I have the file "gradmethod.dat" that contains the values ​​of the 3D coordinates:

"gradmethod.dat" is

0.4166337995    -0.0003214561   0.1735863062
0.0036860331    0.0076438475    0.0014742969
0.0035385391    -2.73017951816883E-006  1.25214454652422E-005
3.13060831250342E-005   6.49204488768879E-005   1.06346687900047E-007
3.00533925319392E-005   -2.31878619722447E-008  9.03219844602389E-010

I need for each pair of coordinates to draw the vector. How can I make it?

For example, enter image description here

I have now.. enter image description here

Full code:

            every axis/.append style={font=\normalsize},
            scaled ticks=false,
            yticklabel style={
            /pgf/number format/precision=2,
            /pgf/number format/fixed,
            /pgf/number format/fixed zerofill},

            ymin=-1.05, ymax=1.05,
            xmin=-5.0, xmax=5.0,

%drawing contour of the 3d function         
\addplot3[contour gnuplot={levels={0.5, 2.5, 10.0,20.0},
                contour label style={nodes={font=\small}}},
                samples=80, domain=-5:5,y domain=-1.0:1.0,
        very thick]{x^2+25*y^2};

%drawing vectors    
\addplot table{gradmethod.dat};
\caption{График линий уровня целевой функции.}
  • You have three columns; is that the 2d projection of the 3d vector? And please paste the full code so that we can have the same code to work on. – percusse Nov 3 '14 at 15:17
  • Yes, it is the projection of the 3D vector. It was necessary to draw the contour of the 3D function f(x,y)=x^2+25*y^2. – Danila Semenov Nov 3 '14 at 15:44
  • Anyone can help me with the question? – Danila Semenov Nov 4 '14 at 9:01

I am not 100% sure if I have understood your question right, so please let me know if I don't.

Some notes in advance:

  • Because the contour gnuplot part is unrelated to the question I have not included this in my solution.
  • I present a general solution which also works for 3D graphs and thus I show it as this. Of course you can simply change the view or you can just use a corresponding \addplot (instead of the \addplot3) command to make it look like a 2D plot.
  • I have changed your provided data points, because they where so small, that you would only see one arrow.

For more details on the solutions works, please have a look at the comments in the code

% used PGFPlots v1.14
    % adapted data file
        4.166337995 -0.0321456  0.1735863062
        0.36860331  0.7643847   0.014742969
        -3.5385391  -0.0273017  0.1252144546
        0.3130608   0.0649204   0.1063466879
        0.3005339   -0.0231878  0.9032198446
        % use this `compat' level or higher to use the advanced features for
        % positioning the axis labels
    % because of a bug in PGFPlotsTable
    % (https://sourceforge.net/p/pgfplots/bugs/109/)
    % it is currently not possible to directly use a loaded table, so we have
    % to save it to a file ...
        % to store the end points of the vectors create some additional columns
        create on use/accumx/.style={
            create col/expr={\prevrow{0}+\pgfmathaccuma}
        create on use/accumy/.style={
            create col/expr={\prevrow{1}+\pgfmathaccuma}
        create on use/accumz/.style={
            create col/expr={\prevrow{2}+\pgfmathaccuma}
        % state the columns here which should be saved to the file
%            % use this to view the 3D plot from the top which is what you want
%            % (see also comment below)
%            view={0}{90},
            xmin=-5.0,      xmax=5.0,
            ymin=-1.05,     ymax=1.05,
            xlabel=$x_1$,   ylabel=$x_2$,
            % -----------------------------------------------------------------
            % you can either choose `\addplot' to show the desired result or
            % you use `\addplot3' for the general case and provide in addition
            % the `view' key.
            \addplot3+ [
                % state where the vectors for the quiver should come from
                % (here I enlarged the values, because the values are that small,
                % that only one arrow would be seen. Now it are at least two ...)
                % here we just add some other style stuff which hopefully
                % is self-explanatory
                no markers,
                % (this option has to be in brackets, because otherwise have
                %  round brackets in round brackets which raise an error)
            % the vectors should always start at the previous point,
            % why we use the additionally created table columns
            ] table [x=accumx,y=accumy,z=accumz] {modified.dat};
            % -----------------------------------------------------------------

image showing the result of above code

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