lesson4.ipynb

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      "name": "lesson4.ipynb",
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      "name": "python3",
      "display_name": "Python 3"
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  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
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      "source": [
        "<a href=\"https://colab.research.google.com/github/onolab-tmu/audio-processing-100-knocks/blob/master/lesson4.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "R6fPTh-JidTP",
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      },
      "source": [
        "# パイソンのNumpyで線形台数\n",
        "\n",
        "## 先週のリマインド"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "yZJzclF3o57a",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import numpy as np  # アレー演算と線形台数\n",
        "import matplotlib.pyplot as plt  # 図\n",
        "from scipy.io import wavfile  # オーディオファイルの読み込み\n",
        "from IPython.display import Audio  # ノートブックでのオーディオ再生"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "cu-o3ifzlBmd",
        "colab_type": "text"
      },
      "source": [
        "## Numpyでアレー演算\n",
        "\n",
        "`numpy`はアレー演算と線形代数のパッケージ\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "2JutUn0AmDNY",
        "colab_type": "text"
      },
      "source": [
        "１次元アレーか**ベクトル**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "yVrRpPPZlH0Y",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 54
        },
        "outputId": "3f67e726-6f32-4a34-d5fb-c5a6a8b3585c"
      },
      "source": [
        "a_1d = np.array([1, 0.5, -2])\n",
        "print(a_1d)\n",
        "print(\"The shape of this array is\", a_1d.shape)"
      ],
      "execution_count": 29,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[ 1.   0.5 -2. ]\n",
            "The shape of this array is (3,)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "KAcjYl2slSPH",
        "colab_type": "text"
      },
      "source": [
        "0から、`N-1`までの整数"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "PEV45pcAlbBc",
        "colab_type": "code",
        "colab": {
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          "height": 35
        },
        "outputId": "ea417dcc-8926-4d02-ec4d-8004ec3a8d93"
      },
      "source": [
        "N = 10\n",
        "a = np.arange(N+1)\n",
        "print(a)"
      ],
      "execution_count": 32,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[ 0  1  2  3  4  5  6  7  8  9 10]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "qBldl2iJlpLh",
        "colab_type": "text"
      },
      "source": [
        "１から、`N-1`まで、2つずつ"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "7JULYxS9ljtc",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        },
        "outputId": "44ea59b9-1c4b-444c-bbcc-2f82100f3ed9"
      },
      "source": [
        "b = np.arange(2, N, 3)\n",
        "print(b)"
      ],
      "execution_count": 35,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[2 5 8]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "8Dcn0gkXl0QB",
        "colab_type": "text"
      },
      "source": [
        "`N`から、１まで"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "fFNKBgT4l5vn",
        "colab_type": "code",
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          "height": 35
        },
        "outputId": "3d0bed8d-bed5-4206-9a5d-fe3777d7390f"
      },
      "source": [
        "c = np.arange(N, 0, -1)\n",
        "print(c)"
      ],
      "execution_count": 17,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[10  9  8  7  6  5  4  3  2  1]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_b8rUQS0mwgW",
        "colab_type": "text"
      },
      "source": [
        "行列・２次元アレーも作れます"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "hq7OTT4dm1iX",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 72
        },
        "outputId": "d4adf552-702f-46a2-d064-76db3fa47ee9"
      },
      "source": [
        "a_2d = np.array(\n",
        "    [[1, 2, 3],\n",
        "     [4, 5, 6]]\n",
        ")\n",
        "print(a_2d)\n",
        "print(\"The size of this array is\", a_2d.shape)"
      ],
      "execution_count": 18,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[[1 2 3]\n",
            " [4 5 6]]\n",
            "The size of this array is (2, 3)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "8BBnFjkZmVBq",
        "colab_type": "text"
      },
      "source": [
        "示したサイズの`0`入りのアレーも作れます"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "1yFn90I_mhwj",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        },
        "outputId": "94ddd451-6478-4081-8cd7-249a901b9371"
      },
      "source": [
        "my_empty_array = np.zeros(10)\n",
        "print(my_empty_array)"
      ],
      "execution_count": 19,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "vzvcQ3cln2R9",
        "colab_type": "text"
      },
      "source": [
        "２次元も出来ます"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "arxaT7EAn4iG",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 109
        },
        "outputId": "60dc01da-0cad-4dc5-8aa9-57e4943af8a3"
      },
      "source": [
        "# shape は`(4, 3)`, 括弧は大事です！\n",
        "my_empty_array_2d = np.zeros((4, 3))\n",
        "print(my_empty_array_2d)\n",
        "print(\"The shape of this array is\", my_empty_array_2d.shape)"
      ],
      "execution_count": 20,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[[0. 0. 0.]\n",
            " [0. 0. 0.]\n",
            " [0. 0. 0.]\n",
            " [0. 0. 0.]]\n",
            "The shape of this array is (4, 3)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "OEH2zqbcmnmd",
        "colab_type": "text"
      },
      "source": [
        "同じく、`1`だけのアレーも作れます"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "_0eMSjQJmr7f",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 109
        },
