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

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

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

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 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