##### https://github.com/cran/rstpm2
Tip revision: 936fa17
test-nmmin.cpp
#include <RcppArmadillo.h>
#include <vector>
#include <map>
#include "c_optim.h"

#ifdef DO_PROF
#include <gperftools/profiler.h>
#include <iostream>
#include <iomanip>
#include <ctime>
#include <sstream>
#endif

namespace rstpm2 {

// import namespaces
using namespace Rcpp;
using namespace arma;
// typedefs
typedef bool constraintfn(int, double *, void *);
// enums
enum IntervalCensoring {RightCensored, ExactTime, LeftCensored, IntervalCensored};
// structs
struct li_constraint { vec li; double constraint; };
li_constraint operator+(li_constraint const &left, li_constraint const &right) {
li_constraint out = {left.li+right.li,left.constraint+right.constraint};
return out;
}
return out;
}
// constants
const double log2pi = std::log(2.0 * M_PI); //
// Hadamard element-wise multiplication for the _columns_ of a matrix with a vector
mat rmult(mat const &m, vec const &v) {
mat out(m);
out.each_col() %= v;
return out;
}
mat lmult(vec const &v, mat const &m) {
return rmult(m, v);
}
// print utilities
void Rprint(NumericMatrix const & m) {
for (int i=0; i<m.nrow(); ++i) {
for (int j=0; j<m.ncol(); ++j)
Rprintf("%f ", m(i,j));
Rprintf("\n");
}
}
void Rprint(NumericVector const & v) {
for (int i=0; i<v.size(); ++i)
Rprintf("%f ", v(i));
Rprintf("\n");
}
void Rprint(uvec const & v) {
for (size_t i=0; i<v.size(); ++i)
Rprintf("%i ", v(i));
Rprintf("\n");
}
void Rprint(vec const & v) {
for (size_t i=0; i<v.size(); ++i)
Rprintf("%f ", v(i));
Rprintf("\n");
}
void Rprint(rowvec const & v) {
for (size_t i=0; i<v.size(); ++i)
Rprintf("%f ", v(i));
Rprintf("\n");
}
void Rprint(mat const & m) {
for (size_t i=0; i<m.n_rows; ++i) {
for (size_t j=0; j<m.n_cols; ++j)
Rprintf("%f ", m(i,j));
Rprintf("\n");
}
}
void Rprint(cube const & m) {
for (size_t k=0; k<m.n_slices; ++k) {
Rprintf("[");
for (size_t i=0; i<m.n_rows; ++i) {
for (size_t j=0; j<m.n_cols; ++j)
Rprintf("%f ", m(i,j,k));
Rprintf("\n");
}
Rprintf("]\n");
}
}
// vectorised functions
vec pnorm01(vec const &x) {
vec out(x.size());
double const *xi = x.begin();
for(double &o : out)
o = R::pnorm5(*xi++, 0, 1, true, false);
return out;
}
vec pnorm01_log(vec const &x) {
vec out(x.size());
double const *xi = x.begin();
for(double &o : out)
o = R::pnorm5(*xi++, 0, 1, true, true);
return out;
}
/* \frac \partial{\partial x} \log \Phi(x) = \frac{\phi(x)}{\Phi(x)} */
vec dpnorm01_log(vec const &x) {
vec out(x.size());
double const *xi = x.begin();
for(double &o : out){
double const xv = *xi++;
if(xv > -10){
double const dv     = R::dnorm4(xv, 0, 1    , 0L),
pv     = R::pnorm5(xv, 0, 1, 1L, 0L);
o = dv / pv;
} else {
double const log_dv = R::dnorm4(xv, 0, 1    , 1L),
log_pv = R::pnorm5(xv, 0, 1, 1L, 1L);
o = std::exp(log_dv - log_pv);
}
}
return out;
}
vec qnorm01(vec const &x) {
vec out(x.size());
double const *xi = x.begin();
for(double &o : out)
o = R::qnorm5(*xi++, 0, 1, true, false);
return out;
}
vec dnorm01(vec const &x) {
vec out(x.size());
double const *xi = x.begin();
for(double &o : out)
o = R::dnorm4(*xi++, 0, 1, false);
return out;
}
// we could use templates for the following...
vec logit(vec const & p) {
return log(p/(1-p));
}
vec expit(vec const & x) {
return 1/(1+exp(-x));
}
double logit(double p) {
return log(p/(1-p));
}
double expit(double x) {
return 1/(1+exp(-x));
}
// utility for fast ragged sums
RcppExport SEXP tapplySum(SEXP s_y, SEXP s_group) {
NumericVector y(s_y);
NumericVector group(s_group);
NumericVector::iterator iy, igroup;
std::map<double,double> out;
for (iy = y.begin(), igroup = group.begin(); iy != y.end(); ++iy, ++igroup) {
out[*igroup] += *iy;
}
return wrap(out);
}
// https://github.com/RcppCore/rcpp-gallery/issues/123#issue-553642056
arma::vec dmvnrm_arma(arma::mat const &x,
arma::rowvec const &mean,
arma::mat const &sigma,
bool const logd = false) {
int n = x.n_rows;
int xdim = x.n_cols;
arma::vec out(n);
arma::mat const rooti = arma::inv(trimatu(arma::chol(sigma)));
double const rootisum = arma::sum(log(rooti.diag())),
constants = -xdim/2.0 * log2pi,
other_terms = rootisum + constants;

arma::rowvec z;
for (int i=0; i < n; i++) {
z      = (x.row(i) - mean) * rooti;
out(i) = other_terms - 0.5 * arma::dot(z, z);
}

if (logd == false)
out = exp(out);
return(out);
}
double dmvnrm_arma(arma::vec const &x,
arma::vec const &mean,
arma::mat const &sigma,
bool const logd = false) {
int xdim = x.n_elem;
arma::mat const rooti = arma::inv(trimatu(arma::chol(sigma)));
double const rootisum = arma::sum(log(rooti.diag())),
constants = -xdim/2.0 * log2pi,
other_terms = rootisum + constants;

auto z = (x - mean).t() * rooti;
double out = other_terms - 0.5 * arma::dot(z, z);

if (logd == false)
out = exp(out);
return(out);
}

public:
virtual vec link(vec const &S) const = 0;
virtual vec ilink(vec const &x) const = 0;
virtual vec h(vec const &eta, vec const &etaD) const  = 0;
virtual vec H(vec const &eta) const = 0;
virtual mat gradH(vec const &eta, mat const &X) const = 0;
mat const &XD) const = 0;
};
public:
vec link(vec const &S) const  {
return log(-log(S));
}
vec ilink(vec const &x) const {
return exp(-exp(x));
}
vec h(vec const &eta, vec const &etaD) const {
}
vec H(vec const &eta) const {
return exp(eta);
}
mat gradH(vec const &eta, mat const &X) const {
return rmult(X,exp(eta));
}
mat const &XD) const {
return rmult(XD, exp(eta)) + rmult(X, etaD % exp(eta));
}
cube hessianH(vec const &beta, mat const &X) const {
cube c(beta.size(), beta.size(), X.n_rows);
for (size_t i=0; i<X.n_rows; ++i)
c.slice(i) = X.row(i).t()*X.row(i)*exp(dot(X.row(i),beta));
return c;
}
cube hessianh(vec const &beta, mat const &X, mat const &XD) const {
cube c(beta.size(), beta.size(), X.n_rows);
for (size_t i=0; i<X.n_rows; ++i) {
rowvec Xi = X.row(i);
rowvec XDi = XD.row(i);
c.slice(i) = (XDi.t()*Xi + Xi.t()*XDi + dot(XDi,beta)*Xi.t()*Xi)*exp(dot(Xi,beta));
}
return c;
}

