Tensor Puzzlers.ipynb

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        "# Tensor Puzzles\n",
        "- by [Sasha Rush](http://rush-nlp.com) - [srush_nlp](https://twitter.com/srush_nlp) (with Marcos Treviso)\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "When learning a tensor programming language like PyTorch or Numpy it\n",
        "is tempting to rely on the standard library (or more honestly\n",
        "StackOverflow) to find a magic function for everything.  But in\n",
        "practice, the tensor language is extremely expressive, and you can\n",
        "do most things from first principles and clever use of broadcasting.\n",
        "\n",
        "\n",
        "\n",
        "This is a collection of 21 tensor puzzles. Like chess puzzles these are\n",
        "not meant to simulate the complexity of a real program, but to practice\n",
        "in a simplified environment. Each puzzle asks you to reimplement one\n",
        "function in the NumPy standard library without magic.\n",
        "\n",
        "\n",
        "I recommend running in Colab. Click here and copy the notebook to get start.\n",
        "\n",
        "[![Open In Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/srush/Tensor-Puzzles/blob/main/Tensor%20Puzzlers.ipynb)"
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      "source": [
        "from lib import draw_examples, make_test, run_test\n",
        "import torch\n",
        "import numpy as np\n",
        "from torchtyping import TensorType as TT\n",
        "import warnings\n",
        "warnings.filterwarnings('ignore')  # Ignore all warnings\n",
        "\n",
        "tensor = torch.tensor"
      ]
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        "## Rules\n",
        "\n",
        "1. These puzzles are about *broadcasting*. Know this rule."
      ]
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        "![](https://pbs.twimg.com/media/FQywor0WYAssn7Y?format=png&name=large)"
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        "2. Each puzzle needs to be solved in 1 line (<80 columns) of code.\n",
        "3. You are allowed @, arithmetic, comparison, `shape`, any indexing (e.g. `a[:j], a[:, None], a[arange(10)]`), and previous puzzle functions.\n",
        "4. You are *not allowed* anything else. No `view`, `sum`, `take`, `squeeze`, `tensor`."
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      "source": [
        "5. You can start with these two functions:"
      ]
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              "       0.0, 1.0, 0.0), diagram=ApplyTransform(transform=Affine(1.0, 0.0, 0.0,\n",
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              "       0.0, 1.0, 0.0), diagram=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44ce6b00>, diagram1=ApplyTransform(transform=Affine(1.0, 0.0, -1.0,\n",
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              "       0.0, 1.0, 0.0), diagram=ApplyTransform(transform=Affine(1.0, 0.0, 0.0,\n",
              "       -0.0, 1.0, 0.0), diagram=Empty()))), diagram2=Primitive(shape=Path(loc_trails=[Located(trail=Trail(segments=[Segment(offset=Vec2(1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, 1.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(-1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, -1.0), origin=Vec2(0.0, 0.0))], closed=True), location=Vec2(0.0, 0.0))]), style=Style(line_width_=None, line_color_=None, fill_color_=<Color orange>, fill_opacity_=0.46, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, 0.5,\n",
              "       0.0, 1.0, -0.5))), diagram2=ApplyTransform(transform=Affine(1.0, 0.0, 1.5,\n",
              "       0.0, 1.0, 0.0), diagram=ApplyTransform(transform=Affine(1.0, 0.0, 0.0,\n",
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              "       0.0, 1.0, 0.0))), diagram2=ApplyTransform(transform=Affine(1.0, 0.0, 15.50005,\n",
              "       0.0, 1.0, 0.0), diagram=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44ce7790>, diagram1=ApplyTransform(transform=Affine(1.0, 0.0, -4.0,\n",
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              "       0.0, 1.0, -0.5)), diagram2=ApplyTransform(transform=Affine(1.0, 0.0, 0.5,\n",
              "       0.0, 1.0, 0.0), diagram=ApplyTransform(transform=Affine(1.0, 0.0, 0.0,\n",
              "       -0.0, 1.0, 0.0), diagram=Empty()))), diagram2=Primitive(shape=Path(loc_trails=[Located(trail=Trail(segments=[Segment(offset=Vec2(1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, 1.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(-1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, -1.0), origin=Vec2(0.0, 0.0))], closed=True), location=Vec2(0.0, 0.0))]), style=Style(line_width_=None, line_color_=None, fill_color_=<Color orange>, fill_opacity_=0.46, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, 0.5,\n",
              "       0.0, 1.0, -0.5))), diagram2=ApplyTransform(transform=Affine(1.0, 0.0, 1.5,\n",
              "       0.0, 1.0, 0.0), diagram=ApplyTransform(transform=Affine(1.0, 0.0, 0.0,\n",
              "       -0.0, 1.0, 0.0), diagram=Empty()))), diagram2=Primitive(shape=Path(loc_trails=[Located(trail=Trail(segments=[Segment(offset=Vec2(1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, 1.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(-1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, -1.0), origin=Vec2(0.0, 0.0))], closed=True), location=Vec2(0.0, 0.0))]), style=Style(line_width_=None, line_color_=None, fill_color_=<Color orange>, fill_opacity_=0.52, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, 1.5,\n",
              "       0.0, 1.0, -0.5))), diagram2=ApplyTransform(transform=Affine(1.0, 0.0, 2.5,\n",
              "       0.0, 1.0, 0.0), diagram=ApplyTransform(transform=Affine(1.0, 0.0, 0.0,\n",
              "       -0.0, 1.0, 0.0), diagram=Empty()))), diagram2=Primitive(shape=Path(loc_trails=[Located(trail=Trail(segments=[Segment(offset=Vec2(1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, 1.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(-1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, -1.0), origin=Vec2(0.0, 0.0))], closed=True), location=Vec2(0.0, 0.0))]), style=Style(line_width_=None, line_color_=None, fill_color_=<Color orange>, fill_opacity_=0.5800000000000001, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, 2.5,\n",
              "       0.0, 1.0, -0.5))), diagram2=ApplyTransform(transform=Affine(1.0, 0.0, 3.5,\n",
              "       0.0, 1.0, 0.0), diagram=ApplyTransform(transform=Affine(1.0, 0.0, 0.0,\n",
              "       -0.0, 1.0, 0.0), diagram=Empty()))), diagram2=Primitive(shape=Path(loc_trails=[Located(trail=Trail(segments=[Segment(offset=Vec2(1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, 1.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(-1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, -1.0), origin=Vec2(0.0, 0.0))], closed=True), location=Vec2(0.0, 0.0))]), style=Style(line_width_=None, line_color_=None, fill_color_=<Color orange>, fill_opacity_=0.64, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, 3.5,\n",
              "       0.0, 1.0, -0.5))), diagram2=ApplyTransform(transform=Affine(1.0, 0.0, 4.5,\n",
              "       0.0, 1.0, 0.0), diagram=ApplyTransform(transform=Affine(1.0, 0.0, 0.0,\n",
              "       -0.0, 1.0, 0.0), diagram=Empty()))), diagram2=Primitive(shape=Path(loc_trails=[Located(trail=Trail(segments=[Segment(offset=Vec2(1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, 1.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(-1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, -1.0), origin=Vec2(0.0, 0.0))], closed=True), location=Vec2(0.0, 0.0))]), style=Style(line_width_=None, line_color_=None, fill_color_=<Color orange>, fill_opacity_=0.7, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, 4.5,\n",
              "       0.0, 1.0, -0.5))), diagram2=ApplyTransform(transform=Affine(1.0, 0.0, 5.5,\n",
              "       0.0, 1.0, 0.0), diagram=ApplyTransform(transform=Affine(1.0, 0.0, 0.0,\n",
              "       -0.0, 1.0, 0.0), diagram=Empty()))), diagram2=Primitive(shape=Path(loc_trails=[Located(trail=Trail(segments=[Segment(offset=Vec2(1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, 1.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(-1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, -1.0), origin=Vec2(0.0, 0.0))], closed=True), location=Vec2(0.0, 0.0))]), style=Style(line_width_=None, line_color_=None, fill_color_=<Color orange>, fill_opacity_=0.76, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, 5.5,\n",
              "       0.0, 1.0, -0.5))), diagram2=ApplyTransform(transform=Affine(1.0, 0.0, 6.5,\n",
              "       0.0, 1.0, 0.0), diagram=ApplyTransform(transform=Affine(1.0, 0.0, 0.0,\n",
              "       -0.0, 1.0, 0.0), diagram=Empty()))), diagram2=Primitive(shape=Path(loc_trails=[Located(trail=Trail(segments=[Segment(offset=Vec2(1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, 1.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(-1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, -1.0), origin=Vec2(0.0, 0.0))], closed=True), location=Vec2(0.0, 0.0))]), style=Style(line_width_=None, line_color_=None, fill_color_=<Color orange>, fill_opacity_=0.8200000000000001, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, 6.5,\n",
              "       0.0, 1.0, -0.5))), diagram2=ApplyTransform(transform=Affine(1.0, 0.0, 7.5,\n",
              "       0.0, 1.0, 0.0), diagram=ApplyTransform(transform=Affine(1.0, 0.0, 0.0,\n",
              "       -0.0, 1.0, 0.0), diagram=Empty()))), diagram2=Primitive(shape=Path(loc_trails=[Located(trail=Trail(segments=[Segment(offset=Vec2(1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, 1.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(-1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, -1.0), origin=Vec2(0.0, 0.0))], closed=True), location=Vec2(0.0, 0.0))]), style=Style(line_width_=None, line_color_=None, fill_color_=<Color orange>, fill_opacity_=0.88, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, 7.5,\n",
              "       0.0, 1.0, -0.5)))), diagram2=Empty())))))), diagram2=Empty())))"
            ]
          },
          "execution_count": 2,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "def arange(i: int):\n",
        "    \"Use this function to replace a for-loop.\"\n",
        "    return torch.tensor(range(i))\n",
        "\n",
        "draw_examples(\"arange\", [{\"\" : arange(i)} for i in [5, 3, 9]])"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 3,
      "id": "aa922d9d",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 321
        },
        "execution": {
          "iopub.execute_input": "2022-07-13T00:15:16.701951Z",
          "iopub.status.busy": "2022-07-13T00:15:16.701616Z",
          "iopub.status.idle": "2022-07-13T00:15:16.795294Z",
          "shell.execute_reply": "2022-07-13T00:15:16.794635Z"
        },
        "id": "aa922d9d",
        "outputId": "968f6f5d-cb76-40a5-e72f-03cf0c4a480f"
      },
      "outputs": [
        {
          "data": {
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            ],
            "text/plain": [
              "Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44bfe620>, diagram1=Primitive(shape=Path(loc_trails=[Located(trail=Trail(segments=[Segment(offset=Vec2(9.600119999999999, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, 20.40012), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(-9.600119999999999, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, -20.40012), origin=Vec2(0.0, 0.0))], closed=True), location=Vec2(0.0, 0.0))]), style=Style(line_width_=None, line_color_=None, fill_color_=<Color white>, fill_opacity_=None, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, -4.800059999999999,\n",
              "       0.0, 1.0, -10.20006)), diagram2=ApplyTransform(transform=Affine(1.0, 0.0, -0.0,\n",
              "       0.0, 1.0, -9.60006), diagram=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44bfcf10>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44bfd0c0>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44bfcbe0>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44bfc730>, diagram1=Primitive(shape=Spacer(width=0, height=1), style=Style(line_width_=None, line_color_=None, fill_color_=None, fill_opacity_=None, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, 0.0,\n",
              "       0.0, 1.0, 0.0)), diagram2=Primitive(shape=Text(text='broadcast', font_size=0.75), style=Style(line_width_=(<WidthType.NORMALIZED: 2>, 0), line_color_=None, fill_color_=<Color black>, fill_opacity_=None, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, 0.0,\n",
              "       0.0, 1.0, 0.5))), diagram2=Primitive(shape=Spacer(width=0, height=1), style=Style(line_width_=None, line_color_=None, fill_color_=None, fill_opacity_=None, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, 0.0,\n",
              "       0.0, 1.0, 1.0001))), diagram2=ApplyTransform(transform=Affine(1.0, 0.0, 0.0,\n",
              "       0.0, 1.0, 9.0001), diagram=ApplyTransform(transform=Affine(1.0, 0.0, -4.0,\n",
              "       0.0, 1.0, -6.0), diagram=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44bfc190>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44befc40>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44bef820>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44bef3a0>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44bd7bb0>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44bd7640>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44bd72e0>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44bd6dd0>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44bd4700>, diagram1=ApplyTransform(transform=Affine(1.0, 0.0, -5e-05,\n",
              "       0.0, 1.0, -0.25005), diagram=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44b07dc0>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44b07880>, diagram1=Primitive(shape=Spacer(width=0, height=0.5), style=Style(line_width_=None, line_color_=None, fill_color_=None, fill_opacity_=None, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, 0.0,\n",
              "       0.0, 1.0, 0.0)), diagram2=Primitive(shape=Text(text='a', font_size=0.5), style=Style(line_width_=(<WidthType.NORMALIZED: 2>, 0.0), line_color_=None, fill_color_=<Color black>, fill_opacity_=None, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, 0.0,\n",
              "       0.0, 1.0, 0.25))), diagram2=Primitive(shape=Spacer(width=0, height=0.5), style=Style(line_width_=None, line_color_=None, fill_color_=None, fill_opacity_=None, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, 0.0,\n",
              "       0.0, 1.0, 0.5001)))), diagram2=Empty()), diagram2=Primitive(shape=Spacer(width=1.0, height=0), style=Style(line_width_=None, line_color_=None, fill_color_=None, fill_opacity_=None, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, 0.50005,\n",
              "       0.0, 1.0, 0.0))), diagram2=ApplyTransform(transform=Affine(1.0, 0.0, 3.00005,\n",
              "       0.0, 1.0, 0.0), diagram=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44bd53c0>, diagram1=ApplyTransform(transform=Affine(1.0, 0.0, -1.5,\n",
              "       0.0, 1.0, -0.0), diagram=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44b25ff0>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44b24ca0>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44b24f70>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44b24d00>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44b07ac0>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44b04e50>, diagram1=Primitive(shape=Path(loc_trails=[Located(trail=Trail(segments=[Segment(offset=Vec2(1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, 1.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(-1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, -1.0), origin=Vec2(0.0, 0.0))], closed=True), location=Vec2(0.0, 0.0))]), style=Style(line_width_=None, line_color_=None, fill_color_=None, fill_opacity_=None, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, -0.5,\n",
              "       0.0, 1.0, -0.5)), diagram2=ApplyTransform(transform=Affine(1.0, 0.0, 0.5,\n",
              "       0.0, 1.0, 0.0), diagram=ApplyTransform(transform=Affine(1.0, 0.0, 0.0,\n",
              "       -0.0, 1.0, 0.0), diagram=Empty()))), diagram2=Primitive(shape=Path(loc_trails=[Located(trail=Trail(segments=[Segment(offset=Vec2(1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, 1.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(-1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, -1.0), origin=Vec2(0.0, 0.0))], closed=True), location=Vec2(0.0, 0.0))]), style=Style(line_width_=None, line_color_=None, fill_color_=<Color orange>, fill_opacity_=0.46, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, 0.5,\n",
              "       0.0, 1.0, -0.5))), diagram2=ApplyTransform(transform=Affine(1.0, 0.0, 1.5,\n",
              "       0.0, 1.0, 0.0), diagram=ApplyTransform(transform=Affine(1.0, 0.0, 0.0,\n",
              "       -0.0, 1.0, 0.0), diagram=Empty()))), diagram2=Primitive(shape=Path(loc_trails=[Located(trail=Trail(segments=[Segment(offset=Vec2(1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, 1.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(-1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, -1.0), origin=Vec2(0.0, 0.0))], closed=True), location=Vec2(0.0, 0.0))]), style=Style(line_width_=None, line_color_=None, fill_color_=<Color orange>, fill_opacity_=0.52, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, 1.5,\n",
              "       0.0, 1.0, -0.5))), diagram2=ApplyTransform(transform=Affine(1.0, 0.0, 2.5,\n",
              "       0.0, 1.0, 0.0), diagram=ApplyTransform(transform=Affine(1.0, 0.0, 0.0,\n",
              "       -0.0, 1.0, 0.0), diagram=Empty()))), diagram2=Primitive(shape=Path(loc_trails=[Located(trail=Trail(segments=[Segment(offset=Vec2(1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, 1.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(-1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, -1.0), origin=Vec2(0.0, 0.0))], closed=True), location=Vec2(0.0, 0.0))]), style=Style(line_width_=None, line_color_=None, fill_color_=<Color orange>, fill_opacity_=0.5800000000000001, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, 2.5,\n",
              "       0.0, 1.0, -0.5)))), diagram2=Empty()))), diagram2=Primitive(shape=Spacer(width=1.0, height=0), style=Style(line_width_=None, line_color_=None, fill_color_=None, fill_opacity_=None, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, 5.50005,\n",
              "       0.0, 1.0, 0.0))), diagram2=ApplyTransform(transform=Affine(1.0, 0.0, 7.00005,\n",
              "       0.0, 1.0, 0.0), diagram=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44bd6050>, diagram1=ApplyTransform(transform=Affine(1.0, 0.0, -0.0,\n",
              "       0.0, 1.0, -1.0), diagram=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44b48f70>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44b481c0>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44b27d60>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44b26aa0>, diagram1=Primitive(shape=Path(loc_trails=[Located(trail=Trail(segments=[Segment(offset=Vec2(1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, 1.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(-1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, -1.0), origin=Vec2(0.0, 0.0))], closed=True), location=Vec2(0.0, 0.0))]), style=Style(line_width_=None, line_color_=None, fill_color_=None, fill_opacity_=None, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, -0.5,\n",
              "       0.0, 1.0, -0.5)), diagram2=ApplyTransform(transform=Affine(1.0, 0.0, 0.0,\n",
              "       0.0, 1.0, 0.5), diagram=ApplyTransform(transform=Affine(0.0, 1.0, 0.0,\n",
              "       -1.0, 0.0, 0.0), diagram=Empty()))), diagram2=Primitive(shape=Path(loc_trails=[Located(trail=Trail(segments=[Segment(offset=Vec2(1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, 1.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(-1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, -1.0), origin=Vec2(0.0, 0.0))], closed=True), location=Vec2(0.0, 0.0))]), style=Style(line_width_=None, line_color_=None, fill_color_=<Color orange>, fill_opacity_=0.46, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, -0.5,\n",
              "       0.0, 1.0, 0.5))), diagram2=ApplyTransform(transform=Affine(1.0, 0.0, 0.0,\n",
              "       0.0, 1.0, 1.5), diagram=ApplyTransform(transform=Affine(0.0, 1.0, 0.0,\n",
              "       -1.0, 0.0, 0.0), diagram=Empty()))), diagram2=Primitive(shape=Path(loc_trails=[Located(trail=Trail(segments=[Segment(offset=Vec2(1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, 1.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(-1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, -1.0), origin=Vec2(0.0, 0.0))], closed=True), location=Vec2(0.0, 0.0))]), style=Style(line_width_=None, line_color_=None, fill_color_=<Color orange>, fill_opacity_=0.52, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, -0.5,\n",
              "       0.0, 1.0, 1.5)))), diagram2=Empty()))), diagram2=Primitive(shape=Spacer(width=1.0, height=0), style=Style(line_width_=None, line_color_=None, fill_color_=None, fill_opacity_=None, dashing_=None, output_size=None), transform=Affine(0.0, 1.0, 0.0,\n",
              "       -1.0, 0.0, 2.0))), diagram2=ApplyTransform(transform=Affine(1.0, 0.0, 0.0,\n",
              "       0.0, 1.0, 5.0), diagram=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44bdf580>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44bdef50>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44bdebf0>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44bde6e0>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44bd7ee0>, diagram1=ApplyTransform(transform=Affine(1.0, 0.0, -5e-05,\n",
              "       0.0, 1.0, -0.25005), diagram=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44b49b70>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44b49630>, diagram1=Primitive(shape=Spacer(width=0, height=0.5), style=Style(line_width_=None, line_color_=None, fill_color_=None, fill_opacity_=None, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, 0.0,\n",
              "       0.0, 1.0, 0.0)), diagram2=Primitive(shape=Text(text='b', font_size=0.5), style=Style(line_width_=(<WidthType.NORMALIZED: 2>, 0.0), line_color_=None, fill_color_=<Color black>, fill_opacity_=None, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, 0.0,\n",
              "       0.0, 1.0, 0.25))), diagram2=Primitive(shape=Spacer(width=0, height=0.5), style=Style(line_width_=None, line_color_=None, fill_color_=None, fill_opacity_=None, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, 0.0,\n",
              "       0.0, 1.0, 0.5001)))), diagram2=Empty()), diagram2=Primitive(shape=Spacer(width=1.0, height=0), style=Style(line_width_=None, line_color_=None, fill_color_=None, fill_opacity_=None, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, 0.50005,\n",
              "       0.0, 1.0, 0.0))), diagram2=ApplyTransform(transform=Affine(1.0, 0.0, 3.00005,\n",
              "       0.0, 1.0, 0.0), diagram=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44bdcca0>, diagram1=ApplyTransform(transform=Affine(1.0, 0.0, -0.0,\n",
              "       0.0, 1.0, -2.0), diagram=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44b63070>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44b62080>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44b61ea0>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44b60eb0>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44b60cd0>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44b60b80>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44b4bac0>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44b4a770>, diagram1=Primitive(shape=Path(loc_trails=[Located(trail=Trail(segments=[Segment(offset=Vec2(1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, 1.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(-1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, -1.0), origin=Vec2(0.0, 0.0))], closed=True), location=Vec2(0.0, 0.0))]), style=Style(line_width_=None, line_color_=None, fill_color_=None, fill_opacity_=None, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, -0.5,\n",
