{ "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Numerical Derivatives" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Finite differences\n", "\n", "The numerical derivatives like\n", "$$\n", "f'(x) = \\lim_{h \\to 0} \\frac{f(x+h) - f(x)}{h}~.\n", "$$\n", "\n", "Are evaluated using finite differences\n", "\n", "The simplest methods are\n", "\n", "## Forward difference\n", "$$\n", "f'(x) \\simeq \\frac{f(x+h) - f(x)}{h}~.\n", "$$\n", "\n", "The truncation error can be estimated through the Taylor theorem\n", "$$\n", "R_{\\rm forw} = -\\frac{1}{2}h f''(x) + \\mathcal{O}(h^2)\n", "$$\n", "\n", "## Backward difference\n", "$$\n", "f'(x) \\simeq \\frac{f(x) - f(x-h)}{h}~.\n", "$$\n", "\n", "The truncation error:\n", "$$\n", "R_{\\rm back} = \\frac{1}{2}h f''(x) + \\mathcal{O}(h^2)\n", "$$\n", "\n", "## Central difference\n", "\n", "Take the average of forward and backward differences to cancel out the $\\mathcal{O}(h)$ term in the error estimate:\n", "\n", "$$\n", "f'(x) \\simeq \\frac{f(x+h) - f(x-h)}{2h}~.\n", "$$\n", "\n", "The truncation error:\n", "$$\n", "R_{\\rm cent} = -\\frac{1}{6}h^2 f'''(x) + \\mathcal{O}(h^3)\n", "$$" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "def df_forward(f,x,h):\n", " return (f(x+h) - f(x)) / h\n", "\n", "def df_backward(f,x,h):\n", " return (f(x) - f(x-h)) / h\n", "\n", "def df_central(f,x,h):\n", " return (f(x+h) - f(x-h)) / (2. * h)" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", " \n", "def f(x):\n", " return np.exp(x)\n", "\n", "def df(x):\n", " return np.exp(x)\n", "\n", "def d2f(x):\n", " return np.exp(x)\n", "\n", "def d3f(x):\n", " return np.exp(x)\n", "\n", "def d4f(x):\n", " return np.exp(x)\n", "\n", "def d5f(x):\n", " return np.exp(x)" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "h f'(0) Relative error \n", "1 4.670774270471606 0.7182818284590456 \n", "0.1 2.858841954873883 0.051709180756477874\n", "0.01 2.7319186557871245 0.005016708416805288\n", "0.001 2.7196414225332255 0.0005001667082294914\n", "0.0001 2.718417747082924 5.000166739738369e-05\n", "1e-05 2.7182954199567173 5.000032568337868e-06\n", "1e-06 2.7182831874306146 4.999377015549417e-07\n", "1e-07 2.7182819684057336 5.1483509544443144e-08\n", "1e-08 2.7182818218562943 2.429016271026634e-09\n", "1e-09 2.7182820439008992 7.925662890392757e-08\n", "1e-10 2.7182833761685288 5.693704999536528e-07\n", "1e-11 2.7183144624132183 1.2005360824447243e-05\n", "1e-12 2.7187141427020833 0.00015903952213936482\n", "1e-13 2.717825964282383 0.000167703058560452\n", "1e-14 2.708944180085382 0.0034351288655586204\n", "1e-15 3.108624468950438 0.1435990324493588 \n", "1e-16 0.0 1.0 \n", "1e-17 0.0 1.0 \n", "1e-18 0.0 1.0 \n", "1e-19 0.0 1.0 \n" ] } ], "source": [ "print(\"{:<10} {:<20} {:<20}\".format('h',\"f'(0)\",\"Relative error\"))\n", "x0 = 1.\n", "\n", "arr_h = []\n", "arr_df = []\n", "arr_err = []\n", "arr_err_theo = []\n", "arr_err_theo_full = []\n", "epsm = 10**-16 # Machine epsilon\n", "\n", "for i in range(0,-20,-1):\n", " h = 10**i\n", " df_val = df_forward(f, x0,h)\n", " df_err = abs((df_val - df(x0)) / df(x0))\n", " print(\"{:<10} {:<20} {:<20}\".format(h,df_val,df_err))\n", " arr_h.append(h)\n", " arr_df.append(df_val)\n", " arr_err.append(df_err)\n", " df_err_theo = abs(0.5*h*d2f(x0)/df(x0))\n", " arr_err_theo.append(df_err_theo)\n", " df_err_theo_full = df_err_theo + 2. * epsm / h\n", " arr_err_theo_full.append(df_err_theo_full)\n", " \n", "arr_df_forw = arr_df[:]\n", "arr_err_forw = arr_err[:]\n", "arr_err_theo_forw = arr_err_theo[:]\n", "arr_err_theo_full_forw = arr_err_theo_full[:]" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "h f'(0) Relative error \n", "1 1.718281828459045 0.36787944117144233 \n", "0.1 2.5867871730209524 0.048374180359596904\n", "0.01 2.704735610978304 0.004983374916801915\n", "0.001 2.7169231404782224 0.0004998333751114198\n", "0.0001 2.7181459188962975 4.999833399342759e-05\n", "1e-05 2.7182682370785467 4.999989462496166e-06\n", "1e-06 2.718280469160561 5.000579666768477e-07\n", "1e-07 2.7182816886295313 5.144040337599916e-08\n", "1e-08 2.7182818218562943 2.429016271026634e-09\n", "1e-09 2.7182815998116894 8.411466144598084e-08\n", "1e-10 2.7182789352764303 1.0643424035454313e-06\n", "1e-11 2.7182700534922333 4.3317682105436e-06 \n", "1e-12 2.7182700534922333 4.3317682105436e-06 \n", "1e-13 2.717825964282383 0.000167703058560452\n", "1e-14 2.708944180085382 0.0034351288655586204\n", "1e-15 2.6645352591003757 0.019772257900549463\n", "1e-16 0.0 1.0 \n", "1e-17 0.0 1.0 \n", "1e-18 0.0 1.0 \n", "1e-19 0.0 1.0 \n" ] } ], "source": [ "print(\"{:<10} {:<20} {:<20}\".format('h',\"f'(0)\",\"Relative error\"))\n", "\n", "arr_h = []\n", "arr_df = []\n", "arr_err = []\n", "arr_err_theo = []\n", "arr_err_theo_full = []\n", "\n", "for i in range(0,-20,-1):\n", " h = 10**i\n", " df_val = df_backward(f, x0,h)\n", " df_err = abs((df_val - df(x0)) / df(x0))\n", " print(\"{:<10} {:<20} {:<20}\".format(h,df_val,df_err))\n", " arr_h.append(h)\n", " arr_df.append(df_val)\n", " arr_err.append(df_err)\n", " df_err_theo = abs(0.5*h*d2f(x0)/df(x0))\n", " arr_err_theo.append(df_err_theo)\n", " df_err_theo_full = df_err_theo + 2. * epsm / h\n", " arr_err_theo_full.append(df_err_theo_full)\n", " \n", "arr_df_back = arr_df[:]\n", "arr_err_back = arr_err[:]\n", "arr_err_theo_back = arr_err_theo[:]\n", "arr_err_theo_full_back = arr_err_theo_full[:]" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "h f'(0) Relative error \n", "1 3.194528049465325 0.17520119364380154 \n", "0.1 2.7228145639474177 0.001667500198440488\n", "0.01 2.718327133382714 1.6666750001686406e-05\n", "0.001 2.718282281505724 1.6666655903580706e-07\n", "0.0001 2.718281832989611 1.66670197804557e-09\n", "1e-05 2.718281828517632 2.1552920850702018e-11\n", "1e-06 2.718281828295588 6.013256095296185e-11\n", "1e-07 2.7182818285176324 