{ "cells": [ { "cell_type": "markdown", "id": "fefa10b6-d616-4cce-929c-3f16604d3e67", "metadata": {}, "source": [ "# Taylor models of univariate functions\n", "\n", "(by Sean Cowan)\n", "\n", "This notebook introduces the application of Taylor models to univariate functions." ] }, { "cell_type": "markdown", "id": "048fec6e-9c23-40b1-ae72-1b7354a3f4d3", "metadata": {}, "source": [ "## Importing stuff" ] }, { "cell_type": "code", "execution_count": 1, "id": "bc1c4a85-2c69-4099-ab75-a66cbdd520ee", "metadata": {}, "outputs": [], "source": [ "from pyaudi import gdual_double as gdual, taylor_model, int_d\n", "from pyaudi import exp, log, sin\n", "import numpy as np\n", "import scipy as sci\n", "from itertools import product\n", "import matplotlib.pyplot as plt\n", "import matplotlib.colors as col\n", "import seaborn as sns\n", "\n", "from plotting_functions import plot_orders" ] }, { "cell_type": "markdown", "id": "4ca1a371-823f-4fe5-af2a-42f1de23d503", "metadata": {}, "source": [ "## Exponential\n", "\n", "First, an exponential function is used to plot the Taylor Model of the function on the domain $[-0.5, 0.5]$. The exponential is chosen as it monotically increases, which should make it easy for a truncated Taylor series of a low order to approximate the function reasonably well. The function is defined as:\n", "$$f(x) = e^x$$" ] }, { "cell_type": "code", "execution_count": 2, "id": "16136b28-e5f4-4488-80a9-ae40b93594fa", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def func(x):\n", " if isinstance(x, taylor_model):\n", " return exp(x)\n", " elif isinstance(x, float):\n", " return np.exp(1) ** x\n", "\n", "domain_size = 0.5\n", "exp_points = {\"x\": 0.0}\n", "dom = {\"x\": int_d(exp_points[\"x\"] - domain_size, exp_points[\"x\"] + domain_size)}\n", "rem = int_d(0.0, 0.0)\n", "\n", "ax = plot_orders(func, rem, exp_points, dom, orders=[2, 3, 4], buffer=0.0)\n", "ax.grid()\n", "ax.set_xlabel('x')\n", "ax.set_ylabel('f(x)'); # <-- to suppress notebook text output\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 3, "id": "6ce9599c-02aa-43fa-bae4-07195e19b422", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ax = plot_orders(func, rem, exp_points, dom, orders=[2, 3, 4], buffer=0.0)\n", "ax.grid()\n", "ax.set_xlim([0.35, 0.3525])\n", "ax.set_ylim([1.395, 1.45])\n", "ax.set_xlabel('x')\n", "ax.set_ylabel('f(x)');" ] }, { "cell_type": "markdown", "id": "2fe82ed6-490c-400f-b0a8-b861052650e5", "metadata": {}, "source": [ "## Sine wave\n", "\n", "Second, the Taylor model of a sine function is plotted on the domain $[0, 2 \\pi]$. The sine wave is periodic, and therefore more difficult to approximate. It can be seen that higher orders are needed to approximate the function with the same level of accuracy as compared to the exponential function. The function is defined as:\n", "$$f(x) = \\sin(x)$$" ] }, { "cell_type": "code", "execution_count": 4, "id": "179bf7d1-b9c4-494b-9373-a847b3adb58e", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def func(x):\n", " if isinstance(x, taylor_model):\n", " return sin(x)\n", " else:\n", " return np.sin(x)\n", "\n", "domain_size = 3.14\n", "exp_points = {\"x\": 0.0}\n", "dom = {\"x\": int_d(exp_points[\"x\"] - domain_size, exp_points[\"x\"] + domain_size)}\n", "rem = int_d(0.0, 0.0)\n", "\n", "ax = plot_orders(func, rem, exp_points, dom, orders=[4, 5, 6], buffer=0.0)\n", "ax.grid()\n", "ax.set_ylim([-5, 5])\n", "ax.set_ylabel('f(x)')\n", "ax.set_xlabel('x');" ] }, { "cell_type": "markdown", "id": "81aa9fc9-cf65-4238-9ec0-516579c92b68", "metadata": {}, "source": [ "Here, we show what it looks like if you center the expansion around a point that is not at the center of the domain, but rather at the edge." ] }, { "cell_type": "code", "execution_count": 5, "id": "b5446b26-2cc9-42ec-b8ad-1ba5ddf23d30", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def func(x):\n", " if isinstance(x, taylor_model):\n", " return sin(x)\n", " else:\n", " return np.sin(x)\n", "\n", "exp_points = {\"x\": 0.9}\n", "dom = {\"x\": int_d(-1.0, 1.0)}\n", "rem = int_d(0.0, 0.0)\n", "\n", "ax = plot_orders(func, rem, exp_points, dom, orders=[4, 5, 6], buffer=0.0)\n", "ax.grid()\n", "# ax.set_ylim([-5, 5])\n", "ax.set_ylabel('f(x)')\n", "ax.set_xlabel('x');" ] }, { "cell_type": "markdown", "id": "63b266b4-c9e0-49b3-9439-ea9ef7714bf5", "metadata": {}, "source": [ "## 6-th order power-sine\n", "\n", "Finally, a 6-th order power-sine function is used as a more challenging example. The Taylor model of the function is evaluated on the domain $[-0.5, 1.0]$. The function is defined as:\n", "$$f(x) = x \\cdot (x - 1.1) \\cdot (x + 2) \\cdot (x + 2.2) \\cdot (x + 2.5) \\cdot (x + 3) \\cdot \\sin(1.7 \\cdot x + 0.5)$$" ] }, { "cell_type": "code", "execution_count": 8, "id": "8948cbfc-5382-4154-b047-6c3018e463a7", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def func(x):\n", " if isinstance(x, taylor_model):\n", " return x * (x - 1.1) * (x + 2) * (x + 2.2) * (x + 2.5) * (x + 3) * sin(1.7 * x + 0.5)\n", " else:\n", " return x * (x - 1.1) * (x + 2) * (x + 2.2) * (x + 2.5) * (x + 3) * np.sin(1.7 * x + 0.5)\n", "\n", "exp_point = {\"x\": 0.0}\n", "rem_bound = int_d(0.0, 0.0)\n", "domain = {\"x\": int_d(-0.5, 1.0)}\n", "\n", "ax = plot_orders(func, rem_bound, exp_point, domain, orders=[5, 6, 7], buffer=0.0)\n", "ax.set_xlabel('x')\n", "ax.set_ylabel('f(x)');" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.13.3" } }, "nbformat": 4, "nbformat_minor": 5 }