};
public:
vec link(vec const &S) const {
if (thetaAO==0)
return log(-log(S));
else return log((exp(log(S)*(-thetaAO))-1)/thetaAO);
}
vec ilink(vec const &eta) const {
if (thetaAO==0)
return exp(-exp(eta));
else
return exp(-log(thetaAO*exp(eta)+1)/thetaAO);
}
vec h(vec const &eta, vec const &etaD) const {
if (thetaAO==0)
}
vec H(vec const &eta) const {
if (thetaAO==0)
return exp(eta);
else return log(thetaAO*exp(eta)+1)/thetaAO;
}
mat gradH(vec const &eta, mat const &X) const {
if (thetaAO==0)
return rmult(X,exp(eta));
else
return rmult(X,exp(eta)/(1+thetaAO*exp(eta)));
}
mat const &XD) const {
if (thetaAO==0)
return rmult(XD, exp(eta)) + rmult(X, etaD % exp(eta));
else {
vec denom = (thetaAO*exp(eta)+1) % (thetaAO*exp(eta)+1);
}
}
double thetaAO;
List args = as<List>(sexp);
thetaAO = as<double>(args["thetaAO"]);
}
};
// Useful relationship: d/dx expit(x)=expit(x)*expit(-x)
public:
vec link(vec const &S) const {
return -logit(S);
}
vec ilink(vec const &x) const {
return expit(-x);
}
// vec h(vec eta, vec etaD) { return etaD % exp(eta) % expit(-eta); }
vec h(vec const &eta, vec const &etaD) const {
}
vec H(vec const &eta) const {
return -log(expit(-eta));
}
mat gradH(vec const &eta, mat const &X) const {
return rmult(X,expit(eta));
}
mat const &XD) const {
// return rmult(X, etaD % exp(eta) % expit(-eta)) -
// 	rmult(X, exp(2*eta) % etaD % expit(-eta) % expit(-eta)) +
// 	rmult(XD, exp(eta) % expit(-eta));
return rmult(XD, expit(eta)) +
rmult(X, expit(eta) % expit(-eta) % etaD);
}
cube hessianH(vec const &beta, mat const &X) const {
cube c(beta.size(), beta.size(), X.n_rows);
for (size_t i=0; i<X.n_rows; ++i) {
colvec Xi = X.row(i);
double Xibeta = dot(Xi,beta);
c.slice(i) = Xi.t()*Xi*expit(Xibeta)*expit(-Xibeta);
}
return c;
}
cube hessianh(vec const &beta, mat const &X, mat const &XD) const {
cube c(beta.size(), beta.size(), X.n_rows);
for (size_t i=0; i<X.n_rows; ++i) {
colvec Xi = X.row(i);
colvec XDi = XD.row(i);
double Xibeta = dot(Xi,beta);
c.slice(i) = XDi.t()*Xi*expit(Xibeta) + Xi.t()*XDi*expit(-Xibeta)*expit(Xibeta);
}
return c;
}
};
public:
vec link(vec const &S) const {
return -qnorm01(S);
}
vec ilink(vec const &eta) const {
return pnorm01(-eta);
}
vec H(vec const &eta) const {
return -pnorm01_log(-eta);
}
vec h(vec const &eta, vec const &etaD) const {
}
mat gradH(vec const &eta, mat const &X) const {
return rmult(X, dpnorm01_log(-eta));
}
mat const &XD) const {
vec const dpnrm_log = dpnorm01_log(-eta);
return rmult(X , -eta % etaD % dpnrm_log) +
rmult     (X , etaD % dpnrm_log % dpnrm_log) +
rmult     (XD, dpnrm_log);
}
// incomplete implementation
cube hessianh(vec const &beta, mat const &X, mat const &XD) const {
cube c(beta.size(), beta.size(), X.n_rows, fill::zeros);
return c;
}
// incomplete implementation
cube hessianH(vec const &beta, mat const &X) const {
cube c(beta.size(), beta.size(), X.n_rows, fill::zeros);
return c;
}
};
public:
vec link(vec const &S) const {
return -log(S);
}
vec ilink(vec const &x) const {
return exp(-x);
}
vec h(vec const &eta, vec const &etaD) const {
}
vec H(vec const &eta) const {
return eta;
}
mat const &XD) const {
return XD;
}
mat gradH(vec const &eta, mat const &X) const {
return X;
}
cube hessianh(vec const &beta, mat const &X, mat const &XD) const {
cube c(beta.size(), beta.size(), X.n_rows, fill::zeros);
return c;
}
cube hessianH(vec const &beta, mat const &X) const {
cube c(beta.size(), beta.size(), X.n_rows, fill::zeros);
return c;
}
};
// wrappers to call class methods from C
template<class T>
double optimfunction(int n, double * beta, void * void_obj) {
T * obj = static_cast<T*>(void_obj);
vec coef(beta,n);
double value = obj->objective(coef % obj->parscale);
if (obj->bfgs.trace>1) {
Rprintf("beta="); Rprint(coef);
Rprintf("objective=%.10g\n",value);
};
// R_CheckUserInterrupt();  /* be polite -- did the user hit ctrl-C? */
return value;
}
template<class T>
void optimgradient(int n, double * beta, double * grad, void * void_obj) {
T * obj = static_cast<T*>(void_obj);
vec coef(beta,n);
if (obj->bfgs.trace>1) {
Rprintf("beta="); Rprint(coef);
}
if (obj->bfgs.trace>2) {
Rprintf("parscale="); Rprint(obj->parscale);
}
vec gr = obj->gradient(coef % obj->parscale);
if (obj->bfgs.trace>1) {
}
// if (obj->bfgs.trace>2) {
// }
for (int i=0; i<n; ++i) grad[i] = gr[i];
}
template<class T>
void optimfunction_nlm(int n, double * beta, double * f, void * void_obj) {
T * obj = static_cast<T*>(void_obj);
vec coef(beta,n);
*f = obj->objective(coef % obj->parscale);
}
class BFGS2 : public BFGS {
public:
NumericMatrix calc_hessian(optimgr gr, void * ex) {
if (parscale.size()==0) REprintf("parscale is not defined for BFGS2::calc_hessian.\n");
int n = coef.size();
NumericVector df1(n);
NumericVector df2(n);
NumericMatrix hess(n,n);
double tmp;
for(int i=0; i<n; ++i) {
tmp = coef[i];
coef[i] = tmp + epshess/parscale[i];
gr(n, &coef[0], &df1[0], ex);
coef[i] = tmp - epshess/parscale[i];
gr(n, &coef[0], &df2[0], ex);
for (int j=0; j<n; ++j)
hess(i,j) = (df1[j] - df2[j]) / (2*epshess);
coef[i] = tmp;
}
// now symmetrize
for(int i=0; i<n; ++i)
for(int j=i; j<n; ++j)
if (i != j)
hess(i,j) = hess(j,i) = (hess(i,j) + hess(j,i)) / 2.0;
return hess; // wrap()?
}
vec parscale;
};
public:
NumericMatrix calc_hessian(optimfn fn, void * ex, int debug = 0) {
if (parscale.size()==0) REprintf("parscale is not defined for NelderMead2::calc_hessian.");
int n = coef.size();
NumericMatrix hess(n,n);
double tmpi,tmpj,f1,f0,fm1,hi,hj,fij,fimj,fmij,fmimj;
f0 = fn(n,&coef[0],ex);
for(int i=0; i<n; ++i) {
tmpi = coef[i];
hi = epshess*(1.0+std::abs(tmpi))/parscale[i];
coef[i] = tmpi + hi;
f1=fn(n, &coef[0], ex);
coef[i] = tmpi - hi;
fm1=fn(n, &coef[0], ex);
// hess(i,i) = (-f2 +16.0*f1 - 30.0*f0 + 16.0*fm1 -fm2)/(12.0*hi*hi);
hess(i,i) = (f1 - 2.0*f0 + fm1)/(hi*hi*parscale[i]*parscale[i]);
coef[i] = tmpi;
for (int j=i; j<n; ++j) {
if (i != j) {
tmpj = coef[j];
hj = epshess*(1.0+std::abs(tmpj))/parscale[j];
coef[i] = tmpi + hi;
coef[j] = tmpj + hj;
fij=fn(n, &coef[0], ex);
coef[i] = tmpi + hi;
coef[j] = tmpj - hj;
fimj=fn(n, &coef[0], ex);
coef[i] = tmpi - hi;
coef[j] = tmpj + hj;
fmij=fn(n, &coef[0], ex);
coef[i] = tmpi - hi;
coef[j] = tmpj - hj;
fmimj=fn(n, &coef[0], ex);
hess(j,i) = hess(i,j) = (fij-fimj-fmij+fmimj)/(4.0*hi*hj*parscale[i]*parscale[j]);
coef[i] = tmpi;
coef[j] = tmpj;
}
}
}
if (debug>1) Rprint(hess);
return hess;
}
vec parscale;
};
class Nlm2 : public Nlm {
public:
NumericMatrix calc_hessian(fcn_p fn, void * ex, int debug = 0) {
if (parscale.size()==0) REprintf("parscale is not defined for Nlm2::calc_hessian.");
int n = coef.size();
NumericMatrix hess(n,n);
double tmpi,tmpj,f1,f0,fm1,hi,hj,fij,fimj,fmij,fmimj;
fn(n,&coef[0],&f0,ex);
for(int i=0; i<n; ++i) {
tmpi = coef[i];
hi = epshess*(1.0+std::abs(tmpi))/parscale[i];
coef[i] = tmpi + hi;
fn(n, &coef[0], &f1, ex);
coef[i] = tmpi - hi;
fn(n, &coef[0], &fm1, ex);
// hess(i,i) = (-f2 +16.0*f1 - 30.0*f0 + 16.0*fm1 -fm2)/(12.0*hi*hi);
hess(i,i) = (f1 - 2.0*f0 + fm1)/(hi*hi*parscale[i]*parscale[i]);
coef[i] = tmpi;
for (int j=i; j<n; ++j) {
if (i != j) {
tmpj = coef[j];
hj = epshess*(1.0+std::abs(tmpj))/parscale[j];
coef[i] = tmpi + hi;
coef[j] = tmpj + hj;
fn(n, &coef[0], &fij, ex);
coef[i] = tmpi + hi;
coef[j] = tmpj - hj;
fn(n, &coef[0], &fimj, ex);
coef[i] = tmpi - hi;
coef[j] = tmpj + hj;
fn(n, &coef[0], &fmij, ex);
coef[i] = tmpi - hi;
coef[j] = tmpj - hj;
fn(n, &coef[0], &fmimj, ex);
hess(j,i) = hess(i,j) = (fij-fimj-fmij+fmimj)/(4.0*hi*hj*parscale[i]*parscale[j]);
coef[i] = tmpi;
coef[j] = tmpj;
}
}
}
return hess;
}
vec parscale;
};

/** @brief Macro to define the optimisation functions. Defined as a macro
because the C API needs to pass a 'This' template parameter
which varies for the different classes (alternatively, this
could be defined using the curiously recurring template
pattern).
**/
#define OPTIM_FUNCTIONS							\
void optimWithConstraintBFGS(NumericVector init) {			\
bool satisfied;							\
this->bfgs.coef = init;						\
if (this->robust_initial) {					\
optimNoHessianNM(this->bfgs.coef,50);				\
}									\
this->kappa = this->kappa_init;					\
do {								\
this->bfgs.optim(&optimfunction<This>, &optimgradient<This>, this->bfgs.coef, (void *) this); \
vec vcoef(&this->bfgs.coef[0],this->n);				\
satisfied = this->feasible(vcoef % this->parscale);		\
if (!satisfied) this->kappa *= 2.0;				\
} while ((!satisfied) && this->kappa < 1.0e3);			\
if (this->bfgs.trace > 0 && this->kappa>1.0) Rprintf("kappa=%f\n",this->kappa); \
this->bfgs.hessian = this->bfgs.calc_hessian(&optimgradient<This>, (void *) this); \
}									\
void optimNoHessianNM(NumericVector init, int maxit = 50) {		\
nm.hessianp = false;						\
nm.parscale = this->parscale;					\
nm.maxit = maxit;							\
nm.optim(&optimfunction<This>, init, (void *) this);		\
this->bfgs.coef = nm.coef;					\
}									\
void optimWithConstraintNM(NumericVector init) {			\
bool satisfied;							\
nm.hessianp = false;						\
nm.parscale = this->parscale;					\
this->kappa = this->kappa_init;					\
do {								\
nm.optim(&optimfunction<This>, init, (void *) this);		\
vec vcoef(&nm.coef[0],this->n);					\
satisfied = this->feasible(vcoef % this->parscale);		\
if (!satisfied) this->kappa *= 2.0;				\
} while ((!satisfied) && this->kappa < this->maxkappa);		\
if (this->bfgs.trace > 1) Rprintf("Calculating hessian...\n");	\
nm.hessian = nm.calc_hessian(&optimfunction<This>, (void *) this, this->bfgs.trace); \
this->bfgs.coef = nm.coef;					\
this->bfgs.hessian = nm.hessian;					\
}									\
void optimWithConstraintNlm(NumericVector init) {			\
bool satisfied;							\
Nlm2 nm;								\
nm.gradtl = nm.steptl = this->reltol;				\
nm.parscale = this->parscale;					\
this->kappa = this->kappa_init;					\
do {								\
nm.optim(&optimfunction_nlm<This>, init, (void *) this);	\
vec vcoef(&nm.coef[0],this->n);					\
satisfied = this->feasible(vcoef % this->parscale);		\
if (!satisfied) this->kappa *= 2.0;				\
} while ((!satisfied) && this->kappa < 1.0e3);			\
if (this->bfgs.trace > 0 && this->kappa>1.0) Rprintf("kappa=%f\n",this->kappa); \
nm.hessian = nm.calc_hessian(&optimfunction_nlm<This>, (void *) this); \
this->bfgs.coef = nm.coef;					\
this->bfgs.hessian = nm.hessian;					\
}									\
void optimWithConstraint(NumericVector init) {			\
if (this->bfgs.trace > 0) Rprintf("Starting optimization\n");	\
optimWithConstraintNM(init);					\
else if (this->optimiser == "Nlm")				\
optimWithConstraintNlm(init);					\
else								\
optimWithConstraintBFGS(init);					\
}

