Advanced_Numba_Tutorial_for_Machine_Learning_Researchers.ipynb

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        "<a href=\"https://colab.research.google.com/github/jman4162/Accelerated-Python-Computing-for-ML-Applications/blob/main/Advanced_Numba_Tutorial_for_Machine_Learning_Researchers.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
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      "source": [
        "# Advanced Numba Tutorial for Machine Learning Researchers\n",
        "\n",
        "Name: John Hodge\n",
        "\n",
        "Date: 10/09/24\n",
        "\n",
        "# Advanced Numba Tutorial for Machine Learning Researchers\n",
        "\n",
        "## Overview\n",
        "\n",
        "This advanced tutorial explores Numba, a powerful just-in-time (JIT) compiler for Python, tailored specifically for machine learning researchers. We'll delve into techniques to accelerate common ML tasks, covering basic JIT compilation, parallel processing, custom data types, GPU acceleration, and profiling. By the end, you'll be equipped to significantly optimize your Python code for machine learning applications.\n",
        "\n",
        "## Introduction\n",
        "\n",
        "In the fast-paced world of machine learning, computational efficiency is crucial. As datasets expand and models grow more complex, researchers often encounter performance bottlenecks that hinder experimentation and model development. Numba addresses this challenge by compiling Python code to native machine instructions, dramatically speeding up numerical and scientific computations without the need for low-level language rewrites.\n",
        "\n",
        "This tutorial is designed for ML researchers familiar with Python and NumPy who want to elevate their code optimization skills. We'll explore how Numba can accelerate common machine learning tasks and algorithms, potentially reducing execution times from hours to minutes.\n",
        "\n",
        "Key topics include:\n",
        "\n",
        "1. Basic JIT compilation\n",
        "2. Parallel processing for multi-core CPUs\n",
        "3. Custom data types for complex algorithms\n",
        "4. GPU acceleration for massively parallel computations\n",
        "5. Profiling and optimization techniques\n",
        "\n",
        "While Numba is powerful, it's not a universal solution. We'll discuss best practices, common pitfalls, and when to use Numba versus other optimization methods. By the end, you'll be able to unlock the full potential of your Python code for machine learning, enabling faster prototyping, quicker iterations, and the ability to work with larger datasets on standard hardware.\n",
        "\n",
        "Let's begin our journey into the world of high-performance Python for machine learning!\n",
        "\n",
        "## Prerequisites\n",
        "\n",
        "Before we begin, make sure you have the following libraries installed and import the necessary libraries:"
      ],
      "metadata": {
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      }
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {
        "id": "uRKesTudj9nN"
      },
      "outputs": [],
      "source": [
        "!pip install -q numba numpy matplotlib scikit-learn"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import numba\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "from sklearn.datasets import make_classification\n",
        "from time import time"
      ],
      "metadata": {
        "id": "_ZaSi8MkkdDu"
      },
      "execution_count": 2,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "## 1. Basic JIT Compilation\n",
        "\n",
        "Let's start with a quick refresher on basic JIT compilation:"
      ],
      "metadata": {
        "id": "wFEyx6oLmI93"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "@numba.jit(nopython=True)\n",
        "def euclidean_distance(x1, x2):\n",
        "    return np.sqrt(np.sum((x1 - x2)**2))\n",
        "\n",
        "# Test the function\n",
        "x1 = np.array([1, 2, 3])\n",
        "x2 = np.array([4, 5, 6])\n",
        "print(f\"Distance: {euclidean_distance(x1, x2)}\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "JEVviGU3kfkW",
        "outputId": "19fbc863-3d73-4862-d29c-7658035c5e8b"
      },
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Distance: 5.196152422706632\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## 2. Parallel Processing with Numba\n",
        "\n",
        "Numba allows for easy parallelization of computations. Let's implement a parallel K-means clustering algorithm:"
      ],
      "metadata": {
        "id": "n-w7MoMnmL3a"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "@numba.jit(nopython=True, parallel=True)\n",
        "def kmeans(X, k, max_iterations=100):\n",
        "    n_samples, n_features = X.shape\n",
        "\n",
        "    # Initialize centroids randomly\n",
        "    centroids = X[np.random.choice(n_samples, k, replace=False)]\n",
        "\n",
        "    for _ in range(max_iterations):\n",
        "        # Assign points to nearest centroid\n",
        "        labels = np.empty(n_samples, dtype=np.int64)\n",
        "        for i in numba.prange(n_samples):\n",
        "            min_dist = np.inf\n",
        "            for j in range(k):\n",
        "                dist = np.sum((X[i] - centroids[j])**2)\n",
        "                if dist < min_dist:\n",
        "                    min_dist = dist\n",
        "                    labels[i] = j\n",
        "\n",
        "        # Update centroids\n",
        "        new_centroids = np.zeros((k, n_features))\n",
        "        counts = np.zeros(k)\n",
        "        for i in numba.prange(n_samples):\n",
        "            new_centroids[labels[i]] += X[i]\n",
        "            counts[labels[i]] += 1\n",
        "\n",
        "        for i in range(k):\n",
        "            if counts[i] > 0:\n",
        "                new_centroids[i] /= counts[i]\n",
        "\n",
        "        # Check for convergence\n",
        "        if np.all(centroids == new_centroids):\n",
        "            break\n",
        "\n",
        "        centroids = new_centroids\n",
        "\n",
        "    return labels, centroids\n",
        "\n",
        "# Generate sample data\n",
        "X, _ = make_classification(n_samples=10000, n_features=20, n_informative=3, n_redundant=10, n_classes=3, random_state=42)\n",
        "\n",
        "# Run K-means\n",
        "start_time = time()\n",
        "labels, centroids = kmeans(X, k=3)\n",
        "end_time = time()\n",
        "\n",
        "print(f\"K-means clustering completed in {end_time - start_time:.4f} seconds\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "J0wdVrW6kjSh",
        "outputId": "2e45e6d9-871a-41a1-daa8-58f2e7bbb414"
      },
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "K-means clustering completed in 9.8693 seconds\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## 3. Custom Data Types with Numba\n",
        "\n",
        "Numba allows you to define custom data types, which can be useful for complex algorithms:"
      ],
      "metadata": {
        "id": "MZusowhbmTjG"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "from numba import types\n",
        "from numba.experimental import jitclass\n",
        "\n",
        "spec = [\n",
        "    ('value', types.float64[:]),\n",
        "    ('gradient', types.float64[:])\n",
        "]\n",
        "\n",
        "@jitclass(spec)\n",
        "class Parameter:\n",
        "    def __init__(self, n_features):\n",
        "        self.value = np.zeros(n_features)\n",
        "        self.gradient = np.zeros(n_features)\n",
        "\n",
        "    def update(self, learning_rate):\n",
        "        self.value -= learning_rate * self.gradient\n",
        "        self.gradient.fill(0)\n",
        "\n",
        "@numba.jit(nopython=True)\n",
        "def logistic_regression(X, y, learning_rate=0.01, n_iterations=1000):\n",
        "    n_samples, n_features = X.shape\n",
        "    weights = Parameter(n_features)\n",
        "    bias = Parameter(1)\n",
        "\n",
        "    for _ in range(n_iterations):\n",
        "        for i in range(n_samples):\n",
        "            z = 0.0\n",
        "            for j in range(n_features):\n",
        "                z += X[i, j] * weights.value[j]\n",
        "            z += bias.value[0]\n",
        "            y_pred = 1 / (1 + np.exp(-z))\n",
        "\n",
        "            error = y_pred - y[i]\n",
        "            for j in range(n_features):\n",
        "                weights.gradient[j] += error * X[i, j]\n",
        "            bias.gradient[0] += error\n",
        "\n",
        "        weights.update(learning_rate)\n",
        "        bias.update(learning_rate)\n",
        "\n",
        "    return weights.value, bias.value[0]\n",
        "\n",
        "# Generate sample data\n",
        "X, y = make_classification(n_samples=10000, n_features=20, n_informative=2, n_redundant=10, n_classes=2, random_state=42)\n",
        "\n",
        "# Run logistic regression\n",
        "start_time = time()\n",
        "weights, bias = logistic_regression(X, y)\n",
        "end_time = time()\n",
        "\n",
        "print(f\"Logistic regression completed in {end_time - start_time:.4f} seconds\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "X_9pq8etkoZw",
        "outputId": "3073797f-973e-4361-c841-462210e185cf"
      },
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Logistic regression completed in 1.5645 seconds\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## 4. GPU Acceleration with Numba\n",
        "\n",