              "       0.0, 1.0, -0.5)), diagram2=ApplyTransform(transform=Affine(1.0, 0.0, 0.0,\n",
              "       0.0, 1.0, 0.5), diagram=ApplyTransform(transform=Affine(0.0, 1.0, 0.0,\n",
              "       -1.0, 0.0, 0.0), diagram=Empty()))), diagram2=Primitive(shape=Path(loc_trails=[Located(trail=Trail(segments=[Segment(offset=Vec2(1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, 1.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(-1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, -1.0), origin=Vec2(0.0, 0.0))], closed=True), location=Vec2(0.0, 0.0))]), style=Style(line_width_=None, line_color_=None, fill_color_=<Color orange>, fill_opacity_=0.46, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, -0.5,\n",
              "       0.0, 1.0, 0.5))), diagram2=ApplyTransform(transform=Affine(1.0, 0.0, 0.0,\n",
              "       0.0, 1.0, 1.5), diagram=ApplyTransform(transform=Affine(0.0, 1.0, 0.0,\n",
              "       -1.0, 0.0, 0.0), diagram=Empty()))), diagram2=Primitive(shape=Path(loc_trails=[Located(trail=Trail(segments=[Segment(offset=Vec2(1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, 1.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(-1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, -1.0), origin=Vec2(0.0, 0.0))], closed=True), location=Vec2(0.0, 0.0))]), style=Style(line_width_=None, line_color_=None, fill_color_=<Color orange>, fill_opacity_=0.52, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, -0.5,\n",
              "       0.0, 1.0, 1.5))), diagram2=ApplyTransform(transform=Affine(1.0, 0.0, 0.0,\n",
              "       0.0, 1.0, 2.5), diagram=ApplyTransform(transform=Affine(0.0, 1.0, 0.0,\n",
              "       -1.0, 0.0, 0.0), diagram=Empty()))), diagram2=Primitive(shape=Path(loc_trails=[Located(trail=Trail(segments=[Segment(offset=Vec2(1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, 1.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(-1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, -1.0), origin=Vec2(0.0, 0.0))], closed=True), location=Vec2(0.0, 0.0))]), style=Style(line_width_=None, line_color_=None, fill_color_=<Color orange>, fill_opacity_=0.5800000000000001, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, -0.5,\n",
              "       0.0, 1.0, 2.5))), diagram2=ApplyTransform(transform=Affine(1.0, 0.0, 0.0,\n",
              "       0.0, 1.0, 3.5), diagram=ApplyTransform(transform=Affine(0.0, 1.0, 0.0,\n",
              "       -1.0, 0.0, 0.0), diagram=Empty()))), diagram2=Primitive(shape=Path(loc_trails=[Located(trail=Trail(segments=[Segment(offset=Vec2(1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, 1.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(-1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, -1.0), origin=Vec2(0.0, 0.0))], closed=True), location=Vec2(0.0, 0.0))]), style=Style(line_width_=None, line_color_=None, fill_color_=<Color orange>, fill_opacity_=0.64, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, -0.5,\n",
              "       0.0, 1.0, 3.5)))), diagram2=Empty()))), diagram2=Primitive(shape=Spacer(width=1.0, height=0), style=Style(line_width_=None, line_color_=None, fill_color_=None, fill_opacity_=None, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, 5.50005,\n",
              "       0.0, 1.0, 0.0))), diagram2=ApplyTransform(transform=Affine(1.0, 0.0, 7.00005,\n",
              "       0.0, 1.0, 0.0), diagram=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44bdd960>, diagram1=ApplyTransform(transform=Affine(1.0, 0.0, -0.5,\n",
              "       0.0, 1.0, -0.0), diagram=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44b68fa0>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44b636a0>, diagram1=Primitive(shape=Path(loc_trails=[Located(trail=Trail(segments=[Segment(offset=Vec2(1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, 1.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(-1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, -1.0), origin=Vec2(0.0, 0.0))], closed=True), location=Vec2(0.0, 0.0))]), style=Style(line_width_=None, line_color_=None, fill_color_=None, fill_opacity_=None, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, -0.5,\n",
              "       0.0, 1.0, -0.5)), diagram2=ApplyTransform(transform=Affine(1.0, 0.0, 0.5,\n",
              "       0.0, 1.0, 0.0), diagram=ApplyTransform(transform=Affine(1.0, 0.0, 0.0,\n",
              "       -0.0, 1.0, 0.0), diagram=Empty()))), diagram2=Primitive(shape=Path(loc_trails=[Located(trail=Trail(segments=[Segment(offset=Vec2(1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, 1.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(-1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, -1.0), origin=Vec2(0.0, 0.0))], closed=True), location=Vec2(0.0, 0.0))]), style=Style(line_width_=None, line_color_=None, fill_color_=<Color orange>, fill_opacity_=0.46, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, 0.5,\n",
              "       0.0, 1.0, -0.5)))), diagram2=Empty()))))), diagram2=Primitive(shape=Spacer(width=1.0, height=0), style=Style(line_width_=None, line_color_=None, fill_color_=None, fill_opacity_=None, dashing_=None, output_size=None), transform=Affine(0.0, 1.0, 0.0,\n",
              "       -1.0, 0.0, 8.0))), diagram2=ApplyTransform(transform=Affine(1.0, 0.0, 0.0,\n",
              "       0.0, 1.0, 11.0), diagram=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44bef070>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44beeb00>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44bee7a0>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44bee290>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44bdf850>, diagram1=ApplyTransform(transform=Affine(1.0, 0.0, -5e-05,\n",
              "       0.0, 1.0, -0.25005), diagram=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44b69b40>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44b69690>, diagram1=Primitive(shape=Spacer(width=0, height=0.5), style=Style(line_width_=None, line_color_=None, fill_color_=None, fill_opacity_=None, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, 0.0,\n",
              "       0.0, 1.0, 0.0)), diagram2=Primitive(shape=Text(text='ret', font_size=0.5), style=Style(line_width_=(<WidthType.NORMALIZED: 2>, 0.0), line_color_=None, fill_color_=<Color black>, fill_opacity_=None, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, 0.0,\n",
              "       0.0, 1.0, 0.25))), diagram2=Primitive(shape=Spacer(width=0, height=0.5), style=Style(line_width_=None, line_color_=None, fill_color_=None, fill_opacity_=None, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, 0.0,\n",
              "       0.0, 1.0, 0.5001)))), diagram2=Empty()), diagram2=Primitive(shape=Spacer(width=1.0, height=0), style=Style(line_width_=None, line_color_=None, fill_color_=None, fill_opacity_=None, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, 0.50005,\n",
              "       0.0, 1.0, 0.0))), diagram2=ApplyTransform(transform=Affine(1.0, 0.0, 3.00005,\n",
              "       0.0, 1.0, 0.0), diagram=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44bec640>, diagram1=ApplyTransform(transform=Affine(1.0, 0.0, -1.5,\n",
              "       0.0, 1.0, -2.0), diagram=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44bb53f0>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44bb4e20>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44ba87f0>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44ba8280>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44b97bb0>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44b97160>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44b82fb0>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44b825f0>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44b76260>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44b75ff0>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44b74f70>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44b74d30>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44b6bc10>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44b6b100>, diagram1=Primitive(shape=Path(loc_trails=[Located(trail=Trail(segments=[Segment(offset=Vec2(1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, 1.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(-1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, -1.0), origin=Vec2(0.0, 0.0))], closed=True), location=Vec2(0.0, 0.0))]), style=Style(line_width_=None, line_color_=None, fill_color_=None, fill_opacity_=None, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, -0.5,\n",
              "       0.0, 1.0, -0.5)), diagram2=ApplyTransform(transform=Affine(1.0, 0.0, 0.5,\n",
              "       0.0, 1.0, 0.0), diagram=ApplyTransform(transform=Affine(1.0, 0.0, 0.0,\n",
              "       -0.0, 1.0, 0.0), diagram=Empty()))), diagram2=Primitive(shape=Path(loc_trails=[Located(trail=Trail(segments=[Segment(offset=Vec2(1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, 1.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(-1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, -1.0), origin=Vec2(0.0, 0.0))], closed=True), location=Vec2(0.0, 0.0))]), style=Style(line_width_=None, line_color_=None, fill_color_=<Color orange>, fill_opacity_=0.46, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, 0.5,\n",
              "       0.0, 1.0, -0.5))), diagram2=ApplyTransform(transform=Affine(1.0, 0.0, 1.5,\n",
              "       0.0, 1.0, 0.0), diagram=ApplyTransform(transform=Affine(1.0, 0.0, 0.0,\n",
              "       -0.0, 1.0, 0.0), diagram=Empty()))), diagram2=Primitive(shape=Path(loc_trails=[Located(trail=Trail(segments=[Segment(offset=Vec2(1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, 1.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(-1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, -1.0), origin=Vec2(0.0, 0.0))], closed=True), location=Vec2(0.0, 0.0))]), style=Style(line_width_=None, line_color_=None, fill_color_=<Color orange>, fill_opacity_=0.52, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, 1.5,\n",
              "       0.0, 1.0, -0.5))), diagram2=ApplyTransform(transform=Affine(1.0, 0.0, 2.5,\n",
              "       0.0, 1.0, 0.0), diagram=ApplyTransform(transform=Affine(1.0, 0.0, 0.0,\n",
              "       -0.0, 1.0, 0.0), diagram=Empty()))), diagram2=Primitive(shape=Path(loc_trails=[Located(trail=Trail(segments=[Segment(offset=Vec2(1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, 1.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(-1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, -1.0), origin=Vec2(0.0, 0.0))], closed=True), location=Vec2(0.0, 0.0))]), style=Style(line_width_=None, line_color_=None, fill_color_=<Color orange>, fill_opacity_=0.5800000000000001, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, 2.5,\n",
              "       0.0, 1.0, -0.5))), diagram2=ApplyTransform(transform=Affine(1.0, 0.0, 0.0,\n",
              "       0.0, 1.0, 0.5), diagram=ApplyTransform(transform=Affine(0.0, 1.0, 0.0,\n",
              "       -1.0, 0.0, 0.0), diagram=Empty()))), diagram2=ApplyTransform(transform=Affine(1.0, 0.0, 0.0,\n",
              "       0.0, 1.0, 1.0), diagram=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44b828c0>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44b82650>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44b815d0>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44b81390>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44b77eb0>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44b777f0>, diagram1=Primitive(shape=Path(loc_trails=[Located(trail=Trail(segments=[Segment(offset=Vec2(1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, 1.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(-1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, -1.0), origin=Vec2(0.0, 0.0))], closed=True), location=Vec2(0.0, 0.0))]), style=Style(line_width_=None, line_color_=None, fill_color_=<Color orange>, fill_opacity_=0.46, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, -0.5,\n",
              "       0.0, 1.0, -0.5)), diagram2=ApplyTransform(transform=Affine(1.0, 0.0, 0.5,\n",
              "       0.0, 1.0, 0.0), diagram=ApplyTransform(transform=Affine(1.0, 0.0, 0.0,\n",
              "       -0.0, 1.0, 0.0), diagram=Empty()))), diagram2=Primitive(shape=Path(loc_trails=[Located(trail=Trail(segments=[Segment(offset=Vec2(1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, 1.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(-1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, -1.0), origin=Vec2(0.0, 0.0))], closed=True), location=Vec2(0.0, 0.0))]), style=Style(line_width_=None, line_color_=None, fill_color_=<Color orange>, fill_opacity_=0.52, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, 0.5,\n",
              "       0.0, 1.0, -0.5))), diagram2=ApplyTransform(transform=Affine(1.0, 0.0, 1.5,\n",
              "       0.0, 1.0, 0.0), diagram=ApplyTransform(transform=Affine(1.0, 0.0, 0.0,\n",
              "       -0.0, 1.0, 0.0), diagram=Empty()))), diagram2=Primitive(shape=Path(loc_trails=[Located(trail=Trail(segments=[Segment(offset=Vec2(1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, 1.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(-1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, -1.0), origin=Vec2(0.0, 0.0))], closed=True), location=Vec2(0.0, 0.0))]), style=Style(line_width_=None, line_color_=None, fill_color_=<Color orange>, fill_opacity_=0.5800000000000001, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, 1.5,\n",
              "       0.0, 1.0, -0.5))), diagram2=ApplyTransform(transform=Affine(1.0, 0.0, 2.5,\n",
              "       0.0, 1.0, 0.0), diagram=ApplyTransform(transform=Affine(1.0, 0.0, 0.0,\n",
              "       -0.0, 1.0, 0.0), diagram=Empty()))), diagram2=Primitive(shape=Path(loc_trails=[Located(trail=Trail(segments=[Segment(offset=Vec2(1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, 1.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(-1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, -1.0), origin=Vec2(0.0, 0.0))], closed=True), location=Vec2(0.0, 0.0))]), style=Style(line_width_=None, line_color_=None, fill_color_=<Color orange>, fill_opacity_=0.64, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, 2.5,\n",
              "       0.0, 1.0, -0.5))))), diagram2=ApplyTransform(transform=Affine(1.0, 0.0, 0.0,\n",
              "       0.0, 1.0, 1.5), diagram=ApplyTransform(transform=Affine(0.0, 1.0, 0.0,\n",
              "       -1.0, 0.0, 0.0), diagram=Empty()))), diagram2=ApplyTransform(transform=Affine(1.0, 0.0, 0.0,\n",
              "       0.0, 1.0, 2.0), diagram=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44b97430>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44b971c0>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44b96140>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44b95f00>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44b94ee0>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44b834c0>, diagram1=Primitive(shape=Path(loc_trails=[Located(trail=Trail(segments=[Segment(offset=Vec2(1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, 1.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(-1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, -1.0), origin=Vec2(0.0, 0.0))], closed=True), location=Vec2(0.0, 0.0))]), style=Style(line_width_=None, line_color_=None, fill_color_=<Color orange>, fill_opacity_=0.52, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, -0.5,\n",
              "       0.0, 1.0, -0.5)), diagram2=ApplyTransform(transform=Affine(1.0, 0.0, 0.5,\n",
              "       0.0, 1.0, 0.0), diagram=ApplyTransform(transform=Affine(1.0, 0.0, 0.0,\n",
              "       -0.0, 1.0, 0.0), diagram=Empty()))), diagram2=Primitive(shape=Path(loc_trails=[Located(trail=Trail(segments=[Segment(offset=Vec2(1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, 1.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(-1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, -1.0), origin=Vec2(0.0, 0.0))], closed=True), location=Vec2(0.0, 0.0))]), style=Style(line_width_=None, line_color_=None, fill_color_=<Color orange>, fill_opacity_=0.5800000000000001, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, 0.5,\n",
              "       0.0, 1.0, -0.5))), diagram2=ApplyTransform(transform=Affine(1.0, 0.0, 1.5,\n",
              "       0.0, 1.0, 0.0), diagram=ApplyTransform(transform=Affine(1.0, 0.0, 0.0,\n",
              "       -0.0, 1.0, 0.0), diagram=Empty()))), diagram2=Primitive(shape=Path(loc_trails=[Located(trail=Trail(segments=[Segment(offset=Vec2(1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, 1.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(-1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, -1.0), origin=Vec2(0.0, 0.0))], closed=True), location=Vec2(0.0, 0.0))]), style=Style(line_width_=None, line_color_=None, fill_color_=<Color orange>, fill_opacity_=0.64, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, 1.5,\n",
              "       0.0, 1.0, -0.5))), diagram2=ApplyTransform(transform=Affine(1.0, 0.0, 2.5,\n",
              "       0.0, 1.0, 0.0), diagram=ApplyTransform(transform=Affine(1.0, 0.0, 0.0,\n",
              "       -0.0, 1.0, 0.0), diagram=Empty()))), diagram2=Primitive(shape=Path(loc_trails=[Located(trail=Trail(segments=[Segment(offset=Vec2(1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, 1.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(-1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, -1.0), origin=Vec2(0.0, 0.0))], closed=True), location=Vec2(0.0, 0.0))]), style=Style(line_width_=None, line_color_=None, fill_color_=<Color orange>, fill_opacity_=0.7, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, 2.5,\n",
              "       0.0, 1.0, -0.5))))), diagram2=ApplyTransform(transform=Affine(1.0, 0.0, 0.0,\n",
              "       0.0, 1.0, 2.5), diagram=ApplyTransform(transform=Affine(0.0, 1.0, 0.0,\n",
              "       -1.0, 0.0, 0.0), diagram=Empty()))), diagram2=ApplyTransform(transform=Affine(1.0, 0.0, 0.0,\n",
              "       0.0, 1.0, 3.0), diagram=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44b9feb0>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44b9fd30>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44b9ece0>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44b9ead0>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44b9db10>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44b9d030>, diagram1=Primitive(shape=Path(loc_trails=[Located(trail=Trail(segments=[Segment(offset=Vec2(1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, 1.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(-1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, -1.0), origin=Vec2(0.0, 0.0))], closed=True), location=Vec2(0.0, 0.0))]), style=Style(line_width_=None, line_color_=None, fill_color_=<Color orange>, fill_opacity_=0.5800000000000001, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, -0.5,\n",
              "       0.0, 1.0, -0.5)), diagram2=ApplyTransform(transform=Affine(1.0, 0.0, 0.5,\n",
              "       0.0, 1.0, 0.0), diagram=ApplyTransform(transform=Affine(1.0, 0.0, 0.0,\n",
              "       -0.0, 1.0, 0.0), diagram=Empty()))), diagram2=Primitive(shape=Path(loc_trails=[Located(trail=Trail(segments=[Segment(offset=Vec2(1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, 1.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(-1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, -1.0), origin=Vec2(0.0, 0.0))], closed=True), location=Vec2(0.0, 0.0))]), style=Style(line_width_=None, line_color_=None, fill_color_=<Color orange>, fill_opacity_=0.64, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, 0.5,\n",
              "       0.0, 1.0, -0.5))), diagram2=ApplyTransform(transform=Affine(1.0, 0.0, 1.5,\n",
              "       0.0, 1.0, 0.0), diagram=ApplyTransform(transform=Affine(1.0, 0.0, 0.0,\n",
              "       -0.0, 1.0, 0.0), diagram=Empty()))), diagram2=Primitive(shape=Path(loc_trails=[Located(trail=Trail(segments=[Segment(offset=Vec2(1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, 1.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(-1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, -1.0), origin=Vec2(0.0, 0.0))], closed=True), location=Vec2(0.0, 0.0))]), style=Style(line_width_=None, line_color_=None, fill_color_=<Color orange>, fill_opacity_=0.7, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, 1.5,\n",
              "       0.0, 1.0, -0.5))), diagram2=ApplyTransform(transform=Affine(1.0, 0.0, 2.5,\n",
              "       0.0, 1.0, 0.0), diagram=ApplyTransform(transform=Affine(1.0, 0.0, 0.0,\n",
              "       -0.0, 1.0, 0.0), diagram=Empty()))), diagram2=Primitive(shape=Path(loc_trails=[Located(trail=Trail(segments=[Segment(offset=Vec2(1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, 1.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(-1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, -1.0), origin=Vec2(0.0, 0.0))], closed=True), location=Vec2(0.0, 0.0))]), style=Style(line_width_=None, line_color_=None, fill_color_=<Color orange>, fill_opacity_=0.76, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, 2.5,\n",
              "       0.0, 1.0, -0.5))))), diagram2=ApplyTransform(transform=Affine(1.0, 0.0, 0.0,\n",
              "       0.0, 1.0, 3.5), diagram=ApplyTransform(transform=Affine(0.0, 1.0, 0.0,\n",
              "       -1.0, 0.0, 0.0), diagram=Empty()))), diagram2=ApplyTransform(transform=Affine(1.0, 0.0, 0.0,\n",
              "       0.0, 1.0, 4.0), diagram=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44bb4b50>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44babf40>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44bab910>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44bab6d0>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44baa710>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44ba9c30>, diagram1=Primitive(shape=Path(loc_trails=[Located(trail=Trail(segments=[Segment(offset=Vec2(1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, 1.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(-1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, -1.0), origin=Vec2(0.0, 0.0))], closed=True), location=Vec2(0.0, 0.0))]), style=Style(line_width_=None, line_color_=None, fill_color_=<Color orange>, fill_opacity_=0.64, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, -0.5,\n",
              "       0.0, 1.0, -0.5)), diagram2=ApplyTransform(transform=Affine(1.0, 0.0, 0.5,\n",
              "       0.0, 1.0, 0.0), diagram=ApplyTransform(transform=Affine(1.0, 0.0, 0.0,\n",
              "       -0.0, 1.0, 0.0), diagram=Empty()))), diagram2=Primitive(shape=Path(loc_trails=[Located(trail=Trail(segments=[Segment(offset=Vec2(1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, 1.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(-1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, -1.0), origin=Vec2(0.0, 0.0))], closed=True), location=Vec2(0.0, 0.0))]), style=Style(line_width_=None, line_color_=None, fill_color_=<Color orange>, fill_opacity_=0.7, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, 0.5,\n",
              "       0.0, 1.0, -0.5))), diagram2=ApplyTransform(transform=Affine(1.0, 0.0, 1.5,\n",
              "       0.0, 1.0, 0.0), diagram=ApplyTransform(transform=Affine(1.0, 0.0, 0.0,\n",
              "       -0.0, 1.0, 0.0), diagram=Empty()))), diagram2=Primitive(shape=Path(loc_trails=[Located(trail=Trail(segments=[Segment(offset=Vec2(1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, 1.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(-1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, -1.0), origin=Vec2(0.0, 0.0))], closed=True), location=Vec2(0.0, 0.0))]), style=Style(line_width_=None, line_color_=None, fill_color_=<Color orange>, fill_opacity_=0.76, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, 1.5,\n",
              "       0.0, 1.0, -0.5))), diagram2=ApplyTransform(transform=Affine(1.0, 0.0, 2.5,\n",
              "       0.0, 1.0, 0.0), diagram=ApplyTransform(transform=Affine(1.0, 0.0, 0.0,\n",
              "       -0.0, 1.0, 0.0), diagram=Empty()))), diagram2=Primitive(shape=Path(loc_trails=[Located(trail=Trail(segments=[Segment(offset=Vec2(1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, 1.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(-1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, -1.0), origin=Vec2(0.0, 0.0))], closed=True), location=Vec2(0.0, 0.0))]), style=Style(line_width_=None, line_color_=None, fill_color_=<Color orange>, fill_opacity_=0.8200000000000001, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, 2.5,\n",