2.155308422199237e-11\n", "1e-08 2.7182818218562943 2.429016271026634e-09\n", "1e-09 2.7182818218562943 2.429016271026634e-09\n", "1e-10 2.7182811557224795 2.474859517958893e-07\n", "1e-11 2.7182922579527258 3.836796306951821e-06\n", "1e-12 2.7184920980971583 7.735387696441061e-05\n", "1e-13 2.717825964282383 0.000167703058560452\n", "1e-14 2.708944180085382 0.0034351288655586204\n", "1e-15 2.8865798640254066 0.06191338727440458 \n", "1e-16 0.0 1.0 \n", "1e-17 0.0 1.0 \n", "1e-18 0.0 1.0 \n", "1e-19 0.0 1.0 \n" ] } ], "source": [ "print(\"{:<10} {:<20} {:<20}\".format('h',\"f'(0)\",\"Relative error\"))\n", "\n", "arr_h = []\n", "arr_df = []\n", "arr_err = []\n", "arr_err_theo = []\n", "arr_err_theo_full = []\n", "\n", "for i in range(0,-20,-1):\n", " h = 10**i\n", " df_val = df_central(f, x0,h)\n", " df_err = abs((df_val - df(x0)) / df(x0))\n", " print(\"{:<10} {:<20} {:<20}\".format(h,df_val,df_err))\n", " arr_h.append(h)\n", " arr_df.append(df_val)\n", " arr_err.append(df_err)\n", " df_err_theo = abs(h**2 * d3f(x0)/df(x0)/6.)\n", " arr_err_theo.append(df_err_theo)\n", " df_err_theo_full = df_err_theo + epsm / h\n", " arr_err_theo_full.append(df_err_theo_full)\n", "\n", "arr_df_cent = arr_df[:]\n", "arr_err_cent = arr_err[:]\n", "arr_err_theo_cent = arr_err_theo[:]\n", "arr_err_theo_full_cent = arr_err_theo_full[:]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To improve the approximation error use more than two function evaluations, e.g.\n", "$$\n", "f'(x) \\simeq \\frac{A f(x+2h) + B f(x+h) + C f(x) + D f(x-h) + E f(x-2h)}{h} + \\mathcal{O}(h^4)\n", "$$\n", "\n", "Determine $A,B,C,D,E$ from from Taylor expansion of $f(x)$:\n", "$$\n", "f'(x) \\simeq \\frac{-f(x+2h)+8f(x+h)-8f(x-h)+f(x-2h)}{12h} + \\frac{h^4}{30} f^{(5)} (x)\n", "$$" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "def df_central2(f,x,h):\n", " return (-f(x+2.*h) + 8. * f(x+h) - 8. * f(x-h) + f(x - 2.*h)) / (12. * h)" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "h f'(0) Relative error \n", "1 2.6162326091190815 0.03754180978276775 \n", "0.1 2.718272756726489 3.3373039032555605e-06\n", "0.01 2.7182818275529415 3.3333689946350053e-10\n", "0.001 2.7182818284586054 1.6173757744640934e-13\n", "0.0001 2.7182818284602708 4.5090476136574727e-13\n", "1e-05 2.7182818284769237 6.577164778196963e-12\n", "1e-06 2.718281828295588 6.013256095296185e-11\n", "1e-07 2.7182818296278555 4.299813100967634e-10\n", "1e-08 2.7182818070533203 7.874726058271109e-09\n", "1e-09 2.718281747841426 2.9657564717135134e-08\n", "1e-10 2.7182804155737963 5.197714357668605e-07\n", "1e-11 2.7182885572093105 2.4753688874237083e-06\n", "1e-12 2.7187141427020833 0.00015903952213936482\n", "1e-13 2.718196038623925 3.156031660224946e-05\n", "1e-14 2.7200464103316335 0.0006491533931890901\n", "1e-15 2.849572429871235 0.04829911307857894 \n", "1e-16 0.0 1.0 \n", "1e-17 3.7007434154171883 0.36142741958257013 \n", "1e-18 