tame/core/vector/arithmetic.xml

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<?xml version="1.0" encoding="utf-8"?>
<!--
Copyright (C) 2014-2023 Ryan 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="Vector arithmetic">
<import package="../base" />
<import package="../numeric/common" />
<import package="../numeric/minmax" />
<import package="list" />
<section title="Vectors">
<!-- for the time being, the vectors must be of the same length, or the first
vector must be the longer (otherwise the values will not properly add)
-->
<template name="_vadd_" desc="Produce a vector resulting from the addition of two vectors">
<param name="@a@" desc="First vector to add" />
<param name="@b@" desc="Second vector to add" />
<param name="@into@" desc="Variable to yield vector into" />
<param name="@yields@" desc="Value to yield (useless)">
<text>__</text>
<param-value name="@into@" />
</param>
<param name="@gendesc@" desc="Generator description (for @into@)">
<text>Sum of vectors </text>
<param-value name="@a@" />
<text> and </text>
<param-value name="@b@" />
</param>
<param name="@sym@" desc="Generator symbol">
<!-- empty by default -->
<text></text>
</param>
<rate yields="@yields@">
<c:sum of="@a@" index="k" generates="@into@" desc="@gendesc@" sym="@sym@">
<c:value-of name="@a@" index="k" />
<c:value-of name="@b@" index="k" />
</c:sum>
</rate>
</template>
<template name="_vsum_" desc="Yield sum of all elements of a vector as a scalar">
<param name="@of@" desc="Vector to sum" />
<param name="@yields@" desc="Name of scalar to yield" />
<rate yields="@yields@">
<c:sum of="@of@" />
</rate>
</template>
\ref{_vproduct_} produces the product of two vectors:
$V_k = A_k B_k$.
<template name="_vproduct_"
desc="Vector product">
<param name="@vector_a@" desc="First vector" />
<param name="@vector_b@" desc="Second vector" />
<c:apply name="_vproduct"
vector_a="@vector_a@"
vector_b="@vector_b@" />
</template>
\ref{_vproduct} is its helper function for recursion.
<function name="_vproduct"
desc="Vector product">
<param name="vector_a" type="float" set="vector"
desc="First vector" />
<param name="vector_b" type="float" set="vector"
desc="Second vector" />
<param name="k" type="integer"
desc="Current index" />
<t:cons-until-empty set="vector_a" index="k" car="value_a">
<c:product>
<c:value-of name="value_a" />
<!-- TODO: TAME bug where index variables always compile to args -->
<c:value-of name="vector_b">
<c:index>
<c:value-of name="k" />
</c:index>
</c:value-of>
</c:product>
</t:cons-until-empty>
</function>
</section>
<section title="Matrices">
\ref{_mproduct_} produces the product of two matrices:
$M_{ij} = A_{ij} B_{ij}$.
<template name="_mproduct_"
desc="Matrix product">
<param name="@matrix_a@" desc="First matrix" />
<param name="@matrix_b@" desc="Second matrix" />
<c:apply name="_mproduct"
matrix_a="@matrix_a@"
matrix_b="@matrix_b@"
k="ZERO" />
</template>
\ref{_mproduct} is its helper function for recursion.
\ref{_vproduct_} is used to reduce the problem to the product of
and array of~vectors.
<function name="_mproduct"
desc="Matrix product">
<param name="matrix_a" type="float" set="matrix"
desc="First matrix" />
<param name="matrix_b" type="float" set="matrix"
desc="Second matrix" />
<param name="k" type="integer"
desc="Current index" />
<t:cons-until-empty set="matrix_a" index="k" car="vector_a">
<c:let>
<c:values>
<c:value name="vector_b" type="float" set="vector"
desc="Second vector">
<c:value-of name="matrix_b">
<c:index>
<c:value-of name="k" />
</c:index>
</c:value-of>
</c:value>
</c:values>
<t:vproduct vector_a="vector_a"
vector_b="vector_b" />
</c:let>
</t:cons-until-empty>
</function>
</section>
</package>