There are at least 4 different (in code a-d) ways to access items in lists/arrays. Out of curiosity I wanted to see what happens with different combinations. I selected 6 different (in code A-F) input scenarios and tested them 2 levels deep. That means potentially 4*4*6=96 tests.
\documentclass{standalone}
\usepackage{tikz}
\usepackage{ifthen}
\begin{document}
\message{^^J}
\begin{tikzpicture}
\def \A {{{{9, 8, 7}}, {{6, 5}}}}
\def \B {{{9, 8, 7}, {6, 5}}}
\def \C {{9, 8, 7}}
\def \D {{{9, 8, 7}}, {{6, 5}}}
\def \E {{9, 8, 7}, {6, 5}}
\def \F {9, 8, 7}
\def \tests#1#2#3
{
\begingroup
\edef \depth {3.0}
\edef \olddepth {#3}
\def \arecurse {0}
\def \brecurse {0}
\def \crecurse {0}
\def \drecurse {0}
\pgfmathparse{\olddepth + 1}
\edef\newdepth{\pgfmathresult}
\ifthenelse{\equal{\newdepth}{\depth}}{}
{
\message{input (#1):}
\message{#2 ^^J}
%% a
\message{ foreach (#1+a):}
\foreach \x in #2
{
\xdef \aa {\x}
\message{\aa ^^J}
\breakforeach
}
%% b
\message{ pgfmatharray (#1+b):}
\pgfmatharray{#2}{0}
\edef \bb {\pgfmathresult}
\message{\bb ^^J}
%% c
\message{ pgfmathparse + index (#1+c):}
\ifthenelse{\equal{#1}{Ba} \or
\equal{#1}{Da} \or
\equal{#1}{F}}
{
\def \crecurse {1}
\message{Error ^^J}
}{
\pgfmathparse{#2[0]}
\edef \cc {\pgfmathresult}
\message{\cc ^^J}
}
%% d
\message{ pgfmathparse + array (#1+d):}
\ifthenelse{\equal{#1}{Ad} \or
\equal{#1}{Ba} \or
\equal{#1}{Bd} \or
\equal{#1}{D} \or
\equal{#1}{Da} \or
\equal{#1}{E} \or
\equal{#1}{F}}
{
\def \drecurse {1}
\message{Error ^^J}
}{
\pgfmathparse{array(#2, 0)}
\edef \dd {\pgfmathresult}
\message{\dd ^^J}
}
\ifthenelse{\arecurse = 0}{\tests{#1a}{\aa}{\newdepth}}{}
\ifthenelse{\brecurse = 0}{\tests{#1b}{\bb}{\newdepth}}{}
\ifthenelse{\crecurse = 0}{\tests{#1c}{\cc}{\newdepth}}{}
\ifthenelse{\drecurse = 0}{\tests{#1d}{\dd}{\newdepth}}{}
}
\endgroup
}
\tests{A}{\A}{0.0}
\tests{B}{\B}{0.0}
\tests{C}{\C}{0.0}
\tests{D}{\D}{0.0}
\tests{E}{\E}{0.0}
\tests{F}{\F}{0.0}
\end{tikzpicture}
\end{document}
In output, the performed operations can be deduced from the string inside parentheses. For example (Aa+b) or (Aab) means using input A:{{{{9, 8, 7}}, {{6, 5}}}} to /foreach to select the first item followed by \pgfmatharray to select the first item. Some combinations will produce an error so they are skipped by \ifthenelse for the code to complete.
There are some interesting results. Some of the inputs, I know, are abominable, but curiosity makes me ask why the particular things produce the outputs?