37.00743415417188 12.6142741958257 \n", "1e-19 370.07434154171887 135.14274195825703 \n" ] } ], "source": [ "print(\"{:<10} {:<20} {:<20}\".format('h',\"f'(0)\",\"Relative error\"))\n", "\n", "arr_h = []\n", "arr_df = []\n", "arr_err = []\n", "arr_err_theo = []\n", "arr_err_theo_full = []\n", "\n", "for i in range(0,-20,-1):\n", " h = 10**i\n", " df_val = df_central2(f, x0,h)\n", " df_err = abs((df_val - df(x0)) / df(x0))\n", " print(\"{:<10} {:<20} {:<20}\".format(h,df_val,df_err))\n", " arr_h.append(h)\n", " arr_df.append(df_val)\n", " arr_err.append(df_err)\n", " df_err_theo = abs(h**4 * d5f(x0)/df(x0)/30.)\n", " arr_err_theo.append(df_err_theo)\n", " df_err_theo_full = df_err_theo + 3. * epsm / (2. * h)\n", " arr_err_theo_full.append(df_err_theo_full)\n", " \n", "arr_df_cent2 = arr_df[:]\n", "arr_err_cent2 = arr_err[:]\n", "arr_err_theo_cent2 = arr_err_theo[:]\n", "arr_err_theo_full_cent2 = arr_err_theo_full[:]" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import matplotlib.pyplot as plt\n", "\n", "params = {'legend.fontsize': 'large',\n", " 'axes.labelsize': 'x-large',\n", " 'axes.titlesize':'x-large',\n", " 'xtick.labelsize':'x-large',\n", " 'ytick.labelsize':'x-large',\n", " 'xtick.direction':'in',\n", " 'ytick.direction':'in',\n", " }\n", "plt.rcParams.update(params)\n", "\n", "plt.title(\"Accuracy of the numerical derivative\")\n", "plt.xlabel(\"${h}$\", fontsize=18)\n", "plt.ylabel(\"relative error\", fontsize=18)\n", "plt.xscale('log')\n", "plt.yscale('log')\n", "plt.ylim(1.e-13,1.)\n", "plt.scatter(arr_h, arr_err_forw, color=\"red\",label=\"Forward diff. ${O(h)}$\")\n", "plt.plot(arr_h, arr_err_theo_forw, color=\"red\",linestyle=\"--\")\n", "plt.plot(arr_h, arr_err_theo_full_forw, color=\"red\")\n", "plt.scatter(arr_h, arr_err_back, color=\"blue\",label=\"Backward diff. ${O(h)}$\")\n", "plt.plot(arr_h, arr_err_theo_back, color=\"blue\",linestyle=\"--\")\n", "plt.plot(arr_h, arr_err_theo_full_back, color=\"blue\")\n", "plt.scatter(arr_h, arr_err_cent, color=\"orange\",label=\"Central diff. ${O(h^2)}$\")\n", "plt.plot(arr_h, arr_err_theo_cent, color=\"orange\",linestyle=\"--\")\n", "plt.plot(arr_h, arr_err_theo_full_cent, color=\"orange\")\n", "plt.scatter(arr_h, arr_err_cent2, color=\"purple\",label=\"Central diff. ${O(h^4)}$\")\n", "plt.plot(arr_h, arr_err_theo_cent2, color=\"purple\",linestyle=\"--\")\n", "plt.plot(arr_h, arr_err_theo_full_cent2, color=\"purple\")\n", "\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## High-order derivatives\n", "\n", "Central difference for the 2nd derivative\n", "$$\n", "f''(x) \\simeq \\frac{f'(x+h/2) - f'(x-h/2)}{h}\n", "$$\n", "\n", "Apply the central difference again to $f'(x+h/2)$ and $f'(x-h/2)$:\n", "$$\n", "f''(x) \\simeq \\frac{f(x+h) - 2f(x) - f(x-h)}{h^2}\n", "$$\n", "\n", "The truncation error:\n", "$$\n", "R_{f''_{\\rm cent}(x)} = -\\frac{1}{12} h^2 f^{(4)}(x)\n", "$$" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [], "source": [ "def d2f_central(f,x,h):\n", " return (f(x+h) - 2*f(x) + f(x-h)) / (h**2)" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "h f''(0) Relative error \n", "1 2.9524924420125602 0.08616126963048779 \n", "0.1 2.720547818529306 0.0008336111607475982\n", "0.01 2.718304480882061 8.333360720313657e-06\n", "0.001 2.7182820550031295 8.334091116267528e-08\n", "0.0001 2.7182818662652153 1.3908112763964208e-08\n", "1e-05 2.718287817060627 2.2030834032893657e-06\n", "1e-06 2.7182700534922333 4.3317682105436e-06 \n", "1e-07 2.797762022055395 0.029239129204423227\n", "1e-08 0.0 1.0 \n", "1e-09 444.08920985006256 162.3712903499084 \n", "1e-10 44408.920985006254 16336.129034990841 \n", "1e-11 4440892.098500626 1633711.903499084 \n", "1e-12 444089209.85006267 163371289.34990844 \n", "1e-13 0.0 1.0 \n", "1e-14 0.0 1.0 \n", "1e-15 444089209850062.56 163371290349907.4 \n", "1e-16 0.0 1.0 \n", "1e-17 0.0 1.0 \n", "1e-18 0.0 1.0 \n", "1e-19 0.0 1.0 \n" ] } ], "source": [ "print(\"{:<10} {:<20} {:<20}\".format('h',\"f''(0)\",\"Relative error\"))\n", "\n", "arr_h = []\n", "arr_d2f = []\n", "arr_err = []\n", "arr_err_theo = []\n", "arr_err_theo_full = []\n", "\n", "for i in range(0,-20,-1):\n", " h = 10**i\n", " d2f_val = d2f_central(f, x0,h)\n", " d2f_err = abs((d2f_val - d2f(x0)) / d2f(x0))\n", " print(\"{:<10} {:<20} {:<20}\".format(h,d2f_val,d2f_err))\n", " arr_h.append(h)\n", " arr_d2f.append(d2f_val)\n", " arr_err.append(d2f_err)\n", " df_err_theo = abs(h**2 * d4f(x0)/df(x0)/12.)\n", " arr_err_theo.append(df_err_theo)\n", " df_err_theo_full = df_err_theo + 4. * epsm / h**2\n", " arr_err_theo_full.append(df_err_theo_full)\n", "\n", "arr_d2f_cent = arr_df[:]\n", "arr_errd2f_cent = arr_err[:]\n", "arr_errd2f_theo_cent = arr_err_theo[:]\n", "arr_errd2f_theo_full_cent = arr_err_theo_full[:]" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import matplotlib.pyplot as plt\n", "\n", "params = {'legend.fontsize': 'large',\n", " 'axes.labelsize': 'x-large',\n", " 'axes.titlesize':'x-large',\n", " 'xtick.labelsize':'x-large',\n", " 'ytick.labelsize':'x-large',\n", " 'xtick.direction':'in',\n", " 'ytick.direction':'in',\n", " }\n", "plt.rcParams.update(params)\n", "\n", "plt.title(\"Accuracy of the 2nd numerical derivative ${f''(x)}$\")\n", "plt.xlabel(\"${h}$\", fontsize=18)\n", "plt.ylabel(\"relative error\", fontsize=18)\n", "plt.xscale('log')\n", "plt.yscale('log')\n", "plt.ylim(1.e-9,1.)\n", "plt.scatter(arr_h, arr_errd2f_cent, color=\"red\",label=\"Central diff. ${O(h^2)}$\")\n", "plt.plot(arr_h, arr_errd2f_theo_cent, color=\"red\",linestyle=\"--\")\n", "plt.plot(arr_h, arr_errd2f_theo_full_cent, color=\"red\")\n", "\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Automatic differentiation" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Preliminaries \n", "\n", "We will use \n", "- `jax`: https://docs.jax.dev/\n", "- or `MyGrad`: https://mygrad.readthedocs.io/en/latest/ \n", "which implement automatic differentiation\n", "\n", "Install `jax` if not already: https://docs.jax.dev/en/latest/installation.html\n", "\n", "```bash\n", "pip install -U jax\n", "```" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Consider a polynomial function\n", "$$\n", "f(x) = x^3 - 2x^2 + x - 2.