// struct for data
struct BaseData {
mat X, XD, X0, X1;
vec bhazard,wt,wt0,event,time,offset;
vec map0;
uvec ind0, which0;
};
// Main class for Stpm2 (fully parametric)
class Stpm2 : public BaseData {
public:
typedef Stpm2 This;
Stpm2(SEXP sexp) : bfgs() {
List list = as<List>(sexp);
else {
return;
}
bfgs.coef = init = as<NumericVector>(list["init"]);
X = as<mat>(list["X"]);
XD = as<mat>(list["XD"]);
bhazard = as<vec>(list["bhazard"]);
wt = as<vec>(list["wt"]);
event = as<vec>(list["event"]);
time = as<vec>(list["time"]);
offset = as<vec>(list["offset"]);
delayed = as<bool>(list["delayed"]);
interval = as<bool>(list["interval"]);
n = nbeta = init.size(); // number of parameters
N = X.n_rows; // number of observations
X1 = as<mat>(list["X1"]);
X0 = as<mat>(list["X0"]);
wt0.set_size(N); wt0.fill(0.0);
if (delayed) {
wt0 = as<vec>(list["wt0"]);
}
// if (interval) {
// 	X1 = as<mat>(list["X1"]);
// }
map0 = as<vec>(list["map0"]); // length N map for X->X0
full_which0 = as<vec>(list["which0"]); // length N map for X0->X
ind0 = as<uvec>(list["ind0"]); // length N boolean for X0
ttype = as<vec>(list["ttype"]);
kappa_init = kappa = as<double>(list["kappa"]);
maxkappa = as<double>(list["maxkappa"]);
optimiser = as<std::string>(list["optimiser"]);
bfgs.trace = as<int>(list["trace"]);
reltol = bfgs.reltol = as<double>(list["reltol"]);
robust_initial = as<bool>(list["robust_initial"]);
bfgs.hessianp = false;
bfgs.parscale = parscale = as<vec>(list["parscale"]);
which0 = removeNaN(full_which0);
}
// log-likelihood components and constraints
// Note: the li and gradli components depend on other variables (bhazard, wt, wt0, wt, event);
//       calculations should *not* be done on subsets
virtual ~Stpm2() {
}
li_constraint li_right_censored(vec eta, vec etaD) {
vec eps = h*0.0 + 1.0e-16;
double constraint = kappa/2.0 * (sum(h % h % (h<0)) +
sum(H % H % (H<0)));
h = max(h,eps);
H = max(H,eps);
vec li = wt % event % log(h) - wt % H;
li_constraint out = {li, constraint};
return out;
}
li_constraint li_left_truncated(vec eta0) {
double constraint = kappa/2.0 * sum(H0 % H0 % (H0<0));
vec eps = H0*0.0 + 1.0e-16;
vec li = wt0 % max(H0,eps);
li_constraint out = {li, constraint};
return out;
}
li_constraint li_interval(vec eta, vec etaD, vec eta1) {
double constraint = 0.0;
vec eps = H*0.0 + 1e-16;
H = max(H,eps);
H1 = max(H1,eps);
h = max(h,eps);
vec li(N,fill::zeros);
uvec index;
index = find(ttype == 0); // right censored
if (any(index)) {
li(index) -= wt(index) % H(index);
constraint += kappa/2.0 * sum(H(index) % H(index) % (H(index)<0));
}
index = find(ttype == 1); // exact
if (any(index)) {
li(index) += wt(index) % (log(h(index)) - H(index));
constraint += kappa/2.0 * (sum(H(index) % H(index) % (H(index)<0))+
sum(h(index) % h(index) % (h(index)<0)));
}
index = find(ttype == 2); // left censored
if (any(index)) {
li(index) += wt(index) % log(1-exp(-H(index)));
constraint += kappa/2.0 * sum(H(index) % H(index) % (H(index)<0));
}
index = find(ttype == 3); // interval censored
if (any(index)) {
li(index) += wt(index) % log(exp(-H(index)) - exp(-H1(index)));
constraint += kappa/2.0 * (sum(H(index) % H(index) % (H(index)<0))+
sum(H1(index) % H1(index) % (H1(index)<0)));
}
li_constraint out = {li, constraint};
return out;
}
li_constraint li(vec eta, vec etaD, vec eta0, vec eta1, vec beta) {
if (interval) {
}
else {
if (delayed && !eta0.empty()) {
li_constraint s0 = li_left_truncated(eta0+offset(which0));
s.constraint += s0.constraint;
if (bfgs.trace > 0) {
Rprint(which0);
}
s.li(which0) += s0.li;
}
return s;
}
}
vec getli(vec beta) {
vec vbeta = beta;
vbeta.resize(nbeta);
li_constraint lic = li(X*vbeta, XD*vbeta, X0*vbeta, X1*vbeta, beta);
return lic.li;
}
vec vbeta = beta;
vbeta.resize(nbeta);
}
// negative log-likelihood
double objective(vec beta) {
vec vbeta = beta;
vbeta.resize(nbeta);
li_constraint s = li(X * vbeta, XD * vbeta, X0 * vbeta, X1 * vbeta, beta);
return -sum(s.li) + s.constraint;
}
// finite-differencing of the gradient for the objective
vec fdgradient(vec beta, double eps = 1.0e-8) {
int n = beta.size();
for (int i=0; i<n; ++i) {
vec lower(beta);
vec upper(beta);
upper(i) += eps;
lower(i) -= eps;
grad(i) = (objective(upper) - objective(lower)) / 2.0 / eps;
}
}
double f(vec beta, int i, double delta) {
double betai = beta(i);
beta(i) += delta;
double y = objective(beta);
beta(i) = betai;
return y;
}
double f2(vec beta, int i, int j, double epsi, double epsj) {
double betai = beta(i), betaj = beta(j);
beta(i) += epsi;
beta(j) += epsj;
double y = objective(beta);
beta(i) = betai;
beta(j) = betaj;
return y;
}
mat fdhessian(vec beta) {
int n = beta.size();
mat hessian(n,n);
double eps0 = pow(datum::eps,1.0/3.0);
double epsi, epsj;
for (int i=0; i<n; ++i) {
for (int j=i; j<n; ++j) {
if (i==j) {
epsi = eps0*(1+std::abs(beta(i)));
hessian(i,i) = (-f(beta,i,2.0*epsi)+16.0*f(beta,i,epsi)-30.0*f(beta,i,0.0)+16.0*f(beta,i,-epsi)-
f(beta,i,-2.0*epsi))/12.0/epsi/epsi;
} else {
epsi = eps0*(1+std::abs(beta(i)));
epsj = eps0*(1+std::abs(beta(j)));
hessian(i,j) = hessian(j,i) = (f2(beta,i,j,epsi,epsj)-f2(beta,i,j,epsi,-epsj)-f2(beta,i,j,-epsi,epsj)+f2(beta,i,j,-epsi,-epsj))/4.0/epsi/epsj;
}
}
}
return hessian;
}
// Note: gradH and gradh are currently calculated at eta and etaD and may not satisfy the constraints,
//       while H and h may be transformed for the constraints
vec eps = h*0.0 + 1.0e-16;
mat Xconstraint = kappa * (rmult(gradh, h % (h<0)) +
// h = max(h,eps);
return out;
}
vec eps = H0*0.0 + 1.0e-16;
mat Xconstraint = kappa * rmult(gradH0, H0 % (H0<0));
return out;
}
mat X, mat XD, mat X1) {
vec eps = H*0.0 + 1e-16;
// mat Xconstraint = kappa * (rmult(gradH, H % (H<eps))+
mat Xconstraint = X * 0.0;
H = max(H,eps);
H1 = max(H1,eps);
h = max(h,eps);
mat li(N,n,fill::zeros);
uvec index;
index = find(ttype == 0); // right censored
if (any(index)) {
Xconstraint.rows(index) += kappa*(rmult(gradH.rows(index), H(index) % (H(index)<eps(index))));
}
index = find(ttype == 1); // exact
if (any(index)) {
Xconstraint.rows(index) += kappa*(rmult(gradH.rows(index), H(index) % (H(index)<eps(index))) +
}
index = find(ttype == 2); // left censored
if (any(index)) {
li.rows(index) += rmult(-gradH.rows(index),-exp(-H(index)) / (1-exp(-H(index))) % wt(index));
Xconstraint.rows(index) += kappa*(rmult(gradH.rows(index), H(index) % (H(index)<eps(index))));
}
index = find(ttype == 3); // interval censored
if (any(index)) {
vec V = wt(index) / (exp(-H(index)) - exp(-H1(index)));
li.rows(index) += rmult(gradH1.rows(index),V % exp(-H1(index))) -
Xconstraint.rows(index) += kappa*(rmult(gradH.rows(index), H(index) % (H(index)<eps(index))) +
}
return out;
}
mat X, mat XD, mat X0, mat X1, vec beta) {
else {
if (delayed) {
s.constraint.rows(which0) += s0.constraint;
}
return s;
}
}
// gradient of the negative log-likelihood
gradli_constraint gc = gradli(X * beta, XD * beta, X0 * beta, X1 * beta,
X, XD, X0, X1, beta);
rowvec dconstraint = sum(gc.constraint,0);
vec gr(n);
for (size_t i = 0; i<beta.size(); ++i) {
gr[i] = vgr[i];// - dconstraint[i];
}
return -gr;
}
bool feasible(vec beta) {
vec eta = X * beta;
vec etaD = XD * beta;
bool condition = all((h>0) % (H>0));
if (delayed) {
vec eta0 = X0 * beta;
// vec etaD0 = XD0 * beta;
condition = condition && all(H0>0);
}
return condition;
}
void pre_process() {
for (int i = 0; i<n; ++i) init[i] /= parscale[i];
}
void post_process() {
for (int i = 0; i<n; ++i) {
bfgs.coef[i] *= parscale[i];
init[i] *= parscale[i];
}
}
OPTIM_FUNCTIONS;
// NumericMatrix calcHessian(NumericVector nvbeta) {
//   // not defined for interval-censored or probit link
//   vec beta(&nvbeta[0],n);
//   vec eta = X * beta;
//   vec etaD = XD * beta;
//   mat hessian = -arma::sum(hessianH,2);
//   if (delayed)
// 	hessian += arma::sum(hessianH0,2);
//   for (int i=0; i<N; ++i)
// 	hessian += event(i)/h(i)*hessianh.slice(i) -
//   return wrap(-hessian);
// }
uvec map0f(uvec index) {
return removeNaN(this->map0(index));
}
uvec which0f(uvec index) {
vec which = this->full_which0(index);
return find(which == which);
}
uvec removeNaN(vec x) {
vec newx = x;
uvec index = find(newx == newx); // NaN != NaN
newx = newx(index);
return conv_to<uvec>::from(newx);
}
SEXP return_modes() { return wrap(-1); } // used in NormalSharedFrailties
SEXP return_variances() { return wrap(-1); } // used in NormalSharedFrailties
NumericVector init;
vec parscale, ttype, full_which0;
double kappa_init, kappa, maxkappa, reltol;
bool delayed, interval, robust_initial;
int n, N, nbeta;
BFGS2 bfgs;
std::string optimiser;
};

// penalised smoothers
// _Not_ sub-classes of Pstpm2, hence the longer function signatures
class SmoothLogH {
public:
struct Smoother {
int first_para, last_para;
mat S;
bool first;
};
SmoothLogH(SEXP sexp) {
List list = as<List>(sexp);
List lsmooth = as<List>(list["smooth"]);
for(int i=0; i<lsmooth.size(); ++i) {
List lsmoothi = as<List>(lsmooth[i]);
List lsmoothiS = as<List>(lsmoothi["S"]);
Smoother smoothi =  {
as<int>(lsmoothi["first.para"]) - 1,
as<int>(lsmoothi["last.para"]) - 1,
as<mat>(lsmoothiS[0]),
true
};
smooth.push_back(smoothi);
if (lsmoothiS.size()==2) {
Smoother smoothi2 =  {
as<int>(lsmoothi["first.para"]) - 1,
as<int>(lsmoothi["last.para"]) - 1,
as<mat>(lsmoothiS[1]),
false
};
smooth.push_back(smoothi2);
}
}
}
double penalty(vec vbeta, vec sp) {
double value = 0.0;
for (size_t i=0; i < smooth.size(); ++i) {
Smoother smoothi = smooth[i];
value += sp[i]/2 *
dot(vbeta.subvec(smoothi.first_para,smoothi.last_para),
smoothi.S * vbeta.subvec(smoothi.first_para,smoothi.last_para));
}
return value;
}
vec penalty_gradient(vec vbeta, vec sp) {
int n = vbeta.size();
rowvec vgr(n, fill::zeros);
for (size_t i=0; i < smooth.size(); ++i) {
Smoother smoothi = smooth[i];
vgr.subvec(smoothi.first_para,smoothi.last_para) +=
sp[i] * (smoothi.S * vbeta.subvec(smoothi.first_para,smoothi.last_para)).t();
}
vec gr(n);
for (int i=0; i<n; ++i) gr[i] = vgr[i];
return gr;
}
vec traces(mat X) {
vec values(smooth.size(), fill::zeros);
for (size_t i=0; i < smooth.size(); ++i) {
Smoother smoothi = smooth[i];
for (size_t j=smoothi.first_para; j <= static_cast<size_t>(smoothi.last_para); ++j)
values[i] += X(j,j);
// if (!smoothi.first) values[i]=0.0; // edf for second smoother matrix: ignore
}
return values;
}
std::vector<Smoother> smooth;
};
// // TODO: include first_para and last_para class data for the traces() method
// class SmoothHaz {
// public:
//   struct Smoother {
//     mat X0, X1, X2, X3;
//     vec w;
//     double lambda;
//   };
//   SmoothHaz(SEXP sexp) {
//     List list = as<List>(sexp);
//     List lsmooth = as<List>(list["smooth"]);
//     for(int i=0; i<lsmooth.size(); ++i) {
// 	List lsmoothi = as<List>(lsmooth[i]);
// 	Smoother smoothi =  {
// 	  as<mat>(lsmoothi["X0"]),
// 	  as<mat>(lsmoothi["X1"]),
// 	  as<mat>(lsmoothi["X2"]),
// 	  as<mat>(lsmoothi["X3"]),
// 	  as<vec>(lsmoothi["w"]),
// 	  as<double>(lsmoothi["lambda"])
// 	};
// 	smooth.push_back(smoothi);
//     }
//   }
//   double penalty(vec vbeta, vec sp) {
//     double value = 0.0;
//     for (size_t i=0; i < smooth.size(); ++i) {
// 	Smoother obj = smooth[i];
// 	vec s0 = obj.X0 * vbeta;
// 	vec s1 = obj.X1 * vbeta;
// 	vec s2 = obj.X2 * vbeta;
// 	vec s3 = obj.X3 * vbeta;
// 	vec h2 = exp(s0) % (s3 + 3*s1%s2 + s1%s1%s1);
// 	value += sp[i]/2 * obj.lambda * sum(obj.w % h2 % h2);
//     }
//     return value;
//   }
// vec penalty_gradient(vec vbeta, vec sp) {
//   int n = vbeta.size();
//   rowvec vgr(n, fill::zeros);
//   for (size_t i=0; i < smooth.size(); ++i) {
//     Smoother obj = smooth[i];
//     vec s0 = obj.X0 * vbeta;
//     vec s1 = obj.X1 * vbeta;
//     vec s2 = obj.X2 * vbeta;
//     vec s3 = obj.X3 * vbeta;
//     vec h2 = exp(s0) % (s3 + 3*s1%s2 + s1%s1%s1);
//     mat dh2sq_dbeta =
// 	2*lmult(h2 % exp(s0),
// 		obj.X3+3*(rmult(obj.X1,s2)+rmult(obj.X2,s1))+3*lmult(s1%s1,obj.X1))+
// 	2*lmult(h2 % h2,obj.X0);
//     vgr += sp[i]*obj.lambda*sum(lmult(obj.w, dh2sq_dbeta),0);
//   }
//   vec gr(n);
//   for (int i = 0; i<n; ++i) gr[i] = vgr[i];
//   return gr;
// }
//   std::vector<Smoother> smooth;
// };
template<class T>
double pstpm2_multivariate_step(int n, double * logsp_ptr, void * model_ptr) {
T * model = static_cast<T *>(model_ptr);
vec logsp(logsp_ptr,n);
R_CheckUserInterrupt();  /* be polite -- did the user hit ctrl-C? */
return model->multivariate_step(logsp);
}
template<class T>
double pstpm2_first_step(double logsp, void * model_ptr) {
T * model = static_cast<T *>(model_ptr);
R_CheckUserInterrupt();  /* be polite -- did the user hit ctrl-C? */
return model->first_step(logsp);
}
template<class T>
void pstpm2_multivariate_stepNlm(int n, double * logsp_ptr, double * objective, void * model_ptr) {
T * model = static_cast<T *>(model_ptr);
vec logsp(logsp_ptr,n);
R_CheckUserInterrupt();  /* be polite -- did the user hit ctrl-C? */
*objective = model->multivariate_step(logsp);
}

