        },
        "id": "KO7VDvIOiLTa",
        "outputId": "675cbb35-ec3c-49af-8e0d-97f05c85978d"
      },
      "source": [
        "# Jl /(a+1)^2\n",
        "hessian_jl_ap1_ap1 = gradient_jl_ap1.diff(a[i+1])\n",
        "hessian_code_jl_a_ap1 = to_matlab(hessian_jl_ap1_ap1)\n",
        "hessian_code_jl_a_ap1"
      ],
      "execution_count": 75,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "string"
            },
            "text/plain": [
              "'(leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*(2*leftpoints(idx+1, 1) - 2*rightpoints(idx+1, 1)) + (leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*(2*leftpoints(idx+1, 2) - 2*rightpoints(idx+1, 2))'"
            ]
          },
          "metadata": {},
          "execution_count": 75
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 87
        },
        "id": "X5lsaq50UPZk",
        "outputId": "b570f92a-abf9-4884-c56e-17410a7908bf"
      },
      "source": [
        "# Jp /a^2\n",
        "hessian_jp_a_a = gradient_jp_a.diff(a[i])\n",
        "hessian_code_jp_a_a = to_matlab(hessian_jp_a_a)\n",
        "hessian_code_jp_a_a"
      ],
      "execution_count": 76,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "string"
            },
            "text/plain": [
              "'// Not supported in C:\\n// DiracDelta\\n// DiracDelta\\ngamma*DiracDelta(alpha(idx) - 1) - gamma*DiracDelta(alpha(idx)) + 2*(-((-leftpoints(idx, 1) + rightpoints(idx, 1))*(-(leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) - rightpoints(idx-1, 2) + rightpoints(idx, 2))/power(-(leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) - rightpoints(idx-1, 1) + rightpoints(idx, 1), 2) + (leftpoints(idx, 2) - rightpoints(idx, 2))/(-(leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) - rightpoints(idx-1, 1) + rightpoints(idx, 1)))/(1 + power(-(leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) - rightpoints(idx-1, 2) + rightpoints(idx, 2), 2)/power(-(leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) - rightpoints(idx-1, 1) + rightpoints(idx, 1), 2)) + ((leftpoints(idx, 1) - rightpoints(idx, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) - (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx+1, 2) - rightpoints(idx, 2))/power((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) - (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx+1, 1) - rightpoints(idx, 1), 2) + (-leftpoints(idx, 2) + rightpoints(idx, 2))/((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) - (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx+1, 1) - rightpoints(idx, 1)))/(1 + power((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) - (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx+1, 2) - rightpoints(idx, 2), 2)/power((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) - (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx+1, 1) - rightpoints(idx, 1), 2)))*(-1.0/2.0*(-2*leftpoints(idx, 1) + 2*rightpoints(idx, 1))*((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) - (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx+1, 1) - rightpoints(idx, 1)) - 1.0/2.0*(-2*leftpoints(idx, 2) + 2*rightpoints(idx, 2))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) - (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx+1, 2) - rightpoints(idx, 2)))/power(power((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) - (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx+1, 1) - rightpoints(idx, 1), 2) + power((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) - (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx+1, 2) - rightpoints(idx, 2), 2), 3.0/2.0) + (-3.0/2.0*(-2*leftpoints(idx, 1) + 2*rightpoints(idx, 1))*((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) - (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx+1, 1) - rightpoints(idx, 1)) - 3.0/2.0*(-2*leftpoints(idx, 2) + 2*rightpoints(idx, 2))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) - (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx+1, 2) - rightpoints(idx, 2)))*(-1.0/2.0*(-2*leftpoints(idx, 1) + 2*rightpoints(idx, 1))*((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) - (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx+1, 1) - rightpoints(idx, 1)) - 1.0/2.0*(-2*leftpoints(idx, 2) + 2*rightpoints(idx, 2))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) - (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx+1, 2) - rightpoints(idx, 2)))*(atan(((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) - (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx+1, 2) - rightpoints(idx, 2))/((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) - (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx+1, 1) - rightpoints(idx, 1))) - atan((-(leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) - rightpoints(idx-1, 2) + rightpoints(idx, 2))/(-(leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) - rightpoints(idx-1, 1) + rightpoints(idx, 1))))/power(power((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) - (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx+1, 1) - rightpoints(idx, 1), 2) + power((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) - (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx+1, 2) - rightpoints(idx, 2), 2), 5.0/2.0) + ((-leftpoints(idx, 1) + rightpoints(idx, 1))*(leftpoints(idx, 1) - rightpoints(idx, 1)) + (-leftpoints(idx, 2) + rightpoints(idx, 2))*(leftpoints(idx, 2) - rightpoints(idx, 2)))*(atan(((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) - (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx+1, 2) - rightpoints(idx, 2))/((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) - (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx+1, 1) - rightpoints(idx, 1))) - atan((-(leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) - rightpoints(idx-1, 2) + rightpoints(idx, 2))/(-(leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) - rightpoints(idx-1, 1) + rightpoints(idx, 1))))/power(power((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) - (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx+1, 1) - rightpoints(idx, 1), 2) + power((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) - (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx+1, 2) - rightpoints(idx, 2), 2), 3.0/2.0) + (-((-2*leftpoints(idx, 1) + 2*rightpoints(idx, 1))*(-leftpoints(idx, 1) + rightpoints(idx, 1))*(-(leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) - rightpoints(idx-1, 2) + rightpoints(idx, 2))/power(-(leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) - rightpoints(idx-1, 1) + rightpoints(idx, 1), 3) + 2*(-leftpoints(idx, 1) + rightpoints(idx, 1))*(leftpoints(idx, 2) - rightpoints(idx, 2))/power(-(leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) - rightpoints(idx-1, 1) + rightpoints(idx, 1), 2))/(1 + power(-(leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) - rightpoints(idx-1, 2) + rightpoints(idx, 2), 2)/power(-(leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) - rightpoints(idx-1, 1) + rightpoints(idx, 1), 2)) - (-(-2*leftpoints(idx, 1) + 2*rightpoints(idx, 1))*power(-(leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) - rightpoints(idx-1, 2) + rightpoints(idx, 2), 2)/power(-(leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) - rightpoints(idx-1, 1) + rightpoints(idx, 1), 3) - (2*leftpoints(idx, 2) - 2*rightpoints(idx, 2))*(-(leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) - rightpoints(idx-1, 2) + rightpoints(idx, 2))/power(-(leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) - rightpoints(idx-1, 1) + rightpoints(idx, 1), 2))*((-leftpoints(idx, 1) + rightpoints(idx, 1))*(-(leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) - rightpoints(idx-1, 2) + rightpoints(idx, 2))/power(-(leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) - rightpoints(idx-1, 1) + rightpoints(idx, 1), 2) + (leftpoints(idx, 2) - rightpoints(idx, 2))/(-(leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) - rightpoints(idx-1, 1) + rightpoints(idx, 1)))/power(1 + power(-(leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) - rightpoints(idx-1, 2) + rightpoints(idx, 2), 2)/power(-(leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) - rightpoints(idx-1, 1) + rightpoints(idx, 1), 2), 2) + ((leftpoints(idx, 1) - rightpoints(idx, 1))*(2*leftpoints(idx, 1) - 2*rightpoints(idx, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) - (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx+1, 2) - rightpoints(idx, 2))/power((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) - (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx+1, 1) - rightpoints(idx, 1), 3) + 2*(leftpoints(idx, 1) - rightpoints(idx, 1))*(-leftpoints(idx, 2) + rightpoints(idx, 2))/power((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) - (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx+1, 1) - rightpoints(idx, 1), 2))/(1 + power((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) - (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx+1, 2) - rightpoints(idx, 2), 2)/power((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) - (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx+1, 1) - rightpoints(idx, 1), 2)) + ((leftpoints(idx, 1) - rightpoints(idx, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) - (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx+1, 2) - rightpoints(idx, 2))/power((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) - (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx+1, 1) - rightpoints(idx, 1), 2) + (-leftpoints(idx, 2) + rightpoints(idx, 2))/((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) - (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx+1, 1) - rightpoints(idx, 1)))*(-(2*leftpoints(idx, 1) - 2*rightpoints(idx, 1))*power((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) - (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx+1, 2) - rightpoints(idx, 2), 2)/power((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) - (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx+1, 1) - rightpoints(idx, 1), 3) - (-2*leftpoints(idx, 2) + 2*rightpoints(idx, 2))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) - (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx+1, 2) - rightpoints(idx, 2))/power((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) - (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx+1, 1) - rightpoints(idx, 1), 2))/power(1 + power((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) - (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx+1, 2) - rightpoints(idx, 2), 2)/power((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) - (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx+1, 1) - rightpoints(idx, 1), 2), 2))/sqrt(power((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) - (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx+1, 1) - rightpoints(idx, 1), 2) + power((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) - (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx+1, 2) - rightpoints(idx, 2), 2))'"
            ]
          },
          "metadata": {},
          "execution_count": 76
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "l4UXg0s-jiYo",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 87
        },
        "outputId": "80a22351-6857-4fec-8395-8bbb6e821a0a"
      },
      "source": [
        "# Jp /a*a+1\n",
        "hessian_jp_a_ap1 = gradient_jp_a.diff(a[i+1])\n",
        "hessian_code_jp_a_ap1 = to_matlab(hessian_jp_a_ap1)\n",
        "hessian_code_jp_a_ap1"
      ],
      "execution_count": 77,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "string"
            },
            "text/plain": [
              "'(((-2*leftpoints(idx+1, 1) + 2*rightpoints(idx+1, 1))*(leftpoints(idx, 1) - rightpoints(idx, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) - (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx+1, 2) - rightpoints(idx, 2))/power((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) - (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx+1, 1) - rightpoints(idx, 1), 3) + (-leftpoints(idx+1, 1) + rightpoints(idx+1, 1))*(-leftpoints(idx, 2) + rightpoints(idx, 2))/power((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) - (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx+1, 1) - rightpoints(idx, 1), 2) + (leftpoints(idx, 1) - rightpoints(idx, 1))*(leftpoints(idx+1, 2) - rightpoints(idx+1, 2))/power((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) - (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx+1, 1) - rightpoints(idx, 1), 2))/(1 + power((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) - (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx+1, 2) - rightpoints(idx, 2), 2)/power((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) - (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx+1, 1) - rightpoints(idx, 1), 2)) + (-(-2*leftpoints(idx+1, 1) + 2*rightpoints(idx+1, 1))*power((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) - (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx+1, 2) - rightpoints(idx, 2), 2)/power((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) - (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx+1, 1) - rightpoints(idx, 1), 3) - (2*leftpoints(idx+1, 2) - 2*rightpoints(idx+1, 2))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) - (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx+1, 2) - rightpoints(idx, 2))/power((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) - (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx+1, 1) - rightpoints(idx, 1), 2))*((leftpoints(idx, 1) - rightpoints(idx, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) - (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx+1, 2) - rightpoints(idx, 2))/power((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) - (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx+1, 1) - rightpoints(idx, 1), 2) + (-leftpoints(idx, 2) + rightpoints(idx, 2))/((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) - (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx+1, 1) - rightpoints(idx, 1)))/power(1 + power((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) - (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx+1, 2) - rightpoints(idx, 2), 2)/power((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) - (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx+1, 1) - rightpoints(idx, 1), 2), 2))/sqrt(power((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) - (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx+1, 1) - rightpoints(idx, 1), 2) + power((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) - (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx+1, 2) - rightpoints(idx, 2), 