# Difference between revisions of "Main Page"

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==Introduction== | ==Introduction== | ||

− | Welcome to LibMIA | + | Welcome to LibMIA. |

+ | |||

+ | LibMIA is a software library designed to make manipulation of multi-indexed arrays (MIAs) easy. Technical computing packages, such as MATLAB, GNU Octave, and SciPy, support matrix algebra, making code look remarkably similar to what a scientist or practitioner would write on paper. However, matrices are not well-suited to work with and operate on MIAs, such as those found in digital imagery. What's needed is a formalism and supporting software designed for MIAs. | ||

+ | |||

+ | ==MIA Formalism== | ||

+ | |||

+ | If you're familiar with Einstein notation, then you already know much of MIA formalism. Nonetheless, there are important differences. | ||

+ | |||

+ | An inner product, <math>c</math>, between two arrays <math>a_{i}</math> and <math>b_{i}</math>, each of dimension <math>n</math>, is the summation of the products of all corresponding elements: | ||

+ | ;<math> | ||

+ | c=\sum_{i=1}^{n}a_{i}b_{i} | ||

+ | </math> |

## Revision as of 21:44, 26 April 2012

## Introduction

Welcome to LibMIA.

LibMIA is a software library designed to make manipulation of multi-indexed arrays (MIAs) easy. Technical computing packages, such as MATLAB, GNU Octave, and SciPy, support matrix algebra, making code look remarkably similar to what a scientist or practitioner would write on paper. However, matrices are not well-suited to work with and operate on MIAs, such as those found in digital imagery. What's needed is a formalism and supporting software designed for MIAs.

## MIA Formalism

If you're familiar with Einstein notation, then you already know much of MIA formalism. Nonetheless, there are important differences.

An inner product, <math>c</math>, between two arrays <math>a_{i}</math> and <math>b_{i}</math>, each of dimension <math>n</math>, is the summation of the products of all corresponding elements:

- <math>

c=\sum_{i=1}^{n}a_{i}b_{i}

</math>