matplotlib.pyplot<\/strong>\u00a0sub-module contains many plotting functions to create various kinds of plots. So we begin\u00a0 by importing\u00a0matplotlib.pyplot\u00a0and using\u00a0%matplotib\u00a0Jupyter magic\u00a0to display plots in the notebook.<\/p>\nBefore you can plot, you need to import the neccessary modules. You do that using the code below:<\/p>\n
# you need to import numpy and pyplot<\/span>\nimport<\/span> numpy<\/span> as<\/span> np<\/span>\nimport<\/span> matplotlib.pyplot<\/span> as<\/span> plt<\/span>\n%<\/span>matplotlib inline\n<\/pre>\n <\/p>\n
2. Basic Plotting<\/strong><\/h5>\nLet’s look at how to create a basic 2D plot. The procedure is:<\/p>\n
\n- Create a sequence that represents x\u00a0values.<\/li>\n
- Create a sequence the represents the y\u00a0values.<\/li>\n
- Use\u00a0plt.plot(x,y,[fmt],**kwargs<\/strong>). [fmt]\u00a0is an (optional) format string while **kwargs\u00a0are also (optional) keyword arguments the specifies the line properties of the plot.<\/li>\n
- Use\u00a0pyplot\u00a0<\/strong>functions to add features to the plot such as gridlines,\u00a0 title, legend, etc.<\/li>\n
- Use\u00a0plt.show()<\/strong>\u00a0to display the resulting figure.<\/li>\n<\/ul>\n
Example i<\/strong>, the code below, produces the line plot shown<\/p>\nx =<\/span> [-<\/span>6<\/span>, -<\/span>5<\/span>, -<\/span>2<\/span>, 0<\/span>, 1<\/span>, 3<\/span>, 4<\/span>]\ny =<\/span> [1<\/span>, 2<\/span>, -<\/span>1<\/span>, 1<\/span>, -<\/span>4<\/span>, 3<\/span>, 2<\/span>]\n\nplt.<\/span>plot(x,y)\nplt.<\/span>show()\n<\/pre>\n <\/p>\n
![\"\"](\"https:\/\/www.kindsonthegenius.com\/wp-content\/uploads\/2020\/09\/Plot-1.jpg\")
<\/p>\n
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Example ii<\/strong>, a second plot. But notice the\u00a0 that the edges of the curve are sharp edges.<\/p>\nx =<\/span> [-<\/span>3<\/span>, -<\/span>2<\/span>, -<\/span>1<\/span>, 0<\/span>, 1<\/span>, 2<\/span>, 3<\/span>]\ny =<\/span>[5<\/span>, 4<\/span>,1<\/span>, 0<\/span>,1<\/span>,4<\/span>, 5<\/span>]\n\nplt.<\/span>plot(x, y)\nplt.<\/span>show()\n<\/pre>\n <\/p>\n
![\"\"](\"https:\/\/www.kindsonthegenius.com\/wp-content\/uploads\/2020\/09\/Plot-2.jpg\")
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Example iii<\/strong>, now we would plot a smooth curve by using a larger number of points. The code and curve are shown below<\/p>\n<\/p>\n
# Smooth curve is produced by using large number of data points<\/span>\nx =<\/span> np.<\/span>linspace(-<\/span>3<\/span>,3<\/span>,200<\/span>)\ny =<\/span> x**<\/span>2<\/span>\n\nplt.<\/span>plot(x, y)\nplt.<\/span>show()\n<\/pre>\n <\/p>\n
![\"\"](\"https:\/\/www.kindsonthegenius.com\/wp-content\/uploads\/2020\/09\/Plot3.jpg\")
<\/p>\n
Now, you know how to create basic plots, let’s now see how to format our plot.<\/p>\n
<\/p>\n
3. Properties of a Line<\/strong><\/h5>\nSome of the properties of the line you can set includes, color, alpha(transparency), style, width, markers etc. These properties can be set by giving additional attributes to the plot method. The table below shows that attributes you can use to format your plot<\/p>\n
