Seminars/03-numpy/numpy.ipynb

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      "source": [
        "# `Практикум по программированию на языке Python`\n",
        "<br>\n",
        "\n",
        "## `Занятие 3: Numpy и матрично-векторные вычисления`\n",
        "## `Воробьев Сергей (tg: @serv01)`\n",
        "#### `Москва, 2023`\n",
        "Автор ноутбука – Находнов Максим (nakhodnov17@gmail.com)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "GaGh9SZ_wr4w"
      },
      "source": [
        "О чём можно узнать из этого ноутбука:\n",
        "\n",
        "* операции при работе с массивами\n",
        "* многомерные массивы\n",
        "* изменение размеров массивов\n",
        "* broadcasting\n",
        "* продвинутая индексация\n",
        "* view и копирование\n",
        "* свёртка\n",
        "* разные прикладные задачи"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {
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        },
        "id": "Uw8BOvbawr4x"
      },
      "outputs": [],
      "source": [
        "import warnings\n",
        "warnings.filterwarnings('ignore')"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_vWCVV6Swr4x"
      },
      "source": [
        "### `Представление матрицы в Python`\n",
        "\n",
        "Простейший вариант - список списков:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 2,
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      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[1, 2, 3]\n",
            "[4, 5, 6]\n",
            "[7, 8, 9]\n",
            "\n",
            "[1, 0, 0]\n",
            "[0, 2, 0]\n",
            "[0, 0, 3]\n",
            "\n"
          ]
        }
      ],
      "source": [
        "A = [\n",
        "    [1, 2, 3],\n",
        "    [4, 5, 6],\n",
        "    [7, 8, 9],\n",
        "]\n",
        "\n",
        "B = [\n",
        "    [1, 0, 0],\n",
        "    [0, 2, 0],\n",
        "    [0, 0, 3],\n",
        "]\n",
        "\n",
        "def print_matrix(A):\n",
        "    for row in A:\n",
        "        print(row)\n",
        "    print()\n",
        "\n",
        "print_matrix(A)\n",
        "print_matrix(B)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "dKv37qo0wr4y"
      },
      "source": [
        "### `Представление матрицы в Python`"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "vPiP2TIzwr4y"
      },
      "source": [
        "<font color='brown'>**Задача 1.** Задайте матрицу `C` размером $9$ на $10$, в которой $ij$-ый элемент будет равен $10 i + j$. Не используйте библиотеку `numpy`!</font>"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 3,
      "metadata": {
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        "id": "YwPfAfMawr4y"
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      "outputs": [],
      "source": [
        "### your code here\n",
        "C = []\n",
        "for idx in range(9):\n",
        "    C.append([])\n",
        "    for jdx in range(10):\n",
        "        C[-1].append(10 * idx + jdx)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "NChglwqowr4y"
      },
      "source": [
        "Проверьте себя:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 4,
      "metadata": {
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          "end_time": "2022-09-22T07:34:44.917671Z",
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        "deletable": false,
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        "run_control": {
          "frozen": true
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      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]\n",
            "[10, 11, 12, 13, 14, 15, 16, 17, 18, 19]\n",
            "[20, 21, 22, 23, 24, 25, 26, 27, 28, 29]\n",
            "[30, 31, 32, 33, 34, 35, 36, 37, 38, 39]\n",
            "[40, 41, 42, 43, 44, 45, 46, 47, 48, 49]\n",
            "[50, 51, 52, 53, 54, 55, 56, 57, 58, 59]\n",
            "[60, 61, 62, 63, 64, 65, 66, 67, 68, 69]\n",
            "[70, 71, 72, 73, 74, 75, 76, 77, 78, 79]\n",
            "[80, 81, 82, 83, 84, 85, 86, 87, 88, 89]\n",
            "\n"
          ]
        }
      ],
      "source": [
        "assert len(C) == 9\n",
        "assert len(C[0]) == 10\n",
        "assert C[8][3] == 83\n",
        "\n",
        "print_matrix(C)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "8FB9MFXOwr4z"
      },
      "source": [
        "### `Представление матрицы в Python`"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "e2Jit5kAwr4z"
      },
      "source": [
        "Одна из проблем списков — отсутствие поэлементных и матричных операций.\n",
        "\n",
        "Другой недостаток — работа со списками не позволяет использовать векторные инструкции в процессоре, которые на порядки ускоряют матричные вычисления"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ojyJOPxNwr4z"
      },
      "source": [
        "Попробуем самостоятельно реализовать несколько методов для матричных вычислений, работающих с представлением матриц в виде списков.\n",
        "\n",
        "Для оценки производительности будем использовать *декооратор* `timed`:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 5,
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          "end_time": "2022-09-22T08:00:50.167484Z",
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        },
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      "source": [
        "def timed(method):\n",
        "    import time\n",
        "    def __timed(*args, **kw):\n",
        "        time_start = time.time()\n",
        "        result = method(*args, **kw)\n",
        "        time_end = time.time()\n",
        "\n",
        "        print('{}  {:.3f} ms\\n'.format(method.__name__,\n",
        "                                      (time_end - time_start) * 1000))\n",
        "        return result\n",
        "\n",
        "    return __timed"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "473o8z9Cwr4z"
      },
      "source": [
        "### `Опишем базовые операции: сложение`"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 7,
      "metadata": {
        "ExecuteTime": {
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          "start_time": "2022-09-22T08:00:50.484748Z"
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        },
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      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "matrix_add  0.013 ms\n",
            "\n",
            "[2, 2, 3]\n",
            "[4, 7, 6]\n",
            "[7, 8, 12]\n",
            "\n"
          ]
        }
      ],
      "source": [
        "@timed\n",
        "def matrix_add(A, B):\n",
        "    # skip correctness of dimensions check\n",
        "\n",
        "    n, m = len(A), len(A[0])\n",
        "    C = [[0.0 for _ in range(m)] for _ in range(n)]\n",
        "\n",
        "    for i in range(n):\n",
        "        for j in range(m):\n",
        "            C[i][j] = A[i][j] + B[i][j]\n",
        "    return C\n",
        "\n",
        "print_matrix(matrix_add(A, B))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "gdqjbjMowr4z"
      },
      "source": [
        "### `Опишем базовые операции: транспонирование`"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 8,
      "metadata": {
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        },
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        },
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        "outputId": "b5eb1fc8-3a3d-4223-e45d-e2a530a7d6f2"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "matrix_transpose  0.012 ms\n",
            "\n",
            "[1, 4, 7]\n",
            "[2, 5, 8]\n",
            "[3, 6, 9]\n",
            "\n"
          ]
        }
      ],
      "source": [
        "@timed\n",
        "def matrix_transpose(A):\n",
        "    n, m = len(A), len(A[0])\n",
        "    C = [[0.0 for _ in range(n)] for _ in range(m)]\n",
        "\n",
        "    for i in range(n):\n",
        "        for j in range(m):\n",
        "            C[j][i] = A[i][j]\n",
        "    return C\n",
        "\n",
        "print_matrix(matrix_transpose(A))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "xowumGI7wr40"
      },
      "source": [
        "### `Опишем базовые операции: умножение`"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 9,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:00:51.093622Z",
          "start_time": "2022-09-22T08:00:51.084622Z"
        },
        "colab": {
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        },
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        "outputId": "13bedaa6-0c7d-4ae4-b9a4-a765e02ddb2a"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "matrix_transpose  0.009 ms\n",
            "\n",
            "matrix_mul  1.176 ms\n",
            "\n",
            "[1, 4, 9]\n",
            "[4, 10, 18]\n",
            "[7, 16, 27]\n",
            "\n"
          ]
        }
      ],
      "source": [
        "def dot(a, b):\n",
        "    return sum(x * y for (x, y) in zip(a, b))\n",
        "\n",
        "@timed\n",
        "def matrix_mul(A, B):\n",
        "    # check correctness of dimensions\n",
        "    n, m = len(A), len(B[0])\n",
        "    C = [[0.0 for _ in range(n)] for _ in range(m)]\n",
        "\n",
        "    B_T = matrix_transpose(B)\n",
        "    for i in range(n):\n",
        "        for j in range(m):\n",
        "            C[i][j] = dot(A[i], B_T[j])\n",
        "    return C\n",
        "\n",
        "print_matrix(matrix_mul(A, B))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "hESzT5BAwr40"
      },
      "source": [
        "### `Библиотека NumPy`\n",
        "\n",
        "- Позволяет работать с многомерными массивами<br><br>\n",
        "\n",
        "- Реализует множество базовых матричных операций<br><br>\n",
        "\n",
        "- Работает на порядки быстрее самописных реализаций в Python<br><br>\n",
        "\n",
        "- Поддерживается большинством сторонних модулей, работающих с матрицами<br><br>"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 10,
      "metadata": {
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          "start_time": "2022-09-22T08:00:51.428515Z"
        },
        "id": "yhd52Fo5wr40"
      },
      "outputs": [],
      "source": [
        "# from numpy import * — НЕ ДЕЛАЙТЕ ТАК\n",
        "import numpy as np"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Arbt3otLwr40"
      },
      "source": [
        "Текущая версия:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 11,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:00:51.756417Z",
          "start_time": "2022-09-22T08:00:51.748417Z"
        },
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 36
        },
        "id": "ZJmUoqHawr40",
        "outputId": "c4cc72bb-6054-4359-89e1-36f12a71f669"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "'1.23.5'"
            ],
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "string"
            }
          },
          "metadata": {},
          "execution_count": 11
        }
      ],
      "source": [
        "np.__version__"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "fXJ5nrGfwr40"
      },
      "source": [
        "### `Почему NumPy быстрая`\n",
        "\n",
        "- Значительная часть кода написана на C<br><br>\n",
        "\n",
        "- Базовым классом является `ndarray`, имеющий следующие отличия от списков:\n",
        "\n",
        "    1. NumPy array имеет фиксированную длину, задаваемую в момент его создания (списки в Python могут менять размер динамически)\n",
        "\n",
        "    2. Все элементы в NumPy array имеют один тип<br><br>\n",
        "\n",
        "- NumPy array хранится в памяти в виде одного последовательного блока, что позволяет эффективно использовать процессорный кэш и векторные инструкции<br><br>\n",
        "\n",
        "- NumPy можно подключить к высокооптимизированным библиотекам для матричной алгебры (BLAS, LAPACK, Intel MKL)<br><br>\n",
        "\n",
        "- Часть матричных операций может быть распараллелена при наличии в системе нескольких потоков\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "uSZUFyR0wr40"
      },
      "source": [
        "### `Способы создания NumPy array`\n",
        "\n",
        "1. Пустой\n",
        "2. Заполненный нулями\n",
        "3. Заполненный единицами\n",
        "4. Заполненный нужным значением"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 12,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:00:52.259961Z",
          "start_time": "2022-09-22T08:00:52.252963Z"
        },
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        },
        "id": "1fR_01Yywr40",
        "outputId": "6fffa68b-4b5f-46fe-a36f-847225f94aa5"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[4.89521082e-310 0.00000000e+000 2.05833592e-312]\n",
            " [6.79038654e-313 2.14321575e-312 2.27053550e-312]]\n"
          ]
        }
      ],
      "source": [
        "print(np.empty(shape=[2, 3]))  # values are arbitrary"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 13,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:00:52.445821Z",
          "start_time": "2022-09-22T08:00:52.436823Z"
        },
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        },
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      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0. 0. 0.]\n",
            " [0. 0. 0.]]\n"
          ]
        }
      ],
      "source": [
        "print(np.zeros([2, 3]))"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 17,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:00:52.637411Z",
          "start_time": "2022-09-22T08:00:52.620413Z"
        },
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "PfwcgUEzwr41",
        "outputId": "a46cd75d-1f47-4269-f273-8c61548a5032"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[1. 1. 1.]\n",
            " [1. 1. 1.]]\n"
          ]
        }
      ],
      "source": [
        "print(np.ones([2, 3]))"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 18,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:00:52.811524Z",
          "start_time": "2022-09-22T08:00:52.796522Z"
        },
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "A-9ZRE2cwr41",
        "outputId": "2a025ab5-888f-4ae8-cf69-986a0a92215f"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[3. 3. 3.]\n",
            " [3. 3. 3.]]\n"
          ]
        }
      ],
      "source": [
        "print(np.full([2, 3], 3.0))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "HoRH-xt3wr41"
      },
      "source": [
        "### `Способы создания NumPy array`"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "mKIXI1tvwr41"
      },
      "source": [
        "Указанные четыре функции имеют аналоги с суффиксом `*_like`, которые создают массив того же размера, что передан в качестве агрумента:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 19,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:00:53.349381Z",
          "start_time": "2022-09-22T08:00:53.340382Z"
        },
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        },
        "id": "g2t8BacVwr41",
        "outputId": "cd26d9aa-81ac-4bc0-9442-bb33cdeb425c"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[[0. 0. 0.]\n",
            "  [0. 0. 0.]]]\n",
            "[[[1. 1. 1.]\n",
            "  [1. 1. 1.]]]\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "((1, 2, 3), (1, 2, 3))"
            ]
          },
          "metadata": {},
          "execution_count": 19
        }
      ],
      "source": [
        "a = np.zeros([1, 2, 3])\n",
        "b = np.ones_like(a)\n",
        "\n",
        "print(a)\n",
        "print(b)\n",
        "a.shape, b.shape"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "bojUa9bTwr41"
      },
      "source": [
        "### `Способы создания NumPy array`"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T06:39:48.680889Z",
          "start_time": "2022-09-22T06:39:48.665891Z"
        },
        "id": "oKWCgGswwr41"
      },
      "source": [
        "Для создания одномерных массивов можно передавать их длину в виде целого числа:  "
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 20,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:00:53.848404Z",
          "start_time": "2022-09-22T08:00:53.844405Z"
        },
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "SrPT9GXHwr41",
        "outputId": "3ddec04c-6304-45a5-9415-2f573830f26f"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([0., 0., 0., 0., 0.])"
            ]
          },
          "metadata": {},
          "execution_count": 20
        }
      ],
      "source": [
        "np.zeros(5)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "uwkfZ7i-wr41"
      },
      "source": [
        "Для одномерного массива тоже можно писать кортеж:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 26,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:00:54.224988Z",
          "start_time": "2022-09-22T08:00:54.213989Z"
        },
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "GZUjrZCJwr41",
        "outputId": "9656a84b-afd1-4116-b73b-cb07b9f3eaa0"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([0., 0., 0., 0., 0.])"
            ]
          },
          "metadata": {},
          "execution_count": 26
        }
      ],
      "source": [
        "np.zeros(shape=(5,))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T06:40:43.168313Z",
          "start_time": "2022-09-22T06:40:43.152313Z"
        },
        "id": "WCgk64rCwr41"
      },
      "source": [
        "Для больших размерностей, так задавать массив нельзя.\n",
        "\n",
        "Так неправильно:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 29,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:00:54.993400Z",
          "start_time": "2022-09-22T08:00:54.588400Z"
        },
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 183
        },
        "id": "-T4yOEnvwr4_",
        "outputId": "62e31319-f82e-40d8-c0b8-134afc0b6e58"
      },
      "outputs": [
        {
          "output_type": "error",
          "ename": "TypeError",
          "evalue": "ignored",
          "traceback": [
            "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
            "\u001b[0;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
            "\u001b[0;32m<ipython-input-29-0252f51f341f>\u001b[0m in \u001b[0;36m<cell line: 1>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mzeros\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m5\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m7\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
            "\u001b[0;31mTypeError\u001b[0m: Cannot interpret '7' as a data type"
          ]
        }
      ],
      "source": [
        "np.zeros(5, 7)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_knsxNc8wr4_"
      },
      "source": [
        "### `Способы создания NumPy array`\n",
        "\n",
        "5. На основе списков"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 30,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:00:54.994402Z",
          "start_time": "2022-09-22T08:00:54.994402Z"
        },
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "nzcJ_3Anwr4_",
        "outputId": "d496cdc5-3e06-4b09-e728-b365473a4dc1"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[1 2 3]\n",
            " [4 5 6]]\n"
          ]
        }
      ],
      "source": [
        "print(np.array([[1, 2, 3], [4, 5, 6]]))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6WQUq88twr4_"
      },
      "source": [
        "Число элементов должно удовлетворять размерности, numpy попытается преобразовать типы:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 31,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:00:55.604748Z",
          "start_time": "2022-09-22T08:00:55.596747Z"
        },
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "AyeEvbRAwr4_",
        "outputId": "7afc3683-13c0-44db-903d-7ca8480629b7"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[list([1, 2, 3]) list([4, 6])]\n"
          ]
        }
      ],
      "source": [
        "print(np.array([[1, 2, 3], [4, 6]]))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "kjDsvKhmwr4_"
      },
      "source": [
        "Тип можно указать явно, и неправильное число элементов приведёт к ошибке:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 32,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:00:55.940391Z",
          "start_time": "2022-09-22T08:00:55.924393Z"
        },
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 201
        },
        "id": "wbGe0lAxwr4_",
        "outputId": "1a05efdd-58f6-450e-c57d-1d8542920a84"
      },
      "outputs": [
        {
          "output_type": "error",
          "ename": "ValueError",
          "evalue": "ignored",
          "traceback": [
            "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
            "\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)",
            "\u001b[0;32m<ipython-input-32-f29d5103418c>\u001b[0m in \u001b[0;36m<cell line: 1>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0marray\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m2\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m3\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0;36m4\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m6\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdtype\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mfloat32\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
            "\u001b[0;31mValueError\u001b[0m: setting an array element with a sequence. The requested array has an inhomogeneous shape after 1 dimensions. The detected shape was (2,) + inhomogeneous part."
