function lik = lik_inputdependentweibull(varargin)
%LIK_INPUTDEPENDENTWEIBULL  Create a (right censored) input dependent Weibull likelihood structure 
%
%  Description
%    LIK = LIK_INPUTDEPENDENTWEIBULL('PARAM1',VALUE1,'PARAM2,VALUE2,...) 
%    creates a likelihood structure for a right censored input dependent
%    Weibull survival model in which the named parameters have the
%    specified values. Any unspecified parameters are set to default 
%    values.
%  
%    LIK = LIK_INPUTDEPENDENTWEIBULL(LIK,'PARAM1',VALUE1,'PARAM2,VALUE2,...)
%    modify a likelihood structure with the named parameters
%    altered with the specified values.
%
%    Parameters for Weibull likelihood [default]
%      shape       - shape parameter r [1]
%      shape_prior - prior for shape [prior_logunif]
%  
%    Note! If the prior is 'prior_fixed' then the parameter in
%    question is considered fixed and it is not handled in
%    optimization, grid integration, MCMC etc.
%
%    The likelihood is defined as follows:
%                       __ n
%      p(y|f1, f2, z) = || i=1 [ r_i^(1-z_i) exp( (1-z_i)*(-f1_i)
%                           +(1-z_i)*(r_i-1)*log(y_i)
%                           -exp(-f1_i)*y_i^r_i) ]
%
%    where r_i=r*exp(f2_i) is the shape parameter of Weibull distribution.
%    z is a vector of censoring indicators with z = 0 for uncensored event
%    and z = 1 for right censored event. Here the second latent variable f2
%    implies the input dependance to the shape parameter in the original
%    Weibull likelihood.
%
%    When using the Weibull likelihood you can give the
%    vector z as an extra parameter to each function that requires
%    also y. For example, you can call gp_optim as follows:
%      gp_optim(gp, x, y, 'z', z)
%    If z is not given or it is empty, then usual likelihood for
%    uncensored data is used
%
%  See also
%    GP_SET, LIK_*, PRIOR_*
%
% Copyright (c) 2011 Jaakko Riihimäki
% Copyright (c) 2011 Aki Vehtari
% Copyright (c) 2012 Ville Tolvanen

% This software is distributed under the GNU General Public
% License (version 3 or later); please refer to the file
% License.txt, included with the software, for details.

  ip=inputParser;
  ip.FunctionName = 'LIK_INPUTDEPENDENTWEIBULL';
  ip.addOptional('lik', [], @isstruct);
  ip.addParamValue('shape',1, @(x) isscalar(x) && x>0);
  ip.addParamValue('shape_prior',prior_logunif(), @(x) isstruct(x) || isempty(x));
  ip.parse(varargin{:});
  lik=ip.Results.lik;
  
  if isempty(lik)
    init=true;
    lik.nondiagW=true;
    lik.type = 'Inputdependent-Weibull';
  else
    if ~isfield(lik,'type') || ~isequal(lik.type,'Weibull')
      error('First argument does not seem to be a valid likelihood function structure')
    end
    init=false;
  end

  % Initialize parameters
  if init || ~ismember('shape',ip.UsingDefaults)
    lik.shape = ip.Results.shape;
  end
  % Initialize prior structure
  if init
    lik.p=[];
  end
  if init || ~ismember('shape_prior',ip.UsingDefaults)
    lik.p.shape=ip.Results.shape_prior;
  end
  
  if init
    % Set the function handles to the subfunctions
    lik.fh.pak = @lik_inputdependentweibull_pak;
    lik.fh.unpak = @lik_inputdependentweibull_unpak;
    lik.fh.lp = @lik_inputdependentweibull_lp;
    lik.fh.lpg = @lik_inputdependentweibull_lpg;
    lik.fh.ll = @lik_inputdependentweibull_ll;
    lik.fh.llg = @lik_inputdependentweibull_llg;    
    lik.fh.llg2 = @lik_inputdependentweibull_llg2;
    lik.fh.llg3 = @lik_inputdependentweibull_llg3;
    lik.fh.invlink = @lik_inputdependentweibull_invlink;
    lik.fh.predy = @lik_inputdependentweibull_predy;
    lik.fh.recappend = @lik_inputdependentweibull_recappend;
  end

