From a77503130c5f291ad3f52c0a3cbabf66efa188b4 Mon Sep 17 00:00:00 2001 From: "Ryan C. Cooper" Date: Fri, 3 Jan 2020 16:31:55 -0500 Subject: [PATCH] finished problems for 01-03 --- .../world_population_1900-2020-checkpoint.csv | 5 + data/world_population_1900-2020.csv | 5 + ...ouble_Floating_Point_Format-checkpoint.png | Bin 0 -> 9373 bytes .../create_notebook-checkpoint.png | Bin 0 -> 31544 bytes .../freefall-checkpoint.png | Bin 0 -> 38559 bytes .../jupyter-main-checkpoint.png | Bin 0 -> 20522 bytes .../new_notebook-checkpoint.png | Bin 0 -> 28706 bytes .../.ipynb_checkpoints/slicing-checkpoint.png | Bin 0 -> 16094 bytes .../variables-checkpoint.png | Bin 0 -> 35249 bytes .../02_Getting-started-checkpoint.ipynb | 81 ++++++ .../03-Numerical_error-checkpoint.ipynb | 238 +++++++++++++----- notebooks/02_Getting-started.ipynb | 81 ++++++ notebooks/03-Numerical_error.ipynb | 238 +++++++++++++----- 13 files changed, 510 insertions(+), 138 deletions(-) create mode 100644 data/.ipynb_checkpoints/world_population_1900-2020-checkpoint.csv create mode 100644 data/world_population_1900-2020.csv create mode 100644 images/.ipynb_checkpoints/1236px-IEEE_754_Double_Floating_Point_Format-checkpoint.png create mode 100644 images/.ipynb_checkpoints/create_notebook-checkpoint.png create mode 100644 images/.ipynb_checkpoints/freefall-checkpoint.png create mode 100644 images/.ipynb_checkpoints/jupyter-main-checkpoint.png create mode 100644 images/.ipynb_checkpoints/new_notebook-checkpoint.png create mode 100644 images/.ipynb_checkpoints/slicing-checkpoint.png create mode 100644 images/.ipynb_checkpoints/variables-checkpoint.png diff --git a/data/.ipynb_checkpoints/world_population_1900-2020-checkpoint.csv b/data/.ipynb_checkpoints/world_population_1900-2020-checkpoint.csv new file mode 100644 index 0000000..8515c3a --- /dev/null +++ b/data/.ipynb_checkpoints/world_population_1900-2020-checkpoint.csv @@ -0,0 +1,5 @@ +year,population +1900,1578000000 +1950,2526000000 +2000,6127000000 +2020,7795482000 diff --git a/data/world_population_1900-2020.csv 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\u001b[0;34m(\u001b[0m\u001b[0mp2\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0mp1\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m/\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mp2\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0mp1\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 8\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 9\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mp1\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m+\u001b[0m\u001b[0mslope\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0mp1\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;31mIndexError\u001b[0m: index 2 is out of bounds for axis 0 with size 2" + ] + } + ], + "source": [ + "# test cases for linInterp\n", + "p1=np.array([0,1])\n", + "p2=np.array([2,2])\n", + "linInterp(1,p1,p2) # answer should be 1.5" + ] + }, + { + "cell_type": "code", + "execution_count": 94, + "metadata": {}, + "outputs": [ + { + "ename": "IndexError", + "evalue": "index 2 is out of bounds for axis 0 with size 2", + "output_type": "error", + "traceback": [ + "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", + "\u001b[0;31mIndexError\u001b[0m Traceback (most recent call last)", + "\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m\u001b[0m\n\u001b[1;32m 1\u001b[0m \u001b[0mp1\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0marray\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m11\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m3\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 2\u001b[0m \u001b[0mp2\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0marray\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m12\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m5\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 3\u001b[0;31m \u001b[0mlinInterp\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m11.25\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mp1\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mp2\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;31m# answer should be -3.5\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m", + "\u001b[0;32m\u001b[0m in \u001b[0;36mlinInterp\u001b[0;34m(x, p1, p2)\u001b[0m\n\u001b[1;32m 5\u001b[0m \u001b[0;32mand\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 6\u001b[0m p2=np.array([x2,y2])'''\n\u001b[0;32m----> 7\u001b[0;31m \u001b[0mslope\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mp2\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0mp1\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m/\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mp2\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0mp1\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 8\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 9\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mp1\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m+\u001b[0m\u001b[0mslope\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0mp1\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;31mIndexError\u001b[0m: index 2 is out of bounds for axis 0 with size 2" + ] + } + ], + "source": [ + "p1=np.array([11,-3])\n", + "p2=np.array([12,-5])\n", + "linInterp(11.25,p1,p2) # answer should be -3.5" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] } ], "metadata": { diff --git a/notebooks/.ipynb_checkpoints/03-Numerical_error-checkpoint.ipynb b/notebooks/.ipynb_checkpoints/03-Numerical_error-checkpoint.ipynb index c49ee15..9455e89 100644 --- a/notebooks/.ipynb_checkpoints/03-Numerical_error-checkpoint.ipynb +++ b/notebooks/.ipynb_checkpoints/03-Numerical_error-checkpoint.ipynb @@ -230,7 +230,7 @@ }, { "cell_type": "code", - "execution_count": 100, + "execution_count": 174, "metadata": { "slideshow": { "slide_type": "fragment" @@ -246,7 +246,7 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 175, "metadata": { "slideshow": { "slide_type": "subslide" @@ -254,18 +254,24 @@ }, "outputs": [ { - "data": { - "text/plain": [ - "Text(0,0.5,'velocity (m/s)')" - ] - }, - "execution_count": 6, - "metadata": {}, - "output_type": "execute_result" + "ename": "ValueError", + "evalue": "x and y must have same first dimension, but have shapes (2,) and (100000,)", + "output_type": "error", + "traceback": [ + "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", + "\u001b[0;31mValueError\u001b[0m Traceback (most recent call last)", + "\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mplot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mt\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mv_an\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m'-'\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mlabel\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'analytical'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 2\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mplot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mt\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mv_numerical\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m'o-'\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mlabel\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'numerical'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 3\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlegend\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 4\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mxlabel\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'time (s)'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 5\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mylabel\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'velocity (m/s)'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;32m/opt/miniconda3/lib/python3.7/site-packages/matplotlib/pyplot.py\u001b[0m in \u001b[0;36mplot\u001b[0;34m(scalex, scaley, data, *args, **kwargs)\u001b[0m\n\u001b[1;32m 2793\u001b[0m return gca().plot(\n\u001b[1;32m 2794\u001b[0m *args, scalex=scalex, scaley=scaley, **({\"data\": data} if data\n\u001b[0;32m-> 2795\u001b[0;31m is not None else {}), **kwargs)\n\u001b[0m\u001b[1;32m 2796\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 2797\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;32m/opt/miniconda3/lib/python3.7/site-packages/matplotlib/axes/_axes.py\u001b[0m in \u001b[0;36mplot\u001b[0;34m(self, scalex, scaley, data, *args, **kwargs)\u001b[0m\n\u001b[1;32m 1664\u001b[0m \"\"\"\n\u001b[1;32m 1665\u001b[0m \u001b[0mkwargs\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mcbook\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mnormalize_kwargs\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mmlines\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mLine2D\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_alias_map\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1666\u001b[0;31m \u001b[0mlines\u001b[0m \u001b[0;34m=\u001b[0m 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raise ValueError(\"x and y must have same first dimension, but \"\n\u001b[0;32m--> 270\u001b[0;31m \"have shapes {} and {}\".format(x.shape, y.shape))\n\u001b[0m\u001b[1;32m 271\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mndim\u001b[0m \u001b[0;34m>\u001b[0m \u001b[0;36m2\u001b[0m \u001b[0;32mor\u001b[0m \u001b[0my\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mndim\u001b[0m \u001b[0;34m>\u001b[0m \u001b[0;36m2\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 272\u001b[0m raise ValueError(\"x and y can be no greater than 2-D, but have \"\n", + "\u001b[0;31mValueError\u001b[0m: x and y must have same first dimension, but have shapes (2,) and (100000,)" + ] }, { "data": { - "image/png": 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\n", 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\n", 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" ] @@ -680,12 +686,50 @@ "\n", "We will make use of methods (1) and (4) in this example. \n", "\n", - "We can visualize how the approximation approaches the exact solution with