foreach works quite consistently
input: foreach:
(A): {{{9, 8, 7}}, {{6, 5}}} (A+a): {{9, 8, 7}}, {{6, 5}}
(Aa): {{9, 8, 7}}, {{6, 5}} (Aa+a): {9, 8, 7}
(Ab): {9}{8}{7} (Ab+a): {9}{8}{7}
(Ac): {{9}{8}{7}} (Ac+a): {9}{8}{7}
(Ad): {9}{8}{7} (Ad+a): {9}{8}{7}
(B): {{9, 8, 7}, {6, 5}} (B+a): {9, 8, 7}, {6, 5}
(Ba): {9, 8, 7}, {6, 5} (Ba+a): 9, 8, 7
(Bb): {9}{8}{7} (Bb+a): {9}{8}{7}
(Bc): {{9}{8}{7}} (Bc+a): {9}{8}{7}
(Bd): {9}{8}{7} (Bd+a): {9}{8}{7}
(C): {9, 8, 7} (C+a): 9, 8, 7
(Ca): 9, 8, 7 (Ca+a): 9
(Cb): 9 (Cb+a): 9
(Cc): 9 (Cc+a): 9
(Cd): 9 (Cd+a): 9
(D): {{9, 8, 7}}, {{6, 5}} (D+a): {9, 8, 7}
(Da): {9, 8, 7} (Da+a): 9, 8, 7
(Db): {9}{8}{7} (Db+a): {9}{8}{7}
(Dc): {{9}{8}{7}}{{6}{5}} (Dc+a): {{9}{8}{7}}{{6}{5}}
(E): {9, 8, 7}, {6, 5} (E+a): 9, 8, 7
(Ea): 9, 8, 7 (Ea+a): 9
(Eb): {9}{8}{7} (Eb+a): {9}{8}{7}
(Ec): {{9}{8}{7}}{6} (Ec+a): {{9}{8}{7}}{6}
(F): 9, 8, 7 (F+a): 9
(Fa): 9 (Fa+a): 9
(Fb): 9 (Fb+a): 9
There is a definite difference between pgfmath* workings. pgfmatharray and pgfmathparse + array are clearly close to each other. The latter just seems to choke every once a while so the former is preferred.
pgfmathparse + index is clearly the odd one out. It seems somewhat inconsistent, for example the case of (E+c).
The cases where the result is 5,6, or 7 are interesting. Why return the last element if return anything at all when trying to access the first one? It looks like the macro parses the input and just returns the last item that is left.
Why the difference between the pgfmath* versions at all?
The interesting question is which one to use? They obviously return different things even with sane input.
input: pgfmatharray: pgfmathparse + array: pgfmathparse + index:
(A): {{{9, 8, 7}}, {{6, 5}}} (A+b): {9}{8}{7} (A+d): {9}{8}{7} (A+c): {{9}{8}{7}}
(Aa): {{9, 8, 7}}, {{6, 5}} (Aa+b): 9 (Aa+d): 9 (Aa+c): 9
(Ab): {9}{8}{7} (Ab+b): 7 (Ab+d): 7 (Ab+c): 7
(Ac): {{9}{8}{7}} (Ac+b): 7 (Ac+d): 7 (Ac+c): 7
(Ad): {9}{8}{7} (Ad+b): 7 (Ad+d): Error (Ad+c): 7
(B): {{9, 8, 7}, {6, 5}} (B+b): {9}{8}{7} (B+d): {9}{8}{7} (B+c): {{9}{8}{7}}
(Ba): {9, 8, 7}, {6, 5} (Ba+b): 9 (Ba+d): Error (Ba+c): Error
(Bb): {9}{8}{7} (Bb+b): 7 (Bb+d): 7 (Bb+c): 7
(Bc): {{9}{8}{7}} (Bc+b): 7 (Bc+d): 7 (Bc+c): 7
(Bd): {9}{8}{7} (Bd+b): 7 (Bd+d): Error (Bd+c): 7
(C): {9, 8, 7} (C+b): 9 (C+d): 9 (C+c): 9
(Ca): 9, 8, 7 (Ca+b): 9 (Ca+d): 9 (Ca+c): 9
(Cb): 9 (Cb+b): 9 (Cb+d): 9 (Cb+c): 9
(Cc): 9 (Cc+b): 9 (Cc+d): 9 (Cc+c): 9
(Cd): 9 (Cd+b): 9 (Cd+d): 9 (Cd+c): 9
(D): {{9, 8, 7}}, {{6, 5}} (D+b): {9}{8}{7} (D+d): Error (D+c): {{9}{8}{7}}{{6}{5}}
(Da): {9, 8, 7} (Da+b): 9 (Da+d): Error (Da+c): Error
(Db): {9}{8}{7} (Db+b): 7 (Db+d): 7 (Db+c): 7
(Dc): {{9}{8}{7}}{{6}{5}} (Dc+b): 5 (Dc+d): 5 (Dc+c): 5
(E): {9, 8, 7}, {6, 5} (E+b): {9}{8}{7} (E+d): Error (E+c): {{9}{8}{7}}{6}
(Ea): 9, 8, 7 (Ea+b): 9 (Ea+d): 9 (Ea+c): 9
(Eb): {9}{8}{7} (Eb+b): 7 (Eb+d): 7 (Eb+c): 7
(Ec): {{9}{8}{7}}{6} (Ec+b): 6 (Ec+d): 6 (Ec+c): 6
(F): 9, 8, 7 (F+b): 9 (F+d): Error (F+c): Error
(Fa): 9 (Fa+b): 9 (Fa+d): 9 (Fa+c): 9
(Fb): 9 (Fb+b): 9 (Fb+d): 9 (Fb+c): 9
Same input should give same results. When input is sorted these stand out. There is something going on there.