end

function [w,s,h] = lik_inputdependentweibull_pak(lik)
%LIK_INPUTDEPENDENTWEIBULL_PAK  Combine likelihood parameters into one vector.
%
%  Description 
%    W = LIK_INPUTDEPENDENTWEIBULL_PAK(LIK) takes a likelihood structure LIK and
%    combines the parameters into a single row vector W. This is a 
%    mandatory subfunction used for example in energy and gradient 
%    computations.
%     
%       w = log(lik.shape)
%
%   See also
%   LIK_INPUTDEPENDENTWEIBULL_UNPAK, GP_PAK
  
  w=[];s={};h=[];
  if ~isempty(lik.p.shape)
    w = log(lik.shape);
    s = [s; 'log(weibull.shape)'];
    h = [h 0];
    [wh, sh, hh] = lik.p.shape.fh.pak(lik.p.shape);
    w = [w wh];
    s = [s; sh];
    h = [h hh];
  end
end


function [lik, w] = lik_inputdependentweibull_unpak(lik, w)
%LIK_INPUTDEPENDENTWEIBULL_UNPAK  Extract likelihood parameters from the vector.
%
%  Description
%    [LIK, W] = LIK_INPUTDEPENDENTWEIBULL_UNPAK(W, LIK) takes a likelihood
%    structure LIK and extracts the parameters from the vector W
%    to the LIK structure. This is a mandatory subfunction used 
%    for example in energy and gradient computations.
%     
%   Assignment is inverse of  
%       w = log(lik.shape)
%
%   See also
%   LIK_INPUTDEPENDENTWEIBULL_PAK, GP_UNPAK

  if ~isempty(lik.p.shape)
    lik.shape = exp(w(1));
    w = w(2:end);
    [p, w] = lik.p.shape.fh.unpak(lik.p.shape, w);
    lik.p.shape = p;
  end
end


function lp = lik_inputdependentweibull_lp(lik, varargin)
%LIK_INPUTDEPENDENTWEIBULL_LP  log(prior) of the likelihood parameters
%
%  Description
%    LP = LIK_INPUTDEPENDENTWEIBULL_LP(LIK) takes a likelihood structure LIK and
%    returns log(p(th)), where th collects the parameters. This 
%    subfunction is needed when there are likelihood parameters.
%
%  See also
%    LIK_INPUTDEPENDENTWEIBULL_LLG, LIK_INPUTDEPENDENTWEIBULL_LLG3, LIK_INPUTDEPENDENTWEIBULL_LLG2, GPLA_E
  

% If prior for shape parameter, add its contribution
  lp=0;
  if ~isempty(lik.p.shape)
    lp = lik.p.shape.fh.lp(lik.shape, lik.p.shape) +log(lik.shape);
  end
  
end


function lpg = lik_inputdependentweibull_lpg(lik)
%LIK_INPUTDEPENDENTWEIBULL_LPG  d log(prior)/dth of the likelihood 
%                parameters th
%
%  Description
%    E = LIK_INPUTDEPENDENTWEIBULL_LPG(LIK) takes a likelihood structure LIK and
%    returns d log(p(th))/dth, where th collects the parameters.
%    This subfunction is needed when there are likelihood parameters.
%
%  See also
%    LIK_INPUTDEPENDENTWEIBULL_LLG, LIK_INPUTDEPENDENTWEIBULL_LLG3, LIK_INPUTDEPENDENTWEIBULL_LLG2, GPLA_G
  
  lpg=[];
  if ~isempty(lik.p.shape)            
    % Evaluate the gprior with respect to shape
    ggs = lik.p.shape.fh.lpg(lik.shape, lik.p.shape);
    lpg = ggs(1).*lik.shape + 1;
    if length(ggs) > 1
      lpg = [lpg ggs(2:end)];
    end
  end
end  

function ll = lik_inputdependentweibull_ll(lik, y, ff, z)
%LIK_INPUTDEPENDENTWEIBULL_LL  Log likelihood
%
%  Description
%    LL = LIK_INPUTDEPENDENTWEIBULL_LL(LIK, Y, F, Z) takes a likelihood
%    structure LIK, survival times Y, censoring indicators Z, and
%    latent values F. Returns the log likelihood, log p(y|f,z).
%    This subfunction is needed when using Laplace approximation 
%    or MCMC for inference with non-Gaussian likelihoods. This 
%    subfunction is also used in information criteria (DIC, WAIC) 
%    computations.
%
%  See also
%    LIK_INPUTDEPENDENTWEIBULL_LLG, LIK_INPUTDEPENDENTWEIBULL_LLG3, LIK_INPUTDEPENDENTWEIBULL_LLG2, GPLA_E
  