2)) + (-((-leftpoints(idx, 1) + rightpoints(idx, 1))*(-(leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) - rightpoints(idx-1, 2) + rightpoints(idx, 2))/power(-(leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) - rightpoints(idx-1, 1) + rightpoints(idx, 1), 2) + (leftpoints(idx, 2) - rightpoints(idx, 2))/(-(leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) - rightpoints(idx-1, 1) + rightpoints(idx, 1)))/(1 + power(-(leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) - rightpoints(idx-1, 2) + rightpoints(idx, 2), 2)/power(-(leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) - rightpoints(idx-1, 1) + rightpoints(idx, 1), 2)) + ((leftpoints(idx, 1) - rightpoints(idx, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) - (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx+1, 2) - rightpoints(idx, 2))/power((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) - (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx+1, 1) - rightpoints(idx, 1), 2) + (-leftpoints(idx, 2) + rightpoints(idx, 2))/((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) - (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx+1, 1) - rightpoints(idx, 1)))/(1 + power((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) - (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx+1, 2) - rightpoints(idx, 2), 2)/power((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) - (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx+1, 1) - rightpoints(idx, 1), 2)))*(-1.0/2.0*(2*leftpoints(idx+1, 1) - 2*rightpoints(idx+1, 1))*((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) - (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx+1, 1) - rightpoints(idx, 1)) - 1.0/2.0*(2*leftpoints(idx+1, 2) - 2*rightpoints(idx+1, 2))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) - (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx+1, 2) - rightpoints(idx, 2)))/power(power((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) - (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx+1, 1) - rightpoints(idx, 1), 2) + power((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) - (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx+1, 2) - rightpoints(idx, 2), 2), 3.0/2.0) + ((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*(leftpoints(idx, 1) - rightpoints(idx, 1)) + (leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*(leftpoints(idx, 2) - rightpoints(idx, 2)))*(atan(((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) - (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx+1, 2) - rightpoints(idx, 2))/((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) - (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx+1, 1) - rightpoints(idx, 1))) - atan((-(leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) - rightpoints(idx-1, 2) + rightpoints(idx, 2))/(-(leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) - rightpoints(idx-1, 1) + rightpoints(idx, 1))))/power(power((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) - (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx+1, 1) - rightpoints(idx, 1), 2) + power((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) - (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx+1, 2) - rightpoints(idx, 2), 2), 3.0/2.0) + (-3.0/2.0*(2*leftpoints(idx+1, 1) - 2*rightpoints(idx+1, 1))*((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) - (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx+1, 1) - rightpoints(idx, 1)) - 3.0/2.0*(2*leftpoints(idx+1, 2) - 2*rightpoints(idx+1, 2))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) - (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx+1, 2) - rightpoints(idx, 2)))*(-1.0/2.0*(-2*leftpoints(idx, 1) + 2*rightpoints(idx, 1))*((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) - (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx+1, 1) - rightpoints(idx, 1)) - 1.0/2.0*(-2*leftpoints(idx, 2) + 2*rightpoints(idx, 2))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) - (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx+1, 2) - rightpoints(idx, 2)))*(atan(((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) - (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx+1, 2) - rightpoints(idx, 2))/((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) - (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx+1, 1) - rightpoints(idx, 1))) - atan((-(leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) - rightpoints(idx-1, 2) + rightpoints(idx, 2))/(-(leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) - rightpoints(idx-1, 1) + rightpoints(idx, 1))))/power(power((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) - (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx+1, 1) - rightpoints(idx, 1), 2) + power((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) - (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx+1, 2) - rightpoints(idx, 2), 2), 