# Vector Dot Product (dotprod)

This module provides interfaces for computing a vector dot product between two equally-sized vectors. Dot products are commonly used in digital signal processing for communications, particularly in filtering and matrix operations. Given two vectors of equal length $$\vec{x} = \left[x(0),x(1),\ldots,x(N-1)\right]^T$$ and $$\vec{v} = \left[v(0),v(1),\ldots,v(N-1)\right]^T$$ , the vector dot product between them is computed as

$$\vec{x} \cdot \vec{v} = \vec{x}^T \vec{v} = \sum_{k=0}^{N-1}{ x(k) v(k) }$$

A number of other liquid modules rely on dotprod , such as filtering and equalization.

## Specific machine architectures

The vector dot product has a complexity of $$\ord(N)$$ multiply-and-accumulate operations. Because of its prevalence in multimedia applications, a considerable amount of research has been put into computing the vector dot product as efficiently as possible. Software-defined radio is no exception as basic profiling will likely demonstrate that a considerable portion of the processor is spent computing it. Certain machine architectures have specific instructions for computing vector dot products, particularly those which use a single instruction for multiple data (SIMD) such as MMX, SSE, AltiVec, etc.

## Interface

There are effectively two ways to use the dotprod module. In the first and most general case, a vector dot product is computed on two input vectors $$\vec{x}$$ and $$\vec{v}$$ whose values are not known a priori . In the second case, a dotprod object is created around vector $$\vec{v}$$ which does not change (or rarely changes) throughout its life cycle. This is the more convenient method for filtering objects which don't usually have time-dependent coefficients. Listed below is a simple interface example to the dotprod module object:


#include <liquid/liquid.h>

int main() {
// create input arrays
float x[] = { 1.0f,  2.0f,  3.0f,  4.0f,  5.0f};
float v[] = { 0.1f, -0.2f,  1.0f, -0.2f,  0.1f};
float y;

// run the basic vector dot product, store in 'y'
dotprod_rrrf_run(x,v,5,&y);

// create dotprod object and execute, store in 'y'
dotprod_rrrf q = dotprod_rrrf_create(v,5);
dotprod_rrrf_execute(q,x,&y);
dotprod_rrrf_destroy(q);
}



In both cases the dotprod can be easily integrated with the window object ( [section-buffer-window] ) for managing input data and alignment. There are three types of dot product objects and are listed in [tab-dotprod-objects] .


.. table [tab-dotprod-objects]
caption:dotprod object types
_precision_ & _input/output_    & _coefficients_    &  _interface_
_float_     & real              & real              & dotprod_rrrf
_float_     & complex           & complex           & dotprod_cccf
_float_     & complex           & real              & dotprod_crcf


Listed below is a brief description of the dotprod object interfaces. While the types are described using the dotprod_rrrf object, the same holds true for all other types.

• dotprod_rrrf_run(h,x,n,y) executes a vector dot product between two vectors $$\vec{h}$$ and $$\vec{x}$$ , each of length $$n$$ and stores the result in the output $$y$$ . This is not a structured method and does not require creating a dotprod object, however does not take advantage of SIMD instructions if available. Rather than speed, its intent is to provide a simple interface to demonstrate functional correctness.
• dotprod_rrrf_create(v,n) creates a dotprod object with coefficients $$\vec{v}$$ of length $$n$$ .
• dotprod_rrrf_recreate(q,v,n) recreates a dotprod object with a new set of coefficients $$\vec{v}$$ with a (possibly) different length $$n$$ .
• dotprod_rrrf_destroy(q) destroys a dotprod object, freeing all internally-allocated memory.
• dotprod_rrrf_print(q) prints the object internals to the screen.
• dotprod_rrrf_execute(q,x,y) executes a dot product with an input vector $$\vec{x}$$ and stores the result in $$y$$ .