These functions enable various calculations and checks on the current simplex:
optimsimplex.centerCompute the center of the current simplex.
optimsimplex.checkCheck the consistency of the data in the current simplex.
optimsimplex.deltafvCompute the vector of function value differences with respect to the function value at the first vertex (the lowest).
optimsimplex.deltafvmaxCompute the difference of function
value between the lowest and the highest vertices. It is expected that the
first vertex (this$x[1,]) is associated with the smallest function
value and that the last vertex (this$x[nbve,]) is associated with
the highest function value.
optimsimplex.dirmatCompute the matrix of simplex direction, i.e. the matrix of differences of vertice coordinates with respect to the first vertex.
optimsimplex.fvmeanCompute the mean of the function values in the current simplex.
optimsimplex.fvstdevCompute the standard deviation of the function values in the current simplex.
optimsimplex.fvvarianceCompute the variance of the function values in the current simplex.
optimsimplex.sizeDetermines the size of the simplex.
optimsimplex.sortSort the simplex by increasing order of function value, so the smallest function is at the first vertex.
optimsimplex.xbarCompute the center of n vertices, by
excluding the vertex with index iexcl. The default of iexcl
is the number of vertices: in that case, if the simplex is sorted in
increasing function value order, the worst vertex is excluded.
optimsimplex.center(this = NULL)
optimsimplex.check(this = NULL)
optimsimplex.deltafv(this = NULL)
optimsimplex.deltafvmax(this = NULL)
optimsimplex.dirmat(this = NULL)
optimsimplex.fvmean(this = NULL)
optimsimplex.fvstdev(this = NULL)
optimsimplex.fvvariance(this = NULL)
optimsimplex.size(this = NULL, method = NULL)
optimsimplex.sort(this = NULL)
optimsimplex.xbar(this = NULL, iexcl = NULL)The current simplex.
The method to use to compute the size of the simplex. The available methods are the following:
(this is the default) The sigmamplus size is the maximum 2-norm length of the vector from each vertex to the first vertex. It requires one loop over the vertices.
The sigmaminus size is the minimum 2-norm length of the vector from each vertex to the first vertex. It requires one loop over the vertices.
The 'Nash' size is the sum of the norm of the norm-1 length of the vector from the given vertex to the first vertex. It requires one loop over the vertices.
The diameter is the maximum norm-2 length of all the edges of the simplex. It requires 2 nested loops over the vertices.
The index of the vertex to exclude in center computation.
optimsimplex.centerReturn a vector of length nbve, where nbve is the number of vertices in the current simplex.
optimsimplex.checkReturn an error message if the dimensions of the various elements of the current simplex do not match.
optimsimplex.deltafvReturn a column vector of length nbve-1.
optimsimplex.deltafvmaxReturn a numeric scalar.
optimsimplex.dirmatReturn a n x n numeric matrix, where n is the dimension of the space of the simplex.
optimsimplex.fvmeanReturn a numeric scalar.
optimsimplex.fvstdevReturn a numeric scalar.
optimsimplex.fvvarianceReturn a numeric scalar.
optimsimplex.sizeReturn a numeric scalar.
optimsimplex.sortReturn an updated simplex object.
optimsimplex.xbarReturn a row vector of length n.
"Compact Numerical Methods For Computers - Linear Algebra and Function Minimization", J.C. Nash, 1990, Chapter 14. Direct Search Methods
"Iterative Methods for Optimization", C.T. Kelley, 1999, Chapter 6., section 6.2