this method. The process of approaching the \"true\" solution is called **convergence**. " + "We can visualize how the approximation approaches the exact solution with this method. The process of approaching the \"true\" solution is called **convergence**. \n", + "\n", + "First, we solve for `n=2` steps, so t=[0,2]. We can time the solution to get a sense of how long the computation will take for larger values of `n`. " ] }, { "cell_type": "code", - "execution_count": 90, + "execution_count": 226, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "CPU times: user 288 µs, sys: 3 µs, total: 291 µs\n", + "Wall time: 303 µs\n" + ] + } + ], + "source": [ + "%%time\n", + "n=2\n", + "\n", + "v_analytical,v_numerical,t=freefall(n);" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The block of code above assigned three variables from the function `freefall`. \n", + "\n", + "1. `v_analytical` = $v_{terminal}\\tanh{\\left(\\frac{gt}{v_{terminal}}\\right)}$\n", + "\n", + "2. `v_numerical` = Euler step integration of $\\frac{dv}{dt}= g - \\frac{c}{m}v^2$\n", + "\n", + "3. `t` = timesteps from 0..2 with `n` values, here t=np.array([0,2])\n", + "\n", + "All three variables have the same length, so we can plot them and visually compare `v_analytical` and `v_numerical`. This is the comparison method (1) from above. " + ] + }, + { + "cell_type": "code", + "execution_count": 227, "metadata": {}, "outputs": [], "source": [ @@ -695,22 +739,22 @@ }, { "cell_type": "code", - "execution_count": 131, + "execution_count": 228, "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "" + "" ] }, - "execution_count": 131, + "execution_count": 228, "metadata": {}, "output_type": "execute_result" }, { "data": { - "image/png": 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\n", 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\n", 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" ] @@ -722,10 +766,6 @@ } ], "source": [ - "n=2\n", - "\n", - "v_analytical,v_numerical,t=freefall(n);\n", - "\n", "plt.plot(t,v_numerical,'o',label=str(n)+' Euler steps')\n", "plt.plot(t,v_analytical,label='analytical')\n", "plt.title('First 2 seconds of freefall')\n", @@ -740,7 +780,7 @@ "source": [ "## Exercise\n", "\n", - "Try adjusting `N` in the code above to watch the solution converge. You should notice the Euler approximation becomes almost indistinguishable from the analytical solution as `N` increases. " + "Try adjusting `n` in the code above to watch the solution converge. You should notice the Euler approximation becomes almost indistinguishable from the analytical solution as `n` increases. " ] }, { @@ -758,15 +798,15 @@ }, { "cell_type": "code", - "execution_count": 157, + "execution_count": 232, "metadata": {}, "outputs": [], "source": [ "N=100\n", - "error=np.zeros(N)\n", + "error=np.zeros(N) # initialize an N-valued array of relative errors\n", "n=np.logspace(2,5,N) # create an array from 10^2 to 10^5 with N values\n", "for i in range(0,N):\n", - " v_an,v_num,t=freefall(n[i])\n", + " v_an,v_num,t=freefall(n[i]) # return the analytical and numerical solutions to our equation\n", " error[i]=(v_num[-1]-v_an[-1])/v_an[-1] #calculate relative error in velocity at final time t=2 s\n", "\n", " " @@ -774,46 +814,7 @@ }, { "cell_type": "code", - "execution_count": 158, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "array([2. , 2.03030303, 2.06060606, 2.09090909, 2.12121212,\n", - " 2.15151515, 2.18181818, 2.21212121, 2.24242424, 2.27272727,\n", - " 2.3030303 , 2.33333333, 2.36363636, 2.39393939, 2.42424242,\n", - " 2.45454545, 2.48484848, 2.51515152, 2.54545455, 2.57575758,\n", - " 2.60606061, 2.63636364, 2.66666667, 2.6969697 , 2.72727273,\n", - " 2.75757576, 2.78787879, 2.81818182, 2.84848485, 2.87878788,\n", - " 2.90909091, 2.93939394, 2.96969697, 3. , 3.03030303,\n", - " 3.06060606, 3.09090909, 3.12121212, 3.15151515, 3.18181818,\n", - " 3.21212121, 3.24242424, 3.27272727, 3.3030303 , 3.33333333,\n", - " 3.36363636, 3.39393939, 3.42424242, 3.45454545, 3.48484848,\n", - " 3.51515152, 3.54545455, 3.57575758, 3.60606061, 3.63636364,\n", - " 3.66666667, 3.6969697 , 3.72727273, 3.75757576, 3.78787879,\n", - " 3.81818182, 3.84848485, 3.87878788, 3.90909091, 3.93939394,\n", - " 3.96969697, 4. , 4.03030303, 4.06060606, 4.09090909,\n", - " 4.12121212, 4.15151515, 4.18181818, 4.21212121, 4.24242424,\n", - " 4.27272727, 4.3030303 , 4.33333333, 4.36363636, 4.39393939,\n", - " 4.42424242, 4.45454545, 4.48484848, 4.51515152, 4.54545455,\n", - " 4.57575758, 4.60606061, 4.63636364, 4.66666667, 4.6969697 ,\n", - " 4.72727273, 4.75757576, 4.78787879, 4.81818182, 4.84848485,\n", - " 4.87878788, 4.90909091, 4.93939394, 4.96969697, 5. ])" - ] - }, - "execution_count": 158, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "np.log10(n)" - ] - }, - { - "cell_type": "code", - "execution_count": 162, + "execution_count": 233, "metadata": {}, "outputs": [ { @@ -822,13 +823,13 @@ "Text(0.5, 1.0, 'Truncation and roundoff error \\naccumulation in log-log plot')" ] }, - "execution_count": 162, + "execution_count": 