          ]
        }
      ],
      "source": [
        "np.array([[1, 2, 3], [4, 6]], dtype=np.float32)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "wjLlRXyXwr5A"
      },
      "source": [
        "### `Способы создания NumPy array`"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "TVOmKwM-wr5A"
      },
      "source": [
        "6. Последовательность целых чисел заданной длины"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 33,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:00:56.462636Z",
          "start_time": "2022-09-22T08:00:56.444636Z"
        },
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "gfIvNgVfwr5A",
        "outputId": "b597f4b0-7fc8-42f9-a5f7-5d9d1a9aa6e2"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([2, 3, 4, 5, 6, 7, 8, 9])"
            ]
          },
          "metadata": {},
          "execution_count": 33
        }
      ],
      "source": [
        "# Синтаксис аналогичен функции `range`, но в этом случае данные хранятся в памяти\n",
        "np.arange(2, 10)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "T5Lel60xwr5A"
      },
      "source": [
        "7. Разбиение отрезка на равные подотрезки (в исходном и log-масштабе)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 34,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:00:56.793292Z",
          "start_time": "2022-09-22T08:00:56.788293Z"
        },
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "d4VagN5Xwr5A",
        "outputId": "adb12a8f-a135-4169-d021-cec826f498bb"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(array([0.  , 0.25, 0.5 , 0.75, 1.  ]),\n",
              " array([ 1.        ,  1.77827941,  3.16227766,  5.62341325, 10.        ]))"
            ]
          },
          "metadata": {},
          "execution_count": 34
        }
      ],
      "source": [
        "np.linspace(0.0, 1.0, 5), np.logspace(0.0, 1.0, 5)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "PtdBWt4ewr5A"
      },
      "source": [
        "### `Способы создания NumPy array`"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "I9yvPc7Pwr5A"
      },
      "source": [
        "<font color='brown'>**Задача 2.** Задайте массив `result` размером $50$ на $30$, состоящий из троек:</font>"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 156,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:00:57.341436Z",
          "start_time": "2022-09-22T08:00:57.333435Z"
        },
        "id": "MPyhcybPwr5A"
      },
      "outputs": [],
      "source": [
        "### your code here"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T06:50:02.269559Z",
          "start_time": "2022-09-22T06:50:02.253560Z"
        },
        "id": "xQR34U0Twr5A"
      },
      "source": [
        "<font color='brown'>**Задача 3.** Какая размерность будет у массива, полученного с помощью команды `np.array([[1], [2]])`?</font>"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 155,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:00:57.737381Z",
          "start_time": "2022-09-22T08:00:57.732381Z"
        },
        "id": "oyC6xj-awr5A"
      },
      "outputs": [],
      "source": [
        "### your answer here"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_COuXwvCwr5A"
      },
      "source": [
        "### `Важные параметры создания ndarray`\n",
        "\n",
        "- `shape` — список или кортеж с размерностями создаваемого массива<br><br>\n",
        "\n",
        "- `dtype` — указание типа элементов массива, если массив создаётся на базе объектов из Python, то должно существовать преобразование из типа этих объектов в указываемый тип<br><br>\n",
        "\n",
        "- `order` — порядок хранения данных в памяти, по строкам (C-order) или же по столбцам (Fortran-order). По-умолчанию используется C-order"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "HfYuRYe9wr5A"
      },
      "source": [
        "### `Отличие классов np.ndarray и np.matrix`\n",
        "\n",
        "- `ndarray` — более общий класс, поддерживающий все возможные операции<br><br>\n",
        "\n",
        "- `matrix` — более узкий класс, наследующий `ndarray`. Он поддерживает несколько операций и атрибутов, специфичных для матриц, в удобной нотации<br><br>\n",
        "\n",
        "- При этом все те же операции можно применять и к `ndarray`, если он двумерный и состоит из чисел (начиная с Python 3.5 умножение можно записать как `A @ B`)<br><br>\n",
        "\n",
        "- Рекомендуется пользоваться `ndarray`, чтобы не вносить путаницу в код и не проверять каждый раз, какого именно типа массив будет обрабатываться"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "-X602HWMwr5A"
      },
      "source": [
        "### `Изменение размерности`\n",
        "\n",
        "`reshape` позволяет изменить размерности массива __без изменения общего числа элементов__:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 44,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:00:58.477418Z",
          "start_time": "2022-09-22T08:00:58.460419Z"
        },
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Of438spcwr5A",
        "outputId": "ba6f5e23-4f6c-40f6-80d5-e1326bcde54d"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[[0. 0.]\n",
            "  [0. 0.]\n",
            "  [0. 0.]]\n",
            "\n",
            " [[0. 0.]\n",
            "  [0. 0.]\n",
            "  [0. 0.]]] (2, 3, 2)\n"
          ]
        }
      ],
      "source": [
        "a = np.zeros([2, 3, 2])\n",
        "print(a, a.shape)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 4,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:00:58.635377Z",
          "start_time": "2022-09-22T08:00:58.620382Z"
        },
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Nvgef8pSwr5A",
        "outputId": "b537408f-e0a6-43a2-dec0-1ef35ac55c54"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]] (1, 12) \n",
            "\n",
            "[[[10.  0.]\n",
            "  [ 0.  0.]\n",
            "  [ 0.  0.]]\n",
            "\n",
            " [[ 0.  0.]\n",
            "  [ 0.  0.]\n",
            "  [ 0.  0.]]] (2, 3, 2)\n"
          ]
        }
      ],
      "source": [
        "b = a.reshape((1, 2 * 3 * 2))\n",
        "print(b, b.shape, '\\n')\n",
        "\n",
        "b[0][0] = 10  # 'b' is a new view on the same data\n",
        "\n",
        "print(a, a.shape)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "uewceKE-wr5A"
      },
      "source": [
        "Можно проверить, не пересекаются ли в памяти два массива:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 54,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:00:58.976164Z",
          "start_time": "2022-09-22T08:00:58.964165Z"
        },
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "OZsMH_BVwr5B",
        "outputId": "a19d0f37-880a-45b2-9400-81cad024b3b9"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "True"
            ]
          },
          "metadata": {},
          "execution_count": 54
        }
      ],
      "source": [
        "np.may_share_memory(a, b)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "K6EtDPvcwr5B"
      },
      "source": [
        "### `Изменение размерности`\n",
        "\n",
        "Отметим, что практически все методы `np.ndarray` доступны в виде функций модуля NumPy:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:00:59.369040Z",
          "start_time": "2022-09-22T08:00:59.364040Z"
        },
        "id": "BPynKsCPwr5B",
        "outputId": "d3244124-4eae-416a-d72f-05bf73450452"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "[[10.  0.]\n",
            " [ 0.  0.]\n",
            " [ 0.  0.]\n",
            " [ 0.  0.]\n",
            " [ 0.  0.]\n",
            " [ 0.  0.]] (6, 2)\n"
          ]
        }
      ],
      "source": [
        "c = np.reshape(b, (2 * 3, 2))\n",
        "print(c, c.shape)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "AcvwfuF6wr5B"
      },
      "source": [
        "Размерность можно изменить и напрямую:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:00:59.760289Z",
          "start_time": "2022-09-22T08:00:59.748291Z"
        },
        "id": "mcaT6p2Qwr5B",
        "outputId": "5e5935df-55b9-4120-d369-387ac6a2f0e6"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "[[10.  0.  0.  0.  0.  0.  0.  0.  0.  0.  0.  0.]] (1, 12)\n"
          ]
        }
      ],
      "source": [
        "c.shape = (1, 2 * 3 * 2)\n",
        "print(c, c.shape)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "pdyUtJ9dwr5B"
      },
      "source": [
        "Можно \"не заполнять\" одну размерность итогового массива, она заполнится автоматически:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:01:00.106443Z",
          "start_time": "2022-09-22T08:01:00.095443Z"
        },
        "id": "8lOQoeaKwr5B",
        "outputId": "dce7a305-32f3-4f92-9585-943795a42768"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "[[[10.  0.  0.]\n",
            "  [ 0.  0.  0.]]\n",
            "\n",
            " [[ 0.  0.  0.]\n",
            "  [ 0.  0.  0.]]] (2, 2, 3)\n"
          ]
        }
      ],
      "source": [
        "d = c.reshape(2, -1, 3)\n",
        "print(d, d.shape)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "EWOlj6NHwr5B"
      },
      "source": [
        "### `Про размерности массивов`"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:01:00.468365Z",
          "start_time": "2022-09-22T08:01:00.452366Z"
        },
        "id": "Z0MQzXmgwr5B",
        "outputId": "d862ae5c-8e6d-42f2-bc89-5416141a1496"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "(3,)\n",
            "(1, 3)\n",
            "(3, 1)\n"
          ]
        }
      ],
      "source": [
        "a = np.array([1, 2, 3])\n",
        "b = np.array([[1, 2, 3]])\n",
        "c = np.array([[1], [2], [3]])\n",
        "print(a.shape)\n",
        "print(b.shape)\n",
        "print(c.shape)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "vYY6S2XLwr5B"
      },
      "source": [
        "- Данные лежат в памяти одним и тем же образом\n",
        "\n",
        "- Вопрос только во `view` $==$ способ индексации $==$ число и порядок индексов"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:01:00.875757Z",
          "start_time": "2022-09-22T08:01:00.861758Z"
        },
        "id": "UFrsvVyFwr5B",
        "outputId": "ef7bbf82-082a-436b-b7f3-85e9950cf1d2"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "1 2 2\n"
          ]
        }
      ],
      "source": [
        "print(a.ndim, b.ndim, c.ndim)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "VUDkhIMHwr5B"
      },
      "source": [
        "Полезная для понимания происходящего статья: https://stackoverflow.com/questions/22053050/difference-between-numpy-array-shape-r-1-and-r"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "BYoT3PORwr5B"
      },
      "source": [
        "### `View и копирование`"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T07:39:53.556863Z",
          "start_time": "2022-09-22T07:39:53.547862Z"
        },
        "id": "dfs7hQK2wr5B"
      },
      "source": [
        "View ссылается на те же данные, но позволяет задать другие размерности массива."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 18,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:01:01.648315Z",
          "start_time": "2022-09-22T08:01:01.644315Z"
        },
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "jliMqS10wr5C",
        "outputId": "7357ef76-18b8-43a8-9856-8f4056c410a6"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9]),\n",
              " array([[0, 1, 2, 3, 4],\n",
              "        [5, 6, 7, 8, 9]]))"
            ]
          },
          "metadata": {},
          "execution_count": 18
        }
      ],
      "source": [
        "x = np.arange(10)\n",
        "v = x.view()\n",
        "v.shape = (2, 5)\n",
        "x, v"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 20,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:01:01.835160Z",
          "start_time": "2022-09-22T08:01:01.821161Z"
        },
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "3EoZmpDewr5C",
        "outputId": "5e7441b9-414e-4c65-9d6b-008ad8e43ed1"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(array([100,   1,   2,   3,   4,   5,   6,   7,   8,   9]),\n",
              " array([[100,   1,   2,   3,   4],\n",
              "        [  5,   6,   7,   8,   9]]))"
            ]
          },
          "metadata": {},
          "execution_count": 20
        }
      ],
      "source": [
        "v[0, 0] = 100\n",
        "x, v"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Yjt1J9skwr5C"
      },
      "source": [
        "Если нужно получить копию массива, чтобы не портить переданные данные, пользуйтесь методом `copy`:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 21,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:01:02.209355Z",
          "start_time": "2022-09-22T08:01:02.204358Z"
        },
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "jO834vnWwr5C",
        "outputId": "9e0ba724-2ed4-46ca-fbde-ccd1d83a6612"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9]), array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0]))"
            ]
          },
          "metadata": {},
          "execution_count": 21
        }
      ],
      "source": [
        "x = np.arange(10)\n",
        "y = x.copy()\n",
        "y[:] = 0\n",
        "x, y"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "SdPjbZTZwr5C"
      },
      "source": [
        "### `Индексирование`\n",
        "\n",
        "- Всё аналогично спискам, можно делать срезы и использовать отрицательные индексы\n",
        "- Индексы и срезы в многомерных массивах не обязательно разделять квадратными скобками\n",
        "- Подробное описание: https://docs.scipy.org/doc/numpy/reference/arrays.indexing.html"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:01:02.589352Z",
          "start_time": "2022-09-22T08:01:02.572353Z"
        },
        "id": "YsCcQukCwr5C",
        "outputId": "52b14299-77fa-4d15-af71-c4409d1d1b71"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "[[1 2 3]\n",
            " [3 4 5]] \n",
            "\n",
            "[1 2 3] \n",
            "\n",
            "[1 2 3] \n",
            "\n",
            "2 \n",
            "\n",
            "4 \n",
            "\n",
            "4 \n",
            "\n",
            "[1 2]\n"
          ]
        }
      ],
      "source": [
        "a = np.array([[1, 2, 3], [3, 4, 5]])\n",
        "\n",
        "print(a, '\\n')\n",
        "print(a[0], '\\n')\n",
        "print(a[0, 0: 100500], '\\n')\n",
        "print(a[0][1], '\\n')\n",
        "print(a[-1][-2], '\\n')\n",
        "print(a[-1, -2], '\\n')\n",
        "print(a[0, 0: -1])"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "x2tVErrBwr5C"
      },
      "source": [
        "### `Индексирование`\n",
        "\n",
        "Важное отличие от питоновских списков: при slicing возвращается **view**, а не копия! Это позволяет присваивать значения подматрицам."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 69,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:01:02.984334Z",
          "start_time": "2022-09-22T08:01:02.972333Z"
        },
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "xRk5cj2ywr5C",
        "outputId": "1ea27596-531b-4fe0-9192-2a880feffdd3"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[1 2 3]\n",
            " [3 4 5]] \n",
            "\n",
            "[[ 1 10  3]\n",
            " [ 3 10  5]] \n",
            "\n"
          ]
        }
      ],
      "source": [
        "a = np.array([[1, 2, 3], [3, 4, 5]])\n",
        "print(a, '\\n')\n",
        "\n",
        "a[:, 1] = 10\n",
        "print(a, '\\n')"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "PbwdsTlYwr5C"
      },
      "source": [
        "### `Логическое индексирование`\n",
        "\n",
        "Индексирование можно производить по логическому массиву такого же размера:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 82,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:01:03.361856Z",
          "start_time": "2022-09-22T08:01:03.355858Z"
        },
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "bUkL1GLWwr5C",
        "outputId": "5f21bc9f-b836-4192-9adb-f5e638ee289c"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[0 1 2 3 4 5 6 7 8 9] \n",
            "\n",
            "[ True False  True False  True False  True False  True False] \n",
            "\n",
            "[0 2 4 6 8] \n",
            "\n"
          ]
        }
      ],
      "source": [
        "a = np.arange(10)\n",
        "i = np.array([j % 2 == 0 for j in range(10)])\n",
        "\n",
        "print(a, '\\n')\n",
        "print(i, '\\n')\n",
        "print(a[i], '\\n')"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "LHOpSaZ8wr5C"
      },
      "source": [
        "При этом такие слайсы также позволяют менять исходный массив:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:01:03.771346Z",
          "start_time": "2022-09-22T08:01:03.756348Z"
        },
        "id": "MFYOUVVYwr5C",
        "outputId": "6281a1f0-7392-41b6-a243-c414f3cb3d29"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([11,  1, 11,  3, 11,  5, 11,  7, 11,  9])"
            ]
          },
          "execution_count": 38,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "a[i] = 11\n",
        "a"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "v83Kflrewr5C"
      },
      "source": [
        "### `Логическое индексирование`\n",
        "\n",
        "С помощью функции `where`, можно находить индексы элементов, заданные маской:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 85,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:01:04.180832Z",
          "start_time": "2022-09-22T08:01:04.163832Z"
        },
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "qEf8WN2Gwr5C",
