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  "Title": "Functions for Nonlinear Least Squares Solutions - Updated 2022",
  "Version": "2025.02.16",
  "Date": "2025-02-16",
  "Authors@R": "c(person(given = c(\"John\", \"C\"), family = \"Nash\", \nrole = c(\"aut\", \"cre\"), email = \"nashjc@uottawa.ca\"),\nperson(given = \"Duncan\", family = \"Murdoch\", role = \"aut\",\nemail = \"murdoch.duncan@gmail.com\"),\nperson(given= \"Fernando\", family = \"Miguez\", role=\"ctb\",\nemail=\"femiguez@iastate.edu\"),\nperson(given= \"Arkajyoti\", family = \"Bhattacharjee\", role=\"ctb\",\nemail=\"arkastat98@gmail.com\"))",
  "Maintainer": "John C Nash <nashjc@uottawa.ca>",
  "Description": "Provides tools for working with nonlinear least squares\nproblems. For the estimation of models reliable and robust\ntools than nls(), where the the Gauss-Newton method frequently\nstops with 'singular gradient' messages. This is accomplished\nby using, where possible, analytic derivatives to compute the\nmatrix of derivatives and a stabilization of the solution of\nthe estimation equations. Tools for approximate or externally\nsupplied derivative matrices are included. Bounds and masks on\nparameters are handled properly.",
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    "nlsSimplify",
    "nlxb",
    "numericDerivR",
    "nvec",
    "pctrl",
    "pnls",
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    "prt",
    "pshort",
    "rawres",
    "resgr",
    "resss",
    "SSlogisJN",
    "SSmod2rjfun",
    "sysDerivs",
    "sysSimplifications",
    "wrapnlsr"
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      "title": "fitted.nlsr",
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      "title": "jaback",
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    },
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      "title": "model2rjfun",
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        "model2rjfun",
        "model2ssgrfun",
        "modelexpr",
        "SSmod2rjfun"
      ]
    },
    {
      "page": "nlfb",
      "title": "nlfb: nonlinear least squares modeling by functions",
      "topics": [
        "nlfb"
      ]
    },
    {
      "page": "nlsDeriv",
      "title": "nlsDeriv Functions to take symbolic derivatives.",
      "topics": [
        "codeDeriv",
        "fnDeriv",
        "nlsDeriv"
      ]
    },
    {
      "page": "nlsr",
      "title": "nlsr function",
      "topics": [
        "nlsr"
      ]
    },
    {
      "page": "nlsr.control",
      "title": "nlsr.control",
      "topics": [
        "nlsr.control"
      ]
    },
    {
      "page": "nlsr.package",
      "title": "nlsr-package Tools for solving nonlinear least squares problems The package provides some tools related to using the Nash variant of Marquardt's algorithm for nonlinear least squares. Jacobians can usually be developed by automatic or symbolic derivatives.",
      "topics": [
        "nlsr.package"
      ]
    },
    {
      "page": "nlsrSS",
      "title": "nlsrSS - solve selfStart nonlinear least squares with nlsr package",
      "topics": [
        "nlsrSS"
      ]
    },
    {
      "page": "nlxb",
      "title": "nlxb: nonlinear least squares modeling by formula",
      "topics": [
        "nlxb"
      ]
    },
    {
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      "title": "numericDerivR: numerically evaluates the gradient of an expression. All in R",
      "topics": [
        "numericDerivR"
      ]
    },
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      "title": "pctrl",
      "topics": [
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      "topics": [
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      ]
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      "title": "predict.nlsr",
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        "predict.nlsr"
      ]
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      "title": "print.nlsr",
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        "print.nlsr"
      ]
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      "title": "prt",
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    },
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      "title": "pshort",
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      "title": "rawres",
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      "title": "resgr",
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      "title": "resid.nlsr",
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    },
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      "title": "Alternative self start for three-parameter logistic function SSlogis",
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      "author": "John C. Nash",
      "engine": "knitr::rmarkdown",
      "headings": [
        "Overview and objectives",
        "0. Issues remaining to address and TODOS",
        "nls() uses different models with different algorithm choices",
        "MINOR -- Bounds specification and warnings for nlsLM and nls.lm",
        "MINOR -- nlsLM and nls.lm do not warn of out of bounds initial parameters",
        "Bounded minimization with minpack.lm",
        "TODOS",
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        "nlxb",
        "model2rjfun, model2ssgrfun, modelexpr",
        "nlfb -- minimize nonlinear least squares residual functions",
        "coef.nlsr",
        "print.nlsr",
        "summary.nlsr",
        "wrapnlsr",
        "resgr, resss",
        "nlsDeriv, codeDeriv, fnDeriv, newDeriv",
        "nlsSimplify and related functions",
        "2. Analytic versus approximate Jacobians",
        "Specifying approximations to nlfb",
        "Specifying Jacobian approximations to nlxb",
        "3. Weighted nonlinear regression",
        "Static weights",
        "Dynamic weights via the wfct() function",
        "Weights built into a one-sided model function",
        "4. Relative offset and other convergence criteria",
        "Overview of the ROCC test",
        "Some implementation ideas for the ROCC",
        "Other convergence and termination tests",
        "5. Implementation of nonlinear least squares methods",
        "Gauss-Newton variants",
        "Choices",
        "Using matrix decompositions",
        "6. Fixed parameters",
        "Motivation for fixed parameters",
        "Background for fixed parameters",
        "Internal structures to specify fixed parameters",
        "Proposed approaches to fix parameters",
        "Examples of use of fixed parameters",
