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@Hasenpfote
Last active July 28, 2021 11:22
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Plotting derivatives using PyTorch.
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{
"nbformat": 4,
"nbformat_minor": 0,
"metadata": {
"colab": {
"name": "pytorch_plot_derivatives.ipynb",
"provenance": [],
"collapsed_sections": [],
"authorship_tag": "ABX9TyNhILf4SUdd761uhGujIzCX",
"include_colab_link": true
},
"kernelspec": {
"name": "python3",
"display_name": "Python 3"
},
"language_info": {
"name": "python"
},
"accelerator": "GPU"
},
"cells": [
{
"cell_type": "markdown",
"metadata": {
"id": "view-in-github",
"colab_type": "text"
},
"source": [
"<a href=\"https://colab.research.google.com/gist/Hasenpfote/95dddcf6cdf1365e8b227ff46e3140de/pytorch_plot_derivatives.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
]
},
{
"cell_type": "code",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "U3XD4lXTr2Lx",
"outputId": "29eaff1d-9060-4140-86a5-87152df912c5"
},
"source": [
"!python --version"
],
"execution_count": 38,
"outputs": [
{
"output_type": "stream",
"text": [
"Python 3.7.11\n"
],
"name": "stdout"
}
]
},
{
"cell_type": "code",
"metadata": {
"id": "GqVohPAy91vP"
},
"source": [
"import torch\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt"
],
"execution_count": 39,
"outputs": []
},
{
"cell_type": "code",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 35
},
"id": "XjiXG_ilrFw7",
"outputId": "d1721553-04d2-4fbe-efbd-3c430ba35c77"
},
"source": [
"torch.__version__"
],
"execution_count": 40,
"outputs": [
{
"output_type": "execute_result",
"data": {
"application/vnd.google.colaboratory.intrinsic+json": {
"type": "string"
},
"text/plain": [
"'1.9.0+cu102'"
]
},
"metadata": {
"tags": []
},
"execution_count": 40
}
]
},
{
"cell_type": "code",
"metadata": {
"id": "TE3Pd4gbFoA5"
},
"source": [
"def ordinal(n):\n",
" return str(n) + \\\n",
" {1: 'st', 2: 'nd', 3: 'rd'}.get(4 if 10 <= n % 100 < 20 else n % 10, 'th')\n",
"\n",
"def plot_derivative(fn, order=0, start=-10.0, end=10.0, steps=100):\n",
" x = torch.linspace(start, end, steps, dtype=torch.float, requires_grad=True)\n",
" dydx = fn(x)\n",
" for _ in range(order):\n",
" dydx = torch.autograd.grad(dydx.sum(), x, create_graph=True)[0]\n",
"\n",
" fig, ax = plt.subplots(figsize=(4, 3))\n",
" ax.set_xlabel('x')\n",
" ax.set_ylabel('y')\n",
" ax.set_title('{} order derivative'.format(ordinal(order)))\n",
" ax.grid(True)\n",
" ax.plot(x.cpu().detach().numpy(), dydx.cpu().detach().numpy())\n",
"\n",
" fig.suptitle(fn.__name__, y=1.05)\n",
" plt.show()\n",
"\n",
"def plot_derivatives(fn, order=1, start=-10.0, end=10.0, steps=100):\n",
" num_derivatives = order + 1\n",
" num_cols = num_derivatives if num_derivatives < 3 else 3\n",
" num_rows = num_derivatives // num_cols + (1 if num_derivatives > 3 else 0)\n",
"\n",
" fig, axs = plt.subplots(nrows=num_rows, ncols=num_cols, figsize=(4*num_cols, 3*num_rows))\n",
" if type(axs) != np.ndarray:\n",
" axs = np.array([axs])\n",
"\n",
" for i, ax in enumerate(axs.reshape(-1)):\n",
" ax.axis('off')\n",
"\n",
" x = torch.linspace(start, end, steps, dtype=torch.float, requires_grad=True)\n",
" dydx = fn(x)\n",
" h = x.cpu().detach().numpy()\n",
"\n",
" for i, ax in enumerate(axs.reshape(-1)[:num_derivatives]):\n",
" ax.axis('on')\n",
" #ax.set_aspect(1./ax.axes.get_data_ratio())\n",
" ax.set_xlabel('x')\n",
" ax.set_ylabel('y')\n",
" ax.set_title('{} order derivative'.format(ordinal(i)))\n",
" ax.grid(True)\n",
" ax.plot(h, dydx.cpu().detach().numpy())\n",
" dydx = torch.autograd.grad(dydx.sum(), x, create_graph=True)[0]\n",
"\n",
" fig.tight_layout()\n",
" fig.suptitle(fn.__name__, y=1.05)\n",
" plt.show()"
],
"execution_count": 41,
"outputs": []
},
{
"cell_type": "markdown",
"metadata": {
"id": "6g6hcumVkpw_"
},
"source": [
"## $sigmoid{(x)}$"
]
},
{
"cell_type": "code",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 492
},
"id": "-wYTSbSJXbA-",
"outputId": "45a7b72d-46b6-43b8-8e55-7d0ea9050084"
},
"source": [
"# https://pytorch.org/docs/stable/nn.functional.html\n",
"plot_derivative(fn=torch.sigmoid, order=2)\n",
"plot_derivatives(fn=torch.sigmoid, order=2)"
],
"execution_count": 42,
"outputs": [
{
"output_type": "display_data",
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 288x216 with 1 Axes>"
