Plot line colors and legend colors don't match

When I plot these functions and make a legend, the colors for the lines don't match the colors in the legend. Also, the plot reused the same blue color (at least) twice.

% This file plots gamma as a function of v/c as well as some of its Taylor
% expansions

clear; clf;

syms gamma_voc(voc); % gamma wrt v/c
syms T0(x) T1(x) T2(x) T3(x) T4(x)

% The functions are symbolically defined so I can do symbolic operations
gamma_voc(voc) = 1./sqrt(1-voc^2);
T0(x) = ones(size(x))*1;
T1(x) = ones(size(x))*1;
T2(x) = 1+(1/2)*x^2;
T3(x) = 1+(1/2)*x^2;
T4(x) = 1+(1/2)*x^2+(1/24)*x^4;

% The symbolically defined functions can't be used numerically, so use
% these instead
gamma_voc_FUN = matlabFunction(gamma_voc);
T0_FUN = matlabFunction(T0);
T1_FUN = matlabFunction(T1);
T2_FUN = matlabFunction(T2);
T3_FUN = matlabFunction(T3);
T4_FUN = matlabFunction(T4);

% Now that we have our functions, let's plot them

grid on;
hold on;
axis([-2 2 0 4]);
daspect([1 1 1]);
lw = 5;

x = -1:0.01:1; % domain of gamma(v/c)
y = gamma_voc_FUN(x); plot(x,y,'LineWidth',lw);

x = -2:0.01:2; % Visible domain of Taylor series expansions
y = T0_FUN(x); plot(x,y,'LineWidth',lw);
y = T1_FUN(x); plot(x,y,'LineWidth',lw);
y = T2_FUN(x); plot(x,y,'LineWidth',lw);
y = T3_FUN(x); plot(x,y,'LineWidth',lw);
y = T4_FUN(x); plot(x,y,'LineWidth',lw);

legend('gamma','T0','T1','T2','T3','T4');

[Stephen23]

"Also, the plot reused the same blue color (at least) twice."

Each time you call plot is independent from the other calls, and it will start the colors from the first one again. If you want to automatically cycle through the line ColorOrder colors, then you should do one of these:

• set the axes NextPlot property to 'add'.
• use hold on (only since MATLAB R2014b).
• use just one plot call.

Then you will get an automatic cycling of the line colors (from the axes ColorOrder).

[Robert Whitlock]

hold on was being used. Thank you for letting me know about other ways I could achieve the effect I was looking for.

Answer 1

[jonas]

This question is asked almost on a daily basis. Use plot handles as input to the legend function, and you won't have this problem.

h(1)=plot(x,y,'LineWidth',lw);
h(2)=plot(x,y,'LineWidth',lw);
...

legend(h,'gamma','T0',...);

Alternatively, use the 'DisplayName' property to store the label directly in the line handle.

h(1)=plot(x,y,'LineWidth',lw,'DisplayName','T0');
h(2)=plot(x,y,'LineWidth',lw,'DisplayName','T1');
...
legend(h)

[Robert Whitlock]

I had tried this, but it did not work; I get an error "Unable to perform assignment because the left and right sides have a different number of elements." on line 39.

% This file plots gamma as a function of v/c as well as some of its Taylor
% expansions

clear; clf;

syms gamma_voc(voc); % gamma wrt v/c
syms T0(x) T1(x) T2(x) T3(x) T4(x)

% The functions are symbolically defined so I can do symbolic operations
gamma_voc(voc) = 1./sqrt(1-voc^2);
T0(x) = ones(size(x))*1;
T1(x) = ones(size(x))*1;
T2(x) = 1+(1/2)*x^2;
T3(x) = 1+(1/2)*x^2;
T4(x) = 1+(1/2)*x^2+(1/24)*x^4;

% The symbolically defined functions can't be used numerically, so use
% these instead
gamma_voc_FUN = matlabFunction(gamma_voc);
T0_FUN = matlabFunction(T0);
T1_FUN = matlabFunction(T1);
T2_FUN = matlabFunction(T2);
T3_FUN = matlabFunction(T3);
T4_FUN = matlabFunction(T4);

% Now that we have our functions, let's plot them

grid on;
hold on;
axis([-2 2 0 4]);
daspect([1 1 1]);
lw = 5;

x = -1:0.01:1; % domain of gamma(v/c)
y = gamma_voc_FUN(x); h(1) = plot(x,y,'LineWidth',lw);

x = -2:0.01:2; % Visible domain of Taylor series expansions
y = T0_FUN(x); h(2) = plot(x,y,'LineWidth',lw);
y = T1_FUN(x); h(3) = plot(x,y,'LineWidth',lw);
y = T2_FUN(x); h(4) = plot(x,y,'LineWidth',lw);
y = T3_FUN(x); h(5) = plot(x,y,'LineWidth',lw);
y = T4_FUN(x); h(6) = plot(x,y,'LineWidth',lw);

%legend(h,'gamma','T0','T1','T2','T3','T4');
legend(h);

Error:

Unable to perform assignment because the left and right sides have a different number of elements.