template<class Stpm2Type = Stpm2, class Smooth = SmoothLogH>
class Pstpm2 : public Stpm2Type, public Smooth {
public:
typedef Pstpm2<Stpm2Type,Smooth> This;
Pstpm2(SEXP sexp) : Stpm2Type(sexp), Smooth(sexp) {
List list = as<List>(sexp);
sp = as<vec>(list["sp"]);
reltol_search = as<double>(list["reltol_search"]);
reltol_outer = as<double>(list["reltol_outer"]);
alpha = as<double>(list["alpha"]);
criterion = as<int>(list["criterion"]);
outer_optim = as<int>(list["outer_optim"]);
}
double objective(vec beta) {
return Stpm2Type::objective(beta) + Smooth::penalty(beta,sp);
}
double objective0(vec beta) {
return Stpm2Type::objective(beta);
}
}
}
OPTIM_FUNCTIONS;
double calc_edf(NumericMatrix hessian0) {
double max_edf = this->bfgs.hessian.ncol();
mat m;
bool flag = arma::solve(m, as<mat>(this->bfgs.hessian), as<mat>(hessian0));
double edf = flag ? arma::trace(m) : (max_edf*2.0);
if (edf<0.0) edf = max_edf*2.0;
return edf;
}
double first_step(double logsp) {
sp[0] = exp(logsp);
this->pre_process();
this->optimWithConstraint(this->init);
// this->bfgs.hessian = this->bfgs.calc_hessian(&optimgradient<This>, (void *) this);
NumericMatrix hessian0 = this->bfgs.calc_hessian(&optimgradient<Stpm2Type>, (void *) this);
if (this->bfgs.trace > 1)  {
Rprintf("Debug on trace calculation. Coef:\n");
Rprint(this->bfgs.coef);
if (this->bfgs.trace > 1) {
Rprintf("Hessian0:\n");
Rprint(hessian0);
Rprintf("Hessian:\n");
Rprint(this->bfgs.hessian);
}
}
double edf = calc_edf(hessian0);
double negll = this->bfgs.calc_objective(&optimfunction<Stpm2Type>, (void *) this);
double gcv =  negll + alpha*edf;
double bic =  negll + alpha*edf*log(sum(this->event));
this->init = this->bfgs.coef;
if (this->bfgs.trace > 0)
Rprintf("sp=%f\tedf=%f\tnegll=%f\tgcv=%f\tbic=%f\talpha=%f\n",sp[0],edf,negll,gcv,bic,alpha);
this->post_process();
return criterion==1 ? gcv : bic;
}
double multivariate_step(vec logsp) {
this->pre_process();
double lsp = -9.0, usp = 9.0;
for (size_t i=0; i < sp.size(); ++i)
sp[i] = exp(bound(logsp[i],lsp,usp));
if (this->bfgs.trace > 0) {
for (size_t i = 0; i < sp.size(); ++i)
Rprintf("sp[%i]=%f\t",i,sp[i]);
}
this->optimWithConstraint(this->init);
this->bfgs.hessian = this->bfgs.calc_hessian(&optimgradient<This>, (void *) this);
NumericMatrix hessian0 = this->bfgs.calc_hessian(&optimgradient<Stpm2Type>, (void *) this);
double edf = calc_edf(hessian0);
double negll = this->bfgs.calc_objective(&optimfunction<Stpm2Type>, (void *) this);
double gcv =  negll + alpha*edf;
double bic =  2.0*negll + alpha*edf*log(sum(this->event));
this->init = this->bfgs.coef;
// simple boundary constraints
double constraint = 0.0;
// double kappa = 1.0;
for (size_t i=0; i < sp.size(); ++i) {
if (logsp[i] < lsp)
constraint +=  pow(logsp[i]-lsp,2.0);
if (logsp[i] > usp)
constraint +=  pow(logsp[i]-usp,2.0);
}
double objective =  criterion==1 ?
gcv + this->kappa/2.0*constraint :
bic + this->kappa/2.0*constraint;
if (this->bfgs.trace > 0) {
Rprintf("edf=%f\tnegll=%f\tgcv=%f\tbic=%f\tobjective=%f\n",edf,negll,gcv,bic,objective);
}
this->post_process();
return objective;
}
SEXP optim_fixed() {
this->pre_process();
this->optimWithConstraint(this->init);
this->bfgs.hessian = this->bfgs.calc_hessian(&optimgradient<This>, (void *) this);
NumericMatrix hessian0 = this->bfgs.calc_hessian(&optimgradient<Stpm2Type>, (void *) this);
mat Proj = solve(as<mat>(wrap(this->bfgs.hessian)),as<mat>(wrap(hessian0)));
double edf = trace(Proj);
NumericVector edf_var = as<NumericVector>(wrap(Smooth::traces(Proj)));
this->post_process();
return List::create(_("sp")=wrap(sp),
_("coef")=wrap(this->bfgs.coef),
_("hessian")=wrap(this->bfgs.hessian),
_("edf")=wrap(edf),
_("edf_var")=wrap(edf_var),
_("kappa")=wrap(this->kappa)
);
}
SEXP optim_first() {
this->bfgs.reltol = reltol_search;
double opt_sp = exp(Brent_fmin(log(0.001),log(1000.0),&(pstpm2_first_step<This>),(void *) this,reltol_outer));
sp[0] = opt_sp;
this->bfgs.reltol = this->reltol;
return optim_fixed();
}
SEXP optim_multivariate() {
else return optim_multivariate_Nlm();
}
this->kappa = 10.0;
nm.reltol = reltol_outer;
nm.maxit = 500;
nm.hessianp = false;
nm.parscale = this->parscale;
this->bfgs.reltol = reltol_search;
NumericVector logsp(sp.size());
for (size_t i=0; i < sp.size(); ++i)
logsp[i] = log(sp[i]);
bool satisfied;
do {
nm.optim(&pstpm2_multivariate_step<This>, logsp, (void *) this);
satisfied = true;
for (size_t i=0; i < sp.size(); ++i)
if (logsp[i]< -9.0 || logsp[i] > 9.0) satisfied = false;
if (!satisfied) this->kappa *= 2.0;
} while (!satisfied && this->kappa<1.0e5);
for (int i=0; i < nm.coef.size(); ++i)
sp[i] = exp(nm.coef[i]);
this->bfgs.coef = this->init;
this->bfgs.reltol = this->reltol;
return optim_fixed();
}
SEXP optim_multivariate_Nlm() {
this->kappa = this->kappa_init;
Nlm2 nm;
nm.itnlim = 100;
// nm.hessianp = false;
nm.parscale = this->parscale;
this->bfgs.reltol = reltol_search;
NumericVector logsp(sp.size());
for (size_t i=0; i < sp.size(); ++i)
logsp[i] = log(sp[i]);
bool satisfied;
do {
nm.optim(&pstpm2_multivariate_stepNlm<This>, logsp, (void *) this);
satisfied = true;
for (size_t i=0; i < sp.size(); ++i)
if (logsp[i]< -9.0 || logsp[i] > 9.0) satisfied = false;
if (!satisfied) this->kappa *= 2.0;
} while (!satisfied && this->kappa<1.0e5);
for (int i=0; i < nm.coef.size(); ++i)
sp[i] = exp(nm.coef[i]);
this->bfgs.coef = this->init;
this->bfgs.reltol = this->reltol;
return optim_fixed();
}
vec sp;
double alpha, reltol_search, reltol_outer;
int criterion, outer_optim;
};
// template<class Smooth, class Stpm2>
// void pstpm2_step_multivariate_nlm(int n, double * logsp, double * f, void *ex) {
//   *f = pstpm2_step_multivariate<Smooth,Stpm2>(n, logsp, ex);
// };

