Create one linear line plots from each row of data in table

Question

I have a table where the data has the following format:

| x    | y    | dydx  |
|------|------|-------|
| x1   | y1   | dydx1 |
| x2   | y2   | dydx2 |
| x3   | y3   | dydx3 |

I want to create a plot with multiple linear lines with the following expression: y(x_sub) = y_i + dydx_i * (x_sub-x_i)

where, i is the row number in the table and x_sub is the range [x_i - a, x_i + a], where a is some specified value. So, each line will be centered at x_i. I have attached a plot (generated with Matlab) that shows the green and black lines centered at x_i and use the y and dydx values in the table.

I am using pgfplot to create my plots. I would greatly appreciate any guidance on this. Thanks!

Answer 1

If I understood you correctly, this might be something like what you're after.

%%%%%%%%
%% the following only for example
\RequirePackage{filecontents}
% the filecontents environment writes its content to the specified file
\begin{filecontents*}{data.dat}
x y dydx
0 2 1
1 1 -1
2 3 0.5
\end{filecontents*}
%%%%%%%

\documentclass[border=5mm]{standalone}
\usepackage{pgfplotstable}
\begin{document}
\begin{tikzpicture}
\pgfplotstableread{data.dat}\mydata
% get number of rows in table
% subtract 1 because row indexing starts at zero
\pgfplotstablegetrowsof{\mydata}
\pgfmathtruncatemacro{\NumRows}{\pgfplotsretval-1}


\begin{axis}[
  xmin=-5,
  xmax=5,
  samples=2
]

\pgfmathsetmacro{\AxRange}{\pgfkeysvalueof{/pgfplots/xmax}-\pgfkeysvalueof{/pgfplots/xmin}}

\pgfplotsinvokeforeach{0,...,\NumRows}{ % loop over rows

  % extract the data from the table
  \pgfplotstablegetelem{#1}{x}\of\mydata % x is column name
  \pgfmathsetmacro{\X}{\pgfplotsretval}
  \pgfplotstablegetelem{#1}{y}\of\mydata
  \pgfmathsetmacro{\Y}{\pgfplotsretval}
  \pgfplotstablegetelem{#1}{dydx}\of\mydata
  \pgfmathsetmacro{\DYDX}{\pgfplotsretval}

  % calculate start and end of domain for line
  \pgfmathsetmacro{\DomainStart}{\X-\AxRange*0.1}
  \pgfmathsetmacro{\DomainEnd}{\X+\AxRange*0.1}

  % plot
  \addplot +[domain=\DomainStart:\DomainEnd,mark=none,thick] {\Y + \DYDX * (x-\X)};
}

\end{axis}
\end{tikzpicture}
\end{document}