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some more improvements to the doxygen documentation
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‎DOCS/groups-usr.dox

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@defgroup ggesx ggesx: Schur form, expert
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@}
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@defgroup geev_driver_grp DMD driver, Dynamic Mode Decomposition
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@{
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@defgroup gedmd gedmd: dmd
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@}
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@defgroup geev_comp_grp Eig computational routines
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@{
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@defgroup gebal gebal: balance matrix

‎SRC/cgedmd.f90

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!> \brief \b CGEDMD
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!> \brief \b CGEDMD computes the Dynamic Mode Decomposition (DMD) for a pair of data snapshot matrices.
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!
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! =========== DOCUMENTATION ===========
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!
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!
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!............................................................
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!> \par Purpose:
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!> =============
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! =============
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!> \verbatim
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!> CGEDMD computes the Dynamic Mode Decomposition (DMD) for
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!> a pair of data snapshot matrices. For the input matrices
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!> \endverbatim
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!............................................................
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!> \par References:
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!> ================
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! ================
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!> \verbatim
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!> [1] P. Schmid: Dynamic mode decomposition of numerical
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!> and experimental data,
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!> \endverbatim
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!......................................................................
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!> \par Developed and supported by:
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!> ================================
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! ================================
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!> \verbatim
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!> Developed and coded by Zlatko Drmac, Faculty of Science,
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!> University of Zagreb; drmac@math.hr
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!> \endverbatim
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!......................................................................
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!> \par Distribution Statement A:
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!> ==============================
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! ==============================
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!> \verbatim
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!> Approved for Public Release, Distribution Unlimited.
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!> Cleared by DARPA on September 29, 2022
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!
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!> \author Zlatko Drmac
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!
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!> \ingroup dmd
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!> \ingroup gedmd
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!
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!.............................................................
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!.............................................................

‎SRC/cgedmdq.f90

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!> \brief \b CGEDMDQ
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!> \brief \b CGEDMDQ computes the Dynamic Mode Decomposition (DMD) for a pair of data snapshot matrices.
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!
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! =========== DOCUMENTATION ===========
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!
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!
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!............................................................
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!> \par Purpose:
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!> =============
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! =============
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!> \verbatim
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!> CGEDMDQ computes the Dynamic Mode Decomposition (DMD) for
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!> a pair of data snapshot matrices, using a QR factorization
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!> \endverbatim
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!............................................................
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!> \par References:
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!> ================
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! ================
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!> \verbatim
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!> [1] P. Schmid: Dynamic mode decomposition of numerical
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!> and experimental data,
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!> \endverbatim
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!......................................................................
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!> \par Developed and supported by:
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!> ================================
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! ================================
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!> \verbatim
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!> Developed and coded by Zlatko Drmac, Faculty of Science,
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!> University of Zagreb; drmac@math.hr
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!> \endverbatim
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!......................................................................
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!> \par Developed and supported by:
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!> ================================
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! ================================
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!> \verbatim
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!> Approved for Public Release, Distribution Unlimited.
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!> Cleared by DARPA on September 29, 2022
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!
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!> \author Zlatko Drmac
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!
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!> \ingroup dmd
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!> \ingroup gedmd
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!
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!.............................................................
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!.............................................................

‎SRC/dgedmd.f90

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!> \brief \b DGEDMD
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!> \brief \b DGEDMD computes the Dynamic Mode Decomposition (DMD) for a pair of data snapshot matrices.
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!
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! =========== DOCUMENTATION ===========
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!
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!
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!............................................................
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!> \par Purpose:
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!> =============
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! =============
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!> \verbatim
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!> DGEDMD computes the Dynamic Mode Decomposition (DMD) for
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!> a pair of data snapshot matrices. For the input matrices
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!> \endverbatim
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!............................................................
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!> \par References:
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!> ================
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! ================
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!> \verbatim
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!> [1] P. Schmid: Dynamic mode decomposition of numerical
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!> and experimental data,
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!> \endverbatim
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!......................................................................
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!> \par Developed and supported by:
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!> ================================
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! ================================
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!> \verbatim
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!> Developed and coded by Zlatko Drmac, Faculty of Science,
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!> University of Zagreb; drmac@math.hr
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!> \endverbatim
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!......................................................................
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!> \par Distribution Statement A:
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!> ==============================
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! ==============================
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!> \verbatim
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!> Approved for Public Release, Distribution Unlimited.
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!> Cleared by DARPA on September 29, 2022
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!
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!> \ingroup gedmd
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‎SRC/dgedmdq.f90

