## How to solve Hermitian positive-banded matrix equation using Python SciPy?

Updated on 25-Nov-2021 06:36:52
The linear function named scipy.linalg.solveh_banded is used to solve the banded matrix equation. In the below given example we will be solving the banded system Hx = b where −$$\mathrm{H} = \begin{bmatrix} 8 & 2-1j&0 &0 \ 2+1j & 5& 1j & -2-1j0\ 0 & -1j& 9& \ 0 & 0& -2+1j& 6 \end{bmatrix} \mathrm{b}=\begin{bmatrix} 1\ 1+1j\ 1-2j\ 0 \end{bmatrix}$$For our example below, we will be putting the upper diagonal in the array hb −Examplefrom scipy.linalg import solveh_banded hb = np.array([[0, 2-1j, 1j, -2-1j],  [8, 5, 9, 6 ]]) b = np.array([1, 1+1j, 1-2j, 0]) x = solveh_banded(hb, b) ... Read More

## Which linear function of SciPy is used to solve Hermitian positive-definite banded matrix equation?

Updated on 24-Nov-2021 11:21:35
The linear function named scipy.linalg.solveh_banded is used to solve Hermitian positive-definite banded matrix equations. The form of this function is as follows −scipy.linalg.solveh_banded(ab, b, overwrite_ab=False, overwrite_b=False, lower=False, check_finite=True)This linear function will solve the equation ax = b for x where a is Hermitian positivedefinite banded matrix.The banded matrix a is stored in ab in lower or upper diagonal ordered form as follows −ab[u + i - j, j] == a[i, j] (if upper form; i= j)The example of ab in the upper form is given as follows − *    *   a02   a13   a24  a35 * ... Read More

## Which linear function of SciPy is used to solve a banded matrix equation?

Updated on 25-Nov-2021 06:50:00
The linear function named scipy.linalg.solve_banded is used to solve the banded matrix equation. The form of this function is as follows −scipy.linalg.solve_banded(l_and_u, ab, b, overwrite_ab=False, overwrite_b=False, debug=None, check_finite=True)This linear function will solve the equation ax = b for x where a is a banded matrix.The banded matrix a is stored in ab by using the matrix diagonal ordered form as follows −ab[u + i - j, j] == a[i, j]The example of ab is given as follows −*       a01 a12 a23 a34 a45 a00 a11 a22 a33 a44 a55 a10 a21 a32 a43 a54 * a20 a31 ... Read More

## Comparing ‘cubic’ and ‘linear’ 1-D interpolation using SciPy library

Updated on 24-Nov-2021 11:08:27
Below python script will compare the ‘cubic’ and ‘linear’ interpolation on same data using SciPy library −ExampleFirst let’s generate some data to implement interpolation on that −import numpy as np from scipy.interpolate import interp1d import matplotlib.pyplot as plt A = np.linspace(0, 10, num=11, endpoint=True) B = np.cos(-A**2/9.0) print (A, B)OutputThe above script will generate the following points between 0 and 4 − [ 0. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.] [ 1. 0.99383351 0.90284967 0.54030231 -0.20550672 -0.93454613 -0.65364362 0.6683999 0.67640492 -0.91113026 0.11527995]Now, let’s plot these points as follows −plt.plot(A, B, '.') plt.show()Now, based on fixed data ... Read More

## How to implement ‘cubic’ 1-D interpolation using SciPy library?

Updated on 24-Nov-2021 11:05:04
To implement ‘cubic’ 1-D interpolation using SciPy, we need to specify the kind of interpolation as ‘cubic’ in the ‘kind’ parameter of scipy.interpolate.interp1d class. Let’s see the example below to understand it−ExampleFirst let’s generate some data to implement interpolation on that −import numpy as np from scipy.interpolate import interp1d import matplotlib.pyplot as plt A = np.linspace(0, 10, num=11, endpoint=True) B = np.cos(-A**2/9.0) print (A, B)OutputThe above script will generate the following points between 0 and 4 − [ 0. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.] [ 1. 0.99383351 0.90284967 0.54030231 -0.20550672 -0.93454613 -0.65364362 0.6683999 0.67640492 -0.91113026 ... Read More

## What is interpolation and how can we implement it in the SciPy Python library?

Updated on 24-Nov-2021 10:58:54
Interpolation is a method of generating a value between two given points on a line or a curve. In machine learning, interpolation is used to substitute the missing values in a dataset. This method of filling the missing values is called imputation. Another important use of interpolation is to smooth the discrete points in a dataset.SciPy provides us a module named scipy.interpolate having many functions with the help of which we can implement interpolation.ExampleIn the below example we will implement Interpolation by using the scipy.interpolate() package −First let’s generate some data to implement interpolation on that −import numpy as np ... Read More

## What is the use of scipy.interpolate.interp1d class of SciPy python library?

Updated on 14-Dec-2021 11:48:18
The scipy.interpolate.interp1d(x, y, kind, axis, copy, bounds_error, fill_value, assumesorted) class of SciPy library, as name implies, is used to interpolate a 1-Dimensional function. Here, x and y are the arrays of values which are used to approximate some function, say f; y=f(x). The output of this class is a function whose call method uses interpolation to find the value of new points.Below is given the detailed explanation of its parameters −Parametersx − (N, ) array_likeIt is a 1-dimensional array of real values.y − (…, N, …) array_likeIt is a N-dimensional array of real values. The condition is that the length ... Read More

## How to find the Eigenvalues and Eigenvectors of a square matrix using SciPy?

Updated on 14-Dec-2021 11:09:15
We can find the Eigenvalues and Eigenvectors for a square matrix, say A, with the help of following relation −SciPy library has scipy.linalg.eig() function for computing the eigenvalues and eigenvectors of a square matrix.Let’s understand how we can use this function to calculate the inverse of a matrix −ExampleEigenvalues and Eigenvectors of a 2 by 2 matrix#Importing the scipy package import scipy #Importing the numpy package import numpy as np #Declaring the numpy array(Square Matrix) A = np.array([[3, 3.5], [3.2, 3.6]]) #Passing the values to scipy.linalg.eig() function eigvalues, eigvectors = scipy.linalg.eig(A) #Printing the result for eigenvalues print(eigvalues) ... Read More

## Finding inverse of a square matrix using SciPy library

Updated on 24-Nov-2021 13:42:44
SciPy library has scipy.linalg.inv() function for finding the inverse of a square matrix. Let’s understand how we can use this function to calculate the inverse of a matrix −ExampleInverse of a 2 by 2 matrix#Importing the scipy package import scipy.linalg #Importing the numpy package import numpy as np #Declaring the numpy array (Square Matrix) A = np.array([[3, 3.5], [3.2, 3.6]]) #Passing the values to scipy.linalg.inv() function M = scipy.linalg.inv(A) #Printing the result print('Inverse of {} is {}'.format(A, M))OutputInverse of [[3. 3.5] [3.2 3.6]] is [[-9. 8.75] [ 8. -7.5 ]]ExampleInverse of a 3 by 3 ... Read More

## Finding determinant of a square matrix using SciPy library

Updated on 24-Nov-2021 10:35:59
The determinant of a matrix, denoted by |A|, is a scalar value that can be calculated from a square matrix. With the help of the determinant of a matrix, we can find the inverse of a matrix and other things that are useful in the systems of linear equations, calculus, etc. The function named scipy.linalg.det() calculates the determinant of a square matrix.Let’s understand it with the below given examples −ExampleCalculating determinant of 2 by 2 matrix#Importing the scipy package import scipy #Importing the numpy package import numpy as np #Declaring the numpy array (Square Matrix) X = np.array([[5, ... Read More