As\u00a0SciPy is open source<\/strong>, it has a very active and vibrant community of developers due to which there are enormous number of modules present for a vast amount of scientific applications and calculations available with SciPy. Some of the complex mathematical operations which can be performed with SciPy are:<\/p>\n SciPy can be compared to most command and standard libraries like GSL library for C++ and Matlab. As SciPy is built on top of NumPy package, these two packages can be integrated completely as well. If you can think of a mathematical operation which needs to be done, make sure you check SciPy library before you implement that module on your own because in most cases, SciPy have all the operations for you fully implemented already.<\/p>\n Let\u2019s install SciPy library before we move to the actual examples and concepts. There are two ways to install this package. First one includes using the Python package manager, pip:<\/p>\n The second way relates to Anaconda, we can install the package as:<\/span><\/p>\n<\/div>\n<\/div>\n Once the library is installed, we can import it as:<\/span><\/p>\n Finally, as we will be using\u00a0NumPy<\/a>\u00a0as well (It is recommended that for all\u00a0NumPy<\/a>\u00a0operations, we use NumPy directly instead of going through the SciPy package):<\/span><\/p>\n <\/p>\n It is possible that in some cases, we will also like to plot our results for which we will use the\u00a0Matplotlib<\/a>\u00a0library. Perform the following import for that library:<\/span><\/p>\n <\/p>\n I will be using the Anaconda manager for all the examples in this lesson. I will launch a Jupyter Notebook for the same:<\/p>\n Now that we are ready with all the import statements to write some code, let\u2019s start diving into SciPy package with some practical examples.<\/p>\n We will start by looking at simple Polynomial equations. There are two ways with which we can integrate Polynomial functions into our program. We can make use of\u00a0poly1d<\/em>\u00a0class which makes use of coefficients or the roots of a polynomial for initialising a polynomial. Let\u2019s look at an example:<\/p>\n When we run this example, we will see the following output:<\/span><\/p>\n Clearly, the polynomial representation of the equation is printed as the output so that the result is pretty easy to understand. We can perform various operations on this polynomial as well, like square it, find its derivative or even solve it for a value of x. Let\u2019s try doing all of these in the next example:<\/span><\/p>\n print<\/span>(<\/span>“Derivative of Polynomial:\u00a0\\n<\/span>“<\/span>)<\/span> print<\/span>(<\/span>“Solving the Polynomial:\u00a0\\n<\/span>“<\/span>)<\/span> When we run this example, we will see the following output:<\/span><\/p>\n Just when I was thinking that this is all we could do with SciPy, I remembered that we can integrate a Polynomial as well. Let\u2019s run a final example with Polynomials:<\/span><\/p>\n The integer we pass tells the package how many times to integrate the polynomial:<\/span><\/p>\n We can simply pass another integer which tells the package how many times to integrate this polynomial.