        "7. Capabilities added to nlsr in the 2022 version",
        "Numerical approximations to Jacobians",
        "Self start models",
        "Models with partially linear parameters",
        "8. Capabilities still missing from nlsr",
        "Automatic differentiation of functional models",
        "Indexed parameters",
        "9. Nonlinear equations and other non-modelling problems",
        "Appendix A: Providing exogenous data",
        "Appendix B: Derivative approximation in nls()",
        "From nls.R",
        "From nls.c",
        "nlsr::numericDerivR.R",
        "Appendix C: A comparison of nlsr::nlxb with nls and minpack::nlsLM",
        "Principal differences",
        "Derivative information",
        "Consequences of different derivative computations",
        "Timing comparisons",
        "Programmatic modelling functions",
        "Functional expression of residuals and Jacobian",
        "Marquardt stabilization",
        "Criterion used to terminate the iteration",
        "Output of the modelling functions",
        "Prediction",
        "An illustrative nonlinear regression problem",
        "nls",
        "nlsr",
        "minpack.lm",
        "Problems that are NOT regressions",
        "A check on the Brown and Dennis calculation via function minimization",
        "References"
      ],
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      "modified": "2024-04-06 14:57:36",
      "commits": 2
    },
    {
      "source": "nlsr-derivs.Rmd",
      "filename": "nlsr-derivs.html",
      "title": "nlsr and Other Approaches to Derivatives in R",
      "author": "John C. Nash",
      "engine": "knitr::rmarkdown",
      "headings": [
        "Available analytic differentiation tools",
        "How the tools are used",
        "stats (i.e., the base R installation)",
        "nlsr",
        "Deriv",
        "Ryacas",
        "Derivatives and simplifications -- base R",
        "Derivatives and simplifications -- package nlsr",
        "Derivatives table",
        "Notes:",
        "Simplifying algebraic expressions",
        "Derivatives and simplifications -- package Deriv",
        "Simplifications",
        "Comparison with other approaches",
        "check modelexpr() works with an ssgrfun ??",
        "test model2rjfun vs model2rjfunx ??",
        "Need more extensive discussion of Simplify??",
        "Issues of programming on the language",
        "Another issue:",
        "Indexed parameters or variables",
        "References"
      ],
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      "modified": "2024-04-06 14:57:36",
      "commits": 2
    },
    {
      "source": "Intro-to-nlsr.Rmd",
      "filename": "Intro-to-nlsr.pdf",
      "title": "An introduction to nlsr",
      "author": "John C. Nash",
      "engine": "knitr::rmarkdown",
      "headings": [
        "What does nlsr do?",
        "Output object",
        "Jacobian calculation",
        "Stabilization of Gauss-Newton computations",
        "Programming language",
        "An illustrative example",
        "Problem setup",
        "Solution attempts with nls()",
        "Solution attempts with nlsr tools",
        "Solution attempts with minpack.lm",
        "Solution attempts with wrapnlsr() wrapper",
        "Commentary",
        "Extracting standard errors from nlsr solutions",
        "selfStart options",
        "SSlogisJN.R for the 3-parameter logistic",
        "Running selfStart models with nlxb()",
        "Starting parameters for the Logistic3U model",
        "Jacobian computation",
        "Bounds constraints on parameters",
        "Functional specification of nonlinear least squares problems",
        "Weighted nonlinear regression",
        "Static weights",
        "Weights that are functions of the model parameters",
        "Models that use multiple functional forms",
        "Two straight lines",
        "The WOOD test function",
        "Ongoing efforts",
        "References"
      ],
      "created": "2023-09-03 16:56:00",
      "modified": "2024-04-06 15:04:41",
      "commits": 5
    },
    {
      "source": "FixedParameters.Rmd",
      "filename": "FixedParameters.html",
      "title": "Specifying and Using Fixed Parameters in Nonlinear Estimation",
      "author": "John C. Nash",
      "engine": "knitr::rmarkdown",
      "headings": [
        "Motivation",
        "Background",
        "Internal structures",
        "Proposed algorithmic approaches",
        "Examples of use",
        "For optimx",
        "An extensible bell-curve model",
        "References"
      ],
      "created": "2023-09-03 16:56:00",
      "modified": "2024-04-06 14:57:36",
      "commits": 2
    },
    {
      "source": "R-analytic-derivatives.Rmd",
      "filename": "R-analytic-derivatives.html",
      "title": "Symbolic and analytical derivatives in R",
      "author": "John C. Nash",
      "engine": "knitr::rmarkdown",
      "headings": [
        "Available analytic differentiation tools",
        "How the tools are used",
        "stats (i.e., the base R installation)",
        "nlsr",
        "Deriv",
        "Ryacas",
        "Derivatives and simplifications -- base R",
        "Derivatives and simplifications -- package nlsr",
        "Derivatives table",
        "Notes:",
        "Simplifying algebraic expressions",
        "Derivatives and simplifications -- package Deriv",
        "Simplifications",
        "Comparison with other approaches",
        "check modelexpr() works with an ssgrfun ??",
        "test model2rjfun vs model2rjfunx ??",
        "Need more extensive discussion of Simplify??",
        "Issues of programming on the language",
        "Indexed parameters or variables",
        "Appendix D: A comparison of nlsr::nlxb with nls and minpack::nlsLM",
        "Principal differences",
        "Derivative information",
        "Consequences of different derivative computations",
        "Timing comparisons",
        "Programmatic modelling functions",
        "Functional expression of residuals and Jacobian",
        "Marquardt stabilization",
        "Criterion used to terminate the iteration",
        "Output of the modelling functions",
        "Prediction",
        "An illustrative nonlinear regression problem",
        "nls",
        "minpack.lm",
        "Problems that are NOT regressions",
        "A check on the Brown and Dennis calculation via function minimization",
        "References"
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      "created": "2023-09-03 16:56:00",
      "modified": "2024-04-06 14:57:36",
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