233, "metadata": {}, "output_type": "execute_result" }, { "data": { - "image/png": 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\n", 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\n", 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" ] @@ -850,7 +851,9 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "In the above plot \"Truncation and roundoff error accumulation in log-log plot\", we see that around N=20,000 steps we stop decreasing the error with more steps. This is because we are approaching the limit of how precise we can store a number using a 32-bit floating point number. " + "In the above plot \"Truncation and roundoff error accumulation in log-log plot\", we see that around N=20,000 steps we stop decreasing the error with more steps. This is because we are approaching the limit of how precise we can store a number using a 32-bit floating point number. \n", + "\n", + "In any computational solution, there will be some point of similar diminishing in terms of accuracy (error) and computational time (in this case, number of timesteps). If you were to attempt a solution for N=1 billion, the solution could take $\\approx$(1 billion)*(200 $\\mu$s\\[cpu time for n=2\\])$\\approx$55 hours, but would not increase the accuracy of the solution. " ] }, { @@ -862,7 +865,104 @@ "* Numerical integration with the Euler approximation\n", "* The source of truncation errors\n", "* The source of roundoff errors\n", - "* " + "* How to time a numerical solution or a function\n", + "* How to compare solutions\n", + "* The definition of absolute error and relative error\n", + "* How a numerical solution converges" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Problems\n", + "\n", + "1. The growth of populations of organisms has many engineering and scientific applications. One of the simplest\n", + "models assumes that the rate of change of the population p is proportional to the existing population at any time t:\n", + "\n", + " $\\frac{dp}{dt} = k_g p$\n", + "\n", + " where $t$ is time in years, and $k_g$ is growth rate in \\[1/years\\]. \n", + " \n", + " The world population has been increasing dramatically, let's make a prediction based upon the [following data](https://worldpopulationhistory.org/map/2020/mercator/1/0/25/) saved in [world_population_1900-2020.csv](../data/world_population_1900-2020.csv):\n", + " \n", + " |year| world population |\n", + " |---|---|\n", + " |1900|1,578,000,000|\n", + " |1950|2,526,000,000|\n", + " |2000|6,127,000,000|\n", + " |2020|7,795,482,000|\n", + " \n", + " a. Calculate the average population growth, $\\frac{\\Delta p}{\\Delta t}$, from 1900-1950, 1950-2000, and 2000-2020\n", + " \n", + " b. Determine the average growth rates. $k_g$, from 1900-1950, 1950-2000, and 2000-2020\n", + " \n", + " c. Use a growth rate of $k_g=0.013$ [1/years] and compare the analytical solution (use initial condition p(1900) = 1578000000) to the Euler integration for time steps of 20 years from 1900 to 2020 (Hint: use method (1)- plot the two solutions together with the given data) \n", + " \n", + " d. Discussion question: If you decrease the time steps further and the solution converges, will it converge to the actual world population? Why or why not? \n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 301, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " year population\n", + "0 1900 1578000000\n", + "1 1950 2526000000\n", + "2 2000 6127000000\n", + "3 2020 7795482000\n" + ] + } + ], + "source": [ + "import pandas as pd\n", + "data = pd.read_csv('../data/world_population_1900-2020.csv')\n", + "print(data)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "2. In the freefall example we used smaller time steps to decrease the **truncation error** in our Euler approximation. Another way to decrease approximation error is to continue expanding the Taylor series. Consider the function f(x)\n", + "\n", + " $f(x)=e^x = 1+x+\\frac{x^2}{2!}+\\frac{x^3}{3!}+\\frac{x^4}{4!}+...$\n", + "\n", + " We can approximate $e^x$ as $1+x$ (first order), $1+x+x^2/2$ (second order), and so on each higher order results in smaller error. \n", + " \n", + " a. Use the given `exptaylor` function to approximate the value of exp(1) with a second-order Taylor series expansion. What is the relative error compared to `np.exp(1)`?\n", + " \n", + " b. Time the solution for a second-order Taylor series and a tenth-order Taylor series. How long would a 100,000-order series take (approximate this, you don't have to run it)\n", + " \n", + " c. Plot the relative error as a function of the Taylor series expansion order from first order upwards. (Hint: use method (4) in the comparison methods from the \"Truncation and roundoff error accumulation in log-log plot\" figure)" + ] + }, + { + "cell_type": "code", + "execution_count": 273, + "metadata": {}, + "outputs": [], + "source": [ + "from math import factorial\n", + "def exptaylor(x,n):\n", + " '''Taylor series expansion about x=0 for the function e^x\n", + " the full expansion follows the function\n", + " e^x = 1+ x + x**2/2! + x**3/3! + x**4/4! + x**5/5! +...'''