How to graph a Piecewise function?

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Walshaikhli
Walshaikhli 2015-3-10
评论： Walter Roberson 2018-1-9
I need to graph a piecewise function in terms of theta for a Homework assignment.
I must first create a 100 element vector for the values of theta between 0 and 2*pi. After that I must use a loop and a conditional statement to plot the graph. Here is what I have so far:
Theta= 0:(2*pi)/100:2*pi; %the vector lists 100 elements(0 < Theta < 2Pi)
if (0 <= Theta) && (Theta <= pi/2)
%0<= Theta<= pi/2
Eq1= 6*(2*Theta - .5*sin(2*Theta))/pi
elseif (pi/2 <= Theta) && (Theta <= 2*pi/3)
%pi/2 <= Theta <= 2*pi/3
Eq2= 6
elseif (2*pi/3 <= Theta) && (Theta <= 4*pi/3)
%2*pi/3 <= Theta <= 4*pi/3
Eq3=7.5 - (1 - .5* cos(1.5* (Theta - (2*pi/3))))
elseif (4*pi/3 <= Theta) && (Theta <= 3*pi/2)
%4*pi/3 <= Theta <= 3*pi/2
Eq4= 3
elseif (3*pi/2 <= Theta) && (Theta <= 7*pi/4)
%3*pi/2<=Theta<=7*pi/4
Eq5= 3 - 1.5*((Theta - 3*(pi/2))/(pi/4))^2
elseif (7*pi/4 <= Theta) && (Theta <= 2*pi)
%7*pi/4 <= Theta <= 2*pi
Eq6= 1.5*(1 - ((Theta - 7*(pi/4/(pi/4)))^2
end
figure
plot(Theta, Eq1, Theta,Eq2,Theta,Eq3,Theta,Eq4,Theta,Eq5)
Everything is coming out jacked up, or not coming up at all... Please help! I know that I should place a loop, but where would it go?

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采纳的回答

Thorsten
Thorsten 2015-3-10
%Theta= 0:(2*pi)/100:2*pi; %the vector lists 100 elemants between 0 and 2Pi
% Actually these are 101 elements;
% use
Theta = linspace(0, 2*pi, 100);
F = nan(size(Theta));
% logical indexing
ind = 0 <= Theta & Theta <= pi/2;
F(ind) = 6*(2*Theta(ind) - .5*sin(2*Theta(ind)))/pi;
% just one value, no ind variable necessary
F(pi/2 <= Theta & Theta <= 2*pi/3) = 6;
ind = 2*pi/3 <= Theta & Theta <= 4*pi/3;
F(ind) = 7.5 - (1 - 0.5* cos(1.5* (Theta(ind) - (2*pi/3))));
F(4*pi/3 <= Theta & Theta <= 3*pi/2) = 3;
ind = 3*pi/2 <= Theta & Theta <= 7*pi/4;
% use .^ to work on the whole vector
F(ind) = 3 - 1.5*((Theta(ind) - 3*(pi/2))/(pi/4)).^2;
ind = 7*pi/4 <= Theta & Theta <= 2*pi;
% some ) were missing, I added them at the end;
% PLEASE CHECK IF THIS IS THE RIGHT FUNCTION!!!
F(ind) = 1.5*(1 - ((Theta(ind) - 7*(pi/4/(pi/4))))).^2;
plot(Theta, F)
  3 个评论
显示 1更早的评论
Martin Vatshelle
Martin Vatshelle 2018-1-9
plotting the vertical lines between the pieces does not look good. Any simple way to break lines at the steps?
Walter Roberson
Walter Roberson 2018-1-9
When you plot() or line(), any nan or inf or -inf will be interpreted as a request to stop drawing the line and resume when the coordinates are finite.

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更多回答（1 个）

Image Analyst
Image Analyst 2015-3-10
This kind of construct does not work
if 0 <= Theta <= pi/2
You need to do it in two comparisons, like this
if (0 <= Theta) && (Theta <= pi/2)
Each one of those things in the parentheses will product a true or false result. If you AND them together, you will get what you tried to do.
  2 个评论
John D'Errico
John D'Errico 2015-3-10
编辑：John D'Errico 2015-3-10
Note that Theta is a vector. if statements will still fail to produce the proper result if they are applied to a vector.
You will need to loop over those elements, or use another scheme to determine the location of each point.
Image Analyst
Image Analyst 2015-3-10
Good point. I didn't notice that because of the bad formatting, which can be fixed after viewing this: http://www.mathworks.com/matlabcentral/answers/13205-tutorial-how-to-format-your-question-with-markup

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