  if numel(z)==0
    % no censoring by default
    z=0;
  end

  f=ff(:);
  n=size(y,1);
  f1=f(1:n);
  f2=f((n+1):2*n);
  expf2=exp(f2);
  expf2(isinf(expf2))=realmax;
  a = lik.shape;
  ll = sum((1-z).*(log(a*expf2) + (a*expf2-1).*log(y)-f1) - exp(-f1).*y.^(a*expf2));

end

function llg = lik_inputdependentweibull_llg(lik, y, ff, param, z)
%LIK_INPUTDEPENDENTWEIBULL_LLG  Gradient of the log likelihood
%
%  Description 
%    LLG = LIK_INPUTDEPENDENTWEIBULL_LLG(LIK, Y, F, PARAM) takes a likelihood
%    structure LIK, survival times Y, censoring indicators Z and
%    latent values F. Returns the gradient of the log likelihood
%    with respect to PARAM. At the moment PARAM can be 'param' or
%    'latent'. This subfunction is needed when using Laplace 
%    approximation or MCMC for inference with non-Gaussian likelihoods.
%
%  See also
%    LIK_INPUTDEPENDENTWEIBULL_LL, LIK_INPUTDEPENDENTWEIBULL_LLG2, LIK_INPUTDEPENDENTWEIBULL_LLG3, GPLA_E

  if numel(z)==0
    % no censoring by default
    z=0;
  end

  f=ff(:);
  n=size(y,1);
  f1=f(1:n);
  f2=f((n+1):2*n);
  expf2=exp(f2);
  expf2(isinf(expf2))=realmax;
  a = lik.shape;
  switch param
    case 'param'      
      llg = sum((1-z).*(1./a + expf2.*log(y)) - exp(-f1).*y.^(a.*expf2).*log(y).*expf2);
      % correction for the log transformation
      llg = llg.*lik.shape;
    case 'latent'
      llg1 = -(1-z) + exp(-f1).*y.^(a.*expf2);
      llg2 = (1-z).*(1 + a.*expf2.*log(y)) - exp(-f1).*y.^(a.*expf2).*log(y).*a.*expf2;
      llg = [llg1; llg2];
  end
end

function llg2 = lik_inputdependentweibull_llg2(lik, y, ff, param, z)
%LIK_INPUTDEPENDENTWEIBULL_LLG2  Second gradients of the log likelihood
%
%  Description        
%    LLG2 = LIK_INPUTDEPENDENTWEIBULL_LLG2(LIK, Y, F, PARAM) takes a
%    likelihood structure LIK, survival times Y, censoring indicators Z,
%    and latent values F. Returns the hessian of the log likelihood with
%    respect to PARAM. LLG2 is a (2*length(y)) x 2 matrix containing the
%    non-zero elements of the Hessian matrix. This subfunction is needed
%    when using Laplace approximation or EP for  inference with
%    non-Gaussian likelihoods.
%
%  See also
%    LIK_INPUTDEPENDENTWEIBULL_LL, LIK_INPUTDEPENDENTWEIBULL_LLG,
%    LIK_INPUTDEPENDENTWEIBULL_LLG3, GPLA_E 

  if numel(z)==0
    % no censoring by default
    z=0;
  end

  a = lik.shape;
  f=ff(:);
  n=size(y,1);
  f1=f(1:n);
  f2=f((n+1):2*n);
  expf2=exp(f2);
  expf2(isinf(expf2))=realmax;
  switch param
    case 'param'
      
    case 'latent'
      t1=exp(-f1).*y.^(a.*expf2);
      t2=log(y).*a.*expf2;
      t3=t1.*t2;
      
      llg2_11 = -t1;
      llg2_12 = t3;
      llg2_22 = (1-z).*t2 - (t2 + 1).*t3;
      
      llg2 = [llg2_11 llg2_12; llg2_12 llg2_22];