/**
Extension of stpm2 and pstpm2 to include gamma shared frailties with a cluster variable
**/
template<class Base>
class GammaSharedFrailty : public Base {
public:
typedef std::vector<int> Index;
typedef std::map<int,Index> IndexMap;
typedef GammaSharedFrailty<Base> This;
GammaSharedFrailty(SEXP sexp) : Base(sexp) {
List list = as<List>(sexp);
ivec cluster = as<ivec>(list["cluster"]);
recurrent = as<bool>(list["recurrent"]);
this->nbeta = this->n - 1;
// wragged array indexed by a map of vectors
for (size_t id=0; id<cluster.size(); ++id) {
clusters[cluster[id]].push_back(id);
if (this->delayed && this->ind0[id])
cluster_delayed[cluster[id]].push_back(id);
}
}
/**
Objective function for a Gamma shared frailty
Assumes that weights == 1.
**/
double objective(vec beta) {
vec vbeta = beta;
vbeta.resize(this->nbeta);
// copy across to this->bfgs.coef?
li_constraint s = li(this->X * vbeta, this->XD * vbeta, this->X0 * vbeta, this->X1 * vbeta, beta);
return -sum(s.li) + s.constraint;
}
vec getli(vec beta) {
vec vbeta = beta;
vbeta.resize(this->nbeta);
li_constraint lic = li(this->X*vbeta, this->XD*vbeta, this->X0*vbeta, this->X1*vbeta, beta);
return lic.li;
}
vec vbeta = beta;
vbeta.resize(this->nbeta);
}
li_constraint li(vec eta, vec etaD, vec eta0, vec eta1, vec beta) {
vec ll(clusters.size(), fill::zeros);
int n = beta.size();
vec vbeta(beta); // logtheta is the last parameter in beta
vbeta.resize(this->nbeta);
double theta = exp(beta[n-1]);
eta = this->X * vbeta + this->offset;
double constraint = this->kappa/2.0 * (sum(h % h % (h<0)) + sum(H % H % (H<0)));
vec eps = h*0.0 + 1.0e-16;
h = max(h,eps);
H = max(H,eps);
vec H0;
if (this->delayed) {
eta0 = this->X0 * vbeta + this->offset(this->which0);
constraint += this->kappa/2.0 * sum(H0 % H0 % (H0<0));
}
int i=0;
for (IndexMap::iterator it=clusters.begin(); it!=clusters.end(); ++it, ++i) {
uvec index = conv_to<uvec>::from(it->second);
int mi = sum(this->event(index));
double sumH = sum(H(index));
double sumHenter = 0.0;
ll(i) += sum(log(h(index)) % this->event(index)); // shared
if (this->delayed && !cluster_delayed[it->first].empty()) {
uvec ind00 = conv_to<uvec>::from(cluster_delayed[it->first]);
sumHenter = sum(H0(Base::map0f(ind00)));
}
if (recurrent) { // for calendar timescale
ll(i) += -(1.0/theta+mi)*log(1.0+theta*(sumH - sumHenter)); // Rondeau et al (2005)
} else { // for clustered data or gap timescale
ll(i) += -(1.0/theta+mi)*log(1.0+theta*sumH) + 1.0/theta*log(1.0+theta*sumHenter); // Rondeau et al
}
// Note: log(gamma(1/theta+mi)/gamma(1/theta)*theta^mi) = sum_k=1^mi (log(1+theta(mi-k))) (mi>0); 0 (otherwise)
if (mi>0) {
for (int k=1; k<=mi; ++k)
ll(i) += log(1.0+theta*(mi-k));
}
}
li_constraint out;
out.constraint=constraint;
out.li = ll;
return out;
}
vec vbeta = beta;
vbeta.resize(this->nbeta);
gradli_constraint gc = gradli(this->X*vbeta, this->XD*vbeta, this->X0*vbeta, this->X1*vbeta, this->X, this->XD, this->X0, this->X1, beta);
rowvec dconstraint = sum(gc.constraint,0);
vec gr(beta.size());
for (size_t i = 0; i<beta.size(); ++i) {
gr[i] = vgr[i];// - dconstraint[i];
}
return -gr;
}
gradli_constraint gradli(vec eta, vec etaD, vec eta0, vec eta1, mat X, mat XD, mat X0, mat X1,
vec beta) {
int n = beta.size();
mat gr = zeros<mat>(clusters.size(), n);
mat grconstraint = zeros<mat>(clusters.size(), n);
vec vbeta(beta); // theta is the last parameter in beta
vbeta.resize(n-1);
double theta = exp(beta[n-1]);
// eta = this->X * vbeta;
// etaD = this->XD * vbeta;
vec eps = h*0.0 + 1.0e-16;
h = max(h,eps);
H = max(H,eps);
vec H0;
if (this->delayed) {
// vec eta0 = this->X0 * vbeta;
// vec etaD0 = this->XD0 * vbeta;
}
int i=0;
for (IndexMap::iterator it=clusters.begin(); it!=clusters.end(); ++it, ++i) {
int mi=0;
double sumH = 0.0, sumHenter = 0.0;
// vec grconstraint = zeros<vec>(n-1);
for (Index::iterator j=it->second.begin(); j!=it->second.end(); ++j) {
sumH += H(*j);
if (this->event(*j)==1) {
mi++;
}
if (this->delayed  && this->ind0[*j]) {
int jj = this->map0[*j];
sumHenter += H0(jj);
grconstraint(i,span(0,n-2)) += this->kappa * (gradH0.row(jj) * H0(jj) * (H0(jj)<0));
}
grconstraint(i,span(0,n-2)) += this->kappa * ((gradh.row(*j) * h(*j) * (h(*j)<0)) + (gradH.row(*j) * H(*j) * (H(*j)<0)));
}
for (int k=0; k<n-1; ++k) {
if (recurrent) {
} else {
}
}
if (recurrent) {
// axiom: D(-(1/exp(btheta)+mi)*log(1+exp(btheta)*H),btheta)
// axiom: D(log(Gamma(1/exp(btheta)+mi))-log(Gamma(1/exp(btheta)))+mi*btheta,btheta)
double H = sumH - sumHenter;
// gr(i,n-1) += ((1+theta*H)*log(1+H*theta)-H*mi*theta*theta - H*theta)/(H*theta*theta + theta) + (-R::digamma(1.0/theta+mi)+R::digamma(1/theta)+mi*theta)/theta;
gr(i,n-1) += ((1+theta*H)*log(1+H*theta)-H*mi*theta*theta - H*theta)/(H*theta*theta + theta);
} else {
// axiom: D(-(1/exp(btheta)+mi)*log(1+exp(btheta)*H),btheta)
// axiom: D(1.0/exp(btheta)*log(1+exp(btheta)*H0),btheta)
gr(i,n-1) += ((1+sumH*theta)*log(1+sumH*theta)-sumH*mi*theta*theta-sumH*theta)/(sumH*theta*theta+theta);
gr(i,n-1) += (-(1+sumHenter*theta)*log(sumHenter*theta+1)+sumHenter*theta)/(sumHenter*theta*theta+theta);
}
if (mi>0) {
for (int k=1; k<=mi; ++k)
// axiom: D(log(1+exp(btheta)*(mi-k)),btheta)
gr(i,n-1) += theta*(mi-k)/(1.0+theta*(mi-k));
}
}
return grli;
}
bool feasible(vec beta) {
vec coef(beta);
coef.resize(this->n-1);
return Base::feasible(coef);
}
OPTIM_FUNCTIONS;
IndexMap clusters, cluster_delayed;
bool recurrent;
};

/**
Extension of stpm2 and pstpm2 to include Clayton copula
**/
template<class Base>
class ClaytonCopula : public Base {
public:
typedef std::vector<int> Index;
typedef std::map<int,Index> IndexMap;
typedef ClaytonCopula<Base> This;
ClaytonCopula(SEXP sexp) : Base(sexp) {
List list = as<List>(sexp);
ivec cluster = as<ivec>(list["cluster"]);
this->nbeta = this->n - 1;
// wragged array indexed by a map of vectors
for (size_t id=0; id<cluster.size(); ++id) {
clusters[cluster[id]].push_back(id);
}
}
/**
Objective function for a Clayton copula
Assumes that weights == 1.
**/
double objective(vec beta) {
vec vbeta = beta;
vbeta.resize(this->nbeta);
// copy across to this->bfgs.coef?
li_constraint s = li(this->X * vbeta, this->XD * vbeta, this->X0 * vbeta, this->X1 * vbeta, beta);
return -sum(s.li) + s.constraint;
}
vec getli(vec beta) {
vec vbeta = beta;
vbeta.resize(this->nbeta);
li_constraint lic = li(this->X*vbeta, this->XD*vbeta, this->X0*vbeta, this->X1*vbeta, beta);
return lic.li;
}
mat getgradli(vec beta) { // WRONG - DO NOT USE!
vec vbeta = beta;
vbeta.resize(this->nbeta);
}
li_constraint li(vec eta, vec etaD, vec eta0, vec eta1, vec beta) {
vec ll(clusters.size(), fill::zeros);
int n = beta.size();
vec vbeta(beta); // logtheta is the last parameter in beta
vbeta.resize(this->nbeta);
double itheta = exp(-beta[n-1]); // NOTE: INVERSE OF THE VARIANCE
eta = this->X * vbeta + this->offset;
double constraint = this->kappa/2.0 * (sum(h % h % (h<0)) + sum(H % H % (H<0)));
vec eps = h*0.0 + 1.0e-16;
h = max(h,eps);
H = max(H,eps);
int i=0;
for (IndexMap::iterator it=clusters.begin(); it!=clusters.end(); ++it, ++i) {
uvec index = conv_to<uvec>::from(it->second);
int ni = (it->second).size();
int mi = sum(this->event(index));
double logScopula = -itheta*log(sum(exp(H(index)/itheta)) - ni + 1);
// Rprintf("ni=%i, mi=%i, log(Scopula)=%g\n",ni,mi,logScopula);
if (mi==0) {
ll(i) = logScopula;
}
else {
ll(i) = logScopula/itheta*(itheta+mi);
// Rprintf("ll(i)=%g\n",ll(i));
ll(i) += sum((log(h(index))+H(index)/itheta) % this->event(index));
for (int k=1; k<=mi; ++k)
ll(i) += log(itheta+k-1.0) - log(itheta);
}
}
li_constraint out;
out.constraint=constraint;
out.li = ll;
return out;
}
vec gradient(vec beta) { // WRONG - DO NOT USE!
vec vbeta = beta;
vbeta.resize(this->nbeta);
gradli_constraint gc = gradli(this->X*vbeta, this->XD*vbeta, this->X0*vbeta, this->X1*vbeta, this->X, this->XD, this->X0, this->X1, beta);
rowvec dconstraint = sum(gc.constraint,0);
vec gr(beta.size());
for (size_t i = 0; i<beta.size(); ++i) {
gr[i] = vgr[i];// - dconstraint[i];
}
return -gr;
}
gradli_constraint gradli(vec eta, vec etaD, vec eta0, vec eta1, mat X, mat XD, mat X0, mat X1, vec beta) { // WRONG - DO NOT USE!
int n = beta.size();
mat gr = zeros<mat>(clusters.size(), n);
mat grconstraint = zeros<mat>(clusters.size(), n);
vec vbeta(beta); // theta is the last parameter in beta
vbeta.resize(n-1);
double itheta = exp(-beta[n-1]);
// eta = this->X * vbeta;
// etaD = this->XD * vbeta;
vec eps = h*0.0 + 1.0e-16;
h = max(h,eps);
H = max(H,eps);
int i=0;
for (IndexMap::iterator it=clusters.begin(); it!=clusters.end(); ++it, ++i) {
uvec index = conv_to<uvec>::from(it->second);
int ni = (it->second).size();
int mi = sum(this->event(index));
double Scopula0 = sum(exp(H(index)/itheta)) - ni + 1;
for (Index::iterator j=it->second.begin(); j!=it->second.end(); ++j) {
if (this->event(*j)==1) {
}
grconstraint(i,span(0,n-2)) += this->kappa * ((gradh.row(*j) * h(*j) * (h(*j)<0)) + (gradH.row(*j) * H(*j) * (H(*j)<0)));
}
for (int k=0; k<n-1; ++k) {
}
if (mi>0) {
for (int k=0; k<n-1; ++k) {
}
}
}
return grli;
}
bool feasible(vec beta) {
vec coef(beta);
coef.resize(this->n-1);
return Base::feasible(coef);
}
OPTIM_FUNCTIONS;
IndexMap clusters;
};

