{"cells":[{"cell_type":"markdown","metadata":{"id":"dhjq1enstyMC"},"source":["# An Introduction to Making Plots with Python"]},{"cell_type":"markdown","metadata":{"id":"rF_JC4d1tyME"},"source":["The matplotlib plotting library for Python (part of pylab) makes publication quality figures that are easy to modify and save. "]},{"cell_type":"markdown","metadata":{"id":"NrdT2cBXtyMF"},"source":["## 1. A Simple Example"]},{"cell_type":"markdown","metadata":{"id":"Nzs8IKgjtyMG"},"source":["The example below plots $\\cos(2\\pi t)$ vs. $t$."]},{"cell_type":"code","execution_count":1,"metadata":{"colab":{"base_uri":"https://localhost:8080/","height":265},"id":"WEnUDgPdtyMG","executionInfo":{"status":"ok","timestamp":1653065744609,"user_tz":420,"elapsed":7,"user":{"displayName":"Alan DeWeerd","userId":"09086135147919405400"}},"outputId":"1b9184e7-97ce-4606-b780-402a983602fb"},"outputs":[{"output_type":"display_data","data":{"text/plain":["<Figure size 432x288 with 1 Axes>"],"image/png":"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\n"},"metadata":{"needs_background":"light"}}],"source":["import pylab as pl\n","\n","t = pl.linspace(0.0, 2.0, 100) \n","y = pl.cos(2*pl.pi*t)  \n","pl.figure()\n","pl.plot(t, y)\n","pl.show()"]},{"cell_type":"markdown","metadata":{"id":"HJkanWaJtyMH"},"source":["The first line loads **`pylab`** library. (Note that the  **`numpy`** library has some of the same functions, like **`linspace`** and **`arrary`**, but not the plotting funcitons.)\n","\n","The **`linspace`** function returns a list of evenly spaced numbers from the first argument to the second argument, where the number of elements is given by the third argument.  Many of the functions in Python are “vectorized” which means that they can accept a list (or array) as input. For example, when the **`cos`** function has an argument t that is a list, it will return a list. That means that `y` will be a list containing the cosines of the elements in the list `t`.\n","\n","The **`figure`** command opens a new figure window. If you want a second plot to appear in a different figure, you should put another **`figure`** command before the next **`plot`** command. If you want multiple plots to appear in a single figure, all of the **`plot`** commands should be below a single **`figure`** command.\n","\n","The first argument of the **`plot`** command contains the horizontal coordinates and the second contains the vertical coordinates. In other words, the example above makes a plot of `y` vs. `t`. \n","\n","The **`show`** command tells Python to draw any figures. It should appear after the last\n","plotting command."]