5.0/2.0) + (-1.0/2.0*(-2*leftpoints(idx, 1) + 2*rightpoints(idx, 1))*((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) - (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx+1, 1) - rightpoints(idx, 1)) - 1.0/2.0*(-2*leftpoints(idx, 2) + 2*rightpoints(idx, 2))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) - (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx+1, 2) - rightpoints(idx, 2)))*((-leftpoints(idx+1, 1) + rightpoints(idx+1, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) - (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx+1, 2) - rightpoints(idx, 2))/power((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) - (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx+1, 1) - rightpoints(idx, 1), 2) + (leftpoints(idx+1, 2) - rightpoints(idx+1, 2))/((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) - (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx+1, 1) - rightpoints(idx, 1)))/((1 + power((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) - (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx+1, 2) - rightpoints(idx, 2), 2)/power((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) - (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx+1, 1) - rightpoints(idx, 1), 2))*power(power((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) - (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx+1, 1) - rightpoints(idx, 1), 2) + power((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) - (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx+1, 2) - rightpoints(idx, 2), 2), 3.0/2.0))'"
            ]
          },
          "metadata": {},
          "execution_count": 77
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "amDXPaX2jp3T",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 87
        },
        "outputId": "f9dd1094-77fe-4e7e-b883-ddfbe7cfaf4b"
      },
      "source": [
        "# Jp /a*a-1\n",
        "hessian_jp_a_am1 = gradient_jp_a.diff(a[i-1])\n",
        "hessian_code_jp_a_am1 = to_matlab(hessian_jp_a_am1)\n",
        "hessian_code_jp_a_am1"
      ],
      "execution_count": 78,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "string"
            },
            "text/plain": [
              "'(-((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*(leftpoints(idx, 2) - rightpoints(idx, 2))/power(-(leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) - rightpoints(idx-1, 1) + rightpoints(idx, 1), 2) + (2*leftpoints(idx-1, 1) - 2*rightpoints(idx-1, 1))*(-leftpoints(idx, 1) + rightpoints(idx, 1))*(-(leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) - rightpoints(idx-1, 2) + rightpoints(idx, 2))/power(-(leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) - rightpoints(idx-1, 1) + rightpoints(idx, 1), 3) + (-leftpoints(idx, 1) + rightpoints(idx, 1))*(-leftpoints(idx-1, 2) + rightpoints(idx-1, 2))/power(-(leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) - rightpoints(idx-1, 1) + rightpoints(idx, 1), 2))/(1 + power(-(leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) - rightpoints(idx-1, 2) + rightpoints(idx, 2), 2)/power(-(leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) - rightpoints(idx-1, 1) + rightpoints(idx, 1), 2)) - (-(2*leftpoints(idx-1, 1) - 2*rightpoints(idx-1, 1))*power(-(leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) - rightpoints(idx-1, 2) + rightpoints(idx, 2), 2)/power(-(leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) - rightpoints(idx-1, 1) + rightpoints(idx, 1), 3) - (-2*leftpoints(idx-1, 2) + 2*rightpoints(idx-1, 2))*(-(leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) - rightpoints(idx-1, 2) + rightpoints(idx, 2))/power(-(leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) - rightpoints(idx-1, 1) + rightpoints(idx, 1), 2))*((-leftpoints(idx, 1) + rightpoints(idx, 1))*(-(leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) - rightpoints(idx-1, 2) + rightpoints(idx, 2))/power(-(leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) - rightpoints(idx-1, 1) + rightpoints(idx, 1), 2) + (leftpoints(idx, 2) - rightpoints(idx, 2))/(-(leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) - rightpoints(idx-1, 1) + rightpoints(idx, 1)))/power(1 + power(-(leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) - rightpoints(idx-1, 2) + rightpoints(idx, 2), 2)/power(-(leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) - rightpoints(idx-1, 1) + rightpoints(idx, 1), 2), 2))/sqrt(power((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) - (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx+1, 1) - rightpoints(idx, 1), 2) + power((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) - (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx+1, 2) - rightpoints(idx, 2), 2)) - (-1.0/2.0*(-2*leftpoints(idx, 1) + 2*rightpoints(idx, 1))*((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) - (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx+1, 1) - rightpoints(idx, 