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  "Title": "Objects and Methods for Multi-Companion Matrices",
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  "Authors@R": "person(given = c(\"Georgi\", \"N.\"), family = \"Boshnakov\", \nrole = c(\"cre\", \"aut\"), email = \"georgi.boshnakov@manchester.ac.uk\",\ncomment = c(ORCID = \"0000-0003-2839-346X\"))",
  "Description": "Provides a class for multi-companion matrices with methods\nfor arithmetic and factorization.  A method for generation of\nmulti-companion matrices with prespecified spectral properties\nis provided, as well as some utilities for periodically\ncorrelated and multivariate time series models. See Boshnakov\n(2002) <doi:10.1016/S0024-3795(01)00475-X> and Boshnakov &\nIqelan (2009) <doi:10.1111/j.1467-9892.2009.00617.x>.",
  "URL": "https://geobosh.github.io/mcompanion/ (doc),\nhttps://github.com/GeoBosh/mcompanion (devel)",
  "BugReports": "https://github.com/GeoBosh/mcompanion/issues",
  "RdMacros": "Rdpack",
  "License": "GPL (>= 2)",
  "Collate": "mc.R mcompanion.R utils_Jordan.R mat.R sim.R class_MC.R\nclass_MF.R class_Jordan.R chains_smc.R class_SMC.R\nclass_mcSpec.R",
  "Repository": "https://geobosh.r-universe.dev",
  "Date/Publication": "2025-10-24 18:49:13 UTC",
  "RemoteUrl": "https://github.com/geobosh/mcompanion",
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    "User": "root"
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  "Author": "Georgi N. Boshnakov [cre, aut] (ORCID:\n<https://orcid.org/0000-0003-2839-346X>)",
  "Maintainer": "Georgi N. Boshnakov <georgi.boshnakov@manchester.ac.uk>",
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  "_created": "2026-10-04T07:36:49.000Z",
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  "_topics": [
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    "matrices",
    "periodic",
    "time-series"
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  "_realowner": "geobosh",
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      "date": "2017-08-29"
    },
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      "version": "0.5-0",
      "date": "2019-12-15"
    },
    {
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      "date": "2019-12-18"
    },
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  "_exports": [
    "chain_ind",
    "chains_to_list",
    "coerce",
    "from_Jordan",
    "initialize",
    "is_mc_bottom",
    "Jordan_matrix",
    "JordanDecomposition",
    "make_mcchains",
    "make_mcev",
    "make_mcgev",
    "make_mcmatrix",
    "mc_0chains",
    "mc_chain_extend",
    "mc_chain_merge",
    "mc_chain_scale",
    "mc_chain_subset",
    "mc_chains_triangulate",
    "mc_eigen",
    "mc_eigenvalues",
    "mc_factorize",
    "mc_factors",
    "mc_from_factors",
    "mc_from_filter",
    "mc_full",
    "mc_leftc",
    "mc_matrix",
    "mc_order",
    "mc.0chain.complete",
    "mc.0chain.dx",
    "mc.0chain.struct",
    "mc.0chain.structfill",
    "mC.non0chain.extend",
    "mCompanion",
    "mcSpec",
    "mcStable",
    "mf_order",
    "mf_period",
    "mf_poles",
    "mf_VSform",
    "null_complement",
    "permute_synch",
    "permute_var",
    "rblockmult",
    "reduce_chains_simple",
    "sim_chains",
    "sim_mc",
    "sim_pcfilter",
    "spec_core",
    "spec_root0",
    "spec_root1",
    "spec_seeds1",
    "t",
    "VAR2pcfilter"
  ],
  "_help": [
    {
      "page": "mcompanion-package",
      "title": "Objects and Methods for Multi-Companion Matrices",
      "topics": [
        "mcompanion-package",
        "mcompanion"
      ]
    },
    {
      "page": "jordan",
      "title": "Utilities for Jordan matrices",
      "topics": [
        "chains_to_list",
        "chain_ind",
        "from_Jordan",
        "Jordan_matrix"
      ]
    },
    {
      "page": "JordanDecomposition",
      "title": "Create objects representing Jordan decompositions",
      "topics": [
        "JordanDecomposition",
        "JordanDecomposition,ANY,ANY-method",
        "JordanDecomposition,JordanDecomposition,missing-method",
        "JordanDecomposition,list,missing-method",
        "JordanDecomposition,missing,matrix-method",
        "JordanDecomposition,missing,missing-method",
        "JordanDecomposition,number,matrix-method",
        "JordanDecomposition,number,missing-method",
        "JordanDecomposition,SmallMultiCompanion,missing-method",
        "JordanDecomposition-methods"
      ]
    },
    {
      "page": "JordanDecompositionDefault-class",
      "title": "A basic class for Jordan decompositions",
      "topics": [
        "coerce,JordanDecompositionDefault,matrix-method",
        "initialize,JordanDecompositionDefault-method",
        "JordanDecomposition-class",
        "JordanDecompositionDefault-class"
      ]
    },
    {
      "page": "make_mcev",
      "title": "Create a multi-companion eigenvector",
      "topics": [
        "make_mcev",
        "make_mcgev"
      ]
    },
    {
      "page": "make_mcmatrix",
      "title": "Generate a multi-companion matrix from spectral description",
      "topics": [
        "make_mcchains",
        "make_mcmatrix"
      ]
    },
    {
      "page": "mc_chain_extend",
      "title": "Extend multi-companion eigenvectors",
