Description of algorithm in words

Question

I would like to write an algorithm in a very verbose matter. I want to write a couple of for loops and the rest is pretty much text. I include here the code I am using with algpseudocode imported as follows:

\usepackage[noend]{algpseudocode}
\usepackage{algorithm}

Code for the algorithm:

\begin{algorithm}
  \caption{Backpropagation learning algorithm}
  \begin{algorithmic}
  \For {d in data}
    Forwards Pass \hfill \\
      Starting from the input layer, use eq. \ref{update} to do a forward pass trough the network, computing the activities of the neurons at each layer.
    Backwards Pass \hfill \\
    Compute the derivatives of the error function with respect to the output layer activities
      \For {layer in layers}
        Compute the derivatives of the error function with respect to the inputs of the upper layer neurons
        Compute the derivatives of the error function with respect to the weights between the outer layer and the layer below
        Compute the derivatives of the error function with respect to the activities of the layer below
      \EndFor
      Updates the weights.
\EndFor
\end{algorithmic}

\end{algorithm}

Of course this works, but it is a complete hack and it is rendered horribly. From the documentation of the package, I figure that it is not made to support this.

Am I right? Is there a different package I should use?

Edit: I would like the final output to look something like this:

for e in epochs:
  for d in data:
     Forward pass:
        Starting from the input layer, use eq. \ref{update} to do a forward pass trough the network, computing the activities of the neurons at each layer.
     Backward pass:
          Compute the derivatives of the error function with respect to the output layer activities 
          for layer in layers:
              Compute the derivatives of the error function with respect to the inputs of the upper layer neurons
              Compute the derivatives of the error function with respect to the weights between the outer layer and the layer below
              Compute the derivatives of the error function with respect to the activities of the layer below

          Updates the weights.

Thank you!

Answer 1

You can use the standard algorithmic environment (I suppose you can do the same with algpseudocode, if you insist).

If you want the headers "Forward Pass" and "Backward Pass" to be formatted as you have them in your question, you'll have to provide the extra indentation; I'm defining two extra commands (intended to be nested) for this purpose, using underlined small caps for the header.

\usepackage{algorithmic}
\usepackage{algorithm}

% Define a \HEADER{Title} ... \ENDHEADER block
\makeatletter
\newcommand{\HEADER}[1]{\ALC@it\underline{\textsc{#1}}\begin{ALC@g}}
\newcommand{\ENDHEADER}{\end{ALC@g}}
\makeatother

And then:

\begin{algorithm}
  \caption{Backpropagation learning algorithm}
  \begin{algorithmic}
  \FOR{d in data}
    \HEADER{Forwards Pass}
      \STATE Starting from the input layer, use eq.~\ref{update} to do
      a forward pass trough the network, computing the activities of the
      neurons at each layer.
    \ENDHEADER
    \HEADER{Backwards Pass}
      \STATE Compute the derivatives of the error function with respect
      to the output layer activities
      \FOR{layer in layers}
        \STATE Compute the derivatives of the error function with respect
        to the inputs of the upper layer neurons
        \STATE Compute the derivatives of the error function with respect
        to the weights between the outer layer and the layer below
        \STATE Compute the derivatives of the error function with respect
        to the activities of the layer below
      \ENDFOR
      \STATE Updates the weights.
    \ENDHEADER
  \ENDFOR
\end{algorithmic}
\end{algorithm}

---

UPDATE: If you want the extra indentation mentioned in your comment, you can add a \STATEI command together with \HEADER ... \ENDHEADER in your preamble, and use it instead of \STATE wherever there's more than one line:

% Define a \STATE command with hanging indentation
\newcommand{\STATEI}[1]{\STATE
  \begin{tabular}{@{}p{\dimexpr \textwidth-\labelwidth-\ALC@tlm}@{}}%
    \hangindent \algorithmicindent
    \hangafter 1
    #1
  \end{tabular}
}

then use it like:

\STATEI{Compute the derivatives of the error function with respect
        to the output layer activities.}