329 lines
10 KiB
XML
329 lines
10 KiB
XML
<?xml version="1.0" encoding="utf-8"?>
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<!--
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Copyright (C) 2014-2023 Ryan Specialty, LLC.
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This file is part of tame-core.
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tame-core is free software: you can redistribute it and/or modify it
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under the terms of the GNU General Public License as
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published by the Free Software Foundation, either version 3 of the
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License, or (at your option) any later version.
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This program is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with this program. If not, see <http://www.gnu.org/licenses/>.
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-->
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<package xmlns="http://www.lovullo.com/rater"
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xmlns:c="http://www.lovullo.com/calc"
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xmlns:t="http://www.lovullo.com/rater/apply-template"
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core="true"
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title="Maximum and Minimum Elements">
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<import package="../base" />
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<import package="../when" />
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<import package="../numeric/common" />
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<import package="../numeric/minmax" />
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<section title="Vector Reduction">
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Two types of reductions are provided for minimum and maximum respectively:
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\ref{_minreduce_} and \ref{_maxreduce_}.\footnote{
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This is because TAME does not have first-class functions.}
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They both produce scalar values of the minimums and maximums
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(respectively) of vectors.
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<template name="_minreduce_"
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desc="Reduce a vector to its minimum">
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<param name="@values@" desc="Values to reduce" />
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<param name="@isvector@" desc="Set to 'true' if the nodes should
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not be wrapped in c:vector" />
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<param name="@label@" desc="Application label">
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<!-- default empty -->
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<text></text>
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</param>
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<c:apply name="_minreduce" label="@label@">
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<c:arg name="vector">
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<if name="@isvector@" eq="true">
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<param-copy name="@values@" />
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</if>
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<unless name="@isvector@" eq="true">
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<c:vector>
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<param-copy name="@values@" />
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</c:vector>
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</unless>
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</c:arg>
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</c:apply>
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</template>
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<function name="_minreduce"
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desc="Minimum value in a vector">
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<param name="vector" type="float" set="vector"
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desc="Vector to find minimum of" />
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<c:let>
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<c:values>
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<c:value name="length" type="integer"
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desc="Length of vector">
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<c:length-of>
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<c:value-of name="vector" />
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</c:length-of>
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</c:value>
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</c:values>
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<c:cases>
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<c:case label="Empty vector">
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<t:when-eq name="length" value="#0" />
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<c:value-of name="#0" />
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</c:case>
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<c:case label="Single-element vector">
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<t:when-eq name="length" value="#1" />
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<c:value-of name="vector">
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<c:index>
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<c:value-of name="#0" />
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</c:index>
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</c:value-of>
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</c:case>
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<c:otherwise label="Non-empty vector">
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<c:apply name="min">
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<c:arg name="min1">
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<c:value-of name="vector">
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<c:index>
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<c:value-of name="#0" />
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</c:index>
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</c:value-of>
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</c:arg>
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<c:arg name="min2">
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<c:recurse>
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<c:arg name="vector">
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<c:cdr>
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<c:value-of name="vector" />
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</c:cdr>
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</c:arg>
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</c:recurse>
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</c:arg>
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</c:apply>
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</c:otherwise>
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</c:cases>
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</c:let>
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</function>
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<template name="_maxreduce_"
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desc="Reduce a set to its maximum">
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<param name="@values@" desc="Values to reduce" />
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<param name="@isvector@" desc="Set to 'true' if the nodes should
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not be wrapped in c:vector" />
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<param name="@label@" desc="Application label">
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<!-- default empty -->
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<text></text>
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</param>
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<c:apply name="maxreduce" label="@label@">
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<c:arg name="maxreduce_set">
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<!-- if we were not provided with a vector (default), create
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one out of the given nodes -->
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<unless name="@isvector@" eq="true">
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<c:vector>
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<param-copy name="@values@" />
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</c:vector>
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</unless>
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<!-- if they told us that they have provided a vector, then
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do not create one -->
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<if name="@isvector@" eq="true">
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<param-copy name="@values@" />
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</if>
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</c:arg>
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</c:apply>
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</template>
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\ref{maxreduce} is the~function encapsulated by the template and
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may be applied directly.
