Exercise 1.9.3 The MATLAB m-file shown below produces matrices of discretized convection-diffusion operators of various sizes.function C = condif (n,c)* C is a square convection-diffusion matrix% of order n^2. The user must supply n and% the convection coefficients c(1:2).I = speye (n):sparse (1:n-1,2;n,1,n,n);N =(1-c (1)) *N - (1+c (1)) *N';(1-c (2)) *NF1 = 2*IF2 = 2*I(1+c (2)) *N' ;C = kron (I,F1) + kron (F2, I); [Q2] (Section 1.6/1.9: Sparse Systems; Example 1.9.1) In this exercise we will walk throughthe exact steps of Example 1.9.1 using MATLAB.(a) Create the file condif.m that is exactly the MATLAB code given in Exercise 1.9.3,on the bottom of page 109 in [1].(b) Create an 81 × 81 matrix A in MATLAB via: A = condif(9,[0.2 5])(c) Compute the LU decomposition of A via: [L,U,P](d) View the nonzero structure of A and the added factors L+ U using spy ().(e) Reorder the columns of A using MATLAB's builtin column-wise minimum degreeroutine colamd () to produce A. Refactor the reordered Å, and then look at themodified nonzero structure of the reordered A and its added factors L+U.lu (A)

a) Please find attached code: function C = condif(n,c)% C is a square convection diffusion matrix%…

Answered: function C = condif (n,c) * c is a…

function C = condif (n,c) * c is a square convection-diffusion matrix of order n^2. The user must supply n and % the convection coefficients c(1:2). I = speye (n): N = sparse (1:n-1,2:n,1,n, n); N%3D

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Question

Exercise 1.9.3 The MATLAB m-file shown below produces matrices of discretized convection-
diffusion operators of various sizes.
function C = condif (n,c)
* C is a square convection-diffusion matrix
% of order n^2. The user must supply n and
% the convection coefficients c(1:2).
I = speye (n):
sparse (1:n-1,2;n,1,n,n);
N =
(1-c (1)) *N - (1+c (1)) *N';
(1-c (2)) *N
F1 = 2*I
F2 = 2*I
(1+c (2)) *N' ;
C = kron (I,F1) + kron (F2, I);

[Q2] (Section 1.6/1.9: Sparse Systems; Example 1.9.1) In this exercise we will walk through
the exact steps of Example 1.9.1 using MATLAB.
(a) Create the file condif.m that is exactly the MATLAB code given in Exercise 1.9.3,
on the bottom of page 109 in [1].
(b) Create an 81 × 81 matrix A in MATLAB via: A = condif(9,[0.2 5])
(c) Compute the LU decomposition of A via: [L,U,P]
(d) View the nonzero structure of A and the added factors L+ U using spy ().
(e) Reorder the columns of A using MATLAB's builtin column-wise minimum degree
routine colamd () to produce A. Refactor the reordered Å, and then look at the
modified nonzero structure of the reordered A and its added factors L+U.
lu (A)

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