minc.c File Reference

Finds the minimum of a multi-parameter function with parameter constraints. More...

#include "mdb.h"

Go to the source code of this file.

Functions
double	minc (double *fn, double *x, double *dx, double *dx_lim, double *xlo, double *xhi, long np, long ns_max, long p_flag)
	Finds the minimum of a multi-parameter function with constraints.

Detailed Description

Finds the minimum of a multi-parameter function with parameter constraints.

This file contains the implementation of the minc() function, which searches for the minimum of a multi-parameter function while respecting constraints on the parameter ranges.

Copyright

• (c) 2002 The University of Chicago, as Operator of Argonne National Laboratory.
• (c) 2002 The Regents of the University of California, as Operator of Los Alamos National Laboratory.

License

This file is distributed under the terms of the Software License Agreement found in the file LICENSE included with this distribution.

Author

M. Borland, C. Saunders, R. Soliday

Definition in file minc.c.

Function Documentation

minc()

double minc	(	double *	fn,
		double *	x,
		double *	dx,
		double *	dx_lim,
		double *	xlo,
		double *	xhi,
		long	np,
		long	ns_max,
		long	p_flag )

Finds the minimum of a multi-parameter function with constraints.

The minc() function searches for the minimum value of a user-defined multi-parameter function, allowing constraints on the range of each parameter. It iteratively adjusts the parameters within specified limits to find the function's minimum value.

Parameters

fn	Pointer to the function to be minimized.
x	Array of starting values for the parameters.
dx	Array of step sizes for each parameter.
dx_lim	Array of step size limits for each parameter.
xlo	Array of lower bounds for the parameters.
xhi	Array of upper bounds for the parameters.
np	Number of parameters.
ns_max	Maximum number of steps to take before increasing the step size.
p_flag	If >= 0, prints information during the minimization process.

Returns

The minimum value of the function.

Definition at line 40 of file minc.c.

{
  register long i, n_steps, pc;
  register double f0, f1, _dx;
  long flag, *constraint, at_upper, at_lower;
 
  pc = 0;
  constraint = tmalloc(sizeof(long) * np);
  for (i = 0; i < np; i++)
    constraint[i] = xlo[i] != xhi[i];
 
  f0 = (*fn)(x);
 
  do {
    for (i = flag = 0; i < np; i++) {
      if (fabs(_dx = dx[i]) < dx_lim[i]) {
        flag++;
        continue;
      }
      x[i] += _dx;
      if (constraint[i]) {
        if (x[i] < xlo[i]) {
          x[i] = xlo[i] + 2 * (dx[i] = fabs(_dx) / 2);
          continue;
        }
        if (x[i] > xhi[i]) {
          x[i] = xhi[i] + 2 * (dx[i] = -fabs(_dx) / 2);
          continue;
        }
      }
      f1 = (*fn)(x);
      n_steps = 0;
      if (f1 > f0) {
        dx[i] = _dx = -_dx;
        x[i] += 2 * _dx;
        if (constraint[i]) {
          if (x[i] < xlo[i]) {
            x[i] = xlo[i] + 2 * (dx[i] = fabs(_dx) / 2);
            continue;
          }
          if (x[i] > xhi[i]) {
            x[i] = xhi[i] + 2 * (dx[i] = -fabs(_dx) / 2);
            continue;
          }
        }
        f1 = (*fn)(x);
      }
      while (f1 < f0) {
        if (n_steps++ == ns_max) {
          n_steps = 0;
          dx[i] = _dx = 2 * _dx;
        }
        f0 = f1;
        x[i] += _dx;
        if (constraint[i]) {
          if (x[i] < xlo[i]) {
            x[i] = xlo[i] + 2 * (dx[i] = fabs(_dx));
            break;
          }
          if (x[i] > xhi[i]) {
            x[i] = xhi[i] + 2 * (dx[i] = -fabs(_dx));
            break;
          }
        }
        f1 = (*fn)(x);
      }
      dx[i] /= 2;
      x[i] -= _dx;
    }
    if (pc++ == p_flag) {
      printf("%.16le\n", f0);
      for (i = 0; i < np; i++)
        printf("%.16le\t%.16le\n", x[i], dx[i]);
      pc = 0;
    }
  } while (flag != np);
  return (f0);
}