tame/core/vector/arithmetic.xml

<?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"
  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 accumulate="none" 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>