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项目作者： dmbates

项目描述 ：
Nonlinear regression in Julia
高级语言： Julia
项目地址: git://github.com/dmbates/NLreg.jl.git
创建时间： 2013-09-12T17:47:04Z
项目社区：https://github.com/dmbates/NLreg.jl
开源协议：
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Nonlinear regression

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This package is an experiment in using the Zygote automatic differentiation package and the lowrankupdate! function in the LinearAlgebra package to solve the linear least squares problem for a Gauss-Newton update.

The data are represented as a Tables.RowTable, which is a vector of NamedTuples. The model parameters are also a NamedTuple. The model function is given as a function of two arguments - the parameters and a data row.

Example - a Michaelis-Menten fit

In the
Michaelis-Menten model
for enzyme kinetics,

  1. v = Vm * c / (K + c)

the relationship between the velocity, v, of a reaction and the
concentration, c, of the substrate depends on two parameters; Vm,
the maximum velocity and K, the Michaelis parameter. The Vm
parameter occurs linearly in this expression whereas K is a
nonlinear parameter.

  1. julia> using CSV, DataFrames, NLreg
  3. julia> datadir = normpath(joinpath(dirname(pathof(NLreg)), "..", "data"));
  5. julia> PurTrt = first(groupby(CSV.read(joinpath(datadir, "Puromycin.csv")), :state))
  6. 12×3 SubDataFrame
  7. │ Row │ conc    │ rate    │ state   │
  8. │     │ Float64 │ Float64 │ String  │
  9. ├─────┼─────────┼─────────┼─────────┤
  10. │ 1   │ 0.02    │ 76.0    │ treated │
  11. │ 2   │ 0.02    │ 47.0    │ treated │
  12. │ 3   │ 0.06    │ 97.0    │ treated │
  13. ⋮
  14. │ 9   │ 0.56    │ 191.0   │ treated │
  15. │ 10  │ 0.56    │ 201.0   │ treated │
  16. │ 11  │ 1.1     │ 207.0   │ treated │
  17. │ 12  │ 1.1     │ 200.0   │ treated │
  19. julia> pm1 = fit(NLregModel, PurTrt, :rate, (p,d) -> p.Vm * d.conc/(p.K + d.conc),
  20.                   (Vm = 200., K = 0.05))
  21. Nonlinear regression model fit by maximum likelihood
  23. Data schema (response variable is rate)
  24. Tables.Schema:
  25.  :conc   Float64
  26.  :rate   Float64
  27.  :state  String
  28. Number of observations:                  12
  30. Parameter estimates
  31. ───────────────────────────────────────
  32.       Estimate   Std.Error  t-statistic
  33. ───────────────────────────────────────
  34. Vm  212.684     6.94715        30.6145
  35. K     0.064121  0.00828092      7.74322
  36. ───────────────────────────────────────
  38. Sum of squared residuals at convergence: 1195.4488145417758
  39. Achieved convergence criterion:          8.798637504793927e-6