tame/core/vector/minmax.xml

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<?xml version="1.0" encoding="utf-8"?>
<!--
Copyright (C) 2014-2022 Ryan Specialty Group, 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"
title="Maximum and Minimum Elements">
<import package="../base" />
<import package="../when" />
<import package="../numeric/common" />
<import package="../numeric/minmax" />
<section title="Vector Reduction">
Two types of reductions are provided for minimum and maximum respectively:
\ref{_minreduce_} and \ref{_maxreduce_}.\footnote{
This is because TAME does not have first-class functions.}
They both produce scalar values of the minimums and maximums
(respectively) of vectors.
<template name="_minreduce_"
desc="Reduce a vector to its minimum">
<param name="@values@" desc="Values to reduce" />
<param name="@isvector@" desc="Set to 'true' if the nodes should
not be wrapped in c:vector" />
<param name="@label@" desc="Application label">
<!-- default empty -->
<text></text>
</param>
<c:apply name="_minreduce" label="@label@">
<c:arg name="vector">
<if name="@isvector@" eq="true">
<param-copy name="@values@" />
</if>
<unless name="@isvector@" eq="true">
<c:vector>
<param-copy name="@values@" />
</c:vector>
</unless>
</c:arg>
</c:apply>
</template>
<function name="_minreduce"
desc="Minimum value in a vector">
<param name="vector" type="float" set="vector"
desc="Vector to find minimum of" />
<c:let>
<c:values>
<c:value name="length" type="integer"
desc="Length of vector">
<c:length-of>
<c:value-of name="vector" />
</c:length-of>
</c:value>
</c:values>
<c:cases>
<c:case label="Empty vector">
<t:when-eq name="length" value="#0" />
<c:value-of name="#0" />
</c:case>
<c:case label="Single-element vector">
<t:when-eq name="length" value="#1" />
<c:value-of name="vector">
<c:index>
<c:value-of name="#0" />
</c:index>
</c:value-of>
</c:case>
<c:otherwise label="Non-empty vector">
<c:apply name="min">
<c:arg name="min1">
<c:value-of name="vector">
<c:index>
<c:value-of name="#0" />
</c:index>
</c:value-of>
</c:arg>
<c:arg name="min2">
<c:recurse>
<c:arg name="vector">
<c:cdr>
<c:value-of name="vector" />
</c:cdr>
</c:arg>
</c:recurse>
</c:arg>
</c:apply>
</c:otherwise>
</c:cases>
</c:let>
</function>
<template name="_maxreduce_"
desc="Reduce a set to its maximum">
<param name="@values@" desc="Values to reduce" />
<param name="@isvector@" desc="Set to 'true' if the nodes should
not be wrapped in c:vector" />
<param name="@label@" desc="Application label">
<!-- default empty -->
<text></text>
</param>
<c:apply name="maxreduce" label="@label@">
<c:arg name="maxreduce_set">
<!-- if we were not provided with a vector (default), create
one out of the given nodes -->
<unless name="@isvector@" eq="true">
<c:vector>
<param-copy name="@values@" />
</c:vector>
</unless>
<!-- if they told us that they have provided a vector, then
do not create one -->
<if name="@isvector@" eq="true">
<param-copy name="@values@" />
</if>
</c:arg>
</c:apply>
</template>
\ref{maxreduce} is the~function encapsulated by the template and
may be applied directly.
