MINPACK
所属分类：collect
开发工具：Julia
文件大小：0KB
下载次数：0
上传日期：2021-01-11 15:09:44
上 传 者：
sh-1993
说明： cminpack多元根查找例程的包装器，
(Wrapper for cminpack multivariate root finding routines,)
文件列表:
.JuliaFormatter.toml (79, 2023-11-16)
.codecov.yml (15, 2023-11-16)
LICENSE.md (1166, 2023-11-16)
Project.toml (514, 2023-11-16)
deps/ (0, 2023-11-16)
deps/build.jl (846, 2023-11-16)
notes.md (1094, 2023-11-16)
src/ (0, 2023-11-16)
src/MINPACK.jl (5663, 2023-11-16)
src/wrappers.jl (21073, 2023-11-16)
test/ (0, 2023-11-16)
test/runtests.jl (16060, 2023-11-16)
# MINPACK
[](https://travis-ci.org/sglyon/MINPACK.jl)
[](https://ci.appveyor.com/project/spencerlyon2/minpack-jl)
[](https://coveralls.io/github/sglyon/MINPACK.jl?branch=master)
[](http://codecov.io/github/sglyon/MINPACK.jl?branch=master)
Julia interface to [cminpack](https://github.com/devernay/cminpack), a C/C++ rewrite of the MINPACK software (originally in fortran).
## Usage
Usage is quite simple, there are two main API methods:
```julia
fsolve(f!::Function, x0::Vector{Float64}, m::Int=length(x0); tol::Float64=1e-8,
show_trace::Bool=false, tracing::Bool=false, method::Symbol=:hybr,
iterations::Int=typemax(Int), io::IO=STDOUT, kwargs...)
fsolve(f!::Function, g!::Function, x0::Vector{Float64}, m::Int=length(x0);
tol::Float64=1e-8, show_trace::Bool=false, tracing::Bool=false,
method::Symbol=:hybr, iterations::Int=typemax(Int), io::IO=STDOUT,
kwargs...)
```
The functions `f!` and `g!` should accept the current point (call it `x`) as the _second_ argument and fill the first argument with the function values and Jacobian matrix, repsectively. If no Jacobian is passed, one will be approximated using finite differences.
Example:
```julia
julia> using MINPACK
julia> function f!(fvec, x)
fvec[1] = (x[1]+3)*(x[2]^3-7)+18
fvec[2] = sin(x[2]*exp(x[1])-1)
fvec
end;
julia> function g!(fjac, x)
fjac[1, 1] = x[2]^3 - 7
fjac[1, 2] = 3 * (x[1] + 3) * x[2]*x[2]
fjac[2, 1] = x[2] * exp(x[1]) * cos(x[2] * exp(x[1]) - 1)
fjac[2, 2] = exp(x[1]) * cos(x[2] * exp(x[1]) - 1)
fjac
end
g! (generic function with 2 methods)
julia> res_jac = fsolve(f!, g!, ones(2))
Results of Nonlinear Solver Algorithm
* Algorithm: Modified Powell (User Jac, Expert)
* Starting Point: [1.0, 1.0]
* Zero: [6.05177e-12, 1.0]
* Inf-norm of residuals: 0.000000
* Convergence: true
* Message: algorithm estimates that the relative error between x and the solution is at most tol
* Total time: 0.033416 seconds
* Function Calls: 0
* Jacobian Calls (df/dx): 0
julia> res_nojac = fsolve(f!, ones(2))
Results of Nonlinear Solver Algorithm
* Algorithm: Modified Powell
* Starting Point: [1.0, 1.0]
* Zero: [6.05138e-12, 1.0]
* Inf-norm of residuals: 0.000000
* Convergence: true
* Message: algorithm estimates that the relative error between x and the solution is at most tol
* Total time: 0.000024 seconds
* Function Calls: 0
* Jacobian Calls (df/dx): 0
```
The additional available keyword arguments captured by `;kwargs...` vary by the method used.
The keyword argument `method` can take on different value depending on which method of `fsolve` you are calling.
Available methods for the version where only `f!` is pased are:
- `:hybr`: Modified version of Powell's algorithm. Uses MINPACK routine [`hybrd1`](https://github.com/devernay/cminpack/blob/d1f5f5a273862ca1bbcf58394e4ac060d9e22c76/hybrd1.c)
- `:lm`: Levenberg-Marquardt. Uses MINPACK routine [`lmdif1`](https://github.com/devernay/cminpack/blob/d1f5f5a273862ca1bbcf58394e4ac060d9e22c76/lmdif1.c)
- `:lmdif`: Advanced Levenberg-Marquardt (more options available with `;kwargs...`). See MINPACK routine [`lmdif`](https://github.com/devernay/cminpack/blob/d1f5f5a273862ca1bbcf58394e4ac060d9e22c76/lmdif.c) for more information
- `:hybrd`: Advacned modified version of Powell's algorithm (more options available with `;kwargs...`). See MINPACK routine [`hybrd`](https://github.com/devernay/cminpack/blob/d1f5f5a273862ca1bbcf58394e4ac060d9e22c76/hybrd.c) for more information
Available methods for the version where both `f!` and `g!` are passed are:
- `:hybr`: Advacned modified version of Powell's algorithm with user supplied Jacobian. Additional arguments are available via `;kwargs...`. See MINPACK routine [`hybrj`](https://github.com/devernay/cminpack/blob/d1f5f5a273862ca1bbcf58394e4ac060d9e22c76/hybrj.c) for more information
- `:lm`: Advanced Levenberg-Marquardt with user supplied Jacobian. Additional arguments are available via `;kwargs...`. See MINPACK routine [`lmder`](https://github.com/devernay/cminpack/blob/d1f5f5a273862ca1bbcf58394e4ac060d9e22c76/lmder.c) for more information
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