(Beta Release) STDMD (i.e. Streaming Total Dynamic Mode Decomposition) is a variant of a data-driven dimensionality reduction method. More...

Inheritance diagram for STDMD:

[legend]

Collaboration diagram for STDMD:

[legend]

Public Member Functions
	TypeName ("STDMD")
	Runtime type information. More...

	STDMD ()=delete
	No default construct. More...

	STDMD (const word &name, const Time &runTime, const dictionary &dict)
	Construct from Time and dictionary. More...

	STDMD (const STDMD &)=delete
	No copy construct. More...

void	operator= (const STDMD &)=delete
	No copy assignment. More...

virtual	~STDMD ()=default
	Destructor. More...

virtual bool	read (const dictionary &)
	Read STDMD settings. More...

virtual bool	execute ()
	Execute STDMD. More...

virtual bool	write ()
	Write STDMD output. More...

Public Member Functions inherited from fvMeshFunctionObject
	TypeName ("fvMeshFunctionObject")
	Runtime type information. More...

	fvMeshFunctionObject (const word &name, const Time &runTime, const dictionary &dict)
	Construct from Time and dictionary. More...

	fvMeshFunctionObject (const word &name, const objectRegistry &obr, const dictionary &dict)
	Construct from the region objectRegistry and dictionary. More...

virtual	~fvMeshFunctionObject ()=default
	Destructor. More...

Public Member Functions inherited from regionFunctionObject
	TypeName ("regionFunctionObject")
	Runtime type information. More...

	regionFunctionObject (const word &name, const Time &runTime, const dictionary &dict)
	Construct from Time and dictionary. More...

	regionFunctionObject (const word &name, const objectRegistry &obr, const dictionary &dict)
	Construct from the region objectRegistry and dictionary. More...

virtual	~regionFunctionObject ()=default
	Destructor. More...

template<class ObjectType >
const ObjectType *	lookupObjectPtr (const word &fieldName) const
	Deprecated(2018-10) More...

template<class ObjectType >
ObjectType *	lookupObjectRefPtr (const word &fieldName) const
	Deprecated(2018-10) More...

Public Member Functions inherited from stateFunctionObject
	stateFunctionObject (const word &name, const Time &runTime)
	Construct from components. More...

virtual	~stateFunctionObject ()=default
	Destructor. More...

dictionary &	propertyDict ()
	Return access to the property dictionary. More...

bool	foundProperty (const word &entryName) const
	Return true if the property exists. More...

label	getTrigger () const
	Get the current trigger index. More...

bool	setTrigger (const label triggeri)
	Set the current trigger index. More...

bool	getDict (const word &entryName, dictionary &dict) const
	Set dictionary, return true if set. More...

bool	getObjectDict (const word &objectName, const word &entryName, dictionary &dict) const
	Set dictionary from named object, return true if set. More...

template<class Type >
Type	getProperty (const word &entryName, const Type &defaultValue=Type(Zero)) const
	Retrieve generic property. More...

template<class Type >
bool	getProperty (const word &entryName, Type &value) const
	Set generic property, return true if set. More...

template<class Type >
void	setProperty (const word &entryName, const Type &value)
	Add generic property. More...

template<class Type >
Type	getObjectProperty (const word &objectName, const word &entryName, const Type &defaultValue=Type(Zero)) const
	Retrieve generic property from named object. More...

template<class Type >
bool	getObjectProperty (const word &objectName, const word &entryName, Type &value) const
	Set generic property from named object, return true if set. More...

template<class Type >
void	setObjectProperty (const word &objectName, const word &entryName, const Type &value)
	Add generic property from named object. More...

template<class Type >
void	setResult (const word &entryName, const Type &value)
	Add result. More...

template<class Type >
void	setObjectResult (const word &objectName, const word &entryName, const Type &value)
	Add result from named object. More...

template<class Type >
Type	getResult (const word &entryName, const Type &defaultValue=Type(Zero)) const
	Retrieve result. More...

template<class Type >
Type	getObjectResult (const word &objectName, const word &entryName, const Type &defaultValue=Type(Zero)) const
	Retrieve result from named object. More...

template<class Type >
bool	getObjectResult (const word &objectName, const word &entryName, Type &value) const
	Set result from named object, return true if set. More...

word	resultType (const word &entryName) const
	Retrieve the result type. More...

word	objectResultType (const word &objectName, const word &entryName) const
	Return the type of result. More...