        "Numba can also leverage CUDA-enabled GPUs for even faster computations. Here's an example of matrix multiplication on GPU:"
      ],
      "metadata": {
        "id": "hZW1k_8Hmka6"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "!nvidia-smi"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "uS4Cb9-XnwU9",
        "outputId": "ac51074c-2882-41d5-f945-212f64b48aa5"
      },
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Wed Oct  9 23:31:36 2024       \n",
            "+---------------------------------------------------------------------------------------+\n",
            "| NVIDIA-SMI 535.104.05             Driver Version: 535.104.05   CUDA Version: 12.2     |\n",
            "|-----------------------------------------+----------------------+----------------------+\n",
            "| GPU  Name                 Persistence-M | Bus-Id        Disp.A | Volatile Uncorr. ECC |\n",
            "| Fan  Temp   Perf          Pwr:Usage/Cap |         Memory-Usage | GPU-Util  Compute M. |\n",
            "|                                         |                      |               MIG M. |\n",
            "|=========================================+======================+======================|\n",
            "|   0  Tesla T4                       Off | 00000000:00:04.0 Off |                    0 |\n",
            "| N/A   44C    P8               9W /  70W |      0MiB / 15360MiB |      0%      Default |\n",
            "|                                         |                      |                  N/A |\n",
            "+-----------------------------------------+----------------------+----------------------+\n",
            "                                                                                         \n",
            "+---------------------------------------------------------------------------------------+\n",
            "| Processes:                                                                            |\n",
            "|  GPU   GI   CI        PID   Type   Process name                            GPU Memory |\n",
            "|        ID   ID                                                             Usage      |\n",
            "|=======================================================================================|\n",
            "|  No running processes found                                                           |\n",
            "+---------------------------------------------------------------------------------------+\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "from numba import cuda\n",
        "\n",
        "@cuda.jit\n",
        "def matrix_mul(A, B, C):\n",
        "    i, j = cuda.grid(2)\n",
        "    if i < C.shape[0] and j < C.shape[1]:\n",
        "        tmp = 0.\n",
        "        for k in range(A.shape[1]):\n",
        "            tmp += A[i, k] * B[k, j]\n",
        "        C[i, j] = tmp\n",
        "\n",
        "# Generate sample matrices\n",
        "A = np.random.rand(1000, 1000)\n",
        "B = np.random.rand(1000, 1000)\n",
        "C = np.zeros((1000, 1000))\n",
        "\n",
        "# Configure the blocks\n",
        "threadsperblock = (16, 16)\n",
        "blockspergrid_x = (A.shape[0] + threadsperblock[0] - 1) // threadsperblock[0]\n",
        "blockspergrid_y = (B.shape[1] + threadsperblock[1] - 1) // threadsperblock[1]\n",
        "blockspergrid = (blockspergrid_x, blockspergrid_y)\n",
        "\n",
        "# Run the kernel\n",
        "start_time = time()\n",
        "d_A = cuda.to_device(A)\n",
        "d_B = cuda.to_device(B)\n",
        "d_C = cuda.to_device(C)\n",
        "matrix_mul[blockspergrid, threadsperblock](d_A, d_B, d_C)\n",
        "cuda.synchronize()\n",
        "C = d_C.copy_to_host()\n",
        "end_time = time()\n",
        "\n",
        "print(f\"GPU matrix multiplication completed in {end_time - start_time:.4f} seconds\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "PbtLv_5Ak_bH",
        "outputId": "8cdc7d9d-3673-433c-ebf7-b014fb8b8045"
      },
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "GPU matrix multiplication completed in 1.8560 seconds\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## 5. Profiling and Optimization"
      ],
      "metadata": {
        "id": "ruo3hOxGmoTR"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import cProfile\n",
        "import numba\n",
        "import numpy as np\n",
        "\n",
        "@numba.jit(nopython=True)\n",
        "def complex_function(x, y):\n",
        "    result = 0\n",
        "    for i in range(x.shape[0]):\n",
        "        for j in range(y.shape[0]):\n",
        "            result += np.sin(x[i]) * np.cos(y[j])\n",
        "    return result\n",
        "\n",
        "x = np.random.rand(1000)\n",
        "y = np.random.rand(1000)\n",
        "\n",
        "cProfile.run('complex_function(x, y)')"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ZNAfIi-4lES3",
        "outputId": "32213207-8538-4ad6-f137-d14ebb5dba1e"
      },
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
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            "         237932 function calls (222960 primitive calls) in 0.848 seconds\n",
            "\n",
            "   Ordered by: standard name\n",
            "\n",
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            "        1    0.000    0.000    0.000    0.000 byteflow.py:379(op_NOP)\n",
            "        4    0.000    0.000    0.000    0.000 byteflow.py:455(op_LOAD_GLOBAL)\n",
            "        3    0.000    0.000    0.000    0.000 byteflow.py:473(op_LOAD_CONST)\n",
            "        4    0.000    0.000    0.000    0.000 byteflow.py:478(op_LOAD_ATTR)\n",
            "        8    0.000    0.000    0.000    0.000 byteflow.py:491(op_LOAD_FAST)\n",
            "       36    0.000    0.000    0.000    0.000 byteflow.py:52(__init__)\n",
            "        4    0.000    0.000    0.000    0.000 byteflow.py:521(op_STORE_FAST)\n",
            "        8    0.000    0.000    0.000    0.000 byteflow.py:76(__init__)\n",
            "        2    0.000    0.000    0.000    0.000 byteflow.py:856(op_JUMP_ABSOLUTE)\n",
            "        1    0.000    0.000    0.000    0.000 byteflow.py:867(op_RETURN_VALUE)\n",
            "        1    0.000    0.000    0.000    0.000 byteflow.py:89(__init__)\n",
            "        1    0.000    0.000    0.003    0.003 byteflow.py:94(run)\n",
            "        1    0.000    0.000    0.000    0.000 caching.py:82(load_overload)\n",
            "        1    0.000    0.000    0.000    0.000 caching.py:85(save_overload)\n",
            "        3    0.000    0.000    0.000    0.000 callconv.py:101(get_return_type)\n",
            "        1    0.000    0.000    0.000    0.000 callconv.py:108(init_call_helper)\n",
            "        2    0.000    0.000    0.008    0.004 callconv.py:122(raise_error)\n",
            "        1    0.000    0.000    0.001    0.001 callconv.py:152(decode_arguments)\n",
            "        7    0.000    0.000    0.001    0.000 callconv.py:161(_get_arg_packer)\n",
            "        1    0.000    0.000    0.000    0.000 callconv.py:370(_make_call_helper)\n",
            "        1    0.000    0.000    0.000    0.000 callconv.py:373(return_value)\n",
            "        2    0.000    0.000    0.000    0.000 callconv.py:380(build_excinfo_struct)\n",
            "        2    0.000    0.000    0.001    0.000 callconv.py:397(set_static_user_exc)\n",
            "        2    0.000    0.000    0.001    0.001 callconv.py:454(return_user_exc)\n",
            "        2    0.000    0.000    0.004    0.002 callconv.py:468(unpack_dynamic_exception)\n",
            "        2    0.000    0.000    0.006    0.003 callconv.py:520(unpack_exception)\n",
            "       16    0.000    0.000    0.000    0.000 callconv.py:60(__init__)\n",
            "        2    0.000    0.000    0.000    0.000 callconv.py:726(_get_try_state)\n",
            "        2    0.000    0.000    0.000    0.000 callconv.py:736(check_try_status)\n",
            "        3    0.000    0.000    0.000    0.000 callconv.py:774(_return_errcode_raw)\n",
            "        2    0.000    0.000    0.001    0.000 callconv.py:777(_get_return_status)\n",
            "        3    0.000    0.000    0.001    0.000 callconv.py:801(get_function_type)\n",
            "        1    0.000    0.000    0.000    0.000 callconv.py:813(decorate_function)\n",
            "        1    0.000    0.000    0.000    0.000 callconv.py:819(<listcomp>)\n",
            "        2    0.000    0.000    0.000    0.000 callconv.py:838(type_may_always_need_nrt)\n",
            "        2    0.000    0.000    0.000    0.000 callconv.py:856(get_arguments)\n",
            "        4    0.000    0.000    0.000    0.000 callconv.py:862(_get_return_argument)\n",
            "        5    0.000    0.000    0.000    0.000 callconv.py:865(_get_excinfo_argument)\n",
            "        2    0.004    0.002    0.008    0.004 callconv.py:868(call_function)\n",
            "        3    0.000    0.000    0.000    0.000 callconv.py:912(__init__)\n",
            "        3    0.000    0.000    0.000    0.000 callconv.py:952(create_error_model)\n",
            "        1    0.000    0.000    0.034    0.034 callwrapper.py:101(build)\n",
            "        1    0.000    0.000    0.000    0.000 callwrapper.py:11(__init__)\n",
            "        1    0.000    0.000    0.030    0.030 callwrapper.py:126(build_wrapper)\n",
            "        1    0.000    0.000    0.000    0.000 callwrapper.py:129(<listcomp>)\n",
            "        1    0.000    0.000    0.004    0.004 callwrapper.py:197(get_env)\n",
            "        2    0.000    0.000    0.014    0.007 callwrapper.py:20(add_arg)\n",
