fstats_levenberg_marquardt Module

Uses

- fstats_regression
- iso_fortran_env
- fstats_errors
- linalg
- ieee_arithmetic

Variables

Type	Visibility	Attributes		Name		Initial
integer(kind=int32),	public,	parameter	::	FS_LEVENBERG_MARQUARDT_UPDATE	=	1
integer(kind=int32),	public,	parameter	::	FS_NIELSEN_UPDATE	=	3
integer(kind=int32),	public,	parameter	::	FS_QUADRATIC_UPDATE	=	2

Derived Types

type, public :: lm_solver_options

Options to control the Levenberg-Marquardt solver.

Components

Type	Visibility	Attributes		Name		Initial
real(kind=real64),	public		::	damping_decrease_factor			The factor to use when decreasing the damping parameter.
real(kind=real64),	public		::	damping_increase_factor			The factor to use when increasing the damping parameter.
real(kind=real64),	public		::	finite_difference_step_size			The step size used for the finite difference calculations of the Jacobian matrix.
integer(kind=int32),	public		::	method			The solver method to utilize. - FS_LEVENBERG_MARQUARDT_UPDATE: - FS_QUADRATIC_UPDATE: - FS_NIELSEN_UDPATE:

Type-Bound Procedures

procedure, public :: set_to_default => lm_set_default_settings

Subroutines

public subroutine nonlinear_least_squares(fun, x, y, params, ymod, resid, weights, maxp, minp, stats, alpha, controls, settings, info, status, cov, args)

Performs a nonlinear regression to fit a model using a version of the Levenberg-Marquardt algorithm.

Arguments

Type	Intent	Optional	Attributes		Name
procedure(regression_function),	intent(in),		pointer	::	fun	A pointer to the regression_function to evaluate.
real(kind=real64),	intent(in)			::	x(:)	The M-element array containing independent data.
real(kind=real64),	intent(in)			::	y(:)	The M-element array containing dependent data.
real(kind=real64),	intent(inout)			::	params(:)	On input, the N-element array containing the initial estimate of the model parameters. On output, the computed model parameters.
real(kind=real64),	intent(out)			::	ymod(:)	An M-element array where the modeled dependent data will be written.
real(kind=real64),	intent(out)			::	resid(:)	An M-element array where the model residuals will be written.
real(kind=real64),	intent(in),	optional,	target	::	weights(:)	An optional M-element array allowing the weighting of individual points.
real(kind=real64),	intent(in),	optional,	target	::	maxp(:)	An optional N-element array that can be used as upper limits on the parameter values. If no upper limit is requested for a particular parameter, utilize a very large value. The internal default is to utilize huge() as a value.
real(kind=real64),	intent(in),	optional,	target	::	minp(:)	An optional N-element array that can be used as lower limits on the parameter values. If no lower limit is requested for a particalar parameter, utilize a very large magnitude, but negative, value. The internal default is to utilize -huge() as a value.
type(regression_statistics),	intent(out),	optional		::	stats(:)	An optional N-element array that, if supplied, will be used to return statistics about the fit for each parameter.
real(kind=real64),	intent(in),	optional		::	alpha	The significance level at which to evaluate the confidence intervals. The default value is 0.05 such that a 95% confidence interval is calculated.
type(iteration_controls),	intent(in),	optional		::	controls	An optional input providing custom iteration controls.
type(lm_solver_options),	intent(in),	optional		::	settings	An optional input providing custom settings for the solver.
type(convergence_info),	intent(out),	optional,	target	::	info	An optional output that can be used to gain information about the iterative solution and the nature of the convergence.
procedure(iteration_update),	intent(in),	optional,	pointer	::	status	An optional pointer to a routine that can be used to extract iteration information.
real(kind=real64),	intent(out),	optional,	dimension(:,:)	::	cov	An optional N-by-N matrix that, if supplied, will be used to return the covariance matrix, computed from an SVD of the final weighted Jacobian. Rank diagnostics are available in info when requested.
class(*),	intent(inout),	optional		::	args	An optional argument allowing the passing in/out of data for the fun routine.