vector/arithmetic: Add _{v,m}product_
Products of vectors and matrices respectively. It's surprising that this was unneeded until now based on the requirements of the projects we have done thusfar---dot products and other features have been sufficient. * vector/arithmetic.xml (_vproduct_, _mproduct_): New templates. (_vproduct, _mproduct): New functions.master
parent
24e578c7ae
commit
5000e35891
|
@ -26,9 +26,11 @@
|
||||||
<import package="../base" />
|
<import package="../base" />
|
||||||
<import package="../numeric/common" />
|
<import package="../numeric/common" />
|
||||||
<import package="../numeric/minmax" />
|
<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
|
<!-- 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)
|
vector must be the longer (otherwise the values will not properly add)
|
||||||
-->
|
-->
|
||||||
|
@ -71,5 +73,104 @@
|
||||||
<c:sum of="@of@" />
|
<c:sum of="@of@" />
|
||||||
</rate>
|
</rate>
|
||||||
</template>
|
</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:debug-to-console>
|
||||||
|
<c:value-of name="k" />
|
||||||
|
</c:debug-to-console>
|
||||||
|
</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>
|
</package>
|
||||||
|
|
||||||
|
|
Loading…
Reference in New Issue