              "       0.0, 1.0, -0.5)))))), diagram2=Empty()))), diagram2=Primitive(shape=Spacer(width=1.0, height=0), style=Style(line_width_=None, line_color_=None, fill_color_=None, fill_opacity_=None, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, 5.50005,\n",
              "       0.0, 1.0, 0.0))), diagram2=ApplyTransform(transform=Affine(1.0, 0.0, 7.00005,\n",
              "       0.0, 1.0, 0.0), diagram=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44bed510>, diagram1=ApplyTransform(transform=Affine(1.0, 0.0, -0.5,\n",
              "       0.0, 1.0, -1.0), diagram=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44bbfee0>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44bbeb60>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44bbd840>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44bbd480>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44bb72e0>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44bb6800>, diagram1=Primitive(shape=Path(loc_trails=[Located(trail=Trail(segments=[Segment(offset=Vec2(1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, 1.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(-1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, -1.0), origin=Vec2(0.0, 0.0))], closed=True), location=Vec2(0.0, 0.0))]), style=Style(line_width_=None, line_color_=None, fill_color_=None, fill_opacity_=None, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, -0.5,\n",
              "       0.0, 1.0, -0.5)), diagram2=ApplyTransform(transform=Affine(1.0, 0.0, 0.5,\n",
              "       0.0, 1.0, 0.0), diagram=ApplyTransform(transform=Affine(1.0, 0.0, 0.0,\n",
              "       -0.0, 1.0, 0.0), diagram=Empty()))), diagram2=Primitive(shape=Path(loc_trails=[Located(trail=Trail(segments=[Segment(offset=Vec2(1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, 1.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(-1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, -1.0), origin=Vec2(0.0, 0.0))], closed=True), location=Vec2(0.0, 0.0))]), style=Style(line_width_=None, line_color_=None, fill_color_=<Color orange>, fill_opacity_=0.46, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, 0.5,\n",
              "       0.0, 1.0, -0.5))), diagram2=ApplyTransform(transform=Affine(1.0, 0.0, 0.0,\n",
              "       0.0, 1.0, 0.5), diagram=ApplyTransform(transform=Affine(0.0, 1.0, 0.0,\n",
              "       -1.0, 0.0, 0.0), diagram=Empty()))), diagram2=ApplyTransform(transform=Affine(1.0, 0.0, 0.0,\n",
              "       0.0, 1.0, 1.0), diagram=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44bbd270>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44bb7ac0>, diagram1=Primitive(shape=Path(loc_trails=[Located(trail=Trail(segments=[Segment(offset=Vec2(1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, 1.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(-1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, -1.0), origin=Vec2(0.0, 0.0))], closed=True), location=Vec2(0.0, 0.0))]), style=Style(line_width_=None, line_color_=None, fill_color_=<Color orange>, fill_opacity_=0.46, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, -0.5,\n",
              "       0.0, 1.0, -0.5)), diagram2=ApplyTransform(transform=Affine(1.0, 0.0, 0.5,\n",
              "       0.0, 1.0, 0.0), diagram=ApplyTransform(transform=Affine(1.0, 0.0, 0.0,\n",
              "       -0.0, 1.0, 0.0), diagram=Empty()))), diagram2=Primitive(shape=Path(loc_trails=[Located(trail=Trail(segments=[Segment(offset=Vec2(1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, 1.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(-1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, -1.0), origin=Vec2(0.0, 0.0))], closed=True), location=Vec2(0.0, 0.0))]), style=Style(line_width_=None, line_color_=None, fill_color_=<Color orange>, fill_opacity_=0.52, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, 0.5,\n",
              "       0.0, 1.0, -0.5))))), diagram2=ApplyTransform(transform=Affine(1.0, 0.0, 0.0,\n",
              "       0.0, 1.0, 1.5), diagram=ApplyTransform(transform=Affine(0.0, 1.0, 0.0,\n",
              "       -1.0, 0.0, 0.0), diagram=Empty()))), diagram2=ApplyTransform(transform=Affine(1.0, 0.0, 0.0,\n",
              "       0.0, 1.0, 2.0), diagram=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44bbf790>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44bbec80>, diagram1=Primitive(shape=Path(loc_trails=[Located(trail=Trail(segments=[Segment(offset=Vec2(1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, 1.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(-1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, -1.0), origin=Vec2(0.0, 0.0))], closed=True), location=Vec2(0.0, 0.0))]), style=Style(line_width_=None, line_color_=None, fill_color_=<Color orange>, fill_opacity_=0.52, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, -0.5,\n",
              "       0.0, 1.0, -0.5)), diagram2=ApplyTransform(transform=Affine(1.0, 0.0, 0.5,\n",
              "       0.0, 1.0, 0.0), diagram=ApplyTransform(transform=Affine(1.0, 0.0, 0.0,\n",
              "       -0.0, 1.0, 0.0), diagram=Empty()))), diagram2=Primitive(shape=Path(loc_trails=[Located(trail=Trail(segments=[Segment(offset=Vec2(1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, 1.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(-1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, -1.0), origin=Vec2(0.0, 0.0))], closed=True), location=Vec2(0.0, 0.0))]), style=Style(line_width_=None, line_color_=None, fill_color_=<Color orange>, fill_opacity_=0.5800000000000001, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, 0.5,\n",
              "       0.0, 1.0, -0.5)))))), diagram2=Empty())))))))), diagram2=Empty())))"
            ]
          },
          "execution_count": 3,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "# Example of broadcasting.\n",
        "examples = [(arange(4), arange(5)[:, None]) ,\n",
        "            (arange(3)[:, None], arange(2))]\n",
        "draw_examples(\"broadcast\", [{\"a\": a, \"b\":b, \"ret\": a + b} for a, b in examples])"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 4,
      "id": "0554b7e3",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 321
        },
        "execution": {
          "iopub.execute_input": "2022-07-13T00:15:16.799098Z",
          "iopub.status.busy": "2022-07-13T00:15:16.798780Z",
          "iopub.status.idle": "2022-07-13T00:15:16.910897Z",
          "shell.execute_reply": "2022-07-13T00:15:16.910310Z"
        },
        "id": "0554b7e3",
        "lines_to_end_of_cell_marker": 0,
        "lines_to_next_cell": 1,
        "outputId": "91e181fe-aa2a-460a-b3c1-9b6559e30d33"
      },
      "outputs": [
        {
          "data": {
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            "text/plain": [
              "Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44929420>, diagram1=Primitive(shape=Path(loc_trails=[Located(trail=Trail(segments=[Segment(offset=Vec2(16.80012, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, 14.400239999999998), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(-16.80012, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, -14.400239999999998), origin=Vec2(0.0, 0.0))], closed=True), location=Vec2(0.0, 0.0))]), style=Style(line_width_=None, line_color_=None, fill_color_=<Color white>, fill_opacity_=None, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, -8.40006,\n",
              "       0.0, 1.0, -7.200119999999999)), diagram2=ApplyTransform(transform=Affine(1.0, 0.0, -0.0,\n",
              "       0.0, 1.0, -6.6001199999999995), diagram=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c449281c0>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c4491bf40>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c4491b9a0>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c4491b4f0>, diagram1=Primitive(shape=Spacer(width=0, height=1), style=Style(line_width_=None, line_color_=None, fill_color_=None, fill_opacity_=None, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, 0.0,\n",
              "       0.0, 1.0, 0.0)), diagram2=Primitive(shape=Text(text='where', font_size=0.75), style=Style(line_width_=(<WidthType.NORMALIZED: 2>, 0), line_color_=None, fill_color_=<Color black>, fill_opacity_=None, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, 0.0,\n",
              "       0.0, 1.0, 0.5))), diagram2=Primitive(shape=Spacer(width=0, height=1), style=Style(line_width_=None, line_color_=None, fill_color_=None, fill_opacity_=None, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, 0.0,\n",
              "       0.0, 1.0, 1.0001))), diagram2=ApplyTransform(transform=Affine(1.0, 0.0, 0.0,\n",
              "       0.0, 1.0, 6.50015), diagram=ApplyTransform(transform=Affine(1.0, 0.0, -7.0,\n",
              "       0.0, 1.0, -4.00005), diagram=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c4491b280>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c4491a9e0>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c4491a650>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c4491a080>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44919e40>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44919a50>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44ace0b0>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44acd930>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44acd6c0>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44accfd0>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44accd00>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44acc670>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44acc340>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44ac3cd0>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44ac3940>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44ac3400>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44ab6fe0>, diagram1=ApplyTransform(transform=Affine(1.0, 0.0, -5e-05,\n",
              "       0.0, 1.0, -0.25005), diagram=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44a0a4d0>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44a0b700>, diagram1=Primitive(shape=Spacer(width=0, height=0.5), style=Style(line_width_=None, line_color_=None, fill_color_=None, fill_opacity_=None, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, 0.0,\n",
              "       0.0, 1.0, 0.0)), diagram2=Primitive(shape=Text(text='q', font_size=0.5), style=Style(line_width_=(<WidthType.NORMALIZED: 2>, 0.0), line_color_=None, fill_color_=<Color black>, fill_opacity_=None, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, 0.0,\n",
              "       0.0, 1.0, 0.25))), diagram2=Primitive(shape=Spacer(width=0, height=0.5), style=Style(line_width_=None, line_color_=None, fill_color_=None, fill_opacity_=None, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, 0.0,\n",
              "       0.0, 1.0, 0.5001)))), diagram2=Empty()), diagram2=Primitive(shape=Spacer(width=1.0, height=0), style=Style(line_width_=None, line_color_=None, fill_color_=None, fill_opacity_=None, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, 0.50005,\n",
              "       0.0, 1.0, 0.0))), diagram2=ApplyTransform(transform=Affine(1.0, 0.0, 1.5000499999999999,\n",
              "       0.0, 1.0, 0.0), diagram=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44ab7700>, diagram1=Primitive(shape=Path(loc_trails=[Located(trail=Trail(segments=[Segment(offset=Vec2(1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, 1.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(-1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, -1.0), origin=Vec2(0.0, 0.0))], closed=True), location=Vec2(0.0, 0.0))]), style=Style(line_width_=None, line_color_=None, fill_color_=None, fill_opacity_=None, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, -0.5,\n",
              "       0.0, 1.0, -0.5)), diagram2=Empty()))), diagram2=Primitive(shape=Spacer(width=1.0, height=0), style=Style(line_width_=None, line_color_=None, fill_color_=None, fill_opacity_=None, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, 2.50005,\n",
              "       0.0, 1.0, 0.0))), diagram2=ApplyTransform(transform=Affine(1.0, 0.0, 4.00005,\n",
              "       0.0, 1.0, 0.0), diagram=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44ab7dc0>, diagram1=ApplyTransform(transform=Affine(1.0, 0.0, -0.5,\n",
              "       0.0, 1.0, -0.0), diagram=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44a0b5b0>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44a08e20>, diagram1=Primitive(shape=Path(loc_trails=[Located(trail=Trail(segments=[Segment(offset=Vec2(1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, 1.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(-1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, -1.0), origin=Vec2(0.0, 0.0))], closed=True), location=Vec2(0.0, 0.0))]), style=Style(line_width_=None, line_color_=None, fill_color_=None, fill_opacity_=None, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, -0.5,\n",
              "       0.0, 1.0, -0.5)), diagram2=ApplyTransform(transform=Affine(1.0, 0.0, 0.5,\n",
              "       0.0, 1.0, 0.0), diagram=ApplyTransform(transform=Affine(1.0, 0.0, 0.0,\n",
              "       -0.0, 1.0, 0.0), diagram=Empty()))), diagram2=Primitive(shape=Path(loc_trails=[Located(trail=Trail(segments=[Segment(offset=Vec2(1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, 1.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(-1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, -1.0), origin=Vec2(0.0, 0.0))], closed=True), location=Vec2(0.0, 0.0))]), style=Style(line_width_=None, line_color_=None, fill_color_=<Color orange>, fill_opacity_=0.46, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, 0.5,\n",
              "       0.0, 1.0, -0.5)))), diagram2=Empty()))), diagram2=Primitive(shape=Spacer(width=1.0, height=0), style=Style(line_width_=None, line_color_=None, fill_color_=None, fill_opacity_=None, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, 5.50005,\n",
              "       0.0, 1.0, 0.0))), diagram2=ApplyTransform(transform=Affine(1.0, 0.0, 7.00005,\n",
              "       0.0, 1.0, 0.0), diagram=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44ac0b50>, diagram1=ApplyTransform(transform=Affine(1.0, 0.0, -0.5,\n",
              "       0.0, 1.0, -0.0), diagram=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44a247c0>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44bff190>, diagram1=Primitive(shape=Path(loc_trails=[Located(trail=Trail(segments=[Segment(offset=Vec2(1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, 1.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(-1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, -1.0), origin=Vec2(0.0, 0.0))], closed=True), location=Vec2(0.0, 0.0))]), style=Style(line_width_=None, line_color_=None, fill_color_=None, fill_opacity_=None, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, -0.5,\n",
              "       0.0, 1.0, -0.5)), diagram2=ApplyTransform(transform=Affine(1.0, 0.0, 0.5,\n",
              "       0.0, 1.0, 0.0), diagram=ApplyTransform(transform=Affine(1.0, 0.0, 0.0,\n",
              "       -0.0, 1.0, 0.0), diagram=Empty()))), diagram2=Primitive(shape=Path(loc_trails=[Located(trail=Trail(segments=[Segment(offset=Vec2(1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, 1.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(-1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, -1.0), origin=Vec2(0.0, 0.0))], closed=True), location=Vec2(0.0, 0.0))]), style=Style(line_width_=None, line_color_=None, fill_color_=<Color orange>, fill_opacity_=0.46, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, 0.5,\n",
              "       0.0, 1.0, -0.5)))), diagram2=Empty()))), diagram2=Primitive(shape=Spacer(width=1.0, height=0), style=Style(line_width_=None, line_color_=None, fill_color_=None, fill_opacity_=None, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, 8.50005,\n",
              "       0.0, 1.0, 0.0))), diagram2=ApplyTransform(transform=Affine(1.0, 0.0, 10.00005,\n",
              "       0.0, 1.0, 0.0), diagram=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44ac1930>, diagram1=ApplyTransform(transform=Affine(1.0, 0.0, -0.5,\n",
              "       0.0, 1.0, -0.5), diagram=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44a01300>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44a00f40>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44a26380>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44a25840>, diagram1=Primitive(shape=Path(loc_trails=[Located(trail=Trail(segments=[Segment(offset=Vec2(1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, 1.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(-1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, -1.0), origin=Vec2(0.0, 0.0))], closed=True), location=Vec2(0.0, 0.0))]), style=Style(line_width_=None, line_color_=None, fill_color_=None, fill_opacity_=None, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, -0.5,\n",
              "       0.0, 1.0, -0.5)), diagram2=ApplyTransform(transform=Affine(1.0, 0.0, 0.5,\n",
              "       0.0, 1.0, 0.0), diagram=ApplyTransform(transform=Affine(1.0, 0.0, 0.0,\n",
              "       -0.0, 1.0, 0.0), diagram=Empty()))), diagram2=Primitive(shape=Path(loc_trails=[Located(trail=Trail(segments=[Segment(offset=Vec2(1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, 1.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(-1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, -1.0), origin=Vec2(0.0, 0.0))], closed=True), location=Vec2(0.0, 0.0))]), style=Style(line_width_=None, line_color_=None, fill_color_=<Color orange>, fill_opacity_=0.46, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, 0.5,\n",
              "       0.0, 1.0, -0.5))), diagram2=ApplyTransform(transform=Affine(1.0, 0.0, 0.0,\n",
              "       0.0, 1.0, 0.5), diagram=ApplyTransform(transform=Affine(0.0, 1.0, 0.0,\n",
              "       -1.0, 0.0, 0.0), diagram=Empty()))), diagram2=ApplyTransform(transform=Affine(1.0, 0.0, 0.0,\n",
              "       0.0, 1.0, 1.0), diagram=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44a00d30>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44a245b0>, diagram1=Primitive(shape=Path(loc_trails=[Located(trail=Trail(segments=[Segment(offset=Vec2(1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, 1.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(-1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, -1.0), origin=Vec2(0.0, 0.0))], closed=True), location=Vec2(0.0, 0.0))]), style=Style(line_width_=None, line_color_=None, fill_color_=<Color orange>, fill_opacity_=0.46, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, -0.5,\n",
              "       0.0, 1.0, -0.5)), diagram2=ApplyTransform(transform=Affine(1.0, 0.0, 0.5,\n",
              "       0.0, 1.0, 0.0), diagram=ApplyTransform(transform=Affine(1.0, 0.0, 0.0,\n",
              "       -0.0, 1.0, 0.0), diagram=Empty()))), diagram2=Primitive(shape=Path(loc_trails=[Located(trail=Trail(segments=[Segment(offset=Vec2(1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, 1.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(-1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, -1.0), origin=Vec2(0.0, 0.0))], closed=True), location=Vec2(0.0, 0.0))]), style=Style(line_width_=None, line_color_=None, fill_color_=None, fill_opacity_=None, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, 0.5,\n",
              "       0.0, 1.0, -0.5)))))), diagram2=Empty()))), diagram2=Primitive(shape=Spacer(width=1.0, height=0), style=Style(line_width_=None, line_color_=None, fill_color_=None, fill_opacity_=None, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, 11.50005,\n",
              "       0.0, 1.0, 0.0))), diagram2=ApplyTransform(transform=Affine(1.0, 0.0, 13.00005,\n",
              "       0.0, 1.0, 0.0), diagram=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44ac2680>, diagram1=ApplyTransform(transform=Affine(1.0, 0.0, -0.5,\n",
              "       0.0, 1.0, -0.5), diagram=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44a69690>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44a692d0>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44a03190>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44a026b0>, diagram1=Primitive(shape=Path(loc_trails=[Located(trail=Trail(segments=[Segment(offset=Vec2(1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, 1.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(-1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, -1.0), origin=Vec2(0.0, 0.0))], closed=True), location=Vec2(0.0, 0.0))]), style=Style(line_width_=None, line_color_=None, fill_color_=None, fill_opacity_=None, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, -0.5,\n",
              "       0.0, 1.0, -0.5)), diagram2=ApplyTransform(transform=Affine(1.0, 0.0, 0.5,\n",
              "       0.0, 1.0, 0.0), diagram=ApplyTransform(transform=Affine(1.0, 0.0, 0.0,\n",
              "       -0.0, 1.0, 0.0), diagram=Empty()))), diagram2=Primitive(shape=Path(loc_trails=[Located(trail=Trail(segments=[Segment(offset=Vec2(1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, 1.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(-1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, -1.0), origin=Vec2(0.0, 0.0))], closed=True), location=Vec2(0.0, 0.0))]), style=Style(line_width_=None, line_color_=None, fill_color_=<Color orange>, fill_opacity_=0.46, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, 0.5,\n",
              "       0.0, 1.0, -0.5))), diagram2=ApplyTransform(transform=Affine(1.0, 0.0, 0.0,\n",
              "       0.0, 1.0, 0.5), diagram=ApplyTransform(transform=Affine(0.0, 1.0, 0.0,\n",
              "       -1.0, 0.0, 0.0), diagram=Empty()))), diagram2=ApplyTransform(transform=Affine(1.0, 0.0, 0.0,\n",
              "       0.0, 1.0, 1.0), diagram=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44a690c0>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44a03820>, diagram1=Primitive(shape=Path(loc_trails=[Located(trail=Trail(segments=[Segment(offset=Vec2(1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, 1.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(-1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, -1.0), origin=Vec2(0.0, 0.0))], closed=True), location=Vec2(0.0, 0.0))]), style=Style(line_width_=None, line_color_=None, fill_color_=<Color orange>, fill_opacity_=0.46, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, -0.5,\n",
              "       0.0, 1.0, -0.5)), diagram2=ApplyTransform(transform=Affine(1.0, 0.0, 0.5,\n",
              "       0.0, 1.0, 0.0), diagram=ApplyTransform(transform=Affine(1.0, 0.0, 0.0,\n",
              "       -0.0, 1.0, 0.0), diagram=Empty()))), diagram2=Primitive(shape=Path(loc_trails=[Located(trail=Trail(segments=[Segment(offset=Vec2(1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, 1.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(-1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, -1.0), origin=Vec2(0.0, 0.0))], closed=True), location=Vec2(0.0, 0.0))]), style=Style(line_width_=None, line_color_=None, fill_color_=None, fill_opacity_=None, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, 0.5,\n",
              "       0.0, 1.0, -0.5)))))), diagram2=Empty()))), diagram2=Primitive(shape=Spacer(width=1.0, height=0), style=Style(line_width_=None, line_color_=None, fill_color_=None, fill_opacity_=None, dashing_=None, output_size=None), transform=Affine(0.0, 1.0, 0.0,\n",
              "       -1.0, 0.0, 1.5))), diagram2=ApplyTransform(transform=Affine(1.0, 0.0, 0.0,\n",
              "       0.0, 1.0, 3.0), diagram=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44ae5cc0>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44ae5570>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44ae5300>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44ae4c10>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44ae4940>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44ae4550>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44ad7f40>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44ad7910>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44ad7580>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44ad6fe0>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44ace260>, diagram1=ApplyTransform(transform=Affine(1.0, 0.0, -5e-05,\n",