    case 'latent+param'      
      t1=expf2.*log(y);
      t2=exp(-f1).*y.^(a.*expf2);
      t3=t1.*t2;
      llg2_1 = t3;
      llg2_2 = (1-z).*t1 - (t1.*a + 1).*t3;
      llg2 = [llg2_1; llg2_2];
      % correction due to the log transformation
      llg2 = llg2.*lik.shape;
  end
end    

function llg3 = lik_inputdependentweibull_llg3(lik, y, ff, param, z)
%LIK_INPUTDEPENDENTWEIBULL_LLG3  Third gradients of the log likelihood
%
%  Description
%    LLG3 = LIK_INPUTDEPENDENTWEIBULL_LLG3(LIK, Y, F, PARAM) takes a likelihood
%    structure LIK, survival times Y, censoring indicators Z and
%    latent values F and returns the third gradients of the log
%    likelihood with respect to PARAM. At the moment PARAM can be
%    only 'latent'. LLG3 is a vector with third gradients. This 
%    subfunction is needed when using Laplace approximation for 
%    inference with non-Gaussian likelihoods.
%
%  See also
%    LIK_INPUTDEPENDENTWEIBULL_LL, LIK_INPUTDEPENDENTWEIBULL_LLG, LIK_INPUTDEPENDENTWEIBULL_LLG2, GPLA_E, GPLA_G

  if numel(z)==0
    % no censoring by default
    z=0;
  end

  a = lik.shape;
  f=ff(:);
  n=size(y,1);
  f1=f(1:n);
  f2=f((n+1):2*n);
  expf2=exp(f2);
  expf2(isinf(expf2))=realmax;
  switch param
    case 'param'
      
    case 'latent'
      t1=a.*expf2.*log(y);
      t2=exp(-f1).*y.^(a.*expf2);
      t3=t2.*t1;
      t4=t3.*t1;
      
      nl=2;
      llg3=zeros(nl,nl,nl,n);

      llg3(1,1,1,:) = t2;
      
      llg3(2,2,1,:) = t4 + t3;
      llg3(2,1,2,:) = llg3(2,2,1,:);
      llg3(1,2,2,:) = llg3(2,2,1,:);
      
      llg3(2,1,1,:) = -t3;
      llg3(1,2,1,:) = llg3(2,1,1,:);
      llg3(1,1,2,:) = llg3(2,1,1,:);
      
      llg3(2,2,2,:) = (1-z).*t1 - t4.*t1 - 3.*t4 - t3;
      
    case 'latent2+param'
      t1 = log(y).*expf2;
      t2 = exp(-f1).*y.^(a*expf2);
      t3 = t2.*t1;
      t4 = t3.*t1;
      llg3_11 = -t3;
      llg3_12 = a.*t4 + t3;
      llg3_22 = (1-z).*t1 - a.^2.*t4.*t1 - 3.*a.*t4 - t3;
      
      llg3 = [diag(llg3_11) diag(llg3_12); diag(llg3_12) diag(llg3_22)];
      % correction due to the log transformation
      llg3 = llg3.*lik.shape;
  end
end


function [lpy, Ey, Vary] = lik_inputdependentweibull_predy(lik, Ef, Varf, yt, zt)
%LIK_INPUTDEPENDENTWEIBULL_PREDY  Returns the predictive mean, variance and density of y
%
%  Description   
%    LPY = LIK_INPUTDEPENDENTWEIBULL_PREDY(LIK, EF, VARF YT, ZT)
%    Returns logarithm of the predictive density PY of YT, that is 
%        p(yt | zt) = \int p(yt | f, zt) p(f|y) df.
%    This requires also the survival times YT, censoring indicators ZT.
%    This subfunction is needed when computing posterior predictive 
%    distributions for future observations.
%
%    [LPY, EY, VARY] = LIK_INPUTDEPENDENTWEIBULL_PREDY(LIK, EF, VARF) takes a
%    likelihood structure LIK, posterior mean EF and posterior
%    Variance VARF of the latent variable and returns the
%    posterior predictive mean EY and variance VARY of the
%    observations related to the latent variables. This subfunction
%    is needed when computing posterior predictive distributions for 
%    future observations.
%        
%
%  See also
%    GPLA_PRED, GPEP_PRED, GPMC_PRED

  if numel(zt)==0
    % no censoring
    zt=zeros(size(yt));
  end

  yc = 1-zt;
  r = lik.shape;
  