        "outputId": "741b131d-75c8-4628-f0da-0de91a22d4cb"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(array([5, 6, 7, 8, 9]),)"
            ]
          },
          "metadata": {},
          "execution_count": 85
        }
      ],
      "source": [
        "np.where(a > 4)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "a-P5YcG6wr5C"
      },
      "source": [
        "В случае одного аргумента `np.where` вернет `tuple`. Смотри документацию или [тут](https://stackoverflow.com/questions/50646102/what-is-the-purpose-of-numpy-where-returning-a-tuple)"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "c = np.arange(12).reshape(3, 2, 2)\n",
        "np.where(c > 4)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "KHhfRakU3UHt",
        "outputId": "d3d78191-da7a-447a-ab51-22f96b57503f"
      },
      "execution_count": 165,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(array([1, 1, 1, 2, 2, 2, 2]),\n",
              " array([0, 1, 1, 0, 0, 1, 1]),\n",
              " array([1, 0, 1, 0, 1, 0, 1]),\n",
              " array([0, 0, 0, 0, 0, 0, 0]),\n",
              " array([0, 0, 0, 0, 0, 0, 0]))"
            ]
          },
          "metadata": {},
          "execution_count": 165
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "c"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "-CFDACQidw8r",
        "outputId": "104e1ae0-7a3c-4a4d-9e26-4172f0acaed8"
      },
      "execution_count": 164,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[[ 0,  1],\n",
              "        [ 2,  3]],\n",
              "\n",
              "       [[ 4,  5],\n",
              "        [ 6,  7]],\n",
              "\n",
              "       [[ 8,  9],\n",
              "        [10, 11]]])"
            ]
          },
          "metadata": {},
          "execution_count": 164
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "np.where(a > 4, a, 0)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "L5swxmcO4PZP",
        "outputId": "caf47112-686b-4cda-9804-55625292cbed"
      },
      "execution_count": 103,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([0, 0, 0, 0, 0, 5, 6, 7, 8, 9])"
            ]
          },
          "metadata": {},
          "execution_count": 103
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "TwEw250-wr5C"
      },
      "source": [
        "<font color='brown'> **Задача 4.** Даны два вектора одинаковой длины: `a` и `b`. Оставить в этих векторах только те элементы, которые соответствуют позициям ненулевых элементов в обоих векторах. </font>"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 23,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:01:04.735350Z",
          "start_time": "2022-09-22T08:01:04.724353Z"
        },
        "id": "9GCC65okwr5D"
      },
      "outputs": [],
      "source": [
        "a = np.array([0, 1, 0, 2, 3])\n",
        "b = np.array([1, 5, 2, 0, 6])"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 25,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:01:04.940352Z",
          "start_time": "2022-09-22T08:01:04.925355Z"
        },
        "id": "85yByMX4wr5D"
      },
      "outputs": [],
      "source": [
        "### your code here"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "wDfM7JoXwr5D"
      },
      "source": [
        "Проверьте себя:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 26,
      "metadata": {
        "deletable": false,
        "editable": false,
        "run_control": {
          "frozen": true
        },
        "id": "5qm-RBWowr5D"
      },
      "outputs": [],
      "source": [
        "assert a.tolist() == [1, 3]\n",
        "assert b.tolist() == [5, 6]"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "SO0LrqkVwr5D"
      },
      "source": [
        "### `Сложное индексирование`\n",
        "\n",
        "По каждой размерности подаются массивы одинаковых размеров, элементы которых соответствуют индексам каждой размерности. Тогда, на выходе будет массив размера этих массивов, элементы которого будут соответствовать элементам исходного массива, взятых в точках, соответствующих поданным массивам."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 91,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:01:05.735426Z",
          "start_time": "2022-09-22T08:01:05.732425Z"
        },
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "eqHfbt0bwr5D",
        "outputId": "a34b3693-f906-4ed5-b616-8fda146d7d2c"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[1, 2, 3],\n",
              "       [4, 5, 6]])"
            ]
          },
          "metadata": {},
          "execution_count": 91
        }
      ],
      "source": [
        "X = np.array([[1, 2, 3], [4, 5, 6]])\n",
        "X"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:01:05.924335Z",
          "start_time": "2022-09-22T08:01:05.916335Z"
        },
        "id": "L3rNZd0Jwr5D",
        "outputId": "d0dde84c-e600-4d93-918b-2bb7d47bc870"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "(array([2, 6]), array([2, 1]))"
            ]
          },
          "execution_count": 43,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "X[[0, 1], [1, 2]], X[[0, 0], [1, 0]]"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:01:06.109378Z",
          "start_time": "2022-09-22T08:01:06.092380Z"
        },
        "id": "LEcrXd2xwr5D",
        "outputId": "cebe2cd4-3b63-4f33-fad4-e0ba3609190e"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([[[ 0,  1,  2,  3],\n",
              "        [ 4,  5,  6,  7]],\n",
              "\n",
              "       [[ 8,  9, 10, 11],\n",
              "        [12, 13, 14, 15]],\n",
              "\n",
              "       [[16, 17, 18, 19],\n",
              "        [20, 21, 22, 23]]])"
            ]
          },
          "execution_count": 44,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "Y = np.arange(24).reshape((3, 2, 4))\n",
        "Y"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:01:06.298410Z",
          "start_time": "2022-09-22T08:01:06.279410Z"
        },
        "id": "NWiIuyIuwr5D",
        "outputId": "aa64d6f1-5782-4323-87da-dcef00005648"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([[10, 14],\n",
              "       [ 1,  5]])"
            ]
          },
          "execution_count": 45,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "Y[[1, 0], :, [2, 1]]"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "sMQcb_lUwr5D"
      },
      "source": [
        "### `Сокращенная индексация`\n",
        "\n",
        "Если у вас есть многомерный массив, а вам, например, надо взять определенные индексы только с последней размерности, то можно написать так:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:01:06.677537Z",
          "start_time": "2022-09-22T08:01:06.662539Z"
        },
        "id": "SF53jczKwr5D",
        "outputId": "889a37db-0496-42d9-9a3a-f757cef5db87"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "[[[ 0  5 10 15]\n",
            "  [20 25 30 35]]\n",
            "\n",
            " [[40 45 50 55]\n",
            "  [60 65 70 75]]]\n"
          ]
        },
        {
          "data": {
            "text/plain": [
              "(2, 2, 4)"
            ]
          },
          "execution_count": 46,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "x = np.arange(80).reshape((2, 2, 4, 5))\n",
        "\n",
        "print(x[..., 0])\n",
        "x[..., 0].shape"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "WKT9fBoiwr5D"
      },
      "source": [
        "Более хитрый пример:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:01:07.059608Z",
          "start_time": "2022-09-22T08:01:07.045609Z"
        },
        "id": "2Uyq_Rs_wr5D",
        "outputId": "a1f65797-e7d7-4bd2-88e2-d5da7854bade"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "[[[516 518]\n",
            "  [520 522]\n",
            "  [524 526]]\n",
            "\n",
            " [[576 578]\n",
            "  [580 582]\n",
            "  [584 586]]\n",
            "\n",
            " [[636 638]\n",
            "  [640 642]\n",
            "  [644 646]]\n",
            "\n",
            " [[696 698]\n",
            "  [700 702]\n",
            "  [704 706]]]\n"
          ]
        },
        {
          "data": {
            "text/plain": [
              "(4, 3, 2)"
            ]
          },
          "execution_count": 47,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "x = np.arange(720).reshape((3, 4, 5, 3, 2, 2))\n",
        "\n",
        "print(x[2, :, 3, ..., 0])\n",
        "x[2, :, 3, ..., 0].shape"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "FV_fLkBVwr5D"
      },
      "source": [
        "### `Арифметические операции`\n",
        "\n",
        "- Арифметические операции в общем случае по-элементные и требуют одинакового размера операндов<br>\n",
        "\n",
        "- Но часто NumPy может применять их к операндам разного размера с помощью broadcasting, то есть правил обработки операндов разного размера<br><br>\n",
        "\n",
        "Примеры операций с массивами одного размера:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 29,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:01:07.483335Z",
          "start_time": "2022-09-22T08:01:07.468336Z"
        },
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Lf_4cys_wr5E",
        "outputId": "3371a858-2883-4ec6-b313-337d92f56195"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[1 2 3]\n",
            " [4 5 6]\n",
            " [7 8 9]] \n",
            "\n",
            " [[1 0 0]\n",
            " [0 2 0]\n",
            " [0 0 3]] \n",
            "\n",
            " [[ 2  4  6]\n",
            " [ 8 10 12]\n",
            " [14 16 18]] \n",
            "\n",
            " [[ 2  2  3]\n",
            " [ 4  7  6]\n",
            " [ 7  8 12]]\n"
          ]
        }
      ],
      "source": [
        "A, B = np.array(A), np.array(B)  # were declared previously\n",
        "\n",
        "print(A, '\\n\\n', B, '\\n\\n', 2 * A, '\\n\\n', A + B)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "T5Wamqumwr5E"
      },
      "source": [
        "### `Поэлементные арифметические операции`"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 30,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:01:07.881483Z",
          "start_time": "2022-09-22T08:01:07.868481Z"
        },
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "NLuiSggUwr5E",
        "outputId": "2dc78bf3-1d24-456f-a490-1a990eccf001"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[ 0.84147098,  0.90929743,  0.14112001],\n",
              "       [-0.7568025 , -0.95892427, -0.2794155 ],\n",
              "       [ 0.6569866 ,  0.98935825,  0.41211849]])"
            ]
          },
          "metadata": {},
          "execution_count": 30
        }
      ],
      "source": [
        "np.sin(A)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 31,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:01:08.099286Z",
          "start_time": "2022-09-22T08:01:08.093285Z"
        },
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Cb--ILeOwr5E",
        "outputId": "f05584a2-2d86-41cb-ddfa-91e50369fd37"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[1, 2, 3],\n",
              "       [4, 5, 6],\n",
              "       [7, 8, 9]])"
            ]
          },
          "metadata": {},
          "execution_count": 31
        }
      ],
      "source": [
        "np.abs(A)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 32,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:01:08.303328Z",
          "start_time": "2022-09-22T08:01:08.293329Z"
        },
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "AbdIrzASwr5E",
        "outputId": "b50dad68-74a1-474d-edfe-a1239b6462c4"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[1.        , 1.41421356, 1.73205081],\n",
              "       [2.        , 2.23606798, 2.44948974],\n",
              "       [2.64575131, 2.82842712, 3.        ]])"
            ]
          },
          "metadata": {},
          "execution_count": 32
        }
      ],
      "source": [
        "A ** 0.5"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T07:19:36.696313Z",
          "start_time": "2022-09-22T07:19:36.683314Z"
        },
        "id": "JnHmtvFBwr5E"
      },
      "source": [
        "Поэлементые операции сравнения:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 33,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:01:08.696455Z",
          "start_time": "2022-09-22T08:01:08.678456Z"
        },
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "59RrLNAMwr5E",
        "outputId": "e9c076fa-0b65-4eea-fc2c-eb8e6fa5c047"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[False, False, False],\n",
              "       [ True,  True,  True],\n",
              "       [ True,  True,  True]])"
            ]
          },
          "metadata": {},
          "execution_count": 33
        }
      ],
      "source": [
        "A > 3"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "wIWBy9Vlwr5E"
      },
      "source": [
        "### `Матричные арифметические операции`"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 34,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:01:09.092838Z",
          "start_time": "2022-09-22T08:01:09.079837Z"
        },
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "0cuAz2RYwr5E",
        "outputId": "c89086d6-ecbd-418e-f8c4-33b0e4a800a2"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0 2 3]\n",
            " [4 3 6]\n",
            " [7 8 6]]\n"
          ]
        }
      ],
      "source": [
        "print(A - B)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 35,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:01:09.312868Z",
          "start_time": "2022-09-22T08:01:09.300868Z"
        },
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "PbqVDUWJwr5E",
        "outputId": "eb3f5c1a-dfd8-450d-f95d-ac8e48621222"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[ 1  0  0]\n",
            " [ 0 10  0]\n",
            " [ 0  0 27]]\n"
          ]
        }
      ],
      "source": [
        "print(A * B)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 36,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:01:09.504270Z",
          "start_time": "2022-09-22T08:01:09.501269Z"
        },
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "sNG4QwuIwr5E",
        "outputId": "f9a21388-e69a-4ba1-b1bd-843bd4ec8a53"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[1.         0.         0.        ]\n",
            " [0.         0.4        0.        ]\n",
            " [0.         0.         0.33333333]]\n"
          ]
        }
      ],
      "source": [
        "print(B / A)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 37,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:01:09.709313Z",
          "start_time": "2022-09-22T08:01:09.700313Z"
        },
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "YPXwQduPwr5E",
        "outputId": "847481fc-65f3-4b28-aca0-92c0ffa09e1b"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[ 1  4  9]\n",
            " [ 4 10 18]\n",
            " [ 7 16 27]]\n"
          ]
        }
      ],
      "source": [
        "print(A @ B)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_jaAXGggwr5E"
      },
      "source": [
        "### `Фиктивная размерность`"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "nqXtoHlpwr5E"
      },
      "source": [
        "Два способа добавить фиктивную размерность в произвольный массив:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:01:10.323226Z",
          "start_time": "2022-09-22T08:01:10.308228Z"
        },
        "id": "0UEvpbowwr5E",
        "outputId": "91d3f68e-5c13-4c38-8767-af6fd4ee1245"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "(2, 1, 2, 3)"
            ]
          },
          "execution_count": 57,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "d[:, np.newaxis].shape"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:01:10.526305Z",
          "start_time": "2022-09-22T08:01:10.509305Z"
        },
        "id": "ONIZK7ZIwr5F",
        "outputId": "f5c2b22b-4753-4d29-a1ad-1a9564e82b6e"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "(1, 2, 2, 3)"
            ]
          },
          "execution_count": 58,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "d[None, :].shape"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T07:25:03.648117Z",
          "start_time": "2022-09-22T07:25:03.633117Z"
        },
        "id": "DGeBZLgUwr5F"
      },
      "source": [
        "Для одномерного массива можно использовать `reshape`:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:01:10.922302Z",
          "start_time": "2022-09-22T08:01:10.908303Z"
        },
        "id": "CpBCcb-jwr5F",
        "outputId": "8e784e7a-452f-46b9-a573-c8a8ce9762e3"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "(array([0, 1, 2, 3, 4, 5, 6]),\n",
              " array([[0],\n",
              "        [1],\n",
              "        [2],\n",
              "        [3],\n",
              "        [4],\n",
              "        [5],\n",
              "        [6]]))"
            ]
          },
          "execution_count": 59,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "x = np.arange(7)\n",
        "\n",
        "x, x.reshape(-1, 1)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T07:24:04.521584Z",
          "start_time": "2022-09-22T07:24:04.513585Z"
        },
        "id": "o-aB0SESwr5F"
      },
      "source": [
        "Зачем нужно добавлять фиктивную размерность? Например, чтобы проводить различные операции с массивами неравного размера."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "gqVFDiQ3wr5F"
      },
      "source": [
        "### `Broadcasting`\n",
        "\n",
        "Подробное описание: http://docs.scipy.org/doc/numpy/user/basics.broadcasting.html"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_mY240Rbwr5F"
      },
      "source": [
