Public Member Functions | List of all members
STDMD Class Reference

Streaming Total Dynamic Mode Decomposition (i.e. STDMD) is a variant of dynamic mode decomposition. More...

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Public Member Functions

 TypeName ("STDMD")
 
 STDMD (const fvMesh &mesh, const word &name, const dictionary &dict)
 
 STDMD (const STDMD &)=delete
 
void operator= (const STDMD &)=delete
 
virtual ~STDMD ()=default
 
virtual bool initialise (const RMatrix &z)
 
virtual bool update (const RMatrix &z)
 
virtual bool fit ()
 
virtual bool read (const dictionary &dict)
 
- Public Member Functions inherited from DMDModel
 TypeName ("DMDModel")
 
 declareRunTimeSelectionTable (autoPtr, DMDModel, dictionary,(const fvMesh &mesh, const word &name, const dictionary &dict),(mesh, name, dict))
 
 DMDModel (const fvMesh &mesh, const word &name, const dictionary &dict)
 
 DMDModel (const DMDModel &)=delete
 
void operator= (const DMDModel &)=delete
 
virtual ~DMDModel ()=default
 
virtual void reconstruct (const wordList modes)
 
label nComponents (const word &fieldName) const
 
template<class Type >
bool nComponents (const word &fieldName, label &nComps) const
 
- Public Member Functions inherited from writeFile
 writeFile (const objectRegistry &obr, const fileName &prefix, const word &name="undefined", const bool writeToFile=true)
 
 writeFile (const objectRegistry &obr, const fileName &prefix, const word &name, const dictionary &dict, const bool writeToFile=true)
 
 writeFile (const writeFile &wf)
 
virtual ~writeFile ()=default
 
virtual OFstream & file ()
 
virtual bool writeToFile () const
 
virtual bool canWriteHeader () const
 
virtual label charWidth () const
 
virtual void writeCommented (Ostream &os, const string &str) const
 
virtual void writeTabbed (Ostream &os, const string &str) const
 
virtual void writeHeader (Ostream &os, const string &str) const
 
virtual void writeCurrentTime (Ostream &os) const
 
virtual void writeBreak (Ostream &os) const
 
template<class Type >
void writeHeaderValue (Ostream &os, const string &property, const Type &value) const
 

Additional Inherited Members

- Static Public Member Functions inherited from DMDModel
static autoPtr< DMDModel > New (const fvMesh &mesh, const word &name, const dictionary &dict)
 
- Static Public Attributes inherited from writeFile
static label addChars = 8
 
- Protected Member Functions inherited from writeFile
void initStream (Ostream &os) const
 
fileName baseFileDir () const
 
fileName baseTimeDir () const
 
virtual autoPtr< OFstream > createFile (const word &name, scalar timeValue) const
 
virtual autoPtr< OFstream > createFile (const word &name) const
 
virtual void resetFile (const word &name)
 
Omanip< int > valueWidth (const label offset=0) const
 
void operator= (const writeFile &)=delete
 
- Protected Attributes inherited from DMDModel
const fvMesh & mesh_
 
const word name_
 
- Protected Attributes inherited from writeFile
const objectRegistry & fileObr_
 
const fileName prefix_
 
word fileName_
 
autoPtr< OFstream > filePtr_
 
label writePrecision_
 
bool writeToFile_
 
bool updateHeader_
 
bool writtenHeader_
 
bool useUserTime_
 
scalar startTime_
 

Detailed Description

Streaming Total Dynamic Mode Decomposition (i.e. STDMD) is a variant of dynamic mode decomposition.

Among other Dynamic Mode Decomposition (DMD) variants, STDMD is presumed to provide the general DMD method capabilities alongside economised and feasible memory and CPU usage.

The code implementation corresponds to Figs. 15-16 of the first citation below, more broadly to Section 2.4.

References: 

    DMD and mode-sorting algorithms (tags:K, HRDC, KZ, HWR):
        Kiewat, M. (2019).
        Streaming modal decomposition approaches for vehicle aerodynamics.
        PhD thesis. Munich: Technical University of Munich.
        URL:mediatum.ub.tum.de/doc/1482652/1482652.pdf

        Hemati, M. S., Rowley, C. W.,
        Deem, E. A., & Cattafesta, L. N. (2017).
        De-biasing the dynamic mode decomposition
        for applied Koopman spectral analysis of noisy datasets.
        Theoretical and Computational Fluid Dynamics, 31(4), 349-368.
        DOI:10.1007/s00162-017-0432-2

        Kou, J., & Zhang, W. (2017).
        An improved criterion to select
        dominant modes from dynamic mode decomposition.
        European Journal of Mechanics-B/Fluids, 62, 109-129.
        DOI:10.1016/j.euromechflu.2016.11.015

        Hemati, M. S., Williams, M. O., & Rowley, C. W. (2014).
        Dynamic mode decomposition for large and streaming datasets.
        Physics of Fluids, 26(11), 111701.
        DOI:10.1063/1.4901016

    Parallel classical Gram-Schmidt process (tag:Ka):
        Katagiri, T. (2003).
        Performance evaluation of parallel
        Gram-Schmidt re-orthogonalization methods.
        In: Palma J. M. L. M., Sousa A. A., Dongarra J., Hernández V. (eds)
        High Performance Computing for Computational Science — VECPAR 2002.
        Lecture Notes in Computer Science, vol 2565, p. 302-314.
        Berlin, Heidelberg: Springer.
        DOI:10.1007/3-540-36569-9_19