1)) - 1.0/2.0*(-2*leftpoints(idx, 2) + 2*rightpoints(idx, 2))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) - (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx+1, 2) - rightpoints(idx, 2)))*((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*(-(leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) - rightpoints(idx-1, 2) + rightpoints(idx, 2))/power(-(leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) - rightpoints(idx-1, 1) + rightpoints(idx, 1), 2) + (-leftpoints(idx-1, 2) + rightpoints(idx-1, 2))/(-(leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) - rightpoints(idx-1, 1) + rightpoints(idx, 1)))/((1 + power(-(leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) - rightpoints(idx-1, 2) + rightpoints(idx, 2), 2)/power(-(leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) - rightpoints(idx-1, 1) + rightpoints(idx, 1), 2))*power(power((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) - (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx+1, 1) - rightpoints(idx, 1), 2) + power((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) - (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx+1, 2) - rightpoints(idx, 2), 2), 3.0/2.0))'"
            ]
          },
          "metadata": {},
          "execution_count": 78
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "5dqqQPZOkEjK",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 87
        },
        "outputId": "fcf86f8e-6588-4dd9-b185-1182ed641882"
      },
      "source": [
        "# Jp /a+1*ap1\n",
        "hessian_jp_ap1_ap1 = gradient_jp_ap1.diff(a[i+1])\n",
        "hessian_code_jp_ap1_ap1 = to_matlab(hessian_jp_ap1_ap1)\n",
        "hessian_code_jp_ap1_ap1"
      ],
      "execution_count": 79,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "string"
            },
            "text/plain": [
              "'((-leftpoints(idx+1, 1) + rightpoints(idx+1, 1))*(leftpoints(idx+1, 1) - rightpoints(idx+1, 1)) + (-leftpoints(idx+1, 2) + rightpoints(idx+1, 2))*(leftpoints(idx+1, 2) - rightpoints(idx+1, 2)))*(atan(((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) - (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx+1, 2) - rightpoints(idx, 2))/((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) - (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx+1, 1) - rightpoints(idx, 1))) - atan((-(leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) - rightpoints(idx-1, 2) + rightpoints(idx, 2))/(-(leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) - rightpoints(idx-1, 1) + rightpoints(idx, 1))))/power(power((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) - (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx+1, 1) - rightpoints(idx, 1), 2) + power((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) - (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx+1, 2) - rightpoints(idx, 2), 2), 3.0/2.0) + (-3.0/2.0*(2*leftpoints(idx+1, 1) - 2*rightpoints(idx+1, 1))*((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) - (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx+1, 1) - rightpoints(idx, 1)) - 3.0/2.0*(2*leftpoints(idx+1, 2) - 2*rightpoints(idx+1, 2))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) - (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx+1, 2) - rightpoints(idx, 2)))*(-1.0/2.0*(2*leftpoints(idx+1, 1) - 2*rightpoints(idx+1, 1))*((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) - (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx+1, 1) - rightpoints(idx, 1)) - 1.0/2.0*(2*leftpoints(idx+1, 2) - 2*rightpoints(idx+1, 2))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) - (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx+1, 2) - rightpoints(idx, 2)))*(atan(((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) - (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx+1, 2) - rightpoints(idx, 2))/((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) - (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx+1, 1) - rightpoints(idx, 1))) - atan((-(leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) - rightpoints(idx-1, 2) + rightpoints(idx, 2))/(-(leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) - rightpoints(idx-1, 1) + rightpoints(idx, 1))))/power(power((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) - (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx+1, 1) - rightpoints(idx, 1), 2) + power((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) - (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx+1, 2) - rightpoints(idx, 2), 2), 5.0/2.0) + 2*(-1.0/2.0*(2*leftpoints(idx+1, 1) - 2*rightpoints(idx+1, 1))*((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) - (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx+1, 1) - rightpoints(idx, 1)) - 1.0/2.0*(2*leftpoints(idx+1, 2) - 2*rightpoints(idx+1, 2))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) - (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx+1, 