tame/core/vector/fold.xml

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<?xml version="1.0"?>
<!--
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
under the terms of the GNU General Public License as
published by the Free Software Foundation, either version 3 of the
License, or (at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program. If not, see <http://www.gnu.org/licenses/>.
-->
<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>