input: pgfmatharray: pgfmathparse + array: pgfmathparse + index:
(Ca): 9, 8, 7 (Ca+b): 9 (Ca+d): 9 (Ca+c): 9
(Ea): 9, 8, 7 (Ea+b): 9 (Ea+d): 9 (Ea+c): 9
(F): 9, 8, 7 (F+b): 9 (F+d): Error (F+c): Error
(C): {9, 8, 7} (C+b): 9 (C+d): 9 (C+c): 9
(Da): {9, 8, 7} (Da+b): 9 (Da+d): Error (Da+c): Error
(Ba): {9, 8, 7}, {6, 5} (Ba+b): 9 (Ba+d): Error (Ba+c): Error
(E): {9, 8, 7}, {6, 5} (E+b): {9}{8}{7} (E+d): Error (E+c): {{9}{8}{7}}{6}
(Ab): {9}{8}{7} (Ab+b): 7 (Ab+d): 7 (Ab+c): 7
(Bb): {9}{8}{7} (Bb+b): 7 (Bb+d): 7 (Bb+c): 7
(Db): {9}{8}{7} (Db+b): 7 (Db+d): 7 (Db+c): 7
(Eb): {9}{8}{7} (Eb+b): 7 (Eb+d): 7 (Eb+c): 7
(Ad): {9}{8}{7} (Ad+b): 7 (Ad+d): Error (Ad+c): 7
(Bd): {9}{8}{7} (Bd+b): 7 (Bd+d): Error (Bd+c): 7
(Aa): {{9, 8, 7}}, {{6, 5}} (Aa+b): 9 (Aa+d): 9 (Aa+c): 9
(D): {{9, 8, 7}}, {{6, 5}} (D+b): {9}{8}{7} (D+d): Error (D+c): {{9}{8}{7}}{{6}{5}}
(Ec): {{9}{8}{7}}{6} (Ec+b): 6 (Ec+d): 6 (Ec+c): 6
(Eca): {{9}{8}{7}}{6} (Eca+b): 6 (Eca+d): Error (Eca+c): 6
The original output
input (A): {{{9, 8, 7}}, {{6, 5}}}
foreach (A+a): {{9, 8, 7}}, {{6, 5}}
pgfmatharray (A+b): {9}{8}{7}
pgfmathparse + index (A+c): {{9}{8}{7}}
pgfmathparse + array (A+d): {9}{8}{7}
input (Aa): {{9, 8, 7}}, {{6, 5}}
foreach (Aa+a): {9, 8, 7}
pgfmatharray (Aa+b): 9
pgfmathparse + index (Aa+c): 9
pgfmathparse + array (Aa+d): 9
input (Ab): {9}{8}{7}
foreach (Ab+a): {9}{8}{7}
pgfmatharray (Ab+b): 7 % 1. Why last?
pgfmathparse + index (Ab+c): 7 % 1. Why last?
pgfmathparse + array (Ab+d): 7 % 1. Why last?
input (Ac): {{9}{8}{7}}
foreach (Ac+a): {9}{8}{7}
pgfmatharray (Ac+b): 7 % 1. Why last?
pgfmathparse + index (Ac+c): 7 % 1. Why last?
pgfmathparse + array (Ac+d): 7 % 1. Why last?
input (Ad): {9}{8}{7}
foreach (Ad+a): {9}{8}{7}
pgfmatharray (Ad+b): 7 % 1. Why last?
pgfmathparse + index (Ad+c): 7 % 1. Why last?
pgfmathparse + array (Ad+d): Error % 2. Why differ from (Ab+d)?
input (B): {{9, 8, 7}, {6, 5}}
foreach (B+a): {9, 8, 7}, {6, 5}
pgfmatharray (B+b): {9}{8}{7}
pgfmathparse + index (B+c): {{9}{8}{7}}
pgfmathparse + array (B+d): {9}{8}{7}
input (Ba): {9, 8, 7}, {6, 5}
foreach (Ba+a): 9, 8, 7
pgfmatharray (Ba+b): 9
pgfmathparse + index (Ba+c): Error
pgfmathparse + array (Ba+d): Error
input (Bb): {9}{8}{7}
foreach (Bb+a): {9}{8}{7}
pgfmatharray (Bb+b): 7 % 1. Why last?
pgfmathparse + index (Bb+c): 7 % 1. Why last?
