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 anduser_interaction, information on user stops (see settings). The backend may define additional fields. 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 be0(maximum number of iterations exceeded),2(parameter change less than specified precision in two consecutive iterations), or3(improvement in objective function – e.g. sum of squares – less than specified), or-1(algorithm aborted by a user function).See also: nonlin_curvefit.
The fields of the settings structure can be set with optimset.
For settings common to all frontends (including these for statistics) see Common frontend options.
For additional settings common to all optimization frontends see Common optimization options.
Algorithm:
| "lm_svd_feasible"
|
weightsdfdpdfdp was specified by the user, the informational structure has
the fields f: value of residuals for current parameters, reshaped
to a column vector, fixed: logical vector indicating which
parameters are not optimized, so these partial derivatives need not be
computed and can be set to zero, diffp, diff_onesided,
lbound, ubound: identical to the user settings of this
name, plabels: 1-dimensional cell-array of column-cell-arrays,
each column with labels for all parameters; the first column contains
the numerical indices of the parameters; the second and third columns,
present for structure based parameter handling, see
Parameter structures, contain the names of the parameters and the subindices of
the parameters, see
Non-scalar parameters, respectively. The default
jacobian function will call the model function with the second argument
set with fields f: as the f passed to the jacobian
function, plabels: cell-array of 1x1 cell-arrays with the entries
of the column-cell-arrays of plabels as passed to the jacobian
function corresponding to current parameter, side: 0 for
one-sided interval, 1 or 2, respectively, for the sides of
a two-sided interval, and parallel: logical scalar indicating
parallel computation of partial derivatives. This information can be
useful if the model function can omit some computations depending on the
currently computed partial derivative.
complex_step_derivative_ffalse. Estimate Jacobian of model
function with complex step derivative approximation. Use only if you
know that your model function is suitable for this. No user function for
the Jacobian (dfdp) must be specified.
plot_cmduser_interaction instead (see
Common optimization options).
Please see Parameter structures.
Please see Residual optimization and choose backend from menu under `Optimization backends'.