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>