\n", "$$\n", "\n", "Its derivative is\n", "$$\n", "f'(x) = 3 x^2 - 4x + 1\n", "$$" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " x f(x) df/dx\n", "0.0 -1.0000 1.0000\n", "0.2 -0.8720 0.3200\n", "0.4 -0.8560 -0.1200\n", "0.6 -0.9040 -0.3200\n", "0.8 -0.9680 -0.2800\n", "1.0 -1.0000 0.0000\n", "1.2 -0.9520 0.5200\n", "1.4 -0.7760 1.2800\n", "1.6 -0.4240 2.2800\n", "1.8 0.1520 3.5200\n", "2.0 1.0000 5.0000\n", "2.2 2.1680 6.7200\n", "2.4 3.7040 8.6800\n", "2.6 5.6560 10.8800\n", "2.8 8.0720 13.3200\n" ] } ], "source": [ "def f(x):\n", " return x**3 - 2*x**2 + x - 1\n", "\n", "def df(x):\n", " return 3 * x**2 - 4 * x + 1\n", "\n", "# Print f(x) and f'(x) for x=0,1,2\n", "# Output in column format\n", "# Print header\n", "print(f\"{'x':>3s} {'f(x)':>10s} {'df/dx':>10s}\")\n", "x_values = np.arange(0, 3, 0.2)\n", "for x in x_values:\n", " print(f\"{x:3.1f} {f(x):10.4f} {df(x):10.4f}\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now use automatic differentiation with `jax` if forward (`jvp`) and reverse (`grad`) modes" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " x f(x) df/dx_analyt df/dx_ad_forw df/dx_ad_reve\n", "0.0 -1.0000 1.0000 1.0000 1.0000\n", "0.2 -0.8720 0.3200 0.3200 0.3200\n", "0.4 -0.8560 -0.1200 -0.1200 -0.1200\n", "0.6 -0.9040 -0.3200 -0.3200 -0.3200\n", "0.8 -0.9680 -0.2800 -0.2800 -0.2800\n", "1.0 -1.0000 0.0000 0.0000 0.0000\n", "1.2 -0.9520 0.5200 0.5200 0.5200\n", "1.4 -0.7760 1.2800 1.2800 1.2800\n", "1.6 -0.4240 2.2800 2.2800 2.2800\n", "1.8 0.1520 3.5200 3.5200 3.5200\n", "2.0 1.0000 5.0000 5.0000 5.0000\n", "2.2 2.1680 6.7200 6.7200 6.7200\n", "2.4 3.7040 8.6800 8.6800 8.6800\n", "2.6 5.6560 10.8800 10.8800 10.8800\n", "2.8 8.0720 13.3200 13.3200 13.3200\n" ] } ], "source": [ "import jax.numpy as jnp\n", "from jax import grad\n", "from jax import jvp\n", "\n", "# Autodiff derivative forward mode\n", "def dfdx_auto_forward(func, x):\n", " x_val = jnp.array(x)\n", " dx = jnp.array(1.0)\n", " y, dy = jvp(func, (x_val,), (dx,))\n", " return dy\n", "\n", "# Autodiff derivative reverse mode\n", "def dfdx_auto_reverse(func, x):\n", " return grad(func)(x)\n", "\n", "\n", "print(f\"{'x':>3s} {'f(x)':>10s} {'df/dx_analyt':>15s} {'df/dx_ad_forw':>15s} {'df/dx_ad_reve':>15s}\")\n", "x_values = np.arange(0, 3, 0.2)\n", "for x in x_values:\n", " print(f\"{x:3.1f} {f(x):10.4f} {df(x):15.4f} {dfdx_auto_forward(f,x):15.4f} {dfdx_auto_reverse(f,x):15.4f}\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## A more involved example\n", "\n", "Automatic differentiation can be combined with other numerical methods.