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!> \brief \b DGEDMDQ
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!> \brief \b DGEDMDQ computes the Dynamic Mode Decomposition (DMD) for a pair of data snapshot matrices.
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!
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! =========== DOCUMENTATION ===========
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!
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!
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!............................................................
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!> \par Purpose:
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!> =============
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! =============
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!> \verbatim
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!> DGEDMDQ computes the Dynamic Mode Decomposition (DMD) for
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!> a pair of data snapshot matrices, using a QR factorization
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!> \endverbatim
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!............................................................
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!> \par References:
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! ================
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!> \verbatim
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!> [1] P. Schmid: Dynamic mode decomposition of numerical
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!> and experimental data,
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!> \endverbatim
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!......................................................................
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!> \par Developed and supported by:
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!> ================================
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! ================================
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!> \verbatim
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!> Developed and coded by Zlatko Drmac, Faculty of Science,
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!> University of Zagreb; drmac@math.hr
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!> \endverbatim
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!......................................................................
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!> \par Distribution Statement A:
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!> ==============================
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! ==============================
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!> \verbatim
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!> Approved for Public Release, Distribution Unlimited.
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!> \ingroup gedmd
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‎SRC/sgedmd.f90

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!> \brief \b SGEDMD
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!> \brief \b SGEDMD computes the Dynamic Mode Decomposition (DMD) for a pair of data snapshot matrices.
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!
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! =========== DOCUMENTATION ===========
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!
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!> \par Purpose:
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! =============
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!> \verbatim
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! SGEDMD computes the Dynamic Mode Decomposition (DMD) for
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! a pair of data snapshot matrices. For the input matrices
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! X and Y such that Y = A*X with an unaccessible matrix
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! A, SGEDMD computes a certain number of Ritz pairs of A using
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! the standard Rayleigh-Ritz extraction from a subspace of
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! range(X) that is determined using the leading left singular
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! vectors of X. Optionally, SGEDMD returns the residuals
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! of the computed Ritz pairs, the information needed for
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! a refinement of the Ritz vectors, or the eigenvectors of
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! the Exact DMD.
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! For further details see the references listed
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! below. For more details of the implementation see [3].
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!> SGEDMD computes the Dynamic Mode Decomposition (DMD) for
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!> a pair of data snapshot matrices. For the input matrices
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!> X and Y such that Y = A*X with an unaccessible matrix
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!> A, SGEDMD computes a certain number of Ritz pairs of A using
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!> the standard Rayleigh-Ritz extraction from a subspace of
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!> range(X) that is determined using the leading left singular
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!> vectors of X. Optionally, SGEDMD returns the residuals
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!> of the computed Ritz pairs, the information needed for
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!> a refinement of the Ritz vectors, or the eigenvectors of
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!> the Exact DMD.
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!> For further details see the references listed
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!> below. For more details of the implementation see [3].
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!> \endverbatim
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!> \par References:
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! ================
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!> \verbatim
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! [1] P. Schmid: Dynamic mode decomposition of numerical
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! and experimental data,
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! Journal of Fluid Mechanics 656, 5-28, 2010.
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! [2] Z. Drmac, I. Mezic, R. Mohr: Data driven modal
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! decompositions: analysis and enhancements,
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! SIAM J. on Sci. Comp. 40 (4), A2253-A2285, 2018.
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! [3] Z. Drmac: A LAPACK implementation of the Dynamic
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! Mode Decomposition I. Technical report. AIMDyn Inc.
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! and LAPACK Working Note 298.
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! [4] J. Tu, C. W. Rowley, D. M. Luchtenburg, S. L.
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! Brunton, N. Kutz: On Dynamic Mode Decomposition:
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! Theory and Applications, Journal of Computational