        "Пусть нам дана матрица $X$ размером $5 \\times 5$ и вектор $y$ длины $5$. Пусть мы хотим прибавить вектор к каждой строке матрицы."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:01:11.744952Z",
          "start_time": "2022-09-22T08:01:11.732954Z"
        },
        "id": "ssX2luVrwr5F",
        "outputId": "95f0d430-8378-4399-e770-9e432dfde3b6"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "(array([[ 0,  1,  2,  3,  4],\n",
              "        [ 5,  6,  7,  8,  9],\n",
              "        [10, 11, 12, 13, 14],\n",
              "        [15, 16, 17, 18, 19],\n",
              "        [20, 21, 22, 23, 24]]),\n",
              " array([0, 1, 2, 3, 4]))"
            ]
          },
          "execution_count": 60,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "x = np.arange(25).reshape(5, 5)\n",
        "y = np.arange(5)\n",
        "\n",
        "x, y"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "fGqD_kiMwr5F"
      },
      "source": [
        "Наивный способ решения проблемы будет работать правильно!"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:01:12.172295Z",
          "start_time": "2022-09-22T08:01:12.156295Z"
        },
        "id": "nfqkNVnIwr5F",
        "outputId": "5bff00a1-ddf6-47c7-fc5a-13f495af08ed"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([[ 0,  2,  4,  6,  8],\n",
              "       [ 5,  7,  9, 11, 13],\n",
              "       [10, 12, 14, 16, 18],\n",
              "       [15, 17, 19, 21, 23],\n",
              "       [20, 22, 24, 26, 28]])"
            ]
          },
          "execution_count": 61,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "x + y"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "eYQcxI4Cwr5F"
      },
      "source": [
        "**Почему?** Правила broadcasting (приведение размеров).\n",
        "\n",
        "1. Если два массива имеют размерности $(a_1, a_2, ..., a_n)$ и $(b_1, b_2, ..., b_n)$ соответственно, то между ними можно проводить поэлементные операции, если для каждого $i$ выполнено одно из трёх условий:\n",
        "    * $a_i = b_i$\n",
        "    * $a_i = 1$\n",
        "    * $b_i = 1$\n",
        "    \n",
        "2. Если поэлементная операция выполняется между массивами разного размера, то к массиву меньшего размера добавляются ведущие фиктивные размерности."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "8KAe7FHwwr5F"
      },
      "source": [
        "### `Арифметика и broadcasting`\n",
        "\n",
        "Если по одному из измерений массивы не равны, и у одного из них эта размерность имеет длину 1, то он будет продублирован по этой размерности:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:01:12.788303Z",
          "start_time": "2022-09-22T08:01:12.780304Z"
        },
        "id": "uQGhIocywr5F",
        "outputId": "9c5a2790-b503-45a4-96b6-8c4961bb0e64"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "[2 2] \n",
            "\n",
            "[[2 3]\n",
            " [4 5]] \n",
            "\n",
            "[[2 3]\n",
            " [4 5]]\n"
          ]
        }
      ],
      "source": [
        "a = np.array([[1, 2], [3, 4]])\n",
        "b = np.array([1])\n",
        "c = np.array([1, 1])\n",
        "\n",
        "print(b + c, '\\n')\n",
        "print(a + b, '\\n')\n",
        "print(a + c)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5PMWVU-Qwr5F"
      },
      "source": [
        "### `Арифметика и broadcasting`\n",
        "\n",
        "Если не совпадает количество размерностей, то массив, у которого их меньше, будет \"добиваться\" слева размерностями длины 1:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:01:13.216291Z",
          "start_time": "2022-09-22T08:01:13.204294Z"
        },
        "id": "TTEMHrccwr5F",
        "outputId": "7b72e766-073c-4aec-e4b2-e9455f176b64"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "[[[2. 2. 2. 2.]\n",
            "  [2. 2. 2. 2.]\n",
            "  [2. 2. 2. 2.]]\n",
            "\n",
            " [[2. 2. 2. 2.]\n",
            "  [2. 2. 2. 2.]\n",
            "  [2. 2. 2. 2.]]]\n"
          ]
        }
      ],
      "source": [
        "a = np.ones((2, 3, 4))\n",
        "b = np.ones(4)\n",
        "\n",
        "print(a + b) # here a.shape=(2, 3, 4) and b.shape is considered to be (1, 1, 4)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "hBWkxmW1wr5F"
      },
      "source": [
        "### `Арифметика и broadcasting`\n",
        "\n",
        "Добавим к массиву вектор-строку:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:01:13.863274Z",
          "start_time": "2022-09-22T08:01:13.852278Z"
        },
        "id": "Bkr1OJBIwr5F",
        "outputId": "700ca1cb-0786-458c-89a6-d529ee808302"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([[2, 4, 6],\n",
              "       [5, 7, 9]])"
            ]
          },
          "execution_count": 64,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "a = np.array([[1, 2, 3], [4, 5, 6]])\n",
        "b = np.array([1, 2, 3])\n",
        "a + b"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "h4m1Ha9nwr5G"
      },
      "source": [
        "Теперь попробуем добавить столбец:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 40,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:01:14.289296Z",
          "start_time": "2022-09-22T08:01:14.278296Z"
        },
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 220
        },
        "id": "m-g9xIGXwr5G",
        "outputId": "a20e2048-0acd-40cd-f506-00c273647e73"
      },
      "outputs": [
        {
          "output_type": "error",
          "ename": "ValueError",
          "evalue": "ignored",
          "traceback": [
            "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
            "\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)",
            "\u001b[0;32m<ipython-input-40-cff7a1376959>\u001b[0m in \u001b[0;36m<cell line: 3>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0ma\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0marray\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m2\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m3\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0;36m4\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m5\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m6\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      2\u001b[0m \u001b[0mb\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0marray\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m2\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 3\u001b[0;31m \u001b[0ma\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0mb\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
            "\u001b[0;31mValueError\u001b[0m: operands could not be broadcast together with shapes (2,3) (2,) "
          ]
        }
      ],
      "source": [
        "a = np.array([[1, 2, 3], [4, 5, 6]])\n",
        "b = np.array([1, 2])\n",
        "a + b"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "WL_cvc7swr5G"
      },
      "source": [
        "### `Арифметика и broadcasting`\n",
        "\n",
        "- Ошибка возникла из-за того, что прибавлялась строка с неправильным размером<br>\n",
        "\n",
        "- Нужно преобразовать строку в столбец (добавить фиктивную размерность), и тогда NumPy поймёт, как с ней работать<br><br>\n",
        "\n",
        "Для этого воспользуемся `reshape` (способ хороший, но далеко не единственный):"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 41,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:01:14.748280Z",
          "start_time": "2022-09-22T08:01:14.740280Z"
        },
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "hiz3iBR8wr5G",
        "outputId": "0c780957-a951-41cd-bcd6-d8ca35101934"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[2, 3, 4],\n",
              "       [6, 7, 8]])"
            ]
          },
          "metadata": {},
          "execution_count": 41
        }
      ],
      "source": [
        "a + np.reshape(b, (2, 1))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "1bY9h9h0wr5G"
      },
      "source": [
        "### `Арифметика и broadcasting`"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Pz1yjQBMwr5G"
      },
      "source": [
        "**Всегда проверяйте операции с броадкастингом! Легко можно напороться на неприятности**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Zj8y_UA2wr5G"
      },
      "source": [
        "<font color='brown'>**Задача 5.** Какие из этих команд будут выполняться с ошибкой?</font>\n",
        "\n",
        "1. `np.ones((2, 3)) + np.ones(3)`\n",
        "\n",
        "2. `np.ones(2) + np.ones((2, 3))`\n",
        "\n",
        "3. `np.zeros((4, 3)) + np.ones((4, 1))`\n",
        "\n",
        "4. `np.zeros((3, 4)) + np.ones((4, 3))`\n",
        "\n",
        "5. `np.zeros((1, 3, 5)) + np.zeros((1, 3))`\n",
        "\n",
        "6. `np.zeros((5, 3, 1)) + np.zeros((1, 5))`"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 48,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:01:16.271798Z",
          "start_time": "2022-09-22T08:01:16.267799Z"
        },
        "id": "wbmythqUwr5G"
      },
      "outputs": [],
      "source": [
        "### your answer here"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "N4Pwr1gSwr5G"
      },
      "source": [
        "<font color='brown'>**Задача 6.** Пусть нам дана матрица $X$ размером $10 \\times 10$ и вектор-столбец $y$ длины $10$. Получите матрицу `result`, полученную прибавлением к каждому столбцу $X$ вектора $y$ (без использования циклов). </font>"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 50,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:01:16.676285Z",
          "start_time": "2022-09-22T08:01:16.668285Z"
        },
        "id": "k9OgjV4gwr5G"
      },
      "outputs": [],
      "source": [
        "x = np.arange(100).reshape(10, 10)\n",
        "y = np.arange(10)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 58,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:01:16.866283Z",
          "start_time": "2022-09-22T08:01:16.853284Z"
        },
        "id": "QnQWIHBlwr5G"
      },
      "outputs": [],
      "source": [
        "## your code here"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "trnkPpR9wr5G"
      },
      "source": [
        "Проверьте себя:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 57,
      "metadata": {
        "deletable": false,
        "editable": false,
        "run_control": {
          "frozen": true
        },
        "id": "VmYK5U1kwr5G"
      },
      "outputs": [],
      "source": [
        "assert result[0][0] == 0\n",
        "for i in range(1, 10):\n",
        "    assert result[i][i-1] == 10 * i + (i - 1) * 2 + 1"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "LL9IMT3Owr5G"
      },
      "source": [
        "### `Матричное умножение`\n",
        "\n",
        "Расмотрим для случая двумерных матриц, кому интересны многомерные, изучайте\n",
        "https://numpy.org/devdocs/reference/generated/numpy.dot.html"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 59,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:01:17.673826Z",
          "start_time": "2022-09-22T08:01:17.659828Z"
        },
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ZWCMRVeWwr5G",
        "outputId": "58d21f48-00b8-446f-8525-6da0835c29cb"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[ 1  4  9]\n",
            " [ 4 10 18]\n",
            " [ 7 16 27]] \n",
            "\n",
            "[[ 1  4  9]\n",
            " [ 4 10 18]\n",
            " [ 7 16 27]] \n",
            "\n",
            "[[ 1  4  9]\n",
            " [ 4 10 18]\n",
            " [ 7 16 27]]\n"
          ]
        }
      ],
      "source": [
        "print(A @ B, '\\n')\n",
        "print(A.dot(B), '\\n')\n",
        "print(np.dot(A, B))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ruKEwUpBwr5G"
      },
      "source": [
        "### `Транспонирование`\n",
        "\n",
        "- Расмотрим для случая двумерных матриц, кому интересны многомерные, изучайте\n",
        "https://stackoverflow.com/questions/32034237/how-does-numpys-transpose-method-permute-the-axes-of-an-array\n",
        "- При транспонировании (как и `reshape`) возвращается ссылка на те же данные"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:01:18.346450Z",
          "start_time": "2022-09-22T08:01:18.340451Z"
        },
        "id": "Sb5c3LQ3wr5H",
        "outputId": "ef023952-ec2a-4bd4-8ebe-ea51b8f16320"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "[[1 2 3]\n",
            " [4 5 6]\n",
            " [7 8 9]] \n",
            "\n",
            " [[1 4 7]\n",
            " [2 5 8]\n",
            " [3 6 9]] \n",
            "\n",
            " [[1 4 7]\n",
            " [2 5 8]\n",
            " [3 6 9]]\n"
          ]
        }
      ],
      "source": [
        "print(A, '\\n\\n', A.T, '\\n\\n', A.transpose())"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Стоит быть осторожным с транспонированием:"
      ],
      "metadata": {
        "id": "vyP2aaxvxnSM"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# in memory: 0, 1, 2, 3\n",
        "a = np.arange(4).reshape(2, 2)\n",
        "b = a.reshape(-1)\n",
        "c = a.T.reshape(-1)\n",
        "np.may_share_memory(a, b), np.may_share_memory(a, c)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "0B2AsZ4ow-DJ",
        "outputId": "cd8a9d34-fcc9-4eda-9eab-eea8f4b66586"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(True, False)"
            ]
          },
          "metadata": {},
          "execution_count": 57
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "d = a.T.view()\n",
        "np.may_share_memory(a, d)\n",
        "d.flags['C_CONTIGUOUS']"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "b1Ltx0q5yX-f",
        "outputId": "0d104fc9-6aa8-4755-a731-991390cca55f"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "False"
            ]
          },
          "metadata": {},
          "execution_count": 62
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "print(a.flags['C_CONTIGUOUS'])\n",
        "print(a.T.flags['C_CONTIGUOUS'])"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "r2LeF-w4xYvr",
        "outputId": "764855f7-3321-4d62-df64-7d002a364f71"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "True\n",
            "False\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ld63YyY4wr5H"
      },
      "source": [
        "### `Сравнение скорости`\n",
        "\n",
        "Воспользуемся декоратором `timed` для сравнения скорости матричных операций, реализованных в `numpy` и написанных выше с помощью списков:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 62,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:01:18.711053Z",
          "start_time": "2022-09-22T08:01:18.708055Z"
        },
        "id": "BtZObWGWwr5H"
      },
      "outputs": [],
      "source": [
        "@timed\n",
        "def matrix_add_np(A, B): return A + B\n",
        "\n",
        "@timed\n",
        "def matrix_mul_np(A, B): return A @ B"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 67,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:01:20.085052Z",
          "start_time": "2022-09-22T08:01:18.909053Z"
        },
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "23AocmUnwr5H",
        "outputId": "2e075f0b-4124-4596-f8b2-f6419b7e93c8"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "matrix_add  690.307 ms\n",
            "\n",
            "matrix_add_np  3.761 ms\n",
            "\n",
            "matrix_transpose  12.119 ms\n",
            "\n",
            "matrix_mul  2138.916 ms\n",
            "\n",
            "matrix_mul_np  8.289 ms\n",
            "\n"
          ]
        }
      ],
      "source": [
        "tmp = [range(1000) for _ in range(1000)]\n",
        "X, Y = np.array(tmp), np.array(tmp)\n",
        "\n",
        "_ = matrix_add(X, Y)\n",
        "_ = matrix_add_np(X, Y)\n",
        "\n",
        "tmp = [range(200) for _ in range(200)]\n",
        "X, Y = np.array(tmp), np.array(tmp)\n",
        "\n",
        "_ = matrix_mul(X, Y)\n",
        "_ = matrix_mul_np(X, Y)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "KUj7neWdwr5H"
      },
      "source": [
        "### `Агрегирующие функции`\n",
        "\n",
        "Подобных функций много, ищите нужное в документации NumPy"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 68,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:01:20.101051Z",
          "start_time": "2022-09-22T08:01:20.086053Z"
        },
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "7EOCromVwr5H",
        "outputId": "919ca7c4-22b3-4493-db79-fe1a67dd0776"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Min element:          1\n",
            "Min element position: 0\n",
            "Max element:          4\n",
            "Mean:                 2.4444444444444446\n",
            "Sum:                  22\n",
            "Median:               3.0\n",
            "Cumulative sum:       [ 1  3  6 10 13 15 16 19 22]\n",
            "Cumulative product:   [   1    2    6   24   72  144  144  432 1296]\n"
          ]
        }
      ],
      "source": [
        "a = np.array([1, 2, 3, 4, 3, 2, 1, 3, 3])\n",
        "\n",
        "print('Min element:          {}'.format(np.min(a)))\n",
        "print('Min element position: {}'.format(np.argmin(a)))\n",
        "print('Max element:          {}'.format(np.max(a)))\n",
        "print('Mean:                 {}'.format(np.mean(a)))\n",
        "print('Sum:                  {}'.format(np.sum(a)))\n",
        "print('Median:               {}'.format(np.median(a)))\n",
        "print('Cumulative sum:       {}'.format(np.cumsum(a)))\n",
        "print('Cumulative product:   {}'.format(np.cumprod(a)))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "uYg01iftwr5H"
      },
      "source": [
        "Что будет происходить в случае многомерного массива?"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "jUzJGy6Zwr5H"