]
},
"metadata": {
"tags": [],
"needs_background": "light"
}
},
{
"output_type": "display_data",
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 864x216 with 3 Axes>"
]
},
"metadata": {
"tags": [],
"needs_background": "light"
}
}
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "5Ta_3jIFloT7"
},
"source": [
"## $e^{x}$"
]
},
{
"cell_type": "code",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 492
},
"id": "bbJUhxVilqRp",
"outputId": "1dd55dc0-0937-4a6d-8974-598632e49795"
},
"source": [
"plot_derivatives(fn=torch.exp, order=2)\n",
"plot_derivative(fn=torch.exp, order=2)"
],
"execution_count": 43,
"outputs": [
{
"output_type": "display_data",
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 864x216 with 3 Axes>"
]
},
"metadata": {
"tags": [],
"needs_background": "light"
}
},
{
"output_type": "display_data",
"data": {
"image/png": "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\n",
"text/plain": [
"<Figure size 288x216 with 1 Axes>"
]
},
"metadata": {
"tags": [],
"needs_background": "light"
}
}
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "rCElqYP2ktRe"
},
"source": [
"## $\\ln{(x)}, \\ln{(1-x)}$"
]
},
{
"cell_type": "code",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 967
},
"id": "6b4GB6AKXra4",
"outputId": "581f30c1-be10-4c0a-cd8a-cd166573d268"
},
"source": [
"log_1_x = lambda x: torch.log(1.0 - x)\n",
"\n",
"plot_derivatives(fn=torch.log, order=2, start=0.0, end=1.0)\n",
"plot_derivative(fn=torch.log, order=2, start=0.0, end=1.0)\n",
"\n",
"plot_derivatives(fn=log_1_x, order=2, start=0.0, end=1.0)\n",
"plot_derivative(fn=log_1_x, order=2, start=0.0, end=1.0)"
],
"execution_count": 44,
"outputs": [
{
"output_type": "display_data",
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 864x216 with 3 Axes>"
]
},
"metadata": {
"tags": [],
"needs_background": "light"
}
},
{
"output_type": "display_data",
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 288x216 with 1 Axes>"
]
},
"metadata": {
"tags": [],
"needs_background": "light"
}
},
{
"output_type": "display_data",
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 864x216 with 3 Axes>"
]
},
"metadata": {
"tags": [],
"needs_background": "light"
}
},
{
"output_type": "display_data",
"data": {
"image/png": "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\n",
"text/plain": [
"<Figure size 288x216 with 1 Axes>"
]
},
"metadata": {
"tags": [],
"needs_background": "light"
}
}
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "hVt2Sib2k3A0"
},
"source": [
"## $\\sin{(x)}$"
]
},
{
"cell_type": "code",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 737
},
"id": "LkSGjhkak7N0",
"outputId": "033f99b2-c7a0-478f-f665-f42f428dd0a1"
},
"source": [
"plot_derivatives(fn=torch.sin, order=2)\n",
"plot_derivative(fn=torch.sin, order=2)\n",
"plot_derivative(fn=lambda x: - torch.sin(x), order=0)"
],
"execution_count": 45,
"outputs": [
{
"output_type": "display_data",
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 864x216 with 3 Axes>"
]
},
"metadata": {
"tags": [],
"needs_background": "light"
}
},
{
"output_type": "display_data",
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 288x216 with 1 Axes>"
]
},
"metadata": {
"tags": [],
"needs_background": "light"
}
},
{
"output_type": "display_data",
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 288x216 with 1 Axes>"
]
},
"metadata": {
"tags": [],
"needs_background": "light"
}
}
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "ObLkiHzNlRhl"
},
"source": [
"## $sinc{(x)} \\equiv \\frac{\\sin{(x)}}{x}$ "
]
},
{
"cell_type": "code",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 492
},
"id": "yP2npYvdlVo6",
"outputId": "14d71f3a-a038-4e2b-8a39-bd7ca69b1ce4"
},
"source": [
"def sinc(x):\n",
" return torch.sin(x) / x\n",
"\n",
"plot_derivatives(fn=sinc, order=2)\n",
"plot_derivative(fn=sinc, order=2)"
],
"execution_count": 46,
"outputs": [
{
"output_type": "display_data",
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 864x216 with 3 Axes>"
]
},
"metadata": {
"tags": [],
"needs_background": "light"
}
},
{
"output_type": "display_data",
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 288x216 with 1 Axes>"
]
},
"metadata": {
"tags": [],
"needs_background": "light"
}
}
]
}
]
}
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