    Parallel direct tall-skinny QR decomposition (tags:BGD, DGHL):
        Benson, A. R., Gleich, D. F., & Demmel, J. (2013).
        Direct QR factorizations for
        tall-and-skinny matrices in MapReduce architectures.
        2013 IEEE International Conference on Big Data.
        DOI:10.1109/bigdata.2013.6691583

        Demmel, J., Grigori, L., Hoemmen, M., & Langou, J. (2012).
        Communication-optimal parallel
        and sequential QR and LU factorizations.
        SIAM Journal on Scientific Computing, 34(1), A206-A239.
        DOI:10.1137/080731992
Usage
Minimal example by using system/controlDict.functions: 
DMD1
{
    // Mandatory/Optional entries
    ...

    // Mandatory entries (unmodifiable)
    DMDModel            STDMD;

    // Conditional mandatory entries (runtime modifiable)

        // Option-1
        interval            5.5;

        // Option-2
        executeInterval     10;

    // Optional entries (runtime modifiable)
    modeSorter          kiewat;
    nGramSchmidt        5;
    maxRank             50;
    nModes              50;
    fMin                0;
    fMax                1000000000;
    nAgglomerationProcs 20;

    // Optional entries (runtime modifiable, yet not recommended)
    minBasis            0.00000001;
    minEVal             0.00000001;
    sortLimiter         500.0;

    // Mandatory/Optional (inherited) entries
    ...
}

where the entries mean:

Property Description Type Reqd Deflt
DMDModel Type: STDMD word yes -
interval STDMD time-step size [s] scalar cndtnl executeInterval*(current time-step of the simulation)
modeSorter Mode-sorting algorithm model word no firstSnapshot
nModes Number of output modes in input frequency range label no GREAT
maxRank Max columns in accumulated matrices label no GREAT
nGramSchmidt Number of Gram-Schmidt iterations label no 5
fMin Min (non-negative) output frequency label no 0
fMax Max output frequency label no GREAT
nAgglomerationProcs Number of processors at each agglomeration unit during the computation of reduced Koopman operator label no 20
minBasis Orthogonal basis expansion threshold scalar no 1e-8
minEVal Min eigenvalue for below eigenvalues are omitted scalar no 1e-8
sortLimiter Max allowable magnitude for mag(eigenvalue)*(number of DMD steps) to be used in modeSorter={kiewat,kouZhang} to avoid overflow errors scalar no 500.0

Options for the modeSorter entry: 

      kiewat        | Modified weighted-amplitude scaling method
      kouZhang      | Weighted-amplitude scaling method
      firstSnapshot | First-snapshot amplitude magnitude method
Note
  • To specify the STDMD time-step size (not necessarily equal to the time step of the simulation), entries of either interval or executeInterval must be available (highest to lowest precedence). While interval allows users to directly specify the STDMD time-step size in seconds, in absence of interval, for convenience, executeInterval allows users to compute the STDMD time-step internally by multiplying itself with the current time-step size of the simulation.
  • Limitation: Restart is currently not available since intermediate writing of STDMD matrices are not supported.
  • Limitation: Non-physical input (e.g. full-zero fields) can upset STDMD.
  • Warning: In modeSorter algorithms of kiewat and kouZhang, a function of $power(x,y)$ exists where x is the magnitude of an eigenvalue, and y is the number of STDMD snapshots. This function poses a risk of overflow errors since, for example, if x ends up above 1.5 with 500 snapshots or more, this function automatically throws the floating point error meaning overflow. Therefore, the domain-range of this function is heuristically constrained by the optional entry sortLimiter which skips the evaluation of this function for a given mag(eigenvalue)*(no. of STDMD steps), i.e. x*y, whose magnitude is larger than sortLimiter.
See also
Source files

Definition at line 302 of file STDMD.H.

Constructor & Destructor Documentation

◆ STDMD() [1/2]

STDMD ( const fvMesh &  mesh,
const word &  name,
const dictionary &  dict 
)

Definition at line 730 of file STDMD.C.

◆ STDMD() [2/2]

STDMD ( const STDMD &  )
delete

◆ ~STDMD()

virtual ~STDMD ( )
virtualdefault

Member Function Documentation

◆ TypeName()

TypeName ( "STDMD"  )

◆ operator=()

void operator= ( const STDMD &  )
delete

◆ initialise()

bool initialise ( const RMatrix &  z)
virtual

Implements DMDModel.

Definition at line 865 of file STDMD.C.

References Matrix::cbegin(), Foam::fileHandler(), Matrix::m(), Foam::mag(), IOobject::NO_READ, IOobject::NO_WRITE, Foam::sqr(), and fileOperation::writeObject().

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◆ update()

bool update ( const RMatrix &  z)
virtual

Implements DMDModel.

Definition at line 921 of file STDMD.C.

References Foam::stringOps::expand(), and Foam::reduce().

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◆ fit()

bool fit ( )
virtual

Implements DMDModel.

Definition at line 958 of file STDMD.C.

References UPstream::master(), and Foam::max().

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◆ read()

bool read ( const dictionary &  dict)
virtual

Implements DMDModel.

Definition at line 778 of file STDMD.C.

References dict, Foam::constant::mathematical::e(), Foam::endl(), MinMax::ge(), Foam::Info, Foam::nl, and Foam::tab.

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The documentation for this class was generated from the following files:

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