2) - rightpoints(idx, 2)))*((-leftpoints(idx+1, 1) + rightpoints(idx+1, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) - (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx+1, 2) - rightpoints(idx, 2))/power((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) - (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx+1, 1) - rightpoints(idx, 1), 2) + (leftpoints(idx+1, 2) - rightpoints(idx+1, 2))/((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) - (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx+1, 1) - rightpoints(idx, 1)))/((1 + power((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) - (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx+1, 2) - rightpoints(idx, 2), 2)/power((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) - (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx+1, 1) - rightpoints(idx, 1), 2))*power(power((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) - (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx+1, 1) - rightpoints(idx, 1), 2) + power((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) - (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx+1, 2) - rightpoints(idx, 2), 2), 3.0/2.0)) + ((-2*leftpoints(idx+1, 1) + 2*rightpoints(idx+1, 1))*(-leftpoints(idx+1, 1) + rightpoints(idx+1, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) - (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx+1, 2) - rightpoints(idx, 2))/power((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) - (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx+1, 1) - rightpoints(idx, 1), 3) + 2*(-leftpoints(idx+1, 1) + rightpoints(idx+1, 1))*(leftpoints(idx+1, 2) - rightpoints(idx+1, 2))/power((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) - (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx+1, 1) - rightpoints(idx, 1), 2))/((1 + power((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) - (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx+1, 2) - rightpoints(idx, 2), 2)/power((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) - (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx+1, 1) - rightpoints(idx, 1), 2))*sqrt(power((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) - (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx+1, 1) - rightpoints(idx, 1), 2) + power((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) - (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx+1, 2) - rightpoints(idx, 2), 2))) + (-(-2*leftpoints(idx+1, 1) + 2*rightpoints(idx+1, 1))*power((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) - (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx+1, 2) - rightpoints(idx, 2), 2)/power((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) - (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx+1, 1) - rightpoints(idx, 1), 3) - (2*leftpoints(idx+1, 2) - 2*rightpoints(idx+1, 2))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) - (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx+1, 2) - rightpoints(idx, 2))/power((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) - (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx+1, 1) - rightpoints(idx, 1), 2))*((-leftpoints(idx+1, 1) + rightpoints(idx+1, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) - (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx+1, 2) - rightpoints(idx, 2))/power((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) - (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx+1, 1) - rightpoints(idx, 1), 2) + (leftpoints(idx+1, 2) - rightpoints(idx+1, 2))/((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) - (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx+1, 1) - rightpoints(idx, 1)))/(power(1 + power((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) - (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx+1, 2) - rightpoints(idx, 2), 2)/power((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) - (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx+1, 1) - rightpoints(idx, 1), 2), 2)*sqrt(power((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) - (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx+1, 1) - rightpoints(idx, 1), 2) + power((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) - (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx+1, 2) - rightpoints(idx, 2), 2)))'"
            ]
          },
          "metadata": {},
          "execution_count": 79
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "qhaQDXCxjvrK",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 87
        },
        "outputId": "38955fa3-7db2-4e4d-f884-54f099a34a3c"
      },
      "source": [
        "# Jp /a+1*a-1\n",
        "hessian_jp_ap1_am1 = gradient_jp_ap1.diff(a[i-1])\n",
        "hessian_code_jp_ap1_am1 = to_matlab(hessian_jp_ap1_am1)\n",
        "hessian_code_jp_ap1_am1"
      ],
      "execution_count": 80,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "string"
