{
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  "Package": "GPoM",
  "Type": "Package",
  "Title": "Generalized Polynomial Modelling",
  "Version": "1.4",
  "Date": "2023-06-16",
  "Authors@R": "c(\nperson(\"Sylvain\", \"Mangiarotti\", email = \"sylvain.mangiarotti@cesbio.cnes.fr\",role = c(\"aut\")),\nperson(\"Mireille\", \"Huc\", email = \"mireille.huc@u-paris2.fr\", role = c(\"cre\",\"aut\")),\nperson(\"Flavie\", \"Le Jean\",role = c(\"ctb\")),\nperson(\"Malika\", \"Chassan\",role = c(\"ctb\")),\nperson(\"Laurent\", \"Drapeau\",role = c(\"ctb\")),\nperson(\"Institut de Recherche pour le Développement\", role =\"fnd\"),\nperson(\"Centre National de la Recherche Scientifique\", role =\"fnd\")\n)",
  "Maintainer": "Mireille Huc <mireille.huc@u-paris2.fr>",
  "Description": "Platform dedicated to the Global Modelling technique. Its\naim is to obtain ordinary differential equations of polynomial\nform directly from time series. It can be applied to single or\nmultiple time series under various conditions of noise, time\nseries lengths, sampling, etc. This platform is developped at\nthe Centre d'Etudes Spatiales de la Biosphere (CESBIO), UMR\n5126 UPS/CNRS/CNES/IRD, 18 av. Edouard Belin, 31401 TOULOUSE,\nFRANCE. The developments were funded by the French program Les\nEnveloppes Fluides et l'Environnement (LEFE, MANU, projets\nGloMo, SpatioGloMo and MoMu). The French program Defi InFiNiTi\n(CNRS) and PNTS are also acknowledged (projects Crops'IChaos\nand Musc & SlowFast). The method is described in the article :\nMangiarotti S. and Huc M. (2019) <doi:10.1063/1.5081448>.",
  "License": "CeCILL-2",
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  "Packaged": {
    "Date": "2026-06-04 07:56:42 UTC",
    "User": "root"
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  "Author": "Sylvain Mangiarotti [aut], Mireille Huc [cre, aut], Flavie Le\nJean [ctb], Malika Chassan [ctb], Laurent Drapeau [ctb],\nInstitut de Recherche pour le Développement [fnd], Centre\nNational de la Recherche Scientifique [fnd]",
  "Repository": "https://cran.r-universe.dev",
  "Date/Publication": "2023-06-16 07:10:10 UTC",
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    "autoGPoMoTest",
    "bDrvFilt",
    "cano2M",
    "combiEq",
    "compDeriv",
    "concat",
    "concatMulTS",
    "d2pMax",
    "derivODEwMultiX",
    "drvSucc",
    "findAllSets",
    "gloMoId",
    "gPoMo",
    "numicano",
    "numiMultiX",
    "numinoisy",
    "p2dMax",
    "poLabs",
    "predictab",
    "pTimEv",
    "regOrd",
    "regSeries",
    "subSysD",
    "testP",
    "visuEq",
    "visuOutGP",
    "wInProd"
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    {
      "name": "allToTest",
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  "_help": [
    {
      "page": "GPoM-package",
      "title": "GPoM package: Generalized Polynomial Modelling",
      "concept": [
        "causal inference",
        "chaos",
        "data learning",
        "global modeling",
        "nonlinear dynamical systems",
        "time series analysis"
      ],
      "topics": [
        "GPoM-package"
      ]
    },
    {
      "page": "allMod_nVar3_dMax2-data-set",
      "title": "Numerical description of a list of eighteen three-dimensional chaotic sytems (see vignette '7_Retro-Modelling')",
      "topics": [
        "allMod_nVar3_dMax2",
        "allMod_nVar3_dMax2 data set"
      ]
    },
    {
      "page": "allToTest",
      "title": "A list providing the description of six models tested by the function 'autoGPoMoTest'.",
      "topics": [
        "allToTest"
      ]
    },
    {
      "page": "autoGPoMoSearch",
      "title": "Automatic search of polynomial Equations",
      "topics": [
        "autoGPoMoSearch"
      ]
    },
    {
      "page": "autoGPoMoTest",
      "title": "Tests the numerical integrability of models and classify their dynamical regime",
      "topics": [
        "autoGPoMoTest"
      ]
    },
    {
      "page": "bDrvFilt",
      "title": "Builds the derivative filter",
      "topics": [
        "bDrvFilt"
      ]
    },
    {
      "page": "cano2M",