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! Dynamics 1(2), 391 -421, 2014.
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!> [1] P. Schmid: Dynamic mode decomposition of numerical
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!> and experimental data,
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!> Journal of Fluid Mechanics 656, 5-28, 2010.
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!> [2] Z. Drmac, I. Mezic, R. Mohr: Data driven modal
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!> decompositions: analysis and enhancements,
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!> SIAM J. on Sci. Comp. 40 (4), A2253-A2285, 2018.
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!> [3] Z. Drmac: A LAPACK implementation of the Dynamic
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!> Mode Decomposition I. Technical report. AIMDyn Inc.
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!> and LAPACK Working Note 298.
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!> [4] J. Tu, C. W. Rowley, D. M. Luchtenburg, S. L.
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!> Brunton, N. Kutz: On Dynamic Mode Decomposition:
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!> Theory and Applications, Journal of Computational
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!> Dynamics 1(2), 391 -421, 2014.
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!> \endverbatim
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!> \par Developed and supported by:
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!> ================================
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! ================================
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!> \verbatim
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! Developed and coded by Zlatko Drmac, Faculty of Science,
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! University of Zagreb; drmac@math.hr
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! In cooperation with
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! AIMdyn Inc., Santa Barbara, CA.
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! and supported by
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! - DARPA SBIR project "Koopman Operator-Based Forecasting
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! for Nonstationary Processes from Near-Term, Limited
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! Observational Data" Contract No: W31P4Q-21-C-0007
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! - DARPA PAI project "Physics-Informed Machine Learning
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! Methodologies" Contract No: HR0011-18-9-0033
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! - DARPA MoDyL project "A Data-Driven, Operator-Theoretic
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! Framework for Space-Time Analysis of Process Dynamics"
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! Contract No: HR0011-16-C-0116
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! Any opinions, findings and conclusions or recommendations
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! expressed in this material are those of the author and
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! do not necessarily reflect the views of the DARPA SBIR
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! Program Office
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!> Developed and coded by Zlatko Drmac, Faculty of Science,
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!> University of Zagreb; drmac@math.hr
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!> In cooperation with
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!> AIMdyn Inc., Santa Barbara, CA.
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!> and supported by
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!> - DARPA SBIR project "Koopman Operator-Based Forecasting
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!> for Nonstationary Processes from Near-Term, Limited
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!> Observational Data" Contract No: W31P4Q-21-C-0007
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!> - DARPA PAI project "Physics-Informed Machine Learning
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!> Methodologies" Contract No: HR0011-18-9-0033
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!> - DARPA MoDyL project "A Data-Driven, Operator-Theoretic
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!> Framework for Space-Time Analysis of Process Dynamics"
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!> Contract No: HR0011-16-C-0116
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!> Any opinions, findings and conclusions or recommendations
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!> expressed in this material are those of the author and
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!> do not necessarily reflect the views of the DARPA SBIR
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!> Program Office
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!> \endverbatim
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!> \par Distribution Statement A:
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!> ==============================
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! ==============================
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!> \verbatim
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!> Distribution Statement A:
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!> Approved for Public Release, Distribution Unlimited.
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‎SRC/sgedmdq.f90

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!> \brief \b SGEDMDQ
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!> \brief \b SGEDMDQ computes the Dynamic Mode Decomposition (DMD) for a pair of data snapshot matrices.
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!
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! =========== DOCUMENTATION ===========
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!> \par Purpose:
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!> \endverbatim
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!> \par References:
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!> and experimental data,
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!> \endverbatim
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!> \par Developed and supported by:
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!> \verbatim
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!> Developed and coded by Zlatko Drmac, Faculty of Science,
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!> University of Zagreb; drmac@math.hr
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!> \endverbatim
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!......................................................................
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!> \par Distribution Statement A:
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!> ==============================
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! ==============================
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!> \verbatim
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!> Approved for Public Release, Distribution Unlimited.
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!.............................................................
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!.............................................................

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