Question

MATLAB: Plot the times elapsed from four methods of solving sparse and full matrices.

I have the following code. I can generate the matrices requires and get the time elapsed for each method printed on the command window. How can I plot the results in a log-log graph?

% Program 2.1 Sparse matrix setup

% Input: n = size of system

% Outputs: sparse matrix a, r.h.s. b

function [a,b] = sparsesetup(n)

e = ones(n,1); n2=n/2;

a = spdiags([-e 3*e -e],-1:1,n,n); % Entries of a

c=spdiags([e/2],0,n,n);c=fliplr(c);a=a+c;

a(n2+1,n2) = -1; a(n2,n2+1) = -1; % Fix up 2 entries

b=zeros(n,1); % Entries of r.h.s. b

b(1)=2.5;b(n)=2.5;b(2:n-1)=1.5;b(n2:n2+1)=1;

disp('For sparse a\b');

tic;a\b;toc;

disp('For sparse Inv(A)*B');

tic;inv(a)*b;toc;

disp('For sparse gmres')

tic;gmres(a,b);toc

disp('For sparse bicg')

tic;bicg(a,b);toc

disp('For full a\b');

tic;full(a)\b;toc;

disp('For full Inv(A)*B');

tic;inv(full(a))*b;toc;

disp('For full gmres')

tic;gmres(full(a),b);toc

disp('For full bicg')

tic;bicg(full(a),b);toc

Answer 1

`Hey,

Note: Brother if you have any queries related the answer please do comment. I would be very happy to resolve all your queries.

clear all
clc
n=2:2:50;
y1=[];
y2=[];
y3=[];
y4=[];
y5=[];
y6=[];
y7=[];
y8=[];
for i=1:length(n)
[~,~,y1(i),y2(i),y3(i),y4(i),y5(i),y6(i),y7(i),y8(i)] = sparsesetup(n(i));
end
loglog(n,y1,n,y2,n,y3,n,y4,n,y5,n,y6,n,y7,n,y8);
legend('For sparse a\b','For sparse Inv(A)*B','For sparse gmres','For sparse bicg','For full a\b','For full Inv(A)*B','For full gmres','For full bicg')
function [a,b,y1,y2,y3,y4,y5,y6,y7,y8] = sparsesetup(n)

e = ones(n,1); n2=n/2;

a = spdiags([-e 3*e -e],-1:1,n,n); % Entries of a

c=spdiags([e/2],0,n,n);c=fliplr(c);a=a+c;

a(n2+1,n2) = -1; a(n2,n2+1) = -1; % Fix up 2 entries

b=zeros(n,1); % Entries of r.h.s. b

b(1)=2.5;b(n)=2.5;b(2:n-1)=1.5;b(n2:n2+1)=1;

disp('For sparse a\b');

tic;a\b;
y1=toc;

disp('For sparse Inv(A)*B');

tic;inv(a)*b;
y2=toc;

disp('For sparse gmres')

tic;gmres(a,b);
y3=toc;

disp('For sparse bicg')

tic;bicg(a,b);
y4=toc;

disp('For full a\b');

tic;full(a)\b;
y5=toc;

disp('For full Inv(A)*B');

tic;inv(full(a))*b;
y6=toc;

disp('For full gmres')

tic;gmres(full(a),b);
y7=toc;

disp('For full bicg')

tic;bicg(full(a),b);
y8=toc;
end

Kindly revert for any queries

Thanks.