Error in PHYS371_HW1 (line 39)
y = T0_FUN(x); h(2) = plot(x,y,'LineWidth',lw);

I assume this is because the x values for my first plot are not the same as the x values for the rest of my plots, but I don't know what to do about it since I don't want to plot gamma outside of [-1,1] but I do want to plot the Taylor series approximations outside of [-1,1].

[jonas]

I dont think its about that.

Can you type

get(gca, 'children')

And paste the output? I suspect you have more lines than you think. What is the size of y? Is it supposed to be more than one line?

[Robert Whitlock]

I found the error: T0 and T1 were constant functions and Matlab wasn't rendering them correctly (looks like not even at all!). Setting the y values for T0 and T1 manually with ones(size(x)) fixed the problem.

[jonas]

What does

"not rendering them correctly"

mean? Im happy you solved the problem but Im afraid you may not have found the actual underlying issue if you believe its a rendering problem. The nature of your error, including the legend but also the plot line colors, strongly suggest you have more more lines in your plot than desired. Your solution is also odd, wont overwriting y with ones defeat the entire purpose? Id suggest not overwriting y and instead concatenate the data in a matrix. Would make the code much easier to debug.

[Robert Whitlock]

jonas, I'm not quite sure what you're asking, but here is a more concrete description of what I did so it might clear things up:

I replaced the lines

y = T0_FUN(x); plot(x,y,'LineWidth',lw);
y = T1_FUN(x); plot(x,y,'LineWidth',lw);

with

y = ones(size(x)); plot(x,y,'LineWidth',lw);
y = ones(size(x)); plot(x,y,'LineWidth',lw);

since T0(x) = 1 and T1(x) = 1 anyway. With these changes, T0_FUN(x) and T1_FUN(x) now plot, whereas before, they did not plot at all. You're right in that I don't quite understand the mechanics of why this would fail, but I suspect that since T0_FUN and T1_FUN are constant functions, they return a single number instead of an array, and so do not plot multiple points (or, in other words, no lines). I would be interested if somebody could shed some light on what is going on.

Regardless, here is the output of get(gca, 'children') that you asked for:

ans = 

    806×1 Line array:

    Line
    Line
    Line
    Line
    Line
    Line
    ... lots of "Line" here until ...
    Line
    Line
    Line
    Line
    Line
    Line
    Line    (T4)
    Line    (T3)
    Line    (T2)
    Line    (T1)
    Line    (T0)
    Line    (gamma)

Here is the result of calling size(y) after each assignment of T0_FUN and T1_FUN to y:

ans =

       1     1

ans =

       1     1

Yes, y is supposed to contain more than one point, yet it seems to be only one point.

[jonas]

Thanks for showing the handles. Perhaps it would be best to remove them again, as the long list makes it kind of hard to follow the discussion.

Let me try explaining what's going on. If you want to plot a single line, then the two input variables x and y should generally have the same size. If they do not have the same size, then usually you get an error.

There is however a special case when you have a vector x of size (1 x n) and one matrix y of size (m x n). In this case, plot will plot every row m against the vector x, as they match in length. In your case, you have a vector x of size (1 x n) and a scalar y of size (1 x 1). This means that you get n number of plots, which are really only single points.

For example, consider this code:

h=plot([1 2],1)

h =

2×1 Line array:

Line
Line

As you can see, you get two line handles as output because y is scalar and x is a vector. In your case, you get the same number of handles as the number of elements in your x-vector. These handles are first in the uistack, so they show up first in the legend.

How to solve?

Make sure your vector x always matches your vector y in size when you plot. In this case, I suspect that the error is in one of your custom functions. Make sure they output a vector and not a scalar, even when y is constant. You can also concatenate your vectors in a single matrix. In doing so, you will also ensure that they have the correct length, as the code will otherwise crash. Avoid producing 800 useless line handles, as this will surely mess up your legend and increase the run-time significantly.

[Robert Whitlock]

Thank you, that explains why it was acting that way!

I also got a reply from another Matlab source (from a bug report) that suggested using @(x)(subs(T0(x)) instead of matlabFunction(T0). This also clears up the problem, and has the advantage that I don't have to explicitly define the symbolically defined T0(x) to have a certain number of rows and columns.

Thanks!