# Multiple plot on same graph

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Hmm! on 3 Dec 2021
Commented: Walter Roberson on 3 Dec 2021
I would like to have these 4 plots on the same graph sheet for easy comparison. Plotting the individual plot works but I am not sure what is the reason why all the 4 plots cannot be plotted at the same time. Relying on benevolent members for assitance.
rng default
n = 30;
% generate the A matrix
D = delsq(numgrid('L',n)); %same as matrix A
bGrid = ones(length(D),1); %same as RHS b vector
M = diag(diag(D));
tol = 1e-8;
maxit = 100;
P = inv(M);
L = ichol(M);
Q = ichol(M,struct('michol','on'));
% pcg
[x0,f0,r0,it0,rv0] = pcg(D,bGrid); %no precond
[x1,f1,r1,it1,rv1] = pcg(D,bGrid,tol,maxit,P); % inv
[x2,f2,r2,it2,rv2] = pcg(D,bGrid,tol,maxit,L,L'); % ichol
[x3,f3,r3,it3,rv3] = pcg(D,bGrid,tol,maxit,Q,Q'); % modified ichol
% plots on same graph
semilogy(0:length(rv0)-1,rv0/norm(bGrid),'-o')
hold on
semilogy(0:length(rv1)-1,rv1/norm(bGrid),'-o')
semilogy(0:length(rv2)-1,rv2/norm(bGrid),'-o')
semilogy(0:length(rv3)-1,rv3/norm(bGrid),'-o')
yline(tol,'r--');
legend('No Preconditioner', 'inv(M)', 'ichol(M)', 'michol(M)', 'Tolerance', 'Location','southwest')
title('Conjugant Gredient Algorithm');
legend('boxoff')

Walter Roberson on 3 Dec 2021
rng default
n = 30;
% generate the A matrix
D = delsq(numgrid('L',n)); %same as matrix A
bGrid = ones(length(D),1); %same as RHS b vector
M = diag(diag(D));
tol = 1e-8;
maxit = 100;
P = inv(M);
L = ichol(M);
Q = ichol(M,struct('michol','on'));
% pcg
[x0,f0,r0,it0,rv0] = pcg(D,bGrid); %no precond
[x1,f1,r1,it1,rv1] = pcg(D,bGrid,tol,maxit,P); % inv
[x2,f2,r2,it2,rv2] = pcg(D,bGrid,tol,maxit,L,L'); % ichol
[x3,f3,r3,it3,rv3] = pcg(D,bGrid,tol,maxit,Q,Q'); % modified ichol
% plots on same graph
semilogy(0:length(rv0)-1,rv0/norm(bGrid),'-or')
hold on
semilogy(0:length(rv1)-1,rv1/norm(bGrid),'--.g')
semilogy(0:length(rv2)-1,rv2/norm(bGrid),':^b')
semilogy(0:length(rv3)-1,rv3/norm(bGrid),'+k')
yline(tol,'r--');
legend('No Preconditioner', 'inv(M)', 'ichol(M)', 'michol(M)', 'Tolerance', 'Location','southwest')
title('Conjugant Gredient Algorithm');
legend('boxoff')
min(rv0),max(rv0)
ans = 1.8506
ans = 52.6747
min(rv1),max(rv1)
ans = 1.9799e-07
ans = 52.6747
min(rv2),max(rv2)
ans = 1.9799e-07
ans = 52.6747
min(rv3),max(rv3)
ans = 1.9799e-07
ans = 52.6747
You are asking to solve the same system of linear equations with different preconditioners, but you are expecting that the differences between the results will be visible on the plot.
There is a notable difference on the first point of rv0 versus the remainder, but on the scale of the plot you cannot tell by the plot.
Walter Roberson on 3 Dec 2021
M = diag(diag(D));
That is a sparse diagonal matrix whose diagonal is the constant 4.
L = ichol(M);
That is a sparse diagonal matrix whose diagonal is the constant 2.
Your arrays are "boring" -- the hints you are providing through the additional parameters are adding essentially no usable new information, so the outputs are all the same (except being different sizes in some cases.)

R2019b

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