      "title": "cano2M : Converts a model in canonical form into a matrix form",
      "topics": [
        "cano2M"
      ]
    },
    {
      "page": "combiEq",
      "title": "combiEq : Combine Equations from different sources",
      "topics": [
        "combiEq"
      ]
    },
    {
      "page": "compDeriv",
      "title": "Computes the successive derivatives of a time series",
      "topics": [
        "compDeriv"
      ]
    },
    {
      "page": "concat",
      "title": "Concat Concatenates separated time series",
      "topics": [
        "concat"
      ]
    },
    {
      "page": "concatMulTS",
      "title": "ConcatMulTS Concatenates separated time series (of single or multiples variables)",
      "topics": [
        "concatMulTS"
      ]
    },
    {
      "page": "d2pMax",
      "title": "Provides the number of polynomial terms 'pMax' given 'dMax' and 'nVar'",
      "topics": [
        "d2pMax"
      ]
    },
    {
      "page": "data_vignetteIII-data-set",
      "title": "Output of the vignette 'III_Modelling'",
      "topics": [
        "data_vignetteIII",
        "data_vignetteIII data set"
      ]
    },
    {
      "page": "data_vignetteVI-data-set",
      "title": "Output of the vignette 'VI_Sensitivity'",
      "topics": [
        "data_vignetteVI",
        "data_vignetteVI data set"
      ]
    },
    {
      "page": "data_vignetteVII-data-set",
      "title": "Output of the vignette 'VII_Retro-Modelling'",
      "topics": [
        "data_vignetteVII",
        "data_vignetteVII data set"
      ]
    },
    {
      "page": "derivODE2",
      "title": "A subfonction for the numerical integration of polynomial equations provided in a generic form following the convetion defined by function 'poLabs'.",
      "topics": [
        "derivODE2"
      ]
    },
    {
      "page": "derivODEwMultiX",
      "title": "deriveODEwMultiX : A Subfonction for the numerical integration of polynomial equations in the generic form defined by function 'poLabs' and with External Forcing F(t)",
      "topics": [
        "derivODEwMultiX"
      ]
    },
    {
      "page": "detectP1limCycl",
      "title": "Detection of limit cycles of period-1",
      "topics": [
        "detectP1limCycl"
      ]
    },
    {
      "page": "drvSucc",
      "title": "drvSucc : Computes the successive derivatives of a time series",
      "topics": [
        "drvSucc"
      ]
    },
    {
      "page": "extractEq",
      "title": "extractEq : Extracts Equations from one system",
      "topics": [
        "extractEq"
      ]
    },
    {
      "page": "findAllSets",
      "title": "Find all possible sets of equation combinations considering an ensemble of possible equation.",
      "topics": [
        "findAllSets"
      ]
    },
    {
      "page": "gloMoId",
      "title": "Global Model Identification",
      "topics": [
        "gloMoId"
      ]
    },
    {
      "page": "gPoMo",
      "title": "Generalized Polynomial Modeling",
      "topics": [
        "gPoMo"
      ]
    },
    {
      "page": "GSproc",
      "title": "Gram-Schmidt procedure",
      "topics": [
        "GSproc"
      ]
    },
    {
      "page": "NDVI",
      "title": "A time series of vegetation index measured from satellite",
      "topics": [
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    {
      "page": "numicano",
      "title": "Numerical Integration of models in ODE of polynomial form",
      "topics": [
        "numicano"
      ]
    },
    {
      "page": "numiMultiX",
      "title": "Numerical Integration polynomial ODEs with Multiple eXternal forcing",
      "topics": [
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      ]
    },
    {
      "page": "numinoisy",
      "title": "Generates time series of deterministic-behavior with stochatic perturbations (measurement and/or dynamical noise)",
      "topics": [
        "numinoisy"
      ]
    },
    {
      "page": "odeBruitMult2",
      "title": "For the numerical integration of ordinary differential equations with dynamical noise.",
      "topics": [
        "odeBruitMult2"
      ]
    },
    {
      "page": "P1FxCh",
      "title": "A data set for testing periodicity",