},{"cell_type":"markdown","metadata":{"id":"cVGemA71tyMJ"},"source":["## 2. More Plotting Options"]},{"cell_type":"markdown","metadata":{"id":"yo8I_FbttyMJ"},"source":["### a. Customizing a Line"]},{"cell_type":"markdown","metadata":{"id":"zufH5a04tyMK"},"source":["Some options for the **`linestyle`** (or **`ls`**) argument are:\n","> \\- =  solid  \n","> -- =  dashed  \n","> : =  dotted  \n","> -. =  dash-dot\n","\n","The **`color`** (or **`c`**) argument sets the color of the line. Some of the options are:\n",">r =  red  \n",">g =  green\t\n",">b =  blue  \n",">k =  black  \n",">c =  cyan  \n",">m =  magenta  \n",">y =  yellow  \n",">w =  white\n","\n","The **`linewidth`** argument adjust the thickness of the line."]},{"cell_type":"code","execution_count":2,"metadata":{"colab":{"base_uri":"https://localhost:8080/","height":265},"id":"dvgJnxgztyML","executionInfo":{"status":"ok","timestamp":1653065745242,"user_tz":420,"elapsed":392,"user":{"displayName":"Alan DeWeerd","userId":"09086135147919405400"}},"outputId":"ca875e29-3584-4de2-915c-d455bc92e7c2"},"outputs":[{"output_type":"display_data","data":{"text/plain":["<Figure size 432x288 with 1 Axes>"],"image/png":"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\n"},"metadata":{"needs_background":"light"}}],"source":["import pylab as pl\n","\n","t = pl.linspace(0.0, 2.0, 100) \n","y = pl.cos(2*pl.pi*t)  \n","pl.figure()\n","pl.plot(t, y, ls='--', color='r', linewidth=2)\n","pl.show()"]},{"cell_type":"markdown","metadata":{"id":"UFK8jUB4tyMN"},"source":["### b. Labels and Limits"]},{"cell_type":"markdown","metadata":{"id":"4H2trKN_tyMO"},"source":["Axis labels can be added with the **`xlabel`** and **`ylabel`** commands. A caption can be added with the **`title`** command.\n","\n","The **`grid`** command can be used to add a grid to the figure. The **`color`** argument can be used with this command.\n","\n","You could also manually set the limits on the axes with the **`xlim`** and **`ylim`** commands, which take two arguments for the lower and upper limits."]},{"cell_type":"code","execution_count":3,"metadata":{"colab":{"base_uri":"https://localhost:8080/","height":295},"id":"i_Ro2bcYtyMO","executionInfo":{"status":"ok","timestamp":1653065745242,"user_tz":420,"elapsed":10,"user":{"displayName":"Alan DeWeerd","userId":"09086135147919405400"}},"outputId":"a4530ab3-49c1-4d1a-989c-af0511c97e90"},"outputs":[{"output_type":"display_data","data":{"text/plain":["<Figure size 432x288 with 1 Axes>"],"image/png":"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\n"},"metadata":{"needs_background":"light"}}],"source":["import pylab as pl\n","\n","t = pl.linspace(0.0, 2.0, 100) \n","y = pl.cos(2*pl.pi*t)  \n","pl.figure()\n","pl.plot(t, y)\n","pl.xlabel('time (s)') \n","pl.ylabel('voltage (mV)') \n","pl.title('A Simple Plot') \n","pl.grid()\n","pl.xlim(0,1.5)\n","pl.ylim(-1.5,1.5)\n","pl.show()"]},{"cell_type":"markdown","metadata":{"id":"O6RkXSY5tyMP"},"source":["### c. Markers, Scatter Plots, and Error Bars"]},{"cell_type":"markdown","metadata":{"id":"DAyDY0WLtyMQ"},"source":["In