  Ef = Ef(:);
  ntest = 0.5*size(Ef,1);
  Ef1=Ef(1:ntest); Ef2=Ef(ntest+1:end);
  %     Varf1=squeeze(Varf(1,1,:)); Varf2=squeeze(Varf(2,2,:));
  if size(Varf,2) == size(Varf,1)
    Varf1=diag(Varf(1:ntest,1:ntest));Varf2=diag(Varf(ntest+1:end,ntest+1:end));
  else
    Varf1=Varf(:,1); Varf2=Varf(:,2);
  end
  
  Ey=[];
  Vary=[];

  % Evaluate the posterior predictive densities of the given observations
  lpy = zeros(length(yt),1);
    
  for i2=1:ntest
    m1=Ef1(i2); m2=Ef2(i2);
    s1=sqrt(Varf1(i2)); s2=sqrt(Varf2(i2));
    % Function handle for Weibull * Gaussian_f1 * Gaussian_f2
    pd=@(f1,f2) exp(yc(i2).*((log(r) + f2) + (r.*exp(f2)-1).*log(yt(i2))-f1) - exp(-f1).*yt(i2).^(r*exp(f2))) ...
      .*norm_pdf(f1,Ef1(i2),sqrt(Varf1(i2))).*norm_pdf(f2,Ef2(i2),sqrt(Varf2(i2)));
    % Integrate over latent variables
    lpy(i2) = log(dblquad(pd, m1-6.*s1, m1+6.*s1, m2-6.*s2, m2+6.*s2));
  end

end


function p = lik_inputdependentweibull_invlink(lik, f, z)
%LIK_INPUTDEPENDENTWEIBULL Returns values of inverse link function
%             
%  Description 
%    P = LIK_INPUTDEPENDENTWEIBULL_INVLINK(LIK, F) takes a likelihood structure LIK and
%    latent values F and returns the values of inverse link function P.
%    This subfunction is needed when using function gp_predprctmu.
%
%     See also
%     LIK_INPUTDEPENDENTWEIBULL_LL, LIK_INPUTDEPENDENTWEIBULL_PREDY

p = exp(f);
end

function reclik = lik_inputdependentweibull_recappend(reclik, ri, lik)
%RECAPPEND  Append the parameters to the record
%
%  Description 
%    RECLIK = LIK_INPUTDEPENDENTWEIBULL__RECAPPEND(RECLIK, RI, LIK) takes a
%    likelihood record structure RECLIK, record index RI and
%    likelihood structure LIK with the current MCMC samples of
%    the parameters. Returns RECLIK which contains all the old
%    samples and the current samples from LIK. This subfunction
%    is needed when using MCMC sampling (gp_mc).
% 
%  See also
%    GP_MC

  if nargin == 2
    % Initialize the record
    reclik.type = 'Inputdependent-Weibull';
    reclik.nondiagW=true;

    % Initialize parameter
%     reclik.shape = [];

    % Set the function handles
    reclik.fh.pak = @lik_inputdependentweibull_pak;
    reclik.fh.unpak = @lik_inputdependentweibull_unpak;
    reclik.fh.lp = @lik_t_lp;
    reclik.fh.lpg = @lik_t_lpg;
    reclik.fh.ll = @lik_inputdependentweibull_ll;
    reclik.fh.llg = @lik_inputdependentweibull_llg;    
    reclik.fh.llg2 = @lik_inputdependentweibull_llg2;
    reclik.fh.llg3 = @lik_inputdependentweibull_llg3;
    reclik.fh.invlink = @lik_inputdependentweibull_invlink;
    reclik.fh.predy = @lik_inputdependentweibull_predy;
    reclik.fh.recappend = @lik_inputdependentweibull_recappend;
    reclik.p=[];
    reclik.p.shape=[];
    if ~isempty(ri.p.shape)
      reclik.p.shape = ri.p.shape;
    end
  else
    % Append to the record
    reclik.shape(ri,:)=lik.shape;
    if ~isempty(lik.p.shape)
      reclik.p.shape = lik.p.shape.fh.recappend(reclik.p.shape, ri, lik.p.shape);
    end
  end
end