      "topics": [
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    },
    {
      "page": "P1FxChP2",
      "title": "A data set for testing periodicity",
      "topics": [
        "P1FxChP2"
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    },
    {
      "page": "p2dMax",
      "title": "p2dMax : provides the maximum polynomial degree 'dMax' given the number of variables 'nVar' and the number of possible polynomial terms 'pMax'.",
      "topics": [
        "p2dMax"
      ]
    },
    {
      "page": "paramId",
      "title": "For parameter Identification",
      "topics": [
        "paramId"
      ]
    },
    {
      "page": "poLabs",
      "title": "Polynomial labels order",
      "topics": [
        "poLabs"
      ]
    },
    {
      "page": "predictab",
      "title": "Estimate the models performance obtained with 'GPoMo' in term of predictability",
      "topics": [
        "predictab"
      ]
    },
    {
      "page": "pTimEv",
      "title": "Model stationnary testing",
      "topics": [
        "pTimEv"
      ]
    },
    {
      "page": "regOrd",
      "title": "Generate the conventional order for polynomial terms in a the polynomial formulation",
      "topics": [
        "regOrd"
      ]
    },
    {
      "page": "regSeries",
      "title": "Estimates the monomial time series",
      "topics": [
        "regSeries"
      ]
    },
    {
      "page": "Rossler-1976-data-set",
      "title": "Time series of the Rossler-1976 system",
      "topics": [
        "Ross76",
        "Rossler-1976 data set"
      ]
    },
    {
      "page": "RosYco",
      "title": "Twelve Rossler-1976 time series (exclusively variable y)",
      "topics": [
        "RosYco"
      ]
    },
    {
      "page": "subSysD",
      "title": "subSysD : Sub-systems Disentangling",
      "topics": [
        "subSysD"
      ]
    },
    {
      "page": "svrlTS",
      "title": "A data set for the global modeling of time series in association",
      "topics": [
        "svrlTS"
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    },
    {
      "page": "testP",
      "title": "Periodic solution test",
      "topics": [
        "testP"
      ]
    },
    {
      "page": "TS",
      "title": "Time series resulting from the integration of a non stationary system",
      "topics": [
        "TS"
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    },
    {
      "page": "TSallMod_nVar3_dMax2-data-set",
      "title": "Time series of three-dimensional chaotic sytems (for vignette 'VII_Retro-Modelling')",
      "topics": [
        "TSallMod_nVar3_dMax2",
        "TSallMod_nVar3_dMax2 data set"
      ]
    },
    {
      "page": "visuEq",
      "title": "Displays the models Equations",
      "topics": [
        "visuEq"
      ]
    },
    {
      "page": "visuOutGP",
      "title": "visuOutGP : get a quick information of gPoMo output",
      "topics": [
        "visuOutGP"
      ]
    },
    {
      "page": "wInProd",
      "title": "Weighted inner product",
      "topics": [
        "wInProd"
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  "_vignettes": [
    {
      "source": "b1_Conventions.Rmd",
      "filename": "b1_Conventions.html",
      "title": "GPoM : 1 Conventions",
      "author": "Sylvain Mangiarotti & Mireille Huc",
      "engine": "knitr::rmarkdown",
      "headings": [
        "Conventions used to describe a polynomial",
        "Definition of a set of polynomial ODE",
        "Numerical integration",
        "Next steps"
      ],
      "created": "2018-07-26 15:20:23",
      "modified": "2020-02-18 13:20:06",
      "commits": 2
    },
    {
      "source": "b2_PreProcessing.Rmd",
      "filename": "b2_PreProcessing.html",
      "title": "GPoM : 2 PreProcessing",
      "author": "Sylvain Mangiarotti & Mireille Huc",
      "engine": "knitr::rmarkdown",
      "headings": [
        "Pre-processing for global modelling",
        "Single time series",
        "Multiple time series",
        "Conclusion and next step"
      ],
      "created": "2018-07-26 15:20:23",
      "modified": "2020-02-18 13:20:06",
      "commits": 2
    },
    {
      "source": "b3_Modelling.Rmd",