/** @brief Wrapper for calling an objective_cluster method
**/
template<class T>
double call_objective_cluster(double bi, void * model_ptr) {
T * model = static_cast<T *>(model_ptr);
return model->objective_cluster(bi);
}
template<class T>
double call_gradient_cluster(double bi, void * model_ptr) {
T * model = static_cast<T *>(model_ptr);
}
/** @brief Wrapper for calling a gradient_cluster method
**/
template<class T>
double call_objective_cluster_bfgs(int n, double *bi, void * model_ptr) {
T * model = static_cast<T *>(model_ptr);
return model->objective_cluster(*bi);
}
template<class T>
void call_gradient_cluster_bfgs(int dim, double * bi, double* out, void * model_ptr) {
T * model = static_cast<T *>(model_ptr);
}
/**
Extension of stpm2 and pstpm2 to include log-normal shared frailties with a cluster variable
**/
template<class Base>
class NormalSharedFrailty : public Base {
public:
typedef std::vector<int> Index;
typedef std::map<int,Index> IndexMap;
typedef NormalSharedFrailty<Base> This;
typedef std::map<int,double> Doubles;
NormalSharedFrailty(SEXP sexp) : Base(sexp) {
List list = as<List>(sexp);
const BaseData fullTmp = {this->X, this->XD, this->X0, this->X1, this->bhazard,
this->wt, this->wt0, this->event, this->time,
this->offset,
this->map0, this->ind0, this->which0};
full = fullTmp;
IntegerVector cluster = as<IntegerVector>(list["cluster"]);
full_Z = Z = as<vec>(list["Z"]);
full_Z0 = Z0 = Z(this->ind0); // this could be size 0...
gauss_x = as<vec>(list["gauss_x"]); // node values
gauss_w = as<vec>(list["gauss_w"]); // probability weights
recurrent = as<bool>(list["recurrent"]);
first = true;
// wragged array indexed by a map of vectors
for (int id=0; id<cluster.size(); ++id) {
clusters[cluster[id]].push_back(id);
}
this->nbeta = this->n - 1;
}
/**
Objective function for a log-normal shared frailty
Assumes that weights == 1.
**/
int n = beta.size();
vec vbeta(beta); // nu=log(variance) is the last parameter in beta; exp(nu)=sigma^2
vbeta.resize(n-1);
// case: alpha for joint model?
double sigma = exp(0.5*beta[n-1]); // standard deviation
int K = gauss_x.size(); // number of nodes
vec wstar = gauss_w/sqrt(datum::pi);
double constraint = 0.0;
double ll = 0.0;
bool left_trunc_not_recurrent = (this->delayed && !this->recurrent && !this->interval);
for (IndexMap::iterator it=clusters.begin(); it!=clusters.end(); ++it) {
clusterDesign(it);
vec eta = this->X * vbeta;
vec etaD = this->XD * vbeta;
vec eta0(1,fill::zeros);
vec eta1(this->X.n_rows,fill::zeros);
if (this->delayed) {
eta0 = this->X0 * vbeta;
eta1 = this->X1 * vbeta;
}
double Lj = 0.0, L0j = 0.0;
for (int k=0; k<K; ++k) {
li_constraint lik, H0ik;
double bi = sqrt(2.0)*sigma*this->gauss_x(k);
if (left_trunc_not_recurrent) {
this->delayed = false;
this->delayed = true;
H0ik = Base::li_left_truncated(eta0+Z0*bi);
L0j += exp(-sum(H0ik.li))*wstar(k);
constraint += H0ik.constraint;
} else {
}
Lj += exp(sum(lik.li))*wstar(k);
constraint += lik.constraint;
}
ll += log(Lj);
if (left_trunc_not_recurrent)
ll -= log(L0j);
}
resetDesign();
return -(ll - constraint);
}
double objective(vec beta) {
}
int n = beta.size();
this->objective_cluster_beta = beta; // for use by objective_cluster()
vec vbeta(beta); // nu=log(variance) is the last parameter in beta; exp(nu)=sigma^2
double sigma = exp(0.5*vbeta(this->n-1)); // standard deviation
vbeta.resize(n-1);
int K = gauss_x.size(); // number of nodes
double constraint = 0.0;
double ll = 0.0;
bool left_trunc_not_recurrent = (this->delayed && !this->recurrent && !this->interval);
for (IndexMap::iterator it=clusters.begin(); it!=clusters.end(); ++it) {
clusterDesign(it);
// cluster-specific mode
double mu;
if (!first) {
// double Tol = this->reltol;
// int Maxit = 100;
// mu = R_zeroin2(-100.0,
// 		 100.0,
// 		 (void *) this,
// 		 &Tol,
// 		 &Maxit);
mu = Brent_fmin(muhat[it->first]-1e-1,
muhat[it->first]+1e-1,
&(call_objective_cluster<This>),
(void *) this,
this->reltol);
}
if (first || std::abs(mu-muhat[it->first])>(1e-1-1e-5))
// if (first || mu>100.0-1e-5 || mu<-100.0+1e-5)
mu = Brent_fmin(-100.0,100.0,&(call_objective_cluster<This>),(void *) this,
this->reltol);
muhat[it->first] = mu;
// cluster-specific variance
double eps = 1e-6;
tauhat[it->first] = tau;
vec eta = this->X * vbeta;
vec etaD = this->XD * vbeta;
vec eta0(1,fill::zeros);
vec eta1(this->X.n_rows,fill::zeros);
if (this->delayed) {
eta0 = this->X0 * vbeta;
eta1 = this->X1 * vbeta;
}
double Lj = 0.0, L0j = 0.0;
for (int k=0; k<K; ++k) {
double g = 0.0, g0 = 0.0;
double bi = mu + sqrt(2.0)*tau*this->gauss_x(k);
li_constraint lik, l0ik;
if (left_trunc_not_recurrent) {
// first: reset such that delayed is true and calculate the likelihood for right censoring
this->delayed = false;
// second: reset for delayed is true and calculate the likelihood for left truncation
this->delayed = true;
l0ik = Base::li_left_truncated(eta0+Z0*bi);
constraint += l0ik.constraint;
g0 = exp(sum(l0ik.li)+R::dnorm(bi,0.0,sigma,1));
L0j += sqrt(2.0)*tau*g0*gauss_w(k)*exp(gauss_x(k)*gauss_x(k));
} else {
}
g = exp(sum(lik.li)+R::dnorm(bi,0.0,sigma,1));
Lj += sqrt(2.0)*tau*g*gauss_w(k)*exp(gauss_x(k)*gauss_x(k));
constraint += lik.constraint;
}
ll += log(Lj);
if (left_trunc_not_recurrent && L0j>0.0)
ll -= log(L0j);
}
resetDesign();
first = false;
return -(ll - constraint);
}
vec getli(vec beta) { vec missing(1,fill::zeros); return missing; }
mat getgradli(vec beta) { mat missing(1,1,fill::zeros); return missing; }
// TODO: redefine li
void resetDesign() {
this->X = full.X;
this->XD = full.XD;
this->bhazard = full.bhazard;
this->wt = full.wt;
this->event = full.event;
this->time = full.time;
this->offset = full.offset;
this->X1 = full.X1;
this->X0 = full.X0;
this->wt0 = full.wt0;
this->which0 = full.which0;
this->Z = full_Z;
this->Z0 = full_Z0;
}
void clusterDesign(IndexMap::iterator it) {
clusterid = it->first;
uvec index = conv_to<uvec>::from(it->second);
this->X = full.X.rows(index);
this->XD = full.XD.rows(index);
this->X1 = full.X1.rows(index);
this->bhazard = full.bhazard(index);
this->wt = full.wt(index);
this->event = full.event(index);
this->time = full.time(index);
this->offset = full.offset(index);
this->Z = full_Z(index);
this->Z0 = vec(1,fill::zeros);
if (this->delayed) {
uvec index0 = Base::map0f(index);
this->X0 = full.X0.rows(index0);
this->wt0 = full.wt0(index0);
this->Z0 = full_Z0(index0);
this->which0 = Base::which0f(index);
}
}
// log(g(bi))
double objective_cluster(double bi) {
vec vbeta = this->objective_cluster_beta; // nu=log(variance) is the last parameter in vbeta
double sigma = exp(0.5*vbeta(this->n-1)); // standard deviation
vbeta.resize(this->n - 1);
vec eta = this->X * vbeta;
vec etaD = this->XD * vbeta;
vec eta0(1,fill::zeros);
vec eta1(this->X.n_rows,fill::zeros);
if (this->delayed) {
eta0 = this->X0 * vbeta;
eta1 = this->X1 * vbeta;
}
double ll = sum(lik.li) + R::dnorm(bi,0.0,sigma,1);
return -ll;
}
vec vbeta = this->objective_cluster_beta; // nu=log(variance) is the last parameter in vbeta
double sigma = exp(0.5*vbeta(this->n-1)); // standard deviation
vbeta.resize(this->n - 1);
vec eta = this->X * vbeta;
vec etaD = this->XD * vbeta;
vec eta0(1,fill::zeros);
vec eta1(this->X1.n_rows,fill::zeros);
if (this->delayed) {
eta0 = this->X0 * vbeta;
eta1 = this->X1 * vbeta;
}
mat X = mat(Z); // mat(this->X.n_rows,1,fill::ones);
mat XD = mat(this->XD.n_rows,1,fill::zeros);
mat X0 = mat(Z0); // mat(this->X0.n_rows,1,fill::ones);
mat X1 = mat(Z); // mat(this->X1.n_rows,1,fill::ones);
}
// double fdhessian(boost::function<double(double x)> f, double x, double eps = 1.0e-6) {
//   return (-f(x+2*eps)+16*f(x+eps)-30*f(x)+16*f(x-eps)-f(x-2*eps))/12.0/eps/eps;
// }
void calculate_modes_and_variances() {
this->objective_cluster_beta = this->bfgs.coef;
for (IndexMap::iterator it=clusters.begin(); it!=clusters.end(); ++it) {
clusterDesign(it);
modes[it->first] = Brent_fmin(-100.0,100.0,&(call_objective_cluster<This>),(void *) this,
this->reltol);
// Abramowitz and Stegun 1972, p. 884
double bi = modes[it->first];
double eps = 1e-6;
double f1 = objective_cluster(bi+2*eps);
double f2 = objective_cluster(bi+eps);
double f3 = objective_cluster(bi);
double f4 = objective_cluster(bi-eps);
double f5 = objective_cluster(bi-2*eps);
double hessian = (-f1+16*f2-30*f3+16*f4-f5)/12.0/eps/eps;
variances[it->first] = 1.0/hessian;
}
resetDesign();
}
}
int n = beta.size();
this->objective_cluster_beta = beta; // for use by objective_cluster()
vec betastar = beta; // we use the last element as bi - is this a good idea?
vec vbeta(beta); // nu=log(variance) is the last parameter in beta; exp(nu)=sigma^2
double sigma = exp(0.5*vbeta(this->n-1)); // standard deviation
vbeta.resize(n-1);
int K = gauss_x.size(); // number of nodes
// rowvec dconstraint(n,fill::zeros);
for (IndexMap::iterator it=clusters.begin(); it!=clusters.end(); ++it) {
clusterDesign(it);
// cluster-specific modes and variances (calculated in the objective function)
double mu = muhat[it->first];
double tau = tauhat[it->first];
mat Zmain(Z);
mat ZD(this->XD.n_rows,1,fill::zeros);
mat Z0main(Z0);
mat Z1(Z);
mat Xstar = join_horiz(this->X, Zmain);
mat XDstar = join_horiz(this->XD, ZD); // assumes time-invariant random effects
mat X0star = join_horiz(this->X0, Z0main);
mat X1star = join_horiz(this->X1, Z1);
double Lj = 0.0;
rowvec numerator(this->n,fill::zeros);
for (int k=0; k<K; ++k) {
double bi = mu + sqrt(2.0)*tau*this->gauss_x(k);
betastar[betastar.size()-1] = bi;
vec etastar = Xstar * betastar;
vec etaDstar = XDstar * betastar;
vec eta0star = X0star * betastar;
vec eta1star = X1star * betastar;
double g = exp(sum(lik.li) + R::dnorm(bi,0.0,sigma,1));
Lj += sqrt(2.0)*tau*g*gauss_w(k)*exp(gauss_x(k)*gauss_x(k));
numerator(span(0,n-2)) += numeratorstar(span(0,n-2));
numerator(n-1) += sqrt(2.0)*tau*gauss_w(k)*exp(gauss_x(k)*gauss_x(k))*g*(- 0.5 + bi*bi/2/sigma/sigma);
}
}
vec gr(n,fill::zeros);
for (int i=0; i<n; i++) gr(i) = gradLi(i); // - dconstraint(i);
resetDesign();
return -gr;
}
int n = beta.size();
double sigma = exp(0.5*beta[n-1]);
mat Zmain(Z);
mat ZD(this->N,1,fill::zeros);
mat Z0main(Z0);
mat Z1(Z);
mat Xstar = join_horiz(this->X, Zmain);
mat XDstar = join_horiz(this->XD, ZD); // assumes time-invariant random effects
mat X0star = join_horiz(this->X0, Z0main);
mat X1star = join_horiz(this->X1, Z1);
int K = gauss_x.size(); // number of nodes
vec wstar = gauss_w/sqrt(datum::pi);
int G = clusters.size();
vec Li(G,fill::zeros);
vec betastar = beta;
rowvec dconstraint(n,fill::zeros);
mat likeli_jk(this->N,K,fill::zeros);
vec likeli_k(K,fill::zeros);
// for K nodes calculation
for (int k=0; k<K; ++k) {
double bi = sqrt(2.0)*sigma*gauss_x[k];
betastar[betastar.size()-1] = bi;
vec etastar = Xstar * betastar;
vec etaDstar = XDstar * betastar;
vec eta0star = X0star * betastar;
vec eta1star = X1star * betastar;
li_constraint lik = Base::li(etastar, etaDstar, eta0star, eta1star,beta);
// adjust the last column of the gradient to account for the variance components:
// chain rule: d lik/d bi * d bi/d nu where bi = sqrt(2)*exp(nu/2)*x_k
dconstraint += sum(gradlik.constraint,0); // ignores clustering??
likeli_jk.col(k) = lik.li;
}
// Iteration in each cluster and get vec Li(g) and mat gradLi(g,n)
int g = 0;
for (IndexMap::iterator it=clusters.begin(); it!=clusters.end(); ++it, ++g) {
uvec index = conv_to<uvec>::from(it->second);
vec likeli_k = exp(sum(likeli_jk.rows(index),0)).t(); // sum  index components at all nodes for cluster i
for(int k=0; k<K; ++k){
}
Li(g) = dot(likeli_k,wstar);
}
// Last step to summarize all clusters
rowvec grad = sum(rmult(gradLi,1/Li),0); // Rows of matrix is multiplied with elements of vector
// if (this->bfgs.trace>0) {
// }
vec gr(n,fill::zeros);
for (int i=0; i<n; i++) gr(i) = grad(i); // - dconstraint(i);
return -gr;
}
bool feasible(vec beta) {
vec coef(beta);
coef.resize(beta.size()-1);
return Base::feasible(coef);
}
SEXP return_modes() {
calculate_modes_and_variances();
return wrap(modes);
}
SEXP return_variances() {
calculate_modes_and_variances();
return wrap(variances);
}
OPTIM_FUNCTIONS;
IndexMap clusters;
vec gauss_x, gauss_w, full_Z, full_Z0, Z, Z0;
BaseData full;
Doubles modes, variances;
vec objective_cluster_beta;
Doubles muhat, tauhat;
int clusterid;
};

