E04CCA is a version of E04CCF that has additional parameters in order to make it safe for use in multithreaded applications (see
Section 5).
| SUBROUTINE E04CCF ( | N, X, F, TOL, IW, W1, W2, W3, W4, W5, W6, FUNCT, MONIT, MAXCAL, IFAIL) |
| INTEGER | N, IW, MAXCAL, IFAIL |
| double precision | X(N), F, TOL, W1(N), W2(N), W3(N), W4(N), W5(IW), W6(IW,N) |
| EXTERNAL | FUNCT, MONIT |
| SUBROUTINE E04CCA ( | N, X, F, TOL, IW, W1, W2, W3, W4, W5, W6, FUNCT, MONIT, MAXCAL, IUSER, RUSER, IFAIL) |
| INTEGER | N, IW, MAXCAL, IUSER(*), IFAIL |
| double precision | X(N), F, TOL, W1(N), W2(N), W3(N), W4(N), W5(IW), W6(IW,N), RUSER(*) |
| EXTERNAL | FUNCT, MONIT |
The method is iterative. A simplex of
n+1 points is set up in the
n-dimensional space of the variables (for example in
2 dimensions the simplex is a triangle) under the assumption that the problem has been scaled so that the values of the independent variables at the minimum are of order unity. The starting point you have provided is the first vertex of the simplex, the remaining
n vertices are generated by the routine. The vertex of the simplex with the largest function value is reflected in the centre of gravity of the remaining vertices and the function value at this new point is compared with the remaining function values. Depending on the outcome of this test the new point is accepted or rejected, a further expansion move may be made, or a contraction may be carried out. See
Nelder and Mead (1965) and
Parkinson and Hutchinson (1972) for more details. When no further progress can be made the sides of the simplex are reduced in length and the method is repeated.
The method tends to be slow, but it is robust and therefore very useful for functions that are subject to inaccuracies.
Nelder J A and Mead R (1965) A simplex method for function minimization
Comput. J. 7 308–313
Parkinson J M and Hutchinson D (1972) An investigation into the efficiency of variants of the simplex method
Numerical Methods for Nonlinear Optimization (ed F A Lootsma) Academic Press
If on entry
IFAIL=0 or
-1, explanatory error messages are output on the current error message unit (as defined by
X04AAF).
On a successful exit the accuracy will be as defined by
TOL.
The time taken by E04CCF/E04CCA depends on the number of variables, the behaviour of the function and the distance of the starting point from the minimum. Each iteration consists of 1 or 2 function evaluations unless the size of the simplex is reduced, in which case n+1 function evaluations are required.
This example finds a minimum of the function
None.