the examples above, the points are connected by lines, but there are so many points that the curve looks smooth. In the **`plot`** command, it is optional to add markers for each point on the list. Some of the options for **`marker`** argument are:\n","> . = points\t\n","> o = circles\t\n",">s = squares\t\n",">D = diamonds  \n",">h = hexagons\t\n",">8 = octagons\t\n",">^ = up triangles  \n",">v = down triangles\n","\n","The **`markersize`** (or **`ms`**) argument is a number used to set the size of the markers. The **`linestyle`** (or **`ls`**) can also be set to **`None`** to show only the markers, which is preferable for most data.\n","\n","The example below uses fewer points so that the markers don't overlap."]},{"cell_type":"code","execution_count":4,"metadata":{"colab":{"base_uri":"https://localhost:8080/","height":265},"id":"wlyNZ6DttyMQ","executionInfo":{"status":"ok","timestamp":1653065745243,"user_tz":420,"elapsed":9,"user":{"displayName":"Alan DeWeerd","userId":"09086135147919405400"}},"outputId":"20671940-3852-4361-9ed4-6919485e029a"},"outputs":[{"output_type":"display_data","data":{"text/plain":["<Figure size 432x288 with 1 Axes>"],"image/png":"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\n"},"metadata":{"needs_background":"light"}}],"source":["import pylab as pl\n","\n","t = pl.linspace(0.0, 2.0, 40) \n","y = pl.cos(2*pl.pi*t)  \n","pl.figure()\n","pl.plot(t, y, ls='None', marker='o', ms=5)\n","pl.show()"]},{"cell_type":"markdown","metadata":{"id":"9kSZ4-OMtyMR"},"source":["Instead of the **`plot`** command, the **`scatter`** command can be used to make a scatter plot, which is useful for plotting data. The **`s`** argument is an integer used to set the size, instead of **`markersize`**. With the **`scatter`** command, you don't have to specify that there is no line. Also, \n","some space is automatically left around the data points (compare the plot below to the one above)."]},{"cell_type":"code","execution_count":5,"metadata":{"colab":{"base_uri":"https://localhost:8080/","height":265},"id":"zoa0r7cOtyMS","executionInfo":{"status":"ok","timestamp":1653065745474,"user_tz":420,"elapsed":239,"user":{"displayName":"Alan DeWeerd","userId":"09086135147919405400"}},"outputId":"6aa87be4-d286-4462-cb33-25d4ad79fceb"},"outputs":[{"output_type":"display_data","data":{"text/plain":["<Figure size 432x288 with 1 Axes>"],"image/png":"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\n"},"metadata":{"needs_background":"light"}}],"source":["import pylab as pl\n","\n","t = pl.linspace(0.0, 2.0, 40) \n","y = pl.cos(2*pl.pi*t)  \n","pl.figure()\n","pl.scatter(t, y, marker='o', s=25)\n","pl.show()"]},{"cell_type":"markdown","metadata":{"id":"mkTUd49rtyMS"},"source":["The **`errorbar`** command can be used to plot data with error bars. The third argument contains the uncertainties for the vertical direction. The optional fourth argument contains the uncertainties for the horizontal direction. Note that this is the opposite order as for the coordinates of the points, because the horizontal uncertainties are optional.