Programming Articles - Page 843 of 3366

The linear function named scipy.linalg.solve_toeplitz is used to solve the Toeplitz matrix equation. The form of this function is as follows −scipy.linalg.solve_toeplitz(c_or_cr, b, check_finite=True)This linear function will solve the equation Tx = b for x where T is the Toeplitz matrix.ParametersBelow are given the parameters of the function scipy.linalg.solve_toeplitz()c_or_cr− array_like or tuple of (array_like, array_like)This parameter is the vector c or tuple of arrays (c, r). Despite the actual shape of c, it will always be converted to a one-dimensional array. If r is not given, the assumption made is r = conjugate(c). Below are given two cases −    ... Read More

In this article we are going to find number of solution of equation n = x + n ⊕ x, i.e we need to find number of values of x possible with given value n such that n = x + n ⊕ x where ⊕ represents XOR operation.Now we will discuss the complete information regarding number of solutions of n = x + n ⊕ x with an appropriate examples.Brute Force MethodWe can simple use brute force approach in order to find number of solution, i.e for given value of n we apply every integer value of x starting ... Read More

In this article, we will explain the approaches to find the number of solutions for the equation x+y+z

In this article, we will describe the important information on solving the number of sinks nodes in a graph. We have a Directed Acyclic Graph with N nodes (1 to N) and M edges in this problem. The goal is to find how many sink nodes are there in the given graph. A sink node is a node that does not produce any outgoing edges. So here is a simple example −Input : n = 4, m = 2 Edges[] = {{2, 3}, {4, 3}} Output : 2Simple Approach to Find the SolutionIn this approach, we will go through ... Read More

In this article, we will provide complete information to determine the number of siblings of a given node in the n-ary tree. We need to find the node's siblings with the value of key as given by the user; if it is non, then output as -1. There is only one approach that we can use −Simple ApproachIn this approach, we will go through all the nodes and check if a child has the same value as the user. If it exists, we answer a number of children - 1(the given value).Example #include using namespace std; class Node { ... 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])

The linear function named scipy.linalg.solve_triangular is used to solve the triangular matrix e8quation. The form of this function is as follows −scipy.linalg.solve_triangular(a, b, trans=0, lower=False, unit_diagonal=False, overwrite_b=False, debug=None, check_finite=True)This linear function will solve the equation ax = b for x where a is a triangular matrix.P ParametersBelow are given the parameters of the function scipy.linalg.solve_triangular() −a− (M, M) array_likeThis parameter represents the triangular matrix.b− (M, ) or (M, N)array_likeThis parameter represents the right-hand side matrix in the equation ax = b.lower− bool, optionalBy using this parameter, we will be able to use only the data that is contained in the ... Read More

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 circulant system Cx = b −Examplefrom scipy.linalg import solve_circulant, solve, circulant, lstsq import numpy as np c = np.array([2, 2, 4]) b = np.array([1, 2, 3]) solve_circulant(c, b)Output array([ 0.75, -0.25, 0.25])ExampleLet’s see a singular example, it will raise an LinAlgError −from scipy.linalg import solve_circulant, solve, circulant, lstsq import numpy as np c = np.array([1, 1, 0, 0]) b = np.array([1, 2, 3, 4]) solve_circulant(c, b)Output -------------------------------------------------------------------------- LinAlgError Traceback (most recent call last) in ... Read More

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

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