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Use DocumenterCitations.jl to manage references
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‎docs/Project.toml‎

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[deps]
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Documenter = "e30172f5-a6a5-5a46-863b-614d45cd2de4"
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DocumenterCitations = "daee34ce-89f3-4625-b898-19384cb65244"
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Interpolations = "a98d9a8b-a2ab-59e6-89dd-64a1c18fca59"
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[compat]

‎docs/make.jl‎

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using Documenter
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using DocumenterCitations
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using Interpolations
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DocMeta.setdocmeta!(
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:(using Interpolations),
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recursive = true,
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)
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bib = CitationBibliography(
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joinpath(@__DIR__, "src", "refs.bib"),
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style = :authoryear,
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)
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makedocs(
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sitename = "Interpolations.jl",
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modules = [Interpolations],
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"Library" => "api.md",
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"News and Changes" => "NEWS.md",
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"Other Interpolation Packages" => "other_packages.md",
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"Bilbiography" => "bibliography.md",
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],
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warnonly = false,
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doctest = true,
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plugins = [bib],
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)
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deploydocs(

‎docs/src/api.md‎

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Public = false
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Order = [:function, :type]
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```
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## Bibliography
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```@bibliography
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Pages = ["api.md"]
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Canonical = false
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```

‎docs/src/bibliography.md‎

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# Bibliography
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```@bibliography
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```
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```@bibliography
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*
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```

‎docs/src/control.md‎

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* [`SteffenMonotonicInterpolation`](@ref) -- it does not overshoot.
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You can read about monotonic interpolation in the following sources:
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```@bibliography
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Pages = []
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Canonical = false
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* Fritsch & Carlson (1980), "Monotone Piecewise Cubic Interpolation", doi:10.1137/0717021.
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* Fritsch & Butland (1984), "A Method for Constructing Local Monotone Piecewise Cubic Interpolants", doi:10.1137/0905021.
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* Steffen (1990), "A Simple Method for Monotonic Interpolation in One Dimension", [URL](http://adsabs.harvard.edu/abs/1990A%26A...239..443S)
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Fritsch1980
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Fritsch1984
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Steffen1990
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```

‎docs/src/devdocs.md‎

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broadcast mechanism by overloading the default `BroadcastStyle`. See
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[Customizing broadcasting](https://docs.julialang.org/en/v1/manual/interfaces/#man-interfaces-broadcasting)
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for more details.
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```@bibliography
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Pages = ["devdocs.md"]
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Canonical = false
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```

‎docs/src/refs.bib‎

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@article{Thévenaz2000,
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author = {Th\'evenaz, P. and Blu, T. and Unser, M.},
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journal = {IEEE Transactions on Medical Imaging},
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title = {Interpolation revisited},
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year = {2000},
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volume = {19},
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number = {7},
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pages = {739-758},
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doi = {10.1109/42.875199}
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}
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@article{Fritsch1980,
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author = {Fritsch, F. N. and Carlson, R. E.},
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title = {Monotone Piecewise Cubic Interpolation},
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journal = {SIAM Journal on Numerical Analysis},
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volume = {17},
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number = {2},
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pages = {238-246},
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year = {1980},
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doi = {10.1137/0717021},
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}
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@article{Fritsch1984,
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author = {Fritsch, F. N. and Butland, J.},
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title = {A Method for Constructing Local Monotone Piecewise Cubic Interpolants},
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journal = {SIAM Journal on Scientific and Statistical Computing},
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volume = {5},
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number = {2},
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pages = {300-304},
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year = {1984},
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doi = {10.1137/0905021},
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}
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@article{Steffen1990,
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author = {{Steffen}, M.},
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title = "{A Simple Method for Monotonic Interpolation in One Dimension}",
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journal = {Astronomy and Astrophysics},
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year = {1990},
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volume = {239},
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pages = {443-450},
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url = {https://adsabs.harvard.edu/abs/1990A%26A...239..443S},
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}
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@article{Eilers1996,
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author = {Paul H. C. Eilers and Brian D. Marx},
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title = {Flexible smoothing with B-splines and penalties},
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volume = {11},
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journal = {Statistical Science},
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number = {2},
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publisher = {Institute of Mathematical Statistics},
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pages = {89 -- 121},
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year = {1996},
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doi = {10.1214/ss/1038425655},
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url = {https://projecteuclid.org/euclid.ss/1038425655},
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}
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@article{Akima1970,
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author = {Akima, Hiroshi},
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title = {A New Method of Interpolation and Smooth Curve Fitting Based on Local Procedures},
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year = {1970},
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publisher = {Association for Computing Machinery},
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address = {New York, NY, USA},
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volume = {17},
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number = {4},
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issn = {0004-5411},
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doi = {10.1145/321607.321609},
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journal = {J. ACM},
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pages = {589--602},
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numpages = {14},
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}

‎src/b-splines/b-splines.jl‎

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`λ` is non-negative. If its value is zero, it falls back to non-regularized interpolation.
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[1] https://projecteuclid.org/euclid.ss/1038425655.
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# References
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- [Eilers and Marx, 1996, Statist. Sci. 11(2), 1996](@cite Eilers1996)
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"""
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function interpolate(A::AbstractArray, it::IT, λ::Real, k::Int) where {IT<:DimSpec{BSpline}}
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interpolate(tweight(A), tcoef(A), A, it, λ, k)

‎src/monotonic/monotonic.jl‎

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"""
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AkimaMonotonicInterpolation
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Monotonic interpolation based on Akima (1970),
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Monotonic interpolation based on [Akima (1970)
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"A New Method of Interpolation and Smooth Curve Fitting Based on Local Procedures",
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doi:10.1145/321607.321609.
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doi:10.1145/321607.321609](@cite Akima1970).
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Tangents are determined at each given point locally,
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results are close to manual drawn curves
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"""
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FritschCarlsonMonotonicInterpolation
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Monotonic interpolation based on Fritsch & Carlson (1980),
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"Monotone Piecewise Cubic Interpolation", doi:10.1137/0717021.
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Monotonic interpolation based on [Fritsch & Carlson (1980),
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"Monotone Piecewise Cubic Interpolation", doi:10.1137/0717021](@cite Fritsch1980).
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Tangents are first initialized, then adjusted if they are not monotonic
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can overshoot for non-monotonic data
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"""
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FritschButlandMonotonicInterpolation
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Monotonic interpolation based on Fritsch & Butland (1984),
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Monotonic interpolation based on [Fritsch & Butland (1984),
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"A Method for Constructing Local Monotone Piecewise Cubic Interpolants",
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doi:10.1137/0905021.
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doi:10.1137/0905021](@cite Fritsch1984).
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Faster than FritschCarlsonMonotonicInterpolation (only requires one pass)
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but somewhat higher apparent "tension".
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"""
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SteffenMonotonicInterpolation
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Monotonic interpolation based on Steffen (1990),
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Monotonic interpolation based on [Steffen (1990),
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"A Simple Method for Monotonic Interpolation in One Dimension",
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http://adsabs.harvard.edu/abs/1990A%26A...239..443S
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http://adsabs.harvard.edu/abs/1990A%26A...239..443S](@cite Steffen1990)
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Only one pass, results usually between FritschCarlson and FritschButland.
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"""

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