Dashed arrows in pb-diagram

Question

I have a commutative diagram written as a diagram environment defined using the package pb-diagram. I'm very satisfied with the appearance of the diagram.

However I need to change some arrows to dashed arrows.

In the pb-diagram manual it is stated that the option for the shaft of an arrow are:

 ..   |  dotted or dashed arrow shaft
 =    |  double line shaft* (“equals sign”)
 !    |  invisible arrow shaft

For instance the command \arrow{e,..} should draw a dotted or dashed arrow shaft.

My question is? How can I make sure that the arrow is dashed instead of dotted? In all examples I tried, the arrow becomes dotted.

I would appreciate any suggestions on how to solve this issue in pb-diagrams. A minimal example is the following.

\documentclass[12pt]{article}
\usepackage{pb-diagram}
\begin{document}
\begin{equation}
\begin{diagram}
\node{A} 
    \arrow{e,t,..}{a} 
    \arrow{s,l,..}{c} 
    \arrow{ese,b,1,..}{u}
\node{B}
    \arrow{e,t,..}{b}
\node{C}
    \arrow{s,r}{d} 
    \arrow{wsw,b,1}{v} \\
\node{D}
    \arrow[2]{e,b}{e} 
\node[2]{H}
\end{diagram}
\end{equation}
\end{document}

All dotted arrows should be dashed arrows.

OBS: I'm aware of the existence of a more advanced package called TikZ, which is more expressive and apparently allows one to have great control of the diagrams. But in this question I'm only interested in how to solve the problem with respect to the package pb-diagram, since the diagram, which is pretty large, is already coded and I just need to add some dashed arrows to finalize it. Additionally, I'm having some trouble to install TikZ on my computer.

Answer 1

Here I found the routine in pb-diagram that placed dots, named \dg@dotvector and made several modifications to it. I replaced the \circle macro that placed each dot with a \rule. However, I needed to have the \rule tilted at the proper angle, so I used \FPdiv and \FParctan and \FPmul to calculate the angle tangent, take the arctangent, and convert to degrees. Then I used \rotatebox to angle the aforementioned \rule to that angle.

EDITED to take advantage of LaRiFaRi's excellent suggestion, thus allowing the simultaneous use of both dot .. and dash -- syntax. In the following MWE, I show both dot and dash lines (and solid lines) in the graph.

\documentclass[12pt]{article}
\usepackage{pb-diagram,fp,graphicx}
\begin{document}
\makeatletter
\@namedef{dgo@--}{\let\dg@VECTOR=\dg@dashvector}% 
\def\dg@dashvector(#1,#2)#3{% 
   \begingroup
   \dg@XTEMP=#1\relax \dg@YTEMP=#2\relax
   \let\dg@NDOTS=\dg@XEND \let\dg@DOTDIAM=\dg@WEND
   % Find number of dots: make x-spacing be DOTSPACING for arrows
   % of |slope| <= 1, and make y-spacing be DOTSPACING otherwise.
   % Thus, true spacing is never more than 30% off from DOTSPACING.
   \dg@NDOTS=\unitlength \multiply\dg@NDOTS #3\relax
   \dg@ZTEMP=\dg@YTEMP \dg@changesign\dg@YTEMP\dg@ZTEMP
   \ifnum\dg@XTEMP>\z@
      \ifnum\dg@YTEMP>\dg@XTEMP
         \multiply\dg@NDOTS\dg@YTEMP \divide\dg@NDOTS\dg@XTEMP \fi
   \else\ifnum\dg@XTEMP<\z@
      \ifnum\dg@YTEMP>-\dg@XTEMP
         \multiply\dg@NDOTS\dg@YTEMP \divide\dg@NDOTS-\dg@XTEMP \fi
   \fi\fi
   \dg@YTEMP=\dg@ZTEMP
   \divide\dg@NDOTS\dgDOTSPACING
   \ifnum\dg@NDOTS>\z@\else \dg@NDOTS=\@ne \fi
   % Compute increment vector between dots; round to \unitlength's.
   % Use NDOTS not DOTSPACING, since DOTSPACING not exactly obeyed.
   \dg@ZTEMP=\unitlength \multiply\dg@ZTEMP #3\relax
   \divide\dg@ZTEMP\dg@NDOTS
   \ifnum\dg@XTEMP=\z@
      \dg@changesign\dg@ZTEMP\dg@YTEMP \dg@YTEMP=\dg@ZTEMP
   \else
      \dg@changesign\dg@ZTEMP\dg@XTEMP
      \multiply\dg@YTEMP\dg@ZTEMP \divide\dg@YTEMP\dg@XTEMP
      \dg@XTEMP=\dg@ZTEMP
   \fi
   \divide\dg@XTEMP\unitlength \divide\dg@YTEMP\unitlength
   % Draw dotted line with \multiput
   % and arrowhead as zero-length \vector
%%% CALCULATE THE ROTATE ANGLE OF THE DASHED LINE
\ifnum\the\dg@XTEMP>0%
  \FPdiv\arang{\the\dg@YTEMP}{\the\dg@XTEMP}%
  \FParctan\arang{\arang}%
  \FPmul\arang{\arang}{57.295}%
\else
  \def\arang{90}%
\fi
%%%%%
   \begin{picture}(0,0)%
      \dg@DOTDIAM=\dgDOTSIZE \divide\dg@DOTDIAM\unitlength
      \multiput(0,0)(\dg@XTEMP,\dg@YTEMP){\dg@NDOTS}{%
%         \circle*{\dg@DOTDIAM}}% REPLACE THIS LINE WITH THE NEXT
         \smash{\rotatebox{\arang}{\rule{2pt}{.5pt}}}}%
      \multiply\dg@XTEMP\dg@NDOTS \multiply\dg@YTEMP\dg@NDOTS
      \put(\dg@XTEMP,\dg@YTEMP){\vector(#1,#2){0}}%
   \end{picture}%
   \endgroup}%
\makeatother
\begin{equation}
\begin{diagram}
\node{A} 
    \arrow{e,t,..}{a} 
    \arrow{s,l,--}{c} 
    \arrow{ese,b,1,--}{u}
\node{B}
    \arrow{e,t,--}{b}
\node{C}
    \arrow{s,r}{d} 
    \arrow{wsw,b,1}{v} \\
\node{D}
    \arrow[2]{e,b}{e} 
\node[2]{H}
\end{diagram}
\end{equation}
\end{document}

For comparison, here is the default behavior of the routine, without modification:

Answer 2

Just in case you change your mind :-)

% arara: pdflatex

\documentclass[12pt]{article}
\usepackage{tikz-cd}

\begin{document}
\begin{equation}
    \begin{tikzcd}[every arrow/.append style={-latex}]
        A
        \arrow[dashed]{r}{a} 
        \arrow[dashed]{d}[swap]{c} 
        \arrow[dashed]{drr}[near start,swap]{u}
        & B
        \arrow[dashed]{r}{b}
        & C
        \arrow{d}{d} 
        \arrow{dll}[near start]{v} \\
        D \arrow{rr}[swap]{e} 
        & 
        & 
        H 
    \end{tikzcd}
\end{equation}
\end{document}