List< word >	objectResultEntries () const
	Retrieve the result entries. More...

List< word >	objectResultEntries (const word &objectName) const
	Return result entries for named object. More...

void	writeResultEntries (Ostream &os) const
	Write the results entries for all objects to stream. More...

void	writeResultEntries (const word &objectName, Ostream &os) const
	Write the results entries for named object to stream. More...

void	writeAllResultEntries (Ostream &os) const
	Write the results entries for all objects to stream. More...

Public Member Functions inherited from timeFunctionObject
	timeFunctionObject (const word &name, const Time &runTime)
	Construct from Time. More...

virtual	~timeFunctionObject ()=default
	Destructor. More...

const Time &	time () const
	Return time database. More...

objectRegistry &	storedObjects ()

const objectRegistry &	storedObjects () const

Public Member Functions inherited from functionObject
virtual const word &	type () const =0
	Runtime type information. More...

	declareRunTimeSelectionTable (autoPtr, functionObject, dictionary,(const word &name, const Time &runTime, const dictionary &dict),(name, runTime, dict))

	functionObject (const word &name)
	Construct from components. More...

autoPtr< functionObject >	clone () const
	Return clone. More...

virtual	~functionObject ()=default
	Destructor. More...

const word &	name () const
	Return the name of this functionObject. More...

virtual bool	execute (const label subIndex)
	Execute using the specified subIndex. More...

virtual bool	end ()
	Called when Time::run() determines that the time-loop exits. More...

virtual bool	adjustTimeStep ()
	Called at the end of Time::adjustDeltaT() if adjustTime is true. More...

virtual bool	filesModified () const
	Did any file get changed during execution? More...

virtual void	updateMesh (const mapPolyMesh &mpm)
	Update for changes of mesh. More...

virtual void	movePoints (const polyMesh &mesh)
	Update for changes of mesh. More...

Public Member Functions inherited from writeFile
	writeFile (const objectRegistry &obr, const fileName &prefix, const word &name="undefined", const bool writeToFile=true)
	Construct from objectRegistry, prefix, fileName. More...

	writeFile (const objectRegistry &obr, const fileName &prefix, const word &name, const dictionary &dict, const bool writeToFile=true)

	writeFile (const writeFile &wf)
	Construct copy. More...

virtual	~writeFile ()=default
	Destructor. More...

virtual OFstream &	file ()
	Return access to the file (if only 1) More...

virtual bool	writeToFile () const
	Flag to allow writing to file. More...

virtual bool	canWriteHeader () const
	Flag to allow writing the header. More...

virtual label	charWidth () const
	Return width of character stream output. More...

virtual void	writeCommented (Ostream &os, const string &str) const
	Write a commented string to stream. More...

virtual void	writeTabbed (Ostream &os, const string &str) const
	Write a tabbed string to stream. More...

virtual void	writeHeader (Ostream &os, const string &str) const
	Write a commented header to stream. More...

virtual void	writeCurrentTime (Ostream &os) const
	Write the current time to stream. More...

virtual void	writeBreak (Ostream &os) const
	Write a break marker to the stream. More...

template<class Type >
void	writeHeaderValue (Ostream &os, const string &property, const Type &value) const
	Write a (commented) header property and value pair. More...

Additional Inherited Members
Static Public Member Functions inherited from functionObject
static autoPtr< functionObject >	New (const word &name, const Time &runTime, const dictionary &dict)
	Select from dictionary, based on its "type" entry. More...