              "       0.0, 1.0, -0.25005), diagram=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44a6a200>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44a69cc0>, diagram1=Primitive(shape=Spacer(width=0, height=0.5), style=Style(line_width_=None, line_color_=None, fill_color_=None, fill_opacity_=None, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, 0.0,\n",
              "       0.0, 1.0, 0.0)), diagram2=Primitive(shape=Text(text='a', font_size=0.5), style=Style(line_width_=(<WidthType.NORMALIZED: 2>, 0.0), line_color_=None, fill_color_=<Color black>, fill_opacity_=None, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, 0.0,\n",
              "       0.0, 1.0, 0.25))), diagram2=Primitive(shape=Spacer(width=0, height=0.5), style=Style(line_width_=None, line_color_=None, fill_color_=None, fill_opacity_=None, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, 0.0,\n",
              "       0.0, 1.0, 0.5001)))), diagram2=Empty()), diagram2=Primitive(shape=Spacer(width=1.0, height=0), style=Style(line_width_=None, line_color_=None, fill_color_=None, fill_opacity_=None, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, 0.50005,\n",
              "       0.0, 1.0, 0.0))), diagram2=ApplyTransform(transform=Affine(1.0, 0.0, 1.5000499999999999,\n",
              "       0.0, 1.0, 0.0), diagram=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44acf5b0>, diagram1=Primitive(shape=Path(loc_trails=[Located(trail=Trail(segments=[Segment(offset=Vec2(1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, 1.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(-1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, -1.0), origin=Vec2(0.0, 0.0))], closed=True), location=Vec2(0.0, 0.0))]), style=Style(line_width_=None, line_color_=None, fill_color_=<Color orange>, fill_opacity_=1.0, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, -0.5,\n",
              "       0.0, 1.0, -0.5)), diagram2=Empty()))), diagram2=Primitive(shape=Spacer(width=1.0, height=0), style=Style(line_width_=None, line_color_=None, fill_color_=None, fill_opacity_=None, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, 2.50005,\n",
              "       0.0, 1.0, 0.0))), diagram2=ApplyTransform(transform=Affine(1.0, 0.0, 4.00005,\n",
              "       0.0, 1.0, 0.0), diagram=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44acfb80>, diagram1=ApplyTransform(transform=Affine(1.0, 0.0, -0.5,\n",
              "       0.0, 1.0, -0.0), diagram=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44a6bf10>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44a6baf0>, diagram1=Primitive(shape=Path(loc_trails=[Located(trail=Trail(segments=[Segment(offset=Vec2(1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, 1.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(-1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, -1.0), origin=Vec2(0.0, 0.0))], closed=True), location=Vec2(0.0, 0.0))]), style=Style(line_width_=None, line_color_=None, fill_color_=<Color orange>, fill_opacity_=0.46, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, -0.5,\n",
              "       0.0, 1.0, -0.5)), diagram2=ApplyTransform(transform=Affine(1.0, 0.0, 0.5,\n",
              "       0.0, 1.0, 0.0), diagram=ApplyTransform(transform=Affine(1.0, 0.0, 0.0,\n",
              "       -0.0, 1.0, 0.0), diagram=Empty()))), diagram2=Primitive(shape=Path(loc_trails=[Located(trail=Trail(segments=[Segment(offset=Vec2(1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, 1.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(-1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, -1.0), origin=Vec2(0.0, 0.0))], closed=True), location=Vec2(0.0, 0.0))]), style=Style(line_width_=None, line_color_=None, fill_color_=<Color orange>, fill_opacity_=0.46, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, 0.5,\n",
              "       0.0, 1.0, -0.5)))), diagram2=Empty()))), diagram2=Primitive(shape=Spacer(width=1.0, height=0), style=Style(line_width_=None, line_color_=None, fill_color_=None, fill_opacity_=None, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, 5.50005,\n",
              "       0.0, 1.0, 0.0))), diagram2=ApplyTransform(transform=Affine(1.0, 0.0, 7.00005,\n",
              "       0.0, 1.0, 0.0), diagram=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44ad4d30>, diagram1=Primitive(shape=Path(loc_trails=[Located(trail=Trail(segments=[Segment(offset=Vec2(1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, 1.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(-1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, -1.0), origin=Vec2(0.0, 0.0))], closed=True), location=Vec2(0.0, 0.0))]), style=Style(line_width_=None, line_color_=None, fill_color_=<Color orange>, fill_opacity_=0.46, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, -0.5,\n",
              "       0.0, 1.0, -0.5)), diagram2=Empty()))), diagram2=Primitive(shape=Spacer(width=1.0, height=0), style=Style(line_width_=None, line_color_=None, fill_color_=None, fill_opacity_=None, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, 8.50005,\n",
              "       0.0, 1.0, 0.0))), diagram2=ApplyTransform(transform=Affine(1.0, 0.0, 10.00005,\n",
              "       0.0, 1.0, 0.0), diagram=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44ad5ae0>, diagram1=Primitive(shape=Path(loc_trails=[Located(trail=Trail(segments=[Segment(offset=Vec2(1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, 1.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(-1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, -1.0), origin=Vec2(0.0, 0.0))], closed=True), location=Vec2(0.0, 0.0))]), style=Style(line_width_=None, line_color_=None, fill_color_=<Color orange>, fill_opacity_=0.46, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, -0.5,\n",
              "       0.0, 1.0, -0.5)), diagram2=Empty()))), diagram2=Primitive(shape=Spacer(width=1.0, height=0), style=Style(line_width_=None, line_color_=None, fill_color_=None, fill_opacity_=None, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, 11.50005,\n",
              "       0.0, 1.0, 0.0))), diagram2=ApplyTransform(transform=Affine(1.0, 0.0, 13.00005,\n",
              "       0.0, 1.0, 0.0), diagram=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44ad6230>, diagram1=ApplyTransform(transform=Affine(1.0, 0.0, -0.0,\n",
              "       0.0, 1.0, -0.5), diagram=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44a6eb90>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44a6d030>, diagram1=Primitive(shape=Path(loc_trails=[Located(trail=Trail(segments=[Segment(offset=Vec2(1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, 1.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(-1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, -1.0), origin=Vec2(0.0, 0.0))], closed=True), location=Vec2(0.0, 0.0))]), style=Style(line_width_=None, line_color_=None, fill_color_=None, fill_opacity_=None, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, -0.5,\n",
              "       0.0, 1.0, -0.5)), diagram2=ApplyTransform(transform=Affine(1.0, 0.0, 0.0,\n",
              "       0.0, 1.0, 0.5), diagram=ApplyTransform(transform=Affine(0.0, 1.0, 0.0,\n",
              "       -1.0, 0.0, 0.0), diagram=Empty()))), diagram2=Primitive(shape=Path(loc_trails=[Located(trail=Trail(segments=[Segment(offset=Vec2(1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, 1.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(-1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, -1.0), origin=Vec2(0.0, 0.0))], closed=True), location=Vec2(0.0, 0.0))]), style=Style(line_width_=None, line_color_=None, fill_color_=<Color orange>, fill_opacity_=1.0, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, -0.5,\n",
              "       0.0, 1.0, 0.5)))), diagram2=Empty()))))), diagram2=Primitive(shape=Spacer(width=1.0, height=0), style=Style(line_width_=None, line_color_=None, fill_color_=None, fill_opacity_=None, dashing_=None, output_size=None), transform=Affine(0.0, 1.0, 0.0,\n",
              "       -1.0, 0.0, 4.5))), diagram2=ApplyTransform(transform=Affine(1.0, 0.0, 0.0,\n",
              "       0.0, 1.0, 5.50005), diagram=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44afd8d0>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44afd180>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44afcf10>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44afc820>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44afc550>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44af3e80>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44af3b50>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44af3520>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44af3190>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44af2bf0>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44ae5e70>, diagram1=ApplyTransform(transform=Affine(1.0, 0.0, -5e-05,\n",
              "       0.0, 1.0, -0.25005), diagram=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44a6f850>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44a6f310>, diagram1=Primitive(shape=Spacer(width=0, height=0.5), style=Style(line_width_=None, line_color_=None, fill_color_=None, fill_opacity_=None, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, 0.0,\n",
              "       0.0, 1.0, 0.0)), diagram2=Primitive(shape=Text(text='b', font_size=0.5), style=Style(line_width_=(<WidthType.NORMALIZED: 2>, 0.0), line_color_=None, fill_color_=<Color black>, fill_opacity_=None, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, 0.0,\n",
              "       0.0, 1.0, 0.25))), diagram2=Primitive(shape=Spacer(width=0, height=0.5), style=Style(line_width_=None, line_color_=None, fill_color_=None, fill_opacity_=None, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, 0.0,\n",
              "       0.0, 1.0, 0.5001)))), diagram2=Empty()), diagram2=Primitive(shape=Spacer(width=1.0, height=0), style=Style(line_width_=None, line_color_=None, fill_color_=None, fill_opacity_=None, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, 0.50005,\n",
              "       0.0, 1.0, 0.0))), diagram2=ApplyTransform(transform=Affine(1.0, 0.0, 1.5000499999999999,\n",
              "       0.0, 1.0, 0.0), diagram=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44ae71c0>, diagram1=Primitive(shape=Path(loc_trails=[Located(trail=Trail(segments=[Segment(offset=Vec2(1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, 1.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(-1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, -1.0), origin=Vec2(0.0, 0.0))], closed=True), location=Vec2(0.0, 0.0))]), style=Style(line_width_=None, line_color_=None, fill_color_=None, fill_opacity_=None, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, -0.5,\n",
              "       0.0, 1.0, -0.5)), diagram2=Empty()))), diagram2=Primitive(shape=Spacer(width=1.0, height=0), style=Style(line_width_=None, line_color_=None, fill_color_=None, fill_opacity_=None, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, 2.50005,\n",
              "       0.0, 1.0, 0.0))), diagram2=ApplyTransform(transform=Affine(1.0, 0.0, 4.00005,\n",
              "       0.0, 1.0, 0.0), diagram=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44ae7790>, diagram1=ApplyTransform(transform=Affine(1.0, 0.0, -0.5,\n",
              "       0.0, 1.0, -0.0), diagram=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44a7dcf0>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44a7ca60>, diagram1=Primitive(shape=Path(loc_trails=[Located(trail=Trail(segments=[Segment(offset=Vec2(1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, 1.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(-1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, -1.0), origin=Vec2(0.0, 0.0))], closed=True), location=Vec2(0.0, 0.0))]), style=Style(line_width_=None, line_color_=None, fill_color_=<Color blue>, fill_opacity_=1.0, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, -0.5,\n",
              "       0.0, 1.0, -0.5)), diagram2=ApplyTransform(transform=Affine(1.0, 0.0, 0.5,\n",
              "       0.0, 1.0, 0.0), diagram=ApplyTransform(transform=Affine(1.0, 0.0, 0.0,\n",
              "       -0.0, 1.0, 0.0), diagram=Empty()))), diagram2=Primitive(shape=Path(loc_trails=[Located(trail=Trail(segments=[Segment(offset=Vec2(1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, 1.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(-1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, -1.0), origin=Vec2(0.0, 0.0))], closed=True), location=Vec2(0.0, 0.0))]), style=Style(line_width_=None, line_color_=None, fill_color_=None, fill_opacity_=None, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, 0.5,\n",
              "       0.0, 1.0, -0.5)))), diagram2=Empty()))), diagram2=Primitive(shape=Spacer(width=1.0, height=0), style=Style(line_width_=None, line_color_=None, fill_color_=None, fill_opacity_=None, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, 5.50005,\n",
              "       0.0, 1.0, 0.0))), diagram2=ApplyTransform(transform=Affine(1.0, 0.0, 7.00005,\n",
              "       0.0, 1.0, 0.0), diagram=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44af0460>, diagram1=ApplyTransform(transform=Affine(1.0, 0.0, -0.5,\n",
              "       0.0, 1.0, -0.0), diagram=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44a7fd00>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44a7e980>, diagram1=Primitive(shape=Path(loc_trails=[Located(trail=Trail(segments=[Segment(offset=Vec2(1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, 1.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(-1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, -1.0), origin=Vec2(0.0, 0.0))], closed=True), location=Vec2(0.0, 0.0))]), style=Style(line_width_=None, line_color_=None, fill_color_=<Color blue>, fill_opacity_=1.0, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, -0.5,\n",
              "       0.0, 1.0, -0.5)), diagram2=ApplyTransform(transform=Affine(1.0, 0.0, 0.5,\n",
              "       0.0, 1.0, 0.0), diagram=ApplyTransform(transform=Affine(1.0, 0.0, 0.0,\n",
              "       -0.0, 1.0, 0.0), diagram=Empty()))), diagram2=Primitive(shape=Path(loc_trails=[Located(trail=Trail(segments=[Segment(offset=Vec2(1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, 1.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(-1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, -1.0), origin=Vec2(0.0, 0.0))], closed=True), location=Vec2(0.0, 0.0))]), style=Style(line_width_=None, line_color_=None, fill_color_=None, fill_opacity_=None, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, 0.5,\n",
              "       0.0, 1.0, -0.5)))), diagram2=Empty()))), diagram2=Primitive(shape=Spacer(width=1.0, height=0), style=Style(line_width_=None, line_color_=None, fill_color_=None, fill_opacity_=None, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, 8.50005,\n",
              "       0.0, 1.0, 0.0))), diagram2=ApplyTransform(transform=Affine(1.0, 0.0, 10.00005,\n",
              "       0.0, 1.0, 0.0), diagram=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44af10f0>, diagram1=ApplyTransform(transform=Affine(1.0, 0.0, -0.5,\n",
              "       0.0, 1.0, -0.0), diagram=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44a85d50>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44a849d0>, diagram1=Primitive(shape=Path(loc_trails=[Located(trail=Trail(segments=[Segment(offset=Vec2(1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, 1.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(-1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, -1.0), origin=Vec2(0.0, 0.0))], closed=True), location=Vec2(0.0, 0.0))]), style=Style(line_width_=None, line_color_=None, fill_color_=<Color blue>, fill_opacity_=1.0, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, -0.5,\n",
              "       0.0, 1.0, -0.5)), diagram2=ApplyTransform(transform=Affine(1.0, 0.0, 0.5,\n",
              "       0.0, 1.0, 0.0), diagram=ApplyTransform(transform=Affine(1.0, 0.0, 0.0,\n",
              "       -0.0, 1.0, 0.0), diagram=Empty()))), diagram2=Primitive(shape=Path(loc_trails=[Located(trail=Trail(segments=[Segment(offset=Vec2(1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, 1.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(-1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, -1.0), origin=Vec2(0.0, 0.0))], closed=True), location=Vec2(0.0, 0.0))]), style=Style(line_width_=None, line_color_=None, fill_color_=None, fill_opacity_=None, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, 0.5,\n",
              "       0.0, 1.0, -0.5)))), diagram2=Empty()))), diagram2=Primitive(shape=Spacer(width=1.0, height=0), style=Style(line_width_=None, line_color_=None, fill_color_=None, fill_opacity_=None, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, 11.50005,\n",
              "       0.0, 1.0, 0.0))), diagram2=ApplyTransform(transform=Affine(1.0, 0.0, 13.00005,\n",
              "       0.0, 1.0, 0.0), diagram=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44af1e40>, diagram1=ApplyTransform(transform=Affine(1.0, 0.0, -0.5,\n",
              "       0.0, 1.0, -0.0), diagram=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44a87d60>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44a869e0>, diagram1=Primitive(shape=Path(loc_trails=[Located(trail=Trail(segments=[Segment(offset=Vec2(1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, 1.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(-1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, -1.0), origin=Vec2(0.0, 0.0))], closed=True), location=Vec2(0.0, 0.0))]), style=Style(line_width_=None, line_color_=None, fill_color_=<Color blue>, fill_opacity_=1.0, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, -0.5,\n",
              "       0.0, 1.0, -0.5)), diagram2=ApplyTransform(transform=Affine(1.0, 0.0, 0.5,\n",
              "       0.0, 1.0, 0.0), diagram=ApplyTransform(transform=Affine(1.0, 0.0, 0.0,\n",
              "       -0.0, 1.0, 0.0), diagram=Empty()))), diagram2=Primitive(shape=Path(loc_trails=[Located(trail=Trail(segments=[Segment(offset=Vec2(1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, 1.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(-1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, -1.0), origin=Vec2(0.0, 0.0))], closed=True), location=Vec2(0.0, 0.0))]), style=Style(line_width_=None, line_color_=None, fill_color_=None, fill_opacity_=None, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, 0.5,\n",
              "       0.0, 1.0, -0.5)))), diagram2=Empty()))))), diagram2=Primitive(shape=Spacer(width=1.0, height=0), style=Style(line_width_=None, line_color_=None, fill_color_=None, fill_opacity_=None, dashing_=None, output_size=None), transform=Affine(0.0, 1.0, 0.0,\n",
              "       -1.0, 0.0, 6.5001))), diagram2=ApplyTransform(transform=Affine(1.0, 0.0, 0.0,\n",
              "       0.0, 1.0, 8.0001), diagram=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c449194e0>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44918d90>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44918b20>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44918430>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c4490ffa0>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c4490fa90>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c4490f760>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c4490f130>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c4490eda0>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c4490e860>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44afda80>, diagram1=ApplyTransform(transform=Affine(1.0, 0.0, -5e-05,\n",
              "       0.0, 1.0, -0.25005), diagram=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44a909d0>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44a90520>, diagram1=Primitive(shape=Spacer(width=0, height=0.5), style=Style(line_width_=None, line_color_=None, fill_color_=None, fill_opacity_=None, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, 0.0,\n",
              "       0.0, 1.0, 0.0)), diagram2=Primitive(shape=Text(text='ret', font_size=0.5), style=Style(line_width_=(<WidthType.NORMALIZED: 2>, 0.0), line_color_=None, fill_color_=<Color black>, fill_opacity_=None, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, 0.0,\n",
              "       0.0, 1.0, 0.25))), diagram2=Primitive(shape=Spacer(width=0, height=0.5), style=Style(line_width_=None, line_color_=None, fill_color_=None, fill_opacity_=None, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, 0.0,\n",
              "       0.0, 1.0, 0.5001)))), diagram2=Empty()), diagram2=Primitive(shape=Spacer(width=1.0, height=0), style=Style(line_width_=None, line_color_=None, fill_color_=None, fill_opacity_=None, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, 0.50005,\n",
              "       0.0, 1.0, 0.0))), diagram2=ApplyTransform(transform=Affine(1.0, 0.0, 1.5000499999999999,\n",
              "       0.0, 1.0, 0.0), diagram=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44afedd0>, diagram1=Primitive(shape=Path(loc_trails=[Located(trail=Trail(segments=[Segment(offset=Vec2(1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, 1.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(-1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, -1.0), origin=Vec2(0.0, 0.0))], closed=True), location=Vec2(0.0, 0.0))]), style=Style(line_width_=None, line_color_=None, fill_color_=None, fill_opacity_=None, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, -0.5,\n",
              "       0.0, 1.0, -0.5)), diagram2=Empty()))), diagram2=Primitive(shape=Spacer(width=1.0, height=0), style=Style(line_width_=None, line_color_=None, fill_color_=None, fill_opacity_=None, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, 2.50005,\n",
              "       0.0, 1.0, 0.0))), diagram2=ApplyTransform(transform=Affine(1.0, 0.0, 4.00005,\n",
              "       0.0, 1.0, 0.0), diagram=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44aff3a0>, diagram1=ApplyTransform(transform=Affine(1.0, 0.0, -0.5,\n",
              "       0.0, 1.0, -0.0), diagram=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44a92e90>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44a92380>, diagram1=Primitive(shape=Path(loc_trails=[Located(trail=Trail(segments=[Segment(offset=Vec2(1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, 1.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(-1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, -1.0), origin=Vec2(0.0, 0.0))], closed=True), location=Vec2(0.0, 0.0))]), style=Style(line_width_=None, line_color_=None, fill_color_=<Color blue>, fill_opacity_=1.0, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, -0.5,\n",
              "       0.0, 1.0, -0.5)), diagram2=ApplyTransform(transform=Affine(1.0, 0.0, 0.5,\n",
              "       0.0, 1.0, 0.0), diagram=ApplyTransform(transform=Affine(1.0, 0.0, 0.0,\n",
              "       -0.0, 1.0, 0.0), diagram=Empty()))), diagram2=Primitive(shape=Path(loc_trails=[Located(trail=Trail(segments=[Segment(offset=Vec2(1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, 1.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(-1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, -1.0), origin=Vec2(0.0, 0.0))], closed=True), location=Vec2(0.0, 0.0))]), style=Style(line_width_=None, line_color_=None, fill_color_=<Color orange>, fill_opacity_=0.46, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, 0.5,\n",
              "       0.0, 1.0, -0.5)))), diagram2=Empty()))), diagram2=Primitive(shape=Spacer(width=1.0, height=0), style=Style(line_width_=None, line_color_=None, fill_color_=None, fill_opacity_=None, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, 5.50005,\n",
              "       0.0, 1.0, 0.0))), diagram2=ApplyTransform(transform=Affine(1.0, 0.0, 7.00005,\n",
              "       0.0, 1.0, 0.0), diagram=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c4490c070>, diagram1=ApplyTransform(transform=Affine(1.0, 0.0, -0.5,\n",
              "       0.0, 1.0, -0.0), diagram=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44a9cf40>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44a93eb0>, diagram1=Primitive(shape=Path(loc_trails=[Located(trail=Trail(segments=[Segment(offset=Vec2(1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, 1.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(-1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, -1.0), origin=Vec2(0.0, 0.0))], closed=True), location=Vec2(0.0, 0.0))]), style=Style(line_width_=None, line_color_=None, fill_color_=<Color blue>, fill_opacity_=1.0, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, -0.5,\n",