            "        1    0.000    0.000    0.000    0.000 callwrapper.py:212(_simplified_return_type)\n",
            "        2    0.000    0.000    0.000    0.000 callwrapper.py:224(debug_print)\n",
            "        4    0.000    0.000    0.004    0.001 callwrapper.py:38(cleanup_arg)\n",
            "        1    0.000    0.000    0.002    0.002 callwrapper.py:66(emit_cleanup)\n",
            "        1    0.000    0.000    0.000    0.000 callwrapper.py:92(__init__)\n",
            "       32    0.000    0.000    0.000    0.000 cffi_utils.py:29(is_ffi_instance)\n",
            "       32    0.000    0.000    0.010    0.000 cffi_utils.py:39(is_cffi_func)\n",
            "        8    0.000    0.000    0.000    0.000 cgutils.py:1184(normalize_ir_text)\n",
            "        2    0.000    0.000    0.000    0.000 cgutils.py:1216(is_nonelike)\n",
            "       20    0.000    0.000    0.042    0.002 cgutils.py:124(_make_refs)\n",
            "       56    0.000    0.000    0.003    0.000 cgutils.py:142(_get_ptr_by_index)\n",
            "        6    0.000    0.000    0.000    0.000 cgutils.py:145(_get_ptr_by_name)\n",
            "       32    0.000    0.000    0.011    0.000 cgutils.py:149(__getattr__)\n",
            "      138    0.000    0.000    0.002    0.000 cgutils.py:158(__setattr__)\n",
            "       32    0.000    0.000    0.011    0.000 cgutils.py:166(__getitem__)\n",
            "       18    0.000    0.000    0.002    0.000 cgutils.py:173(__setitem__)\n",
            "        2    0.000    0.000    0.000    0.000 cgutils.py:202(_getpointer)\n",
            "        6    0.000    0.000    0.000    0.000 cgutils.py:208(_getvalue)\n",
            "       20    0.000    0.000    0.000    0.000 cgutils.py:228(_get_be_type)\n",
            "       32    0.000    0.000    0.000    0.000 cgutils.py:231(_cast_member_to_value)\n",
            "       18    0.000    0.000    0.000    0.000 cgutils.py:234(_cast_member_from_value)\n",
            "        1    0.000    0.000    0.000    0.000 cgutils.py:261(__init__)\n",
            "        7    0.000    0.000    0.000    0.000 cgutils.py:308(__setattr__)\n",
            "       43    0.000    0.000    0.044    0.001 cgutils.py:362(alloca_once)\n",
            "       40    0.003    0.000    0.017    0.000 cgutils.py:417(get_or_insert_function)\n",
            "       19    0.000    0.000    0.005    0.000 cgutils.py:435(add_global_variable)\n",
            "       11    0.000    0.000    0.000    0.000 cgutils.py:44(make_bytearray)\n",
            "        2    0.000    0.000    0.000    0.000 cgutils.py:440(terminate)\n",
            "       14    0.000    0.000    0.000    0.000 cgutils.py:446(get_null_value)\n",
            "        3    0.000    0.000    0.000    0.000 cgutils.py:450(is_null)\n",
            "        4    0.000    0.000    0.000    0.000 cgutils.py:455(is_not_null)\n",
            "        8    0.000    0.000    0.000    0.000 cgutils.py:460(if_unlikely)\n",
            "        2    0.000    0.000    0.000    0.000 cgutils.py:464(if_likely)\n",
            "        2    0.000    0.000    0.000    0.000 cgutils.py:472(increment_index)\n",
            "        4    0.000    0.000    0.023    0.006 cgutils.py:486(for_range)\n",
            "       12    0.000    0.000    0.000    0.000 cgutils.py:56(create_struct_proxy)\n",
            "        4    0.000    0.000    0.023    0.006 cgutils.py:618(loop_nest)\n",
            "        4    0.000    0.000    0.000    0.000 cgutils.py:640(<lambda>)\n",
            "        4    0.000    0.000    0.023    0.006 cgutils.py:646(_loop_nest)\n",
            "        6    0.000    0.000    0.000    0.000 cgutils.py:656(pack_array)\n",
            "        8    0.000    0.000    0.000    0.000 cgutils.py:682(unpack_tuple)\n",
            "        8    0.000    0.000    0.000    0.000 cgutils.py:689(<listcomp>)\n",
            "        2    0.000    0.000    0.001    0.001 cgutils.py:694(get_item_pointer)\n",
            "        2    0.000    0.000    0.000    0.000 cgutils.py:736(get_item_pointer2)\n",
            "       21    0.000    0.000    0.000    0.000 cgutils.py:912(is_pointer)\n",
            "       62    0.000    0.000    0.014    0.000 cgutils.py:929(gep_inbounds)\n",
            "       62    0.000    0.000    0.014    0.000 cgutils.py:936(gep)\n",
            "        1    0.000    0.000    0.000    0.000 cgutils.py:955(pointer_add)\n",
            "       20    0.000    0.000    0.056    0.003 cgutils.py:99(__init__)\n",
            "       11    0.000    0.000    0.002    0.000 cgutils.py:993(global_constant)\n",
            "        1    0.000    0.000    0.000    0.000 cloudpickle.py:1042(_class_reduce)\n",
            "        1    0.000    0.000    0.000    0.000 cloudpickle.py:1260(dump)\n",
            "        1    0.000    0.000    0.000    0.000 cloudpickle.py:1270(__init__)\n",
            "        1    0.000    0.000    0.000    0.000 cloudpickle.py:1307(reducer_override)\n",
            "        1    0.000    0.000    0.000    0.000 cloudpickle.py:195(_is_registered_pickle_by_value)\n",
            "        1    0.000    0.000    0.000    0.000 cloudpickle.py:209(_whichmodule)\n",
            "        1    0.000    0.000    0.000    0.000 cloudpickle.py:242(_should_pickle_by_reference)\n",
            "        1    0.000    0.000    0.000    0.000 cloudpickle.py:278(_lookup_module_and_qualname)\n",
            "        1    0.000    0.000    0.001    0.001 codegen.py:1013(scan_unresolved_symbols)\n",
            "        1    0.000    0.000    0.001    0.001 codegen.py:1032(scan_defined_symbols)\n",
            "        1    0.000    0.000    0.000    0.000 codegen.py:1040(resolve)\n",
            "        1    0.000    0.000    0.000    0.000 codegen.py:1045(<listcomp>)\n",
            "        3    0.000    0.000    0.024    0.008 codegen.py:1058(wrapper)\n",
            "        1    0.000    0.000    0.000    0.000 codegen.py:1082(is_symbol_defined)\n",
            "        1    0.000    0.000    0.007    0.007 codegen.py:1087(_load_defined_symbols)\n",
            "        2    0.000    0.000    0.007    0.003 codegen.py:1091(<setcomp>)\n",
            "        1    0.000    0.000    0.007    0.007 codegen.py:1094(add_module)\n",
            "        5    0.000    0.000    0.000    0.000 codegen.py:1143(target_data)\n",
            "        1    0.000    0.000    0.015    0.015 codegen.py:1150(create_library)\n",
            "        4    0.000    0.000    0.015    0.004 codegen.py:1220(_create_empty_module)\n",
            "        3    0.000    0.000    0.012    0.004 codegen.py:1248(_function_pass_manager)\n",
            "        3    0.000    0.000    0.001    0.000 codegen.py:1258(_pass_manager_builder)\n",
            "        1    0.000    0.000    0.000    0.000 codegen.py:1278(_check_llvm_bugs)\n",
            "        1    0.000    0.000    0.002    0.002 codegen.py:1315(_scan_and_fix_unresolved_refs)\n",
            "        1    0.000    0.000    0.007    0.007 codegen.py:1412(_add_module)\n",
            "        1    0.000    0.000    0.000    0.000 codegen.py:1420(set_env)\n",
            "        3    0.000    0.000    0.000    0.000 codegen.py:32(_parse_refprune_flags)\n",
            "        1    0.000    0.000    0.000    0.000 codegen.py:529(__init__)\n",
            "        1    0.000    0.000    0.000    0.000 codegen.py:542(recorded_timings)\n",
            "        1    0.000    0.000    0.000    0.000 codegen.py:546(codegen)\n",
            "        2    0.000    0.000    0.000    0.000 codegen.py:553(name)\n",
            "        5    0.000    0.000    0.000    0.000 codegen.py:560(_raise_if_finalized)\n",
            "      3/2    0.000    0.000    0.155    0.078 codegen.py:565(_ensure_finalized)\n",
            "        1    0.000    0.000    0.000    0.000 codegen.py:569(create_ir_module)\n",
            "        1    0.000    0.000    0.000    0.000 codegen.py:620(enable_object_caching)\n",
            "        1    0.000    0.000    0.015    0.015 codegen.py:643(__init__)\n",
            "        3    0.000    0.000    0.051    0.017 codegen.py:651(_optimize_functions)\n",
            "        1    0.000    0.000    0.114    0.114 codegen.py:667(_optimize_final_module)\n",
            "        1    0.000    0.000    0.000    0.000 codegen.py:684(_get_module_for_linking)\n",
            "        1    0.000    0.000    0.000    0.000 codegen.py:719(add_linking_library)\n",
            "        3    0.000    0.000    0.148    0.049 codegen.py:723(add_ir_module)\n",
            "        3    0.000    0.000    0.052    0.017 codegen.py:732(add_llvm_module)\n",
            "        1    0.000    0.000    0.155    0.155 codegen.py:739(finalize)\n",
            "        1    0.000    0.000    0.004    0.004 codegen.py:767(_finalize_dynamic_globals)\n",
            "        1    0.000    0.000    0.003    0.003 codegen.py:773(_verify_declare_only_symbols)\n",
            "        1    0.000    0.000    0.040    0.040 codegen.py:781(_finalize_final_module)\n",
            "        1    0.000    0.000    0.000    0.000 codegen.py:880(_object_compiled_hook)\n",
            "        1    0.000    0.000    0.000    0.000 codegen.py:893(_object_getbuffer_hook)\n",
            "        1    0.000    0.000    0.156    0.156 codegen.py:975(get_pointer_to_function)\n",
            "        1    0.000    0.000    0.026    0.026 codegen.py:996(_finalize_specific)\n",
            "       20    0.000    0.000    0.000    0.000 collections.py:43(generic)\n",
            "        8    0.000    0.000    0.000    0.000 common.py:21(iterator_type)\n",
            "      159    0.000    0.000    0.000    0.000 common.py:27(_is_shutting_down)\n",