\todo{This function was originally written before TAME supported
let~expressions and other convenience templates. It has since
been refactored slightly, but can be made to be more concise.}
<!-- TODO: rewrite this to be more concise, with the more lisp-like
recursive strategy of minreduce -->
<function name="maxreduce" desc="Reduce a set to its maximum">
<param name="maxreduce_set" type="float" set="vector"
desc="Set to find max of" />
<c:let>
<c:values>
<c:value name="n" type="integer"
desc="Length of set to reduce">
<c:length-of>
<c:value-of name="maxreduce_set" />
</c:length-of>
</c:value>
</c:values>
<c:cases>
<!-- if we have no values to reduce, then simply return 0 -->
<c:case>
<c:when name="n">
<c:eq>
<c:const value="0"
desc="When there are no elements" />
</c:eq>
</c:when>
<c:const value="0" desc="No value" />
</c:case>
<!-- we have values; perform reduction -->
<c:otherwise>
<c:apply name="_maxreduce">
<c:arg name="_maxreduce_set">
<c:value-of name="maxreduce_set" />
</c:arg>
<c:arg name="_maxreduce_i">
<t:dec>
<c:length-of>
<c:value-of name="maxreduce_set" />
</c:length-of>
</t:dec>
</c:arg>
</c:apply>
</c:otherwise>
</c:cases>
</c:let>
</function>
\ref{_maxreduce} is a~helper function that recursively determines
the maximum value of the given set. It should not be invoked
directly; use \ref{maxreduce} or~\ref{_maxreduce_} instead.
For example, given the vector~\vector{2,4,3,1}, here's the
recursive application:
\begingroup
\def\max{\textrm{max}}
\begin{equation}
\max( 1, \max( 3, max( 4, 2 ) ) )
\\ \yield \max( 1, \max( 3, 4 ) )
\\ \yield \max( 1, 4 )
\\ \yield 4
\end{equation}
\endgroup
\todo{If we eventually support first-class functions, then this
can simply be a~generic reduce function that accepts max/min/etc.}
\todo{This function was written before local variables generated
their own unique symbols; strip the prefixes.}
<function name="_maxreduce"
desc="Recursively reduce a set to its maximum (called by maxreduce)">
<param name="_maxreduce_set" type="float" set="vector"
desc="Set to find max of" />
<param name="_maxreduce_i" type="integer"
desc="Index" />
<c:cases>
<!-- base case: if we're on the last index, do not recurse -->
<c:case>
<c:when name="_maxreduce_i">
<c:eq>
<c:const value="0"
desc="Return when only one element remains" />
</c:eq>
</c:when>
<!-- return the first value -->
<c:value-of name="_maxreduce_set">
<c:index>
<c:const value="0"
desc="First item in set" />
</c:index>
</c:value-of>
</c:case>
<!-- we have more elements in the set; recursively determine
the maximum value -->
<c:otherwise>
<c:apply name="max">
<!-- the first element to compare is our index -->
<c:arg name="max1">
<c:value-of name="_maxreduce_set">
<c:index>
<c:value-of name="_maxreduce_i" />
</c:index>
</c:value-of>
</c:arg>
<!-- and we'll compare to the recursive application of the
same set on the previous index -->
<c:arg name="max2">
<c:apply name="_maxreduce">
<c:arg name="_maxreduce_set">
<c:value-of name="_maxreduce_set" />
</c:arg>
<c:arg name="_maxreduce_i">
<c:sum>
<c:value-of name="_maxreduce_i" />
<c:const value="-1" desc="Decrement index by 1" />
</c:sum>
</c:arg>
</c:apply>
</c:arg>
</c:apply>
</c:otherwise>
</c:cases>
</function>
</section>
<!-- TODO: Everything below this line must be moved. This
technically operates on a matrix as well. -->
<!-- simplifies retrieving the max of a set of values -->
<template name="_maxOfEach_" desc="Take the max of the given set of values">
<param name="@class@" desc="Class to match on" />
<param name="@values@" desc="Individual values without set" />
<param name="@generates@" desc="Value to generate into" />
<param name="@index@" desc="Index to use for rate-each" />
<param name="@yields@" desc="Yield variable">
<text>_</text>
<param-value name="@generates@" />
</param>
<rate-each class="@class@" accumulate="none" yields="@yields@" generates="@generates@" index="@index@">
<c:apply name="maxreduce">
<c:arg name="maxreduce_set">
<c:vector>
<param-copy name="@values@" />
</c:vector>
</c:arg>
</c:apply>
</rate-each>
</template>
</package>