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Einstein summation for MATLAB : Einsum

Authors: Nachar, Stéphane;

Einstein summation for MATLAB : Einsum

Abstract

To reach Moore's law, processor architecture have changed from a high-frequency CPU clock, to core/threads multiplication. This paradigm changement changes the way code must be implemented to unleach simultanously the power of each core with parallelism implementation. Two methods exist to parallize computation : Coarse parallelism and multi-threading. The first one have the ability to use multiple core, the second one prefers using multiple processors in the same core. Multithreading is more common because of multiple core on new processors. In our case, we consider numerical computation commonly used in scientific research. A way to explain some kind of equation is to use Einstein summation notation which was introduced to physics by Albert Einstein in 1916. In computer science, this notation gives also a good paradigm to easily realize some complex computation with multiple tensors like contracting tensors of arbitrary dimension and index. The link with multi-threading is variable broadcasting which allows unleashing multicore power with latest instruction sets. Implementation is already made in Numpy, this article deals with MATLAB implementation.

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
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