Hierarchical Approximate Proper Orthogonal Decomposition
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README.md
hapod.m

README.md

HAPOD - Hierarchical Approximate Proper Orthogonal Decomposition

  • HAPOD - Hierarchical Approximate Proper Orthogonal Decomposition ( http://git.io/hapod )
  • version: 1.2 (2017-20-06)
  • by: Christian Himpe (0000-0003-2194-6754), Stephan Rave (0000-0003-0439-7212)
  • under: BSD 2-Clause License (open-source)
  • summary:

Scope

  • (Truncated) Singular Value Decomposition (SVD)
  • Proper Orthogonal Decomposition (POD)
  • Principal Compoenent Analysis (PCA)
  • Empirical Orthogoanl Functions (EOF)
  • Empirical Eigenfunctions
  • Karhunen Loeve Decomposition
  • Model Reduction | Model Order Redction

Features

  • Standard POD
  • Incremental HAPOD
  • Distributed HAPOD
  • Custom POD backend

Basic Usage

[svec,sval,snfo] = hapod(data,bound,topo,relax,config,mysvd)

Arguments

  • svec {matrix} POD modes (column vectors)
  • sval {vector} Singular values
  • snfo {structure} Information structure

Return Values

  • data {cell array}
  • bound {scalar} L2 projection error bound
  • topo {string} HAPOD graph topology
    • 'none' Standard POD
    • 'incr' Incremental HAPOD
    • 'incr_0' Incremental HAPOD (First node only)
    • 'incr_1' Incremental HAPOD (One intermediary node only)
    • 'incr_r' Incremental HAPOD (Root node only)
    • 'dist' Distributed HAPOD
    • 'dist_0' Distributed HAPOD (First node only)
    • 'dist_1' Distributed HAPOD (One intermediary node only)
    • 'dist_r' Distributed HAPOD (Root node only)
  • relax {scalar} Relaxation parameter in [0,1] by default 0.5.
  • config {structure} Configuration structure by default empty
  • mysvd {handle} Function handle to a custom POD method

Documentation

Information and Configuration Structure

Custom POD Backend

Distributed Memory Parallelization

Cite As

C. Himpe, T. Leibner and S. Rave. "Hierarchical Approximate Proper Orthogonal Decomposition". Preprint, arXiv math.NA: 1607.05210, 2016.