# How to draw the vectors from point to point

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

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,

I have now..

Full code:

%Preamble
%Graphics
\documentclass[a4paper,12pt]{article}
\usepackage{graphicx}
\usepackage{tikz,pgf,pgfplots,pgfplotstable}
contourstyle/.style={
every axis/.append style={font=\normalsize},
scaled ticks=false,
yticklabel style={
anchor=east,
/pgf/number format/precision=2,
/pgf/number format/fixed,
/pgf/number format/fixed zerofill},
width=0.85\textwidth,
height=0.35\textheight}
}
\usetikzlibrary{arrows}
\usetikzlibrary{decorations.markings}

\begin{document}
\begin{figure}[h]
\begin{center}
\begin{tikzpicture}
\begin{axis}[view={0}{90},
contourstyle,
grid,
ymin=-1.05, ymax=1.05,
xmin=-5.0, xmax=5.0,
xlabel=$x_1$,ylabel=$x_2$]

%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
\end{axis}
\end{tikzpicture}
\end{center}
\caption{График линий уровня целевой функции.}
\end{figure}
\end{document}

• 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
\end{filecontents*}
\documentclass[border=5pt]{standalone}
\usepackage{pgfplots}
\usepackage{pgfplotstable}
\usetikzlibrary{
arrows.meta,
}
\pgfplotsset{
% use this compat' level or higher to use the advanced features for
% positioning the axis labels
compat=1.3,
}
% 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 ...
\pgfplotstablesave[
% 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
columns={
[index]0,
[index]1,
[index]2,
accumx,
accumy,
accumz
},
\begin{document}
\begin{tikzpicture}
\begin{axis}[
%            % use this to view the 3D plot from the top which is what you want
%            view={0}{90},
grid,
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.
% 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 ...)
quiver={
u=\thisrow{0},
v=\thisrow{1},
w=\thisrow{2},
},
% here we just add some other style stuff which hopefully
% is self-explanatory
no markers,
thick,
% (this option has to be in brackets, because otherwise have
%  round brackets in round brackets which raise an error)
{-Latex[red]},
% 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};
% -----------------------------------------------------------------
\end{axis}
\end{tikzpicture}
\end{document}