Spectrum colormap for multiple curves

Question

I have been using matlab2tikz to generate a lot of my plots, but I am finding it struggling at this particular job so would like to inquire about how to do it properly in pgfplots / tikz.

Essentially I would like to plot a number of curves on one graph, and have a spectrum color map color them with colors evenly distributed on the spectrum. In MATLAB this is quite simple:

figure
const = linspace(0,pi/4,50)';
x = linspace(0,pi,128);
plots = sin(-const*x)';
noOfLines = length(const);
cmp = jet(noOfLines);
hLine = plot(plots);
for line = 1:noOfLines
set(hLine(line),'Color',cmp(line,:));
end
set(hLine,'LineWidth',1.5);

I can export this with matlab2tikz and compile it which produces this gorgeous plot:

The problem is the tikz code is kind of brute forced. It starts with 50 costumed \definecolor

\definecolor{mycolor1}{rgb}{0.00000,0.00000,0.53846}%
\definecolor{mycolor2}{rgb}{0.00000,0.00000,0.61538}%
\definecolor{mycolor3}{rgb}{0.00000,0.07692,1.00000}% ...

for each color that is going to be used, and then 50 \addplot

\addplot [color=mycolor2,solid,line width=1.5pt,forget plot]
  table[row sep=crcr]{1 0\\
2   -0.000396497032881626\\
3   -0.000792994003429991\\

to plot each line with the correct color. I understand I am asking an aweful lot from matlab2tikz so I guess I would like to know how to do this properly using tikz / pgfplots. I have another data set that is similar but it has a lot more plots and comes out to 1.3 mb, taking a long time to compile.

I am happy with creating a pgfplot from a dataset that is in a text file with just the raw data (which would be the plots matrix in my MATLAB workspace in the above example), but have no idea how to proceed from here. Thanks.

EDIT:

In MATLAB my code will be in the workspace like:

I then dlmwrite it to a .dat file by:

dlmwrite('data.dat',myData,'delimiter', '\t');

Then I try to \addplot3 and get:

This is my dataset:

0.99934 1.0005  1.0007  1.0001  0.99934
1.0029  1.0012  0.99933 0.99862 0.9979
1.0013  0.9988  1.0023  0.99525 0.99771
0.99774 0.99582 0.9943  0.99217 0.98699
0.9912  0.98502 0.97814 0.96116 0.94135
0.97022 0.94084 0.89332 0.83747 0.77688
0.88784 0.75475 0.61326 0.462   0.3339
0.58506 0.30003 0.11623 0.034422    0.0078042
0.099072    0.0090417   0.0031278   0.00023727  0.00050435
-0.0014491  0.00053296  -0.00028736 -0.0021953  0.00056537
-0.0024348  5.2456e-05  0.001471    5.6913e-05  -0.0010844
0.0019199   -0.0023666  0.00065858  -2.7668e-05 0.00034113

Thanks for all your help.

Answer 1

Your const variable appears to be like a y variable and the plotted function is actually f(x,y) = sin(-x*y).

This can be plotted directly in pgfplots:

\documentclass{standalone}

\usepackage{pgfplots}

\pgfplotsset{
    compat=1.11,
    trig format plots=rad,
}

\begin{document}

\begin{tikzpicture}
    \begin{axis}[
        view={0}{0},
        enlarge z limits=false,
        enlarge x limits=upper,
        colormap/jet,
    ]
    \addplot3[
        mesh,
        patch type=line,
        domain=0:pi,samples=128,
        domain y=0:pi/4, samples y=50,
        point meta=y,
    ]
    {sin(-y*x)};
    \end{axis}
\end{tikzpicture}
\end{document}

The key ideas are to make a 3D mesh plot, and visualize the mesh lines by means of their scanlines (i.e. patch type=line) and show only the X/Z plane. I used point meta=y in order to define the y coordinate as color data.

EDIT

The same approach is possible if you place the data matrix into a table:

\documentclass{standalone}

\usepackage{pgfplots}

\pgfplotsset{
    compat=1.11,
}

\begin{document}

\begin{tikzpicture}
    \begin{axis}[
        view={0}{0},
        enlarge z limits=false,
        enlarge x limits=upper,
        colormap/jet,
    ]
    \addplot3[
        mesh,
        patch type=line,
        point meta=y,
    ]
    table {P.dat};
    \end{axis}
\end{tikzpicture}
\end{document}

The data table contains the same data, it is of the form

0.0e0 0.0e0 0.0e0 0.0e0
2.47371e-2 0.0e0 0.0e0 0.0e0
4.94742e-2 0.0e0 0.0e0 0.0e0
7.42113e-2 0.0e0 0.0e0 0.0e0
9.8948401e-2 0.0e0 0.0e0 0.0e0
1.23685501e-1 0.0e0 0.0e0 0.0e0
1.4842259e-1 0.0e0 0.0e0 0.0e0
1.7315968e-1 0.0e0 0.0e0 0.0e0
1.9789677e-1 0.0e0 0.0e0 0.0e0
[...]
3.0673993e0 0.0e0 0.0e0 0.0e0
3.0921364e0 0.0e0 0.0e0 0.0e0
3.1168735e0 0.0e0 0.0e0 0.0e0
3.1416106e0 0.0e0 0.0e0 0.0e0

0.0e0 1.60283e-2 0.0e0 1.60283e-2
2.47371e-2 1.60283e-2 -3.8e-4 1.60283e-2
4.94742e-2 1.60283e-2 -8.0e-4 1.60283e-2
7.42113e-2 1.60283e-2 -1.19e-3 1.60283e-2
9.8948401e-2 1.60283e-2 -1.59e-3 1.60283e-2
[...]

It is given in scanlines (please ignore the fourth column; I exported it together with my color data which is the y coordinate). The precise format is described in the pgfplots manual (section about 3d plots).

NOTE: pgfplots cannot transpose the data file. Consequently, it will only show scanlines along a specific axis. You will need to transpose it if it does not fit.