\n", "\n", "Consider the Dawson function:\n", "$$\n", "D_+(x) = e^{-x^2} \\int_0^x e^{t^2} dt.\n", "$$\n", "\n", "Let us evaluate $D_+(x)$ using 32-point Gaussian quadrature." ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from IntegrateGauss import *\n", "\n", "gaussxw32 = gaussxw(32)\n", "def gaussxwab32(a,b):\n", " x,w = gaussxw32\n", " return 0.5*(b-a)*x+0.5*(b+a),0.5*(b-a)*w\n", "\n", "from jax.numpy import exp\n", "\n", "def DawsonF(x):\n", " def fint(t):\n", " return exp(t**2)\n", " x2 = x**2\n", " gaussx, gaussw = gaussxwab32(0,x)\n", " return exp(-x2) * integrate_quadrature(fint, (gaussx, gaussw))\n", "\n", "# Plot the function from -5 to 5\n", "x = np.linspace(-5, 5, 100)\n", "y = [DawsonF(xi) for xi in x]\n", "plt.plot(x, y, label=\"DawsonF(x)\", color=\"blue\", linestyle=\"-\")\n", "plt.axhline(0, color=\"black\", linestyle=\"--\")\n", "plt.title(\"Dawson function\")\n", "plt.xlabel(\"x\")\n", "plt.ylabel(\"${D_+}(x)$\")\n", "plt.grid()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The derivative of Dawson function can be computed explicitly by differentiating its defition:\n", "$$\n", "D_{+}'(x) = 1 - 2x D_+(x).\n", "$$\n", "\n", "This expression can be used to verify the accuracy of automatic differentiation" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from jax import jvp\n", "\n", "# Analytic derivative\n", "def dDawsonFdx(x):\n", " return 1. - 2. * x * DawsonF(x)\n", "\n", "# Forward mode AD\n", "def dDawsonFdx_auto_forw(x): \n", " return dfdx_auto_forward(DawsonF, x)\n", "# Reverse mode AD\n", "def dDawsonFdx_auto_reve(x): \n", " return dfdx_auto_reverse(DawsonF, x)\n", "\n", "# Plot both derivatives from -5 to 5\n", "x = np.linspace(-5, 5, 100)\n", "df_vals = [dDawsonFdx(xi) for xi in x]\n", "# Use forward mode\n", "df_auto_vals = [dDawsonFdx_auto_forw(xi) for xi in x]\n", "\n", "plt.plot(x, df_vals, label=\"${D_+'(x)}$ analytic\", color=\"blue\", linestyle=\"-\")\n", "plt.plot(x, df_auto_vals, label=\"${D_+'(x)}$ autodiff\", color=\"red\", linestyle=\"--\")\n", "plt.axhline(0, color=\"black\", linestyle=\"--\")\n", "plt.title(\"Derivative of Dawson function\")\n", "plt.xlabel(\"x\")\n", "plt.ylabel(\"dDawsonFdx\")\n", "plt.legend()\n", "plt.grid()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Timing the performance" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Done\n", "CPU times: user 1.95 s, sys: 9.03 ms, total: 1.96 s\n", "Wall time: 2 s\n" ] } ], "source": [ "%%time\n", "\n", "# Timing the autodiff derivative forward mode\n", "x = np.linspace(-5, 5, 100)\n", "df_auto = [dDawsonFdx_auto_forw(xi) for xi in x]\n", "print(\"Done\")" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Done\n", "CPU times: user 5.14 s, sys: 50.1 ms, total: 5.19 s\n", "Wall time: 5.2 s\n" ] } ], "source": [ "%%time\n", "\n", "# Timing the autodiff derivative reverse mode\n", "x = np.linspace(-5, 5, 100)\n", "df_auto = [dDawsonFdx_auto_reve(xi) for