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This method accepts the following custom parameters: This method is selected with method = :trust_region. This is the well-known solution method which relies on a quadraticĪpproximation of the least-squares objective, considered to be valid over aĬompact region centered around the current iterate. The choice between these is achievedīy setting the optional method argument of nlsolve. Three algorithms are currently available. In that case, the syntax is simply:ĭropzeros!(a) # if you also want to remove the sparsity pattern Fine tunings If you do not have a function that compute the Jacobian, it is possible to In turn, there 3 ways of specifying how the Jacobian should be computed: Finite differencing In the following, it is assumed that you have defined a functionį!(F::AbstractVector, x::AbstractVector) or, more generally,į!(F::AbstractArray, x::AbstractArray) computing the residual of the system at point x and putting it into the F argument. This is the most efficient method, because it minimizes the memory allocations. With functions modifying arguments in-place There are various ways of specifying the residuals function and possibly its If r is an object of type SolverResults, thenĬonverged(r) indicates if convergence has occurred. Particular, the field zero of that structure contains the solution ifĬonvergence has occurred. Second, when calling the nlsolve function, it is necessary to give a startingįinally, the nlsolve function returns an object of type SolverResults. Residuals and Jacobianįunctions can take different shapes, see below. In a preallocated matrix passed as first argument. Similarly, the function j! computes the Jacobian of the system and stores it System, and stores them in a preallocated vector passed as first argument. U = exp(x) * cos(x * exp(x) - 1)įirst, note that the function f! computes the residuals of the nonlinear