\n","\n","Unfortunately, the default for the **`errorbar`** command is to connect the points with a line, not to use markers. You should always set the **`linestyle`** (or **`ls`**) to **`None`**. You can also set the **`marker`** in the **`errorbar`** command. You may need to adjust the **`markersize`** (or **`ms`**) so the the error bars are visible. You can adjust the size of the lines at the ends of the error bars with **`capsize`** (the default is zero for no lines)."]},{"cell_type":"code","execution_count":6,"metadata":{"colab":{"base_uri":"https://localhost:8080/","height":265},"id":"PxqBKV0ztyMS","executionInfo":{"status":"ok","timestamp":1653065745708,"user_tz":420,"elapsed":242,"user":{"displayName":"Alan DeWeerd","userId":"09086135147919405400"}},"outputId":"3b54bd56-5deb-44db-a9d6-8585189af5c8"},"outputs":[{"output_type":"display_data","data":{"text/plain":["<Figure size 432x288 with 1 Axes>"],"image/png":"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\n"},"metadata":{"needs_background":"light"}}],"source":["import pylab as pl\n","\n","x = pl.array([1,2,3,4,5]) \n","y = pl.array([0.9,4.1,8.7,16.5,24.9])  \n","xerr = pl.array([0.1,0.1,0.1,0.1,0.1])  \n","yerr = pl.array([0.6,0.9,0.75,0.9,1.2])  \n","pl.figure()\n","pl.errorbar(x, y, yerr, xerr, ls='None', marker='o', ms=4, capsize=2)\n","pl.show()"]},{"cell_type":"markdown","metadata":{"id":"LXv0hHXityMT"},"source":["An alternative is to use the **`scatter`** command to make a scatter plot, and to use the **`errorbar`** command to add error bars. In this example, only vertical error bars are used. Note that this method leaves more space around the data points."]},{"cell_type":"code","execution_count":7,"metadata":{"colab":{"base_uri":"https://localhost:8080/","height":265},"id":"13LnOJGXtyMT","executionInfo":{"status":"ok","timestamp":1653065746180,"user_tz":420,"elapsed":477,"user":{"displayName":"Alan DeWeerd","userId":"09086135147919405400"}},"outputId":"d1887404-291d-4f71-c8ba-3fea0eeab0e6"},"outputs":[{"output_type":"display_data","data":{"text/plain":["<Figure size 432x288 with 1 Axes>"],"image/png":"iVBORw0KGgoAAAANSUhEUgAAAXAAAAD4CAYAAAD1jb0+AAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4yLjIsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+WH4yJAAAROklEQVR4nO3dbWyd5X3H8e9/xt0sQAtdPBZcWKoqicTalTALgVJVbFka2lUl7aoJpHV06ha2tVqaVUGEF2u3N0XK2ow9qF1aUNnWplQ0TVmhTa2AhCoNMwdTwkOTIEIzTEpcohSmWUtw/nvhO6ljbHyOfZ4u+/uRLN/num+f66cLzi+373OOT2QmkqTy/EK7A0iS5sYCl6RCWeCSVCgLXJIKZYFLUqHOa+VkS5cuzeXLl7dySkkq3r59+36amb1Tx1ta4MuXL2doaKiVU0pS8SLix9ONewlFkgplgUtSoSxwSSqUBS5JhbLAJalQFrgkFcoCl6RCWeCSVKiWvpFHkhab7QMHuWPvobO3N61dweZ1Kxty3xa4JDXR5nUreeS5lwG45+ZrGnrfXkKRpEJZ4JJUKAtckgplgUtSoWYt8Ii4NCIeioinI+KpiNhUjX8mIkYi4vHq633NjytJZdk9PMLwkRMMHj7OmtsfZPfwSMPuu5ZXobwGfCozH4uIC4F9ETFQ7duemX/XsDSStIDsHh5h6679nBw/DcDIiTG27toPwIbVffO+/1nPwDPzaGY+Vm2/CjwDzH9mSVrgtu05wNip8XPGxk6Ns23PgYbcf13XwCNiObAaGKyGPhERT0TEXRFx0Qw/szEihiJiaHR0dF5hJakkL54Yq2u8XjUXeERcAHwT+GRmvgJ8AXgbcAVwFPjcdD+XmTsysz8z+3t7X/eRbpK0YF2ypKeu8XrVVOAR0c1EeX81M3cBZOZLmTmemaeBLwFXNSSRJC0QW9avoqe765yxnu4utqxf1ZD7r+VVKAHcCTyTmZ+fNL5s0mEfBJ5sSCJJWiA2rO7jsx96B2/qmqjaviU9fPZD72jIE5hQ26tQ1gAfAfZHxOPV2G3AjRFxBZDA88DNDUkkSQvIhtV97Hz0CND4v4Uya4Fn5g+AmGbXAw1NIkmqi+/ElKRCWeCSVCgLXJIKZYFLUqEscElqou0DBxk8fJzBw8dZfuv9bB842LD7jsxs2J3Npr+/P4eGhlo2nyQtBBGxLzP7p457Bi5JhbLAJalQFrgkFcoCl6RCWeCSVCgLXJIKZYFLUqEscEkqlAUuSYWywCWpUBa4JBXKApekQlngklQoC1ySCmWBS1KhLHBJKpQFLkmFssAlqVAWuCQVygKXpEJZ4JJUKAtckgplgUtSoWYt8Ii4NCIeioinI+KpiNhUjb85IgYi4lD1/aLmx5UknVHLGfhrwKcy83LgauDjEXE5cCuwNzNXAHur25KkFpm1wDPzaGY+Vm2/CjwD9AHXA3dXh90NbGhWSEnS69V1DTwilgOrgUHg4sw8Wu36CXDxDD+zMSKGImJodHR0HlElSZPVXOARcQHwTeCTmfnK5H2ZmUBO93OZuSMz+zOzv7e3d15hJUk/V1OBR0Q3E+X91czcVQ2/FBHLqv3LgGPNiShJmk4tr0IJ4E7gmcz8/KRd9wE3Vds3Ad9ufDxJ0kzOq+GYNcBHgP0R8Xg1dhtwO/CNiPgY8GPgD5oTUZI0nVkLPDN/AMQMu9c2No4kqVa+E1OSCmWBS1KhLHBJKpQFLkmFssAlqVAWuCQVygKXpEJZ4JJUKAtckgplgUtSoSxwSSqUBS5JhbLAJalQFrgkFaqWvwcuSQBsHzjIHXsPnb29ae0KNq9b2cZEi5sFLqlmm9et5JHnXgbgnpuvaXMaeQlFkgplgUtSoSxwSTXbPTzC8JETDB4+zprbH2T38Ei7Iy1qFrikmuweHmHrrv2cHD8NwMiJMbbu2m+Jt5EFLqkm2/YcYOzU+DljY6fG2bbnQJsSyQKXVJMXT4zVNa7ms8Al1eSSJT11jav5LHBJNdmyfhU93V3njPV0d7Fl/ao2JZJv5JFUkw2r+wC45d4nODl+mr4lPWxZv+rsuFrPApdUsw2r+9j56BHAd2J2Ai+hSFKhLHBJKpQFLqlm2wcOMnj4OIOHj7P81vvZPnCw3ZEWtcjMNz4g4i7g/cCxzHx7NfYZ4E+B0eqw2zLzgdkm6+/vz6GhoXkFlqTFJiL2ZWb/1PFazsC/Alw3zfj2zLyi+pq1vCVJjTVrgWfmw8DxFmSRJNVhPtfAPxERT0TEXRFx0UwHRcTGiBiKiKHR0dGZDpMk1WmuBf4F4G3AFcBR4HMzHZiZOzKzPzP7e3t75zidJGmqORV4Zr6UmeOZeRr4EnBVY2NJkmYzpwKPiGWTbn4QeLIxcSRJtZr1rfQRsRO4FlgaES8AnwaujYgrgASeB25uYkZJ0jRmLfDMvHGa4TubkEWSVAffiSlJhbLAJalQFrgkFcoCl6RCWeCSVCgLXJIKZYFLUqEscEkqlAUuSYWywCWpUBa4JBXKApekQlngklQoC1ySCmWBS1KhLHBJKpQFLkmFssAlqVAWuCQVygKXpEJZ4JJUKAtckgplgUtSoSxwSSqUBS5JhbLAJalQFrgkFcoCl6RCWeCSVKhZCzwi7oqIYxHx5KSxN0fEQEQcqr5f1NyYkqSpajkD/wpw3ZSxW4G9mbkC2FvdliS10KwFnpkPA8enDF8P3F1t3w1saHAuSdIs5noN/OLMPFpt/wS4uEF5JEk1mveTmJmZQM60PyI2RsRQRAyNjo7OdzpJUmWuBf5SRCwDqL4fm+nAzNyRmf2Z2d/b2zvH6SRJU821wO8Dbqq2bwK+3Zg4kqRa1fIywp3AfwKrIuKFiPgYcDuwLiIOAb9b3ZYktdB5sx2QmTfOsGttg7NILbd94CB37D109vamtSvYvG5lGxNJtZu1wKWFbPO6lTzy3MsA3HPzNW1OI9XHt9JLUqEscC1qu4dHGD5ygsHDx1lz+4PsHh5pdySpZha4Fq3dwyNs3bWfk+OnARg5McbWXfstcRXDAteitW3PAcZOjZ8zNnZqnG17DrQpkVQfC1yL1osnxuoalzqNBa5F65IlPXWNS53GAteitWX9Knq6u84Z6+nuYsv6VW1KJNXH14Fr0dqwug+AW+59gpPjp+lb0sOW9avOjkudzgLXorZhdR87Hz0C+EYelcdLKFrUtg8cZPDwcQYPH2f5rfezfeBguyNJNYuJP+fdGv39/Tk0NNSy+SRpIYiIfZnZP3XcM3BJKpQFLkmFssAlqVAWuCQVygKXpEJZ4JJUKAtckgplgUtSoSxwSSqUBS5JhbLAJalQFrgkFcoCl6RCWeCSVCgLXJIKZYFLUqEscEkqlAUuSYWa14caR8TzwKvAOPDadB/5I0lqjkZ8Kv1vZ+ZPG3A/kqQ6eAlFkgo13zPwBL4fEQn8S2bumHpARGwENgJcdtll85xOs9k+cJA79h46e3vT2hVsXreyjYkkNct8C/xdmTkSEb8KDETEjzLz4ckHVKW+A6C/vz/nOZ9msXndSh557mUA7rn5mjankdRM87qEkpkj1fdjwLeAqxoRSpI0uzkXeEScHxEXntkG3gM82ahgkqQ3Np8z8IuBH0TED4FHgfsz83uNiaW52j08wvCREwwePs6a2x9k9/BIuyNJapI5XwPPzOeAdzYwi+Zp9/AIW3ft5+T4aQBGToyxddd+ADas7mtnNElN4MsIF5Btew4wdmr8nLGxU+Ns23OgTYkkNZMFvoC8eGKsrnFJZbPAF5BLlvTUNS6pbBb4ArJl/Sp6urvOGevp7mLL+lVtSiSpmRrxt1DUIc48UXnLvU9wcvw0fUt62LJ+lU9gSguUBb7AbFjdx85HjwC+E1Na6LyEIkmFssAlqVAW+AKzfeAgg4ePM3j4OMtvvZ/tAwfbHUlSk0Rm6/5AYH9/fw4NDbVsPklaCCJi33SfeOYZuCQVygKXpEJZ4JJUKAtckgplgUtSoSxwSSqUBS5JhbLAJalQFrgkFcoCl6RCWeCSVKiO/3vg2wcOcsfeQ2dvb1q7gs3rVrYxkSR1ho4/A3/r0vN5U9dEzL4lPbx16fltTiRJnaGjC3z38Ahbd+3n5PhpAEZOjLF11352D4+0OZkktV9HF/i2PQcYOzV+ztjYqXG27TnQpkSS1Dk6usBfPDFW17gkLSYdXeCXLOmpa1ySFpOOLvAt61fR0911zlhPdxdb1q9qUyJJ6hwd/TLCDav7ALjl3ic4OX6aviU9bFm/6uy4JC1m8yrwiLgOuAPoAr6cmbc3JNUkG1b3sfPRIwDcc/M1jb57SSrWnC+hREQX8M/Ae4HLgRsj4vJGBTvDT1mXpOnN5wz8KuDZzHwOICK+DlwPPN2IYGdsXrfSd15K0jTm8yRmH/Dfk26/UI2dIyI2RsRQRAyNjo7OYzpJ0mRNfxVKZu7IzP7M7O/t7W32dJK0aMynwEeASyfdfks1JklqgfkU+H8BKyLirRHxJuAG4L7GxJIkzWbOT2Jm5msR8QlgDxMvI7wrM59qWDJJ0hua1+vAM/MB4IEGZZEk1aGj30ovSZqZBS5JhYrMbN1kEaPAj+f440uBnzYwTqOYqz7mqo+56tOpuWB+2X49M1/3OuyWFvh8RMRQZva3O8dU5qqPuepjrvp0ai5oTjYvoUhSoSxwSSpUSQW+o90BZmCu+pirPuaqT6fmgiZkK+YauCTpXCWdgUuSJrHAJalQHVXgEXFXRByLiCdn2B8R8Q8R8WxEPBERV3ZIrmsj4mcR8Xj19dctynVpRDwUEU9HxFMRsWmaY1q+ZjXmavmaRcQvRcSjEfHDKtffTHPML0bEPdV6DUbE8g7J9dGIGJ20Xn/S7FyT5u6KiOGI+M40+1q+XjXmast6RcTzEbG/mnNomv2NfTxmZsd8Ae8GrgSenGH/+4DvAgFcDQx2SK5rge+0Yb2WAVdW2xcCB4HL271mNeZq+ZpVa3BBtd0NDAJXTznmL4AvVts3APd0SK6PAv/U6v/Hqrn/CvjadP+92rFeNeZqy3oBzwNL32B/Qx+PHXUGnpkPA8ff4JDrgX/NCY8ASyJiWQfkaovMPJqZj1XbrwLP8PpPRWr5mtWYq+WqNfif6mZ39TX1Wfzrgbur7XuBtRERHZCrLSLiLcDvAV+e4ZCWr1eNuTpVQx+PHVXgNajpY9za5JrqV+DvRsRvtHry6lfX1UycvU3W1jV7g1zQhjWrfu1+HDgGDGTmjOuVma8BPwN+pQNyAfx+9Wv3vRFx6TT7m+HvgVuA0zPsb8t61ZAL2rNeCXw/IvZFxMZp9jf08VhagXeqx5j4WwXvBP4R2N3KySPiAuCbwCcz85VWzv1GZsnVljXLzPHMvIKJT5C6KiLe3op5Z1NDrv8AlmfmbwID/Pyst2ki4v3Asczc1+y56lFjrpavV+VdmXkl8F7g4xHx7mZOVlqBd+THuGXmK2d+Bc6Jv5HeHRFLWzF3RHQzUZJfzcxd0xzSljWbLVc716ya8wTwEHDdlF1n1ysizgN+GXi53bky8+XM/L/q5peB32pBnDXAByLieeDrwO9ExL9POaYd6zVrrjatF5k5Un0/BnwLuGrKIQ19PJZW4PcBf1Q9k3s18LPMPNruUBHxa2eu+0XEVUysa9Mf9NWcdwLPZObnZzis5WtWS652rFlE9EbEkmq7B1gH/GjKYfcBN1XbHwYezOrZp3bmmnKd9ANMPK/QVJm5NTPfkpnLmXiC8sHM/MMph7V8vWrJ1Y71iojzI+LCM9vAe4Cpr1xr6ONxXp/I02gRsZOJVycsjYgXgE8z8YQOmflFJj79533As8D/An/cIbk+DPx5RLwGjAE3NPt/4soa4CPA/ur6KcBtwGWTsrVjzWrJ1Y41WwbcHRFdTPyD8Y3M/E5E/C0wlJn3MfEPz79FxLNMPHF9Q5Mz1ZrrLyPiA8BrVa6PtiDXtDpgvWrJ1Y71uhj4VnVech7wtcz8XkT8GTTn8ehb6SWpUKVdQpEkVSxwSSqUBS5JhbLAJalQFrgkFcoCl6RCWeCSVKj/B5HlHyH7+lIiAAAAAElFTkSuQmCC\n"},"metadata":{"needs_background":"light"}}],"source":["import pylab as pl\n","\n","x = pl.array([1,2,3,4,5]) \n","y = pl.array([0.9,4.1,8.7,16.5,24.9])  \n","yerr = pl.array([0.6,0.9,0.75,0.9,1.2])  \n","pl.figure()\n","pl.scatter(x,y)\n","pl.errorbar(x, y, yerr,  ls='None', capsize=2)\n","pl.show()"]},{"cell_type":"markdown","metadata":{"id":"DZX1JHFOtyMT"},"source":["### d. Logarithmic Axes"]},{"cell_type":"markdown","metadata":{"id":"fa9lOp-xtyMT"},"source":["One of the axes can be made logarithmic with the **`semilogx`** or **`semilogy`** function.