\n\n\nProperty<\/strong><\/td>\nDescription<\/strong><\/td>\n<\/tr>\n<\/thead>\n\n\n| alpha (transparency)<\/td>\n | transparency (0.0 transparent through 1.0 opaque)<\/td>\n<\/tr>\n | \n| color\u00a0(or\u00a0c)<\/td>\n | any matplotlib color<\/td>\n<\/tr>\n | \n| label<\/td>\n | text appearing in legend<\/td>\n<\/tr>\n | \n| linestyle\u00a0(or\u00a0ls)<\/td>\n | solid,\u00a0dashed,\u00a0dashdot,\u00a0dotted<\/td>\n<\/tr>\n | \n| linewidth\u00a0(or\u00a0lw)<\/td>\n | set width of the line<\/td>\n<\/tr>\n | \n| marker<\/td>\n | set marker style<\/td>\n<\/tr>\n | \n| markeredgecolor\u00a0(or\u00a0mec)<\/td>\n | any matplotlib color<\/td>\n<\/tr>\n | \n| markerfacecolor\u00a0(or\u00a0mfc)<\/td>\n | any matplotlib color<\/td>\n<\/tr>\n | \n| markersize\u00a0(or\u00a0ms)<\/td>\n | size of the marker<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n Table 1: Properties of a Plot\u00a0 Line<\/p>\n <\/h5>\nWe would apply what we learnt to plot a curve. The curve would be the damped cosine wave curve based on this function<\/p>\n ![\"Damped](\"https:\/\/www.kindsonthegenius.com\/wp-content\/uploads\/2020\/09\/Damped-cosine-wave.jpg\") <\/p>\n
You should learn how to write math functions in Python format. For example the equation in Python will be:
\ny = np.exp(-x**2) * np.cos(2 * np.pi * x)<\/strong><\/em><\/p>\nI guess I’ll cover this in another tutorial.<\/p>\n The complete code is given below. Notice how we have used the attributes specified in Table 1 to set the properties of the curve.<\/p>\n #generate a sequence of 40 values from -2 to 2<\/span>\nx =<\/span> np.<\/span>linspace(-<\/span>2<\/span>,2<\/span>,40<\/span>)\ny =<\/span> np.<\/span>exp(-<\/span>x**<\/span>2<\/span>)*<\/span> np.<\/span>cos(2<\/span>*<\/span>math.<\/span>pi*<\/span>x) #damped cosine wave<\/span>\n\nplt.<\/span>plot(x,y, \n alpha=<\/span>0.4<\/span>, \n label=<\/span>'Damped Cosine Wave'<\/span>, \n color=<\/span>'red'<\/span>, linestyle=<\/span>'dashed'<\/span>, \n linewidth=<\/span>2<\/span>, \n marker=<\/span>'*'<\/span>, \n markersize=<\/span>7<\/span>, \n markerfacecolor=<\/span>'red'<\/span>,\n markeredgecolor=<\/span>'blue'<\/span>)\nplt.<\/span>ylim([-<\/span>2<\/span>,2<\/span>])\nplt.<\/span>legend()\nplt.<\/span>show()\n<\/pre>\n <\/p>\n If you run the code, the resulting curve will be<\/p>\n ![\"Decaying](\"https:\/\/www.kindsonthegenius.com\/wp-content\/uploads\/2020\/09\/Decaying-Cosine-Curve.jpg\") <\/p>\n
I recommend, you change of some of the attributes in the code and see how it affects the curve<\/p>\n <\/p>\n 4. Formatting Your Plot<\/strong><\/h5>\nWe can you a format string to shortcut to add attributes like color, marker, and linestyle to a line plot. For instance, assuming we want to plot the<\/p>\n ![\"Arctan](\"https:\/\/www.kindsonthegenius.com\/wp-content\/uploads\/2020\/09\/Arctan-Function.jpg\") <\/p>\n
The equivalent Python code is given below<\/p>\n x =<\/span> np.<\/span>linspace(-<\/span>5<\/span>,5<\/span>,40<\/span>)\ny =<\/span> 1<\/span>\/<\/span>(1<\/span> +<\/span> x**<\/span>2<\/span>)\nplt.<\/span>plot(x, y, \n color=<\/span>'red'<\/span>, \n marker=<\/span>'s'<\/span>,\n markerfacecolor=<\/span>'blue'<\/span>)\nplt.<\/span>show()\n<\/pre>\n <\/p>\n ![\"\"](\"https:\/\/www.kindsonthegenius.com\/wp-content\/uploads\/2020\/09\/Plot-4.jpg\") <\/p>\n
The code below also achieves the same thing<\/p>\n x =<\/span> np.<\/span>linspace(-<\/span>5<\/span>,5<\/span>,40<\/span>)\ny =<\/span> 1<\/span>\/<\/span>(1<\/span> +<\/span> x**<\/span>2<\/span>)\nplt.<\/span>plot(x, y, \n 'rs--'<\/span>,\n markerfacecolor=<\/span>'blue'<\/span>)\nplt.<\/span>show()\n<\/pre>\n <\/p>\n In the code above, ‘rs—‘ means:<\/p>\n \n- r stands for a red line<\/li>\n