      },
      "source": [
        "### `Агрегирующие функции`\n",
        "\n",
        "В многомерном случае операция применяется к массиву, вытянутому в вектор (flatten):"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 69,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:01:20.433246Z",
          "start_time": "2022-09-22T08:01:20.420248Z"
        },
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "58GTTlgNwr5H",
        "outputId": "3c2450b0-6f34-4789-939f-1c85ec3cd014"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[1 2 3]\n",
            " [4 3 2]\n",
            " [1 3 3]] \n",
            "\n",
            "4\n",
            "[ 1  3  6 10 13 15 16 19 22]\n"
          ]
        }
      ],
      "source": [
        "a = np.array([[1, 2, 3], [4, 3, 2], [1, 3, 3]])\n",
        "print(a, '\\n')\n",
        "print(np.max(a))\n",
        "print(np.cumsum(a))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "TobiMxnNwr5H"
      },
      "source": [
        "Для работы с определёнными размерностям нужно указать явно параметр `axis`:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 70,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:01:21.207849Z",
          "start_time": "2022-09-22T08:01:21.203849Z"
        },
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "OHa5B2kGwr5H",
        "outputId": "8b82cc57-c233-41ab-ae5d-4fce88351b89"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[4 3 3] \n",
            "\n",
            "[[1 3 6]\n",
            " [4 7 9]\n",
            " [1 4 7]]\n"
          ]
        }
      ],
      "source": [
        "print(np.max(a, axis=0), '\\n')\n",
        "print(np.cumsum(a, axis=1))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "yIEmY7Bdwr5H"
      },
      "source": [
        "Как легко запомнить, как работает axis:\n",
        "* после применения функции получится массив, в котором будет отсутствовать размерность указанная в `axis`, но остальные размерности будут иметь такие же значения"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "48iS2mT3wr5H"
      },
      "source": [
        "### `Агрегирующие функции`"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "nXoO-Mnzwr5H"
      },
      "source": [
        "<font color='brown'>**Задача 7.** Дан вектор $x$ и квадратная матрица $D$. Вычислить вектор значений $y_j = argmin_i (x_i + D_{ij})$. </font>"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 72,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:01:22.410865Z",
          "start_time": "2022-09-22T08:01:22.395866Z"
        },
        "id": "N2whjihMwr5H"
      },
      "outputs": [],
      "source": [
        "x = np.array([5, 2, 3, 1])\n",
        "D = np.array([\n",
        "    [1, 2, 3],\n",
        "    [2, 2, 4],\n",
        "    [5, 6, 1],\n",
        "    [2, 4, 5]\n",
        "])"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 74,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:01:23.026153Z",
          "start_time": "2022-09-22T08:01:23.021153Z"
        },
        "id": "6T0TxDgAwr5H"
      },
      "outputs": [],
      "source": [
        "### your code here"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "xfser09gwr5I"
      },
      "source": [
        "Проверьте себя:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "deletable": false,
        "editable": false,
        "run_control": {
          "frozen": true
        },
        "id": "twcERR7wwr5I"
      },
      "outputs": [],
      "source": [
        "assert y.tolist() == [3, 1, 2]"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Cx6aRvM3wr5I"
      },
      "source": [
        "### `Конкатенация массивов`\n",
        "\n",
        "Конкатенировать несколько массивом можно с помощью функций `concatenate` (общий случай), `hstack` и `vstack`:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 75,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:01:23.797110Z",
          "start_time": "2022-09-22T08:01:23.780110Z"
        },
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "p0ZWDq0pwr5I",
        "outputId": "28702804-2926-45ca-b1e8-b03b7d808f09"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[1, 2, 3, 1, 0, 0],\n",
              "       [4, 5, 6, 0, 2, 0],\n",
              "       [7, 8, 9, 0, 0, 3]])"
            ]
          },
          "metadata": {},
          "execution_count": 75
        }
      ],
      "source": [
        "np.hstack([A, B])"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 77,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:01:24.034241Z",
          "start_time": "2022-09-22T08:01:24.021242Z"
        },
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "3rD-PRUswr5I",
        "outputId": "8920adef-7544-4acf-92b8-b51ae57fccf8"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[1, 2, 3],\n",
              "       [4, 5, 6],\n",
              "       [7, 8, 9],\n",
              "       [1, 0, 0],\n",
              "       [0, 2, 0],\n",
              "       [0, 0, 3]])"
            ]
          },
          "metadata": {},
          "execution_count": 77
        }
      ],
      "source": [
        "np.vstack([A, B])"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "I91zVecxwr5I"
      },
      "source": [
        "### `Ещё несколько полезных функций`"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T07:36:35.881026Z",
          "start_time": "2022-09-22T07:36:35.869029Z"
        },
        "id": "KQdeow4Twr5I"
      },
      "source": [
        "Чтобы построить двумерный массив, состоящий из повторений одномерных, можно использовать `np.tile`:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 78,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:01:24.726675Z",
          "start_time": "2022-09-22T08:01:24.707676Z"
        },
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "aN-Jabqpwr5I",
        "outputId": "532aa528-5e4b-4d10-d7bd-0f68abf4fa33"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[2, 3, 4],\n",
              "       [2, 3, 4]])"
            ]
          },
          "metadata": {},
          "execution_count": 78
        }
      ],
      "source": [
        "a = np.array([2, 3, 4])\n",
        "np.tile(a[np.newaxis, :], (2, 1))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T07:37:41.398443Z",
          "start_time": "2022-09-22T07:37:41.381445Z"
        },
        "id": "1eu3K7lBwr5I"
      },
      "source": [
        "Для того, чтобы повторить каждый элемент в массиве, можно использовать `np.repeat`"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 79,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:01:25.101579Z",
          "start_time": "2022-09-22T08:01:25.092580Z"
        },
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "UBz_DJGWwr5I",
        "outputId": "309c2151-2b49-45e3-9cf1-c2212b8c1c0c"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([1, 1, 2, 2, 3, 3])"
            ]
          },
          "metadata": {},
          "execution_count": 79
        }
      ],
      "source": [
        "np.repeat([1, 2, 3], repeats=2, axis=0)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 80,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:01:25.304654Z",
          "start_time": "2022-09-22T08:01:25.292654Z"
        },
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "PWMFuXWMwr5I",
        "outputId": "129035fa-2868-45ec-a94a-6e3d15b5aaae"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "True\n",
            "False\n",
            "[ True False False]\n"
          ]
        }
      ],
      "source": [
        "print(np.all(A == A))\n",
        "print(np.all(A == B))\n",
        "print(np.all(A == [1, 2, 3], axis=1))"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 81,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:01:25.541219Z",
          "start_time": "2022-09-22T08:01:25.532218Z"
        },
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "a0f9xH_cwr5I",
        "outputId": "57ccad28-b75a-4f92-a000-d721479d66cc"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[ 1,  4,  9],\n",
              "       [16, 25, 36],\n",
              "       [49, 64, 81]])"
            ]
          },
          "metadata": {},
          "execution_count": 81
        }
      ],
      "source": [
        "func = np.vectorize(lambda x: x ** 2)\n",
        "func(A)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "cAL2E2wMwr5I"
      },
      "source": [
        "### `Типы и преобразование типов`"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T07:42:39.477459Z",
          "start_time": "2022-09-22T07:42:39.459459Z"
        },
        "id": "BehCdO1kwr5I"
      },
      "source": [
        "Атрибут `dtype` хранит информацию о типе массива:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 82,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:01:26.429870Z",
          "start_time": "2022-09-22T08:01:26.419871Z"
        },
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "dThuO45Hwr5I",
        "outputId": "72c3fb7d-b075-4b66-8564-3ec9eaa253a5"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(dtype('int64'), dtype('float64'))"
            ]
          },
          "metadata": {},
          "execution_count": 82
        }
      ],
      "source": [
        "x = np.arange(15)\n",
        "y = np.array([1.5, 2.5])\n",
        "\n",
        "x.dtype, y.dtype"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Sond6TQEwr5I"
      },
      "source": [
        "Преобразование типов осуществляется с помощью метода `astype`:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 83,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:01:26.982577Z",
          "start_time": "2022-09-22T08:01:26.964577Z"
        },
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "qqwiRTH7wr5I",
        "outputId": "898b54f8-8d84-4e25-9885-555b38ea3df2"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "dtype('float64')"
            ]
          },
          "metadata": {},
          "execution_count": 83
        }
      ],
      "source": [
        "x = x.astype(np.float64)\n",
        "x.dtype"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "4pEkll76wr5J"
      },
      "source": [
        "Можно сразу указывать желаемый тип при создании массивов при помощи параметра `dtype`:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 84,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:01:27.623557Z",
          "start_time": "2022-09-22T08:01:27.612558Z"
        },
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "c1UnJdkhwr5J",
        "outputId": "bf827f88-b92b-414a-aa9e-2403c362be74"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([['1', '1', '1'],\n",
              "       ['1', '1', '1']], dtype='<U1')"
            ]
          },
          "metadata": {},
          "execution_count": 84
        }
      ],
      "source": [
        "np.ones((2, 3), dtype=str)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "tgCgt3mtwr5J"
      },
      "source": [
        "### `Примеры задач на матрицы в NumPy`\n",
        "\n",
        "Условие - нельзя использовать\n",
        "- циклы\n",
        "- генераторы списков/списковые включения\n",
        "- map-функции (в т.ч. `np.vectorize`)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Vp2WDDeywr5J"
      },
      "source": [
        "<font color='brown'> **Задача 8**. Пронумеровать в порядке следования максимальные элементы в векторе. Для вектора `[1, 2, 3, 3, 2, 1, 3, 1]` должно получиться `[0, 0, 1, 2, 0, 0, 3, 0]`: </font>"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:01:29.209986Z",
          "start_time": "2022-09-22T08:01:29.203987Z"
        },
        "id": "au3byv6Bwr5J",
        "outputId": "d5c53ead-b84d-4dd0-9486-daa65fa18785"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "[0 0 1 2 0 0 3 0]\n"
          ]
        }
      ],
      "source": [
        "def task_1(a):\n",
        "    pass\n",
        "    ### your code here\n",
        "\n",
        "print(task_1([1, 2, 3, 3, 2, 1, 3, 1]))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "2xBKLH75wr5J"
      },
      "source": [
        "### `Примеры задач на матрицы в NumPy`"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "eU-RJZIFwr5J"
      },
      "source": [
        "<font color='brown'> **Задача 9**. Реализуйте функцию подсчёта произведения ненулевых элементов на диагонали прямоугольной матрицы. Для матрицы `[[1, 0, 1], [2, 0, 2], [3, 0, 3], [4, 4, 4]]` ответом является $3$. Если ненулевых элементов нет, функция должна возвращать `None`: </font>"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:01:29.792969Z",
          "start_time": "2022-09-22T08:01:29.787970Z"
        },
        "id": "WiGTf2Odwr5J",
        "outputId": "aa45fde4-3aa1-40f9-ba16-4ce8711ac0d6"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "3\n"
          ]
        }
      ],
      "source": [
        "def task_2(A):\n",
        "    pass\n",
        "    ### your code here\n",
        "\n",
        "print(task_2(np.array([[1, 0, 1], [2, 0, 2], [3, 0, 3], [4, 4, 4]])))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "2zjHNvH-wr5J"
      },
      "source": [
        "<font color='brown'> **Задача 10**. Найти максимальный элемент в вектор-строке среди элементов, перед которым стоит нулевой. Для `[0, 4, 2, 0, 3, 0, 0, 5, 7, 0]` ответ равен $5$: </font>"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:01:30.312187Z",
          "start_time": "2022-09-22T08:01:30.308187Z"
        },
        "id": "2s5AAFnpwr5J",
        "outputId": "a906afe8-8f6e-4ac7-d49e-af752f29b096"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "5\n"
          ]
        }
      ],
      "source": [
        "def task_3(a):\n",
        "    pass\n",
        "    ### your code here\n",
        "\n",
        "print(task_3(np.array([0, 4, 2, 0, 3, 0, 0, 5, 7, 0])))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "utLC52Sowr5J"
      },
      "source": [
        "### `Примеры задач на матрицы в NumPy`"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "HEB6BOwLwr5J"
      },
      "source": [
        "<font color='brown'> **Задача 11.** Дана матрица размерности $N \\times K$, $N$ - число объектов, $K$ - число признаков.\n",
        "Подсчитать выборочное среднее и ковариационную матрицу без использования\n",
        "функций mean и cov.\n",
        "\n",
        "$$ E[X]={\\frac {1}{n}}\\sum \\limits _{i=1}^{n}x_{i} $$\n",
        "\n",
        "$$ {\\mathrm  {cov}}(X_{{(n)}},Y_{{(n)}})={\\frac  1n}\\sum _{{t=1}}^{n}\\left(X_{t}-\\overline {X}\\right)\\left(Y_{t}-\\overline {Y}\\right)$$\n",
        "\n",
        " </font>"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:01:31.127194Z",
          "start_time": "2022-09-22T08:01:31.116205Z"
        },
        "id": "ohZYwW93wr5J"
      },
      "outputs": [],
      "source": [
        "X = np.arange(32).reshape(8, 4)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:01:31.440245Z",
          "start_time": "2022-09-22T08:01:31.436246Z"
        },
        "id": "5Dmnt6vXwr5J"
      },
      "outputs": [],
      "source": [
        "### your code here"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "deletable": false,
        "editable": false,
        "run_control": {
          "frozen": true
        },
        "id": "sHltEMAswr5J"
      },
      "outputs": [],
      "source": [
        "assert mean.tolist() == [14, 15, 16, 17]\n",
        "assert np.all(cov == 84)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "a_8QasHowr5K"
      },
      "source": [
        "### `Примеры задач на матрицы в NumPy`"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "atDFIj6Mwr5K"
      },
      "source": [
        "<font color='brown'> **Задача 12.** Замените все максимальные элементы матрицы $A$ на $0$. </font>"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:01:32.213508Z",
          "start_time": "2022-09-22T08:01:32.204507Z"
        },
        "id": "8cSrvstzwr5K"
      },
      "outputs": [],
      "source": [
        "A = np.array([\n",
        "    [1, 6, 3],\n",
        "    [6, 2, 1],\n",
        "    [4, 5, 6],\n",
        "    [1, 2, 1],\n",
        "])"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:01:32.415127Z",
          "start_time": "2022-09-22T08:01:32.405128Z"
        },
        "id": "BgIC3Ckhwr5K"
      },
      "outputs": [],
      "source": [
        "### your code here"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "deletable": false,
        "editable": false,
        "run_control": {
          "frozen": true
        },
        "id": "eJohsZqjwr5K"
      },
      "outputs": [],
      "source": [
        "new_A = np.array([\n",
        "    [1, 0, 3],\n",
        "    [0, 2, 1],\n",
        "    [4, 5, 0],\n",
        "    [1, 2, 1],\n",
        "])\n",
        "assert np.all(A == new_A)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "dB4oPZ7gwr5K"
      },
      "source": [
        "### `Примеры задач на матрицы в NumPy`"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "YRHjv7flwr5K"
      },
      "source": [
        "<font color='brown'> **Задача 13.** Вычислить площадь круга единичного диаметра с центром в (0.5, 0.5) методом Монте-Карло. </font>"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 146,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:01:33.440548Z",
          "start_time": "2022-09-22T08:01:33.428548Z"
        },
        "id": "D02rEQIDwr5K"
      },
      "outputs": [],
      "source": [
        "N = 1000\n",
        "X = np.random.uniform(0, 1, size=(N, 2))"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "### your code here"
      ],
      "metadata": {
        "id": "Cd-e5qT-7xQb"
      },
      "execution_count": 145,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "GV5mjSpywr5K"
      },
      "source": [
        "Проверьте себя:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:01:34.029167Z",
          "start_time": "2022-09-22T08:01:34.020167Z"
        },
        "id": "zgUt8XA3wr5K",
        "outputId": "ecbc8626-5a9f-4b7b-980f-3212523170f6"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "0.7853981633974483"
            ]
          },
          "execution_count": 97,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "np.pi / 4"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T07:47:35.599928Z",
          "start_time": "2022-09-22T07:47:35.593928Z"
        },
        "id": "rYLaPdFrwr5K"
      },
      "source": [
        "Постройте график, как значения убывают с итерациями:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 154,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:01:34.821288Z",
          "start_time": "2022-09-22T08:01:34.476288Z"
        },
        "id": "3KCgXG3ewr5K"
      },
      "outputs": [],
      "source": [
        "import matplotlib.pyplot as plt\n",
        "\n",
        "### your code here"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "a = np.arange(10)\n",
        "b = np.ones(10)\n",
        "a.dot(b)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "dmLurvIcH88s",
        "outputId": "6e2f8076-06b3-439c-b4db-1c9237894585"
      },
      "execution_count": 157,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "45.0"
            ]
          },
          "metadata": {},
          "execution_count": 157
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "oMUQgRq2wr5K"
      },
      "source": [
        "### `Примеры задач на матрицы в NumPy`"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "W3R3rmzJwr5K"
      },
      "source": [
        "<font color='brown'> **Задача* 14.** Даны матрицы $A$ размера $(n \\times d)$ и $B$ размера $(m \\times d)$. Найти в $A$ все строки, содержащиеся в $B$, не используя циклы. Оцените сложность полученного алгоритма.  </font>"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:01:35.217158Z",
          "start_time": "2022-09-22T08:01:35.204158Z"
        },
        "id": "S7iLCpORwr5K"
      },
      "outputs": [],
      "source": [
        "A = np.array([\n",
        "    [1, 2, 3],\n",
        "    [1, 2, 1],\n",
        "    [4, 5, 6],\n",
        "    [1, 2, 1],\n",
        "    [4, 2, 1]\n",
        "])\n",
        "\n",
        "B = np.array([\n",
        "    [4, 5, 6],\n",
        "    [4, 5, 6],\n",
        "    [1, 2, 3],\n",
        "    [0, 1, 2]\n",
        "])"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:01:35.705168Z",
          "start_time": "2022-09-22T08:01:35.693169Z"
        },
        "id": "Nuv7_4SLwr5K"
      },
      "outputs": [],
      "source": [
        "### your code here"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "m26Y9MYuwr5K"
      },
      "source": [
        "Проверьте себя:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "deletable": false,
        "editable": false,
        "run_control": {
          "frozen": true
        },
        "id": "g4RiLg93wr5K"
      },
      "outputs": [],
      "source": [
        "assert set(indexes) == {0, 2}"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "tqGZ0fl_wr5L"
      },
      "source": [
        "### `Примеры задач на матрицы в NumPy`"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ETz-vj03wr5L"
      },
      "source": [
        "<font color='brown'> **Задача* 15.** Даны матрицы $A$ размера $(n \\times d)$ и $B$ размера $(m \\times d)$. Посчитайте матрицу попарных расстояний $D$ размера $(n \\times m)$ такую, что $d_{ij} = \\{||a_{i} - b_{j}||\\}_{i,j}^{n, m}$,  используя broadcasting. Оцените сложность полученного алгоритма. Можно ли существенно её улучшить? Подсказка: раскройте квадрат нормы разности. </font>"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:01:37.750359Z",
          "start_time": "2022-09-22T08:01:37.740360Z"
        },
        "id": "HmoFBlBhwr5L",
        "outputId": "a7226bc3-d4da-4d89-c953-103c8ed636c3"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "(array([[ 0.72890567, -0.56970242, -0.62064083],\n",
              "        [-0.36903927, -0.21307698,  0.07165102],\n",
              "        [ 0.80576973, -1.4564149 ,  1.0019793 ],\n",
              "        [ 1.3538047 , -1.6218574 ,  0.91548881]]),\n",
              " array([[-0.9158514 ,  0.9815864 ,  0.02831563],\n",
              "        [ 0.35667976,  0.35565865,  1.45202641],\n",
              "        [-0.23968579,  0.47515444,  0.18428468],\n",
              "        [-0.20075297, -0.7667414 , -1.30009438],\n",
              "        [-0.57350624,  1.53674006, -0.17750855]]))"
            ]
          },
          "execution_count": 101,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "m, n, d = 5, 4, 3\n",
        "\n",
        "A = np.random.randn(n, d)\n",
        "B = np.random.randn(m, d)\n",
        "A, B"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:01:38.362340Z",
          "start_time": "2022-09-22T08:01:38.348341Z"
        },
        "id": "5yOVeVJRwr5L"
      },
      "outputs": [],
      "source": [
        "### your code here"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "a06li61zwr5L"
      },
      "source": [
        "## Бонус. Несколько полезных библиотек"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "7ESiAfxBwr5L"
      },
      "source": [
        "### `Библиотека NetworkX`\n",
        "\n",
        "- Позволяет работать с графами, в узлах которых могут находиться любые объекты<br><br>\n",
        "\n",
        "- Имеет встроенные процедуры создания графов базовых типов<br><br>\n",
        "\n",
        "- Реализует множество алгоритмов на графах, позволяет получать характеристики графов<br><br>\n",
        "\n",
        "- Поддерживается основные форматы хранения графов в файлах<br><br>\n",
        "\n",
        "- Имеет встроенные инструменты для визуализации графов (на базе mathplotlib и GraphViz)<br><br>\n",
        "\n",
        "- В качестве базовой структуры данных использует словарь (`dict`)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "M-l9fUuywr5L"
      },
      "source": [
        "### `Основные классы графов`\n",
        "\n",
        "- `Graph` — простой неориентированнsq граф. Кратные ребра игнорируются, допускаются петли.\n",
        "- `DiGraph` — ориентированный версия `Graph`\n",
        "- `MultiGraph` — неориентированный граф, допускающий кратные ребра\n",
        "- `MultiDiGraph` — ориентированная версия `MultiDiGraph`"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:01:39.106355Z",
          "start_time": "2022-09-22T08:01:38.996357Z"
        },
        "id": "WAhXJASewr5L",
        "outputId": "e35fe878-4a94-482a-9b99-7f80eeba02c7"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "<networkx.classes.graph.Graph at 0x18ac56e0fa0>"
            ]
          },
          "execution_count": 103,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "import networkx as nx\n",
        "G = nx.Graph()\n",
        "G"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "WTFfPSVBwr5L"
      },
      "source": [
        "### `Создание графа`\n",
        "\n",
        "Доступны три способа создания:\n",
        "- Явное добавление вершин и ребер в скрипте\n",
        "- Генерация графа с помощью алгоритмов создания стандартных сетевых топологий\n",
        "- Импортирование существующего графа из файла\n",
        "\n",
        "Явное создание графа:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:01:39.452676Z",
          "start_time": "2022-09-22T08:01:39.435678Z"
        },
        "id": "lLGQTu7Swr5L",
        "outputId": "8f6ee531-c85d-4f7f-f223-49e2527f83da"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "NodeView((1, 2, 3))"
            ]
          },
          "execution_count": 104,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "G.add_node(1)\n",
        "G.add_nodes_from([2, 3])\n",
        "G.nodes"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:01:39.643900Z",
          "start_time": "2022-09-22T08:01:39.636900Z"
        },
        "id": "SCxa8Ji5wr5L",
        "outputId": "b560b64d-75a5-4cb7-df58-7a2537fe208d"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "EdgeView([(1, 2), (1, 3), (2, 3)])"
            ]
          },
          "execution_count": 105,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "G.add_edge(1, 2)\n",
        "G.add_edges_from([(2, 3), (1, 3)])\n",
        "G.edges"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "XG7p40vFwr5L"
      },
      "source": [
        "### `Визуализация графа`\n",
        "\n",
        "Построенный граф можно несложно визуализировать на плоскости средствами NetworkX:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:01:40.069960Z",
          "start_time": "2022-09-22T08:01:39.995954Z"
        },
        "id": "tVP1n5kawr5L",
        "outputId": "4471305d-ebef-4cfa-c145-b4b2271567f6"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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7786qVavy0EMP5dhjj83KlSszOjqac889N51Op+orHl63m2x5JHnmlmTjV5LueNIZ6X09kv3f1xlJFl+anHpVMn95Uvd/5gIEZQQlAPTTc889l9tvvz2rV6/Oxo0bc8opp2R0dDRXXHFFFi1aVPX1DrTp3mT9dcn270w+Ig9l/88fd2ay5Ppk4UXl3bNG/A4lANBXjXmV+K6tybc+kjy0Itm+ofd3RWLyzT+//ankoYt75+/aWuzMGhKUAMBA1PpV4i/ck9x3WvL8nfv+YqLkB9h33vN3Jn9+Wu/xWkRQAgADV5tXiXe7yVM3JmsvSXa/knT39vnx9ia7Xuk93lM3teaV4YISAKhUZZN4t5usvzZZ/5l9f1H2s5KHsu9x9j92C6JSUAIAtTDwSXzDTcmGm8s5q8l3KIGgBABqp++T+Av3vOmZyYqtv7b3yvIGE5QAQK2VPonv2po8+vEkdXlfyBnJIx9r9Ku/BSUA0AilTeLrrk72vJqkLr+7ONG7z7pPVH2RaROUAEDjTHsS33RvsvFL/X8191R19yYb1ySbvlb1TaZFUAIAjTbpSbzb7X0CTm3zZ0bvfg181Xdd/x8FAJiSI03iN//mit7HKQ7s7YGmaiLZ/u1k66NVX2TKBCUA0DoHm8RP6/x19tRs6T5AZyR5+paqbzFlghIAaLX3vve9+dw1V2fFWbtz1Mzi5722M/kvdyc//9vJvCuTzmXJqgeLn5uk99nfG7+c7NxS0oGDISgBgPZ78f50uuOlHLVlLPn8nyV//4/JkveUcuRbdceTlx7ow8H9IygBgPbb9kRvTi7BSccnP7ol2fhHye9+pJQj36oz0rtvgwhKAKD9tj7ae+avBLOPSt51fClHHVx3PNnyWB8foHyCEgBot2432fZk1beYmm3rGvX2QYISAGi3XS8n42NV32Jqxsd6924IQQkAtNv4FD7nu0727qj6BpMmKAGAdpvYXfUNpmfvrqpvMGmCEgBotxmzqr7B9MycXfUNJk1QAgDtNnJM1TeYnplHV32DSROUAEC7zT4hGZlb9S2mZmRu794NUc47fAIA1FWnk8w7K3mprM9HTP7468mr/5z88NXef7/vb5NN23r/+ep/lxxX9EnReWf37t0QghIAaL/5y5OXv1Xam5v/3l8kG9/0cdt/+njvT5Jc/rMFg7IzkixYVuh+gyYoAYD2m7e0tJhMkn/4w9KOOlB3vHffBvE7lABAqz333HO5edVj2bO36ptMUmckOfGCqm8xJYISAGidsbGxfPGLX8z555+fk08+OTf9t/+dJ7acnInMrPpqh9cZSRZfmsxZUPVNpkRQAgCtMDExkfvvvz+/+qu/mne96135+Mc/nqOPPjpr1qzJ5s2bc87lt2dGav40ZXc8OfWqqm8xZX6HEgBotOeeey6rV6/O6tWr8/zzz+fUU0/Nddddl8svvzyLFi164xvnnJMcd2ay/akkE5Xd99BmJMf/VO8FRA0jKAGAxhkbG8tdd92VVatWZe3atTn22GNz6aWXZnR0NOecc046B3vLnU4nWXJ98tDFg7/wpEwk7/utRr1d0H6CEgBohImJiXzjG9/IqlWr8tWvfjU7duzIz/3cz2XNmjVZsWJFjj56Ep8ss/CiZPGHk+fvTLo1mr87M5P3rOzdr4EEJQBQa5OetCfr7C8kP/p6svuV1GP6npHMOj45+4+qvsi0CUoAoHamNWlP1uz5yfJbk7WXlHfhQiaS5bf17tVQghIAqIVSJu3JWrQiWXJDsv4z5Z05XUtuTBbW9fc6J0dQAgCVKn3SnqzTr0n2vJZsuKl/jzGZO5z+6eoevySCEgAYuL5O2pPV6fSepTxqbrL+2vTennsQv1O573GW3JSc0fyYTAQlADAgA520J6vTSc64Jjnu9OSRjyV7Xu3vq787M3svwFl+W+Nn7jcTlABAX1U2aU/FwouTD/1ssu7qZOOXUv6zlfvOe8/K3qvMZ88r8ezqCUoAoHS1mLSnavb85Lw1yeKVyfrPJtu/3fts7e749M/c//PHndF7U/WGvs/kkQhKAKAUtZy0p2Phxcm7L0q2Ppo8fUuy8cu9KOwclXT3HPnn90dk56hk8aW9z+aev6yRn4AzWYISACikEZP2VHU6yYJzen/O+oPkpQeSreuSrY8n29Yl42MH/szI3GTe2cmCZcm8pcmJFyRzFgz+7hUQlADAlDVy0p6uOQuS9/xK70+SdLvJrpeTvTuSvbuSmbOTmUcns09o9bOQhyMoAYBJac2kXVSnk8w5sepb1IqgBAAOq5WTNqUSlADAAYZq0qYwQQkAJDFpM32CEgCGnEmbogQlAAwhkzZlEpQAMCRM2vSLoASAljNp02+CEgBayKTNIAlKAGgJkzZVEZQA0HAmbaomKAGggUza1ImgBICGMGlTV4ISAGrOpE3dCUoAqCGTNk0iKAGgJkzaNJWgBICKmbRpOkEJABUwadMmghIABsSkTVsJSgDoM5M2bScoAaAPTNoME0EJACUxaTOsBCUAFGTSZtgJSgCYBpM2vEFQAsAkmbTh4AQlAByBSRsOT1ACwEGYtGHyBCUA7GPShukRlAAMPZM2FCMoARhKJm0oj6AEYGiYtKE/BCUArWfShv4SlAC0kkkbBkdQAtAaJm2ohqAEoPFM2lAtQQlAI5m0oT4EJQCNYdKGehKUANSeSRvqTVACUEsmbWgOQQlAbZi0oZkEJQCVM2lDswlKACph0ob2EJQADIxJG9pJUALQdyZtaDdBCUBfmLRheAhKAEpj0obhJCgBKMykDcNNUAIwLSZtYD9BCcCkmbSBgxGUAByRSRs4HEEJwEGZtIHJEpQA/JhJG5gOQQmASRsoRFACDCmTNlAWQQkwREzaQD8ISoAhYNIG+klQArSUSRsYFEEJ0CImbaAKghKgBUzaQJUEJUBDmbSBuhCUAA1i0gbqSFACNIBJG6gzQQlQUyZtoCkEJUCNmLSBJhKUADVg0gaaTFACVMSkDbSFoAQYIJM20EaCEmAATNpAmwlKgD4xaQPDQlAClMikDQwjQQlQApM2MMwEJcA0mbQBegQlwBSYtAEOJCgBJsGkDXBoghLgEEzaAJMjKAHexKQNMHWCEiAmbYAiBCUwtEzaAOUQlMBQMWkDlE9QAkPBpA3QP4ISaC2TNsBgCEqgVUzaAIMnKIFWMGkDVEdQAo1l0gaoB0EJNIpJG6B+BCXQCCZtgPoSlEBtmbQBmkFQArVi0gZoHkEJ1IJJG6C5BCVQGZM2QDsISmCgTNoA7SMogYEwaQO0l6AE+sakDTAcBCVQKpM2wPARlEApTNoAw0tQAtNm0gYgEZTAFJm0AXg7QQlMikkbgEMRlMAhmbQBmAxBCbyFSRuAqRKUQBKTNgDTJyhhiJm0ASiDoIQhY9IGoGyCEoaESRuAfhGU0GImbQAGQVBCy5i0ARg0QQktYdIGoCqCEhrMpA1AHQhKaBiTNgB1IyihIUzaANSVoIQaM2kD0ASCEmrGpA1A0whKqAmTNgBNJSihQiZtANpAUMKAmbQBaBtBCQNi0gagrQQl9JFJG4BhICihZCZtAIaNoISSmLQBGFaCEgowaQOAoIQpM2kDwFsJSpgkkzYAHJyghMMwaQPAkQlKeBuTNgBMjaCEfUzaADA9gpKhZtIGgOIEJUPHpA0A5RKUDA2TNgD0h6Ck1UzaANB/gpLWMWkDwGAJSlrDpA0A1RCUNJpJGwCqJyhpHJM2ANSLoKQxTNoAUE+CklozaQNA/QlKasekDQDNIiipDZM2ADSToKRSJm0AaD5BycCZtAGgXQQlA2PSBoB2EpT0lUkbANpPUFI6kzYADBdBSWlM2gAwnAQlhZi0AQBByZSZtAGANxOUTNqzzz6b1atX5/bbbzdpAwA/Jig5rLGxsdx5551ZtWpVvvnNb5q0AYADCEoOYNIGAKZCUPJjJm0AYDoE5ZAzaQMARQnKIWTSBgDKNNxB2e0mu17OrN0/zCnvSmbt/mGyc2Ey+4Skhc/MmbQBgH7odLvdbtWXGJidW5IX70+2PZFsfaz3dXzswO8bmZvMW5rMX9b7+s73J3MWDP6+JTBpAwD91v6g7HaTLY8kz9ySbPxK0h1POiO9r0ey//s6I8niS5NTr0rmL6/9s5eHmrRHR0dN2gBA6dodlJvuTdZfl2z/zuQj8lD2//xxZyZLrk8WXlTePUtysEl7dHTUpA0A9FU7g3LX1mTd1cnGLyWZkWSixMP3nbf4w8nZX0hmzy/x7KkzaQMAVWtfUL5wT/Lox5M9rybdvf17nM7MZNbxybJbk0Ur+vc4B2HSBgDqpD1B2e0mG25K1n8m5T8reSj7HmfJjcnpn+7771aatAGAOmpHUHa7yfprkw03V3eH069JltxQelSatAGAumvH+1BuuKnamNx/h6PmJmdcU/gobzwOADRJ85+hfOGeZO0lVd/iDeffkyy8eFo/atIGAJqo2UG5a2ty32nJ7m1J6vCPMSOZ9Y7kQ9+b9Ku/TdoAQNM1e/Jed3Xv1dy1iMkkmejdZ90nkvPuOPR3mbQBgBZp7jOUm+5NHlpR9S0O7fx7D3jzc5M2ANBGzQzKbjf5y/cl2zdkMG8PNFUzkuPOSH5xfcZee82kDQC0WjOD8uW/Sf7vz1R9iyP63N/8fH7niw9543EAoNWaGZQPX55s/Eqxz+busz17k7/4ztz8/fHXmLQBgFZrXlDu3JL82UmFY/KpTcl//WryxA+SzduTY2Ylp787+c0PJh86q5yrdjsj6Vzyo2TOgnIOBACooRlVX2DKXry/lGcmN25JxnYmv/Zvkj+8IvnsvreyvOj3k/91f+HjkySd7njy0gPlHAYAUFPNe4byb/9z8t3/1pe5e+9EsvQzyc49yXd/r4QDOyPJv/qN5F9X/Ck+AAB91LxnKLc+2rffnZw5I1k0P3n19ZIO7I4nWx4r6TAAgHpq1hubd7vJtidLPfKfdyY79iTbX0++9mTyf9YnK88p8QG2revd29sDAQAt1ayg3PVyMj5W6pG/cUfyP/f9zuSMTvJLP5388WiJDzA+1rv3nBNLPBQAoD6aFZTjZW3Rb/jULyS/vDz54SvJnY/0fo9yd9mL+t4dJR8IAFAfzXpRzj89nfz5aX19iAtv6v0O5aOfL3Gl/uD3kmNPLekwAIB6adaLcmbM6vtD/PLy5PHvJ0//qMRDZ84u8TAAgHppVlCOHNP3h9ixu/d1e5kr9UwftQgAtFezgnL2CcnI3FKOemn7gX+3Zzy5fW1y9L5PzSnFyNzevQEAWqpZL8rpdJJ5ZyUvPVj4qP/wxeSfdiTnn5a8e16y+dXkjoeT7/4w+f3Lkp+YU/y6SZJ5Z3vLIACg1ZoVlEkyf3ny8rcKv7n5ynOS276R/I//l2x9LZk7J1n6L5PfvjS5aGk5V01nJFmwrKTDAADqqXlBOW9pKZ+Uc+m5vT991R3v3RcAoMWa9TuUSfLO9/ee+WuCzkhy4gVV3wIAoK+aF5RzFiSLV9Y/KjsjyeJLe/cFAGix5gVlkpxyVSmzd191x5NTr6r6FgAAfdfMoFxwTnLcmanv9Wckx7+v9wIiAICWq2uRHV6nkyy5PslE1Tc5hInkfb/l7YIAgKHQzKBMkoUXJYs/nHRmVn2Tt+rMTBZ/pHc/AIAh0Ol2u92qLzFtu7Ym952W7H4l9Xi2ckYy+x3JB7+XzJ5f9WUAAAaiuc9QJr1oW35r6hGTSTKRLL9NTAIAQ6XZQZkki1YkS26o+hY9S25MFl5c9S0AAAaq+UGZJKdf0/tT+R0+Xe0dAAAq0OzfoXyzbjfZcHOy/tr0OnkQM/i+x1lyU3KGmAQAhlN7gnK/Tfcmj3ws2fNq0t3bv8fpzExmHd/7nUkzNwAwxNoXlEnv1d/rrk42finlP1u577zFH0nO/kIye16JZwMANE87g3K/Tfcm6z+bbP9277O1i3xc4/6fP+7M3puqe59JAIAkbQ/KpPe7lVsfTZ6+Jdn45V4Udo5KunuO/LP7I7JzVLL40t5nc89f5hNwAADepP1B+WY7tyQvPZBsXZdsfTzZti4ZHzvw+0bmJvPOThYsS+YtTU68IJmzYPD3BQBogOEKyrfrdpNdLyd7dyR7dyUzZyczj05mn+BZSACASRruoAQAoLB2vLE5AACVEZQAABQiKAEAKERQAgBQiKAEAKAQQQkAQCGCEgCAQgQlAACFCEoAAAoRlAAAFCIoAQAoRFACAFCIoAQAoBBBCQBAIYISAIBCBCUAAIUISgAAChGUAAAUIigBAChEUAIAUIigBACgEEEJAEAhghIAgEIEJQAAhQhKAAAKEZQAABQiKAEAKOT/A1hd4W6aDvwEAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "nx.draw_circular(G, node_color='orange', node_size=1000, with_labels=True)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "zpEfKDHbwr5L"
      },
      "source": [
        "### `Удаление данных из графа`\n",
        "\n",
        "Можно удалить ребра:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:01:40.352128Z",
          "start_time": "2022-09-22T08:01:40.340128Z"
        },
        "id": "2lvTI4-ewr5L",
        "outputId": "a32777d4-c3e9-47f6-e619-ed55fbc13e20"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "EdgeView([(1, 2), (2, 3)])"
            ]
          },
          "execution_count": 107,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "G.remove_edge(1, 3)\n",
        "G.edges"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "q-JVT0x3wr5L"
      },
      "source": [
        "Можно удалить вершину (будут удалены все инцидентные ребра):"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:01:40.716425Z",
          "start_time": "2022-09-22T08:01:40.708427Z"
        },
        "id": "u0RaYFtzwr5L",
        "outputId": "9301871a-67a1-4e26-e7e7-71e42af2ebfe"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "EdgeView([])"
            ]
          },
          "execution_count": 108,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "G.remove_node(2)\n",
        "G.edges"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "IO7Y9np_wr5M"
      },
      "source": [
        "Можно очистить весь граф:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:01:41.093654Z",
          "start_time": "2022-09-22T08:01:41.083656Z"
        },
        "id": "JcYhWdDwwr5M",
        "outputId": "c2647c04-6d8a-4052-dbf0-0b8ad5baebf5"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "0 0\n"
          ]
        }
      ],
      "source": [
        "G.clear()\n",
        "print(G.number_of_edges(), G.number_of_nodes())"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "whFzBCIYwr5M"
      },
      "source": [
        "### `Генерация графов`\n",
        "\n",
        "Известные стандартные графы можно создавать с помощью встроенных методов:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:01:41.550134Z",
          "start_time": "2022-09-22T08:01:41.492133Z"
        },
        "id": "_Xn3vxcTwr5M",
        "outputId": "84874db8-8db9-44a5-ec5f-152b2fdaea2b"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "K_5 = nx.complete_graph(5)\n",
        "nx.draw_circular(K_5, node_color='orange', node_size=1000, with_labels=True)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "KIJkg3D2wr5M"
      },
      "source": [
        "### `Генерация графов`\n",
        "\n",
        "Генерировать также можно случайные графы:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:01:41.994118Z",