\n", + " if n<1:\n", + " print('lowest order expansion is 0 where e^x = 1')\n", + " return 1\n", + " else:\n", + " ex = 1+x # define the first-order taylor series result\n", + " for i in range(1,n):\n", + " ex+=x**(i+1)/factorial(i+1) # add the nth-order result for each step in loop\n", + " return ex\n", + " " ] } ], diff --git a/notebooks/02_Getting-started.ipynb b/notebooks/02_Getting-started.ipynb index e9f2736..1e798a5 100644 --- a/notebooks/02_Getting-started.ipynb +++ b/notebooks/02_Getting-started.ipynb @@ -1758,6 +1758,87 @@ "# given X and Y arrays\n", "X,Y=np.meshgrid(np.arange(0,10),np.arange(0,10))" ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "4. The following linear interpolation function has an error. It is supposed to return y(x) given the the two points $p_1=[x_1,~y_1]$ and $p_2=[x_2,~y_2]$. Currently, it just returns and error." + ] + }, + { + "cell_type": "code", + "execution_count": 92, + "metadata": {}, + "outputs": [], + "source": [ + "def linInterp(x,p1,p2):\n", + " '''linear interplation function\n", + " return y(x) given the two endpoints \n", + " p1=np.array([x1,y1])\n", + " and\n", + " p2=np.array([x2,y2])'''\n", + " slope = (p2[2]-p1[2])/(p2[1]-p1[1])\n", + " \n", + " return p1[2]+slope*(x - p1[1])\n", + " " + ] + }, + { + "cell_type": "code", + "execution_count": 93, + "metadata": {}, + "outputs": [ + { + "ename": "IndexError", + "evalue": "index 2 is out of bounds for axis 0 with size 2", + "output_type": "error", + "traceback": [ + "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", + "\u001b[0;31mIndexError\u001b[0m Traceback (most recent call last)", + "\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m\u001b[0m\n\u001b[1;32m 2\u001b[0m \u001b[0mp1\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0marray\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 3\u001b[0m \u001b[0mp2\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0marray\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 4\u001b[0;31m \u001b[0mlinInterp\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mp1\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mp2\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;31m# answer should be 1.5\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m", + "\u001b[0;32m\u001b[0m in \u001b[0;36mlinInterp\u001b[0;34m(x, p1, p2)\u001b[0m\n\u001b[1;32m 5\u001b[0m \u001b[0;32mand\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 6\u001b[0m p2=np.array([x2,y2])'''\n\u001b[0;32m----> 7\u001b[0;31m \u001b[0mslope\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mp2\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0mp1\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m/\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mp2\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0mp1\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 8\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 9\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mp1\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m+\u001b[0m\u001b[0mslope\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0mp1\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;31mIndexError\u001b[0m: index 2 is out of bounds for axis 0 with size 2" + ] + } + ], + "source": [ + "# test cases for linInterp\n", + "p1=np.array([0,1])\n", + "p2=np.array([2,2])\n", + "linInterp(1,p1,p2) # answer should be 1.5" + ] + }, + { + "cell_type": "code", + "execution_count": 94, + "metadata": {}, + "outputs": [ + { + "ename": "IndexError", + "evalue": "index 2 is out of bounds for axis 0 with size 2", + "output_type": "error", + "traceback": [ + "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", + "\u001b[0;31mIndexError\u001b[0m Traceback (most recent call last)", + "\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m\u001b[0m\n\u001b[1;32m 1\u001b[0m \u001b[0mp1\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0marray\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m11\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m3\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 2\u001b[0m \u001b[0mp2\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0marray\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m12\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m5\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 3\u001b[0;31m \u001b[0mlinInterp\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m11.25\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mp1\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mp2\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;31m# answer should be -3.5\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m", + "\u001b[0;32m\u001b[0m in \u001b[0;36mlinInterp\u001b[0;34m(x, p1, p2)\u001b[0m\n\u001b[1;32m 5\u001b[0m \u001b[0;32mand\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 6\u001b[0m p2=np.array([x2,y2])'''\n\u001b[0;32m----> 7\u001b[0;31m \u001b[0mslope\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mp2\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0mp1\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m/\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mp2\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0mp1\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 8\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 9\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mp1\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m+\u001b[0m\u001b[0mslope\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0mp1\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;31mIndexError\u001b[0m: index 2 is out of bounds for axis 0 with size 2" + ] + } + ], + "source": [ + "p1=np.array([11,-3])\n", + "p2=np.array([12,-5])\n", + "linInterp(11.25,p1,p2) # answer should be -3.5" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] } ], "metadata": { diff --git a/notebooks/03-Numerical_error.ipynb b/notebooks/03-Numerical_error.ipynb index c49ee15..9455e89 100644 --- a/notebooks/03-Numerical_error.ipynb +++ b/notebooks/03-Numerical_error.ipynb @@ -230,7 +230,7 @@ }, { "cell_type": "code", - "execution_count": 100, + "execution_count": 174, "metadata": { "slideshow": { "slide_type": "fragment" @@ -246,7 +246,7 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 175, "metadata": { "slideshow": { "slide_type": "subslide" @@ -254,18 +254,24 @@ }, "outputs": [ { - "data": { - "text/plain": [ - "Text(0,0.5,'velocity (m/s)')" - ] - }, - "execution_count": 6, - "metadata": {}, - "output_type": "execute_result" + "ename": "ValueError", + "evalue": "x and y must have same first dimension, but have shapes (2,) and (100000,)", + "output_type": "error", + "traceback": [ + "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", + "\u001b[0;31mValueError\u001b[0m Traceback (most recent call last)", + "\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mplot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mt\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mv_an\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m'-'\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mlabel\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'analytical'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 2\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mplot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mt\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mv_numerical\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m'o-'\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mlabel\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'numerical'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 3\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlegend\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 4\u001b[0m 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"\u001b[0;32m/opt/miniconda3/lib/python3.7/site-packages/matplotlib/axes/_axes.py\u001b[0m in \u001b[0;36mplot\u001b[0;34m(self, scalex, scaley, data, *args, **kwargs)\u001b[0m\n\u001b[1;32m 1664\u001b[0m \"\"\"\n\u001b[1;32m 1665\u001b[0m \u001b[0mkwargs\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mcbook\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mnormalize_kwargs\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mmlines\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mLine2D\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_alias_map\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1666\u001b[0;31m \u001b[0mlines\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_get_lines\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m 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raise ValueError(\"x and y must have same first dimension, but \"\n\u001b[0;32m--> 270\u001b[0;31m \"have shapes {} and {}\".format(x.shape, y.shape))\n\u001b[0m\u001b[1;32m 271\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mndim\u001b[0m \u001b[0;34m>\u001b[0m \u001b[0;36m2\u001b[0m \u001b[0;32mor\u001b[0m \u001b[0my\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mndim\u001b[0m \u001b[0;34m>\u001b[0m \u001b[0;36m2\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 272\u001b[0m raise ValueError(\"x and y can be no greater than 2-D, but have \"\n", + "\u001b[0;31mValueError\u001b[0m: x and y must have same first dimension, but have shapes (2,) and (100000,)" + ] }, { "data": { - "image/png": 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\n", 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\n", 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" ] @@ -680,12 +686,50 @@ "\n", "We will make use of methods (1) and (4) in this example. \n", "\n", - "We can visualize how the approximation approaches the exact solution with this method. The process of approaching the \"true\" solution is called **convergence**. " + "We can visualize how the approximation approaches the exact solution with this method. The process of approaching the \"true\" solution is called **convergence**. \n", + "\n", + "First, we solve for `n=2` steps, so t=[0,2]. We can time the solution to get a sense