% update gradients from an initial gradient set, such that the updated gradients are evenly distributed.
%
% USAGE:
% [gradCell, xopt, fopt, retcode] = OptimalSamplingMultiShellCNLO(gradCellInitial, param)
%
% INPUT (required)
% gradCellInitial : N_k x 3 gradient matrices, where each row is a point in sphere. k=1,2,...,K
% param.w : weight for single shell term. 0<w<1. 0.5 is the default value.
%
% INPUT (optional)
% param.solver : 'nlopt' (default): use sqp solver (SLSQP) in NLOPT.
% 'matlab': use fmincon (sqp solver).
% param.cartesian : true (default): use cartesian coordinate (with unit equality constraint);
% false: use spherical coordinate (no unit equality constraint).
%
% param.localCon : 0: do not use local constraint
% 1: use local constraint for the distance between samples in results and samples in initialization to reduce the inequality constraint.
% It is faster, and with an appropriate localConAngle, it can obtain the same results as it is set as false.
% 2 (default): repeat the CNLO with a fixed localConAngle until the result keeps the same.
%
% param.localConAngle : It is the maximal angular change between samples in results and samples in initialization.
% It is used when param.localCon is 1 or 2. The default value is 0.1 radian, if it is not given.
% If localConAngle>pi/2, then the result is the same as the results without localCon.
%
%
% OUTPUT
% gradCell : Kx1 cell, each element is a gradient matrix.
%
%
% Reference:
% 1. "Single- and Multiple-Shell Uniform Sampling Schemes for Diffusion MRI Using Spherical Codes",
% Jian Cheng, Dinggang Shen, Pew-Thian Yap, Peter J. Basser, IEEE Transactions on Medical Imaging, 2017.
% 2. "Novel single and multiple shell uniform sampling schemes for diffusion MRI using spherical codes",
% Jian Cheng, Dinggang Shen, Pew-Thian Yap, Peter J. Basser, MICCAI 2015.
%
% Copyright (c) 2015, Jian Cheng <jian.cheng.1983@gmail.com>