\n","Both axes can be made logarithmic using the **`loglog`** function. It is simplest to make graph using **`plot`**, **`scatter`**, or **`errorbar`** followed by a command make one or both axes logarithmic as shown below.\n","\n","For logarithmic scales, including grid lines makes it much easier to estimate values on a\n","graph. The command \n","<blockquote>grid(which='both')</blockquote>\n","will put grid lines at both the major tick marks and at the minor tick marks in between."]},{"cell_type":"code","execution_count":8,"metadata":{"colab":{"base_uri":"https://localhost:8080/","height":265},"id":"dtmLSnCrtyMT","executionInfo":{"status":"ok","timestamp":1653065746464,"user_tz":420,"elapsed":289,"user":{"displayName":"Alan DeWeerd","userId":"09086135147919405400"}},"outputId":"504b6313-7c3e-4804-bf09-6de8a1e8c6a2"},"outputs":[{"output_type":"display_data","data":{"text/plain":["<Figure size 432x288 with 1 Axes>"],"image/png":"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\n"},"metadata":{"needs_background":"light"}}],"source":["import pylab as pl\n","\n","x = pl.array([1,2,3]) \n","y = pl.array([10,80,200])  \n","pl.figure()\n","pl.scatter(x,y)\n","pl.semilogy()\n","pl.grid(which='both')\n","pl.show()"]},{"cell_type":"markdown","metadata":{"id":"hta_hzQJtyMT"},"source":["If a logarithmic horizontal axis is used on the horizontal axis, it is better to use the **`logspace`** function to plot a curve (for example, a theoretical curve). It returns returns a list of numbers from 10 to the power of the first argument to 10 to the power of the second argument, where the number of elements is given by the third argument.  The numbers will be evenly spaced on a logarithmic scale. For example, **`logspace(2,4,50)`** will return 50 numbers from $10^2 = 100$ to $10^4 = 10000$. In the example below, not how much smoother the curve made using the **`logspace`** function is, especailly for small $x$. The curve made with the **`linspace`** function only has two points with $x<100$."]},{"cell_type":"code","execution_count":9,"metadata":{"colab":{"base_uri":"https://localhost:8080/","height":269},"id":"DN7UvfQOtyMU","executionInfo":{"status":"ok","timestamp":1653065746719,"user_tz":420,"elapsed":267,"user":{"displayName":"Alan DeWeerd","userId":"09086135147919405400"}},"outputId":"e4623626-49c7-42b4-b1a1-737ac2ccc679"},"outputs":[{"output_type":"display_data","data":{"text/plain":["<Figure size 432x288 with 1 Axes>"],"image/png":"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\n"},"metadata":{"needs_background":"light"}}],"source":["import pylab as pl\n","\n","xtheory1 = pl.linspace(10, 1000, 20)\n","ytheory1 = 1.0/(xtheory1+10.)