              "       0.0, 1.0, -0.5)), diagram2=ApplyTransform(transform=Affine(1.0, 0.0, 0.5,\n",
              "       0.0, 1.0, 0.0), diagram=ApplyTransform(transform=Affine(1.0, 0.0, 0.0,\n",
              "       -0.0, 1.0, 0.0), diagram=Empty()))), diagram2=Primitive(shape=Path(loc_trails=[Located(trail=Trail(segments=[Segment(offset=Vec2(1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, 1.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(-1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, -1.0), origin=Vec2(0.0, 0.0))], closed=True), location=Vec2(0.0, 0.0))]), style=Style(line_width_=None, line_color_=None, fill_color_=<Color orange>, fill_opacity_=0.46, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, 0.5,\n",
              "       0.0, 1.0, -0.5)))), diagram2=Empty()))), diagram2=Primitive(shape=Spacer(width=1.0, height=0), style=Style(line_width_=None, line_color_=None, fill_color_=None, fill_opacity_=None, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, 8.50005,\n",
              "       0.0, 1.0, 0.0))), diagram2=ApplyTransform(transform=Affine(1.0, 0.0, 10.00005,\n",
              "       0.0, 1.0, 0.0), diagram=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c4490cd90>, diagram1=ApplyTransform(transform=Affine(1.0, 0.0, -0.5,\n",
              "       0.0, 1.0, -0.5), diagram=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44aa5750>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44aa5330>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44a9efb0>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44a9e4a0>, diagram1=Primitive(shape=Path(loc_trails=[Located(trail=Trail(segments=[Segment(offset=Vec2(1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, 1.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(-1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, -1.0), origin=Vec2(0.0, 0.0))], closed=True), location=Vec2(0.0, 0.0))]), style=Style(line_width_=None, line_color_=None, fill_color_=<Color blue>, fill_opacity_=1.0, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, -0.5,\n",
              "       0.0, 1.0, -0.5)), diagram2=ApplyTransform(transform=Affine(1.0, 0.0, 0.5,\n",
              "       0.0, 1.0, 0.0), diagram=ApplyTransform(transform=Affine(1.0, 0.0, 0.0,\n",
              "       -0.0, 1.0, 0.0), diagram=Empty()))), diagram2=Primitive(shape=Path(loc_trails=[Located(trail=Trail(segments=[Segment(offset=Vec2(1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, 1.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(-1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, -1.0), origin=Vec2(0.0, 0.0))], closed=True), location=Vec2(0.0, 0.0))]), style=Style(line_width_=None, line_color_=None, fill_color_=<Color orange>, fill_opacity_=0.46, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, 0.5,\n",
              "       0.0, 1.0, -0.5))), diagram2=ApplyTransform(transform=Affine(1.0, 0.0, 0.0,\n",
              "       0.0, 1.0, 0.5), diagram=ApplyTransform(transform=Affine(0.0, 1.0, 0.0,\n",
              "       -1.0, 0.0, 0.0), diagram=Empty()))), diagram2=ApplyTransform(transform=Affine(1.0, 0.0, 0.0,\n",
              "       0.0, 1.0, 1.0), diagram=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44aa5090>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44a9f6a0>, diagram1=Primitive(shape=Path(loc_trails=[Located(trail=Trail(segments=[Segment(offset=Vec2(1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, 1.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(-1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, -1.0), origin=Vec2(0.0, 0.0))], closed=True), location=Vec2(0.0, 0.0))]), style=Style(line_width_=None, line_color_=None, fill_color_=<Color orange>, fill_opacity_=0.46, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, -0.5,\n",
              "       0.0, 1.0, -0.5)), diagram2=ApplyTransform(transform=Affine(1.0, 0.0, 0.5,\n",
              "       0.0, 1.0, 0.0), diagram=ApplyTransform(transform=Affine(1.0, 0.0, 0.0,\n",
              "       -0.0, 1.0, 0.0), diagram=Empty()))), diagram2=Primitive(shape=Path(loc_trails=[Located(trail=Trail(segments=[Segment(offset=Vec2(1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, 1.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(-1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, -1.0), origin=Vec2(0.0, 0.0))], closed=True), location=Vec2(0.0, 0.0))]), style=Style(line_width_=None, line_color_=None, fill_color_=None, fill_opacity_=None, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, 0.5,\n",
              "       0.0, 1.0, -0.5)))))), diagram2=Empty()))), diagram2=Primitive(shape=Spacer(width=1.0, height=0), style=Style(line_width_=None, line_color_=None, fill_color_=None, fill_opacity_=None, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, 11.50005,\n",
              "       0.0, 1.0, 0.0))), diagram2=ApplyTransform(transform=Affine(1.0, 0.0, 13.00005,\n",
              "       0.0, 1.0, 0.0), diagram=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c4490dae0>, diagram1=ApplyTransform(transform=Affine(1.0, 0.0, -0.5,\n",
              "       0.0, 1.0, -0.5), diagram=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44ab5de0>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44ab4c10>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44aa7640>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44aa6350>, diagram1=Primitive(shape=Path(loc_trails=[Located(trail=Trail(segments=[Segment(offset=Vec2(1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, 1.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(-1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, -1.0), origin=Vec2(0.0, 0.0))], closed=True), location=Vec2(0.0, 0.0))]), style=Style(line_width_=None, line_color_=None, fill_color_=<Color blue>, fill_opacity_=1.0, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, -0.5,\n",
              "       0.0, 1.0, -0.5)), diagram2=ApplyTransform(transform=Affine(1.0, 0.0, 0.5,\n",
              "       0.0, 1.0, 0.0), diagram=ApplyTransform(transform=Affine(1.0, 0.0, 0.0,\n",
              "       -0.0, 1.0, 0.0), diagram=Empty()))), diagram2=Primitive(shape=Path(loc_trails=[Located(trail=Trail(segments=[Segment(offset=Vec2(1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, 1.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(-1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, -1.0), origin=Vec2(0.0, 0.0))], closed=True), location=Vec2(0.0, 0.0))]), style=Style(line_width_=None, line_color_=None, fill_color_=None, fill_opacity_=None, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, 0.5,\n",
              "       0.0, 1.0, -0.5))), diagram2=ApplyTransform(transform=Affine(1.0, 0.0, 0.0,\n",
              "       0.0, 1.0, 0.5), diagram=ApplyTransform(transform=Affine(0.0, 1.0, 0.0,\n",
              "       -1.0, 0.0, 0.0), diagram=Empty()))), diagram2=ApplyTransform(transform=Affine(1.0, 0.0, 0.0,\n",
              "       0.0, 1.0, 1.0), diagram=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44ab5720>, diagram1=Compose(envelope=<chalk.envelope.Envelope object at 0x7f0c44ab45e0>, diagram1=Primitive(shape=Path(loc_trails=[Located(trail=Trail(segments=[Segment(offset=Vec2(1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, 1.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(-1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, -1.0), origin=Vec2(0.0, 0.0))], closed=True), location=Vec2(0.0, 0.0))]), style=Style(line_width_=None, line_color_=None, fill_color_=<Color orange>, fill_opacity_=1.0, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, -0.5,\n",
              "       0.0, 1.0, -0.5)), diagram2=ApplyTransform(transform=Affine(1.0, 0.0, 0.5,\n",
              "       0.0, 1.0, 0.0), diagram=ApplyTransform(transform=Affine(1.0, 0.0, 0.0,\n",
              "       -0.0, 1.0, 0.0), diagram=Empty()))), diagram2=Primitive(shape=Path(loc_trails=[Located(trail=Trail(segments=[Segment(offset=Vec2(1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, 1.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(-1.0, 0.0), origin=Vec2(0.0, 0.0)), Segment(offset=Vec2(0.0, -1.0), origin=Vec2(0.0, 0.0))], closed=True), location=Vec2(0.0, 0.0))]), style=Style(line_width_=None, line_color_=None, fill_color_=None, fill_opacity_=None, dashing_=None, output_size=None), transform=Affine(1.0, 0.0, 0.5,\n",
              "       0.0, 1.0, -0.5)))))), diagram2=Empty())))))))), diagram2=Empty())))"
            ]
          },
          "execution_count": 4,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "def where(q, a, b):\n",
        "    \"Use this function to replace an if-statement.\"\n",
        "    return (q * a) + (~q) * b\n",
        "\n",
        "# In diagrams, orange is positive/True, white is zero/False, and blue is negative.\n",
        "\n",
        "examples = [(tensor([False]), tensor([10]), tensor([0])),\n",
        "            (tensor([False, True]), tensor([1, 1]), tensor([-10, 0])),\n",
        "            (tensor([False, True]), tensor([1]), tensor([-10, 0])),\n",
        "            (tensor([[False, True], [True, False]]), tensor([1]), tensor([-10, 0])),\n",
        "            (tensor([[False, True], [True, False]]), tensor([[0], [10]]), tensor([-10, 0])),\n",
        "           ]\n",
        "draw_examples(\"where\", [{\"q\": q, \"a\":a, \"b\":b, \"ret\": where(q, a, b)} for q, a, b in examples])"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "06ef7f29",
      "metadata": {
        "id": "06ef7f29"
      },
      "source": [
        "## Puzzle 1 - ones\n",
        "\n",
        "Compute [ones](https://numpy.org/doc/stable/reference/generated/numpy.ones.html) - the vector of all ones."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 5,
      "id": "e46e4ada",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 321
        },
        "execution": {
          "iopub.execute_input": "2022-07-13T00:15:16.915061Z",
          "iopub.status.busy": "2022-07-13T00:15:16.914716Z",
          "iopub.status.idle": "2022-07-13T00:15:17.727959Z",
          "shell.execute_reply": "2022-07-13T00:15:17.727364Z"
        },
        "id": "e46e4ada",
        "outputId": "0746acd8-5631-4ecd-b303-8d33b4f64376"
      },
      "outputs": [
        {
          "data": {
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              "<svg xmlns=\"http://www.w3.org/2000/svg\" xmlns:ev=\"http://www.w3.org/2001/xml-events\" xmlns:xlink=\"http://www.w3.org/1999/xlink\" baseProfile=\"full\" height=\"300\" version=\"1.1\" width=\"779\"><defs><marker id=\"arrow\" markerHeight=\"3.5\" markerWidth=\"5\" orient=\"auto\" refX=\"5.0\" refY=\"1.7\"><polygon points=\"0,0 5,1.75 0,3.5\"/></marker></defs><g style=\"fill:white;\"><g transform=\"matrix(1.0, 0.0, 0.0, 1.0, 389.9796012239267, 150.00000000000003)\"><g transform=\"matrix(47.61619064760877, 0.0, 0.0, 47.61619064760877, 0.0, 0.0)\"><g><g transform=\"matrix(1.0, 0.0, 0.0, 1.0, -0.0, 2.220446049250313e-16)\"><g><g style=\"fill: #ffffff;stroke: black;stroke-width: 2.3369999999999997;\" transform=\"matrix(1.0, 0.0, 0.0, 1.0, -7.800059999999999, -3.0001799999999994)\"><path d=\"M 0.0 0.0 L 15.600119999999999 0.0 L 15.600119999999999 6.000359999999999 L 0.0 6.000359999999999 L 0.0 0.0 Z\" style=\"vector-effect: non-scaling-stroke;\"/></g><g transform=\"matrix(1.0, 0.0, 0.0, 1.0, -0.0, -2.4001799999999998)\"><g><g><g><g><g style=\"stroke: black;stroke-width: 2.3369999999999997;\" transform=\"matrix(1.0, 0.0, 0.0, 1.0, 0.0, 0.0)\"><g/></g><g style=\"fill: #000000;stroke: black;stroke-width: 0.0;\" transform=\"matrix(1.0, 0.0, 0.0, 1.0, 0.0, 0.5)\"><text style=\"text-align:center; text-anchor:middle; dominant-baseline:middle;\n",
              "                      font-family:sans-serif; font-weight: bold;\n",
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              "                      font-size:0.5px;\n",
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              "                      font-family:sans-serif; font-weight: bold;\n",
              "                      font-size:0.5px;\n",
              "                      vector-effect: non-scaling-stroke;\" transform=\"translate(-5e-05, 0)\">yours</text></g></g><g style=\"stroke: black;stroke-width: 2.3369999999999997;\" transform=\"matrix(1.0, 0.0, 0.0, 1.0, 0.0, 0.5001)\"><g/></g></g></g><g/></g><g style=\"stroke: black;stroke-width: 2.3369999999999997;\" transform=\"matrix(1.0, 0.0, 0.0, 1.0, 0.50005, 0.0)\"><g/></g></g><g transform=\"matrix(1.0, 0.0, 0.0, 1.0, 2.50005, 0.0)\"><g><g transform=\"matrix(1.0, 0.0, 0.0, 1.0, -1.0, -0.0)\"><g><g><g><g><g style=\"fill: #ffa500;stroke: black;stroke-width: 2.3369999999999997;fill-opacity: 0.46;\" transform=\"matrix(1.0, 0.0, 0.0, 1.0, -0.5, -0.5)\"><path d=\"M 0.0 0.0 L 1.0 0.0 L 1.0 1.0 L 0.0 1.0 L 0.0 0.0 Z\" style=\"vector-effect: non-scaling-stroke;\"/></g><g transform=\"matrix(1.0, 0.0, 0.0, 1.0, 0.5, 0.0)\"><g transform=\"matrix(1.0, -0.0, 0.0, 1.0, 0.0, 0.0)\"><g/></g></g></g><g style=\"fill: #ffa500;stroke: black;stroke-width: 2.3369999999999997;fill-opacity: 0.46;\" transform=\"matrix(1.0, 0.0, 0.0, 1.0, 0.5, -0.5)\"><path d=\"M 0.0 0.0 L 1.0 0.0 L 1.0 1.0 L 0.0 1.0 L 0.0 0.0 Z\" style=\"vector-effect: non-scaling-stroke;\"/></g></g><g transform=\"matrix(1.0, 0.0, 0.0, 1.0, 1.5, 0.0)\"><g transform=\"matrix(1.0, -0.0, 0.0, 1.0, 0.0, 0.0)\"><g/></g></g></g><g style=\"fill: #ffa500;stroke: black;stroke-width: 2.3369999999999997;fill-opacity: 0.46;\" transform=\"matrix(1.0, 0.0, 0.0, 1.0, 1.5, -0.5)\"><path d=\"M 0.0 0.0 L 1.0 0.0 L 1.0 1.0 L 0.0 1.0 L 0.0 0.0 Z\" style=\"vector-effect: non-scaling-stroke;\"/></g></g></g><g/></g></g></g><g style=\"stroke: black;stroke-width: 2.3369999999999997;\" transform=\"matrix(1.0, 0.0, 0.0, 1.0, 4.50005, 0.0)\"><g/></g></g><g transform=\"matrix(1.0, 0.0, 0.0, 1.0, 6.50005, 0.0)\"><g><g transform=\"matrix(1.0, 0.0, 0.0, 1.0, -1.0, -0.0)\"><g><g><g><g><g style=\"fill: #ffa500;stroke: black;stroke-width: 2.3369999999999997;fill-opacity: 0.46;\" transform=\"matrix(1.0, 0.0, 0.0, 1.0, -0.5, -0.5)\"><path d=\"M 0.0 0.0 L 1.0 0.0 L 1.0 1.0 L 0.0 1.0 L 0.0 0.0 Z\" style=\"vector-effect: non-scaling-stroke;\"/></g><g transform=\"matrix(1.0, 0.0, 0.0, 1.0, 0.5, 0.0)\"><g transform=\"matrix(1.0, -0.0, 0.0, 1.0, 0.0, 0.0)\"><g/></g></g></g><g style=\"fill: #ffa500;stroke: black;stroke-width: 2.3369999999999997;fill-opacity: 0.46;\" transform=\"matrix(1.0, 0.0, 0.0, 1.0, 0.5, -0.5)\"><path d=\"M 0.0 0.0 L 1.0 0.0 L 1.0 1.0 L 0.0 1.0 L 0.0 0.0 Z\" style=\"vector-effect: non-scaling-stroke;\"/></g></g><g transform=\"matrix(1.0, 0.0, 0.0, 1.0, 1.5, 0.0)\"><g transform=\"matrix(1.0, -0.0, 0.0, 1.0, 0.0, 0.0)\"><g/></g></g></g><g style=\"fill: #ffa500;stroke: black;stroke-width: 2.3369999999999997;fill-opacity: 0.46;\" transform=\"matrix(1.0, 0.0, 0.0, 1.0, 1.5, -0.5)\"><path d=\"M 0.0 0.0 L 1.0 0.0 L 1.0 1.0 L 0.0 1.0 L 0.0 0.0 Z\" style=\"vector-effect: non-scaling-stroke;\"/></g></g></g><g/></g></g></g><g style=\"stroke: black;stroke-width: 2.3369999999999997;\" transform=\"matrix(1.0, 0.0, 0.0, 1.0, 8.50005, 0.0)\"><g/></g></g><g transform=\"matrix(1.0, 0.0, 0.0, 1.0, 11.00005, 0.0)\"><g><g transform=\"matrix(1.0, 0.0, 0.0, 1.0, -1.5, -0.0)\"><g><g><g><g><g><g><g style=\"fill: #ffa500;stroke: black;stroke-width: 2.3369999999999997;fill-opacity: 0.46;\" transform=\"matrix(1.0, 0.0, 0.0, 1.0, -0.5, -0.5)\"><path d=\"M 0.0 0.0 L 1.0 0.0 L 1.0 1.0 L 0.0 1.0 L 0.0 0.0 Z\" style=\"vector-effect: non-scaling-stroke;\"/></g><g transform=\"matrix(1.0, 0.0, 0.0, 1.0, 0.5, 0.0)\"><g transform=\"matrix(1.0, -0.0, 0.0, 1.0, 0.0, 0.0)\"><g/></g></g></g><g style=\"fill: #ffa500;stroke: black;stroke-width: 2.3369999999999997;fill-opacity: 0.46;\" transform=\"matrix(1.0, 0.0, 0.0, 1.0, 0.5, -0.5)\"><path d=\"M 0.0 0.0 L 1.0 0.0 L 1.0 1.0 L 0.0 1.0 L 0.0 0.0 Z\" style=\"vector-effect: non-scaling-stroke;\"/></g></g><g transform=\"matrix(1.0, 0.0, 0.0, 1.0, 1.5, 0.0)\"><g transform=\"matrix(1.0, -0.0, 0.0, 1.0, 0.0, 0.0)\"><g/></g></g></g><g style=\"fill: #ffa500;stroke: black;stroke-width: 2.3369999999999997;fill-opacity: 0.46;\" transform=\"matrix(1.0, 0.0, 0.0, 1.0, 1.5, -0.5)\"><path d=\"M 0.0 0.0 L 1.0 0.0 L 1.0 1.0 L 0.0 1.0 L 0.0 0.0 Z\" style=\"vector-effect: non-scaling-stroke;\"/></g></g><g transform=\"matrix(1.0, 0.0, 0.0, 1.0, 2.5, 0.0)\"><g transform=\"matrix(1.0, -0.0, 0.0, 1.0, 0.0, 0.0)\"><g/></g></g></g><g style=\"fill: #ffa500;stroke: black;stroke-width: 2.3369999999999997;fill-opacity: 0.46;\" transform=\"matrix(1.0, 0.0, 0.0, 1.0, 2.5, -0.5)\"><path d=\"M 0.0 0.0 L 1.0 0.0 L 1.0 1.0 L 0.0 1.0 L 0.0 0.0 Z\" style=\"vector-effect: non-scaling-stroke;\"/></g></g></g><g/></g></g></g></g></g></g></g></g><g/></g></g></g></g><g/></g></g></g></g></svg>"
            ],
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              "<IPython.core.display.SVG object>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "def ones_spec(out):\n",
        "    for i in range(len(out)):\n",
        "        out[i] = 1\n",
        "\n",
        "def ones(i: int) -> TT[\"i\"]:\n",
        "    return arange(i+1)[1:] - arange(i)\n",
        "\n",
        "test_ones = make_test(\"one\", ones, ones_spec, add_sizes=[\"i\"])"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 6,
      "id": "65dadb3d",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 461
        },
        "execution": {
          "iopub.execute_input": "2022-07-13T00:15:17.731092Z",
          "iopub.status.busy": "2022-07-13T00:15:17.730771Z",
          "iopub.status.idle": "2022-07-13T00:15:17.734462Z",
          "shell.execute_reply": "2022-07-13T00:15:17.733881Z"
        },
        "id": "65dadb3d",
        "lines_to_next_cell": 2,
        "outputId": "e4e56253-35ee-44cc-8b7e-e5acd04c5fe6"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Correct!\n"
          ]
        },
        {
          "data": {
            "text/html": [
              "\n",
              "    <video alt=\"test\" controls autoplay=1>\n",
              "        <source src=\"https://openpuppies.com/mp4/k5jALH0.mp4\"  type=\"video/mp4\">\n",
              "    </video>\n",
              "    "
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      "source": [
        "run_test(test_ones)"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "d281e56c",
      "metadata": {
        "id": "d281e56c"
      },
      "source": [
        "## Puzzle 2 - sum\n",
        "\n",
        "Compute [sum](https://numpy.org/doc/stable/reference/generated/numpy.sum.html) - the sum of a vector."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 7,
      "id": "eb9f236f",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 321
        },
        "execution": {
          "iopub.execute_input": "2022-07-13T00:15:17.737503Z",
          "iopub.status.busy": "2022-07-13T00:15:17.737190Z",
          "iopub.status.idle": "2022-07-13T00:15:18.496977Z",
          "shell.execute_reply": "2022-07-13T00:15:18.496351Z"
        },
        "id": "eb9f236f",
        "outputId": "c0b2fcae-5a4b-4a9f-8b56-ba8b84231aa4"
      },
      "outputs": [
        {
          "data": {
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              "<IPython.core.display.SVG object>"
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          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "def sum_spec(a, out):\n",
        "    out[0] = 0\n",
        "    for i in range(len(a)):\n",
        "        out[0] += a[i]\n",
        "\n",
        "def sum(a: TT[\"i\"]) -> TT[1]:\n",
        "    return a @ ones(len(a))[:, None]\n",
        "\n",
        "test_sum = make_test(\"sum\", sum, sum_spec)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 8,
      "id": "3f7e2b46",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 444
        },
        "execution": {
          "iopub.execute_input": "2022-07-13T00:15:18.500120Z",
          "iopub.status.busy": "2022-07-13T00:15:18.499809Z",
          "iopub.status.idle": "2022-07-13T00:15:18.503156Z",
          "shell.execute_reply": "2022-07-13T00:15:18.502577Z"
        },
        "id": "3f7e2b46",
        "lines_to_next_cell": 2,
        "outputId": "e78268bc-79af-407d-d72e-3fa151c5ab91"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Correct!\n"
          ]
        },
        {
          "data": {
            "text/html": [
              "\n",
              "    <video alt=\"test\" controls autoplay=1>\n",
              "        <source src=\"https://openpuppies.com/mp4/pn1e9TO.mp4\"  type=\"video/mp4\">\n",
              "    </video>\n",
              "    "
            ],
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              "<IPython.core.display.HTML object>"
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          "execution_count": 8,
          "metadata": {},
          "output_type": "execute_result"
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      ],
      "source": [
        "run_test(test_sum)"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "7b2d68c4",
      "metadata": {
        "id": "7b2d68c4"
      },
      "source": [
        "## Puzzle 3 - outer\n",
        "\n",
        "Compute [outer](https://numpy.org/doc/stable/reference/generated/numpy.outer.html) - the outer product of two vectors."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 9,
      "id": "33e8b424",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 321
        },
        "execution": {
          "iopub.execute_input": "2022-07-13T00:15:18.506196Z",
          "iopub.status.busy": "2022-07-13T00:15:18.505868Z",
          "iopub.status.idle": "2022-07-13T00:15:20.019439Z",
          "shell.execute_reply": "2022-07-13T00:15:20.018755Z"
        },
        "id": "33e8b424",
        "outputId": "8ece00c9-610d-43ac-ed87-a8dd695afe6f"
      },
      "outputs": [
        {
          "data": {
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            ],
            "text/plain": [
              "<IPython.core.display.SVG object>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "def outer_spec(a, b, out):\n",
        "    for i in range(len(out)):\n",
        "        for j in range(len(out[0])):\n",
        "            out[i][j] = a[i] * b[j]\n",
        "\n",
        "def outer(a: TT[\"i\"], b: TT[\"j\"]) -> TT[\"i\", \"j\"]:\n",
        "    return a[:, None] @ b[None, :]\n",
        "\n",
        "test_outer = make_test(\"outer\", outer, outer_spec)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 10,
      "id": "15c04a58",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 444
        },
        "execution": {
          "iopub.execute_input": "2022-07-13T00:15:20.022830Z",
          "iopub.status.busy": "2022-07-13T00:15:20.022513Z",
          "iopub.status.idle": "2022-07-13T00:15:20.026801Z",
          "shell.execute_reply": "2022-07-13T00:15:20.026186Z"
        },
        "id": "15c04a58",
        "outputId": "19d6b821-b3a2-4df3-938e-a1c02e5f67c3"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Correct!\n"
          ]
        },
        {
          "data": {
            "text/html": [
              "\n",
              "    <video alt=\"test\" controls autoplay=1>\n",
              "        <source src=\"https://openpuppies.com/mp4/2m78jPG.mp4\"  type=\"video/mp4\">\n",
              "    </video>\n",
              "    "
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "execution_count": 10,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "run_test(test_outer)"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "ebb1a810",
      "metadata": {
        "id": "ebb1a810"
      },
      "source": [
        "## Puzzle 4 - diag\n",
        "\n",
        "Compute [diag](https://numpy.org/doc/stable/reference/generated/numpy.diag.html) - the diagonal vector of a square matrix."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 11,
      "id": "09ea72c6",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 321
        },
        "execution": {
          "iopub.execute_input": "2022-07-13T00:15:20.030049Z",
          "iopub.status.busy": "2022-07-13T00:15:20.029731Z",
          "iopub.status.idle": "2022-07-13T00:15:21.274448Z",
          "shell.execute_reply": "2022-07-13T00:15:21.273836Z"
        },
        "id": "09ea72c6",
        "outputId": "8cfd80d5-633f-4547-9662-4ecf212ae2fc"
      },
      "outputs": [
        {
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            ],
            "text/plain": [
