dcsrch.f File Reference

Go to the source code of this file.

Functions/Subroutines
subroutine	dcsrch (f, g, stp, ftol, gtol, xtol, stpmin, stpmax, task, isave, dsave)
	This subroutine finds a step that satisfies a sufficient decrease condition and a curvature condition. More...

Function/Subroutine Documentation

dcsrch()

subroutine dcsrch	(	double precision	f,
		double precision	g,
		double precision	stp,
		double precision	ftol,
		double precision	gtol,
		double precision	xtol,
		double precision	stpmin,
		double precision	stpmax,
		character*(*)	task,
		integer, dimension(2)	isave,
		double precision, dimension(13)	dsave
	)

This subroutine finds a step that satisfies a sufficient decrease condition and a curvature condition.

Each call of the subroutine updates an interval with endpoints stx and sty. The interval is initially chosen so that it contains a minimizer of the modified function

  psi(stp) = f(stp) - f(0) - ftol*stp*f'(0).

If psi(stp) <= 0 and f'(stp) >= 0 for some step, then the interval is chosen so that it contains a minimizer of f.

The algorithm is designed to find a step that satisfies the sufficient decrease condition

  f(stp) <= f(0) + ftol*stp*f'(0),

and the curvature condition

  abs(f'(stp)) <= gtol*abs(f'(0)).

If ftol is less than gtol and if, for example, the function is bounded below, then there is always a step which satisfies both conditions.

If no step can be found that satisfies both conditions, then the algorithm stops with a warning. In this case stp only satisfies the sufficient decrease condition.

A typical invocation of dcsrch has the following outline:

   task = 'START'
10 continue
   call dcsrch( ... )
   if (task .eq. 'FG') then
     evaluate the function and the gradient at stp 
   goto 10
   end if

NOTE: The user must no alter work arrays between calls.

Parameters

f	On initial entry f is the value of the function at 0. On subsequent entries f is the value of the function at stp. On exit f is the value of the function at stp.
g	On initial entry g is the derivative of the function at 0. On subsequent entries g is the derivative of the function at stp. On exit g is the derivative of the function at stp.
stp	On entry stp is the current estimate of a satisfactory step. On initial entry, a positive initial estimate must be provided. On exit stp is the current estimate of a satisfactory step if task = 'FG'. If task = 'CONV' then stp satisfies the sufficient decrease and curvature condition.
ftol	On entry ftol specifies a nonnegative tolerance for the sufficient decrease condition. On exit ftol is unchanged.
gtol	On entry gtol specifies a nonnegative tolerance for the curvature condition. On exit gtol is unchanged.
xtol	On entry xtol specifies a nonnegative relative tolerance for an acceptable step. The subroutine exits with a warning if the relative difference between sty and stx is less than xtol. On exit xtol is unchanged.
stpmin	On entry stpmin is a nonnegative lower bound for the step. On exit stpmin is unchanged.
stpmax	On entry stpmax is a nonnegative upper bound for the step. On exit stpmax is unchanged.
task	On initial entry task must be set to 'START'. On exit task indicates the required action: If task(1:2) = 'FG' then evaluate the function and derivative at stp and call dcsrch again. If task(1:4) = 'CONV' then the search is successful. If task(1:4) = 'WARN' then the subroutine is not able to satisfy the convergence conditions. The exit value of stp contains the best point found during the search. If task(1:5) = 'ERROR' then there is an error in the input arguments. On exit with convergence, a warning or an error, the variable task contains additional information.
isave	work array
dsave	work array

Definition at line 94 of file dcsrch.f.

References dcstep().

Referenced by lnsrlb().

Here is the call graph for this function:

Here is the caller graph for this function: