function [find, vaf, outperm, addcon] = unicirac(prox, inperm, kblock)
% UNICIRAC finds and fits a circular
% unidimensional scale using iterative projection to
% a symmetric proximity matrix in the $L_{2}$-norm based on a
% permutation identified through the use of iterative
% quadratic assignment.
%
% syntax: [find, vaf, outperm, addcon] = unicirac(prox, inperm, kblock)
%
% PROX is the input proximity matrix ($n \times n$ with a
% zero main diagonal and a dissimilarity interpretation);
% INPERM is a given starting permutation (assumed to be around the
% circle) of the first $n$ integers;
% FIND is the least-squares optimal matrix (with
% variance-accounted-for of VAF) to PROX having a circular
% anti-Robinson form for the row and column
% object ordering given by the ending permutation OUTPERM.
% The spacings among the objects are given by the diagonal entries
% in FIND (and the extreme (1,n) entry in FIND). KBLOCK
% defines the block size in the use of the iterative quadratic
% assignment routine. The additive constant for the model is
% given by ADDCON.
n = size(prox,1);
[outperm,rawindex,allperms,index] = order(prox,targcir(n),inperm,kblock);
[fit,vaf,addcon] = cirfitac(prox,outperm);
if (any(outperm-inperm) ~= 0)
inperm = outperm;
[outperm,rawindex,allperms,index] = order(prox,fit,inperm,kblock);
[fit,vaf,addcon] = cirfitac(prox,outperm);
end
find = fit;