              "<IPython.core.display.SVG object>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "def diag_spec(a, out):\n",
        "    for i in range(len(a)):\n",
        "        out[i] = a[i][i]\n",
        "\n",
        "def diag(a: TT[\"i\", \"i\"]) -> TT[\"i\"]:\n",
        "    return a[arange(len(a)), arange(len(a))]\n",
        "\n",
        "\n",
        "test_diag = make_test(\"diag\", diag, diag_spec)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 12,
      "id": "5d4c3641",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 527
        },
        "execution": {
          "iopub.execute_input": "2022-07-13T00:15:21.277837Z",
          "iopub.status.busy": "2022-07-13T00:15:21.277486Z",
          "iopub.status.idle": "2022-07-13T00:15:21.281005Z",
          "shell.execute_reply": "2022-07-13T00:15:21.280409Z"
        },
        "id": "5d4c3641",
        "outputId": "3fa8aa5f-2d6f-4111-99a2-ebccb81b9e4d"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Correct!\n"
          ]
        },
        {
          "data": {
            "text/html": [
              "\n",
              "    <video alt=\"test\" controls autoplay=1>\n",
              "        <source src=\"https://openpuppies.com/mp4/pCAIlxD.mp4\"  type=\"video/mp4\">\n",
              "    </video>\n",
              "    "
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "execution_count": 12,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "run_test(test_diag)"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "0ffdce80",
      "metadata": {
        "id": "0ffdce80"
      },
      "source": [
        "## Puzzle 5 - eye\n",
        "\n",
        "Compute [eye](https://numpy.org/doc/stable/reference/generated/numpy.eye.html) - the identity matrix."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 13,
      "id": "4fda43df",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 321
        },
        "execution": {
          "iopub.execute_input": "2022-07-13T00:15:21.283997Z",
          "iopub.status.busy": "2022-07-13T00:15:21.283689Z",
          "iopub.status.idle": "2022-07-13T00:15:22.155854Z",
          "shell.execute_reply": "2022-07-13T00:15:22.155222Z"
        },
        "id": "4fda43df",
        "outputId": "d360bb38-9ab4-4571-a539-9462fdb3e755"
      },
      "outputs": [
        {
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0.0 L 1.0 1.0 L 0.0 1.0 L 0.0 0.0 Z\" style=\"vector-effect: non-scaling-stroke;\"/></g></g></g></g></g><g/></g></g></g></g></g></g></g></g><g/></g></g></g></g><g/></g></g></g></g></svg>"
            ],
            "text/plain": [
              "<IPython.core.display.SVG object>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "def eye_spec(out):\n",
        "    for i in range(len(out)):\n",
        "        out[i][i] = 1\n",
        "\n",
        "def eye(j: int) -> TT[\"j\", \"j\"]:\n",
        "    return where(arange(j) == arange(j)[:, None], 1, 0)\n",
        "\n",
        "test_eye = make_test(\"eye\", eye, eye_spec, add_sizes=[\"j\"])"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 14,
      "id": "1c2ec691",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 415
        },
        "execution": {
          "iopub.execute_input": "2022-07-13T00:15:22.159088Z",
          "iopub.status.busy": "2022-07-13T00:15:22.158772Z",
          "iopub.status.idle": "2022-07-13T00:15:22.162208Z",
          "shell.execute_reply": "2022-07-13T00:15:22.161597Z"
        },
        "id": "1c2ec691",
        "outputId": "1ba2a9d0-00cd-4c3e-9fc2-9d655d86f0dd"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Correct!\n"
          ]
        },
        {
          "data": {
            "text/html": [
              "\n",
              "    <video alt=\"test\" controls autoplay=1>\n",
              "        <source src=\"https://openpuppies.com/mp4/9hRi2jN.mp4\"  type=\"video/mp4\">\n",
              "    </video>\n",
              "    "
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "execution_count": 14,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "run_test(test_eye)"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "3ceb0fdd",
      "metadata": {
        "id": "3ceb0fdd"
      },
      "source": [
        "## Puzzle 6 - triu\n",
        "\n",
        "Compute [triu](https://numpy.org/doc/stable/reference/generated/numpy.triu.html) - the upper triangular matrix."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 15,
      "id": "4658f7e5",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 321
        },
        "execution": {
          "iopub.execute_input": "2022-07-13T00:15:22.165226Z",
          "iopub.status.busy": "2022-07-13T00:15:22.164922Z",
          "iopub.status.idle": "2022-07-13T00:15:23.160949Z",
          "shell.execute_reply": "2022-07-13T00:15:23.160294Z"
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        "id": "4658f7e5",
        "outputId": "31236c7f-7b02-4c13-b868-0d787ea6b558"
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1.0 L 0.0 1.0 L 0.0 0.0 Z\" style=\"vector-effect: non-scaling-stroke;\"/></g></g></g></g></g><g/></g></g></g></g></g></g></g></g><g/></g></g></g></g><g/></g></g></g></g></svg>"
            ],
            "text/plain": [
              "<IPython.core.display.SVG object>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "def triu_spec(out):\n",
        "    for i in range(len(out)):\n",
        "        for j in range(len(out)):\n",
        "            if i <= j:\n",
        "                out[i][j] = 1\n",
        "            else:\n",
        "                out[i][j] = 0\n",
        "\n",
        "def triu(j: int) -> TT[\"j\", \"j\"]:\n",
        "    return where(arange(j) >= arange(j)[:, None], 1, 0)\n",
        "\n",
        "\n",
        "test_triu = make_test(\"triu\", triu, triu_spec, add_sizes=[\"j\"])"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 16,
      "id": "b00e3f88",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 444
        },
        "execution": {
          "iopub.execute_input": "2022-07-13T00:15:23.164309Z",
          "iopub.status.busy": "2022-07-13T00:15:23.163987Z",
          "iopub.status.idle": "2022-07-13T00:15:23.167373Z",
          "shell.execute_reply": "2022-07-13T00:15:23.166786Z"
        },
        "id": "b00e3f88",
        "outputId": "d6132638-91ff-4305-e596-39a68e7f131c"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Correct!\n"
          ]
        },
        {
          "data": {
            "text/html": [
              "\n",
              "    <video alt=\"test\" controls autoplay=1>\n",
              "        <source src=\"https://openpuppies.com/mp4/zJx2skh.mp4\"  type=\"video/mp4\">\n",
              "    </video>\n",
              "    "
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "execution_count": 16,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "run_test(test_triu)"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "f3209ef8",
      "metadata": {
        "id": "f3209ef8"
      },
      "source": [
        "## Puzzle 7 - cumsum\n",
        "\n",
        "Compute [cumsum](https://numpy.org/doc/stable/reference/generated/numpy.cumsum.html) - the cumulative sum."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 17,
      "id": "997ee763",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 321
        },
        "execution": {
          "iopub.execute_input": "2022-07-13T00:15:23.170337Z",
          "iopub.status.busy": "2022-07-13T00:15:23.170024Z",
          "iopub.status.idle": "2022-07-13T00:15:24.239732Z",
          "shell.execute_reply": "2022-07-13T00:15:24.239081Z"
        },
        "id": "997ee763",
        "outputId": "e3a1b16d-7a89-4f9b-8584-2467073928b1"
      },
      "outputs": [
        {
          "data": {
            "image/svg+xml": [
              "<svg xmlns=\"http://www.w3.org/2000/svg\" xmlns:ev=\"http://www.w3.org/2001/xml-events\" xmlns:xlink=\"http://www.w3.org/1999/xlink\" baseProfile=\"full\" height=\"300\" version=\"1.1\" width=\"599\"><defs><marker id=\"arrow\" markerHeight=\"3.5\" markerWidth=\"5\" orient=\"auto\" refX=\"5.0\" refY=\"1.7\"><polygon points=\"0,0 5,1.75 0,3.5\"/></marker></defs><g style=\"fill:white;\"><g transform=\"matrix(1.0, 0.0, 0.0, 1.0, 299.985000857094, 150.00000000000003)\"><g transform=\"matrix(34.01166191863867, 0.0, 0.0, 34.01166191863867, 0.0, 0.0)\"><g><g transform=\"matrix(1.0, 0.0, 0.0, 1.0, -0.0, -0.0)\"><g><g style=\"fill: #ffffff;stroke: black;stroke-width: 1.797;\" transform=\"matrix(1.0, 0.0, 0.0, 1.0, -8.40006, -4.200239999999999)\"><path d=\"M 0.0 0.0 L 16.80012 0.0 L 16.80012 8.400479999999998 L 0.0 8.400479999999998 L 0.0 0.0 Z\" style=\"vector-effect: non-scaling-stroke;\"/></g><g transform=\"matrix(1.0, 0.0, 0.0, 1.0, -0.0, -3.6002399999999994)\"><g><g><g><g><g style=\"stroke: black;stroke-width: 1.797;\" transform=\"matrix(1.0, 0.0, 0.0, 1.0, 0.0, 0.0)\"><g/></g><g style=\"fill: #000000;stroke: black;stroke-width: 0.0;\" transform=\"matrix(1.0, 0.0, 0.0, 1.0, 0.0, 0.5)\"><text style=\"text-align:center; text-anchor:middle; dominant-baseline:middle;\n",
              "                      font-family:sans-serif; font-weight: bold;\n",
              "                      font-size:0.75px;\n",
              "                      vector-effect: non-scaling-stroke;\" transform=\"translate(-5e-05, 0)\">cumsum</text></g></g><g style=\"stroke: black;stroke-width: 1.797;\" transform=\"matrix(1.0, 0.0, 0.0, 1.0, 0.0, 1.0001)\"><g/></g></g><g transform=\"matrix(1.0, 0.0, 0.0, 1.0, 0.0, 4.000249999999999)\"><g transform=\"matrix(1.0, 0.0, 0.0, 1.0, -7.0, -2.0000999999999998)\"><g><g><g><g><g><g><g><g><g><g><g><g transform=\"matrix(1.0, 0.0, 0.0, 1.0, -5e-05, -0.25005)\"><g><g><g style=\"stroke: black;stroke-width: 1.797;\" transform=\"matrix(1.0, 0.0, 0.0, 1.0, 0.0, 0.0)\"><g/></g><g style=\"fill: #000000;stroke: black;stroke-width: 0.0;\" transform=\"matrix(1.0, 0.0, 0.0, 1.0, 0.0, 0.25)\"><text style=\"text-align:center; text-anchor:middle; dominant-baseline:middle;\n",
              "                      font-family:sans-serif; font-weight: bold;\n",
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            ],
            "text/plain": [
              "<IPython.core.display.SVG object>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "def cumsum_spec(a, out):\n",
        "    total = 0\n",
        "    for i in range(len(out)):\n",
        "        out[i] = total + a[i]\n",
        "        total += a[i]\n",
        "\n",
        "def cumsum(a: TT[\"i\"]) -> TT[\"i\"]:\n",
        "    return a @ triu(len(a))\n",
        "\n",
        "test_cumsum = make_test(\"cumsum\", cumsum, cumsum_spec)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 18,
      "id": "9145d1cc",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 444
        },
        "execution": {
          "iopub.execute_input": "2022-07-13T00:15:24.243017Z",
          "iopub.status.busy": "2022-07-13T00:15:24.242709Z",
          "iopub.status.idle": "2022-07-13T00:15:24.246110Z",
          "shell.execute_reply": "2022-07-13T00:15:24.245551Z"
        },
        "id": "9145d1cc",
        "lines_to_next_cell": 2,
        "outputId": "b16e21a8-c41f-40b1-bf4e-d3a74a708cff"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Correct!\n"
          ]
        },
        {
          "data": {
            "text/html": [
              "\n",
              "    <video alt=\"test\" controls autoplay=1>\n",
              "        <source src=\"https://openpuppies.com/mp4/DKLBJh7.mp4\"  type=\"video/mp4\">\n",
              "    </video>\n",
              "    "
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              "<IPython.core.display.HTML object>"
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          "execution_count": 18,
          "metadata": {},
          "output_type": "execute_result"
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      ],
      "source": [
        "run_test(test_cumsum)"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "15c09fb6",
      "metadata": {
        "id": "15c09fb6"
      },
      "source": [
        "## Puzzle 8 - diff\n",
        "\n",
        "Compute [diff](https://numpy.org/doc/stable/reference/generated/numpy.diff.html) - the running difference."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 19,
      "id": "47d86d1f",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 321
        },
        "execution": {
          "iopub.execute_input": "2022-07-13T00:15:24.249200Z",
          "iopub.status.busy": "2022-07-13T00:15:24.248891Z",
          "iopub.status.idle": "2022-07-13T00:15:25.183613Z",
          "shell.execute_reply": "2022-07-13T00:15:25.182987Z"
        },
        "id": "47d86d1f",
        "outputId": "86a036b7-9e83-42d6-fdd8-666ce0071a39"
      },
      "outputs": [
        {
          "data": {
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1.0 L 0.0 1.0 L 0.0 0.0 Z\" style=\"vector-effect: non-scaling-stroke;\"/></g></g><g transform=\"matrix(1.0, 0.0, 0.0, 1.0, 3.5, 0.0)\"><g transform=\"matrix(1.0, -0.0, 0.0, 1.0, 0.0, 0.0)\"><g/></g></g></g><g style=\"stroke: black;stroke-width: 2.055;\" transform=\"matrix(1.0, 0.0, 0.0, 1.0, 3.5, -0.5)\"><path d=\"M 0.0 0.0 L 1.0 0.0 L 1.0 1.0 L 0.0 1.0 L 0.0 0.0 Z\" style=\"vector-effect: non-scaling-stroke;\"/></g></g></g><g/></g></g></g></g></g></g></g></g><g/></g></g></g></g><g/></g></g></g></g></svg>"
            ],
            "text/plain": [
              "<IPython.core.display.SVG object>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "def diff_spec(a, out):\n",
        "    out[0] = a[0]\n",
        "    for i in range(1, len(out)):\n",
        "        out[i] = a[i] - a[i - 1]\n",
        "\n",
        "def diff(a: TT[\"i\"], i: int) -> TT[\"i\"]:\n",
        "    return a @ (eye(i) - where(arange(i) - arange(i)[:, None] == 1, 1, 0))\n",
        "\n",
        "test_diff = make_test(\"diff\", diff, diff_spec, add_sizes=[\"i\"])"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 20,
      "id": "bb4eeff6",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 569
        },
        "execution": {
          "iopub.execute_input": "2022-07-13T00:15:25.186875Z",
          "iopub.status.busy": "2022-07-13T00:15:25.186557Z",
          "iopub.status.idle": "2022-07-13T00:15:25.190034Z",
          "shell.execute_reply": "2022-07-13T00:15:25.189482Z"
        },
        "id": "bb4eeff6",
        "outputId": "b3e86b9b-aced-4703-b61e-eaec01b96e4e"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Correct!\n"
          ]
        },
        {
          "data": {
            "text/html": [
              "\n",
              "    <video alt=\"test\" controls autoplay=1>\n",
              "        <source src=\"https://openpuppies.com/mp4/qawCMl5.mp4\"  type=\"video/mp4\">\n",
              "    </video>\n",
              "    "
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "execution_count": 20,
          "metadata": {},
          "output_type": "execute_result"
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      ],
      "source": [
        "run_test(test_diff)"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "74c616c6",
      "metadata": {
        "id": "74c616c6"
      },
      "source": [
        "## Puzzle 9 - vstack\n",
        "\n",
        "Compute [vstack](https://numpy.org/doc/stable/reference/generated/numpy.vstack.html) - the matrix of two vectors"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 21,
      "id": "20a69840",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 321
        },
        "execution": {
          "iopub.execute_input": "2022-07-13T00:15:25.193149Z",
          "iopub.status.busy": "2022-07-13T00:15:25.192804Z",
          "iopub.status.idle": "2022-07-13T00:15:26.641528Z",
          "shell.execute_reply": "2022-07-13T00:15:26.640905Z"
        },
        "id": "20a69840",
        "outputId": "fd6696eb-e3c6-4ae5-fc50-955ad9b1876d"
      },
      "outputs": [
        {
          "data": {
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            ],
            "text/plain": [
              "<IPython.core.display.SVG object>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "def vstack_spec(a, b, out):\n",
        "    for i in range(len(out[0])):\n",
        "        out[0][i] = a[i]\n",
        "        out[1][i] = b[i]\n",
        "\n",
        "def vstack(a: TT[\"i\"], b: TT[\"i\"]) -> TT[2, \"i\"]:\n",
        "    return a + (b - a) * arange(2)[:, None]\n",
        "\n",
        "\n",
        "test_vstack = make_test(\"vstack\", vstack, vstack_spec)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 22,
      "id": "e6cb449b",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 679
        },
        "execution": {
          "iopub.execute_input": "2022-07-13T00:15:26.644713Z",
          "iopub.status.busy": "2022-07-13T00:15:26.644397Z",
          "iopub.status.idle": "2022-07-13T00:15:26.647729Z",
          "shell.execute_reply": "2022-07-13T00:15:26.647154Z"
        },
        "id": "e6cb449b",
        "outputId": "b57ed242-b536-4a07-f4d0-237a2c69e1c0"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Correct!\n"
          ]
        },
        {
          "data": {
            "text/html": [
              "\n",
              "    <video alt=\"test\" controls autoplay=1>\n",
              "        <source src=\"https://openpuppies.com/mp4/Nu4RH7f.mp4\"  type=\"video/mp4\">\n",
              "    </video>\n",
              "    "
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "execution_count": 22,
          "metadata": {},
          "output_type": "execute_result"
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      ],
      "source": [
        "run_test(test_vstack)"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "e3f8a5ae",
      "metadata": {
        "id": "e3f8a5ae"
      },
      "source": [
        "## Puzzle 10 - roll\n",
        "\n",
        "Compute [roll](https://numpy.org/doc/stable/reference/generated/numpy.roll.html) - the vector shifted 1 circular position."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 23,
      "id": "7962491f",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 321
        },
        "execution": {
          "iopub.execute_input": "2022-07-13T00:15:26.650696Z",
          "iopub.status.busy": "2022-07-13T00:15:26.650381Z",
          "iopub.status.idle": "2022-07-13T00:15:27.752738Z",
          "shell.execute_reply": "2022-07-13T00:15:27.752117Z"
        },
        "id": "7962491f",
        "outputId": "ee87754e-0fe0-4924-c20c-c249896658c0"
      },
      "outputs": [
        {
          "data": {
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              "                      font-family:sans-serif; font-weight: bold;\n",
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              "                      font-family:sans-serif; font-weight: bold;\n",
              "                      font-size:0.5px;\n",
              "                      vector-effect: non-scaling-stroke;\" transform=\"translate(-5e-05, 0)\">target</text></g></g><g style=\"stroke: black;stroke-width: 1.6710000000000003;\" transform=\"matrix(1.0, 0.0, 0.0, 1.0, 0.0, 0.5001)\"><g/></g></g></g><g/></g><g style=\"stroke: black;stroke-width: 1.6710000000000003;\" transform=\"matrix(1.0, 0.0, 0.0, 1.0, 0.50005, 0.0)\"><g/></g></g><g transform=\"matrix(1.0, 0.0, 0.0, 1.0, 2.50005, 0.0)\"><g><g transform=\"matrix(1.0, 0.0, 0.0, 1.0, -1.0, -0.0)\"><g><g><g><g><g style=\"stroke: black;stroke-width: 1.6710000000000003;\" transform=\"matrix(1.0, 0.0, 0.0, 1.0, -0.5, -0.5)\"><path d=\"M 0.0 0.0 L 1.0 0.0 L 1.0 1.0 L 0.0 1.0 L 0.0 0.0 Z\" style=\"vector-effect: non-scaling-stroke;\"/></g><g transform=\"matrix(1.0, 0.0, 0.0, 1.0, 0.5, 0.0)\"><g transform=\"matrix(1.0, -0.0, 0.0, 1.0, 0.0, 0.0)\"><g/></g></g></g><g style=\"fill: #ffa500;stroke: black;stroke-width: 1.6710000000000003;fill-opacity: 0.5800000000000001;\" 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-0.5)\"><path d=\"M 0.0 0.0 L 1.0 0.0 L 1.0 1.0 L 0.0 1.0 L 0.0 0.0 Z\" style=\"vector-effect: non-scaling-stroke;\"/></g></g><g transform=\"matrix(1.0, 0.0, 0.0, 1.0, 2.5, 0.0)\"><g transform=\"matrix(1.0, -0.0, 0.0, 1.0, 0.0, 0.0)\"><g/></g></g></g><g style=\"fill: #ffa500;stroke: black;stroke-width: 1.6710000000000003;fill-opacity: 0.46;\" transform=\"matrix(1.0, 0.0, 0.0, 1.0, 2.5, -0.5)\"><path d=\"M 0.0 0.0 L 1.0 0.0 L 1.0 1.0 L 0.0 1.0 L 0.0 0.0 Z\" style=\"vector-effect: non-scaling-stroke;\"/></g></g></g><g/></g></g></g></g></g><g style=\"stroke: black;stroke-width: 1.6710000000000003;\" transform=\"matrix(0.0, -1.0, 1.0, 0.0, 0.0, 3.0001499999999997)\"><g/></g></g><g transform=\"matrix(1.0, 0.0, 0.0, 1.0, 0.0, 4.0001999999999995)\"><g><g><g><g><g><g><g><g transform=\"matrix(1.0, 0.0, 0.0, 1.0, -5e-05, -0.25005)\"><g><g><g style=\"stroke: black;stroke-width: 1.6710000000000003;\" transform=\"matrix(1.0, 0.0, 0.0, 1.0, 0.0, 0.0)\"><g/></g><g style=\"fill: #000000;stroke: 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              "                      font-family:sans-serif; font-weight: bold;\n",
              "                      font-size:0.5px;\n",
              "                      vector-effect: non-scaling-stroke;\" transform=\"translate(-5e-05, 0)\">yours</text></g></g><g style=\"stroke: black;stroke-width: 1.6710000000000003;\" transform=\"matrix(1.0, 0.0, 0.0, 1.0, 0.0, 0.5001)\"><g/></g></g></g><g/></g><g style=\"stroke: black;stroke-width: 1.6710000000000003;\" transform=\"matrix(1.0, 0.0, 0.0, 1.0, 0.50005, 0.0)\"><g/></g></g><g transform=\"matrix(1.0, 0.0, 0.0, 1.0, 2.50005, 0.0)\"><g><g transform=\"matrix(1.0, 0.0, 0.0, 1.0, -1.0, -0.0)\"><g><g><g><g><g style=\"stroke: black;stroke-width: 1.6710000000000003;\" transform=\"matrix(1.0, 0.0, 0.0, 1.0, -0.5, -0.5)\"><path d=\"M 0.0 0.0 L 1.0 0.0 L 1.0 1.0 L 0.0 1.0 L 0.0 0.0 Z\" style=\"vector-effect: non-scaling-stroke;\"/></g><g transform=\"matrix(1.0, 0.0, 0.0, 1.0, 0.5, 0.0)\"><g transform=\"matrix(1.0, -0.0, 0.0, 1.0, 0.0, 0.0)\"><g/></g></g></g><g style=\"fill: #ffa500;stroke: black;stroke-width: 1.6710000000000003;fill-opacity: 0.5800000000000001;\" transform=\"matrix(1.0, 0.0, 0.0, 1.0, 0.5, -0.5)\"><path d=\"M 0.0 0.0 L 1.0 0.0 L 1.0 1.0 L 0.0 1.0 L 0.0 0.0 Z\" style=\"vector-effect: non-scaling-stroke;\"/></g></g><g transform=\"matrix(1.0, 0.0, 0.0, 1.0, 1.5, 0.0)\"><g transform=\"matrix(1.0, -0.0, 0.0, 1.0, 0.0, 0.0)\"><g/></g></g></g><g style=\"stroke: black;stroke-width: 1.6710000000000003;\" transform=\"matrix(1.0, 0.0, 0.0, 1.0, 1.5, -0.5)\"><path d=\"M 0.0 0.0 L 1.0 0.0 L 1.0 1.0 L 0.0 1.0 L 0.0 0.0 Z\" style=\"vector-effect: non-scaling-stroke;\"/></g></g></g><g/></g></g></g><g style=\"stroke: black;stroke-width: 1.6710000000000003;\" transform=\"matrix(1.0, 0.0, 0.0, 1.0, 4.50005, 0.0)\"><g/></g></g><g transform=\"matrix(1.0, 0.0, 0.0, 1.0, 6.50005, 0.0)\"><g><g transform=\"matrix(1.0, 0.0, 0.0, 1.0, -1.0, -0.0)\"><g><g><g><g><g style=\"fill: #0000ff;stroke: black;stroke-width: 1.6710000000000003;fill-opacity: 0.46;\" transform=\"matrix(1.0, 0.0, 0.0, 1.0, -0.5, -0.5)\"><path d=\"M 0.0 0.0 L 1.0 0.0 L 1.0 1.0 L 0.0 1.0 L 0.0 0.0 Z\" style=\"vector-effect: non-scaling-stroke;\"/></g><g transform=\"matrix(1.0, 0.0, 0.0, 1.0, 0.5, 0.0)\"><g transform=\"matrix(1.0, -0.0, 0.0, 1.0, 0.0, 0.0)\"><g/></g></g></g><g style=\"fill: #0000ff;stroke: black;stroke-width: 1.6710000000000003;fill-opacity: 0.46;\" transform=\"matrix(1.0, 0.0, 0.0, 1.0, 0.5, -0.5)\"><path d=\"M 0.0 0.0 L 1.0 0.0 L 1.0 1.0 L 0.0 1.0 L 0.0 0.0 Z\" style=\"vector-effect: non-scaling-stroke;\"/></g></g><g transform=\"matrix(1.0, 0.0, 0.0, 1.0, 1.5, 0.0)\"><g transform=\"matrix(1.0, -0.0, 0.0, 1.0, 0.0, 0.0)\"><g/></g></g></g><g style=\"fill: #0000ff;stroke: black;stroke-width: 1.6710000000000003;fill-opacity: 0.46;\" transform=\"matrix(1.0, 0.0, 0.0, 1.0, 1.5, -0.5)\"><path d=\"M 0.0 0.0 L 1.0 0.0 L 1.0 1.0 L 0.0 1.0 L 0.0 0.0 Z\" style=\"vector-effect: non-scaling-stroke;\"/></g></g></g><g/></g></g></g><g style=\"stroke: black;stroke-width: 1.6710000000000003;\" transform=\"matrix(1.0, 0.0, 0.0, 1.0, 8.50005, 0.0)\"><g/></g></g><g transform=\"matrix(1.0, 0.0, 0.0, 1.0, 11.00005, 0.0)\"><g><g transform=\"matrix(1.0, 0.0, 0.0, 1.0, -1.5, -0.0)\"><g><g><g><g><g><g><g style=\"fill: #ffa500;stroke: black;stroke-width: 1.6710000000000003;fill-opacity: 0.5800000000000001;\" transform=\"matrix(1.0, 0.0, 0.0, 1.0, -0.5, -0.5)\"><path d=\"M 0.0 0.0 L 1.0 0.0 L 1.0 1.0 L 0.0 1.0 L 0.0 0.0 Z\" style=\"vector-effect: non-scaling-stroke;\"/></g><g transform=\"matrix(1.0, 0.0, 0.0, 1.0, 0.5, 0.0)\"><g transform=\"matrix(1.0, -0.0, 0.0, 1.0, 0.0, 0.0)\"><g/></g></g></g><g style=\"stroke: black;stroke-width: 1.6710000000000003;\" transform=\"matrix(1.0, 0.0, 0.0, 1.0, 0.5, -0.5)\"><path d=\"M 0.0 0.0 L 1.0 0.0 L 1.0 1.0 L 0.0 1.0 L 0.0 0.0 Z\" style=\"vector-effect: non-scaling-stroke;\"/></g></g><g transform=\"matrix(1.0, 0.0, 0.0, 1.0, 1.5, 0.0)\"><g transform=\"matrix(1.0, -0.0, 0.0, 1.0, 0.0, 0.0)\"><g/></g></g></g><g style=\"stroke: black;stroke-width: 1.6710000000000003;\" transform=\"matrix(1.0, 0.0, 0.0, 1.0, 1.5, -0.5)\"><path d=\"M 0.0 0.0 L 1.0 0.0 L 1.0 1.0 L 0.0 1.0 L 0.0 0.0 Z\" style=\"vector-effect: non-scaling-stroke;\"/></g></g><g transform=\"matrix(1.0, 0.0, 0.0, 1.0, 2.5, 0.0)\"><g transform=\"matrix(1.0, -0.0, 0.0, 1.0, 0.0, 0.0)\"><g/></g></g></g><g style=\"fill: #ffa500;stroke: black;stroke-width: 1.6710000000000003;fill-opacity: 0.46;\" transform=\"matrix(1.0, 0.0, 0.0, 1.0, 2.5, -0.5)\"><path d=\"M 0.0 0.0 L 1.0 0.0 L 1.0 1.0 L 0.0 1.0 L 0.0 0.0 Z\" style=\"vector-effect: non-scaling-stroke;\"/></g></g></g><g/></g></g></g></g></g></g></g></g><g/></g></g></g></g><g/></g></g></g></g></svg>"
