Jump Discontinuity Functions Open and Close Circle

Question

Wal MathEngineering 2022-2-8

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1645800-jump-discontinuity-functions-open-and-close-circle

编辑： Walter Roberson 2022-2-9

Hello,

Attached below is the code.

I am trying to plot jump discontinuity functions. But I have diffuclties to plot the functions. Also, in my code I tried to show open and close circles. The reason why I need this is to use it in my research paper to introduce some limit defintions. Your help is greatly appreciated.

clc
clear
%%
x = linspace(-pi, pi);
% a piecewise discontinuous function can be plotted using a for loop
for i = 1:length(x)
    X = x(i);
    if x(i) <= 1
        y = x.^2;
        
    elseif x <= 2;
        y = x.^3 - 5;
        
    else
        y = 5 - 2*x;
    end
end
hold on
axis ([-10 10 -10 20])
plot([-8 8],[0 0], 'k-','markersize',2)
plot([0 0], [-10 15],'k-','markersize',2)
plot(X,y,'markersize',12)
title(' Graph of Piecewise Discontinuous f(x)')
legend('y = x^2', 'y = x^3-5','y = 5-2x')
ax = gca;
ax.XAxisLocation = 'origin';
ax.YAxisLocation = 'origin';
grid on

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Answer 1

Turlough Hughes 2022-2-8

1
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1645800-jump-discontinuity-functions-open-and-close-circle#answer_891590

编辑：Turlough Hughes 2022-2-8

在 MATLAB Online 中打开

My preferred approach is to use fplot as follows:

clc, clear

figure(), hold on

axis ([-10 10 -10 20])

fplot(@(x) x.^2, [-pi 1],'.-','MarkerSize',12)

hold on, fplot(@(x) x.^3 - 5, [1 2],'.-','MarkerSize',12)

fplot(@(x) 5 - 2*x, [2 pi],'.-','MarkerSize',12)

% Graph formatting

title('Graph of Piecewise Discontinuous f(x)')

legend('y = x^2', 'y = x^3-5','y = 5-2x')

ax = gca;

ax.XAxisLocation = 'origin';

ax.YAxisLocation = 'origin';

grid on

If you need to you can also return the x and y values from fplot using [x,y] = fplot(___)

Another way you could do it:

clc, clear

x = linspace(-pi, pi);

% index for intervals

idxA = x<=1;

idxB = x>1 & x<=2;

idxC = x>2;

% solve equations

y = [x(idxA).^2, x(idxB).^3-5, 5-2*x(idxC)];

figure(), hold on

axis ([-10 10 -10 20])

plot(x(idxA), y(idxA),'.-','MarkerSize',12)

plot(x(idxB), y(idxB),'.-','MarkerSize',12)

plot(x(idxC), y(idxC), '.-','MarkerSize',12)

title(' Graph of Piecewise Discontinuous f(x)')

legend('y = x^2', 'y = x^3-5','y = 5-2x')

ax = gca;

ax.XAxisLocation = 'origin';

ax.YAxisLocation = 'origin';

grid on

% Alternatively

figure(), plot(x,y,'-','LineWidth',2)

axis ([-10 10 -10 20])

set(gca,'XAxisLocation','origin','YAxisLocation','origin')

for reference you can do the loop as follows. You were almost there, but the mistake you made was not to index the current element and also not indexing where to store the output values within y. Compare the code you have to this and you should get the idea.

for ii = 1:numel(x)

if x(ii) <= 1

y(ii) = x(ii)^2;

elseif x(ii) <= 2

disp(1)

y(ii) = x(ii).^3 - 5;

else

y(ii) = 5 - 2*x(ii);

end

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Wal MathEngineering 2022-2-8

编辑：Walter Roberson 2022-2-9

Thank you for your help.

Can we do in MATLAB open circle and close circle only on the domain of the graph? like in this link:

https://commons.wikimedia.org/wiki/File:Jump_discontinuity_cadlag.svg

Turlough Hughes 2022-2-8

在 MATLAB Online 中打开

I suppose you can do the following (I don't see any dedicated functions for this).

clc, clear

figure(), hold on

axis ([-10 10 -10 20])

fcnA = @(x) x.^2;

fcnB = @(x) x.^3 - 5;

fcnC = @(x) 5 - 2*x;

hp(1) = fplot(fcnA, [-pi 1],'-k','LineWidth',2);

plot(1,fcnA(1), 'ok','MarkerFaceColor','k','LineWidth',2)

hp(2) = fplot(fcnB, [1 2],'-r','LineWidth',2);

plot(1, fcnB(1), 'or','MarkerFaceColor','w','LineWidth',2)

plot(2, fcnB(2), 'or', 'MarkerFaceColor','r','LineWidth',2)

hp(3) = fplot(fcnC, [2 pi],'-b','LineWidth',2);

plot(2, fcnC(2), 'ob','MarkerFaceColor','w','LineWidth',2)

title('Graph of Piecewise Discontinuous f(x)')

legend(hp, 'y = x^2', 'y = x^3-5','y = 5-2x')

ax = gca;

ax.XAxisLocation = 'origin';

ax.YAxisLocation = 'origin';

grid on

scatter might be worth considering also, which allows you to modify the inidividual marker appearances, but it's probably just as easy to use plot as above.

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