Legend don't match with line style

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Patrick on 11 Sep 2022
Commented: Walter Roberson on 12 Sep 2022
w = 2*pi;
k = (0:4);
t_2 = (0:0.01:1)';
T = t_2 * ones(1, 5);
Phi_k = exp(T*diag(k)*w*1i);
%Plot Re{Phi(t)} vs. t, 0 <= t < 1, for k = 0...4, all 5 curves in one
%figure
k = 0;
Phi_0 = exp(T*diag(k)*w*1i);
Phi_1 = exp(T*diag(k+1)*w*1i);
Phi_2 = exp(T*diag(k+2)*w*1i);
Phi_3 = exp(T*diag(k+3)*w*1i);
Phi_4 = exp(T*diag(k+4)*w*1i);
plot(t_2, real(Phi_0), '-.', t_2, real(Phi_1), '--d', t_2, real(Phi_2), ':o', t_2, real(Phi_3), '-.*', t_2, real(Phi_4), '-s');
legend('0th','1st','2nd', '3rd', '4th');
xlabel('t_2'); ylabel('Amplitude');
I'm pretty new in matlab and I don't quite understand why legend isn't doing what I wanted it to do.

Walter Roberson on 11 Sep 2022
k = 0;
Phi_0 = exp(T*diag(k)*w*1i);
T is 101 x 5.
In your earlier calculations k was a vector of length 5 so diag(k) was 5x5, and (101 x 5) * (5 x 5) is well defined giving a 101x5 result that you then multiplied by a scalar w giving a matrix result.
In the present section, k is scalar, so diag(k) is scalar. (101 x 5)*scalar gives a 101x5 result. Then w is scalar so you end up with a matrix result.
When you plot() a 2d matrix, it will generally create one line per column. So you plot 5 lines multiple times, for a total of 25 lines drawn, but only 5 legends.
My guess is that you should construct diag(0:4) but extract one column each time, so 101x5 * 5x1 giving 101x1 results.
But... you already calculated that into Phi_k so just plot the columns of Phi_k
Walter Roberson on 12 Sep 2022
h = plot(t_2, real(Phi_k));
h(1).Linespec = '-.';
h(2).Linespec = '--'; h(2).MarkerShape = 'd';
h(3).Linespec = ':'; h(3).MarkerShape = 'o';
h(4).Linespec = '-.'; h(4).MarkerShape = '*';
h(5).Linespec = '-'; h(5).MarkerShape = 's';

Cris LaPierre on 11 Sep 2022
The legend in MATLAB assigns labels based on the order the line objects are created in. What is perhaps unexpected here is that T is a matrix (101x5), and the result of your calculation of Phis has the same size. You may have expected them to be vectors instead.
In MATLAB, each column is treated as a unique data series, so the first five lines plotted are the 5 columns of Phi_0. You also have 5 legend labels, which get assigned to these five lines, all of which have the same linestyle. MATLAB automatically cycles the colors using the default colororder.
