Programming Articles - Page 844 of 3363

In this article, we will describe every possible approach to find the number of quadruples in which the first 3 terms are in A.P., and the last 3 are in G.P. First, we will explain the basic definition of arithmetic progression(A.P.) and geometric progression (G.P.).Arithmetic progression(A.P.) − It is a sequence of numbers in which the common difference (d) is the same or constant that means a difference of two consecutive numbers is constant. For example: 1, 3, 5, 7, 9 | d = 2Geometric Progression(G.P.) − It is a sequence of numbers in which the common ratios (r) are ... Read More

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

A quadrilateral forms a polygon with four vertices and four edges in Euclidean plane geometry. The name 4-gon etc. Included in other names of quadrilaterals and sometimes they are also known as a square, display style, etc.In this article, we will explain the approaches to finding the number of quadrilaterals possible from the given points. In this problem, we need to find out how many possible quadrilaterals are possible to create with the provided four points ( x, y ) in the cartesian plane. So here is the example for the given problem −Input : A( -2, 8 ), B( ... Read More

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

In this article we will describe the ways to find the number of primes in a subarray. We have an array of positive numbers arr[] and q queries having two integers that denote our range {l, R} we need to find the number of primes in the given range. So below is an example of the given problem −Input : arr[] = {1, 2, 3, 4, 5, 6}, q = 1, L = 0, R = 3 Output : 2 In the given range the primes are {2, 3}. Input : arr[] = {2, 3, 5, 8 ... Read More

In this article, we will explain everything about finding the number of prime pairs in an array using C++. We have an array arr[] of integers, and we need to find all the possible prime pairs present in it. So here is the example for the problem −Input : arr[ ] = { 1, 2, 3, 5, 7, 9 } Output : 6 From the given array, prime pairs are (2, 3), (2, 5), (2, 7), (3, 5), (3, 7), (5, 7) Input : arr[] = {1, 4, 5, 9, 11} Output : 1Approaches to Find ... Read More

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

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

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

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