      "topics": [
        "mc_chain_extend"
      ]
    },
    {
      "page": "mc_eigen",
      "title": "The eigen decomposition of a multi-companion matrix",
      "topics": [
        "mc_eigen",
        "mc_eigenvalues"
      ]
    },
    {
      "page": "mc_factorize",
      "title": "Factorise multi-companion matrices",
      "topics": [
        "mc_factorize",
        "mc_leftc"
      ]
    },
    {
      "page": "mc_factors",
      "title": "Factors of multi-companion matrices",
      "topics": [
        "mc_factors"
      ]
    },
    {
      "page": "mc_from_factors",
      "title": "Multi-companion matrix from factors",
      "topics": [
        "mc_from_factors",
        "mc_from_filter"
      ]
    },
    {
      "page": "mc_matrix",
      "title": "Basic utilities for multi-companion matrices",
      "topics": [
        "is_mc_bottom",
        "mc_full",
        "mc_matrix",
        "mc_order"
      ]
    },
    {
      "page": "mCompanion",
      "title": "Create objects from class MultiCompanion",
      "topics": [
        "initialize,MultiCompanion-method",
        "mCompanion"
      ]
    },
    {
      "page": "mcSpec",
      "title": "Generate objects of class mcSpec",
      "topics": [
        "initialize,mcSpec-method",
        "mcSpec"
      ]
    },
    {
      "page": "mcSpec-class",
      "title": "A class for spectral specifications of multi-companion matrices",
      "topics": [
        "mcSpec-class"
      ]
    },
    {
      "page": "mcStable",
      "title": "Check if an object is stable",
      "topics": [
        "mcStable",
        "mcStable-methods"
      ]
    },
    {
      "page": "mf_VSform",
      "title": "Extract properties of multi-filters",
      "topics": [
        "mf_order",
        "mf_period",
        "mf_poles",
        "mf_VSform"
      ]
    },
    {
      "page": "MultiCompanion-class",
      "title": "Class \"MultiCompanion\"",
      "topics": [
        "%*%,ANY,MultiCompanion-method",
        "%*%,matrix,MultiCompanion-method",
        "%*%,MultiCompanion,ANY-method",
        "%*%,MultiCompanion,matrix-method",
        "%*%,MultiCompanion,MultiCompanion-method",
        "%*%,MultiCompanion,vector-method",
        "%*%,vector,MultiCompanion-method",
        "coerce,dgeMatrix,MultiCompanion-method",
        "coerce,matrix,MultiCompanion-method",
        "coerce,MultiCompanion,dgeMatrix-method",
        "coerce,MultiCompanion,Matrix-method",
        "coerce,MultiCompanion,matrix-method",
        "mcStable,MultiCompanion-method",
        "MultiCompanion-class",
        "t,MultiCompanion-method",
        "[,MultiCompanion,index,index,logical-method",
        "[,MultiCompanion,index,index,missing-method",
        "[,MultiCompanion,index,missing,logical-method",
        "[,MultiCompanion,index,missing,missing-method",
        "[,MultiCompanion,missing,index,logical-method",
        "[,MultiCompanion,missing,index,missing-method"
      ]
    },
    {
      "page": "MultiFilter-class",
      "title": "Class \"MultiFilter\"",
      "topics": [
        "initialize,MultiFilter-method",
        "mcStable,MultiFilter-method",
        "MultiFilter-class",
        "[,MultiFilter,ANY,ANY,ANY-method"
      ]
    },
    {
      "page": "nullComplement",
      "title": "Compute the orthogonal complement of a subspace",
      "topics": [
        "null_complement"
      ]
    },
    {
      "page": "permute_var",
      "title": "Permute rows and columns of matrices",
      "topics": [
        "permute_synch",
        "permute_var"
      ]
    },
    {
      "page": "rblockmult",
      "title": "Right-multiply a matrix by a block",
      "topics": [
        "rblockmult"
      ]
    },
    {
      "page": "sim_mc",
      "title": "Simulate a multi-companion matrix",
      "topics": [
        "sim_mc"
      ]
    },
    {
      "page": "sim_pcfilter",
      "title": "Generate periodic filters",
      "topics": [
        "sim_pcfilter"
      ]
    },
    {
      "page": "SmallMultiCompanion-class",
      "title": "A class for small multi-companion matrices",
      "topics": [
        "coerce,SmallMultiCompanion,matrix-method",
        "initialize,SmallMultiCompanion-method",
        "SmallMultiCompanion-class"
      ]
    },
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      "title": "Parameterise Jordan chains of multi-companion matrices",
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        "spec_core"
      ]
    },
    {
      "page": "spec_root0",
      "title": "Give the spectral parameters for zero eigenvalues of mc-matrices",
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        "spec_root0"
      ]
    },
    {
      "page": "spec_root1",
      "title": "Give the spectral parameters for eigenvalues of mc-matrices equal to one",
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        "spec_root1"
      ]
    },
    {
      "page": "spec_seeds1",
      "title": "Generate seed parameters for unit mc-eigenvectors",
      "topics": [
        "spec_seeds1"
      ]
    },
    {
      "page": "VAR2pcfilter",
      "title": "PAR representations of VAR models",
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      ]
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