Public Attributes inherited from functionObject
bool	log
	Flag to write log into Info. More...

Static Public Attributes inherited from functionObject
static int	debug
	Flag to execute debug content. More...

static bool	postProcess
	Global post-processing mode switch. More...

static word	outputPrefix
	Directory prefix. More...

Static Public Attributes inherited from writeFile
static label	addChars = 8
	Additional characters for writing. More...

Protected Member Functions inherited from fvMeshFunctionObject
	fvMeshFunctionObject (const fvMeshFunctionObject &)=delete
	No copy construct. More...

void	operator= (const fvMeshFunctionObject &)=delete
	No copy assignment. More...

Protected Member Functions inherited from regionFunctionObject
virtual const objectRegistry &	obr () const
	The region or sub-region registry being used. More...

template<class ObjectType >
bool	foundObject (const word &fieldName) const
	Find object (eg, a field) in the (sub) objectRegistry. More...

template<class ObjectType >
const ObjectType *	cfindObject (const word &fieldName) const

template<class ObjectType >
const ObjectType *	findObject (const word &fieldName) const

template<class ObjectType >
ObjectType *	findObject (const word &fieldName)

template<class ObjectType >
ObjectType *	getObjectPtr (const word &fieldName) const

template<class ObjectType >
const ObjectType &	lookupObject (const word &fieldName) const
	Lookup and return object (eg, a field) from the (sub) objectRegistry. More...

template<class ObjectType >
ObjectType &	lookupObjectRef (const word &fieldName) const
	Lookup and return object (eg, a field) from the (sub) objectRegistry. More...

template<class ObjectType >
bool	store (word &fieldName, const tmp< ObjectType > &tfield, bool cacheable=false)
	Store the field in the (sub) objectRegistry under the given name. More...

bool	writeObject (const word &fieldName)
	Write field if present in the (sub) objectRegistry. More...

bool	clearObject (const word &fieldName)
	Clear field from the (sub) objectRegistry if present. More...

void	clearObjects (const wordList &objNames)
	Clear fields from the (sub) objectRegistry if present. More...

	regionFunctionObject (const regionFunctionObject &)=delete
	No copy construct. More...

void	operator= (const regionFunctionObject &)=delete
	No copy assignment. More...

Protected Member Functions inherited from stateFunctionObject
const IOdictionary &	stateDict () const
	Return a const reference to the state dictionary. More...

IOdictionary &	stateDict ()
	Return non-const access to the state dictionary. More...

	stateFunctionObject (const stateFunctionObject &)=delete
	No copy construct. More...

void	operator= (const stateFunctionObject &)=delete
	No copy assignment. More...

Protected Member Functions inherited from timeFunctionObject
void	clearOutputObjects (const wordList &objNames)
	Remove specified items from "functionObjectObjects". More...

	timeFunctionObject (const timeFunctionObject &)=delete
	No copy construct. More...

void	operator= (const timeFunctionObject &)=delete
	No copy assignment. More...

Protected Member Functions inherited from functionObject
word	scopedName (const word &name) const
	Return a scoped name, e.g. used to construct local field names. More...

Protected Member Functions inherited from writeFile
void	initStream (Ostream &os) const
	Initialise the output stream for writing. More...

fileName	baseFileDir () const
	Return the base directory for output. More...

fileName	baseTimeDir () const
	Return the base directory for the current time value. More...

virtual autoPtr< OFstream >	createFile (const word &name, scalar timeValue) const
	Return autoPtr to a new file for a given time. More...

virtual autoPtr< OFstream >	createFile (const word &name) const
	Return autoPtr to a new file using the simulation start time. More...

virtual void	resetFile (const word &name)
	Reset internal file pointer to new file with new name. More...

Omanip< int >	valueWidth (const label offset=0) const
	Return the value width when writing to stream with optional offset. More...

void	operator= (const writeFile &)=delete
	No copy assignment. More...

