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The linear function named scipy.linalg.solve_circulant is used to solve the circulant matrix equation. The form of this function is as follows −scipy.linalg.solve_circulant(c, b, singular=’raise’, tol=None, caxis=-1, baxis=0, outaxis=0)This linear function will solve the equation Cx = b for x where C is a Circulant matrix associated with the vector c.The circulant matrix equation is solved by doing division in Fourier space as follows −x = ifft(fft(b) / fft(c))Here fft is the fast Fourier transform and ifft is the inverse fast Fourier transform.ParametersBelow are given the parameters of the function scipy.linalg.solve_circulant() −c− array_likeThis parameter represents the coefficient of the circulant matrix.b− ... Read More
In this article, we have to find the number of segments or subarrays in a given sequence where elements greater than the given number X.We can count overlapping segments only once, and two contiguous elements or segments should not count separately. So here is the basic example of the given problem −Input : arr[ ] = { 9, 6, 7, 11, 5, 7, 8, 10, 3}, X = 7 Output : 3 Explanation : { 9 }, { 11 } and { 8, 10 } are the segments greater than 7 Input : arr[ ] = { 9, 6, ... Read More
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
In this article, we will explain the approaches to find the number of reflexive relations on a set. In this problem, we are given with number n, and on a set of n natural numbers, we must determine the number of reflexive relations.Reflexive Relation − A relation in a set A is called reflexive if ( a, a ) belongs to R for every 'a' belongs to set A. For example −Input : x = 1 Output : 1 Explanation : set = { 1 }, reflexive relations on A * A : { { 1 } } Input ... Read More
Conceptual clustering is a form of clustering in machine learning that, given a set of unlabeled objects, makes a classification design over the objects. Unlike conventional clustering, which generally identifies groups of like objects, conceptual clustering goes one step further by also discovering characteristic definitions for each group, where each group defines a concept or class.Therefore, conceptual clustering is a two-step process − clustering is implemented first, followed by characterization. Thus, clustering quality is not solely a service of single objects. Most techniques of conceptual clustering adopt a statistical method that uses probability measurements in deciding the concepts or clusters.Probabilistic ... Read More
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
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
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