w = 2*pi;
k = (0:4);
t_2 = (0:0.01:1)';
T = t_2 * ones(1, 5);
Phi_k = exp(T*diag(k)*w*1i);
Phi_0 = exp(T*diag(k)*w*1i)
Phi_0 =
1.0000 + 0.0000i 1.0000 + 0.0000i 1.0000 + 0.0000i 1.0000 + 0.0000i 1.0000 + 0.0000i 1.0000 + 0.0000i 0.9980 + 0.0628i 0.9921 + 0.1253i 0.9823 + 0.1874i 0.9686 + 0.2487i 1.0000 + 0.0000i 0.9921 + 0.1253i 0.9686 + 0.2487i 0.9298 + 0.3681i 0.8763 + 0.4818i 1.0000 + 0.0000i 0.9823 + 0.1874i 0.9298 + 0.3681i 0.8443 + 0.5358i 0.7290 + 0.6845i 1.0000 + 0.0000i 0.9686 + 0.2487i 0.8763 + 0.4818i 0.7290 + 0.6845i 0.5358 + 0.8443i 1.0000 + 0.0000i 0.9511 + 0.3090i 0.8090 + 0.5878i 0.5878 + 0.8090i 0.3090 + 0.9511i 1.0000 + 0.0000i 0.9298 + 0.3681i 0.7290 + 0.6845i 0.4258 + 0.9048i 0.0628 + 0.9980i 1.0000 + 0.0000i 0.9048 + 0.4258i 0.6374 + 0.7705i 0.2487 + 0.9686i -0.1874 + 0.9823i 1.0000 + 0.0000i 0.8763 + 0.4818i 0.5358 + 0.8443i 0.0628 + 0.9980i -0.4258 + 0.9048i 1.0000 + 0.0000i 0.8443 + 0.5358i 0.4258 + 0.9048i -0.1253 + 0.9921i -0.6374 + 0.7705i 1.0000 + 0.0000i 0.8090 + 0.5878i 0.3090 + 0.9511i -0.3090 + 0.9511i -0.8090 + 0.5878i 1.0000 + 0.0000i 0.7705 + 0.6374i 0.1874 + 0.9823i -0.4818 + 0.8763i -0.9298 + 0.3681i 1.0000 + 0.0000i 0.7290 + 0.6845i 0.0628 + 0.9980i -0.6374 + 0.7705i -0.9921 + 0.1253i 1.0000 + 0.0000i 0.6845 + 0.7290i -0.0628 + 0.9980i -0.7705 + 0.6374i -0.9921 - 0.1253i 1.0000 + 0.0000i 0.6374 + 0.7705i -0.1874 + 0.9823i -0.8763 + 0.4818i -0.9298 - 0.3681i 1.0000 + 0.0000i 0.5878 + 0.8090i -0.3090 + 0.9511i -0.9511 + 0.3090i -0.8090 - 0.5878i 1.0000 + 0.0000i 0.5358 + 0.8443i -0.4258 + 0.9048i -0.9921 + 0.1253i -0.6374 - 0.7705i 1.0000 + 0.0000i 0.4818 + 0.8763i -0.5358 + 0.8443i -0.9980 - 0.0628i -0.4258 - 0.9048i 1.0000 + 0.0000i 0.4258 + 0.9048i -0.6374 + 0.7705i -0.9686 - 0.2487i -0.1874 - 0.9823i 1.0000 + 0.0000i 0.3681 + 0.9298i -0.7290 + 0.6845i -0.9048 - 0.4258i 0.0628 - 0.9980i 1.0000 + 0.0000i 0.3090 + 0.9511i -0.8090 + 0.5878i -0.8090 - 0.5878i 0.3090 - 0.9511i 1.0000 + 0.0000i 0.2487 + 0.9686i -0.8763 + 0.4818i -0.6845 - 0.7290i 0.5358 - 0.8443i 1.0000 + 0.0000i 0.1874 + 0.9823i -0.9298 + 0.3681i -0.5358 - 0.8443i 0.7290 - 0.6845i 1.0000 + 0.0000i 0.1253 + 0.9921i -0.9686 + 0.2487i -0.3681 - 0.9298i 0.8763 - 0.4818i 1.0000 + 0.0000i 0.0628 + 0.9980i -0.9921 + 0.1253i -0.1874 - 