of how long the computation will take for larger values of `n`. " ] }, { "cell_type": "code", - "execution_count": 90, + "execution_count": 226, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "CPU times: user 288 µs, sys: 3 µs, total: 291 µs\n", + "Wall time: 303 µs\n" + ] + } + ], + "source": [ + "%%time\n", + "n=2\n", + "\n", + "v_analytical,v_numerical,t=freefall(n);" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The block of code above assigned three variables from the function `freefall`. \n", + "\n", + "1. `v_analytical` = $v_{terminal}\\tanh{\\left(\\frac{gt}{v_{terminal}}\\right)}$\n", + "\n", + "2. `v_numerical` = Euler step integration of $\\frac{dv}{dt}= g - \\frac{c}{m}v^2$\n", + "\n", + "3. `t` = timesteps from 0..2 with `n` values, here t=np.array([0,2])\n", + "\n", + "All three variables have the same length, so we can plot them and visually compare `v_analytical` and `v_numerical`. This is the comparison method (1) from above. " + ] + }, + { + "cell_type": "code", + "execution_count": 227, "metadata": {}, "outputs": [], "source": [ @@ -695,22 +739,22 @@ }, { "cell_type": "code", - "execution_count": 131, + "execution_count": 228, "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "" + "" ] }, - "execution_count": 131, + "execution_count": 228, "metadata": {}, "output_type": "execute_result" }, { "data": { - "image/png": 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\n", 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\n", 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" ] @@ -722,10 +766,6 @@ } ], "source": [ - "n=2\n", - "\n", - "v_analytical,v_numerical,t=freefall(n);\n", - "\n", "plt.plot(t,v_numerical,'o',label=str(n)+' Euler steps')\n", "plt.plot(t,v_analytical,label='analytical')\n", "plt.title('First 2 seconds of freefall')\n", @@ -740,7 +780,7 @@ "source": [ "## Exercise\n", "\n", - "Try adjusting `N` in the code above to watch the solution converge. You should notice the Euler approximation becomes almost indistinguishable from the analytical solution as `N` increases. " + "Try adjusting `n` in the code above to watch the solution converge. You should notice the Euler approximation becomes almost indistinguishable from the analytical solution as `n` increases. " ] }, { @@ -758,15 +798,15 @@ }, { "cell_type": "code", - "execution_count": 157, + "execution_count": 232, "metadata": {}, "outputs": [], "source": [ "N=100\n", - "error=np.zeros(N)\n", + "error=np.zeros(N) # initialize an N-valued array of relative errors\n", "n=np.logspace(2,5,N) # create an array from 10^2 to 10^5 with N values\n", "for i in range(0,N):\n", - " v_an,v_num,t=freefall(n[i])\n", + " v_an,v_num,t=freefall(n[i]) # return the analytical and numerical solutions to our equation\n", " error[i]=(v_num[-1]-v_an[-1])/v_an[-1] #calculate relative error in velocity at final time t=2 s\n", "\n", " " @@ -774,46 +814,7 @@ }, { "cell_type": "code", - "execution_count": 158, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "array([2. , 2.03030303, 2.06060606, 2.09090909, 2.12121212,\n", - " 2.15151515, 2.18181818, 2.21212121, 2.24242424, 2.27272727,\n", - " 2.3030303 , 2.33333333, 2.36363636, 2.39393939, 2.42424242,\n", - " 2.45454545, 2.48484848, 2.51515152, 2.54545455, 2.57575758,\n", - " 2.60606061, 2.63636364, 2.66666667, 2.6969697 , 2.72727273,\n", - " 2.75757576, 2.78787879, 2.81818182, 2.84848485, 2.87878788,\n", - " 2.90909091, 2.93939394, 2.96969697, 3. , 3.03030303,\n", - " 3.06060606, 3.09090909, 3.12121212, 3.15151515, 3.18181818,\n", - " 3.21212121, 3.24242424, 3.27272727, 3.3030303 , 3.33333333,\n", - " 3.36363636, 3.39393939, 3.42424242, 3.45454545, 3.48484848,\n", - " 3.51515152, 3.54545455, 3.57575758, 3.60606061, 3.63636364,\n", - " 3.66666667, 3.6969697 , 3.72727273, 3.75757576, 3.78787879,\n", - " 3.81818182, 3.84848485, 3.87878788, 3.90909091, 3.93939394,\n", - " 3.96969697, 4. , 4.03030303, 4.06060606, 4.09090909,\n", - " 4.12121212, 4.15151515, 4.18181818, 4.21212121, 4.24242424,\n", - " 4.27272727, 4.3030303 , 4.33333333, 4.36363636, 4.39393939,\n", - " 4.42424242, 4.45454545, 4.48484848, 4.51515152, 4.54545455,\n", - " 4.57575758, 4.60606061, 4.63636364, 4.66666667, 4.6969697 ,\n", - " 4.72727273, 4.75757576, 4.78787879, 4.81818182, 4.84848485,\n", - " 4.87878788, 4.90909091, 4.93939394, 4.96969697, 5. ])" - ] - }, - "execution_count": 158, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "np.log10(n)" - ] - }, - { - "cell_type": "code", - "execution_count": 162, + "execution_count": 233, "metadata": {}, "outputs": [ { @@ -822,13 +823,13 @@ "Text(0.5, 1.0, 'Truncation and roundoff error \\naccumulation in log-log plot')" ] }, - "execution_count": 162, + "execution_count": 233, "metadata": {}, "output_type": "execute_result" }, { "data": { - "image/png": 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\n", 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\n", 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" ] @@ -850,7 +851,9 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "In the above plot \"Truncation and