Can you provide the corresponding paper name or information website for the dynamic regularization algorithm program?

hi, Your package is written very well. Thank you very much for your reply. By reading your doctoral dissertation, I can understand your package.However, I encountered some minor issues. The following is the program corresponding to a function in the package. Can you provide some papers, Pseudocode or web addresses about functions DynamicProgrammingQ, DynamicProgrammingQ2, ElasticCurvesReparam, Coordinate Descent, Dynamic Programming and Riemannian BFGS? These functions are written in c++. Due to the lack of Pseudocode and other information, it is very difficult to understand the source code of these functions.

function gam = optimum_reparam(q1,q2,t,lambda,method,w,f1o,f2o) % OPTIMUM_REPARAM Calculates Warping for two SRVFs % -------------------------------------------------------------------------% % This function aligns two SRSF functions using Dynamic Programming % % Usage: gam = optimum_reparam(q1,q2,t) % gam = optimum_reparam(q1,q2,t,lambda) % gam = optimum_reparam(q1,q2,t,lambda,method) % gam = optimum_reparam(q1,q2,t,lambda,method,w,f1o,f2o) % % Input: % q1: srsf of function 1 % q2: srsf of function 2 % t: sample points of function 2 % lambda: controls amount of warping (default = 0) % method: controls which optimization method (default="DP") options are % Dynamic Programming ("DP"), Coordinate Descent ("DP2"), and Riemannian BFGS % ("RBFGSM") % w: controls LRBFGS (default = 0.01) % f1o: initial value of f1, vector or scalar depending on q1, defaults to zero % f2o: initial value of f2, vector or scalar depending on q1, defaults to zero % % Output: % gam: warping function if nargin < 4 lambda = 0.0; method = 'DP1'; w = 0.0; f1o = 0.0; f2o = 0.0; elseif nargin < 5 method = 'DP'; w = 0.0; f1o = 0.0; f2o = 0.0; elseif nargin < 6 w = 0.0; f1o = 0.0; f2o = 0.0; elseif nargin < 7 f1o = 0.0; f2o = 0.0; elseif nargin < 8 f2o = 0.0; end

q1 = q1/norm(q1); q2 = q2/norm(q2); c1 = srvf_to_f(q1,t,f1o); c2 = srvf_to_f(q2,t,f2o); rotated = 0; isclosed = 0; skipm = 0; auto = 0; switch upper(method) case 'DP' [G,T] = DynamicProgrammingQ2(q1',t',q2',t',t',t',lambda); gam0 = interp1(T,G,t); case 'DP1' [gam0] = DynamicProgrammingQ(q2',q1',lambda,0); case 'SIMUL' [s1,s2, g1,g2,~,~,~] = simul_align(c1,c2); u = linspace(0,1,length(g1)); tmin = min(t); tmax = max(t); t2 = t; t2 = (t2-tmin)/(tmax-tmin); gam0 = simul_gam(u,g1,g2,t2,s1,s2,t2); case 'DP2' onlyDP = 1; [opt,swap,~,~] = ElasticCurvesReparam(c1, c2, w, onlyDP, ... rotated, isclosed, skipm, 'LRBFGS', auto); gam0 = opt(1:end-2);

    if swap
        gam0 = invertGamma(gam0);
    end
case 'RBFGS'
    onlyDP = 0;
    [opt,swap,fopts,~] = ElasticCurvesReparam(c1, c2, w, onlyDP,  ...
        rotated, isclosed, skipm, 'LRBFGS', auto);

    if (fopts(1) == 1000)
        onlyDP = 1;
        [opt,swap,~,~] = ElasticCurvesReparam(c1, c2, w, onlyDP,  ...
            rotated, isclosed, skipm, 'LRBFGS', auto);
    end

    gam0 = opt(1:end-2);

    if swap
        gam0 = invertGamma(gam0);
    end
case 'RBFGSM'
    t1 = linspace(0,1,length(t));
    options.verbosity=0;
    options.maxiter=30;
    options.inittype='id';
    options.Tdp=t1;
    M = infspherefactory(t1);
    [q2,~]=initialize(q1,q2,M,options);

    [~,gam0,~, ~, ~]=rlbfgs(q1.',q2.',M,options);

otherwise
    error('Invalid Method')

end

gam = (gam0-gam0(1))/(gam0(end)-gam0(1)); % slight change on scale end

% helper functions function [q20,gam0] = initialize(q1,q2,M,options)

t=M.t;
T=M.T;

switch options.inittype

    % Initialize as identity
    case 'id' 
        gam0=t;
        q20=q2;

    % Initialize by randomly warping q2
    case 'rand' 
        hid=ones(1,T);
        [b,~]=basis_tangent_id(1,t);
        [N,~]=size(b);
        Ninit=options.Ninit;
        htry=zeros(Ninit,T);
        costtry=zeros(Ninit,1);
        for i=1:Ninit
            coeffs=0.2*randn(1,N);
            v=coeffs*b;
            htry(i,:)=M.exp(hid,v,1);
            while sum(htry(i,:)<=0)>0
                coeffs=0.2*randn(1,N);
                v=coeffs*b;
                htry(i,:)=M.exp(hid,v,1);
            end
            costtry(i)=alignment_cost(htry(i,:),q1,q2,M);
        end
        [~,idx]=min(costtry);
        h0=htry(idx,:);
        [q20,gam0]=group_action_SRVF(q2,h0,M);

    % Initialize from dynamic programming solution 
    case 'dp'

        Tdp=options.Tdp;

        % Resample
        if Tdp~=T
            tdp=linspace(0,1,Tdp);
            q1dn=spline(M.t,q1,tdp);
            q2dn=spline(M.t,q2,tdp);
            gamdp=DynamicProgrammingQ(q2dn,q1dn,0,1);
            hdp=sqrt(gradient(gamdp,1/(Tdp-1)));
            h0=spline(tdp,hdp,t); % resample 
            [q20,gam0]=group_action_SRVF(q2,h0,M);
        else
            gam0=DynamicProgrammingQ(q2,q1,0,1);
            [n,~]=size(q2);
            q20=spline(t,q2,gam0).*repmat(sqrt(gradient(gam0,1/(T-1))),n,1);
        end

    case 'sgd'

        options.plotevol=false;
        options.stepsize=0.001;
        [q20,gam0,cost]=sgd(q1,q2,M,options);

end

end

function f = alignment_cost(h,q1,q2k,M)

% Evaluate the cost function f = ||q1 - ((q2,hk),h)||^2.
% h=sqrt{\dot{\gamma}} is a sequential update of cumulative warping hk

t=M.t;
q2new=group_action_SRVF(q2k,h,M);
f=normL2(q1-q2new,t)^2; % Cost

end

function val = normL2(f,t)

val=sqrt(innerProdL2(f,f,t));

end

jdtuck / fdasrvf_MATLAB

Can you provide the corresponding paper name or information website for the dynamic regularization algorithm program? #2