            "        8    0.000    0.000    0.000    0.000 common.py:32(yield_type)\n",
            "       22    0.000    0.000    0.000    0.000 common.py:4(_encode_string)\n",
            "        3    0.000    0.000    0.000    0.000 common.py:49(__init__)\n",
            "        6    0.000    0.000    0.000    0.000 common.py:76(as_array)\n",
            "       75    0.010    0.000    0.010    0.000 common.py:9(_decode_string)\n",
            "        1    0.000    0.000    0.000    0.000 compiler.py:278(sanitize_compile_result_entries)\n",
            "        1    0.000    0.000    0.000    0.000 compiler.py:294(compile_result)\n",
            "        1    0.000    0.000    0.000    0.000 compiler.py:328(__init__)\n",
            "      542    0.000    0.000    0.000    0.000 compiler.py:354(__getattr__)\n",
            "       33    0.000    0.000    0.000    0.000 compiler.py:360(__setattr__)\n",
            "        1    0.000    0.000    0.000    0.000 compiler.py:364(_make_subtarget)\n",
            "        1    0.000    0.000    0.003    0.003 compiler.py:390(__init__)\n",
            "        1    0.000    0.000    0.810    0.810 compiler.py:432(compile_extra)\n",
            "        1    0.000    0.000    0.809    0.809 compiler.py:455(_compile_core)\n",
            "        1    0.000    0.000    0.809    0.809 compiler.py:501(_compile_bytecode)\n",
            "        1    0.000    0.000    0.001    0.001 compiler.py:520(define_pipelines)\n",
            "        1    0.000    0.000    0.001    0.001 compiler.py:540(define_nopython_pipeline)\n",
            "        1    0.000    0.000    0.000    0.000 compiler.py:559(define_nopython_lowering_pipeline)\n",
            "        1    0.000    0.000    0.000    0.000 compiler.py:599(define_typed_pipeline)\n",
            "        1    0.000    0.000    0.000    0.000 compiler.py:635(define_untyped_pipeline)\n",
            "        1    0.000    0.000    0.813    0.813 compiler.py:718(compile_extra)\n",
            "       34    0.000    0.000    0.001    0.000 compiler_lock.py:11(acquire)\n",
            "       34    0.000    0.000    0.001    0.000 compiler_lock.py:15(release)\n",
            "       34    0.001    0.000    0.001    0.000 compiler_lock.py:19(__enter__)\n",
            "       34    0.000    0.000    0.001    0.000 compiler_lock.py:22(__exit__)\n",
            "        1    0.000    0.000    0.000    0.000 compiler_lock.py:25(is_locked)\n",
            "    33/27    0.000    0.000    0.807    0.030 compiler_lock.py:32(_acquire_compile_lock)\n",
            "        1    0.000    0.000    0.000    0.000 compiler_lock.py:52(require_global_compiler_lock)\n",
            "        2    0.000    0.000    0.000    0.000 compiler_machinery.py:103(get_analysis)\n",
            "       52    0.000    0.000    0.000    0.000 compiler_machinery.py:139(__init__)\n",
            "       50    0.000    0.000    0.000    0.000 compiler_machinery.py:143(get_required_set)\n",
            "        8    0.000    0.000    0.000    0.000 compiler_machinery.py:149(add_required)\n",
            "        4    0.000    0.000    0.000    0.000 compiler_machinery.py:177(__init__)\n",
            "       26    0.000    0.000    0.000    0.000 compiler_machinery.py:188(_validate_pass)\n",
            "       26    0.000    0.000    0.000    0.000 compiler_machinery.py:201(add_pass)\n",
            "        4    0.000    0.000    0.000    0.000 compiler_machinery.py:227(_debug_init)\n",
            "       12    0.000    0.000    0.000    0.000 compiler_machinery.py:229(parse)\n",
            "       78    0.000    0.000    0.000    0.000 compiler_machinery.py:24(__enter__)\n",
            "        4    0.000    0.000    0.001    0.000 compiler_machinery.py:246(finalize)\n",
            "        1    0.000    0.000    0.000    0.000 compiler_machinery.py:256(finalized)\n",
            "       26    0.002    0.000    0.806    0.031 compiler_machinery.py:268(_runPass)\n",
            "       78    0.000    0.000    0.777    0.010 compiler_machinery.py:272(check)\n",
            "       78    0.000    0.000    0.000    0.000 compiler_machinery.py:28(__exit__)\n",
            "       52    0.000    0.000    0.000    0.000 compiler_machinery.py:280(debug_print)\n",
            "        1    0.000    0.000    0.808    0.808 compiler_machinery.py:342(run)\n",
            "        1    0.000    0.000    0.000    0.000 compiler_machinery.py:36(__init__)\n",
            "        4    0.000    0.000    0.000    0.000 compiler_machinery.py:370(dependency_analysis)\n",
            "       50    0.000    0.000    0.000    0.000 compiler_machinery.py:385(resolve_requires)\n",
            "        6    0.000    0.000    0.000    0.000 compiler_machinery.py:386(walk)\n",
            "      104    0.000    0.000    0.000    0.000 compiler_machinery.py:41(name)\n",
            "      104    0.000    0.000    0.000    0.000 compiler_machinery.py:429(is_registered)\n",
            "       78    0.000    0.000    0.000    0.000 compiler_machinery.py:432(get)\n",
            "       26    0.000    0.000    0.000    0.000 compiler_machinery.py:69(analysis)\n",
            "       26    0.000    0.000    0.000    0.000 compiler_machinery.py:76(run_initialization)\n",
            "       26    0.000    0.000    0.000    0.000 compiler_machinery.py:91(run_finalizer)\n",
            "       44    0.000    0.000    0.000    0.000 compiler_machinery.py:98(get_analysis_usage)\n",
            "        1    0.000    0.000    0.001    0.001 config.py:151(update)\n",
            "        1    0.000    0.000    0.000    0.000 config.py:184(validate)\n",
            "        1    0.000    0.000    0.001    0.001 config.py:604(reload_config)\n",
            "        2    0.000    0.000    0.000    0.000 consts.py:111(_infer_getattr)\n",
            "        1    0.000    0.000    0.000    0.000 consts.py:18(__init__)\n",
            "     10/8    0.000    0.000    0.001    0.000 consts.py:24(infer_constant)\n",
            "        2    0.000    0.000    0.000    0.000 consts.py:47(_fail)\n",
            "     10/8    0.000    0.000    0.001    0.000 consts.py:56(_do_infer)\n",
            "        4    0.000    0.000    0.000    0.000 consts.py:73(_infer_expr)\n",
            "        2    0.000    0.000    0.000    0.000 containers.py:220(__len__)\n",
            "        8    0.000    0.000    0.000    0.000 containers.py:223(types)\n",
            "       20    0.000    0.000    0.000    0.000 containers.py:233(__init__)\n",
            "      150    0.000    0.000    0.000    0.000 containers.py:243(key)\n",
            "        8    0.000    0.000    0.000    0.000 containers.py:256(__unliteral__)\n",
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            "      100    0.000    0.000    0.000    0.000 containers.py:40(key)\n",
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            "       50    0.000    0.000    0.000    0.000 ir.py:31(__init__)\n",
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            "     1138    0.001    0.000    0.033    0.000 ir.py:351(list_vars)\n",
            "       27    0.000    0.000    0.000    0.000 ir.py:377(__init__)\n",
            "      306    0.000    0.000    0.000    0.000 ir.py:384(__getattr__)\n",
            "       81    0.000    0.000    0.000    0.000 ir.py:389(__setattr__)\n",
            "        1    0.000    0.000    0.000    0.000 ir.py:395(binop)\n",
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            "        2    0.000    0.000    0.000    0.000 ir.py:464(pair_second)\n",
            "        2    0.000    0.000    0.000    0.000 ir.py:471(getiter)\n",
            "        2    0.000    0.000    0.000    0.000 ir.py:478(iternext)\n",
            "        4    0.000    0.000    0.000    0.000 ir.py:493(getattr)\n",
            "        4    0.000    0.000    0.000    0.000 ir.py:501(getitem)\n",
            "        2    0.000    0.000    0.000    0.000 ir.py:518(static_getitem)\n",
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            "        2    0.000    0.000    0.000    0.000 ir.py:538(phi)\n",
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            "       24    0.000    0.000    0.000    0.000 ir.py:591(<genexpr>)\n",
            "       84    0.000    0.000    0.000    0.000 ir.py:593(<genexpr>)\n",
            "      122    0.000    0.000    0.000    0.000 ir.py:605(<genexpr>)\n",
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            "        4    0.000    0.000    0.001    0.000 ir.py:611(infer_constant)\n",
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            "      131    0.000    0.000    0.000    0.000 ir.py:716(__init__)\n",
            "       45    0.000    0.000    0.000    0.000 ir.py:722(__str__)\n",
            "        1    0.000    0.000    0.000    0.000 ir.py:864(__init__)\n",
            "        2    0.000    0.000    0.000    0.000 ir.py:870(__str__)\n",
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            "        4    0.000    0.000    0.000    0.000 ir.py:882(__init__)\n",
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            "        2    0.000    0.000    0.000    0.000 ir_utils.py:551(remove_dels)\n",
            "        4    0.000    0.000    0.000    0.000 itanium_mangler.py:103(mangle_abi_tag)\n",
            "       20    0.000    0.000    0.001    0.000 itanium_mangler.py:107(mangle_identifier)\n",
            "       20    0.000    0.000    0.000    0.000 itanium_mangler.py:118(<listcomp>)\n",
            "     24/4    0.000    0.000    0.000    0.000 itanium_mangler.py:127(mangle_type_or_value)\n",
            "        4    0.000    0.000    0.000    0.000 itanium_mangler.py:154(mangle_templated_ident)\n",