          "start_time": "2022-09-22T08:01:41.876119Z"
        },
        "id": "nlnk214Dwr5M",
        "outputId": "9e4a00e3-a2d5-4f1a-8bfa-b0e76cd5534b"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "er = nx.erdos_renyi_graph(n=10, p=0.4)\n",
        "nx.draw_circular(er, node_color='orange', node_size=1000, with_labels=True)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "e7z8Rqt0wr5M"
      },
      "source": [
        "### `Создание графа из словаря или списка`"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:01:42.310185Z",
          "start_time": "2022-09-22T08:01:42.236184Z"
        },
        "id": "2k_GLD8Vwr5M",
        "outputId": "2e6d8b3e-c14e-4e56-efc5-fe989355453f"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "{('A', 'B'): Text(-0.14333660609105836, 0.4999999999999999, '1.5'),\n",
              " ('A', 'C'): Text(-0.04605598989461876, -0.4263681303277567, '2.0'),\n",
              " ('B', 'C'): Text(0.1893925959856784, -0.07363186967224339, '0.5')}"
            ]
          },
          "execution_count": 112,
          "metadata": {},
          "output_type": "execute_result"
        },
        {
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "g = {'A': {'B': {'weight': 1.5}, 'C': {'weight': 2.0}},\n",
        "     'B': {'C': {'weight': 0.5}}}\n",
        "\n",
        "G = nx.DiGraph(g)\n",
        "\n",
        "pos = nx.spring_layout(G, seed=7)\n",
        "nx.draw(G, pos, node_color='orange', node_size=1000, with_labels=True)\n",
        "labels = nx.get_edge_attributes(G, 'weight')\n",
        "nx.draw_networkx_edge_labels(G, pos, edge_labels=labels)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "U-lZUJhNwr5M"
      },
      "source": [
        "### `Конвертация графа в словарь или список`\n",
        "\n",
        "Конвертация в словарь словарей сохраняет всю информацию:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:01:42.642539Z",
          "start_time": "2022-09-22T08:01:42.636538Z"
        },
        "id": "ascY6rLNwr5M",
        "outputId": "5d4b85e2-681a-435f-acfd-b7820aa58aff"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "{'A': {'B': {'weight': 1.5}, 'C': {'weight': 2.0}},\n",
              " 'B': {'C': {'weight': 0.5}},\n",
              " 'C': {}}"
            ]
          },
          "execution_count": 113,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "nx.convert.to_dict_of_dicts(G)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "MYEPkcoxwr5M"
      },
      "source": [
        "Конвертация в список - только информацию о структуре графа:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:01:43.052680Z",
          "start_time": "2022-09-22T08:01:43.046681Z"
        },
        "id": "rs27fRsnwr5M",
        "outputId": "9b8198ff-7233-4894-b915-1a1758762ea9"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "{'A': ['B', 'C'], 'B': ['C'], 'C': []}"
            ]
          },
          "execution_count": 114,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "nx.convert.to_dict_of_lists(G)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "UHgC2MHkwr5M"
      },
      "source": [
        "### `Операции над графами`"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T07:58:42.011578Z",
          "start_time": "2022-09-22T07:58:41.998584Z"
        },
        "id": "oXuf3X5qwr5M"
      },
      "source": [
        "```python\n",
        "nx.subgraph(G, nodes)         # induced subgraph view of G on nodes in nodes\n",
        "nx.union(G1, G2)              # graph union\n",
        "nx.disjoint_union(G1, G2)     # graph union assuming all nodes are different\n",
        "nx.cartesian_product(G1, G2)  # return Cartesian product graph\n",
        "nx.compose(G1, G2)            # combine graphs identifying nodes common to both\n",
        "nx.complement(G)              # graph complement\n",
        "nx.create_empty_copy(G)       # return an empty copy of the same graph class\n",
        "nx.to_undirected(G)           # return an undirected representation of G\n",
        "nx.to_directed(G)             # return a directed representation of G\n",
        "```"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "OS67_tIiwr5M"
      },
      "source": [
        "### `Операции над графами`\n",
        "\n",
        "Выделение подграфа:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:01:43.934939Z",
          "start_time": "2022-09-22T08:01:43.867939Z"
        },
        "id": "-WfFSy4zwr5M",
        "outputId": "aaba8fed-ba4c-48fe-ff50-036cc667553d"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "G = nx.erdos_renyi_graph(n=7, p=0.4)\n",
        "nx.draw_circular(G, node_color='orange', node_size=1000, with_labels=True)\n",
        "nx.draw_circular(nx.subgraph(G, [0, 1, 4, 5]), node_color='red', node_size=1000, with_labels=True)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "UktCAZ3wwr5M"
      },
      "source": [
        "### `Алгоритмы на графах`\n",
        "\n",
        "В NetworkX реализовано много полезных алгоритмов для анализа и кластеризации графов, полный список есть в документации (https://networkx.org/documentation/stable/reference/algorithms/index.html)\n",
        "\n",
        "Найдем кратчайший путь между парой вершин:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:01:44.328038Z",
          "start_time": "2022-09-22T08:01:44.268050Z"
        },
        "id": "_BIqmFsvwr5N",
        "outputId": "4e4d66c6-28a4-4880-de33-ab8765d45d08"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "[6, 1, 0, 3]\n"
          ]
        },
        {
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "G = nx.full_rary_tree(5, 7)\n",
        "nx.draw(G, node_color='orange', node_size=1000, with_labels=True)\n",
        "print(nx.shortest_path(G, source=6, target=3))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "KTPZn6jGwr5N"
      },
      "source": [
        "### `Алгоритмы на графах`\n",
        "\n",
        "Найдем все клики (полные подграфы) в алгоритме:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:01:44.740102Z",
          "start_time": "2022-09-22T08:01:44.676104Z"
        },
        "id": "zBnLxaOmwr5N",
        "outputId": "b72b6c70-ef16-484d-f131-7d389e3118d4"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "[[0, 1, 2, 3, 4, 5]]"
            ]
          },
          "execution_count": 117,
          "metadata": {},
          "output_type": "execute_result"
        },
        {
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "G = nx.complete_graph(6)\n",
        "nx.draw(G, node_color='orange', node_size=1000, with_labels=True)\n",
        "[e for e in nx.algorithms.clique.find_cliques(G)]"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "DH36CKGAwr5N"
      },
      "source": [
        "### `Алгоритмы на графах`\n",
        "\n",
        "Выделение сообществ методом жадной максимизации модулярности:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:01:45.262113Z",
          "start_time": "2022-09-22T08:01:45.052116Z"
        },
        "id": "zqN-muwdwr5N",
        "outputId": "e61a81f2-1cd8-4622-dc06-045a449d274e"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "[frozenset({0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11}), frozenset({12, 13, 14, 15, 16, 17, 18, 19, 20, 21})]\n"
          ]
        },
        {
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "G = nx.barbell_graph(10, 2)\n",
        "\n",
        "nx.draw_kamada_kawai(G, node_color='orange', node_size=1000, with_labels=True)\n",
        "print(list(nx.algorithms.community.greedy_modularity_communities(G)))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "x0QhA9STwr5N"
      },
      "source": [
        "По факту кластеризация и выделение сообществ — одна и та же задача, но в алгоритмах (и в реализациях) их часто описывают отдельно"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "cSFbHoXfwr5N"
      },
      "source": [
        "### `Введение в библиотеку SciPy`\n",
        "\n",
        "- SciPy — это библиотека для научных вычислений, решения оптимизационных, численных и статистических задач<br><br>\n",
        "- Построена поверх NumPy<br><br>\n",
        "- Эффективно реализует многие методы линейной алгебры и оптимизации<br><br>\n",
        "\n",
        "Полезные ссылки:\n",
        "- https://scipy-lectures.org/intro/scipy.html\n",
        "- https://docs.scipy.org/doc/scipy/reference/"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "UPnB5Fitwr5N"
      },
      "source": [
        "### `Состав SciPy`\n",
        "\n",
        "__Что кратко рассмотрим:__\n",
        "\n",
        "- `linalg` — линейная алгебра\n",
        "- `optimize` — методы оптимизации и решения уравнений\n",
        "- `sparse` — разреженные матрицы\n",
        "- `stats` — вероятностные распределения и статистика"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Vj4xQLdSwr5N"
      },
      "source": [
        "### `Состав SciPy`\n",
        "\n",
        "__Что есть ещё:__\n",
        "\n",
        "- `cluster` — алгоритмы кластеризации\n",
        "- `constants` — физические и математические константы\n",
        "- `fftpack` — инструменты для быстрого преобразования Фурье\n",
        "- `integrate` — интегрирование и решение ОДУ\n",
        "- `interpolate` — интерполяция и сплайны\n",
        "- `io` — библиотека для работы с разными форматами входных и выходных данных\n",
        "- `ndimage` — обработка N-мерных изображений\n",
        "- `odr` — реализация Orthogonal distance regression\n",
        "- `signal` — обработка сигналов\n",
        "- `spatial` — пространственные структуры данных и алгоритмы\n",
        "- `special` — набор специальных полезных функций\n",
        "- `misc` — набор технических инструментов"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "VC30w-Mpwr5N"
      },
      "source": [
        "### `Модуль scipy.linalg`"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:01:46.314698Z",
          "start_time": "2022-09-22T08:01:46.307700Z"
        },
        "id": "fEypgC18wr5N"
      },
      "outputs": [],
      "source": [
        "import numpy as np\n",
        "from scipy import linalg\n",
        "\n",
        "A = np.array([[1,2], [3, 4]])"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:01:46.488867Z",
          "start_time": "2022-09-22T08:01:46.484867Z"
        },
        "id": "zXokNfy7wr5N",
        "outputId": "807c1c8e-c3aa-4895-db6a-90fe37ab57db"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "-2.0"
            ]
          },
          "execution_count": 120,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "linalg.det(A)  # determinant"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:01:46.692959Z",
          "start_time": "2022-09-22T08:01:46.684971Z"
        },
        "id": "onNFEP-pwr5N",
        "outputId": "681e635e-485d-40a8-babf-9245bb8b1f0d"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([[-2. ,  1. ],\n",
              "       [ 1.5, -0.5]])"
            ]
          },
          "execution_count": 121,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "linalg.inv(A)  # inverted matrix"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:01:46.927103Z",
          "start_time": "2022-09-22T08:01:46.909104Z"
        },
        "id": "uwTweyHkwr5N",
        "outputId": "b7c08f61-1061-4e5c-c7f0-2d0622c748a8"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "5.477225575051661"
            ]
          },
          "execution_count": 122,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "linalg.norm(A)  # matrix and vector norms"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "MK6CE_amwr5N"
      },
      "source": [
        "### `Модуль scipy.linalg`"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:01:47.333337Z",
          "start_time": "2022-09-22T08:01:47.316337Z"
        },
        "id": "kessd1cXwr5N",
        "outputId": "fd7883fc-240c-4c9b-a3da-b9ad0bc071eb"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "[-0.37228132+0.j  5.37228132+0.j]\n",
            "[[-0.82456484 -0.41597356]\n",
            " [ 0.56576746 -0.90937671]]\n"
          ]
        }
      ],
      "source": [
        "for e in linalg.eig(A):  # eigen values and vectors\n",
        "    print(e)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:01:47.522405Z",
          "start_time": "2022-09-22T08:01:47.516407Z"
        },
        "id": "ulTIFw_-wr5O",
        "outputId": "2d116b7e-38c7-431b-b096-e5cbe6270aba"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([[1., 2.],\n",
              "       [3., 4.]])"
            ]
          },
          "execution_count": 124,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "U, diags, V_T = linalg.svd(A)  # SVD\n",
        "U @ np.diag(diags) @ V_T"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:01:47.728335Z",
          "start_time": "2022-09-22T08:01:47.716337Z"
        },
        "id": "pBcl5068wr5O",
        "outputId": "bd1edc29-4d15-48e1-afcc-f86df5a63b3d"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([[1., 2.],\n",
              "       [3., 4.]])"
            ]
          },
          "execution_count": 125,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "P, L, U = linalg.lu(A)  # pivoted LU decomposition\n",
        "P @ L @ U"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "S3qlmzi9wr5O"
      },
      "source": [
        "### `Модуль scipy.optimize`\n",
        "\n",
        "Сгенерируем точки с помощью синусоиды с шумом и попробуем восстановить параметры функции"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:01:48.104266Z",
          "start_time": "2022-09-22T08:01:48.100265Z"
        },
        "id": "TK4uBQ6hwr5O"
      },
      "outputs": [],
      "source": [
        "from scipy import optimize"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:01:48.309081Z",
          "start_time": "2022-09-22T08:01:48.300080Z"
        },
        "id": "QPh7mSEnwr5O"
      },
      "outputs": [],
      "source": [
        "x_data = np.linspace(-5, 5, num=50)\n",
        "y_data = 2.9 * np.sin(1.5 * x_data) + np.random.normal(size=50)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:01:48.531094Z",
          "start_time": "2022-09-22T08:01:48.525095Z"
        },
        "id": "DDm2uGYvwr5O"
      },
      "outputs": [],
      "source": [
        "def func_to_fit(x, a, b):\n",
        "    return a * np.sin(b * x)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:01:48.750539Z",
          "start_time": "2022-09-22T08:01:48.740541Z"
        },
        "id": "gqXI04Suwr5O",
        "outputId": "90315fe3-bda4-4742-9277-6fe4d7a8e030"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "[2.85757249 1.47564681]\n"
          ]
        }
      ],
      "source": [
        "params, params_covariance = optimize.curve_fit(func_to_fit, x_data, y_data)\n",
        "print(params)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "j_4qf4Khwr5O"
      },
      "source": [
        "### `Модуль scipy.optimize`\n",
        "\n",
        "Найдём минимум скалярной функции на отрезке (зависит от стартового приближения)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:01:49.212334Z",
          "start_time": "2022-09-22T08:01:49.147334Z"
        },
        "code_folding": [],
        "id": "w0lf7Ht7wr5O",
        "outputId": "ba23deff-512b-4817-b597-8d05d13805e2"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "def f(x):\n",
        "    return x**2 + 10 * np.sin(x)\n",
        "\n",
        "x = np.arange(-8, 8, 0.1)\n",
        "plt.plot(x, f(x))\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:01:49.354590Z",
          "start_time": "2022-09-22T08:01:49.348590Z"
        },
        "id": "juicj10bwr5O",
        "outputId": "d5e3cb0e-4576-45d7-e692-9a68f5cd9ec9"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([3.83746782])"
            ]
          },
          "execution_count": 131,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "result = optimize.minimize(f, x0=4, bounds=((-8, 8),))  # 'bounds' is optional\n",
        "result.x"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "yL26W5kTwr5O"
      },
      "source": [
        "### `Модуль scipy.optimize`\n",
        "\n",
        "Найдём минимум скалярной функции на отрезке (зависит от стартового приближения)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:01:49.778072Z",
          "start_time": "2022-09-22T08:01:49.772072Z"
        },
        "id": "leSss2F_wr5O",
        "outputId": "46997be0-f51c-4faa-f26b-262f7492058b"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([-1.30643988])"
            ]
          },
          "execution_count": 132,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "result = optimize.minimize(f, x0=0, bounds=((-8, 8),))  # 'bounds' is optional\n",
        "result.x"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:01:50.661125Z",
          "start_time": "2022-09-22T08:01:49.989125Z"
        },
        "id": "CBDwRRhWwr5O",
        "outputId": "8922e892-c216-4eb3-92c3-9e21f1ced939"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([-1.30644001])"
            ]
          },
          "execution_count": 133,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "result = optimize.basinhopping(f, x0=4, niter=1000)\n",
        "result.x"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "KlyfK37Uwr5O"
      },
      "source": [
        "Функция `optimize.minimize` имеет параметр `method`, в котором можно определять конкрентный метод оптимизации, подходящий для решаемой задачи"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "EQucNTuNwr5O"
      },
      "source": [
        "### `Модуль scipy.optimize`\n",
        "\n",
        "Найдём нули скалярной функции"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:01:50.676125Z",
          "start_time": "2022-09-22T08:01:50.662125Z"
        },
        "id": "n4CIhvipwr5O",
        "outputId": "069bf870-371b-4c75-e5dc-5029a57af119"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([0.])"