pgfmathparse + array (Bb+d): 7 % 1. Why last?
input (Bc): {{9}{8}{7}}
foreach (Bc+a): {9}{8}{7}
pgfmatharray (Bc+b): 7 % 1. Why last?
pgfmathparse + index (Bc+c): 7 % 1. Why last?
pgfmathparse + array (Bc+d): 7 % 1. Why last?
input (Bd): {9}{8}{7}
foreach (Bd+a): {9}{8}{7}
pgfmatharray (Bd+b): 7 % 1. Why last?
pgfmathparse + index (Bd+c): 7 % 1. Why last?
pgfmathparse + array (Bd+d): Error % 2. Why differ from (Bb+d)?
input (C): {9, 8, 7}
foreach (C+a): 9, 8, 7
pgfmatharray (C+b): 9
pgfmathparse + index (C+c): 9
pgfmathparse + array (C+d): 9
input (Ca): 9, 8, 7
foreach (Ca+a): 9
pgfmatharray (Ca+b): 9
pgfmathparse + index (Ca+c): 9
pgfmathparse + array (Ca+d): 9
input (Cb): 9
foreach (Cb+a): 9
pgfmatharray (Cb+b): 9
pgfmathparse + index (Cb+c): 9
pgfmathparse + array (Cb+d): 9
input (Cc): 9
foreach (Cc+a): 9
pgfmatharray (Cc+b): 9
pgfmathparse + index (Cc+c): 9
pgfmathparse + array (Cc+d): 9
input (Cd): 9
foreach (Cd+a): 9
pgfmatharray (Cd+b): 9
pgfmathparse + index (Cd+c): 9
pgfmathparse + array (Cd+d): 9
input (D): {{9, 8, 7}}, {{6, 5}}
foreach (D+a): {9, 8, 7}
pgfmatharray (D+b): {9}{8}{7}
pgfmathparse + index (D+c): {{9}{8}{7}}{{6}{5}}
pgfmathparse + array (D+d): Error % 3. Why differ from (D+c)?
input (Da): {9, 8, 7}
foreach (Da+a): 9, 8, 7
pgfmatharray (Da+b): 9
pgfmathparse + index (Da+c): Error
pgfmathparse + array (Da+d): Error
input (Db): {9}{8}{7}
foreach (Db+a): {9}{8}{7}
pgfmatharray (Db+b): 7 % 1. Why last?
pgfmathparse + index (Db+c): 7 % 1. Why last?
pgfmathparse + array (Db+d): 7 % 1. Why last?
input (Dc): {{9}{8}{7}}{{6}{5}}
foreach (Dc+a): {{9}{8}{7}}{{6}{5}}
pgfmatharray (Dc+b): 5 % 1. Why last?
pgfmathparse + index (Dc+c): 5 % 1. Why last?
pgfmathparse + array (Dc+d): 5 % 1. Why last?
input (E): {9, 8, 7}, {6, 5}
foreach (E+a): 9, 8, 7
pgfmatharray (E+b): {9}{8}{7}
pgfmathparse + index (E+c): {{9}{8}{7}}{6} % 4. Strange. Why?
pgfmathparse + array (E+d): Error % 3. Why differ from (E+c)?
input (Ea): 9, 8, 7
foreach (Ea+a): 9
pgfmatharray (Ea+b): 9
pgfmathparse + index (Ea+c): 9
pgfmathparse + array (Ea+d): 9
input (Eb): {9}{8}{7}
foreach (Eb+a): {9}{8}{7}
pgfmatharray (Eb+b): 7 % 1. Why last?
pgfmathparse + index (Eb+c): 7 % 1. Why last?
pgfmathparse + array (Eb+d): 7 % 1. Why last?
input (Ec): {{9}{8}{7}}{6}
foreach (Ec+a): {{9}{8}{7}}{6}
pgfmatharray (Ec+b): 6 % 1. Why last?
pgfmathparse + index (Ec+c): 6 % 1. Why last?
pgfmathparse + array (Ec+d): 6 % 1. Why last?
input (F): 9, 8, 7
foreach (F+a): 9
pgfmatharray (F+b): 9
pgfmathparse + index (F+c): Error
pgfmathparse + array (F+d): Error
input (Fa): 9
foreach (Fa+a): 9
pgfmatharray (Fa+b): 9
pgfmathparse + index (Fa+c): 9
pgfmathparse + array (Fa+d): 9
input (Fb): 9
foreach (Fb+a): 9
pgfmatharray (Fb+b): 9
pgfmathparse + index (Fb+c): 9
pgfmathparse + array (Fb+d): 9
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