            "        2    0.000    0.000    0.000    0.000 itanium_mangler.py:163(mangle_args)\n",
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            "        2    0.000    0.000    0.001    0.000 itanium_mangler.py:170(mangle)\n",
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            "        4    0.000    0.000    0.000    0.000 itanium_mangler.py:75(<genexpr>)\n",
            "       28    0.000    0.000    0.000    0.000 itanium_mangler.py:84(_fix_lead_digit)\n",
            "       28    0.000    0.000    0.000    0.000 itanium_mangler.py:94(_len_encoded)\n",
            "        4    0.000    0.000    0.000    0.000 linecache.py:36(getlines)\n",
            "        4    0.000    0.000    0.002    0.000 linker.py:5(link_modules)\n",
            "        8    0.000    0.000    0.000    0.000 listdecl.py:102(generic)\n",
            "       10    0.000    0.000    0.000    0.000 listdecl.py:114(generic)\n",
            "        2    0.000    0.000    0.000    0.000 listdecl.py:90(generic)\n",
            "        3    0.000    0.000    0.000    0.000 llvm_bindings.py:16(_inlining_threshold)\n",
            "        3    0.000    0.000    0.001    0.000 llvm_bindings.py:36(create_pass_manager_builder)\n",
            "        1    0.000    0.000    0.000    0.000 llvm_pass_timings.py:288(__init__)\n",
            "       76    0.000    0.000    0.000    0.000 llvm_pass_timings.py:292(record)\n",
            "        4    0.000    0.000    0.027    0.007 lowering.py:1142(_lower_call_normal)\n",
            "        1    0.000    0.000    0.000    0.000 lowering.py:115(pre_lower)\n",
            "       23    0.000    0.000    0.121    0.005 lowering.py:1170(lower_expr)\n",
            "        1    0.000    0.000    0.000    0.000 lowering.py:137(post_lower)\n",
            "       88    0.000    0.000    0.006    0.000 lowering.py:1412(_alloca_var)\n",
            "       45    0.000    0.000    0.001    0.000 lowering.py:1428(getvar)\n",
            "        7    0.000    0.000    0.000    0.000 lowering.py:143(pre_block)\n",
            "       50    0.000    0.000    0.001    0.000 lowering.py:1442(loadvar)\n",
            "       43    0.000    0.000    0.009    0.000 lowering.py:1460(storevar)\n",
            "       45    0.000    0.000    0.025    0.001 lowering.py:1506(delvar)\n",
            "        9    0.000    0.000    0.006    0.001 lowering.py:1531(alloca)\n",
            "        9    0.000    0.000    0.005    0.001 lowering.py:1536(alloca_lltype)\n",
            "       25    0.000    0.000    0.032    0.001 lowering.py:1556(incref)\n",
            "       54    0.000    0.000    0.024    0.000 lowering.py:1562(decref)\n",
            "       10    0.000    0.000    0.000    0.000 lowering.py:1573(_lit_or_omitted)\n",
            "        1    0.000    0.000    0.000    0.000 lowering.py:175(emit_environment_object)\n",
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            "        1    0.000    0.000    0.001    0.001 lowering.py:212(extract_function_arguments)\n",
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            "        1    0.000    0.000    0.221    0.221 lowering.py:235(lower_function_body)\n",
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            "        1    0.000    0.000    0.003    0.003 lowering.py:29(__init__)\n",
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            "      179    0.000    0.000    0.000    0.000 lowering.py:307(typeof)\n",
            "      115    0.000    0.000    0.000    0.000 lowering.py:310(debug_print)\n",
            "        1    0.000    0.000    0.002    0.002 lowering.py:342(init)\n",
            "      215    0.000    0.000    0.001    0.000 lowering.py:347(_disable_sroa_like_opt)\n",
            "        1    0.000    0.000    0.002    0.002 lowering.py:358(_find_singly_assigned_variable)\n",
            "       32    0.000    0.000    0.000    0.000 lowering.py:389(<listcomp>)\n",
            "        7    0.000    0.000    0.000    0.000 lowering.py:397(pre_block)\n",
            "        7    0.000    0.000    0.000    0.000 lowering.py:435(post_block)\n",
            "       95    0.001    0.000    0.208    0.002 lowering.py:442(lower_inst)\n",
            "       43    0.007    0.000    0.172    0.004 lowering.py:650(lower_assign)\n",
            "        2    0.000    0.000    0.013    0.007 lowering.py:726(lower_binop)\n",
            "        2    0.000    0.000    0.000    0.000 lowering.py:746(cast_result)\n",
            "        3    0.000    0.000    0.000    0.000 lowering.py:75(call_conv)\n",
            "        6    0.000    0.000    0.000    0.000 lowering.py:751(try_static_impl)\n",
            "       14    0.000    0.000    0.000    0.000 lowering.py:752(<genexpr>)\n",
            "        1    0.000    0.000    0.000    0.000 lowering.py:79(init)\n",
            "        2    0.000    0.000    0.018    0.009 lowering.py:796(lower_getitem)\n",
            "        2    0.000    0.000    0.000    0.000 lowering.py:810(<listcomp>)\n",
            "        4    0.000    0.000    0.000    0.000 lowering.py:818(_cast_var)\n",
            "        4    0.000    0.000    0.000    0.000 lowering.py:832(fold_call_args)\n",
            "        4    0.000    0.000    0.000    0.000 lowering.py:847(<listcomp>)\n",
            "        4    0.000    0.000    0.027    0.007 lowering.py:900(lower_call)\n",
            "        1    0.000    0.000    0.000    0.000 lowering.py:96(_compute_def_location)\n",
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            "        2    0.000    0.000    0.000    0.000 mathimpl.py:103(<listcomp>)\n",
            "        2    0.000    0.000    0.000    0.000 mathimpl.py:131(float_impl)\n",
            "        2    0.000    0.000    0.000    0.000 mathimpl.py:98(call_fp_intrinsic)\n",
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            "       17    0.000    0.000    0.001    0.000 misc.py:72(literal)\n",
            "        7    0.000    0.000    0.000    0.000 misc.py:87(maybe_literal)\n",
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            "       15    0.000    0.000    0.001    0.000 models.py:135(contains_nrt_meminfo)\n",
            "       42    0.000    0.000    0.000    0.000 models.py:139(<genexpr>)\n",
            "        2    0.000    0.000    0.000    0.000 models.py:229(__init__)\n",
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            "        1    0.000    0.000    0.000    0.000 models.py:242(as_return)\n",
            "        2    0.000    0.000    0.000    0.000 models.py:245(from_data)\n",
            "       14    0.000    0.000    0.000    0.000 models.py:248(from_argument)\n",
            "        4    0.000    0.000    0.000    0.000 models.py:251(from_return)\n",
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            "        2    0.000    0.000    0.000    0.000 models.py:34(__init__)\n",
            "        2    0.000    0.000    0.000    0.000 models.py:344(inner_models)\n",
            "       10    0.000    0.000    0.000    0.000 models.py:347(has_nrt_meminfo)\n",
            "        8    0.000    0.000    0.000    0.000 models.py:350(get_nrt_meminfo)\n",
            "        4    0.000    0.000    0.000    0.000 models.py:448(get_value_type)\n",
            "        4    0.000    0.000    0.000    0.000 models.py:45(get_data_type)\n",
            "       28    0.000    0.000    0.000    0.000 models.py:457(get_argument_type)\n",
            "        8    0.000    0.000    0.000    0.000 models.py:460(as_argument)\n",
            "        4    0.000    0.000    0.000    0.000 models.py:468(from_argument)\n",
            "      103    0.000    0.000    0.000    0.000 models.py:48(get_argument_type)\n",
            "       18    0.000    0.000    0.000    0.000 models.py:497(traverse)\n",
            "       18    0.000    0.000    0.002    0.000 models.py:498(getter)\n",
            "       18    0.000    0.000    0.000    0.000 models.py:500(<listcomp>)\n",
            "        2    0.000    0.000    0.000    0.000 models.py:503(inner_models)\n",
            "        3    0.000    0.000    0.000    0.000 models.py:53(get_return_type)\n",
            "      132    0.000    0.000    0.000    0.000 models.py:533(get_value_type)\n",
            "       14    0.000    0.000    0.000    0.000 models.py:545(get_argument_type)\n",
            "       14    0.000    0.000    0.000    0.000 models.py:546(<listcomp>)\n",
            "        4    0.000    0.000    0.001    0.000 models.py:551(_as)\n",
            "        2    0.000    0.000    0.001    0.000 models.py:558(_from)\n",
            "        4    0.000    0.000    0.001    0.000 models.py:612(as_argument)\n",
            "        2    0.000    0.000    0.001    0.000 models.py:615(from_argument)\n",
            "      130    0.000    0.000    0.013    0.000 models.py:630(get)\n",
            "       14    0.000    0.000    0.000    0.000 models.py:651(set)\n",
            "      260    0.000    0.000    0.000    0.000 models.py:674(get_field_position)\n",
            "      102    0.000    0.000    0.000    0.000 models.py:685(get_type)\n",
            "       22    0.000    0.000    0.000    0.000 models.py:709(traverse)\n",
            "      102    0.000    0.000    0.013    0.000 models.py:710(getter)\n",
            "       22    0.000    0.000    0.000    0.000 models.py:716(<listcomp>)\n",
            "        8    0.000    0.000    0.000    0.000 models.py:718(inner_models)\n",
            "        2    0.000    0.000    0.000    0.000 models.py:82(load_from_data_pointer)\n",
            "      169    0.000    0.000    0.000    0.000 models.py:89(traverse)\n",