**2  \n","\n","xtheory2 = pl.logspace(1, 3, 20)\n","ytheory2 = 1.0/(xtheory2+10.)**2  \n","\n","pl.figure()\n","pl.plot(xtheory1,ytheory1,label='linspace',c='b')\n","pl.plot(xtheory2,ytheory2,label='logspace',c='g')\n","pl.semilogx()\n","pl.legend()\n","pl.show()"]},{"cell_type":"markdown","metadata":{"id":"GaLDqT0ctyMU"},"source":["## 3. Overlaying Plots"]},{"cell_type":"markdown","metadata":{"id":"ny0My1Z4tyMU"},"source":["As mentioned earlier, multiple plots can appear in the same figure. If you want multiple plots to appear in a single figure, all of the plotting commands should be below a single **`figure`** command. When there are multiple plots, it is helpful to make a legend to label them. This is done be adding a **`label`** argument to each plotting command and using the legend command. The **`loc`** argument can be used to specify the location of the legend."]},{"cell_type":"code","execution_count":10,"metadata":{"colab":{"base_uri":"https://localhost:8080/","height":265},"id":"7t_OmTmNtyMU","executionInfo":{"status":"ok","timestamp":1653065746969,"user_tz":420,"elapsed":260,"user":{"displayName":"Alan DeWeerd","userId":"09086135147919405400"}},"outputId":"61e46bdd-e79f-41d6-abff-a626fd74a0ea"},"outputs":[{"output_type":"display_data","data":{"text/plain":["<Figure size 432x288 with 1 Axes>"],"image/png":"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\n"},"metadata":{"needs_background":"light"}}],"source":["import pylab as pl\n","\n","xtheory = pl.linspace(0.0, 5.0, 100)\n","ytheory = xtheory**2  \n","xdata = pl.array([1,2,3,4,5]) \n","ydata = pl.array([0.9,4.1,8.7,16.5,24.9])  \n","yerr = pl.array([0.6,0.9,0.75,0.9,1.2])  \n","pl.figure()\n","pl.plot(xtheory,ytheory,label='theory')\n","pl.errorbar(xdata, ydata, yerr,  ls='None', marker='o',capsize=2, label='data')\n","pl.legend(loc='upper left')\n","pl.show()"]},{"cell_type":"markdown","metadata":{"id":"6frOJo8ztyMV"},"source":["The previous example shows how to get a smooth curve if you're using a logarithmic scale on the horizontal axis."]},{"cell_type":"markdown","metadata":{"id":"NOHGQ_bctyMV"},"source":["## Additional Documentation"]},{"cell_type":"markdown","metadata":{"id":"pLVzxD2YtyMV"},"source":["Further information is available at:<br>\n","http://matplotlib.sourceforge.net/users/pyplot_tutorial.html (a good place to start)  \n","http://matplotlib.sourceforge.net/ (links to documentation for all commands)"]}],"metadata":{"kernelspec":{"display_name":"Python 3","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":"3.8.5"},"colab":{"name":"Plotting.ipynb","provenance":[],"collapsed_sections":[]}},"nbformat":4,"nbformat_minor":0}