        "outputId": "418e4d93-c38c-4de1-f399-40e21494bd77"
      },
      "source": [
        "my_one_array = np.ones(10)\n",
        "print(\"A 1D array of 1s with shape:\", my_one_array.shape)\n",
        "print(my_one_array)\n",
        "\n",
        "my_one_array_2d = np.ones((2, 4))\n",
        "print(\"A 2D array of 1s with shape:\", my_one_array_2d.shape)\n",
        "print(my_one_array_2d)"
      ],
      "execution_count": 25,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "A 1D array of 1s with shape: (10,)\n",
            "[1. 1. 1. 1. 1. 1. 1. 1. 1. 1.]\n",
            "A 2D array of 1s with shape: (2, 4)\n",
            "[[1. 1. 1. 1.]\n",
            " [1. 1. 1. 1.]]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "F4ZU9qEUqks5",
        "colab_type": "text"
      },
      "source": [
        "## Numpyで線形台数やりましょう！"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "qBDB6tkNqrpX",
        "colab_type": "text"
      },
      "source": [
        "### 第１問\n",
        "\n",
        "次の連立方程式をNumpyでときましょう。\n",
        "\n",
        "$$\n",
        "  \\left\\{\n",
        "    \\begin{array}{rcl}\n",
        "    3 x_1 - 2 x_2 & = & 5 \\\\\n",
        "    -7x_1 + 3 x_2 & = & -10\n",
        "   \\end{array}\n",
        "  \\right.\n",
        "$$\n",
        "\n",
        "連立方程式は行列の形でかけます\n",
        "$$\n",
        "\\mathbf{A} \\mathbf{x} = \\mathbf{b}\n",
        "$$\n",
        "なので、最初はNumpyのアレーで行列$\\mathbf{A}$とベクトル$\\mathbf{b}$を書きます。\n",
        "\n",
        "出来たら、`x = np.linalg.solve(A, b)`でとく事が出来ます。\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "vckGaPGQg_p8",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        },
        "outputId": "eefd932e-c99b-4c69-cc7c-56ff7ad71969"
      },
      "source": [
        "A = np.array(\n",
        "    [[3, -2],\n",
        "     [-7, 3]]\n",
        ")\n",
        "b = np.array([5, -10])\n",
        "x = np.linalg.solve(A, b)\n",
        "print(x)"
      ],
      "execution_count": 40,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[ 1. -1.]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "fqTUEr8rvkcj",
        "colab_type": "text"
      },
      "source": [
        "次は、行列積で、答えを確かめましょう。行列積は`@`オペレーターか、`np.dot`を使えます。"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "oqHf3F0XiFte",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 54
        },
        "outputId": "9b8696f8-7534-4cd8-b3d4-02324d822a44"
      },
      "source": [
        "b_2 = A @ x  # または, b_2 = np.dot(A, x)\n",
        "print(b)\n",
        "print(b_2)"
      ],
      "execution_count": 41,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[  5 -10]\n",
            "[  5. -10.]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "w84ez86m3iTn",
        "colab_type": "text"
      },
      "source": [
        "### 第２問 線形回帰\n",
        "\n",
        "$$\n",
        "y_i = a x_i + b + w_i, \\quad i=1,\\ldots,N\n",
        "$$\n",
        "\n",
        "* $a,b$はコンスタントパラメーター\n",
        "* $w_i$はノイズです\n",
        "\n",
        "$a,b$をデータから求めましょう"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "o4tH8L_Q3h7J",
        "colab_type": "code",
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          "height": 283
        },
        "outputId": "621c3739-2bc9-4db9-8503-ee2088cdaeb5"
      },
      "source": [
        "a = 3.\n",
        "b = -1\n",
        "N = 1000\n",
        "\n",
        "x = np.arange(N)\n",
        "\n",
        "y = a * x + b + 5 * np.random.randn(N)\n",
        "\n",
        "plt.plot(x, y)"
      ],
      "execution_count": 71,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7fbdf90f10f0>]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 71
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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vASDtb6dpNkwRKRaFDn13XwS020f/euDUffQ7cFNh3y8RDZu2gluHTou2e7U5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\nAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Ki9ErbRjIcwJ",
        "colab_type": "text"
      },
      "source": [
        ""
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "bAzgo_KSNkAT",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        },
        "outputId": "7b199650-a3df-4911-98a4-aae911d63076"
      },
      "source": [
        "x_sum_sq = np.sum(x ** 2)\n",
        "x_sum = np.sum(x)\n",
        "xy_sum = np.sum(x * y)\n",
        "y_sum = np.sum(y)\n",
        "\n",
        "A = np.array([[x_sum_sq, x_sum], [x_sum, N]])\n",
        "b = np.array([xy_sum, y_sum])\n",
        "p = np.linalg.solve(A, b)\n",
        "print(p)\n",
        "\n",
        "y_2 = p[0] * x + p[1]"
      ],
      "execution_count": 72,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[ 3.00010405 -1.16907778]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "q_tY-YriG14f",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        },
        "outputId": "dc67db2a-3e3b-42e7-881f-ff850ad65263"
      },
      "source": [
        "A = np.c_[x, np.ones(x.shape)]\n",
        "p = np.linalg.solve(A.T @ A, A.T @ y)\n",
        "print(p)"
      ],
      "execution_count": 69,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[ 2.5984993  -1.37612806]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Krx7-7voL-gr",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 284
        },
        "outputId": "05996ee5-1728-4600-b36a-78aa5d10ca5d"
      },
      "source": [
        "plt.plot(x, y)\n",
        "plt.plot(x, y_2)"
      ],
      "execution_count": 70,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7fbdf91c6080>]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 70
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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jx2v4YfeRlsd1Fkn7TCTEdsbXS85L2kJCt870DPFzyg1YSfLCKm8k7aewvIZH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\n+y2CiiZo7wAAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "AiwaGYYNMMzg",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": 0,
      "outputs": []
    }
  ]
}