            "       15    0.000    0.000    0.000    0.000 models.py:97(traverse_models)\n",
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            "        3    0.000    0.000    0.000    0.000 module.py:145(data_layout)\n",
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            "        2    0.000    0.000    0.000    0.000 module.py:151(declare_intrinsic)\n",
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            "       11    0.000    0.000    0.000    0.000 module.py:52(__init__)\n",
            "        1    0.000    0.000    0.000    0.000 module.py:56(__str__)\n",
            "        9    0.000    0.000    0.000    0.000 module.py:7(__init__)\n",
            "        6    0.000    0.000    0.000    0.000 module.py:76(_dispose)\n",
            "        5    0.000    0.000    0.000    0.000 module.py:89(get_global_variable)\n",
            "      190    0.000    0.000    0.000    0.000 multiarray.py:503(can_cast)\n",
            "       20    0.000    0.000    0.000    0.000 npydecl.py:109(<listcomp>)\n",
            "       20    0.000    0.000    0.000    0.000 npydecl.py:112(<genexpr>)\n",
            "       12    0.000    0.000    0.000    0.000 npydecl.py:185(ufunc)\n",
            "       12    0.000    0.000    0.003    0.000 npydecl.py:196(generic)\n",
            "       36    0.000    0.000    0.000    0.000 npydecl.py:214(<genexpr>)\n",
            "        8    0.000    0.000    0.000    0.000 npydecl.py:238(generic)\n",
            "       20    0.000    0.000    0.000    0.000 npydecl.py:25(_handle_inputs)\n",
            "       20    0.000    0.000    0.000    0.000 npydecl.py:51(<listcomp>)\n",
            "       20    0.000    0.000    0.000    0.000 npydecl.py:53(<listcomp>)\n",
            "       20    0.000    0.000    0.000    0.000 npydecl.py:60(<genexpr>)\n",
            "       20    0.000    0.000    0.000    0.000 npydecl.py:65(<genexpr>)\n",
            "       20    0.000    0.000    0.000    0.000 npydecl.py:70(<listcomp>)\n",
            "        8    0.000    0.000    0.000    0.000 npydecl.py:88(ufunc)\n",
            "       20    0.000    0.000    0.004    0.000 npydecl.py:92(generic)\n",
            "       20    0.000    0.000    0.000    0.000 npydecl.py:94(<listcomp>)\n",
            "        2    0.000    0.000    0.000    0.000 npyfuncs.py:28(_check_arity_and_homogeneity)\n",
            "        4    0.000    0.000    0.000    0.000 npyfuncs.py:41(<genexpr>)\n",
            "        1    0.000    0.000    0.000    0.000 npyfuncs.py:905(np_real_sin_impl)\n",
            "        1    0.000    0.000    0.000    0.000 npyfuncs.py:918(np_real_cos_impl)\n",
            "        4    0.000    0.000    0.001    0.000 npyimpl.py:303(_prepare_argument)\n",
            "        4    0.000    0.000    0.000    0.000 npyimpl.py:457(_unpack_output_types)\n",
            "        2    0.000    0.000    0.000    0.000 npyimpl.py:46(update_indices)\n",
            "        2    0.000    0.000    0.000    0.000 npyimpl.py:464(_unpack_output_values)\n",
            "        2    0.000    0.000    0.000    0.000 npyimpl.py:471(_pack_output_values)\n",
            "        2    0.000    0.000    0.025    0.012 npyimpl.py:478(numpy_ufunc_kernel)\n",
            "        2    0.000    0.000    0.000    0.000 npyimpl.py:49(as_values)\n",
            "        2    0.000    0.000    0.000    0.000 npyimpl.py:490(<listcomp>)\n",
            "        2    0.000    0.000    0.000    0.000 npyimpl.py:517(<listcomp>)\n",
            "        2    0.000    0.000    0.000    0.000 npyimpl.py:518(<listcomp>)\n",
            "        2    0.000    0.000    0.000    0.000 npyimpl.py:523(<listcomp>)\n",
            "        2    0.000    0.000    0.000    0.000 npyimpl.py:530(<listcomp>)\n",
            "        2    0.000    0.000    0.000    0.000 npyimpl.py:532(<listcomp>)\n",
            "        2    0.000    0.000    0.000    0.000 npyimpl.py:533(<listcomp>)\n",
            "        2    0.000    0.000    0.000    0.000 npyimpl.py:554(<listcomp>)\n",
            "        2    0.000    0.000    0.000    0.000 npyimpl.py:636(__init__)\n",
            "        4    0.000    0.000    0.000    0.000 npyimpl.py:641(cast)\n",
            "        4    0.000    0.000    0.001    0.000 npyimpl.py:69(__init__)\n",
            "        2    0.000    0.000    0.000    0.000 npyimpl.py:708(__init__)\n",
            "        2    0.000    0.000    0.001    0.000 npyimpl.py:719(generate)\n",
            "        2    0.000    0.000    0.000    0.000 npyimpl.py:723(<listcomp>)\n",
            "        2    0.000    0.000    0.025    0.012 npyimpl.py:739(do_ufunc)\n",
            "        2    0.000    0.000    0.000    0.000 npyimpl.py:80(create_iter_indices)\n",
            "        2    0.000    0.000    0.000    0.000 npyimpl.py:83(load_data)\n",
            "        2    0.000    0.000    0.000    0.000 npyimpl.py:86(store_data)\n",
            "        2    0.000    0.000    0.000    0.000 npyimpl.py:89(return_val)\n",
            "        3    0.000    0.000    0.000    0.000 npytypes.py:444(__init__)\n",
            "        4    0.000    0.000    0.000    0.000 npytypes.py:463(mangling_args)\n",
            "      241    0.000    0.000    0.000    0.000 npytypes.py:482(key)\n",
            "       20    0.000    0.000    0.000    0.000 npytypes.py:514(is_precise)\n",
            "       72    0.002    0.000    0.002    0.000 npytypes.py:523(__repr__)\n",
            "        7    0.000    0.000    0.000    0.000 nrt.py:19(initialize)\n",
            "        1    0.000    0.000    0.000    0.000 nrt.py:48(_init_guard)\n",
            "        1    0.000    0.000    0.000    0.000 nrt.py:61(library)\n",
            "        1    0.000    0.000    0.012    0.012 numbers.py:1256(literal_int_to_number)\n",
            "        1    0.000    0.000    0.000    0.000 numbers.py:1295(integer_to_float)\n",
            "       20    0.000    0.000    0.000    0.000 numbers.py:1363(constant_integer)\n",
            "        1    0.000    0.000    0.000    0.000 numbers.py:614(real_add_impl)\n",
            "        1    0.000    0.000    0.000    0.000 numbers.py:624(real_mul_impl)\n",
            "       68    0.000    0.000    0.001    0.000 numpy_support.py:125(as_dtype)\n",
            "        3    0.000    0.000    0.000    0.000 numpy_support.py:222(map_layout)\n",
            "       20    0.000    0.000    0.000    0.000 numpy_support.py:276(supported_ufunc_loop)\n",
            "       20    0.000    0.000    0.000    0.000 numpy_support.py:327(numpy_outputs)\n",
            "       20    0.000    0.000    0.000    0.000 numpy_support.py:329(<listcomp>)\n",
            "       24    0.000    0.000    0.000    0.000 numpy_support.py:332(_ufunc_loop_sig)\n",
            "      190    0.001    0.000    0.001    0.000 numpy_support.py:339(ufunc_can_cast)\n",
            "       22    0.001    0.000    0.003    0.000 numpy_support.py:357(ufunc_find_matching_loop)\n",
            "       22    0.000    0.000    0.000    0.000 numpy_support.py:374(<listcomp>)\n",
            "       22    0.000    0.000    0.000    0.000 numpy_support.py:378(<listcomp>)\n",
            "       56    0.000    0.000    0.000    0.000 numpy_support.py:384(<genexpr>)\n",
            "       44    0.000    0.000    0.000    0.000 numpy_support.py:387(choose_types)\n",
            "       44    0.000    0.000    0.000    0.000 numpy_support.py:394(<listcomp>)\n",
            "       44    0.000    0.000    0.000    0.000 numpy_support.py:397(<listcomp>)\n",
            "       64    0.000    0.000    0.000    0.000 numpy_support.py:86(from_dtype)\n",
            "        1    0.000    0.000    0.000    0.000 options.py:15(<lambda>)\n",
            "        1    0.000    0.000    0.000    0.000 options.py:30(parse_as_flags)\n",
            "        1    0.000    0.000    0.000    0.000 options.py:45(_apply)\n",
            "       99    0.000    0.000    0.000    0.000 os.py:675(__getitem__)\n",
            "      100    0.000    0.000    0.000    0.000 os.py:698(__iter__)\n",
            "       99    0.000    0.000    0.000    0.000 os.py:755(encode)\n",
            "      198    0.000    0.000    0.000    0.000 os.py:759(decode)\n",
            "        1    0.000    0.000    0.001    0.001 packer.py:104(from_arguments)\n",
            "        1    0.000    0.000    0.001    0.001 packer.py:109(<listcomp>)\n",
            "        1    0.000    0.000    0.000    0.000 packer.py:115(assign_names)\n",
            "     20/2    0.000    0.000    0.000    0.000 packer.py:123(_assign_names)\n",
            "        3    0.000    0.000    0.000    0.000 packer.py:132(argument_types)\n",
            "       45    0.000    0.000    0.000    0.000 packer.py:137(<genexpr>)\n",
            "        9    0.000    0.000    0.000    0.000 packer.py:140(_flatten)\n",
            "  351/135    0.000    0.000    0.000    0.000 packer.py:144(rec)\n",
            "        7    0.000    0.000    0.000    0.000 packer.py:167(__init__)\n",
            "        7    0.000    0.000    0.000    0.000 packer.py:170(_build_unflatten_code)\n",
            "     49/7    0.000    0.000    0.000    0.000 packer.py:175(rec)\n",
            "        2    0.000    0.000    0.000    0.000 packer.py:190(unflatten)\n",
            "        7    0.000    0.000    0.001    0.000 packer.py:73(__init__)\n",
            "        2    0.000    0.000    0.001    0.001 packer.py:87(as_arguments)\n",
            "        2    0.000    0.000    0.001    0.001 packer.py:97(<listcomp>)\n",
            "        1    0.000    0.000    0.000    0.000 parfor.py:715(__init__)\n",
            "        1    0.000    0.000    0.000    0.000 parfor.py:747(has_setup)\n",