xi in x]\n", "print(\"Done\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## MyGrad\n", "\n", "Now let us try MyGrad from https://github.com/rsokl/MyGrad" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " x f(x) df/dx_analyt df/dx_ad_mygrad\n", "0.0 -1.0000 1.0000 1.0000\n", "0.2 -0.8720 0.3200 0.3200\n", "0.4 -0.8560 -0.1200 -0.1200\n", "0.6 -0.9040 -0.3200 -0.3200\n", "0.8 -0.9680 -0.2800 -0.2800\n", "1.0 -1.0000 0.0000 0.0000\n", "1.2 -0.9520 0.5200 0.5200\n", "1.4 -0.7760 1.2800 1.2800\n", "1.6 -0.4240 2.2800 2.2800\n", "1.8 0.1520 3.5200 3.5200\n", "2.0 1.0000 5.0000 5.0000\n", "2.2 2.1680 6.7200 6.7200\n", "2.4 3.7040 8.6800 8.6800\n", "2.6 5.6560 10.8800 10.8800\n", "2.8 8.0720 13.3200 13.3200\n" ] } ], "source": [ "import mygrad as mg\n", "\n", "def f(x):\n", " return x**3 - 2*x**2 + x - 1\n", "\n", "def df(x):\n", " return 3 * x**2 - 4 * x + 1\n", "\n", "def dfdx_mygrad(func, x):\n", " xx = mg.Tensor(x)\n", " y = func(xx)\n", " y.backward()\n", " return xx.grad\n", "\n", "print(f\"{'x':>3s} {'f(x)':>10s} {'df/dx_analyt':>15s} {'df/dx_ad_mygrad':>15s}\")\n", "x_values = np.arange(0, 3, 0.2)\n", "for x in x_values:\n", " print(f\"{x:3.1f} {f(x):10.4f} {df(x):15.4f} {dfdx_mygrad(f,x):15.4f}\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Dawson function" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "-0.07615901382553736\n" ] } ], "source": [ "from mygrad import exp\n", "\n", "def DawsonF(x):\n", " def fint(t):\n", " return exp(t**2)\n", " x2 = x**2\n", " gaussx, gaussw = gaussxwab32(0,x)\n", " return exp(-x2) * integrate_quadrature(fint, (gaussx, gaussw))\n", "\n", "print(dfdx_mygrad(DawsonF, 1.0))" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Analytic derivative\n", "def dDawsonFdx(x):\n", " return 1. - 2. * x * DawsonF(x)\n", "\n", "dDawsonFdx_mg_reve = lambda x: dfdx_mygrad(DawsonF, x)\n", "\n", "# Plot both derivatives from -5 to 5\n", "x = np.linspace(-5, 5, 100)\n", "df_vals = [dDawsonFdx(xi) for xi in x]\n", "df_auto_vals = [dDawsonFdx_mg_reve(xi) for xi in x]\n", "\n", "plt.plot(x, df_vals, label=\"${D_+'(x)}$ analytic\", color=\"blue\", linestyle=\"-\")\n", "plt.plot(x, df_auto_vals, label=\"${D_+'(x)}$ autodiff\", color=\"red\", linestyle=\"--\")\n", "plt.axhline(0, color=\"black\", linestyle=\"--\")\n", "plt.title(\"Derivative of Dawson function\")\n", "plt.xlabel(\"x\")\n", "plt.ylabel(\"dDawsonFdx\")\n", "plt.legend()\n", "plt.grid()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Done\n", "CPU times: user 305 ms, sys: 7.89 ms, total: 313 ms\n", "Wall time: 312 ms\n" ] } ], "source": [ "%%time\n", "\n", "# Timing the MyGrad autodiff derivative reverse mode\n", "x = np.linspace(-5, 5, 100)\n", "df_auto = [dfdx_mygrad(DawsonF,xi) for xi in x]\n", "# df_auto = dfdx_mygrad(DawsonF,x)\n", "print(\"Done\")" ] } ], "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": "3.10.16" } }, "nbformat": 4, "nbformat_minor": 4 }