            },
            "text/plain": [
              "'-(-1.0/2.0*(2*leftpoints(idx+1, 1) - 2*rightpoints(idx+1, 1))*((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) - (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx+1, 1) - rightpoints(idx, 1)) - 1.0/2.0*(2*leftpoints(idx+1, 2) - 2*rightpoints(idx+1, 2))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) - (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx+1, 2) - rightpoints(idx, 2)))*((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*(-(leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) - rightpoints(idx-1, 2) + rightpoints(idx, 2))/power(-(leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) - rightpoints(idx-1, 1) + rightpoints(idx, 1), 2) + (-leftpoints(idx-1, 2) + rightpoints(idx-1, 2))/(-(leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) - rightpoints(idx-1, 1) + rightpoints(idx, 1)))/((1 + power(-(leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) - rightpoints(idx-1, 2) + rightpoints(idx, 2), 2)/power(-(leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) - rightpoints(idx-1, 1) + rightpoints(idx, 1), 2))*power(power((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) - (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx+1, 1) - rightpoints(idx, 1), 2) + power((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) - (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx+1, 2) - rightpoints(idx, 2), 2), 3.0/2.0))'"
            ]
          },
          "metadata": {},
          "execution_count": 80
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "GsyIpk-Vj3vR",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 87
        },
        "outputId": "c9ef3b36-1e3e-4db9-9d1d-b7f2ee6b2fc3"
      },
      "source": [
        "# Jp /a-1*a-1\n",
        "hessian_jp_am1_am1 = gradient_jp_am1.diff(a[i-1])\n",
        "hessian_code_jp_am1_am1 = to_matlab(hessian_jp_am1_am1)\n",
        "hessian_code_jp_am1_am1"
      ],
      "execution_count": 81,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "string"
            },
            "text/plain": [
              "'-((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*(2*leftpoints(idx-1, 1) - 2*rightpoints(idx-1, 1))*(-(leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) - rightpoints(idx-1, 2) + rightpoints(idx, 2))/power(-(leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) - rightpoints(idx-1, 1) + rightpoints(idx, 1), 3) + 2*(leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*(-leftpoints(idx-1, 2) + rightpoints(idx-1, 2))/power(-(leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) - rightpoints(idx-1, 1) + rightpoints(idx, 1), 2))/((1 + power(-(leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) - rightpoints(idx-1, 2) + rightpoints(idx, 2), 2)/power(-(leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) - rightpoints(idx-1, 1) + rightpoints(idx, 1), 2))*sqrt(power((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) - (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx+1, 1) - rightpoints(idx, 1), 2) + power((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) - (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx+1, 2) - rightpoints(idx, 2), 2))) - ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*(-(leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) - rightpoints(idx-1, 2) + rightpoints(idx, 2))/power(-(leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) - rightpoints(idx-1, 1) + rightpoints(idx, 1), 2) + (-leftpoints(idx-1, 2) + rightpoints(idx-1, 2))/(-(leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) - rightpoints(idx-1, 1) + rightpoints(idx, 1)))*(-(2*leftpoints(idx-1, 1) - 2*rightpoints(idx-1, 1))*power(-(leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) - rightpoints(idx-1, 2) + rightpoints(idx, 2), 2)/power(-(leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) - rightpoints(idx-1, 1) + rightpoints(idx, 1), 3) - (-2*leftpoints(idx-1, 2) + 2*rightpoints(idx-1, 2))*(-(leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) - rightpoints(idx-1, 2) + rightpoints(idx, 2))/power(-(leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) - rightpoints(idx-1, 1) + rightpoints(idx, 1), 2))/(power(1 + power(-(leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) - rightpoints(idx-1, 2) + rightpoints(idx, 2), 2)/power(-(leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) - rightpoints(idx-1, 1) + rightpoints(idx, 1), 2), 2)*sqrt(power((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) - (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx+1, 1) - rightpoints(idx, 1), 2) + power((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) - (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx+1, 2) - rightpoints(idx, 2), 2)))'"
            ]
          },
          "metadata": {},
          "execution_count": 81
        }
      ]
    }
  ]
}