            "        3    0.000    0.000    0.000    0.000 passmanagers.py:111(_dispose)\n",
            "        1    0.000    0.000    0.000    0.000 passmanagers.py:30(__sub__)\n",
            "        2    0.000    0.000    0.000    0.000 passmanagers.py:49(dump_refprune_stats)\n",
            "        3    0.000    0.000    0.000    0.000 passmanagers.py:643(add_target_library_info)\n",
            "        3    0.000    0.000    0.000    0.000 passmanagers.py:656(add_refprune_pass)\n",
            "        2    0.000    0.000    0.114    0.057 passmanagers.py:681(run)\n",
            "        3    0.000    0.000    0.000    0.000 passmanagers.py:738(__init__)\n",
            "       35    0.000    0.000    0.012    0.000 passmanagers.py:744(initialize)\n",
            "       35    0.000    0.000    0.001    0.000 passmanagers.py:751(finalize)\n",
            "       35    0.000    0.000    0.013    0.000 passmanagers.py:758(run)\n",
            "        3    0.000    0.000    0.000    0.000 passmanagers.py:95(create_function_pass_manager)\n",
            "        1    0.000    0.000    0.000    0.000 pickle.py:322(_getattribute)\n",
            "       12    0.000    0.000    0.000    0.000 posixpath.py:140(basename)\n",
            "       16    0.000    0.000    0.000    0.000 posixpath.py:338(normpath)\n",
            "       16    0.000    0.000    0.000    0.000 posixpath.py:377(abspath)\n",
            "       52    0.000    0.000    0.000    0.000 posixpath.py:41(_get_sep)\n",
            "        8    0.000    0.000    0.001    0.000 posixpath.py:466(relpath)\n",
            "        8    0.000    0.000    0.000    0.000 posixpath.py:488(<listcomp>)\n",
            "        8    0.000    0.000    0.000    0.000 posixpath.py:489(<listcomp>)\n",
            "       16    0.000    0.000    0.000    0.000 posixpath.py:60(isabs)\n",
            "       24    0.000    0.000    0.000    0.000 posixpath.py:71(join)\n",
            "        3    0.000    0.000    0.008    0.003 postproc.py:158(_insert_var_dels)\n",
            "        3    0.001    0.000    0.008    0.003 postproc.py:179(_patch_var_dels)\n",
            "      378    0.000    0.000    0.000    0.000 postproc.py:191(<genexpr>)\n",
            "        1    0.000    0.000    0.000    0.000 postproc.py:235(remove_dels)\n",
            "        9    0.000    0.000    0.000    0.000 postproc.py:35(__init__)\n",
            "        9    0.000    0.000    0.001    0.000 postproc.py:38(cfg)\n",
            "        9    0.000    0.000    0.024    0.003 postproc.py:42(usedefs)\n",
            "        9    0.000    0.000    0.003    0.000 postproc.py:46(livemap)\n",
            "        9    0.000    0.000    0.007    0.001 postproc.py:52(deadmaps)\n",
            "        9    0.000    0.000    0.000    0.000 postproc.py:68(__init__)\n",
            "        9    0.000    0.000    0.045    0.005 postproc.py:71(run)\n",
            "     1184    0.001    0.000    0.002    0.000 pprint.py:102(_safe_tuple)\n",
            "       29    0.000    0.000    0.000    0.000 pprint.py:107(__init__)\n",
            "       29    0.000    0.000    0.024    0.001 pprint.py:155(pformat)\n",
            "   739/29    0.002    0.000    0.023    0.001 pprint.py:167(_format)\n",
            "       28    0.000    0.000    0.015    0.001 pprint.py:205(_pprint_dict)\n",
            "       33    0.000    0.000    0.002    0.000 pprint.py:235(_pprint_list)\n",
            "       32    0.000    0.000    0.001    0.000 pprint.py:243(_pprint_tuple)\n",
            "       28    0.002    0.000    0.012    0.000 pprint.py:376(_format_dict_items)\n",
            "    65/33    0.000    0.000    0.002    0.000 pprint.py:412(_format_items)\n",
            "     1353    0.002    0.000    0.015    0.000 pprint.py:453(_repr)\n",
            "2684/1353    0.002    0.000    0.013    0.000 pprint.py:462(format)\n",
            "        2    0.000    0.000    0.004    0.002 pprint.py:469(_pprint_default_dict)\n",
            "2684/1353    0.005    0.000    0.012    0.000 pprint.py:550(_safe_repr)\n",
            "       29    0.000    0.000    0.024    0.001 pprint.py:57(pformat)\n",
            "     2368    0.001    0.000    0.001    0.000 pprint.py:92(__init__)\n",
            "     3637    0.001    0.000    0.001    0.000 pprint.py:95(__lt__)\n",
            "        2    0.000    0.000    0.000    0.000 pythonapi.py:102(__init__)\n",
            "        1    0.000    0.000    0.000    0.000 pythonapi.py:110(__init__)\n",
            "        1    0.000    0.000    0.000    0.000 pythonapi.py:1145(string_from_string)\n",
            "        2    0.000    0.000    0.002    0.001 pythonapi.py:1174(bytes_from_string_and_size)\n",
            "        1    0.000    0.000    0.000    0.000 pythonapi.py:1191(make_none)\n",
            "        1    0.000    0.000    0.000    0.000 pythonapi.py:1196(borrow_none)\n",
            "        2    0.000    0.000    0.000    0.000 pythonapi.py:1285(nrt_adapt_ndarray_from_python)\n",
            "       29    0.000    0.000    0.007    0.000 pythonapi.py:1304(_get_function)\n",
            "        2    0.000    0.000    0.000    0.000 pythonapi.py:1307(alloca_obj)\n",
            "        4    0.000    0.000    0.000    0.000 pythonapi.py:1336(get_null_object)\n",
            "        1    0.000    0.000    0.000    0.000 pythonapi.py:1339(return_none)\n",
            "        2    0.000    0.000    0.001    0.000 pythonapi.py:1353(unserialize)\n",
            "        2    0.000    0.000    0.000    0.000 pythonapi.py:1367(build_dynamic_excinfo_struct)\n",
            "        1    0.000    0.000    0.000    0.000 pythonapi.py:1377(serialize_uncached)\n",
            "        2    0.000    0.000    0.000    0.000 pythonapi.py:1406(serialize_object)\n",
            "        2    0.000    0.000    0.012    0.006 pythonapi.py:1426(to_native_value)\n",
            "        1    0.000    0.000    0.000    0.000 pythonapi.py:1437(from_native_return)\n",
            "        1    0.000    0.000    0.000    0.000 pythonapi.py:1444(from_native_value)\n",
            "        4    0.000    0.000    0.000    0.000 pythonapi.py:1457(reflect_native_value)\n",
            "        4    0.000    0.000    0.000    0.000 pythonapi.py:169(__init__)\n",
            "        1    0.000    0.000    0.000    0.000 pythonapi.py:201(get_env_manager)\n",
            "        1    0.000    0.000    0.004    0.004 pythonapi.py:204(emit_environment_sentry)\n",
            "        1    0.000    0.000    0.000    0.000 pythonapi.py:229(incref)\n",
            "        1    0.000    0.000    0.000    0.000 pythonapi.py:234(decref)\n",
            "        1    0.000    0.000    0.002    0.002 pythonapi.py:263(unpack_tuple)\n",
            "        2    0.000    0.000    0.000    0.000 pythonapi.py:283(err_clear)\n",
            "        7    0.000    0.000    0.005    0.001 pythonapi.py:288(err_set_string)\n",
            "        2    0.000    0.000    0.000    0.000 pythonapi.py:306(raise_object)\n",
            "        2    0.000    0.000    0.000    0.000 pythonapi.py:324(err_set_none)\n",
            "        1    0.000    0.000    0.000    0.000 pythonapi.py:331(err_write_unraisable)\n",
            "       10    0.000    0.000    0.003    0.000 pythonapi.py:375(get_c_object)\n",
            "        7    0.000    0.000    0.000    0.000 pythonapi.py:38(lookup)\n",
            "        1    0.000    0.000    0.000    0.000 pythonapi.py:466(float_from_double)\n",
            "        1    0.000    0.000    0.000    0.000 pythonapi.py:858(gil_ensure)\n",
            "        1    0.000    0.000    0.003    0.003 pythonapi.py:870(gil_release)\n",
            "        2    0.000    0.000    0.044    0.022 rangeobj.py:100(from_range_state)\n",
            "        2    0.000    0.000    0.010    0.005 rangeobj.py:147(iternext)\n",
            "        2    0.000    0.000    0.001    0.001 rangeobj.py:26(range1_impl)\n",
            "        2    0.000    0.000    0.044    0.022 rangeobj.py:87(getiter_range32_impl)\n",
            "       30    0.000    0.000    0.000    0.000 re.py:202(sub)\n",
            "       30    0.000    0.000    0.000    0.000 re.py:288(_compile)\n",
            "       10    0.000    0.000    0.000    0.000 registry.py:10(__init__)\n",
            "        1    0.000    0.000    0.000    0.000 registry.py:25(target_context)\n",
            "        1    0.000    0.000    0.000    0.000 registry.py:32(typing_context)\n",
            "        2    0.002    0.001    0.012    0.006 registry.py:54(apply)\n",
            "      509    0.001    0.000    0.001    0.000 registry.py:67(__getitem__)\n",
            "        1    0.000    0.000    0.000    0.000 removerefctpass.py:15(__init__)\n",
            "        6    0.000    0.000    0.000    0.000 removerefctpass.py:18(visit_Call)\n",
            "        1    0.000    0.000    0.001    0.001 removerefctpass.py:23(_rewrite_function)\n",
            "        1    0.000    0.000    0.001    0.001 removerefctpass.py:37(_legalize)\n",
            "       15    0.000    0.000    0.001    0.000 removerefctpass.py:44(valid_output)\n",
            "        2    0.000    0.000    0.000    0.000 removerefctpass.py:51(valid_input)\n",
            "        1    0.000    0.000    0.001    0.001 removerefctpass.py:99(remove_unnecessary_nrt_usage)\n",
            "        5    0.000    0.000    0.000    0.000 scalars.py:32(__init__)\n",
            "        5    0.000    0.000    0.000    0.000 scalars.py:78(__init__)\n",
            "        1    0.000    0.000    0.000    0.000 serialize.py:193(reducer_override)\n",
            "        1    0.000    0.000    0.000    0.000 serialize.py:52(dumps)\n",
