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HAPOD - Hierarchical Approximate Proper Orthogonal Decomposition

  • HAPOD - Hierarchical Approximate POD ( )
  • version: 1.3 ( 2018-02-09 )
  • by: Christian Himpe (0000-0003-2194-6754), Stephan Rave (0000-0003-0439-7212)
  • under: BSD 2-Clause License (open-source)
  • summary: Distributed or incremental POD / SVD computation


  • (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


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

Basic Usage

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


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

Return Values

  • data {cell array}
  • bound {scalar} L2 mean 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


Information and Configuration Structure

  • nSnapshots - Number of data columns passed to this hapod and its children.
  • nModes - Number of intermediate modes
  • tNode - computational time at this hapod's branch

Custom SVD Backend

Signature, arguments and return values as for Matlab's svd function.

Cite As

C. Himpe, T. Leibner and S. Rave. "Hierarchical Approximate Proper Orthogonal Decomposition". Preprint, arXiv math.NA: 1607.05210, 2017.