Best way to store the sum of few numbers inside a foreach cycle

Question

I would like to perform the sum of some value inside a foreach cycle as in the following example:

\usepackage{amssymb} %maths
\usepackage{amsmath} %maths
\usepackage{booktabs}
\usepackage{tikz}
\usepackage{pgfplots}
\usepackage{ifthen}
\usetikzlibrary{arrows.meta}
\usepackage[utf8]{inputenc} %utile per scrivere direttamente in caratteri accentuati
\begin{document}
\begin{tikzpicture}
\pgfmathsetmacro{\n}{5}
\draw[-Latex](0,0)--(\n+.5,0);
\draw[scale=1,domain=0:\n,smooth,variable=\X,red,thick] plot ({\X},{exp(-\X)});
\foreach \k in {0,...,10}
{
\pgfmathsetmacro{\x}{5*\k/10}
\pgfmathsetmacro{\Y}{exp(-\x)}
\pgfmathsetmacro{\y}{exp(-\x)+rand/3}
\pgfmathsetmacro{\diff}{\y-\Y}
\pgfmathsetmacro{\Diff}{100*(\y-\Y)}
\pgfmathsetmacro{\squareddiff}{abs(\diff^2)}
\fill[](\x,\y)circle(1pt);
\ifthenelse{0<\Diff}{\node[scale=.25,above]at(\x,\y+.1){$(x_{\k},y_{\k})$};
}{\node[scale=.25,below]at(\x,\y-.1){$(x_{\k},y_{\k})$};
}
\draw[dotted](\x,\y)--(\x,\Y);
\node[scale=.2]at(\x,-1.25){$y_{\k}-f(x_{\k})$};
\node[scale=.25]at(\x,-1.5){$\diff$};
\node[scale=.2]at(\x,-1.75){$(y_{\k}-f(x_{\k}))^2$};
\node[scale=.25]at(\x,-2){$\squareddiff$};
\node[]at(2.5,-3){$\sum\limits_{k}^n(y_k-f(x_k))^2=?$};
}
\end{tikzpicture}
\end{document}

Would you please complete your code snippet to a complete and compilable example? — muzimuzhi Z, May 19 '20 at 06:54
@muzimuzhiZ I added something..is it working? Sorry I used to compile with latexit and that's what is needed to compile there. I will provide an image as soon as it will be accepted by the server! — yngabl, May 19 '20 at 07:01

score 9 · Accepted Answer · 2020-05-19T07:08:47.587

The problem is that the ordinary \foreach puts the stuff it is iterating over in groups. There are a few options:

Use \pgfplotsforeachungrouped\k in{0,...,10} instead if you keep loading pgfplots.
Make the macro for the sum global. Works but isn't great.
Just use the ordinary \loop ... \repeat command. This has been used here to declare a pgf function sum.
Use other tools.

This illustrates the third option explicitly.

\documentclass[tikz,border=3mm]{standalone}
\usetikzlibrary{arrows.meta}
\usepackage[utf8]{inputenc} %utile per scrivere direttamente in caratteri accentuati
\begin{document}

\begin{tikzpicture}
% if you ever use the calc library you may want to avoid using `\n`, `\x` and 
% \y for macros but here it is fine.
\pgfmathsetmacro{\n}{5}
\draw[-Latex](0,0)--(\n+.5,0);
\draw[scale=1,domain=0:\n,smooth,variable=\X,red,thick] plot ({\X},{exp(-\X)});
\edef\k{0}
\edef\TotalSquareDiff{0}
\pgfmathsetseed{1}% so that others can cross check
\loop
\pgfmathsetmacro{\x}{5*\k/10}
\pgfmathsetmacro{\Y}{exp(-\x)}
\pgfmathsetmacro{\y}{exp(-\x)+rand/3}
\pgfmathsetmacro{\diff}{\y-\Y}
\pgfmathsetmacro{\Diff}{100*(\y-\Y)}
\pgfmathsetmacro{\squareddiff}{\diff*\diff}
\fill(\x,\y)circle[radius=1pt];
\ifdim0pt<\Diff pt\relax
\node[scale=.25,above]at(\x,\y+.1){$(x_{\k},y_{\k})$};
\else
\node[scale=.25,below]at(\x,\y-.1){$(x_{\k},y_{\k})$};
\fi
\draw[dotted](\x,\y)--(\x,\Y);
\node[scale=.2]at(\x,-1.25){$y_{\k}-f(x_{\k})$};
\node[scale=.25]at(\x,-1.5){$\diff$};
\node[scale=.2]at(\x,-1.75){$(y_{\k}-f(x_{\k}))^2$};
\node[scale=.25]at(\x,-2){$\squareddiff$};
\pgfmathsetmacro{\TotalSquareDiff}{\TotalSquareDiff+\squareddiff}%
\edef\k{\the\numexpr\k+1}
\ifnum\k<11
\repeat
\node at(2.5,-3){$\sum\limits_{k}^n(y_k-f(x_k))^2=\pgfmathprintnumber\TotalSquareDiff$};
\end{tikzpicture}
\end{document}

@yngabl there is also the [third option...] (https://www.goodreads.com/quotes/19197-in-fact-the-mere-act-of-opening-the-box-will) — Rmano, May 19 '20 at 07:59
Quantum physics can say Mass, but if the cat meows and draw with tikz, he is not dead. — Fran, May 19 '20 at 08:53

score 4 · Answer 2 · answered May 19 '20 at 07:51

Here is a solution using remember and evaluate:

\documentclass{standalone}
\usepackage{amssymb} %maths
\usepackage{amsmath} %maths
\usepackage{booktabs}
\usepackage{tikz}
\usepackage{pgfplots}
\usepackage{ifthen}
\usetikzlibrary{arrows.meta}
\usepackage[utf8]{inputenc} %utile per scrivere direttamente in caratteri accentuati
\begin{document}
\begin{tikzpicture}
  \pgfmathsetmacro{\n}{5}
  \draw[-Latex](0,0)--(\n+.5,0);
  \draw[scale=1,domain=0:\n,smooth,variable=\X,red,thick] plot ({\X},{exp(-\X)});
  \foreach \k[
  evaluate=\k as \x using 5*\k/10,
  evaluate=\x as \Y using exp(-\x),
  evaluate=\x as \y using exp(-\x)+rand/3,
  evaluate=\y as \diff using \y-\Y,
  evaluate=\diff as \Diff using 100*\diff,
  evaluate=\diff as \squareddiff using (\diff)^2,
  remember=\totsd as \totsd (initially 0),                   % fake sum
  evaluate=\squareddiff as \totsd using \totsd+\squareddiff, % true sum
  ] in {0,...,10}
  {
    \fill[](\x,\y)circle(1pt);
    \pgfmathsetmacro\mypos{0<\Diff?"south":"north"}
    \node[scale=.25,anchor=\mypos]at(\x,{\y+(0<\Diff?+1:-1)*.1}){$(x_{\k},y_{\k})$};
    \draw[dotted](\x,\y)--(\x,\Y);
    \node[scale=.2]at(\x,-1.25){$y_{\k}-f(x_{\k})$};
    \node[scale=.25]at(\x,-1.5){$\diff$};
    \node[scale=.2]at(\x,-1.75){$(y_{\k}-f(x_{\k}))^2$};
    \node[scale=.25]at(\x,-2){$\squareddiff$};
    \node[scale=.18]at(\x,-2.25){$\sum\limits_{i=1}^{\k}(y_i-f(x_i))^2$};
    \node[scale=.25]at(\x,-2.5){$\totsd$};
  }
\end{tikzpicture}
\end{document}

score 2 · Answer 3 · answered May 19 '20 at 09:38

Here's with “other tools”. The macro \fpshow has an optional argument to use a certain number of decimal digits (rounded), default 2. Just to show the feature, I printed the sum of the squared differences rounded to four digits.

\documentclass{article}
\usepackage{amsmath} %maths
\usepackage{tikz}
\usepackage{pgfplots}
\usepackage{xparse,xfp}

\usepackage{ifthen}
\usetikzlibrary{arrows.meta}
\pgfplotsset{compat=1.17}

\ExplSyntaxOn
\NewDocumentCommand{\fpset}{mm}
 {
  \fp_if_exist:cF { l__yngabl_#1_fp } { \fp_new:c { l__yngabl_#1_fp } }
  \fp_set:cn { l__yngabl_#1_fp } { #2 }
 }
\NewExpandableDocumentCommand{\fpuse}{m}
 {
  \fp_use:c { l__yngabl_#1_fp }
 }
\NewExpandableDocumentCommand{\fpshow}{O{2}m}
 {
  \fp_eval:n { round(\fp_use:c { l__yngabl_#2_fp },#1) }
 }
\NewDocumentCommand{\xforeach}{mmm}
 {
  \cs_set:Nn \__ybgabl_xforeach:n { #3 }
  \int_step_function:nnN { #1 } { #2 } \__ybgabl_xforeach:n
 }
\NewExpandableDocumentCommand{\fpcompareTF}{mmm}
 {
  \fp_compare:nTF { #1 } { #2 } { #3 }
 }
\ExplSyntaxOff


\begin{document}

\begin{tikzpicture}
\fpset{n}{5}
\draw[-Latex](0,0)--(\fpuse{n}+.5,0);
\draw[scale=1,domain=0:\fpuse{n},smooth,variable=\X,red,thick] plot ({\X},{exp(-\X)});
\fpset{total}{0}% initialize the total
\xforeach{0}{10}{
  \fpset{x}{5*\fpeval{#1/10}}
  \fpset{diff}{(-1)**randint(1,2)*rand()/3}
  \fpset{y}{exp(-\fpuse{x})}
  \fpset{sqdiff}{\fpuse{diff}*\fpuse{diff}}
  \fpset{total}{\fpuse{total}+\fpuse{sqdiff}}
  \fill[](\fpuse{x},\fpeval{\fpuse{y}+\fpuse{diff}}) circle(1pt);
  \fpcompareTF{\fpuse{diff}>0}
    { \node[scale=.25,above] at (\fpuse{x},\fpuse{y}+\fpuse{diff}+.1){$(x_{#1},y_{#1})$}; }
    { \node[scale=.25,below] at (\fpuse{x},\fpuse{y}+\fpuse{diff}-.1){$(x_{#1},y_{#1})$}; }
  \draw[dotted](\fpuse{x},\fpuse{y})--(\fpuse{x},\fpeval{\fpuse{y}+\fpuse{diff}});
  \node[scale=.2]at(\fpuse{x},-1.25){$y_{#1}-f(x_{#1})$};
  \node[scale=.25]at(\fpuse{x},-1.5){$\fpshow{diff}$};
  \node[scale=.2]at(\fpuse{x},-1.75){$(y_{#1}-f(x_{#1}))^2$};
  \node[scale=.25]at(\fpuse{x},-2){$\fpshow{sqdiff}$};
}
\node[]at(2.5,-3){$\displaystyle\sum_{k=0}^n(y_k-f(x_k))^2=\fpshow[4]{total}$};
\end{tikzpicture}

\end{document}

Advantages

No group, but variables are set locally in the tikzpicture
No risk to clobber existing macros
Computations are made with 15 decimal digits

Disadvantages

A bit more verbose
Only “pure numbers” can be used

Best way to store the sum of few numbers inside a foreach cycle

3 Answers3