Protected Attributes inherited from fvMeshFunctionObject
const fvMesh &	mesh_
	Reference to the fvMesh. More...

Protected Attributes inherited from regionFunctionObject
word	subRegistryName_
	Name for alternative object registry. More...

const objectRegistry &	obr_
	Reference to the region objectRegistry. More...

const objectRegistry *	obrPtr_
	Pointer to alternative (eg, sub-region) objectRegistry. More...

Protected Attributes inherited from timeFunctionObject
const Time &	time_
	Reference to the time database. More...

Protected Attributes inherited from writeFile
const objectRegistry &	fileObr_
	Reference to the region objectRegistry. More...

const fileName	prefix_
	Prefix. More...

word	fileName_
	Name of file. More...

autoPtr< OFstream >	filePtr_
	File pointer. More...

label	writePrecision_
	Write precision. More...

bool	writeToFile_
	Flag to enable/disable writing to file. More...

bool	updateHeader_

bool	writtenHeader_
	Flag to identify whether the header has been written. More...

bool	useUserTime_

scalar	startTime_
	Start time value. More...

Detailed Description

(Beta Release) STDMD (i.e. Streaming Total Dynamic Mode Decomposition) is a variant of a data-driven dimensionality reduction method.

STDMD is being used as a mathematical post-processing tool to compute a set of dominant modes out of a given flow (or dataset) each of which is associated with a constant frequency and decay rate, so that dynamic features of a given flow may become interpretable, and tractable. 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:

    STDMD 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

    DMD properties:
        Brunton S. L. (2018).
        Dynamic mode decomposition overview.
        Seattle, Washington: University of Washington.
        youtu.be/sQvrK8AGCAo (Retrieved:24-04-20)

Operands:

Operand	Type	Location
`input`	{vol,surface}<Type>Field	$FOAM_CASE/<time>/<inpField>
`output` file	dat	$FOAM_CASE/postProcessing/<FO>/<time>/<file>(s)
`output` field	volScalarField(s)	$FOAM_CASE/<time>/<outField>(s)

where <Type>=Scalar/Vector/SphericalTensor/SymmTensor/Tensor.

Output fields:

      modeReal<modeIndex><field> | Real part of a mode field
      modeImag<modeIndex><field> | Imaginary part of a mode field

Output files:

      uSTDMD.dat                 | Unfiltered STDMD output
      STDMD.dat                  | Filtered STDMD output

wherein for each mode, the following quantities are output into files:

      Frequency
      Magnitude
      Amplitude (real part)
      Amplitude (imaginary part)
      Eigenvalue (real part)
      Eigenvalue (imaginary part)

Note: Operations on boundary fields, e.g. wallShearStress, are currently not available.

Usage

Minimal example by using system/controlDict.functions:

STDMD1
{
    // Mandatory entries (unmodifiable)
    type                STDMD;
    libs                (fieldFunctionObjects);
    field               <inpField>;

    // Conditional mandatory entries (unmodifiable)
    // either of the below
    stdmdInterval       5.5;
    executeInterval     10;

    // Optional entries (unmodifiable)
    modeSorter          kiewat;
    nModes              50;
    maxRank             50;
    nGramSchmidt        5;
    fMin                0;
    fMax                1000000000;

    // Optional entries (run-time modifiable, yet not recommended)
    testEigen           false;
    dumpEigen           false;
    minBasis            0.00000001;
    minEVal             0.00000001;
    absTol              0.001;
    relTol              0.0001;
    sortLimiter         500;

    // Optional (inherited) entries
    ...
}

where the entries mean:

Property	Description	Type	Req'd	Dflt
`type`	Type name: STDMD	word	yes	-
`libs`	Library name: fieldFunctionObjects	word	yes	-
`field`	Name of the operand field	word	yes	-
`stdmdInterval`	STDMD time-step size [s]	scalar	conditional	executeInterval*(current time-step of the simulation)
`modeSorter`	Mode-sorting algorithm variant	word	no	firstSnap
`nModes`	Number of output modes in input freq 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
`testEigen`	Flag to verify eigendecompositions	bool	no	false
`dumpEigen`	Flag to log operands of eigendecomps	bool	no	false
`minBasis`	Orthogonal basis expansion threshold	scalar	no	1e-8
`minEVal`	Min EVal for below EVals are omitted	scalar	no	1e-8
`absTol`	Min abs tol in eigendecomposition tests	scalar	no	1e-4
`relTol`	Relative tol in eigendecomposition tests	scalar	no	1e-6
`sortLimiter`	Maximum allowable magnitude for mag(eigenvalue)*(number of STDMD 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
      firstSnap | Method of first snapshot amplitude magnitude

The inherited entries are elaborated in:

Usage by postProcess utility is not available.

Note

To specify the STDMD time-step size (not necessarily equal to the time step of the simulation), entries of either stdmdInterval or executeInterval must be available (highest to lowest precedence). While stdmdInterval allows users to directly specify the STDMD time-step size in seconds, in absence of stdmdInterval, 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) may upset STDMD.
Warning: DMD is an active research area at the time of writing; therefore, there would be cases whereat oddities might be encountered.
Warning: This STDMD release is the beta release; therefore, small-to-medium changes in input/output interfaces and internal structures should be expected in the next versions.
Warning: In modeSorter algorithms of kiewat and kouZhang, there exists a function of $power(x,y)$ 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

Foam::functionObjects::fvMeshFunctionObject
Foam::functionObjects::writeFile
ExtendedCodeGuide::functionObjects::field::STDMD

Source files

Definition at line 409 of file STDMD.H.

Constructor & Destructor Documentation

◆ STDMD() [1/3]

STDMD ( )

delete

No default construct.

◆ STDMD() [2/3]

STDMD	(	const word &	name,
		const Time &	runTime,
		const dictionary &	dict
	)

Construct from Time and dictionary.

Definition at line 1013 of file STDMD.C.

References Foam::abort(), dict, Foam::endl(), Foam::FatalError, FatalErrorInFunction, Foam::Info, Foam::nl, Foam::read(), runTime, and WarningInFunction.

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◆ STDMD() [3/3]

STDMD ( const STDMD & )

delete

No copy construct.

◆ ~STDMD()

virtual ~STDMD ( )

virtualdefault

Destructor.

Member Function Documentation

◆ TypeName()

TypeName ( "STDMD" )

Runtime type information.

◆ operator=()

void operator= ( const STDMD & )

delete

No copy assignment.

◆ read()

bool read ( const dictionary & dict )

virtual

Read STDMD settings.

Reimplemented from writeFile.

Definition at line 1135 of file STDMD.C.

References dict, Foam::constant::mathematical::e(), Foam::endl(), MinMax< T >::ge(), Foam::Info, Foam::name(), Foam::nl, Foam::blockMeshTools::read(), and Foam::tab.

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◆ execute()

bool execute ( )

virtual

Execute STDMD.

Implements functionObject.

Definition at line 1207 of file STDMD.C.

References Foam::endl(), Log, Foam::name(), Foam::tab, and Foam::type().

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◆ write()

bool write ( )

virtual

Write STDMD output.

Implements functionObject.

Definition at line 1251 of file STDMD.C.

References Foam::endl(), Foam::Info, Log, Foam::name(), Foam::nl, Foam::type(), and WarningInFunction.

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

src/functionObjects/field/STDMD/STDMD.H
src/functionObjects/field/STDMD/STDMD.C
src/functionObjects/field/STDMD/STDMDTemplates.C

Public Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ STDMD() [1/3]

◆ STDMD() [2/3]

◆ STDMD() [3/3]

◆ ~STDMD()

Member Function Documentation

◆ TypeName()

◆ operator=()

◆ read()

◆ execute()

◆ write()