            "       10    0.000    0.000    0.000    0.000 setdecl.py:79(generic)\n",
            "        1    0.000    0.000    0.000    0.000 sigutils.py:22(normalize_signature)\n",
            "        2    0.000    0.000    0.000    0.000 sigutils.py:43(check_type)\n",
            "        2    0.000    0.000    0.000    0.000 slicing.py:15(fix_index)\n",
            "        1    0.000    0.000    0.000    0.000 ssa.py:102(_iterated_domfronts)\n",
            "        1    0.000    0.000    0.000    0.000 ssa.py:108(<dictcomp>)\n",
            "       14    0.000    0.000    0.000    0.000 ssa.py:113(<listcomp>)\n",
            "        1    0.000    0.000    0.000    0.000 ssa.py:120(_compute_phi_locations)\n",
            "        1    0.000    0.000    0.000    0.000 ssa.py:131(_fresh_vars)\n",
            "        2    0.000    0.000    0.000    0.000 ssa.py:141(_get_scope)\n",
            "        1    0.000    0.000    0.006    0.006 ssa.py:146(_find_defs_violators)\n",
            "        1    0.000    0.000    0.000    0.000 ssa.py:161(<listcomp>)\n",
            "       39    0.000    0.000    0.000    0.000 ssa.py:168(<setcomp>)\n",
            "        1    0.000    0.000    0.001    0.001 ssa.py:176(_run_block_analysis)\n",
            "        2    0.000    0.000    0.012    0.006 ssa.py:184(_run_block_rewrite)\n",
            "        2    0.000    0.000    0.000    0.000 ssa.py:201(_make_states)\n",
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            "     2553    0.001    0.000    0.001    0.000 {method 'get' of 'dict' objects}\n",
            "       21    0.000    0.000    0.000    0.000 {method 'get' of 'mappingproxy' objects}\n",
            "        1    0.000    0.000    0.000    0.000 {method 'getvalue' of '_io.BytesIO' objects}\n",
            "       30    0.000    0.000    0.000    0.000 {method 'getvalue' of '_io.StringIO' objects}\n",
            "        2    0.000    0.000    0.000    0.000 {method 'group' of 're.Match' objects}\n",
            "        7    0.000    0.000    0.000    0.000 {method 'index' of 'list' objects}\n",
            "      755    0.000    0.000    0.000    0.000 {method 'index' of 'tuple' objects}\n",
            "      972    0.000    0.000    0.000    0.000 {method 'insert' of 'list' objects}\n",
            "       39    0.000    0.000    0.000    0.000 {method 'intersection' of 'set' objects}\n",
            "       43    0.000    0.000    0.000    0.000 {method 'isalpha' of 'str' objects}\n",
            "       27    0.000    0.000    0.000    0.000 {method 'isdigit' of 'str' objects}\n",
            "       58    0.000    0.000    0.000    0.000 {method 'isidentifier' of 'str' objects}\n",
            "        1    0.000    0.000    0.000    0.000 {method 'items' of 'collections.OrderedDict' objects}\n",
            "      628    0.000    0.000    0.000    0.000 {method 'items' of 'dict' objects}\n",
            "        1    0.000    0.000    0.000    0.000 {method 'items' of 'mappingproxy' objects}\n",
            "        1    0.000    0.000    0.000    0.000 {method 'join' of 'bytes' objects}\n",
            "1823/1804    0.001    0.000    0.019    0.000 {method 'join' of 'str' objects}\n",
            "      132    0.000    0.000    0.000    0.000 {method 'keys' of 'dict' objects}\n",
            "       27    0.000    0.000    0.000    0.000 {method 'lower' of 'str' objects}\n",
            "       79    0.000    0.000    0.000    0.000 {method 'match' of 're.Pattern' objects}\n",
            "       30    0.000    0.000    0.000    0.000 {method 'pop' of 'collections.deque' objects}\n",
            "      746    0.000    0.000    0.000    0.000 {method 'pop' of 'dict' objects}\n",
            "      688    0.000    0.000    0.000    0.000 {method 'pop' of 'list' objects}\n",
            "       74    0.000    0.000    0.000    0.000 {method 'popleft' of 'collections.deque' objects}\n",
            "      497    0.000    0.000    0.000    0.000 {method 'release' of '_thread.RLock' objects}\n",
            "      151    0.000    0.000    0.000    0.000 {method 'remove' of 'list' objects}\n",
            "        1    0.000    0.000    0.000    0.000 {method 'remove' of 'set' objects}\n",
            "       41    0.000    0.000    0.000    0.000 {method 'replace' of 'str' objects}\n",
            "        2    0.000    0.000    0.000    0.000 {method 'reverse' of 'list' objects}\n",
            "       12    0.000    0.000    0.000    0.000 {method 'rfind' of 'str' objects}\n",
            "       83    0.000    0.000    0.000    0.000 {method 'rpartition' of 'str' objects}\n",
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            "      812    0.000    0.000    0.000    0.000 {method 'rstrip' of 'str' objects}\n",
            "        2    0.000    0.000    0.000    0.000 {method 'setdefault' of 'dict' objects}\n",
            "       18    0.000    0.000    0.000    0.000 {method 'sort' of 'list' objects}\n",
            "       58    0.000    0.000    0.000    0.000 {method 'split' of 'str' objects}\n",
            "     2329    0.001    0.000    0.001    0.000 {method 'startswith' of 'str' objects}\n",
            "        3    0.000    0.000    0.000    0.000 {method 'strip' of 'str' objects}\n",
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            "      163    0.000    0.000    0.000    0.000 {method 'update' of 'dict' objects}\n",
            "      154    0.000    0.000    0.000    0.000 {method 'update' of 'set' objects}\n",
            "        3    0.000    0.000    0.000    0.000 {method 'upper' of 'str' objects}\n",
            "       14    0.000    0.000    0.000    0.000 {method 'values' of 'collections.OrderedDict' objects}\n",
            "     2236    0.000    0.000    0.000    0.000 {method 'values' of 'dict' objects}\n",
            "       34    0.000    0.000    0.000    0.000 {method 'with_traceback' of 'BaseException' objects}\n",
            "     2742    0.001    0.000    0.001    0.000 {method 'write' of '_io.StringIO' objects}\n",
            "\n",
            "\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Next Steps\n",
        "\n",
        "Congratulations on completing this advanced Numba tutorial for machine learning! You've gained valuable insights into optimizing Python code for high-performance machine learning tasks. To further enhance your skills and expand your knowledge, consider the following next steps:\n",
        "\n",
        "1. **Practice and Experimentation**: Apply the techniques learned in this tutorial to your own machine learning projects. Experiment with different Numba optimizations and measure their impact on your specific use cases.\n",
        "\n",
        "2. **Explore Advanced CUDA Programming**: If you're interested in GPU acceleration, delve deeper into CUDA programming with Numba. Learn about shared memory, atomic operations, and more complex parallel algorithms.\n",
        "\n",
        "3. **Benchmark Against Other Solutions**: Compare Numba-optimized code with other high-performance computing solutions like Cython, Dask, or pure C/C++ implementations. Understand the trade-offs between development time and execution speed.\n",
        "\n",
        "4. **Contribute to Open Source**: Many machine learning libraries could benefit from Numba optimizations. Consider contributing to open-source projects by optimizing computationally intensive parts of their codebase.\n",
        "\n",
        "5. **Stay Updated**: Numba is continuously evolving. Keep an eye on the official Numba documentation and release notes for new features and improvements.\n",
        "\n",
        "6. **Explore Integration with ML Frameworks**: Investigate how Numba can be integrated with popular machine learning frameworks like scikit-learn, PyTorch, or TensorFlow for custom operations.\n",
        "\n",
        "7. **Attend Conferences and Workshops**: Participate in conferences or workshops focused on high-performance computing in Python to learn from experts and share your experiences.\n",
        "\n",
        "8. **Optimize Full ML Pipelines**: Apply Numba optimizations to entire machine learning pipelines, from data preprocessing to model evaluation, to achieve end-to-end performance improvements.\n",
        "\n",
        "9. **Learn About Memory Management**: Dive deeper into memory management techniques in Numba to handle large datasets efficiently and avoid common pitfalls.\n",
        "\n",
        "10. **Explore Multi-GPU Programming**: If you have access to multiple GPUs, learn how to distribute computations across them using Numba and CUDA.\n",
        "\n",
        "Remember, becoming proficient in high-performance computing for machine learning is an ongoing journey. Continuous practice and staying curious about new developments in the field will help you become a more effective and efficient machine learning researcher or practitioner.\n",
        "\n",
        "Happy coding, and may your models train faster than ever before!"
      ],
      "metadata": {
        "id": "trqou4qJoI_T"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Conclusion\n",
        "\n",
        "This tutorial covered advanced Numba techniques for machine learning researchers, including parallel processing, custom data types, GPU acceleration, and profiling. By leveraging these features, you can significantly speed up your machine learning algorithms and handle larger datasets more efficiently.\n",
        "\n",
        "Remember to always profile your code and compare it with non-Numba implementations to ensure you're getting the expected performance improvements. Happy coding!"
      ],
      "metadata": {
        "id": "MWl-X9wrl_F5"
      }
    }
  ]
}