roundoff error accumulation in log-log plot\", we see that around N=20,000 steps we stop decreasing the error with more steps. This is because we are approaching the limit of how precise we can store a number using a 32-bit floating point number. " + "In the above plot \"Truncation and roundoff error accumulation in log-log plot\", we see that around N=20,000 steps we stop decreasing the error with more steps. This is because we are approaching the limit of how precise we can store a number using a 32-bit floating point number. \n", + "\n", + "In any computational solution, there will be some point of similar diminishing in terms of accuracy (error) and computational time (in this case, number of timesteps). If you were to attempt a solution for N=1 billion, the solution could take $\\approx$(1 billion)*(200 $\\mu$s\\[cpu time for n=2\\])$\\approx$55 hours, but would not increase the accuracy of the solution. " ] }, { @@ -862,7 +865,104 @@ "* Numerical integration with the Euler approximation\n", "* The source of truncation errors\n", "* The source of roundoff errors\n", - "* " + "* How to time a numerical solution or a function\n", + "* How to compare solutions\n", + "* The definition of absolute error and relative error\n", + "* How a numerical solution converges" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Problems\n", + "\n", + "1. The growth of populations of organisms has many engineering and scientific applications. One of the simplest\n", + "models assumes that the rate of change of the population p is proportional to the existing population at any time t:\n", + "\n", + " $\\frac{dp}{dt} = k_g p$\n", + "\n", + " where $t$ is time in years, and $k_g$ is growth rate in \\[1/years\\]. \n", + " \n", + " The world population has been increasing dramatically, let's make a prediction based upon the [following data](https://worldpopulationhistory.org/map/2020/mercator/1/0/25/) saved in [world_population_1900-2020.csv](../data/world_population_1900-2020.csv):\n", + " \n", + " |year| world population |\n", + " |---|---|\n", + " |1900|1,578,000,000|\n", + " |1950|2,526,000,000|\n", + " |2000|6,127,000,000|\n", + " |2020|7,795,482,000|\n", + " \n", + " a. Calculate the average population growth, $\\frac{\\Delta p}{\\Delta t}$, from 1900-1950, 1950-2000, and 2000-2020\n", + " \n", + " b. Determine the average growth rates. $k_g$, from 1900-1950, 1950-2000, and 2000-2020\n", + " \n", + " c. Use a growth rate of $k_g=0.013$ [1/years] and compare the analytical solution (use initial condition p(1900) = 1578000000) to the Euler integration for time steps of 20 years from 1900 to 2020 (Hint: use method (1)- plot the two solutions together with the given data) \n", + " \n", + " d. Discussion question: If you decrease the time steps further and the solution converges, will it converge to the actual world population? Why or why not? \n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 301, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " year population\n", + "0 1900 1578000000\n", + "1 1950 2526000000\n", + "2 2000 6127000000\n", + "3 2020 7795482000\n" + ] + } + ], + "source": [ + "import pandas as pd\n", + "data = pd.read_csv('../data/world_population_1900-2020.csv')\n", + "print(data)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "2. In the freefall example we used smaller time steps to decrease the **truncation error** in our Euler approximation. Another way to decrease approximation error is to continue expanding the Taylor series. Consider the function f(x)\n", + "\n", + " $f(x)=e^x = 1+x+\\frac{x^2}{2!}+\\frac{x^3}{3!}+\\frac{x^4}{4!}+...$\n", + "\n", + " We can approximate $e^x$ as $1+x$ (first order), $1+x+x^2/2$ (second order), and so on each higher order results in smaller error. \n", + " \n", + " a. Use the given `exptaylor` function to approximate the value of exp(1) with a second-order Taylor series expansion. What is the relative error compared to `np.exp(1)`?\n", + " \n", + " b. Time the solution for a second-order Taylor series and a tenth-order Taylor series. How long would a 100,000-order series take (approximate this, you don't have to run it)\n", + " \n", + " c. Plot the relative error as a function of the Taylor series expansion order from first order upwards. (Hint: use method (4) in the comparison methods from the \"Truncation and roundoff error accumulation in log-log plot\" figure)" + ] + }, + { + "cell_type": "code", + "execution_count": 273, + "metadata": {}, + "outputs": [], + "source": [ + "from math import factorial\n", + "def exptaylor(x,n):\n", + " '''Taylor series expansion about x=0 for the function e^x\n", + " the full expansion follows the function\n", + " e^x = 1+ x + x**2/2! + x**3/3! + x**4/4! + x**5/5! +...'''\n", + " if n<1:\n", + " print('lowest order expansion is 0 where e^x = 1')\n", + " return 1\n", + " else:\n", + " ex = 1+x # define the first-order taylor series result\n", + " for i in range(1,n):\n", + " ex+=x**(i+1)/factorial(i+1) # add the nth-order result for each step in loop\n", + " return ex\n", + " " ] } ],