tame/core/vector/fold.xml

<?xml version="1.0"?>
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  Copyright (C) 2018 R-T Specialty, LLC.

  This file is part of tame-core.

  tame-core is free software: you can redistribute it and/or modify it
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-->
<package xmlns="http://www.lovullo.com/rater"
         xmlns:c="http://www.lovullo.com/calc"
         xmlns:t="http://www.lovullo.com/rater/apply-template"
         core="true"
         desc="Folding and Unfolding of Vectors">

  <import package="../base" />
  <import package="filter" export="true" />


  The term ``fold'' is also referred to as ``reduce''---%
    they are synonymous.
  Unless otherwise specified,
    folding occurs left-to-right.

  \emph{Unfolding} is the opposite of a reduction---%
    it \emph{generates} values from existing values.


  <section title="Matrix Folding">
    \ref{_fold-matrix_} folds a matrix into a vector by summing each of
      the~rows.

    <template name="_fold-matrix_"
              desc="Folds matrix into a vector by summing rows">
      <param name="@name@"      desc="Matrix to fold" />
      <param name="@class@"     desc="Iteration vector of desired length" />
      <param name="@generates@" desc="Generator name (to yield)" />

      <param name="@yields@" desc="Yield name">
        <text></text>
      </param>


      <rate-each class="@class@" yields="@yields@"
                 generates="@generates@" index="k">
        <c:let>
          <c:values>
            <c:value name="row" type="float" set="vector"
                     desc="Matrix row">
              <c:value-of name="@name@" index="k" />
            </c:value>
          </c:values>

          <c:sum of="row" />
        </c:let>
      </rate-each>
    </template>
  </section>


  <section title="Matrix Generation">
    \ref{_unfold-vector-grouped_} generates a matrix from a vector---%
      that is, it generates vectors within a vector---%
      by grouping values.

    The \tt{@class@} is used both as a predicate and as a determination of
      the resulting vector's length
        (the~number of rows in the resulting matrix).
    If non-matching,
      no columns will be produced for that respective row.

    \tt{@src@} is the vector to be unfolded,
      containing the raw values to be grouped.

    \tt{@grouping@} \should be the same length as~\ref{@src@} and determines
      the group~(row) in which the respective value should appear.

    \ref{@generates@} names the resulting matrix and~\ref{@desc@} provides
      its description.

    <template name="_unfold-vector-grouped_"
              desc="Unfold vector into a matrix by grouping">
      <param name="@class@"     desc="Iteration vector of desired length" />
      <param name="@src@"       desc="Source vector" />
      <param name="@grouping@"  desc="Grouping vector" />
      <param name="@generates@" desc="Generator name (to yield)" />

      <param name="@desc@" desc="Generator description">
        <text>Unfolded vector </text>
        <param-value name="@src@" />
        <text> grouped by </text>
        <param-value name="@grouping@" />
      </param>

      <param name="@lengthv@" desc="Length vector (of desired length)">
        <param-class-to-yields name="@class@" />
      </param>


      <rate yields="_{@generates@}">
        <c:sum of="@lengthv@" dim="matrix"
               generates="@generates@" index="k"
               desc="@desc@">
          <c:cases>
            <c:case label="Unfold on class vector match">
              <c:when name="@lengthv@" index="k" />
              <c:apply name="vfilter_lookup"
                       vector_pred="@grouping@" vector_src="@src@"
                       value="k"
                       start_index="#0" />
            </c:case>

            <c:otherwise label="Ignore on class vector non-match">
              <c:set />
            </c:otherwise>
          </c:cases>
        </c:sum>
      </rate>
    </template>
  </section>
</package>