- s stands for a square marker<\/li>\n
- — stands for a dashed line<\/li>\n<\/ul>\n
The tables below give the the shortcuts for other attributes<\/p>\n Shortcuts for colors<\/strong><\/p>\n\n\n\nCharacter<\/strong><\/td>\nColor<\/strong><\/td>\n<\/tr>\n<\/thead>\n\n\n| b<\/td>\n | blue<\/td>\n<\/tr>\n | \n| g<\/td>\n | green<\/td>\n<\/tr>\n | \n| r<\/td>\n | red<\/td>\n<\/tr>\n | \n| c<\/td>\n | cyan<\/td>\n<\/tr>\n | \n| m<\/td>\n | magenta<\/td>\n<\/tr>\n | \n| y<\/td>\n | yellow<\/td>\n<\/tr>\n | \n| k<\/td>\n | black<\/td>\n<\/tr>\n | \n| w<\/td>\n | white<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n <\/p>\n Shortcuts for markers<\/strong><\/p>\n\n\n\n| Character<\/td>\n | Marker<\/td>\n<\/tr>\n<\/thead>\n | \n\n| .<\/td>\n | point<\/td>\n<\/tr>\n | \n| o<\/td>\n | circle<\/td>\n<\/tr>\n | \n| v<\/td>\n | triangle down<\/td>\n<\/tr>\n | \n| ^<\/td>\n | triangle up<\/td>\n<\/tr>\n | \n| s<\/td>\n | square<\/td>\n<\/tr>\n | \n| p<\/td>\n | pentagon<\/td>\n<\/tr>\n | \n| *<\/td>\n | star<\/td>\n<\/tr>\n | \n| +<\/td>\n | plus<\/td>\n<\/tr>\n | \n| x<\/td>\n | x<\/td>\n<\/tr>\n | \n| D<\/td>\n | diamond<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n <\/p>\n Shortcuts for linestyles<\/strong><\/p>\n\n\n\n| Character<\/td>\n | Line Style<\/td>\n<\/tr>\n<\/thead>\n | \n\n| –<\/td>\n | solid line style<\/td>\n<\/tr>\n | \n| —<\/td>\n | dashed line style<\/td>\n<\/tr>\n | \n| -.<\/td>\n | dash-dot line style<\/td>\n<\/tr>\n | \n| :<\/td>\n | dotted line style<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/h5>\n5. Pyplot Functions<\/strong><\/h5>\nThere are a number of pyplot\u00a0functions available for us to customize our figures. For example, the table below shows some of them:<\/p>\n \n\n\nFucntion<\/strong><\/td>\nDescription<\/strong><\/td>\n<\/tr>\n<\/thead>\n\n\n| plt.xlim<\/td>\n | sets the x\u00a0limits<\/td>\n<\/tr>\n | \n| plt.ylim<\/td>\n | sets the\u00a0 y\u00a0limits<\/td>\n<\/tr>\n | \n| plt.grid<\/td>\n | adds the grid lines<\/td>\n<\/tr>\n | \n| plt.title<\/td>\n | adds a title<\/td>\n<\/tr>\n | \n| plt.xlabel<\/td>\n | adds a label to the horizontal axis<\/td>\n<\/tr>\n | \n| plt.ylabel<\/td>\n | adds a label to the vertical axis<\/td>\n<\/tr>\n | \n| plt.axis<\/td>\n | sets axis properties (equal,\u00a0off,\u00a0scaled, etc.)<\/td>\n<\/tr>\n | \n| plt.xticks<\/td>\n | sets tick locations on the horizontal axis<\/td>\n<\/tr>\n | \n| plt.yticks<\/td>\n | sets tick locations on the vertical axis<\/td>\n<\/tr>\n | \n| plt.legend<\/td>\n | displays legend for several lines in the same figure<\/td>\n<\/tr>\n | \n| plt.savefig<\/td>\n | save figure (as .png, .pdf, etc.) to working directory<\/td>\n<\/tr>\n | \n| plt.figure<\/td>\n | creates a new figure and set its properties<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n Let’s now apply some of these pyplot<\/strong> functions to create a plot.<\/p>\n <\/p>\n 6. Example 1 – Plotting the Taylor’s Polynomial<\/strong><\/h5>\nNow, we are going to used some the pyplot functions to plot the Taylor’s Polynomial.<\/p>\n This is also called Taylor’s Series and it<\/b>\u00a0is a way to represent\u00a0 a\u00a0 | | | | | | | | | | |