<\/p>\n It is even possible to solve linear equations with SciPy and find their roots, if they exist. To solve linear equations, we represent the set of equations as NumPy arrays and their solution as a separate NumPy arrays. Let\u2019s visualise it with an example where we do the same and make use of\u00a0linalg<\/em>\u00a0package to find the roots of the equations, here are the equations we will be solving:<\/p>\n Let\u2019s solve the above equations:<\/span><\/p>\n equation\u00a0=<\/span>\u00a0np.array<\/span>(<\/span>[<\/span>[<\/span>1<\/span>,<\/span>\u00a05<\/span>]<\/span>,<\/span>\u00a0[<\/span>3<\/span>,<\/span>\u00a07<\/span>]<\/span>]<\/span>)<\/span> roots\u00a0=<\/span>\u00a0linalg.solve<\/span>(<\/span>equation,<\/span>\u00a0solution)<\/span><\/p>\n print<\/span>(<\/span>“Found the roots:”<\/span>)<\/span> print<\/span>(<\/span>“\\n<\/span>\u00a0Dot product should be zero if the solutions are correct:”<\/span>)<\/span> <\/p>\n When we run the above program, we will see that the dot product equation gives zero result, which means that the roots which the program found were correct:<\/span><\/p>\n Fourier Transformations helps us to express a function as separate components that make up that function and guides us about the way through which we can recombine those components to get the original function back.<\/p>\n Let\u2019s look at a simple example of Fourier Transformations where we plot the sum of two cosines using the\u00a0Matplotlib<\/a>\u00a0library:<\/p>\n # Number of sample points<\/span> # sample spacing<\/span> # matplotlib for plotting purposes<\/span>\n
Install SciPy Library<\/strong><\/h3>\n
![\"\"](\"https:\/\/linuxhint.com\/wp-content\/uploads\/2019\/02\/1-8.png\")
<\/p>\nWorking with Polynomial Equations<\/strong><\/h3>\n
\nfirst_polynomial\u00a0=<\/span>\u00a0poly1d(<\/span>[<\/span>3<\/span>,<\/span>\u00a04<\/span>,<\/span>\u00a07<\/span>]<\/span>)<\/span>
\nprint<\/span>(<\/span>first_polynomial)<\/span><\/div>\n![\"\"](\"https:\/\/linuxhint.com\/wp-content\/uploads\/2019\/02\/2-10.png\")
<\/span><\/p>\n
\nprint<\/span>(<\/span>first_polynomial * first_polynomial)<\/span><\/p>\n
\nprint<\/span>(<\/span>first_polynomial.deriv<\/span>(<\/span>)<\/span>)<\/span><\/p>\n
\nprint<\/span>(<\/span>first_polynomial(<\/span>3<\/span>)<\/span>)<\/span><\/div>\n![\"\"](\"https:\/\/linuxhint.com\/wp-content\/uploads\/2019\/02\/3-8.png\")
<\/p>\n
\nprint<\/span>(<\/span>first_polynomial.integ<\/span>(<\/span>1<\/span>)<\/span>)<\/span><\/div>\n![\"\"](\"https:\/\/linuxhint.com\/wp-content\/uploads\/2019\/02\/4-7.png\")
<\/p>\nSolving Linear Equations<\/strong><\/h3>\n
\n3x + 7y\u00a0=<\/span>\u00a09<\/span><\/div>\n
\nsolution\u00a0=<\/span>\u00a0np.array<\/span>(<\/span>[<\/span>[<\/span>6<\/span>]<\/span>,<\/span>\u00a0[<\/span>9<\/span>]<\/span>]<\/span>)<\/span><\/p>\n
\nprint<\/span>(<\/span>roots)<\/span><\/p>\n
\nprint<\/span>(<\/span>equation.dot<\/span>(<\/span>roots)<\/span>\u00a0– solution)<\/span><\/div>\n<\/div>\n![\"\"](\"https:\/\/linuxhint.com\/wp-content\/uploads\/2019\/02\/5-8.png\")
<\/p>\nFourier Transformations with SciPy<\/strong><\/h3>\n
\nN\u00a0=<\/span>\u00a0500<\/span><\/p>\n
\nT\u00a0=<\/span>\u00a01.0<\/span>\u00a0\/\u00a0800.0<\/span>
\nx\u00a0=<\/span>\u00a0np.linspace<\/span>(<\/span>0.0<\/span>,<\/span>\u00a0N*T,<\/span>\u00a0N)<\/span>
\ny\u00a0=<\/span>\u00a0np.cos<\/span>(<\/span>50.0<\/span>\u00a0*\u00a02.0<\/span>* np.pi<\/span>\u00a0* x)<\/span>\u00a0+\u00a00.5<\/span>\u00a0* np.cos<\/span>(<\/span>80.0<\/span>\u00a0*\u00a02.0<\/span>\u00a0* np.pi<\/span>\u00a0* x)<\/span>
\nyf\u00a0=<\/span>\u00a0fft(<\/span>y)<\/span>
\nxf\u00a0=<\/span>\u00a0np.linspace<\/span>(<\/span>0.0<\/span>,<\/span>\u00a01.0<\/span>\/(<\/span>2.0<\/span>\u00a0* T)<\/span>,<\/span>\u00a0N\/\/2<\/span>)<\/span><\/p>\n
\nimport<\/span>\u00a0matplotlib.