template<class T>
double call_objective_clusterND(int n, double * beta, void * model_ptr) {
T * model = static_cast<T *>(model_ptr);
vec bi(beta, n);
return model->objective_cluster(bi);
}
template<class T>
void call_gradient_clusterND(int n, double * beta, double * out, void * model_ptr) {
T * model = static_cast<T *>(model_ptr);
vec bi(beta, n);
for (int i=0; i<n; ++i) out[i] = grad[i];
}
template<class Base>
class NormalSharedFrailty2D : public Base {
public:
typedef std::vector<int> Index;
typedef std::map<int,Index> IndexMap;
typedef NormalSharedFrailty2D<Base> This;
typedef std::map<int,vec> MapVec;
typedef std::map<int,mat> MapMat;
typedef std::map<int,cube> MapCube;
NormalSharedFrailty2D(SEXP sexp) : Base(sexp) {
List list = as<List>(sexp);
const BaseData fullTmp = {this->X, this->XD, this->X0, this->X1, this->bhazard,
this->wt, this->wt0, this->event, this->time,
this->offset,
this->map0, this->ind0, this->which0};
full = fullTmp;
IntegerVector cluster = as<IntegerVector>(list["cluster"]);
full_Z = Z = as<mat>(list["Z"]);
full_Z0 = Z0 = Z.rows(this->ind0); // this could be size 0...
gauss_x = as<vec>(list["gauss_x"]); // node values
gauss_w = as<vec>(list["gauss_w"]); // probability weights
recurrent = as<bool>(list["recurrent"]);
first = true;
// wragged array indexed by a map of vectors
for (int id=0; id<cluster.size(); ++id) {
clusters[cluster[id]].push_back(id);
}
redim = 2;
reparm = 3;
Sigma.set_size(redim,redim);
invSigma.set_size(redim,redim);
SqrtSigma.set_size(redim,redim);
this->nbeta = this->n - reparm;
}
/**
Objective function for normal random effects
**/
double corrtransform(double x) { return 2.0/(1.0+exp(-x))-1.0; }
int n = beta.size();
vec vbeta(beta);
calc_SqrtSigma(beta);
vbeta.resize(n-reparm);
int K = gauss_x.size(); // number of nodes
vec wstar = gauss_w/sqrt(datum::pi);
vec d = sqrt(2.0)*gauss_x;
double constraint = 0.0;
double ll = 0.0;
bool left_trunc_not_recurrent = (this->delayed && !this->recurrent && !this->interval);
vec dk(redim), bi(redim);
for (IndexMap::iterator it=clusters.begin(); it!=clusters.end(); ++it) {
clusterDesign(it);
vec eta = this->X * vbeta;
vec etaD = this->XD * vbeta;
vec eta0(1,fill::zeros);
vec eta1(this->X.n_rows,fill::zeros);
if (this->delayed) {
eta0 = this->X0 * vbeta;
eta1 = this->X1 * vbeta;
}
double Lj = 0.0, L0j = 0.0;
for (int k=0; k<K; ++k) {
for (int kk=0; kk<K; ++kk) {
li_constraint lik, H0ik;
dk(0) = d(k);
dk(1) = d(kk);
bi = SqrtSigma * dk;
if (left_trunc_not_recurrent) {
this->delayed = false;
this->delayed = true;
H0ik = Base::li_left_truncated(eta0+Z0*bi);
L0j += exp(-sum(H0ik.li))*wstar(k)*wstar(kk);
constraint += H0ik.constraint;
} else {
}
Lj += exp(sum(lik.li))*wstar(k)*wstar(kk);
constraint += lik.constraint;
}
}
ll += log(Lj);
if (left_trunc_not_recurrent)
ll -= log(L0j);
}
resetDesign();
return -(ll - constraint);
}
double objective_cluster(vec bi) {
vec vbeta = this->objective_cluster_beta;
vbeta.resize(this->n - reparm);
vec eta = this->X * vbeta;
vec etaD = this->XD * vbeta;
vec eta0(this->Z0.n_rows,fill::zeros);
vec eta1(this->X.n_rows,fill::zeros);
if (this->delayed) {
eta0 = this->X0 * vbeta;
eta1 = this->X1 * vbeta;
}
vec zero(redim,fill::zeros);
double ll = sum(lik.li) + dmvnrm_arma(bi,zero,this->Sigma,true);
return -ll;
}
vec vbeta = this->objective_cluster_beta;
vbeta.resize(this->n - reparm);
vec eta = this->X * vbeta;
vec etaD = this->XD * vbeta;
vec eta0(1,fill::zeros);
vec eta1(this->X1.n_rows,fill::zeros);
if (this->delayed) {
eta0 = this->X0 * vbeta;
eta1 = this->X1 * vbeta;
}
mat X = Z;
mat XD = mat(this->XD.n_rows,redim,fill::zeros);
mat X0 = Z0;
mat X1 = Z;
}
mat calc_SqrtSigma(vec beta, bool calc_inverse = true) {
bool flag;
int n = beta.size();
Sigma.resize(redim,redim);
Sigma(0,0) = exp(beta[n-reparm]);       // variance
double corr = corrtransform(beta[n-2]); // correlation
Sigma(1,1) = exp(beta[n-1]);            // variance
Sigma(0,1) = Sigma(1,0) = corr*sqrt(Sigma(1,1)*Sigma(0,0)); // covariance
if (calc_inverse)
flag = inv(invSigma, Sigma);
flag = chol(SqrtSigma,Sigma); // which version of RcppArmadillo??
if (!flag) { Rprintf("Sigma:\n"); Rprint(Sigma); Rcpp::stop("Matrix sqrt invalid"); }
return SqrtSigma;
}
// gradient in SqrtSigma wrt beta
cube gradSqrtSigma(vec beta, double eps = 1.0e-6) {
cube out(redim,redim,reparm,fill::zeros);
int offseti = beta.size()-reparm;
vec betax;
mat val;
for (int i=0; i<reparm; ++i) {
betax = beta;
betax(offseti+i) += eps;
val = calc_SqrtSigma(betax, false);
betax(offseti+i) -= 2.0*eps;
out.slice(i) = (val - calc_SqrtSigma(betax, false))/2.0/eps;
}
return out;
}
// Sigma and SqrtSigma for the cluster-specific modes
arma::mat tau, sqrttau;
bool flag = inv(tau,
flag = chol(sqrttau,tau); // which version of RcppArmadillo??
if (!flag) { Rprintf("tau:\n"); Rprint(tau); Rcpp::stop("Matrix sqrt invalid"); }
return sqrttau;
}
// gradient for SqrtSigma for the cluster-specific modes
cube out(redim,redim,reparm,fill::zeros);
vec betax;
vec old = this->objective_cluster_beta;
mat val;
for (int i=0; i<reparm; ++i) {
betax = old;
betax(i) += eps;
this->objective_cluster_beta = betax;
betax(i) -= 2.0*eps;
this->objective_cluster_beta = betax;
}
this->objective_cluster_beta = old;
return out;
}
int n = beta.size();
this->objective_cluster_beta = beta; // for use by objective_cluster()
vec vbeta(beta);
calc_SqrtSigma(beta);
vbeta.resize(n-reparm);
int K = gauss_x.size(); // number of nodes
vec wstar = gauss_w/sqrt(datum::pi);
vec d = sqrt(2.0)*gauss_x;
double constraint = 0.0;
double ll = 0.0;
bool left_trunc_not_recurrent = (this->delayed && !this->recurrent && !this->interval);
vec dk(redim), bi(redim);
vec zero(redim,fill::zeros);
for (IndexMap::iterator it=clusters.begin(); it!=clusters.end(); ++it) {
clusterDesign(it);
if (muhat.count(it->first)==0) { // initialise
muhat[it->first].set_size(redim);
for (int i=0; i<redim; ++i)
muhat[it->first](i) = 0.0;
}
// cluster-specific modes
BFGS opt;
opt.optim(&(call_objective_clusterND<This>),
as<NumericVector>(wrap(muhat[it->first])),
(void *) this);
muhat[it->first] = as<vec>(wrap(opt.coef));
// variance for the cluster-specific modes
arma::mat tau, sqrttau;
bool flag = inv(tau,
double dettau = det(tau); // logdet would be more precise
dettauhat[it->first] = dettau;
flag = chol(sqrttau,tau); // which version of RcppArmadillo?
if (!flag) { Rprintf("tau:\n"); Rprint(tau); Rcpp::stop("Matrix sqrt invalid."); }
sqrttauhat[it->first] = sqrttau;
if (this->optimiser=="BFGS")
vec eta = this->X * vbeta;
vec etaD = this->XD * vbeta;
vec eta0(1,fill::zeros);
vec eta1(this->X.n_rows,fill::zeros);
if (this->delayed) {
eta0 = this->X0 * vbeta;
eta1 = this->X1 * vbeta;
}
double Lj = 0.0, L0j = 0.0;
for (int k=0; k<K; ++k) {
for (int kk=0; kk<K; ++kk) {
dk(0) = d(k);
dk(1) = d(kk);
bi = muhat[it->first] + sqrttau * dk;
double g = 0.0, g0 = 0.0;
li_constraint lik, l0ik;
if (left_trunc_not_recurrent) {
this->delayed = false;
this->delayed = true;
l0ik = Base::li_left_truncated(eta0+Z0*bi);
g0 = exp(sum(l0ik.li)+dmvnrm_arma(bi,zero,Sigma,true));
L0j += wstar(k)*wstar(kk)*g0*exp(dot(d,d)/2);
} else {
}
g = exp(sum(lik.li)+dmvnrm_arma(bi,zero,Sigma,true));
Lj += wstar(k)*wstar(kk)*g*exp(dot(d,d)/2);
constraint += lik.constraint;
}
}
ll += log(2.0*datum::pi)*redim/2.0+log(dettau)/2.0+log(Lj);
if (left_trunc_not_recurrent)
ll -= log(L0j);
}
resetDesign();
first = false;
return -(ll - constraint);
}
}
int n = beta.size();
vec vbeta(beta);
vbeta.resize(n-reparm);
calc_SqrtSigma(beta);
if (this->bfgs.trace>1)
int K = gauss_x.size(); // number of nodes
vec wstar = gauss_w/sqrt(datum::pi);
vec d = sqrt(2.0)*gauss_x;
vec dk(redim), bi(redim);
for (IndexMap::iterator it=clusters.begin(); it!=clusters.end(); ++it) {
clusterDesign(it);
uvec index = conv_to<uvec>::from(it->second);
mat Zmain(Z);
mat ZD(this->XD.n_rows,redim,fill::zeros);
mat Z0main(Z0);
mat Z1(Z);
mat Xstar = join_horiz(this->X, Zmain);
mat XDstar = join_horiz(this->XD, ZD); // assumes time-invariant random effects
mat X0star = join_horiz(this->X0, Z0main);
mat X1star = join_horiz(this->X1, Z1);
double L = 0.0;
vec betastar = beta; betastar.resize(beta.size() - reparm + redim);
// for K nodes calculation
for (int k=0; k<K; ++k) {
for (int kk=0; kk<K; ++kk) {
dk(0) = d(k);
dk(1) = d(kk);
bi = SqrtSigma * dk;
cube dbic = gradSqrt.each_slice() % dk;
mat dbi = reshape( mat(dbic.memptr(), dbic.n_elem, 1, false), redim, reparm);
betastar(span(betastar.size()-redim,betastar.size()-1)) = bi;
vec etastar = Xstar * betastar;
vec etaDstar = XDstar * betastar;
vec eta0star = X0star * betastar;
vec eta1star = X1star * betastar;
li_constraint lik = Base::li(etastar, etaDstar, eta0star, eta1star,beta);
// adjust the last columns of the gradient to account for the variance components:
// chain rule: d lik/d bi * d bi/d nu
double Lk = exp(sum(lik.li));
L += Lk*wstar(k)*wstar(kk);
}
}
}
resetDesign();
}
int n = beta.size();
objective_adaptive(beta); // bug check - remove
this->objective_cluster_beta = beta; // for use by objective_cluster()
vec vbeta(beta);
vbeta.resize(n-reparm);
calc_SqrtSigma(beta); // unnecessary?
int K = gauss_x.size(); // number of nodes
vec wstar = gauss_w/sqrt(datum::pi);
vec d = sqrt(2.0)*gauss_x;
vec dk(redim), bi(redim);
vec zero(redim,fill::zeros);
for (IndexMap::iterator it=clusters.begin(); it!=clusters.end(); ++it) {
clusterDesign(it);
uvec index = conv_to<uvec>::from(it->second);
vec mu = muhat[it->first];
mat sqrttau = sqrttauhat[it->first];
mat Zmain(Z);
mat ZD(this->XD.n_rows,redim,fill::zeros);
mat Z0main(Z0);
mat Z1(Z);
mat Xstar = join_horiz(this->X, Zmain);
mat XDstar = join_horiz(this->XD, ZD); // assumes time-invariant random effects
mat X0star = join_horiz(this->X0, Z0main);
mat X1star = join_horiz(this->X1, Z1);
double L = 0.0;
vec betastar = beta; betastar.resize(beta.size() - reparm + redim);
// for K nodes calculation
for (int k=0; k<K; ++k) {
for (int kk=0; kk<K; ++kk) {
dk(0) = d(k);
dk(1) = d(kk);
bi = mu + sqrttau * dk;
cube dbic = gradsqrttau.each_slice() % dk;
mat dbi = reshape( mat(dbic.memptr(), dbic.n_elem, 1, false), redim, reparm);
betastar(span(betastar.size()-redim,betastar.size()-1)) = bi;
vec etastar = Xstar * betastar;
vec etaDstar = XDstar * betastar;
vec eta0star = X0star * betastar;
vec eta1star = X1star * betastar;
li_constraint lik = Base::li(etastar, etaDstar, eta0star, eta1star,beta);
// adjust the last columns of the gradient to account for the variance components:
// chain rule: d lik/d bi * d bi/d nu
double Lk = exp(sum(lik.li)+dmvnrm_arma(bi,zero,Sigma,true));
L += Lk*wstar(k)*wstar(kk)*exp(dot(d,d)/2);
}
}
}
resetDesign();
}
double objective(vec beta) {
}
void resetDesign() {
this->X = full.X;
this->XD = full.XD;
this->bhazard = full.bhazard;
this->wt = full.wt;
this->event = full.event;
this->time = full.time;
this->offset = full.offset;
this->X1 = full.X1;
this->X0 = full.X0;
this->wt0 = full.wt0;
this->which0 = full.which0;
this->Z = full_Z;
this->Z0 = full_Z0;
}
void clusterDesign(IndexMap::iterator it) {
clusterid = it->first;
uvec index = conv_to<uvec>::from(it->second);
this->X = full.X.rows(index);
this->XD = full.XD.rows(index);
this->X1 = full.X1.rows(index);
this->bhazard = full.bhazard(index);
this->wt = full.wt(index);
this->event = full.event(index);
this->offset = full.offset(index);
this->time = full.time(index);
this->Z = full_Z.rows(index);
this->Z0 = mat(1,redim,fill::zeros);
if (this->delayed) {
uvec index0 = Base::map0f(index);
this->X0 = full.X0.rows(index0);
this->wt0 = full.wt0(index0);
this->Z0 = full_Z0.rows(index0);
this->which0 = Base::which0f(index);
}
}
bool feasible(vec beta) {
vec coef(beta);
coef.resize(beta.size()-reparm);
return Base::feasible(coef);
}
void calculate_modes_and_variances() {
vec beta = as<vec>(this->bfgs.coef);
this->objective_cluster_beta = beta;
calc_SqrtSigma(beta);
for (IndexMap::iterator it=clusters.begin(); it!=clusters.end(); ++it) {
clusterDesign(it);
if (muhat.count(it->first)==0) { // initialise
muhat[it->first].set_size(redim);
for (int i=0; i<redim; ++i)
muhat[it->first](i) = 0.0;
}
// cluster-specific modes
BFGS opt;
opt.optim(&(call_objective_clusterND<This>),
as<NumericVector>(wrap(muhat[it->first])),
(void *) this);
muhat[it->first] = as<vec>(wrap(opt.coef));
// cluster-specific variance
arma::mat tau, sqrttau;
bool flag = inv(tau,
double dettau = det(tau);
dettauhat[it->first] = dettau;
flag = chol(sqrttau,tau); // which version of RcppArmadillo?
if (!flag) { Rprintf("tau:\n"); Rprint(tau); Rcpp::stop("Matrix sqrt invalid."); }
sqrttauhat[it->first] = sqrttau;
}
resetDesign();
}
SEXP return_modes() {
calculate_modes_and_variances();
return wrap(muhat);
}
SEXP return_variances() {
calculate_modes_and_variances();
return wrap(sqrttauhat); // actually, these are not variances!
}
OPTIM_FUNCTIONS;
IndexMap clusters;
vec gauss_x, gauss_w;
mat full_Z, full_Z0, Z, Z0;
BaseData full;
MapVec modes;
MapMat variances;
vec objective_cluster_beta;
MapVec muhat;
MapMat sqrttauhat;
std::map<int,double> dettauhat;
int clusterid, redim, reparm;
mat Sigma, SqrtSigma, invSigma;
};