            ],
            "text/plain": [
              "<IPython.core.display.SVG object>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "def roll_spec(a, out):\n",
        "    for i in range(len(out)):\n",
        "        if i + 1 < len(out):\n",
        "            out[i] = a[i + 1]\n",
        "        else:\n",
        "            out[i] = a[i + 1 - len(out)]\n",
        "\n",
        "def roll(a: TT[\"i\"], i: int) -> TT[\"i\"]:\n",
        "    return a[(arange(i) + 1) % i]\n",
        "\n",
        "\n",
        "test_roll = make_test(\"roll\", roll, roll_spec, add_sizes=[\"i\"])"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 24,
      "id": "09103327",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 415
        },
        "execution": {
          "iopub.execute_input": "2022-07-13T00:15:27.755891Z",
          "iopub.status.busy": "2022-07-13T00:15:27.755582Z",
          "iopub.status.idle": "2022-07-13T00:15:27.758982Z",
          "shell.execute_reply": "2022-07-13T00:15:27.758408Z"
        },
        "id": "09103327",
        "outputId": "2ad7e0a0-1f7f-4c28-d2aa-49b980ea9eaa"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Correct!\n"
          ]
        },
        {
          "data": {
            "text/html": [
              "\n",
              "    <video alt=\"test\" controls autoplay=1>\n",
              "        <source src=\"https://openpuppies.com/mp4/Wj2PGRl.mp4\"  type=\"video/mp4\">\n",
              "    </video>\n",
              "    "
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "execution_count": 24,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "run_test(test_roll)"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "adc7dcdd",
      "metadata": {
        "id": "adc7dcdd"
      },
      "source": [
        "## Puzzle 11 - flip\n",
        "\n",
        "Compute [flip](https://numpy.org/doc/stable/reference/generated/numpy.flip.html) - the reversed vector"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 25,
      "id": "1f2d83bb",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 321
        },
        "execution": {
          "iopub.execute_input": "2022-07-13T00:15:27.762023Z",
          "iopub.status.busy": "2022-07-13T00:15:27.761718Z",
          "iopub.status.idle": "2022-07-13T00:15:28.745412Z",
          "shell.execute_reply": "2022-07-13T00:15:28.744797Z"
        },
        "id": "1f2d83bb",
        "outputId": "12302c64-5d45-46cd-c464-bd560a8937c4"
      },
      "outputs": [
        {
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            ],
            "text/plain": [
              "<IPython.core.display.SVG object>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "def flip_spec(a, out):\n",
        "    for i in range(len(out)):\n",
        "        out[i] = a[len(out) - i - 1]\n",
        "\n",
        "def flip(a: TT[\"i\"], i: int) -> TT[\"i\"]:\n",
        "    return a[i - 1 - arange(i)]\n",
        "\n",
        "\n",
        "test_flip = make_test(\"flip\", flip, flip_spec, add_sizes=[\"i\"])"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 26,
      "id": "e5168678",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 444
        },
        "execution": {
          "iopub.execute_input": "2022-07-13T00:15:28.748580Z",
          "iopub.status.busy": "2022-07-13T00:15:28.748257Z",
          "iopub.status.idle": "2022-07-13T00:15:28.751662Z",
          "shell.execute_reply": "2022-07-13T00:15:28.751071Z"
        },
        "id": "e5168678",
        "outputId": "ffdb104d-94d9-4fba-8879-cc3433b004fa"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Correct!\n"
          ]
        },
        {
          "data": {
            "text/html": [
              "\n",
              "    <video alt=\"test\" controls autoplay=1>\n",
              "        <source src=\"https://openpuppies.com/mp4/2m78jPG.mp4\"  type=\"video/mp4\">\n",
              "    </video>\n",
              "    "
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "execution_count": 26,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "run_test(test_flip)"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "fa4469eb",
      "metadata": {
        "id": "fa4469eb"
      },
      "source": [
        "## Puzzle 12 - compress\n",
        "\n",
        "\n",
        "Compute [compress](https://numpy.org/doc/stable/reference/generated/numpy.compress.html) - keep only masked entries (left-aligned)."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 27,
      "id": "f49b8303",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 321
        },
        "execution": {
          "iopub.execute_input": "2022-07-13T00:15:28.754592Z",
          "iopub.status.busy": "2022-07-13T00:15:28.754290Z",
          "iopub.status.idle": "2022-07-13T00:15:30.055478Z",
          "shell.execute_reply": "2022-07-13T00:15:30.054841Z"
        },
        "id": "f49b8303",
        "outputId": "3c0dc869-f966-476f-d4bf-337fb1b2d150"
      },
      "outputs": [
        {
          "data": {
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              "                      font-family:sans-serif; font-weight: bold;\n",
              "                      font-size:0.5px;\n",
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text-anchor:middle; dominant-baseline:middle;\n",
              "                      font-family:sans-serif; font-weight: bold;\n",
              "                      font-size:0.5px;\n",
              "                      vector-effect: non-scaling-stroke;\" transform=\"translate(-5e-05, 0)\">yours</text></g></g><g style=\"stroke: black;stroke-width: 1.2990000000000002;\" transform=\"matrix(1.0, 0.0, 0.0, 1.0, 0.0, 0.5001)\"><g/></g></g></g><g/></g><g style=\"stroke: black;stroke-width: 1.2990000000000002;\" transform=\"matrix(1.0, 0.0, 0.0, 1.0, 0.50005, 0.0)\"><g/></g></g><g transform=\"matrix(1.0, 0.0, 0.0, 1.0, 2.50005, 0.0)\"><g><g transform=\"matrix(1.0, 0.0, 0.0, 1.0, -1.0, -0.0)\"><g><g><g><g><g style=\"fill: #ffa500;stroke: black;stroke-width: 1.2990000000000002;fill-opacity: 0.5800000000000001;\" transform=\"matrix(1.0, 0.0, 0.0, 1.0, -0.5, -0.5)\"><path d=\"M 0.0 0.0 L 1.0 0.0 L 1.0 1.0 L 0.0 1.0 L 0.0 0.0 Z\" style=\"vector-effect: non-scaling-stroke;\"/></g><g transform=\"matrix(1.0, 0.0, 0.0, 1.0, 0.5, 0.0)\"><g transform=\"matrix(1.0, -0.0, 0.0, 1.0, 0.0, 0.0)\"><g/></g></g></g><g style=\"stroke: black;stroke-width: 1.2990000000000002;\" transform=\"matrix(1.0, 0.0, 0.0, 1.0, 0.5, -0.5)\"><path d=\"M 0.0 0.0 L 1.0 0.0 L 1.0 1.0 L 0.0 1.0 L 0.0 0.0 Z\" style=\"vector-effect: non-scaling-stroke;\"/></g></g><g transform=\"matrix(1.0, 0.0, 0.0, 1.0, 1.5, 0.0)\"><g transform=\"matrix(1.0, -0.0, 0.0, 1.0, 0.0, 0.0)\"><g/></g></g></g><g style=\"stroke: black;stroke-width: 1.2990000000000002;\" transform=\"matrix(1.0, 0.0, 0.0, 1.0, 1.5, -0.5)\"><path d=\"M 0.0 0.0 L 1.0 0.0 L 1.0 1.0 L 0.0 1.0 L 0.0 0.0 Z\" style=\"vector-effect: non-scaling-stroke;\"/></g></g></g><g/></g></g></g><g style=\"stroke: black;stroke-width: 1.2990000000000002;\" transform=\"matrix(1.0, 0.0, 0.0, 1.0, 4.50005, 0.0)\"><g/></g></g><g transform=\"matrix(1.0, 0.0, 0.0, 1.0, 6.50005, 0.0)\"><g><g transform=\"matrix(1.0, 0.0, 0.0, 1.0, -1.0, -0.0)\"><g><g><g><g><g style=\"fill: #0000ff;stroke: black;stroke-width: 1.2990000000000002;fill-opacity: 0.7;\" transform=\"matrix(1.0, 0.0, 0.0, 1.0, -0.5, -0.5)\"><path d=\"M 0.0 0.0 L 1.0 0.0 L 1.0 1.0 L 0.0 1.0 L 0.0 0.0 Z\" style=\"vector-effect: non-scaling-stroke;\"/></g><g transform=\"matrix(1.0, 0.0, 0.0, 1.0, 0.5, 0.0)\"><g transform=\"matrix(1.0, -0.0, 0.0, 1.0, 0.0, 0.0)\"><g/></g></g></g><g style=\"fill: #0000ff;stroke: black;stroke-width: 1.2990000000000002;fill-opacity: 0.52;\" transform=\"matrix(1.0, 0.0, 0.0, 1.0, 0.5, -0.5)\"><path d=\"M 0.0 0.0 L 1.0 0.0 L 1.0 1.0 L 0.0 1.0 L 0.0 0.0 Z\" style=\"vector-effect: non-scaling-stroke;\"/></g></g><g transform=\"matrix(1.0, 0.0, 0.0, 1.0, 1.5, 0.0)\"><g transform=\"matrix(1.0, -0.0, 0.0, 1.0, 0.0, 0.0)\"><g/></g></g></g><g style=\"stroke: black;stroke-width: 1.2990000000000002;\" transform=\"matrix(1.0, 0.0, 0.0, 1.0, 1.5, -0.5)\"><path d=\"M 0.0 0.0 L 1.0 0.0 L 1.0 1.0 L 0.0 1.0 L 0.0 0.0 Z\" style=\"vector-effect: non-scaling-stroke;\"/></g></g></g><g/></g></g></g><g style=\"stroke: black;stroke-width: 1.2990000000000002;\" transform=\"matrix(1.0, 0.0, 0.0, 1.0, 8.50005, 0.0)\"><g/></g></g><g transform=\"matrix(1.0, 0.0, 0.0, 1.0, 11.00005, 0.0)\"><g><g transform=\"matrix(1.0, 0.0, 0.0, 1.0, -1.5, -0.0)\"><g><g><g><g><g><g><g style=\"stroke: black;stroke-width: 1.2990000000000002;\" transform=\"matrix(1.0, 0.0, 0.0, 1.0, -0.5, -0.5)\"><path d=\"M 0.0 0.0 L 1.0 0.0 L 1.0 1.0 L 0.0 1.0 L 0.0 0.0 Z\" style=\"vector-effect: non-scaling-stroke;\"/></g><g transform=\"matrix(1.0, 0.0, 0.0, 1.0, 0.5, 0.0)\"><g transform=\"matrix(1.0, -0.0, 0.0, 1.0, 0.0, 0.0)\"><g/></g></g></g><g style=\"stroke: black;stroke-width: 1.2990000000000002;\" transform=\"matrix(1.0, 0.0, 0.0, 1.0, 0.5, -0.5)\"><path d=\"M 0.0 0.0 L 1.0 0.0 L 1.0 1.0 L 0.0 1.0 L 0.0 0.0 Z\" style=\"vector-effect: non-scaling-stroke;\"/></g></g><g transform=\"matrix(1.0, 0.0, 0.0, 1.0, 1.5, 0.0)\"><g transform=\"matrix(1.0, -0.0, 0.0, 1.0, 0.0, 0.0)\"><g/></g></g></g><g style=\"stroke: black;stroke-width: 1.2990000000000002;\" transform=\"matrix(1.0, 0.0, 0.0, 1.0, 1.5, -0.5)\"><path d=\"M 0.0 0.0 L 1.0 0.0 L 1.0 1.0 L 0.0 1.0 L 0.0 0.0 Z\" style=\"vector-effect: non-scaling-stroke;\"/></g></g><g transform=\"matrix(1.0, 0.0, 0.0, 1.0, 2.5, 0.0)\"><g transform=\"matrix(1.0, -0.0, 0.0, 1.0, 0.0, 0.0)\"><g/></g></g></g><g style=\"stroke: black;stroke-width: 1.2990000000000002;\" transform=\"matrix(1.0, 0.0, 0.0, 1.0, 2.5, -0.5)\"><path d=\"M 0.0 0.0 L 1.0 0.0 L 1.0 1.0 L 0.0 1.0 L 0.0 0.0 Z\" style=\"vector-effect: non-scaling-stroke;\"/></g></g></g><g/></g></g></g></g></g></g></g></g><g/></g></g></g></g><g/></g></g></g></g></svg>"
            ],
            "text/plain": [
              "<IPython.core.display.SVG object>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "def compress_spec(g, v, out):\n",
        "    j = 0\n",
        "    for i in range(len(g)):\n",
        "        if g[i]:\n",
        "            out[j] = v[i]\n",
        "            j += 1\n",
        "\n",
        "def compress(g: TT[\"i\", bool], v: TT[\"i\"], i: int) -> TT[\"i\"]:\n",
        "  return v @ ((arange(i) == where(g, cumsum(g*1) - 1, -1)[:, None])*1)\n",
        "\n",
        "test_compress = make_test(\"compress\", compress, compress_spec, add_sizes=[\"i\"])"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 28,
      "id": "9e98d290",
      "metadata": {
        "execution": {
          "iopub.execute_input": "2022-07-13T00:15:30.058645Z",
          "iopub.status.busy": "2022-07-13T00:15:30.058336Z",
          "iopub.status.idle": "2022-07-13T00:15:30.061763Z",
          "shell.execute_reply": "2022-07-13T00:15:30.061166Z"
        },
        "id": "9e98d290",
        "lines_to_next_cell": 2
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Correct!\n"
          ]
        },
        {
          "data": {
            "text/html": [
              "\n",
              "    <video alt=\"test\" controls autoplay=1>\n",
              "        <source src=\"https://openpuppies.com/mp4/2F6j2B4.mp4\"  type=\"video/mp4\">\n",
              "    </video>\n",
              "    "
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "execution_count": 28,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "run_test(test_compress)"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "0e944d79",
      "metadata": {
        "id": "0e944d79",
        "lines_to_next_cell": 2
      },
      "source": [
        "## Puzzle 13 - pad_to\n",
        "\n",
        "\n",
        "Compute pad_to - eliminate or add 0s to change size of vector."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 29,
      "id": "52988720",
      "metadata": {
        "execution": {
          "iopub.execute_input": "2022-07-13T00:15:30.064726Z",
          "iopub.status.busy": "2022-07-13T00:15:30.064418Z",
          "iopub.status.idle": "2022-07-13T00:15:31.162878Z",
          "shell.execute_reply": "2022-07-13T00:15:31.162268Z"
        },
        "id": "52988720",
        "outputId": "7c8b4f9d-fbe1-42f7-e740-bbd8e2a7738a"
      },
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          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "def pad_to_spec(a, out):\n",
        "    for i in range(min(len(out), len(a))):\n",
        "        out[i] = a[i]\n",
        "\n",
        "\n",
        "def pad_to(a: TT[\"i\"], i: int, j: int) -> TT[\"j\"]:\n",
        "    return compress(ones(i) > 0, a, j)\n",
        "\n",
        "\n",
        "test_pad_to = make_test(\"pad_to\", pad_to, pad_to_spec, add_sizes=[\"i\", \"j\"])"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 30,
      "id": "f8e5aee3",
      "metadata": {
        "execution": {
          "iopub.execute_input": "2022-07-13T00:15:31.166060Z",
          "iopub.status.busy": "2022-07-13T00:15:31.165749Z",
          "iopub.status.idle": "2022-07-13T00:15:31.169131Z",
          "shell.execute_reply": "2022-07-13T00:15:31.168580Z"
        },
        "id": "f8e5aee3"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Correct!\n"
          ]
        },
        {
          "data": {
            "text/html": [
              "\n",
              "    <video alt=\"test\" controls autoplay=1>\n",
              "        <source src=\"https://openpuppies.com/mp4/Z0TII8i.mp4\"  type=\"video/mp4\">\n",
              "    </video>\n",
              "    "
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      "source": [
        "run_test(test_pad_to)"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "aee589be",
      "metadata": {
        "id": "aee589be"
      },
      "source": [
        "## Puzzle 14 - sequence_mask\n",
        "\n",
        "\n",
        "Compute [sequence_mask](https://www.tensorflow.org/api_docs/python/tf/sequence_mask) - pad out to length per batch."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 31,
      "id": "6aca6d50",
      "metadata": {
        "execution": {
          "iopub.execute_input": "2022-07-13T00:15:31.172146Z",
          "iopub.status.busy": "2022-07-13T00:15:31.171799Z",
          "iopub.status.idle": "2022-07-13T00:15:33.292198Z",
          "shell.execute_reply": "2022-07-13T00:15:33.291558Z"
        },
        "id": "6aca6d50",
        "outputId": "5f57eaf4-f51a-4fea-c4b2-65174583c823"
      },
      "outputs": [
        {
          "data": {
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            ],
            "text/plain": [
              "<IPython.core.display.SVG object>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "def sequence_mask_spec(values, length, out):\n",
        "    for i in range(len(out)):\n",
        "        for j in range(len(out[0])):\n",
        "            if j < length[i]:\n",
        "                out[i][j] = values[i][j]\n",
        "            else:\n",
        "                out[i][j] = 0\n",
        "\n",
        "def sequence_mask(values: TT[\"i\", \"j\"], length: TT[\"i\", int]) -> TT[\"i\", \"j\"]:\n",
        "    return values * (arange(values.shape[1]) < length[:, None])\n",
        "\n",
        "\n",
        "def constraint_set_length(d):\n",
        "    d[\"length\"] = d[\"length\"] % d[\"values\"].shape[1]\n",
        "    return d\n",
        "\n",
        "\n",
        "test_sequence = make_test(\"sequence_mask\",\n",
        "    sequence_mask, sequence_mask_spec, constraint=constraint_set_length\n",
        ")"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 32,
      "id": "f5646e37",
      "metadata": {
        "execution": {
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          "iopub.status.idle": "2022-07-13T00:15:33.299068Z",
          "shell.execute_reply": "2022-07-13T00:15:33.298467Z"
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        "id": "f5646e37",
        "lines_to_next_cell": 2
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Correct!\n"
          ]
        },
        {
          "data": {
            "text/html": [
              "\n",
              "    <video alt=\"test\" controls autoplay=1>\n",
              "        <source src=\"https://openpuppies.com/mp4/fqHxOGI.mp4\"  type=\"video/mp4\">\n",
              "    </video>\n",
              "    "
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              "<IPython.core.display.HTML object>"
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      "source": [
        "run_test(test_sequence)"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "342fedba",
      "metadata": {
        "id": "342fedba",
        "lines_to_next_cell": 2
      },
      "source": [
        "## Puzzle 15 - bincount\n",
        "\n",
        "Compute [bincount](https://numpy.org/doc/stable/reference/generated/numpy.bincount.html) - count number of times an entry was seen."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 33,
      "id": "b8a0a10c",
      "metadata": {
        "execution": {
          "iopub.execute_input": "2022-07-13T00:15:33.302153Z",
          "iopub.status.busy": "2022-07-13T00:15:33.301837Z",
          "iopub.status.idle": "2022-07-13T00:15:34.370952Z",
          "shell.execute_reply": "2022-07-13T00:15:34.370349Z"
        },
        "id": "b8a0a10c",
        "outputId": "1d462171-f1f0-4111-c9ce-2a15bf628c2a"
      },
      "outputs": [
        {
          "data": {
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              "                      font-family:sans-serif; font-weight: bold;\n",
              "                      font-size:0.75px;\n",
              "                      vector-effect: non-scaling-stroke;\" transform=\"translate(-5e-05, 0)\">bincount</text></g></g><g style=\"stroke: black;stroke-width: 2.184;\" transform=\"matrix(1.0, 0.0, 0.0, 1.0, 0.0, 1.0001)\"><g/></g></g><g transform=\"matrix(1.0, 0.0, 0.0, 1.0, 0.0, 4.000249999999999)\"><g transform=\"matrix(1.0, 0.0, 0.0, 1.0, -8.5, -2.0000999999999998)\"><g><g><g><g><g><g><g><g><g><g><g><g transform=\"matrix(1.0, 0.0, 0.0, 1.0, -5e-05, -0.25005)\"><g><g><g style=\"stroke: black;stroke-width: 2.184;\" transform=\"matrix(1.0, 0.0, 0.0, 1.0, 0.0, 0.0)\"><g/></g><g style=\"fill: #000000;stroke: black;stroke-width: 0.0;\" transform=\"matrix(1.0, 0.0, 0.0, 1.0, 0.0, 0.25)\"><text style=\"text-align:center; text-anchor:middle; dominant-baseline:middle;\n",
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              "                      font-family:sans-serif; font-weight: bold;\n",
              "                      font-size:0.5px;\n",
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              "                      font-family:sans-serif; font-weight: bold;\n",
              "                      font-size:0.5px;\n",
              "                      vector-effect: non-scaling-stroke;\" transform=\"translate(-5e-05, 0)\">yours</text></g></g><g style=\"stroke: black;stroke-width: 2.184;\" transform=\"matrix(1.0, 0.0, 0.0, 1.0, 0.0, 0.5001)\"><g/></g></g></g><g/></g><g style=\"stroke: black;stroke-width: 2.184;\" transform=\"matrix(1.0, 0.0, 0.0, 1.0, 0.50005, 0.0)\"><g/></g></g><g transform=\"matrix(1.0, 0.0, 0.0, 1.0, 3.50005, 0.0)\"><g><g transform=\"matrix(1.0, 0.0, 0.0, 1.0, -1.0, -0.0)\"><g><g><g><g><g style=\"fill: #ffa500;stroke: black;stroke-width: 2.184;fill-opacity: 0.46;\" transform=\"matrix(1.0, 0.0, 0.0, 1.0, -0.5, -0.5)\"><path d=\"M 0.0 0.0 L 1.0 0.0 L 1.0 1.0 L 0.0 1.0 L 0.0 0.0 Z\" style=\"vector-effect: non-scaling-stroke;\"/></g><g transform=\"matrix(1.0, 0.0, 0.0, 1.0, 0.5, 0.0)\"><g transform=\"matrix(1.0, -0.0, 0.0, 1.0, 0.0, 0.0)\"><g/></g></g></g><g style=\"fill: #ffa500;stroke: black;stroke-width: 2.184;fill-opacity: 0.64;\" transform=\"matrix(1.0, 0.0, 0.0, 1.0, 0.5, -0.5)\"><path d=\"M 0.0 0.0 L 1.0 0.0 L 1.0 1.0 L 0.0 1.0 L 0.0 0.0 Z\" style=\"vector-effect: non-scaling-stroke;\"/></g></g><g transform=\"matrix(1.0, 0.0, 0.0, 1.0, 1.5, 0.0)\"><g transform=\"matrix(1.0, -0.0, 0.0, 1.0, 0.0, 0.0)\"><g/></g></g></g><g style=\"stroke: black;stroke-width: 2.184;\" transform=\"matrix(1.0, 0.0, 0.0, 1.0, 1.5, -0.5)\"><path d=\"M 0.0 0.0 L 1.0 0.0 L 1.0 1.0 L 0.0 1.0 L 0.0 0.0 Z\" style=\"vector-effect: non-scaling-stroke;\"/></g></g></g><g/></g></g></g><g style=\"stroke: black;stroke-width: 2.184;\" transform=\"matrix(1.0, 0.0, 0.0, 1.0, 6.50005, 0.0)\"><g/></g></g><g transform=\"matrix(1.0, 0.0, 0.0, 1.0, 9.00005, 0.0)\"><g><g transform=\"matrix(1.0, 0.0, 0.0, 1.0, -1.0, -0.0)\"><g><g><g><g><g style=\"fill: #ffa500;stroke: black;stroke-width: 2.184;fill-opacity: 0.64;\" transform=\"matrix(1.0, 0.0, 0.0, 1.0, -0.5, -0.5)\"><path d=\"M 0.0 0.0 L 1.0 0.0 L 1.0 1.0 L 0.0 1.0 L 0.0 0.0 Z\" style=\"vector-effect: non-scaling-stroke;\"/></g><g transform=\"matrix(1.0, 0.0, 0.0, 1.0, 0.5, 0.0)\"><g transform=\"matrix(1.0, -0.0, 0.0, 1.0, 0.0, 0.0)\"><g/></g></g></g><g style=\"stroke: black;stroke-width: 2.184;\" transform=\"matrix(1.0, 0.0, 0.0, 1.0, 0.5, -0.5)\"><path d=\"M 0.0 0.0 L 1.0 0.0 L 1.0 1.0 L 0.0 1.0 L 0.0 0.0 Z\" style=\"vector-effect: non-scaling-stroke;\"/></g></g><g transform=\"matrix(1.0, 0.0, 0.0, 1.0, 1.5, 0.0)\"><g transform=\"matrix(1.0, -0.0, 0.0, 1.0, 0.0, 0.0)\"><g/></g></g></g><g style=\"stroke: black;stroke-width: 2.184;\" transform=\"matrix(1.0, 0.0, 0.0, 1.0, 1.5, -0.5)\"><path d=\"M 0.0 0.0 L 1.0 0.0 L 1.0 1.0 L 0.0 1.0 L 0.0 0.0 Z\" style=\"vector-effect: non-scaling-stroke;\"/></g></g></g><g/></g></g></g><g style=\"stroke: black;stroke-width: 2.184;\" transform=\"matrix(1.0, 0.0, 0.0, 1.0, 11.50005, 0.0)\"><g/></g></g><g transform=\"matrix(1.0, 0.0, 0.0, 1.0, 14.50005, 0.0)\"><g><g transform=\"matrix(1.0, 0.0, 0.0, 1.0, -2.0, -0.0)\"><g><g><g><g><g><g><g><g><g style=\"fill: #ffa500;stroke: black;stroke-width: 2.184;fill-opacity: 0.5800000000000001;\" transform=\"matrix(1.0, 0.0, 0.0, 1.0, -0.5, -0.5)\"><path d=\"M 0.0 0.0 L 1.0 0.0 L 1.0 1.0 L 0.0 1.0 L 0.0 0.0 Z\" style=\"vector-effect: non-scaling-stroke;\"/></g><g transform=\"matrix(1.0, 0.0, 0.0, 1.0, 0.5, 0.0)\"><g transform=\"matrix(1.0, -0.0, 0.0, 1.0, 0.0, 0.0)\"><g/></g></g></g><g style=\"stroke: black;stroke-width: 2.184;\" transform=\"matrix(1.0, 0.0, 0.0, 1.0, 0.5, -0.5)\"><path d=\"M 0.0 0.0 L 1.0 0.0 L 1.0 1.0 L 0.0 1.0 L 0.0 0.0 Z\" style=\"vector-effect: non-scaling-stroke;\"/></g></g><g transform=\"matrix(1.0, 0.0, 0.0, 1.0, 1.5, 0.0)\"><g transform=\"matrix(1.0, -0.0, 0.0, 1.0, 0.0, 0.0)\"><g/></g></g></g><g style=\"stroke: black;stroke-width: 2.184;\" transform=\"matrix(1.0, 0.0, 0.0, 1.0, 1.5, -0.5)\"><path d=\"M 0.0 0.0 L 1.0 0.0 L 1.0 1.0 L 0.0 1.0 L 0.0 0.0 Z\" style=\"vector-effect: non-scaling-stroke;\"/></g></g><g transform=\"matrix(1.0, 0.0, 0.0, 1.0, 2.5, 0.0)\"><g transform=\"matrix(1.0, -0.0, 0.0, 1.0, 0.0, 0.0)\"><g/></g></g></g><g style=\"stroke: black;stroke-width: 2.184;\" transform=\"matrix(1.0, 0.0, 0.0, 1.0, 2.5, -0.5)\"><path d=\"M 0.0 0.0 L 1.0 0.0 L 1.0 1.0 L 0.0 1.0 L 0.0 0.0 Z\" style=\"vector-effect: non-scaling-stroke;\"/></g></g><g transform=\"matrix(1.0, 0.0, 0.0, 1.0, 3.5, 0.0)\"><g transform=\"matrix(1.0, -0.0, 0.0, 1.0, 0.0, 0.0)\"><g/></g></g></g><g style=\"stroke: black;stroke-width: 2.184;\" transform=\"matrix(1.0, 0.0, 0.0, 1.0, 3.5, -0.5)\"><path d=\"M 0.0 0.0 L 1.0 0.0 L 1.0 1.0 L 0.0 1.0 L 0.0 0.0 Z\" style=\"vector-effect: non-scaling-stroke;\"/></g></g></g><g/></g></g></g></g></g></g></g></g><g/></g></g></g></g><g/></g></g></g></g></svg>"
            ],