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\todo{This function was originally written before TAME supported
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let~expressions and other convenience templates. It has since
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been refactored slightly, but can be made to be more concise.}
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<!-- TODO: rewrite this to be more concise, with the more lisp-like
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recursive strategy of minreduce -->
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<function name="maxreduce" desc="Reduce a set to its maximum">
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<param name="maxreduce_set" type="float" set="vector"
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desc="Set to find max of" />
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<c:let>
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<c:values>
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<c:value name="n" type="integer"
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desc="Length of set to reduce">
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<c:length-of>
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<c:value-of name="maxreduce_set" />
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</c:length-of>
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</c:value>
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</c:values>
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<c:cases>
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<!-- if we have no values to reduce, then simply return 0 -->
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<c:case>
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<c:when name="n">
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<c:eq>
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<c:const value="0"
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desc="When there are no elements" />
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</c:eq>
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</c:when>
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<c:const value="0" desc="No value" />
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</c:case>
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<!-- we have values; perform reduction -->
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<c:otherwise>
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<c:apply name="_maxreduce">
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<c:arg name="_maxreduce_set">
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<c:value-of name="maxreduce_set" />
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</c:arg>
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<c:arg name="_maxreduce_i">
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<t:dec>
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<c:length-of>
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<c:value-of name="maxreduce_set" />
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</c:length-of>
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</t:dec>
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</c:arg>
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</c:apply>
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</c:otherwise>
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</c:cases>
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</c:let>
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</function>
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\ref{_maxreduce} is a~helper function that recursively determines
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the maximum value of the given set. It should not be invoked
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directly; use \ref{maxreduce} or~\ref{_maxreduce_} instead.
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For example, given the vector~\vector{2,4,3,1}, here's the
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recursive application:
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\begingroup
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\def\max{\textrm{max}}
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\begin{equation}
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\max( 1, \max( 3, max( 4, 2 ) ) )
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\\ \yield \max( 1, \max( 3, 4 ) )
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\\ \yield \max( 1, 4 )
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\\ \yield 4
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\end{equation}
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\endgroup
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\todo{If we eventually support first-class functions, then this
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can simply be a~generic reduce function that accepts max/min/etc.}
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\todo{This function was written before local variables generated
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their own unique symbols; strip the prefixes.}
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<function name="_maxreduce"
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desc="Recursively reduce a set to its maximum (called by maxreduce)">
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<param name="_maxreduce_set" type="float" set="vector"
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desc="Set to find max of" />
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<param name="_maxreduce_i" type="integer"
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desc="Index" />
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<c:cases>
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<!-- base case: if we're on the last index, do not recurse -->
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<c:case>
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<c:when name="_maxreduce_i">
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<c:eq>
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<c:const value="0"
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desc="Return when only one element remains" />
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</c:eq>
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</c:when>
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<!-- return the first value -->
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<c:value-of name="_maxreduce_set">
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<c:index>
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<c:const value="0"
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desc="First item in set" />
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</c:index>
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</c:value-of>
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</c:case>
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<!-- we have more elements in the set; recursively determine
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the maximum value -->
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<c:otherwise>
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<c:apply name="max">
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<!-- the first element to compare is our index -->
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<c:arg name="max1">
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<c:value-of name="_maxreduce_set">
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<c:index>
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<c:value-of name="_maxreduce_i" />
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</c:index>
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</c:value-of>
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</c:arg>
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<!-- and we'll compare to the recursive application of the
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same set on the previous index -->
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<c:arg name="max2">
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<c:apply name="_maxreduce">
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<c:arg name="_maxreduce_set">
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<c:value-of name="_maxreduce_set" />
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</c:arg>
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<c:arg name="_maxreduce_i">
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<c:sum>
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<c:value-of name="_maxreduce_i" />
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<c:const value="-1" desc="Decrement index by 1" />
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</c:sum>
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</c:arg>
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</c:apply>
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</c:arg>
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</c:apply>
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</c:otherwise>
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</c:cases>
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</function>
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</section>
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<!-- TODO: Everything below this line must be moved. This
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technically operates on a matrix as well. -->
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<!-- simplifies retrieving the max of a set of values -->
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<template name="_maxOfEach_" desc="Take the max of the given set of values">
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<param name="@class@" desc="Class to match on" />
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<param name="@values@" desc="Individual values without set" />
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<param name="@generates@" desc="Value to generate into" />
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<param name="@index@" desc="Index to use for rate-each" />
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<param name="@yields@" desc="Yield variable">
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<text>_</text>
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<param-value name="@generates@" />
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</param>
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<rate-each class="@class@" yields="@yields@" generates="@generates@" index="@index@">
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<c:apply name="maxreduce">
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<c:arg name="maxreduce_set">
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<c:vector>
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<param-copy name="@values@" />
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</c:vector>
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</c:arg>
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</c:apply>
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</rate-each>
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</template>
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</package>
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