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Function File: [p, resid, cvg, outp] = nonlin_residmin (f, pin)
Function File: [p, resid, cvg, outp] = nonlin_residmin (f, pin, settings)

Frontend for nonlinear minimization of residuals returned by a model function.

The functions supplied by the user have a minimal interface; any additionally needed constants (e.g. observed values) can be supplied by wrapping the user functions into anonymous functions.

The following description applies to usage with vector-based parameter handling. Differences in usage for structure-based parameter handling will be explained separately.

f: function returning the array of residuals. It gets a column vector of real parameters as argument. In gradient determination, this function may be called with an informational second argument, whose content depends on the function for gradient determination.

pin: real column vector of initial parameters.

settings: structure whose fields stand for optional settings referred to below. The fields can be set by optimset().

The returned values are the column vector of final parameters p, the final array of residuals resid, an integer cvg indicating if and how optimization succeeded or failed, and a structure outp with additional information, curently with the fields: niter, the number of iterations and user_interaction, information on user stops (see settings). The backend may define additional fields. If the backend supports it, outp has a field lambda with determined Lagrange multipliers of any constraints, seperated into subfields lower and upper for bounds, eqlin and ineqlin for linear equality and inequality constraints (except bounds), respectively, and eqnonlin and ineqnonlin for general equality and inequality constraints, respectively. cvg is greater than zero for success and less than or equal to zero for failure; its possible values depend on the used backend and currently can be 0 (maximum number of iterations exceeded), 2 (parameter change less than specified precision in two consecutive iterations), or 3 (improvement in objective function – e.g. sum of squares – less than specified), or -1 (algorithm aborted by a user function).

For settings, type optim_doc ("nonlin_residmin").

For desription of structure-based parameter handling, type optim_doc ("parameter structures").

For description of individual backends (currently only one), type optim_doc ("residual optimization") and choose the backend in the menu.

See also: nonlin_curvefit.

Demonstration 1

The following code

  ## Example for linear inequality constraints
  ## (see also the same example in 'demo nonlin_curvefit')

  ## independents
  indep = 1:5;
  ## residual function:
  f = @ (p) p(1) * exp (p(2) * indep) - [1, 2, 4, 7, 14];
  ## initial values:
  init = [.25; .25];
  ## linear constraints, A.' * parametervector + B >= 0
  A = [1; -1]; B = 0; # p(1) >= p(2);
  settings = optimset ("inequc", {A, B});

  ## start optimization
  [p, residuals, cvg, outp] = nonlin_residmin (f, init, settings)

Produces the following output

p =

   0.62034
   0.62034

residuals =

   0.153573   0.145149  -0.010949   0.417915  -0.205878

cvg =  3
outp =

  scalar structure containing the fields:

    user_interaction =

      scalar structure containing the fields:

        stop = [](0x1)
        info = {}(0x1)

    niter =  7
    lambda =

      scalar structure containing the fields:

        lower =

           0
           0

        upper =

           0
           0

        eqlin = [](0x0)
        ineqlin =  269.24
        eqnonlin = [](1x0)
        ineqnonlin = [](1x0)

Package: optim