Ttdfjt

I am using the following code, which is supposed to cut a function in N parts :

documentclass[11pt]article

usepackagetikz
usepackagepgfplots 
pgfplotssetcompat=newest 

begindocument
 resizeboxcolumnwidth!%
 begintikzpicture
 beginaxis
 [
 grid,
 anchor=origin,
 %axis equal=false,
 xmin=0, xmax=1,
 ymin=0, ymax=10,
 minor tick num=1,
 axis lines = middle,
 tick label style=inner sep=2pt, font=footnotesize,
 %
 every axis plot post/.append style=thick,
 samples=500
 ]
 addplot [domain=0:1, color=blue] -2*ln(x);
 endaxis

 % Add lines
 pgfmathsetmacroN4;

 foreach x in N,...,0 
 draw [line width=0.15mm, red] (x/N, 0) -- (x/N, 10);
 
 endtikzpicture
 
enddocument

But, instead of having 5 lines cutting my function from 0 to 1, this is what I have :

Do you have any idea of why this issue appears ?

P.S : Do you have a better way to declare variables than pgfmathsetmacro ?

The coordinate system of the axis is not the same as that of the underlying tikzpicture, so when you add a draw outside the axis you cannot expect the coordinates to correspond to those inside the axis.

Instead, use

pgfmathsetmacroN4;
pgfplotsinvokeforeachN,...,0 % special looping defined by pgfplots
 draw [line width=0.15mm, red] (#1/N, 0) -- (#1/N, 10);
 

before endaxis. (Or an ycomb plot, as in the example below.)

documentclass[11pt]article
usepackagepgfplots 
pgfplotssetcompat=1.16 % it's recommended to use an explicit version number

begindocument
 begintikzpicture
 beginaxis
 [ 
 width=columnwidth, % I would generally not use resizebox
 grid,
 anchor=origin,
 %axis equal=false,
 xmin=0, xmax=1,
 ymin=0, ymax=10,
 minor tick num=1,
 axis lines = middle,
 tick label style=inner sep=2pt, font=footnotesize,
 %
 every axis plot post/.append style=thick,
 samples=500
 ]
 addplot [domain=0:1, color=blue] -2*ln(x);


 pgfmathsetmacroN4;
 pgfplotsinvokeforeachN,...,0 % special looping defined by pgfplots
 draw [line width=0.15mm, red] (#1/N, 0) -- (#1/N, 10);
 

 % alternative: an ycomb plot
 addplot [line width=0.15mm, red, forget plot, ycomb, samples at=4,...,0] (x/4,10);
 endaxis

 endtikzpicture
enddocument

Welcome to TeX.SE!

(Torbjørn T. has been a bit faster than me...)

The problem is that your foreach loop is run in a place where coordinates don't correspond to what you think. You can try adding:

draw[green] (1,0) circle (1pt);

after your loop and you should understand that abscissa 1 in the TikZ xyz coordinate system doesn't correspond to abscissa 1 for the plot.

Inside the axis environment, however, coordinates use the axis coordinate system starting from pgfplots compatibility level 1.11. In older compatibility levels, one can use this coordinate system like this: (axis cs:1,0) for point (1,0) in the axis coordinate system. But let's assume for simplicity of the code that we can afford compatibility level 1.11 or later (otherwise, just add two axis cs:).

In order to use the axis coordinate system to draw your vertical lines, you need to move the foreach loop inside the axis environment. This brings a new difficulty, as things inside that environment are often expanded late: see foreach not behaving in axis environment. Fortunately, both solutions given there work fine. With the simpler solution, the full example becomes:

documentclassarticle
usepackagepgfplots
pgfplotssetcompat=1.11% or later

begindocument
 begintikzpicture
 beginaxis
 [ grid,
 anchor=origin,
 %axis equal=false,
 xmin=0, xmax=1,
 ymin=0, ymax=10,
 minor tick num=1,
 axis lines = middle,
 tick label style=inner sep=2pt, font=footnotesize,
 %
 every axis plot post/.append style=thick,
 samples=500 ]
 addplot [domain=0:1, color=blue] -2*ln(x);

 % Add lines (alternatively: defN4). No semi-colon is needed in
 % either case: these are not TikZ statements.
 pgfmathsetmacroN4

 pgfplotsinvokeforeach N,...,0 
 draw[line width=0.15mm, red] (#1/N, 0) -- (#1/N, 10);
 
 endaxis
 endtikzpicture
enddocument

As said, there is a second way to write the loop:

foreach x in N,...,0 
 edeftempnoexpanddraw [line width=0.15mm, red]
 (x/N, 0) -- (x/N, 10);
 temp

Both give the same outcome.