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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
For some classes of software and certain kinds of software projects, agile software engineering is an acceptable compromise between traditional software engineering and agile software engineering. Agile procedures may provide high-quality systems in a short amount of time. It emphasizes the need for ongoing communication and cooperation between developers and consumers.For effective execution of offshore software development projects with qualities such as shorter time to market and changing company demands, we use agile software development process models. Iterative software development with frequent client delivery is a basic strategy in agile software development that immediately solves one of the primary issues ... Read More
Subarrays are the contiguous part of an array. For example, we consider an array [5, 6, 7, 8], then there are ten non-empty subarrays like (5), (6), (7), (8), (5, 6), (6, 7), (7, 8), (5, 6, 7), (6, 7, 8) and (5, 6, 7, 8).In this guide, we will explain every possible information to find the number of subarrays with odd sums in C++. For finding the number of subarrays with the odd sum, we can use different approaches, so here is a simple example for it −Input : array = {9, 8, 7, 6, 5} Output : 9 ... Read More
In this article, we will solve the number of subarrays having sum in a given range using the C++ program. We have an array arr[] of positive integers, and a range {L, R} and we have to calculate the total number of subarrays having sum in the given range form L to R. So here is the simple example for the problem −Input : arr[] = {1, 4, 6}, L = 3, R = 8 Output : 3 The subarrays are {1, 4}, {4}, {6}. Input : arr[] = {2, 3, 5, 8}, L = 4, ... Read More
If you have ever used C ++, you must know what subarrays are and how useful they are. As we know that, in C++, we can solve multiple mathematical problems easily. So in this article, we will explain the complete information on how we can find M odd numbers with the help of these subarrays in C++.In this problem, we need to find many subarrays formed with the given array and integer m where each subarray contains exactly m odd numbers. So here is the simple example of this approach −Input : array = { 6, 3, 5, 8, 9 ... Read More
In this article, we will solve the problem of finding the number of subarrays whose maximum and minimum elements are the same using C++. Here is the example for the problem −Input : array = { 2, 3, 6, 6, 2, 4, 4, 4 } Output : 12 Explanation : {2}, {3}, {6}, {6}, {2}, {4}, {4}, {4}, {6, 6}, {4, 4}, {4, 4} and { 4, 4, 4 } are the subarrays which can be formed with maximum and minimum element same. Input : array = { 3, 3, 1, 5, 1, 2, 2 } Output : 9 ... Read More
In this article, we will explain everything about solving the number of subarrays having the sum of the form k^m, m >= 0 in C++. Given an array arr[] and an integer K, we need to find the number of subarrays having sum in the form of K^m where m is greater than equal to zero, or we can say we need to find the number of subarrays having sum equal to some non-negative power of K.Input: arr[] = { 2, 2, 2, 2 } K = 2 Output: 8 Sub-arrays with below indexes are valid: [1, 1], ... Read More
The linear function named scipy.linalg.solveh_triangular is used to solve the banded matrix equation. In the below given example we will be solving the triangular system ax = b where −$$\mathrm{a} = \begin{bmatrix} 3 & 0 & 0 & 0\ 2 & 1 & 0 & 0\ 1 &0 &1 &0 \ 1& 1& 1& 1 \end{bmatrix};\; \mathrm{b} =\begin{bmatrix} 1\ 2\ 1\ 2 \end{bmatrix}$$Examplefrom scipy.linalg import solve_triangular import numpy as np a = np.array([[3, 0, 0, 0], [2, 1, 0, 0], [1, 0, 1, 0], [1, 1, 1, 1]]) b = np.array([1, 2, 1, 2]) x = solve_triangular(a, b, lower=True) print (x)Outputarray([ 0.33333333, 1.33333333, 0.66666667, -0.33333333])
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
To successfully build a machine learning project, loading data properly is one of the most important as well as challenging tasks. CSV is the most common format for machine learning projects. It is a simple format which is used to store tabular data.Followings are the three most common approaches in Python with the help of which you can load CSV data for machine learning projects −Using Python Standard LibraryTo load CSV data files, Python standard library provides us with a built-in function namely csv module.ExampleIn this example we will be loading CSV data file of iris flower data set −#Importing ... Read More