      "filename": "b3_Modelling.html",
      "title": "GPoM : 3 Modelling",
      "author": "Sylvain Mangiarotti & Mireille Huc",
      "engine": "knitr::rmarkdown",
      "headings": [
        "Global Modelling",
        "Single time series modelling",
        "Detection of causal couplings and retro-modelling",
        "Generalized global modelling and polynomial a priori structure",
        "Blind separation and modelling of two independant sets of equations",
        "Time series with gaps",
        "Time series in associassion",
        "Output visualization and global models validation"
      ],
      "created": "2018-07-26 15:20:23",
      "modified": "2023-06-16 07:10:10",
      "commits": 3
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    {
      "source": "b4_VisualizeOutputs.Rmd",
      "filename": "b4_VisualizeOutputs.html",
      "title": "GPoM : 4 Visualization of the outputs",
      "author": "Sylvain Mangiarotti & Mireille Huc",
      "engine": "knitr::rmarkdown",
      "headings": [
        "Model vizualization",
        "Next step"
      ],
      "created": "2018-07-26 15:20:23",
      "modified": "2020-02-18 13:20:06",
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    {
      "source": "b5_Predictability.Rmd",
      "filename": "b5_Predictability.html",
      "title": "GPoM : 5 Models predictability",
      "author": "Sylvain Mangiarotti & Mireille Huc",
      "engine": "knitr::rmarkdown",
      "headings": [
        "Model performances",
        "Predictability",
        "Conclusions"
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      "created": "2018-07-26 15:20:23",
      "modified": "2020-02-18 13:20:06",
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    {
      "source": "b6_Sensitivity.Rmd",
      "filename": "b6_Sensitivity.html",
      "title": "GPoM : 6 Approach sensitivity",
      "author": "Sylvain Mangiarotti & Mireille Huc",
      "engine": "knitr::rmarkdown",
      "headings": [
        "Approach sensitivity",
        "Sensitivity to the initial conditions",
        "The original system and data",
        "Model selection",
        "Results",
        "Sensitivity to signal length",
        "Data",
        "Global modelling",
        "Sensitivity to subsampling and resampling",
        "Subsampled time series",
        "Resampled time series",
        "Sensitivity to measurement noise (after smoothing)",
        "Conclusions"
      ],
      "created": "2018-07-26 15:20:23",
      "modified": "2020-02-18 13:20:06",
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      "source": "b7_Retro-modelling.Rmd",
      "filename": "b7_Retro-modelling.html",
      "title": "GPoM : 7 Retro-modelling",
      "author": "Sylvain Mangiarotti & Mireille Huc",
      "engine": "knitr::rmarkdown",
      "headings": [
        "Detection of miscellaneous chaotic systems",
        "The Nosé-Hoover-1986 system",
        "Data",
        "Global modelling",
        "The Genesio-Tesi system (1992)",
        "The Sprott systems",
        "The Spott-F system",
        "The Spott-H system",
        "The Spott-K system",
        "The Spott-O system",
        "The Spott-P system",
        "The Spott-G system",
        "The Spott-M system",
        "The Spott-Q system",
        "The Spott-S system",
        "The Lorenz-1963 system",
        "The Burke and Shaw system (1981)",
        "The Lorenz-1984 system",
        "The Chlouverakis-Sprott system (2004)",
        "The Li system (2007)",
        "The Cord system (Aguirre & Letellier 2012)",
        "Conclusion"
      ],
      "created": "2018-07-26 15:20:23",
      "modified": "2020-02-18 13:20:06",
      "commits": 2
    },
    {
      "source": "a_GeneralIntro.Rmd",
      "filename": "a_GeneralIntro.html",
      "title": "GPoM : General introduction",
      "author": "Sylvain Mangiarotti & Mireille Huc",
      "engine": "knitr::rmarkdown",
      "headings": [
        "Generalized Global Polynomial Modelling (GPoM)"
      ],
      "created": "2018-07-26 15:20:23",
      "modified": "2020-02-18 13:20:06",
      "commits": 2
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