            ]
          },
          "execution_count": 134,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "root = optimize.root(f, x0=1)\n",
        "root.x"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:01:50.852155Z",
          "start_time": "2022-09-22T08:01:50.836158Z"
        },
        "id": "aRwsyaxIwr5O",
        "outputId": "6d43ad3e-5753-4405-e91b-409cc0592253"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([-2.47948183])"
            ]
          },
          "execution_count": 135,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "root2 = optimize.root(f, x0=-2)\n",
        "root2.x"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "B3IqQhWcwr5P"
      },
      "source": [
        "Находим только один корень, ближайший к стартовой точке, нужно идти по сетке для поиска нескольких"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Z1_3wx0iwr5P"
      },
      "source": [
        "### `Модуль scipy.sparse`\n",
        "\n",
        "- Включает в себя набор различных типов разреженных матриц и инструментов для работы с ними\n",
        "- Мы рассмотрим основные форматы разреженных матриц, которые могут быть полезны в приложениях<br><br>\n",
        "\n",
        "\n",
        "- __Coordinate Format (COO)__\n",
        "    - представляет собой 3 массива `row`, `col`, `data`\n",
        "    - `row` содержит номера строк ненулевых элементов\n",
        "    - `col` содержит номера столбцов ненулевых элементов\n",
        "    - `data` содержит сами ненулевые элементы"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:01:51.802853Z",
          "start_time": "2022-09-22T08:01:51.788852Z"
        },
        "id": "YjOvBw30wr5P",
        "outputId": "d787682f-4a05-43c1-c99f-f97af70c8627"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "(array([0, 1, 1, 2], dtype=int32),\n",
              " array([0, 0, 2, 1], dtype=int32),\n",
              " array([1, 4, 6, 8]))"
            ]
          },
          "execution_count": 136,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "from scipy.sparse import coo_matrix\n",
        "\n",
        "S = np.array([[1, 0, 0], [4, 0, 6], [0, 8, 0]])\n",
        "\n",
        "cm = coo_matrix(S)\n",
        "cm.row, cm.col, cm.data"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "3x7VGE0Wwr5P"
      },
      "source": [
        "### `Модуль scipy.sparse`"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Xomqv49Kwr5P"
      },
      "source": [
        "- __Compressed Sparse Row Format (CSR)__\n",
        "    - Представляет собой три массива: `indices`, `indptr`, `data`\n",
        "    - `indices` содержит индексы столбцов ненулевых элементов\n",
        "    - `data` содержит значения ненулевых элементов\n",
        "    - `indptr` содержит старты строк в `indices` и `data` по следующим правилам:<br><br>\n",
        "        - длина `indptr` равна числу строк + 1, последний элемент равен числу ненулевых элементов\n",
        "        - ненулевые значения $i$-й строки лежат в `data[indptr[i]: indptr[i + 1]]`\n",
        "        - их индексы столбцов - в `indices[indptr[i]: indptr[i + 1]]`\n",
        "        - элемент $(i, j)$ доступ в `data[indptr[i]+k]`, где `k` - это позиция `j` в `indices[indptr[i]: indptr[i + 1]]`"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:01:52.823051Z",
          "start_time": "2022-09-22T08:01:52.812052Z"
        },
        "id": "s1dx1j_Cwr5P",
        "outputId": "1a37242e-b260-472a-e9d1-e3169b0b8fc9"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "(array([0, 0, 2, 1], dtype=int32),\n",
              " array([0, 1, 3, 4], dtype=int32),\n",
              " array([1, 4, 6, 8], dtype=int32))"
            ]
          },
          "execution_count": 137,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "from scipy.sparse import csr_matrix\n",
        "\n",
        "S = np.array([[1, 0, 0], [4, 0, 6], [0, 8, 0]])\n",
        "\n",
        "csrm = csr_matrix(S)\n",
        "csrm.indices, csrm.indptr, csrm.data"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "vB4S-a0-wr5P"
      },
      "source": [
        "### `Модуль scipy.sparse`\n",
        "\n",
        "- __Compressed Sparse Column Format (CSC)__\n",
        "    - Представляет собой три массива: `indices`, `indptr`, `data`\n",
        "    - `indices` содержит индексы строк ненулевых элементов\n",
        "    - `data` содержит значения ненулевых элементов\n",
        "    - `indptr` содержит старты столбцов в `indices` и `data` по следующим правилам:<br><br>\n",
        "        - длина `indptr` равна числу столбцов + 1, последний элемент равен числу ненулевых элементов\n",
        "        - ненулевые значения $i$-го столбца лежат в `data[indptr[i]: indptr[i + 1]]`\n",
        "        - их индексы строк - в `indices[indptr[i]: indptr[i + 1]]`\n",
        "        - элемент $(i, j)$ доступ в `data[indptr[j]+k]`, где `k` - это позиция `i` в `indices[indptr[j]: indptr[j + 1]]`"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:01:53.181319Z",
          "start_time": "2022-09-22T08:01:53.172319Z"
        },
        "id": "lqopbprSwr5P",
        "outputId": "81e67dc3-b0ba-40fd-83a2-ab04e5683f53"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "(array([0, 1, 2, 1], dtype=int32),\n",
              " array([0, 2, 3, 4], dtype=int32),\n",
              " array([1, 4, 8, 6], dtype=int32))"
            ]
          },
          "execution_count": 138,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "from scipy.sparse import csc_matrix\n",
        "\n",
        "S = np.array([[1, 0, 0], [4, 0, 6], [0, 8, 0]])\n",
        "\n",
        "cscm = csc_matrix(S)\n",
        "cscm.indices, cscm.indptr, cscm.data"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "TYBURKMrwr5P"
      },
      "source": [
        "### `Модуль scipy.stats`\n",
        "\n",
        "По выборке восстанавливаем параметры известного распределения"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:01:53.887060Z",
          "start_time": "2022-09-22T08:01:53.756060Z"
        },
        "id": "Muwamv1lwr5P",
        "outputId": "005bd0ce-5008-489d-9831-5adf3ce8b09b"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "9.805095456995904 3.5348333765014224\n"
          ]
        }
      ],
      "source": [
        "from scipy import stats\n",
        "\n",
        "samples = np.random.normal(size=1000, loc=9.8, scale=3.5)\n",
        "loc, scale = stats.norm.fit(samples)\n",
        "\n",
        "print(loc, scale)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:01:54.060061Z",
          "start_time": "2022-09-22T08:01:53.940061Z"
        },
        "id": "5xo-xwdEwr5P",
        "outputId": "9ba3e9cb-a2cd-4ff4-bac7-2a4dc772c461"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "0.9841012366717884 4.212599522117305 10.000024072169941 0.9273459800553958\n"
          ]
        }
      ],
      "source": [
        "samples = np.random.beta(a=1, b=4.6, size=5000) + 10\n",
        "\n",
        "a, b, loc, scale = stats.beta.fit(samples)\n",
        "print(a, b, loc, scale)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "w1xiDVGPwr5P"
      },
      "source": [
        "### `Модуль scipy.stats`\n",
        "\n",
        "Посчитаем статистики выборки:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:01:54.467895Z",
          "start_time": "2022-09-22T08:01:54.459896Z"
        },
        "id": "1US_btkwwr5P",
        "outputId": "e6927ede-c063-4d26-e3a8-d9bdc7f0a299"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "-0.01412943515822246"
            ]
          },
          "execution_count": 141,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "samples = np.random.normal(size=1000, loc=0.0, scale=1.0)\n",
        "\n",
        "np.mean(samples)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:01:54.673935Z",
          "start_time": "2022-09-22T08:01:54.668937Z"
        },
        "id": "uqFNybLGwr5P",
        "outputId": "a05ff5d5-bb6c-4a91-90e3-a16d34a971af"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "-0.02531545160897348"
            ]
          },
          "execution_count": 142,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "np.median(samples)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:01:54.893149Z",
          "start_time": "2022-09-22T08:01:54.884150Z"
        },
        "id": "d2YFjeiBwr5P",
        "outputId": "e98555c6-7acd-4c0d-b823-408d7ae02df1"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "-0.02531545160897348"
            ]
          },
          "execution_count": 143,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "stats.scoreatpercentile(samples, 50)  # median"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:01:55.348879Z",
          "start_time": "2022-09-22T08:01:55.332878Z"
        },
        "id": "WFrEqDhAwr5P",
        "outputId": "3cd4e44f-be4d-45e6-db3b-d5bab06169a6"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "1.2743559538218574"
            ]
          },
          "execution_count": 144,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "stats.scoreatpercentile(samples, 90)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "nFghVTMQwr5Q"
      },
      "source": [
        "### `Проверка статистических гипотез`\n",
        "\n",
        "- Общая идея:\n",
        "    - Дана наблюдаемая выборка данных\n",
        "    - Формулируется _гипотеза_ $H_0$ - определённое предположение о распределении вероятностей, лежащем в основе наблюдаемой выборки\n",
        "    - Формулируется альтернативная гипотеза $H_1$\n",
        "    - Выбирается _статистический критерий_ (обычно это какая-то статистика выборки)\n",
        "    - На основании выборки вычисляется значение статистического критерия $T$\n",
        "    - На основании этого значения вычисляется _достигаемый уровень значимости_ $p(T)$ (p-value) - вероятность получить значение критерия такое же или ещё более экстремальное, чем T, при условии справедливости $H_0$\n",
        "    - Если $p(T)$ достаточно мало (например, меньше уровня значимости $\\alpha$), то $H_0$ отвергается\n",
        "\n",
        "\n",
        "- Проверка гипотез доступна в `scipy.stats` и основанном на нем модуле `statsmodel`"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6QdlU-Zfwr5Q"
      },
      "source": [
        "### `Пример: T-критерий`\n",
        "\n",
        "- T-критерий (тест Стьдента) используется для проверки гипотез о\n",
        "    - равенстве матожиданий двух выборок\n",
        "    - равенстве матожидания одной выборки заданному значению<br><br>\n",
        "- В случае двух выборок, которые должны быть из распределения, близкого к нормальному, считается величина\n",
        "$$\n",
        "    t = \\cfrac{m_1 - m_2}{\\sqrt{\\cfrac{d_1}{n_1} - \\cfrac{d_2}{n_2}}},\n",
        "$$\n",
        "где\n",
        "    - $m_i$ - выборочные средние\n",
        "    - $d_i$ - выборочные дисперсии\n",
        "    - $n_i$ - размеры выборок"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "bNejCOXZwr5Q"
      },
      "source": [
        "### `Пример: T-критерий`\n",
        "\n",
        "- Определим функцию для генерации и визуализации выборок из нормального распределения:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:01:56.188997Z",
          "start_time": "2022-09-22T08:01:56.179997Z"
        },
        "id": "AenUl5Crwr5Q"
      },
      "outputs": [],
      "source": [
        "def gen_normal_samples(mean_1, mean_2):\n",
        "    samples1 = np.random.normal(mean_1, size=1000)\n",
        "    samples2 = np.random.normal(mean_2, size=1000)\n",
        "\n",
        "    bins = np.linspace(-4, 4, 30)\n",
        "    histogram1, bins = np.histogram(samples1, bins=bins, density=True)\n",
        "    histogram2, bins = np.histogram(samples2, bins=bins, density=True)\n",
        "\n",
        "    plt.figure(figsize=(6, 4))\n",
        "    plt.hist(samples1, bins=bins, density=True, label=\"Samples 1\")\n",
        "    plt.hist(samples2, bins=bins, density=True, label=\"Samples 2\")\n",
        "    plt.legend(loc='best')\n",
        "    plt.show()\n",
        "\n",
        "    return samples1, samples2"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "TNaluILjwr5Q"
      },
      "source": [
        "- Воспользуемся тестов `scipy.stats.ttest_ind` для проверки гипотезы о равенстве средних выборок:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:01:56.733434Z",
          "start_time": "2022-09-22T08:01:56.724434Z"
        },
        "id": "VwY_CJlXwr5Q"
      },
      "outputs": [],
      "source": [
        "#?stats.ttest_ind\n",
        "\n",
        "#Calculate the T-test for the means of *two independent* samples of scores.\n",
        "\n",
        "#This is a two-sided test for the null hypothesis that 2 independent samples\n",
        "#have identical average (expected) values. This test assumes that the\n",
        "#populations have identical variances by default."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_ongOv-Lwr5Q"
      },
      "source": [
        "### `Пример: T-критерий`\n",
        "\n",
        "- Посчитаем статистический T-тест для случая выборок из нормального распределения с априорно далекими средними:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:01:57.301133Z",
          "start_time": "2022-09-22T08:01:57.181135Z"
        },
        "id": "uUSlLertwr5Q",
        "outputId": "e2c51cf0-55ab-4f88-cd37-1f2fe1958025"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 600x400 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "samples_1, samples_2 = gen_normal_samples(mean_1=0, mean_2=1)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:01:57.584352Z",
          "start_time": "2022-09-22T08:01:57.566353Z"
        },
        "id": "jgAQEYWowr5Q",
        "outputId": "7cf37e54-a81f-4202-deb0-7fb6a9e11d96"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "(-21.046576674343378, 5.5371372236298646e-89)"
            ]
          },
          "execution_count": 148,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "t_score, p_value = stats.ttest_ind(samples_1, samples_2)\n",
        "t_score, p_value"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "EhDxjfR7wr5Q"
      },
      "source": [
        "- Большое по модулю значений `t_score` означает большую разность между двумя порождающими случайными процессами\n",
        "- Значение `p_value` характеризует вероятность того, что обе выборки были порождены процессами с одинаковым матожиданием"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "OrMTIt4Dwr5Q"
      },
      "source": [
        "### `Пример: T-критерий`\n",
        "\n",
        "- Посчитаем статистический T-тест для случая выборок из нормального распределения с априорно близкими средними:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:01:58.530390Z",
          "start_time": "2022-09-22T08:01:58.412391Z"
        },
        "id": "WoEx8z_Fwr5Q",
        "outputId": "6de329c0-3357-4286-fa89-ff73dce4f0c6"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 600x400 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "samples_1, samples_2 = gen_normal_samples(mean_1=-0.005, mean_2=0.005)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2022-09-22T08:01:59.273498Z",
          "start_time": "2022-09-22T08:01:59.261501Z"
        },
        "id": "DuV17ZFWwr5Q",
        "outputId": "a42026d3-b1c1-4bc2-d817-9768a82f4d48"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "(1.1447576071860142, 0.25244669268365644)"
            ]
          },
          "execution_count": 150,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "t_score, p_value = stats.ttest_ind(samples_1, samples_2)\n",
        "t_score, p_value"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Ox32-t_6wr5Q"
      },
      "source": [
        "## `Спасибо за внимание!`"
      ]
    }
  ],
  "metadata": {
    "celltoolbar": "Slideshow",
    "kernelspec": {
      "display_name": "Python 3 (ipykernel)",
      "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": "3.10.6"
    },
    "colab": {
      "provenance": []
    }
  },
  "nbformat": 4,
  "nbformat_minor": 0
}