predictor.m

function [y,or1,or2,dmse] = predictor(x,dmodel)
%PREDICTOR  Predictor for y(x) using the given DACE model.
%
% Call:   y = predictor(x, dmodel)
%         [y, or] = predictor(x, dmodel)
%         [y, dy, mse] = predictor(x, dmodel) 
%         [y, dy, mse, dmse] = predictor(x, dmodel) 
%
% Input
% x      : trial design sites with n dimensions.  
%          For mx trial sites x:
%          If mx = 1, then both a row and a column vector is accepted,
%          otherwise, x must be an mx*n matrix with the sites stored
%          rowwise.
% dmodel : Struct with DACE model; see DACEFIT
%
% Output
% y    : predicted response at x.
% or   : If mx = 1, then or = gradient vector/Jacobian matrix of predictor
%        otherwise, or is an vector with mx rows containing the estimated
%                   mean squared error of the predictor
% Three or four results are allowed only when mx = 1,
% dy   : Gradient of predictor; column vector with  n elements
% mse  : Estimated mean squared error of the predictor;
% dmse : Gradient vector/Jacobian matrix of mse

% hbn@imm.dtu.dk
% Last update August 26, 2002

    or1 = NaN; or2 = NaN; dmse = NaN;	% Default return values
    if isnan(dmodel.beta)
        error('DMODEL has not been found')
    end
    [m,n] = size(dmodel.S);     % number of design sites and number of dimensions
    sx    = size(x);            % number of trial sites and their dimension
    if min(sx) == 1 && n > 1    % Single trial point 
        nx = max(sx);
        if nx == n 
            mx = 1;
            x  = x(:).';
        end
    else
        mx = sx(1);
        nx = sx(2);
    end
    if nx ~= n
        error('Dimension of trial sites should be %d',n)
    end
    % Normalize trial sites  
    x = (x - repmat(dmodel.Ssc(1,:),mx,1)) ./ repmat(dmodel.Ssc(2,:),mx,1);
    q = size(dmodel.Ysc,2);  % number of response functions
    if mx == 1  % one site only
        dx = repmat(x,m,1) - dmodel.S;  % distances to design sites
        if nargout > 1                  % gradient/Jacobian wanted
            [f,df] = feval(dmodel.regr, x);
            [r,dr] = feval(dmodel.corr, dmodel.theta, dx);
            % Scaled Jacobian
            dy = (df * dmodel.beta).' + dmodel.gamma * dr;
            % Unscaled Jacobian
            or1 = dy .* repmat(dmodel.Ysc(2, :)', 1, nx) ./ repmat(dmodel.Ssc(2,:), q, 1);
            if q == 1
                % Gradient as a column vector
                or1 = or1';
            end
            if nargout > 2  % MSE wanted
                rt = dmodel.C \ r;
                u = dmodel.Ft.' * rt - f.';
                v = dmodel.G \ u;
                or2 = repmat(dmodel.sigma2,mx,1) .* repmat((1 + sum(v.^2) - sum(rt.^2))',1,q);
                if nargout > 3  % gradient/Jacobian of MSE wanted
                    % Scaled gradient as a row vector
                    Gv = dmodel.G' \ v;
                    g = (dmodel.Ft * Gv - rt)' * (dmodel.C \ dr) - (df * Gv)';
                    % Unscaled Jacobian
                    dmse = repmat(2 * dmodel.sigma2',1,nx) .* repmat(g ./ dmodel.Ssc(2,:),q,1);
                    if q == 1
                    % Gradient as a column vector
                    dmse = dmse';
                    end
                end
            end
        else  % predictor only
            f = feval(dmodel.regr, x);
            r = feval(dmodel.corr, dmodel.theta, dx);
        end
        % Scaled predictor
        sy = f * dmodel.beta + (dmodel.gamma*r).';
        % Predictor
        y = (dmodel.Ysc(1,:) + dmodel.Ysc(2,:) .* sy)';
	else  % several trial sites
        % Get distances to design sites  
        dx = zeros(mx*m,n);
        kk = 1 : m;
        for k = 1 : mx
            dx(kk,:) = repmat(x(k,:),m,1) - dmodel.S;
            kk = kk + m;
        end
        % Get regression function and correlation
        f = feval(dmodel.regr, x);
        r = feval(dmodel.corr, dmodel.theta, dx);
        r = reshape(r, m, mx);
        % Scaled predictor 
        sy = f * dmodel.beta + (dmodel.gamma * r).';
        % Predictor
        y = repmat(dmodel.Ysc(1,:),mx,1) + repmat(dmodel.Ysc(2,:),mx,1) .* sy;
        if nargout > 1	% MSE wanted
            rt  = dmodel.C \ r;
            u   = dmodel.G \ (dmodel.Ft.' * rt - f.');
            or1 = repmat(dmodel.sigma2,mx,1) .* repmat((1 + sum(u.^2,1) - sum(rt.^2,1))',1,q);
            if  nargout > 2
                disp('WARNING from PREDICTOR.  Only  y  and  or1=mse  are computed')
            end
        end
    end
end

function [r,dr] = corrgauss(theta,d)
%CORRGAUSS  Gaussian correlation function,

    [m,n] = size(d);  % number of differences and dimension of data
    if length(theta) == 1
        theta = repmat(theta,1,n);
    elseif length(theta) ~= n
        error('Length of theta must be 1 or %d',n)
    end
    td = d.^2 .* repmat(-theta(:).',m,1);
    r  = exp(sum(td, 2));
	dr = repmat(-2*theta(:).',m,1) .* d .* repmat(r,1,n);
end

function [f,df] = regpoly0(S)
%REGPOLY0  Zero order polynomial regression function

    f  = ones(size(S,1),1);
	df = zeros(size(S,2),1);
end

function [f,df] = regpoly1(S)
%REGPOLY1  First order polynomial regression function

    f  = [ones(size(S,1),1),S];
	df = [zeros(size(S,2),1),eye(size(S,2))];
end