0.9823i 0.9686 - 0.2487i 1.0000 + 0.0000i 0.0000 + 1.0000i -1.0000 + 0.0000i -0.0000 - 1.0000i 1.0000 - 0.0000i 1.0000 + 0.0000i -0.0628 + 0.9980i -0.9921 - 0.1253i 0.1874 - 0.9823i 0.9686 + 0.2487i 1.0000 + 0.0000i -0.1253 + 0.9921i -0.9686 - 0.2487i 0.3681 - 0.9298i 0.8763 + 0.4818i 1.0000 + 0.0000i -0.1874 + 0.9823i -0.9298 - 0.3681i 0.5358 - 0.8443i 0.7290 + 0.6845i 1.0000 + 0.0000i -0.2487 + 0.9686i -0.8763 - 0.4818i 0.6845 - 0.7290i 0.5358 + 0.8443i 1.0000 + 0.0000i -0.3090 + 0.9511i -0.8090 - 0.5878i 0.8090 - 0.5878i 0.3090 + 0.9511i 1.0000 + 0.0000i -0.3681 + 0.9298i -0.7290 - 0.6845i 0.9048 - 0.4258i 0.0628 + 0.9980i 1.0000 + 0.0000i -0.4258 + 0.9048i -0.6374 - 0.7705i 0.9686 - 0.2487i -0.1874 + 0.9823i 1.0000 + 0.0000i -0.4818 + 0.8763i -0.5358 - 0.8443i 0.9980 - 0.0628i -0.4258 + 0.9048i 1.0000 + 0.0000i -0.5358 + 0.8443i -0.4258 - 0.9048i 0.9921 + 0.1253i -0.6374 + 0.7705i 1.0000 + 0.0000i -0.5878 + 0.8090i -0.3090 - 0.9511i 0.9511 + 0.3090i -0.8090 + 0.5878i 1.0000 + 0.0000i -0.6374 + 0.7705i -0.1874 - 0.9823i 0.8763 + 0.4818i -0.9298 + 0.3681i 1.0000 + 0.0000i -0.6845 + 0.7290i -0.0628 - 0.9980i 0.7705 + 0.6374i -0.9921 + 0.1253i 1.0000 + 0.0000i -0.7290 + 0.6845i 0.0628 - 0.9980i 0.6374 + 0.7705i -0.9921 - 0.1253i 1.0000 + 0.0000i -0.7705 + 0.6374i 0.1874 - 0.9823i 0.4818 + 0.8763i -0.9298 - 0.3681i 1.0000 + 0.0000i -0.8090 + 0.5878i 0.3090 - 0.9511i 0.3090 + 0.9511i -0.8090 - 0.5878i 1.0000 + 0.0000i -0.8443 + 0.5358i 0.4258 - 0.9048i 0.1253 + 0.9921i -0.6374 - 0.7705i 1.0000 + 0.0000i -0.8763 + 0.4818i 0.5358 - 0.8443i -0.0628 + 0.9980i -0.4258 - 0.9048i 1.0000 + 0.0000i -0.9048 + 0.4258i 0.6374 - 0.7705i -0.2487 + 0.9686i -0.1874 - 0.9823i 1.0000 + 0.0000i -0.9298 + 0.3681i 0.7290 - 0.6845i -0.4258 + 0.9048i 0.0628 - 0.9980i 1.0000 + 0.0000i -0.9511 + 0.3090i 0.8090 - 0.5878i -0.5878 + 0.8090i 0.3090 - 0.9511i 1.0000 + 0.0000i -0.9686 + 0.2487i 0.8763 - 0.4818i -0.7290 + 0.6845i 0.5358 - 0.8443i 1.0000 + 0.0000i -0.9823 + 0.1874i 0.9298 - 0.3681i -0.8443 + 0.5358i 0.7290 - 0.6845i 1.0000 + 0.0000i -0.9921 + 0.1253i 0.9686 - 0.2487i -0.9298 + 0.3681i 0.8763 - 0.4818i 1.0000 + 0.0000i -0.9980 + 0.0628i 0.9921 - 0.1253i -0.9823 + 0.1874i 0.9686 - 0.2487i 1.0000 + 0.0000i -1.0000 + 0.0000i 1.0000 - 0.0000i -1.0000 + 0.0000i 1.0000 - 0.0000i 1.0000 + 0.0000i -0.9980 - 0.0628i 0.9921 + 0.1253i -0.9823 - 0.1874i 0.9686 + 0.2487i 1.0000 + 0.0000i -0.9921 - 0.1253i 0.9686 + 0.2487i -0.9298 - 0.3681i 0.8763 + 0.4818i 1.0000 + 0.0000i -0.9823 - 0.1874i 0.9298 + 0.3681i -0.8443 - 0.5358i 0.7290 + 0.6845i 1.0000 + 0.0000i -0.9686 - 0.2487i 0.8763 + 0.4818i -0.7290 - 0.6845i 0.5358 + 0.8443i 1.0000 + 0.0000i -0.9511 - 0.3090i 0.8090 + 0.5878i -0.5878 - 0.8090i 0.3090 + 0.9511i 1.0000 + 0.0000i -0.9298 - 0.3681i 0.7290 + 0.6845i -0.4258 - 0.9048i 0.0628 + 0.9980i 1.0000 + 0.0000i -0.9048 - 0.4258i 0.6374 + 0.7705i -0.2487 - 0.9686i -0.1874 + 0.9823i 1.0000 + 0.0000i -0.8763 - 0.4818i 0.5358 + 0.8443i -0.0628 - 0.9980i -0.4258 + 0.9048i 1.0000 + 0.0000i -0.8443 - 0.5358i 0.4258 + 0.9048i 0.1253 - 0.9921i -0.6374 + 0.7705i 1.0000 + 0.0000i -0.8090 - 0.5878i 0.3090 + 0.9511i 0.3090 - 0.9511i -0.8090 + 0.5878i 1.0000 + 0.0000i -0.7705 - 0.6374i 0.1874 + 0.9823i 0.4818 - 0.8763i -0.9298 + 0.3681i 1.0000 + 0.0000i -0.7290 - 0.6845i 0.0628 + 0.9980i 0.6374 - 0.7705i -0.9921 + 0.1253i 1.0000 + 0.0000i -0.6845 - 0.7290i -0.0628 + 0.9980i 0.7705 - 0.6374i -0.9921 - 0.1253i 1.0000 + 0.0000i -0.6374 - 0.7705i -0.1874 + 0.9823i 0.8763 - 0.4818i -0.9298 - 0.3681i 1.0000 + 0.0000i -0.5878 - 0.8090i -0.3090 + 0.9511i 0.9511 - 0.3090i -0.8090 - 0.5878i 1.0000 + 0.0000i -0.5358 - 0.8443i -0.4258 + 0.9048i 0.9921 - 0.1253i -0.6374 - 0.7705i 1.0000 + 0.0000i -0.4818 - 0.8763i -0.5358 + 0.8443i 0.9980 + 0.0628i -0.4258 - 0.9048i 1.0000 + 0.0000i -0.4258 - 0.9048i -0.6374 + 0.7705i 0.9686 + 0.2487i -0.1874 - 0.9823i 1.0000 + 0.0000i -0.3681 - 0.9298i -0.7290 + 0.6845i 0.9048 + 0.4258i 0.0628 - 0.9980i 1.0000 + 0.0000i -0.3090 - 0.9511i -0.8090 + 0.5878i 0.8090 + 0.5878i 0.3090 - 0.9511i 1.0000 + 0.0000i -0.2487 - 0.9686i -0.8763 + 0.4818i 0.6845 + 0.7290i 0.5358 - 0.8443i 1.0000 + 0.0000i -0.1874 - 0.9823i -0.9298 + 0.3681i 0.5358 + 0.8443i 0.7290 - 0.6845i 1.0000 + 0.0000i -0.1253 - 0.9921i -0.9686 + 0.2487i 0.3681 + 0.9298i 0.8763 - 0.4818i 1.0000 + 0.0000i -0.0628 - 0.9980i -0.9921 + 0.1253i 0.1874 + 0.9823i 0.9686 - 0.2487i 1.0000 + 0.0000i -0.0000 - 1.0000i -1.0000 + 0.0000i 0.0000 + 1.0000i 1.0000 - 0.0000i 1.0000 + 0.0000i 0.0628 - 0.9980i -0.9921 - 0.1253i -0.1874 + 0.9823i 0.9686 + 0.2487i 1.0000 + 0.0000i 0.1253 - 0.9921i -0.9686 - 0.2487i -0.3681 + 0.9298i 0.8763 + 0.4818i 1.0000 + 0.0000i 0.1874 - 0.9823i -0.9298 - 0.3681i -0.5358 + 0.8443i 0.7290 + 0.6845i 1.0000 + 0.0000i 0.2487 - 0.9686i -0.8763 - 0.4818i -0.6845 + 0.7290i 0.5358 + 0.8443i 1.0000 + 0.0000i 0.3090 - 0.9511i -0.8090 - 0.5878i -0.8090 + 0.5878i 0.3090 + 0.9511i 1.0000 + 0.0000i 0.3681 - 0.9298i -0.7290 - 0.6845i -0.9048 + 0.4258i 0.0628 + 0.9980i 1.0000 + 0.0000i 0.4258 - 0.9048i -0.6374 - 0.7705i -0.9686 + 0.2487i -0.1874 + 0.9823i 1.0000 + 0.0000i 0.4818 - 0.8763i -0.5358 - 0.8443i -0.9980 + 0.0628i -0.4258 + 0.9048i 1.0000 + 0.0000i 0.5358 - 0.8443i -0.4258 - 0.9048i -0.9921 - 0.1253i -0.6374 + 0.7705i 1.0000 + 0.0000i 0.5878 - 0.8090i -0.3090 - 0.9511i -0.9511 - 0.3090i -0.8090 + 0.5878i 1.0000 + 0.0000i 0.6374 - 0.7705i -0.1874 - 0.9823i -0.8763 - 0.4818i -0.9298 + 0.3681i 1.0000 + 0.0000i 0.6845 - 0.7290i -0.0628 - 0.9980i -0.7705 - 0.6374i -0.9921 + 0.1253i 1.0000 + 0.0000i 0.7290 - 0.6845i 0.0628 - 0.9980i -0.6374 - 0.7705i -0.9921 - 0.1253i 1.0000 + 0.0000i 0.7705 - 0.6374i 0.1874 - 0.9823i -0.4818 - 0.8763i -0.9298 - 0.3681i 1.0000 + 0.0000i 0.8090 - 0.5878i 0.3090 - 0.9511i -0.3090 - 0.9511i -0.8090 - 0.5878i 1.0000 + 0.0000i 0.8443 - 0.5358i 0.4258 - 0.9048i -0.1253 - 0.9921i -0.6374 - 0.7705i 1.0000 + 0.0000i 0.8763 - 0.4818i 0.5358 - 0.8443i 0.0628 - 0.9980i -0.4258 - 0.9048i 1.0000 + 0.0000i 0.9048 - 0.4258i 0.6374 - 0.7705i 0.2487 - 0.9686i -0.1874 - 0.9823i 1.0000 + 0.0000i 0.9298 - 0.3681i 0.7290 - 0.6845i 0.4258 - 0.9048i 0.0628 - 0.9980i 1.0000 + 0.0000i 0.9511 - 0.3090i 0.8090 - 0.5878i 0.5878 - 0.8090i 0.3090 - 0.9511i 1.0000 + 0.0000i 0.9686 - 0.2487i 0.8763 - 0.4818i 0.7290 - 0.6845i 0.5358 - 0.8443i 1.0000 + 0.0000i 0.9823 - 0.1874i 0.9298 - 0.3681i 0.8443 - 0.5358i 0.7290 - 0.6845i 1.0000 + 0.0000i 0.9921 - 0.1253i 0.9686 - 0.2487i 0.9298 - 0.3681i 0.8763 - 0.4818i 1.0000 + 0.0000i 0.9980 - 0.0628i 0.9921 - 0.1253i 0.9823 - 0.1874i 0.9686 - 0.2487i 1.0000 + 0.0000i 1.0000 - 0.0000i 1.0000 - 0.0000i 1.0000 - 0.0000i 1.0000 - 0.0000i
plot(t_2, real(Phi_0), '-.');
legend('0th','1st','2nd', '3rd', '4th');
xlabel('t_2'); ylabel('Amplitude');

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