template<class T>
SEXP stpm2_model_output_(SEXP args) {
T model(args);
List list = as<List>(args);
std::string return_type = as<std::string>(list["return_type"]);
vec beta(&model.init[0],model.n);
if (return_type == "optim") {
model.pre_process();
model.optimWithConstraint(model.init);
// model.bfgs.hessian = model.bfgs.calc_hessian(&optimgradient<T>, (void *) &model);
// model.bfgs.hessian = model.calcHessian(model.bfgs.coef);
model.post_process();
return List::create(_("fail")=model.bfgs.fail,
_("coef")=wrap(model.bfgs.coef),
_("hessian")=wrap(model.bfgs.hessian),
_("kappa")=wrap(model.kappa));
}
else if (return_type == "objective")
return wrap(model.objective(beta));
else if (return_type == "gradient") {
model.objective(beta); // only needed for updating NormalSharedFrailty
}
else if (return_type == "feasible")
return wrap(model.feasible(beta));
else if (return_type == "modes")
return model.return_modes();
else if (return_type == "variances")
return model.return_variances();
else if (return_type == "li")
return wrap(model.getli(beta));
else {
REprintf("Unknown return_type.\n");
return wrap(-1);
}
}
template<class T>
SEXP pstpm2_model_output_(SEXP args) {
T model(args);
List list = as<List>(args);
std::string return_type = as<std::string>(list["return_type"]);
vec beta(&model.init[0],model.n);
if (return_type == "optim_fixed")
return(model.optim_fixed());
else if (return_type == "optim_first")
return(model.optim_first());
else if (return_type == "optim_multivariate")
return(model.optim_multivariate());
else if (return_type == "objective")
return wrap(model.objective(beta));
else if (return_type == "objective0")
return wrap(model.objective0(beta));
else if (return_type == "gradient") {
model.objective(beta);
}
else if (return_type == "constraint")
return wrap(model.feasible(beta));
else if (return_type == "feasible")
return wrap(model.feasible(beta));
else if (return_type == "li")
return wrap(model.getli(beta));
else if (return_type == "modes")
return model.return_modes();
else if (return_type == "variances")
return model.return_variances();
else {
REprintf("Unknown return_type.\n");
return wrap(-1);
}
}

class prof_class {
public:
prof_class(const std::string &name){
#ifdef DO_PROF
std::stringstream ss;
auto t = std::time(nullptr);
auto tm = *std::localtime(&t);
ss << "profile-" << name
<< std::put_time(&tm, "-%d-%m-%Y-%H-%M-%S.log");
Rcpp::Rcout << "Saving profile output to '" << ss.str() << "'"
<< std::endl;
const std::string s = ss.str();
ProfilerStart(s.c_str());
#endif
}

#ifdef DO_PROF
~prof_class(){
ProfilerStop();
}
#endif
};

RcppExport SEXP model_output(SEXP args) {
prof_class prof("model_output");

List list = as<List>(args);
std::string type = as<std::string>(list["type"]);
if (type=="stpm2") {
return stpm2_model_output_<Stpm2>(args);
}
else if (type=="pstpm2") {
return pstpm2_model_output_<Pstpm2<Stpm2,SmoothLogH> >(args);
}
else if (type=="stpm2_gamma_frailty") {
return stpm2_model_output_<GammaSharedFrailty<Stpm2> >(args);
}
else if (type=="pstpm2_gamma_frailty") {
return pstpm2_model_output_<Pstpm2<GammaSharedFrailty<Stpm2>,SmoothLogH> >(args);
}
else if (type=="stpm2_normal_frailty") {
return stpm2_model_output_<NormalSharedFrailty<Stpm2> >(args);
}
else if (type=="stpm2_normal_frailty_2d") {
return stpm2_model_output_<NormalSharedFrailty2D<Stpm2> >(args);
}
else if (type=="pstpm2_normal_frailty") {
// order is important here
return pstpm2_model_output_<Pstpm2<NormalSharedFrailty<Stpm2>,SmoothLogH> >(args);
}
else if (type=="pstpm2_normal_frailty_2d") {
// order is important here
return pstpm2_model_output_<Pstpm2<NormalSharedFrailty2D<Stpm2>,SmoothLogH> >(args);
}
else if (type=="stpm2_clayton_copula") {
return stpm2_model_output_<ClaytonCopula<Stpm2> >(args);
}
else if (type=="pstpm2_clayton_copula") {
return pstpm2_model_output_<Pstpm2<ClaytonCopula<Stpm2>,SmoothLogH> >(args);
}
else {
REprintf("Unknown model type.\n");
return wrap(-1);
}
}

// Proof of concept for a Weibull cure model
struct CureModel {
int n0, n1, n2;
mat Xshape, Xscale, Xcure;
vec time, status;
};
double fminfn_cureModel(int n, double * beta, void *ex) {
double ll = 0.0;
CureModel * data = (CureModel *) ex;
vec vbeta(&beta[0],n);
vec shape = exp(data->Xshape * vbeta(span(0,data->n0-1)));
vec scale = exp(data->Xscale * vbeta(span(data->n0,data->n1-1)));
vec cure = 1.0/(1.0+exp(-data->Xcure * vbeta(span(data->n1,data->n2-1))));
for (size_t i=0; i < data->time.size(); ++i) {
ll += data->status(i)==1.0 ?
log(1.0-cure(i)) + R::dweibull(data->time(i),shape(i),scale(i),1) :
log(cure(i)+(1.0-cure(i)) * R::pweibull(data->time(i),shape(i),scale(i),0,0));
}
R_CheckUserInterrupt();  /* be polite -- did the user hit ctrl-C? */
return -ll;
}
RcppExport SEXP fitCureModel(SEXP stime, SEXP sstatus, SEXP sXshape,
SEXP sXscale, SEXP sXcure, SEXP sbeta) {
mat Xshape = as<mat>(sXshape);
mat Xscale = as<mat>(sXscale);
mat Xcure = as<mat>(sXcure);
vec time = as<vec>(stime);
vec status = as<vec>(sstatus);
NumericVector init = as<NumericVector>(sbeta);
int n0=Xshape.n_cols;
int n1=n0+Xscale.n_cols;
int n2=n1+Xcure.n_cols;
CureModel data = {n0,n1,n2,Xshape,Xscale,Xcure,time,status};