            "text/plain": [
              "<IPython.core.display.SVG object>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "def bincount_spec(a, out):\n",
        "    for i in range(len(a)):\n",
        "        out[a[i]] += 1\n",
        "\n",
        "def bincount(a: TT[\"i\"], j: int) -> TT[\"j\"]:\n",
        "    return ones(len(a)) @ where((arange(j) == a[:, None]), 1, 0)\n",
        "\n",
        "\n",
        "def constraint_set_max(d):\n",
        "    d[\"a\"] = d[\"a\"] % d[\"return\"].shape[0]\n",
        "    return d\n",
        "\n",
        "\n",
        "test_bincount = make_test(\"bincount\",\n",
        "    bincount, bincount_spec, add_sizes=[\"j\"], constraint=constraint_set_max\n",
        ")"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 34,
      "id": "0d766aec",
      "metadata": {
        "execution": {
          "iopub.execute_input": "2022-07-13T00:15:34.374345Z",
          "iopub.status.busy": "2022-07-13T00:15:34.373778Z",
          "iopub.status.idle": "2022-07-13T00:15:34.377216Z",
          "shell.execute_reply": "2022-07-13T00:15:34.376611Z"
        },
        "id": "0d766aec",
        "lines_to_next_cell": 2
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Correct!\n"
          ]
        },
        {
          "data": {
            "text/html": [
              "\n",
              "    <video alt=\"test\" controls autoplay=1>\n",
              "        <source src=\"https://openpuppies.com/mp4/Vy9JShx.mp4\"  type=\"video/mp4\">\n",
              "    </video>\n",
              "    "
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "execution_count": 34,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "run_test(test_bincount)"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "1ff7e77c",
      "metadata": {
        "id": "1ff7e77c",
        "lines_to_next_cell": 2
      },
      "source": [
        "## Puzzle 16 - scatter_add\n",
        "\n",
        "Compute [scatter_add](https://pytorch-scatter.readthedocs.io/en/1.3.0/functions/add.html) - add together values that link to the same location."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 35,
      "id": "405a800e",
      "metadata": {
        "execution": {
          "iopub.execute_input": "2022-07-13T00:15:34.380250Z",
          "iopub.status.busy": "2022-07-13T00:15:34.379949Z",
          "iopub.status.idle": "2022-07-13T00:15:35.637090Z",
          "shell.execute_reply": "2022-07-13T00:15:35.636472Z"
        },
        "id": "405a800e",
        "outputId": "9f98abc0-8336-4712-a406-bdeb68091f01"
      },
      "outputs": [
        {
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            ],
            "text/plain": [
              "<IPython.core.display.SVG object>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "def scatter_add_spec(values, link, out):\n",
        "    for j in range(len(values)):\n",
        "        out[link[j]] += values[j]\n",
        "\n",
        "def scatter_add(values: TT[\"i\"], link: TT[\"i\"], j: int) -> TT[\"j\"]:\n",
        "    return  values @ where(arange(j) == link[:, None], 1, 0)\n",
        "\n",
        "\n",
        "def constraint_set_max(d):\n",
        "    d[\"link\"] = d[\"link\"] % d[\"return\"].shape[0]\n",
        "    return d\n",
        "\n",
        "\n",
        "test_scatter_add = make_test(\"scatter_add\",\n",
        "    scatter_add, scatter_add_spec, add_sizes=[\"j\"], constraint=constraint_set_max\n",
        ")"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 36,
      "id": "a9ea0110",
      "metadata": {
        "execution": {
          "iopub.execute_input": "2022-07-13T00:15:35.640245Z",
          "iopub.status.busy": "2022-07-13T00:15:35.639897Z",
          "iopub.status.idle": "2022-07-13T00:15:35.643383Z",
          "shell.execute_reply": "2022-07-13T00:15:35.642753Z"
        },
        "id": "a9ea0110",
        "lines_to_next_cell": 2
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Correct!\n"
          ]
        },
        {
          "data": {
            "text/html": [
              "\n",
              "    <video alt=\"test\" controls autoplay=1>\n",
              "        <source src=\"https://openpuppies.com/mp4/Z0TII8i.mp4\"  type=\"video/mp4\">\n",
              "    </video>\n",
              "    "
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "execution_count": 36,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "run_test(test_scatter_add)"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "9020b21b",
      "metadata": {
        "id": "9020b21b"
      },
      "source": [
        "## Puzzle 17 - flatten\n",
        "\n",
        "Compute [flatten](https://numpy.org/doc/stable/reference/generated/numpy.ndarray.flatten.html)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 37,
      "id": "56c917be",
      "metadata": {
        "execution": {
          "iopub.execute_input": "2022-07-13T00:15:35.646407Z",
          "iopub.status.busy": "2022-07-13T00:15:35.646100Z",
          "iopub.status.idle": "2022-07-13T00:15:37.321766Z",
          "shell.execute_reply": "2022-07-13T00:15:37.321136Z"
        },
        "id": "56c917be",
        "lines_to_next_cell": 1,
        "outputId": "cd7874c1-ff7d-44ba-c1b6-3347ec87e373"
      },
      "outputs": [
        {
          "data": {
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            ],
            "text/plain": [
              "<IPython.core.display.SVG object>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "def flatten_spec(a, out):\n",
        "    k = 0\n",
        "    for i in range(len(a)):\n",
        "        for j in range(len(a[0])):\n",
        "            out[k] = a[i][j]\n",
        "            k += 1\n",
        "\n",
        "def flatten(a: TT[\"i\", \"j\"], i:int, j:int) -> TT[\"i * j\"]:\n",
        "    return a[arange(i*j) // j, arange(i*j) % j]\n",
        "    \n",
        "\n",
        "test_flatten = make_test(\"flatten\", flatten, flatten_spec, add_sizes=[\"i\", \"j\"])"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 38,
      "id": "a129e213",
      "metadata": {
        "execution": {
          "iopub.execute_input": "2022-07-13T00:15:37.325238Z",
          "iopub.status.busy": "2022-07-13T00:15:37.324893Z",
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          "shell.execute_reply": "2022-07-13T00:15:37.327760Z"
        },
        "id": "a129e213"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Correct!\n"
          ]
        },
        {
          "data": {
            "text/html": [
              "\n",
              "    <video alt=\"test\" controls autoplay=1>\n",
              "        <source src=\"https://openpuppies.com/mp4/udLK6FS.mp4\"  type=\"video/mp4\">\n",
              "    </video>\n",
              "    "
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              "<IPython.core.display.HTML object>"
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          "execution_count": 38,
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      ],
      "source": [
        "run_test(test_flatten)"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "bc61b4eb",
      "metadata": {
        "id": "bc61b4eb"
      },
      "source": [
        "## Puzzle 18 - linspace\n",
        "\n",
        "Compute [linspace](https://numpy.org/doc/stable/reference/generated/numpy.linspace.html)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 39,
      "id": "115ef19c",
      "metadata": {
        "execution": {
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          "iopub.status.idle": "2022-07-13T00:15:38.652685Z",
          "shell.execute_reply": "2022-07-13T00:15:38.652037Z"
        },
        "id": "115ef19c",
        "outputId": "127fb5d6-ee3d-418c-90c3-9a62311ed399"
      },
      "outputs": [
        {
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              "<IPython.core.display.SVG object>"
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          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "def linspace_spec(i, j, out):\n",
        "    for k in range(len(out)):\n",
        "        out[k] = float(i + (j - i) * k / max(1, len(out) - 1))\n",
        "\n",
        "def linspace(i: TT[1], j: TT[1], n: int) -> TT[\"n\", float]:\n",
        "    return i + arange(n) * (j-i) / (n-1+1e-9)\n",
        "\n",
        "test_linspace = make_test(\"linspace\", linspace, linspace_spec, add_sizes=[\"n\"])"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 40,
      "id": "812a6235",
      "metadata": {
        "execution": {
          "iopub.execute_input": "2022-07-13T00:15:38.655950Z",
          "iopub.status.busy": "2022-07-13T00:15:38.655631Z",
          "iopub.status.idle": "2022-07-13T00:15:38.659029Z",
          "shell.execute_reply": "2022-07-13T00:15:38.658438Z"
        },
        "id": "812a6235",
        "lines_to_next_cell": 2
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Correct!\n"
          ]
        },
        {
          "data": {
            "text/html": [
              "\n",
              "    <video alt=\"test\" controls autoplay=1>\n",
              "        <source src=\"https://openpuppies.com/mp4/6tVqKyM.mp4\"  type=\"video/mp4\">\n",
              "    </video>\n",
              "    "
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              "<IPython.core.display.HTML object>"
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          "execution_count": 40,
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      "source": [
        "run_test(test_linspace)"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "1d107267",
      "metadata": {
        "id": "1d107267"
      },
      "source": [
        "## Puzzle 19 - heaviside\n",
        "\n",
        "Compute [heaviside](https://numpy.org/doc/stable/reference/generated/numpy.heaviside.html)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 41,
      "id": "3becb5f1",
      "metadata": {
        "execution": {
          "iopub.execute_input": "2022-07-13T00:15:38.662023Z",
          "iopub.status.busy": "2022-07-13T00:15:38.661722Z",
          "iopub.status.idle": "2022-07-13T00:15:39.902909Z",
          "shell.execute_reply": "2022-07-13T00:15:39.902243Z"
        },
        "id": "3becb5f1",
        "outputId": "2f7759b1-2567-41e6-ec23-6f9639e62512"
      },
      "outputs": [
        {
          "data": {
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              "                      font-family:sans-serif; font-weight: bold;\n",
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              "                      font-family:sans-serif; font-weight: bold;\n",
              "                      font-size:0.5px;\n",
              "                      vector-effect: non-scaling-stroke;\" transform=\"translate(-5e-05, 0)\">yours</text></g></g><g style=\"stroke: black;stroke-width: 1.398;\" transform=\"matrix(1.0, 0.0, 0.0, 1.0, 0.0, 0.5001)\"><g/></g></g></g><g/></g><g style=\"stroke: black;stroke-width: 1.398;\" transform=\"matrix(1.0, 0.0, 0.0, 1.0, 0.50005, 0.0)\"><g/></g></g><g transform=\"matrix(1.0, 0.0, 0.0, 1.0, 2.50005, 0.0)\"><g><g transform=\"matrix(1.0, 0.0, 0.0, 1.0, -1.0, -0.0)\"><g><g><g><g><g style=\"stroke: black;stroke-width: 1.398;\" transform=\"matrix(1.0, 0.0, 0.0, 1.0, -0.5, -0.5)\"><path d=\"M 0.0 0.0 L 1.0 0.0 L 1.0 1.0 L 0.0 1.0 L 0.0 0.0 Z\" style=\"vector-effect: non-scaling-stroke;\"/></g><g transform=\"matrix(1.0, 0.0, 0.0, 1.0, 0.5, 0.0)\"><g transform=\"matrix(1.0, -0.0, 0.0, 1.0, 0.0, 0.0)\"><g/></g></g></g><g style=\"fill: #ffa500;stroke: black;stroke-width: 1.398;fill-opacity: 0.46;\" transform=\"matrix(1.0, 0.0, 0.0, 1.0, 0.5, -0.5)\"><path d=\"M 0.0 0.0 L 1.0 0.0 L 1.0 1.0 L 0.0 1.0 L 0.0 0.0 Z\" style=\"vector-effect: non-scaling-stroke;\"/></g></g><g transform=\"matrix(1.0, 0.0, 0.0, 1.0, 1.5, 0.0)\"><g transform=\"matrix(1.0, -0.0, 0.0, 1.0, 0.0, 0.0)\"><g/></g></g></g><g style=\"stroke: black;stroke-width: 1.398;\" transform=\"matrix(1.0, 0.0, 0.0, 1.0, 1.5, -0.5)\"><path d=\"M 0.0 0.0 L 1.0 0.0 L 1.0 1.0 L 0.0 1.0 L 0.0 0.0 Z\" style=\"vector-effect: non-scaling-stroke;\"/></g></g></g><g/></g></g></g><g style=\"stroke: black;stroke-width: 1.398;\" transform=\"matrix(1.0, 0.0, 0.0, 1.0, 4.50005, 0.0)\"><g/></g></g><g transform=\"matrix(1.0, 0.0, 0.0, 1.0, 7.00005, 0.0)\"><g><g transform=\"matrix(1.0, 0.0, 0.0, 1.0, -1.5, -0.0)\"><g><g><g><g><g><g><g style=\"fill: #0000ff;stroke: black;stroke-width: 1.398;fill-opacity: 0.5800000000000001;\" transform=\"matrix(1.0, 0.0, 0.0, 1.0, -0.5, -0.5)\"><path d=\"M 0.0 0.0 L 1.0 0.0 L 1.0 1.0 L 0.0 1.0 L 0.0 0.0 Z\" style=\"vector-effect: non-scaling-stroke;\"/></g><g transform=\"matrix(1.0, 0.0, 0.0, 1.0, 0.5, 0.0)\"><g transform=\"matrix(1.0, -0.0, 0.0, 1.0, 0.0, 0.0)\"><g/></g></g></g><g style=\"fill: #ffa500;stroke: black;stroke-width: 1.398;fill-opacity: 0.46;\" transform=\"matrix(1.0, 0.0, 0.0, 1.0, 0.5, -0.5)\"><path d=\"M 0.0 0.0 L 1.0 0.0 L 1.0 1.0 L 0.0 1.0 L 0.0 0.0 Z\" style=\"vector-effect: non-scaling-stroke;\"/></g></g><g transform=\"matrix(1.0, 0.0, 0.0, 1.0, 1.5, 0.0)\"><g transform=\"matrix(1.0, -0.0, 0.0, 1.0, 0.0, 0.0)\"><g/></g></g></g><g style=\"stroke: black;stroke-width: 1.398;\" transform=\"matrix(1.0, 0.0, 0.0, 1.0, 1.5, -0.5)\"><path d=\"M 0.0 0.0 L 1.0 0.0 L 1.0 1.0 L 0.0 1.0 L 0.0 0.0 Z\" style=\"vector-effect: non-scaling-stroke;\"/></g></g><g transform=\"matrix(1.0, 0.0, 0.0, 1.0, 2.5, 0.0)\"><g transform=\"matrix(1.0, -0.0, 0.0, 1.0, 0.0, 0.0)\"><g/></g></g></g><g style=\"stroke: black;stroke-width: 1.398;\" transform=\"matrix(1.0, 0.0, 0.0, 1.0, 2.5, -0.5)\"><path d=\"M 0.0 0.0 L 1.0 0.0 L 1.0 1.0 L 0.0 1.0 L 0.0 0.0 Z\" style=\"vector-effect: non-scaling-stroke;\"/></g></g></g><g/></g></g></g><g style=\"stroke: black;stroke-width: 1.398;\" transform=\"matrix(1.0, 0.0, 0.0, 1.0, 9.50005, 0.0)\"><g/></g></g><g transform=\"matrix(1.0, 0.0, 0.0, 1.0, 12.00005, 0.0)\"><g><g transform=\"matrix(1.0, 0.0, 0.0, 1.0, -1.5, -0.0)\"><g><g><g><g><g><g><g style=\"stroke: black;stroke-width: 1.398;\" transform=\"matrix(1.0, 0.0, 0.0, 1.0, -0.5, -0.5)\"><path d=\"M 0.0 0.0 L 1.0 0.0 L 1.0 1.0 L 0.0 1.0 L 0.0 0.0 Z\" style=\"vector-effect: non-scaling-stroke;\"/></g><g transform=\"matrix(1.0, 0.0, 0.0, 1.0, 0.5, 0.0)\"><g transform=\"matrix(1.0, -0.0, 0.0, 1.0, 0.0, 0.0)\"><g/></g></g></g><g style=\"stroke: black;stroke-width: 1.398;\" transform=\"matrix(1.0, 0.0, 0.0, 1.0, 0.5, -0.5)\"><path d=\"M 0.0 0.0 L 1.0 0.0 L 1.0 1.0 L 0.0 1.0 L 0.0 0.0 Z\" style=\"vector-effect: non-scaling-stroke;\"/></g></g><g transform=\"matrix(1.0, 0.0, 0.0, 1.0, 1.5, 0.0)\"><g transform=\"matrix(1.0, -0.0, 0.0, 1.0, 0.0, 0.0)\"><g/></g></g></g><g style=\"stroke: black;stroke-width: 1.398;\" transform=\"matrix(1.0, 0.0, 0.0, 1.0, 1.5, -0.5)\"><path d=\"M 0.0 0.0 L 1.0 0.0 L 1.0 1.0 L 0.0 1.0 L 0.0 0.0 Z\" style=\"vector-effect: non-scaling-stroke;\"/></g></g><g transform=\"matrix(1.0, 0.0, 0.0, 1.0, 2.5, 0.0)\"><g transform=\"matrix(1.0, -0.0, 0.0, 1.0, 0.0, 0.0)\"><g/></g></g></g><g style=\"stroke: black;stroke-width: 1.398;\" transform=\"matrix(1.0, 0.0, 0.0, 1.0, 2.5, -0.5)\"><path d=\"M 0.0 0.0 L 1.0 0.0 L 1.0 1.0 L 0.0 1.0 L 0.0 0.0 Z\" style=\"vector-effect: non-scaling-stroke;\"/></g></g></g><g/></g></g></g></g></g></g></g></g><g/></g></g></g></g><g/></g></g></g></g></svg>"
            ],
            "text/plain": [
              "<IPython.core.display.SVG object>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "def heaviside_spec(a, b, out):\n",
        "    for k in range(len(out)):\n",
        "        if a[k] == 0:\n",
        "            out[k] = b[k]\n",
        "        else:\n",
        "            out[k] = int(a[k] > 0)\n",
        "\n",
        "def heaviside(a: TT[\"i\"], b: TT[\"i\"]) -> TT[\"i\"]:\n",
        "    return (a == 0) * b + (a < 0) * 0 + (a > 0) * 1\n",
        "\n",
        "\n",
        "\n",
        "test_heaviside = make_test(\"heaviside\", heaviside, heaviside_spec)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 42,
      "id": "357974e8",
      "metadata": {
        "execution": {
          "iopub.execute_input": "2022-07-13T00:15:39.906141Z",
          "iopub.status.busy": "2022-07-13T00:15:39.905812Z",
          "iopub.status.idle": "2022-07-13T00:15:39.909230Z",
          "shell.execute_reply": "2022-07-13T00:15:39.908641Z"
        },
        "id": "357974e8",
        "lines_to_next_cell": 2
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Correct!\n"
          ]
        },
        {
          "data": {
            "text/html": [
              "\n",
              "    <video alt=\"test\" controls autoplay=1>\n",
              "        <source src=\"https://openpuppies.com/mp4/ros6RLC.mp4\"  type=\"video/mp4\">\n",
              "    </video>\n",
              "    "
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "execution_count": 42,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "run_test(test_heaviside)"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "a2d00053",
      "metadata": {
        "id": "a2d00053"
      },
      "source": [
        "## Puzzle 20 - repeat (1d)\n",
        "\n",
        "Compute [repeat](https://pytorch.org/docs/stable/generated/torch.Tensor.repeat.html)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 43,
      "id": "f763b7ce",
      "metadata": {
        "execution": {
          "iopub.execute_input": "2022-07-13T00:15:39.912233Z",
          "iopub.status.busy": "2022-07-13T00:15:39.911925Z",
          "iopub.status.idle": "2022-07-13T00:15:41.190253Z",
          "shell.execute_reply": "2022-07-13T00:15:41.189625Z"
        },
        "id": "f763b7ce",
        "outputId": "17cc8ce0-9d09-4db5-f14f-588edc3bc43a"
      },
      "outputs": [
        {
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0.0)\"><g transform=\"matrix(1.0, -0.0, 0.0, 1.0, 0.0, 0.0)\"><g/></g></g></g><g style=\"stroke: black;stroke-width: 0.9;\" transform=\"matrix(1.0, 0.0, 0.0, 1.0, 0.5, -0.5)\"><path d=\"M 0.0 0.0 L 1.0 0.0 L 1.0 1.0 L 0.0 1.0 L 0.0 0.0 Z\" style=\"vector-effect: non-scaling-stroke;\"/></g></g><g transform=\"matrix(1.0, 0.0, 0.0, 1.0, 1.5, 0.0)\"><g transform=\"matrix(1.0, -0.0, 0.0, 1.0, 0.0, 0.0)\"><g/></g></g></g><g style=\"stroke: black;stroke-width: 0.9;\" transform=\"matrix(1.0, 0.0, 0.0, 1.0, 1.5, -0.5)\"><path d=\"M 0.0 0.0 L 1.0 0.0 L 1.0 1.0 L 0.0 1.0 L 0.0 0.0 Z\" style=\"vector-effect: non-scaling-stroke;\"/></g></g></g></g></g><g/></g></g></g></g></g></g></g></g><g/></g></g></g></g><g/></g></g></g></g></svg>"
            ],
            "text/plain": [
              "<IPython.core.display.SVG object>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "def repeat_spec(a, d, out):\n",
        "    for i in range(d[0]):\n",
        "        for k in range(len(a)):\n",
        "            out[i][k] = a[k]\n",
        "\n",
        "def constraint_set(d):\n",
        "    d[\"d\"][0] = d[\"return\"].shape[0]\n",
        "    return d\n",
        "\n",
        "\n",
        "def repeat(a: TT[\"i\"], d: TT[1]) -> TT[\"d\", \"i\"]:\n",
        "    return ones(d)[:, None] * a\n",
        "\n",
        "test_repeat = make_test(\"repeat\", repeat, repeat_spec, constraint=constraint_set)\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 44,
      "id": "8b91fd1f",
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Correct!\n"
          ]
        },
        {
          "data": {
            "text/html": [
              "\n",
              "    <video alt=\"test\" controls autoplay=1>\n",
              "        <source src=\"https://openpuppies.com/mp4/2Gdl1u7.mp4\"  type=\"video/mp4\">\n",
              "    </video>\n",
              "    "
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "execution_count": 44,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "run_test(test_repeat)"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "30742b35",
      "metadata": {},
      "source": [
        "## Puzzle 21 - bucketize\n",
        "\n",
        "Compute [bucketize](https://pytorch.org/docs/stable/generated/torch.bucketize.html)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 45,
      "id": "7832fda9",
      "metadata": {
        "execution": {
          "iopub.execute_input": "2022-07-13T00:15:41.193726Z",
          "iopub.status.busy": "2022-07-13T00:15:41.193384Z",
          "iopub.status.idle": "2022-07-13T00:15:42.586710Z",
          "shell.execute_reply": "2022-07-13T00:15:42.586092Z"
        },
        "id": "7832fda9",
        "outputId": "bf255360-667b-49ec-a43a-5a795f8120bd"
      },
      "outputs": [
        {
          "data": {
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            ],
            "text/plain": [
              "<IPython.core.display.SVG object>"
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        }
      ],
      "source": [
        "def bucketize_spec(v, boundaries, out):\n",
        "    for i, val in enumerate(v):\n",
        "        out[i] = 0\n",
        "        for j in range(len(boundaries)-1):\n",
        "            if val >= boundaries[j]:\n",
        "                out[i] = j + 1\n",
        "        if val >= boundaries[-1]:\n",
        "            out[i] = len(boundaries)\n",
        "\n",
        "\n",
        "def constraint_set(d):\n",
        "    d[\"boundaries\"] = np.abs(d[\"boundaries\"]).cumsum()\n",
        "    return d\n",
        "\n",
        "\n",
        "def bucketize(v: TT[\"i\"], boundaries: TT[\"j\"]) -> TT[\"i\"]:\n",
        "    return ones(len(boundaries)) @ where(boundaries[:, None] <= v, 1, 0)\n",
        "\n",
        "test_bucketize = make_test(\"bucketize\", bucketize, bucketize_spec,\n",
        "                           constraint=constraint_set)\n",
        "                           "
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 46,
      "id": "4bcf49de",
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Correct!\n"
          ]
        },
        {
          "data": {
            "text/html": [
              "\n",
              "    <video alt=\"test\" controls autoplay=1>\n",
              "        <source src=\"https://openpuppies.com/mp4/DS2IZ6K.mp4\"  type=\"video/mp4\">\n",
              "    </video>\n",
              "    "
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "execution_count": 46,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "run_test(test_bucketize)"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "0dfd6bcd",
      "metadata": {},
      "source": [
        "# Speed Run Mode!\n",
        "\n",
        "What is the smallest you can make each of these?"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 47,
      "id": "dbf265d8",
      "metadata": {
        "execution": {
          "iopub.execute_input": "2022-07-13T00:15:42.589966Z",
          "iopub.status.busy": "2022-07-13T00:15:42.589646Z",
          "iopub.status.idle": "2022-07-13T00:15:42.599516Z",
          "shell.execute_reply": "2022-07-13T00:15:42.598869Z"
        },
        "id": "dbf265d8",
        "outputId": "a9da9a05-4149-4d36-9df3-f473adfa74ac"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "ones 38\n",
            "sum 36\n",
            "outer 34\n",
            "diag 44\n",
            "eye 55\n",
            "triu 55\n",
            "cumsum 27\n",
            "diff 74\n",
            "vstack 43\n",
            "roll 33\n",
            "flip 31\n",
            "compress 70\n",
            "pad_to 38\n",
            "sequence_mask 63\n",
            "bincount 64\n",
            "scatter_add 60\n",
            "flatten 47\n",
            "linspace 45\n",
            "heaviside 51\n",
            "repeat 31\n",
            "bucketize 72\n"
          ]
        }
      ],
      "source": [
        "import inspect\n",
        "fns = (ones, sum, outer, diag, eye, triu, cumsum, diff, vstack, roll, flip,\n",
        "       compress, pad_to, sequence_mask, bincount, scatter_add, flatten, linspace,\n",
        "       heaviside, repeat, bucketize)\n",
        "\n",
        "for fn in fns:\n",
        "    lines = [l for l in inspect.getsource(fn).split(\"\\n\") if not l.strip().startswith(\"#\")]\n",
        "\n",
        "    if len(lines) > 3:\n",
        "        print(fn.__name__, len(lines[2]), \"(more than 1 line)\")\n",
        "    else:\n",
        "        print(fn.__name__, len(lines[1]))"
      ]
    }
  ],
  "metadata": {
    "colab": {
      "provenance": []
    },
    "jupytext": {
      "cell_metadata_filter": "id,-all"
    },
    "kernelspec": {
      "display_name": "tensor-puzzles",
      "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": "3.10.13"
    }
  },
  "nbformat": 4,
  "nbformat_minor": 5
}