static double prior_uk(double x, SEXP da){
int *dm = DIMS_SLOT(da), *Gp = Gp_SLOT(da), k = K_SLOT(da)[0];
int gn = Gp_grp(k, dm[nT_POS], Gp); /* group number of u_k */
double *u = U_SLOT(da), tmp = U_SLOT(da)[k], ans;
u[k] = x ;
ans = prior_u_Gp(gn, da); /* compute log prior for group gn */
u[k] = tmp ;
return ans;
}
/* FIXME: Probably should fold this function into MCMC_S */
static void MCMC_T(SEXP x, double sigma)
{
int *Gp = Gp_SLOT(x), nt = (DIMS_SLOT(x))[nt_POS];
double **st = Alloca(nt, double*);
int *nc = Alloca(nt, int), *nlev = Alloca(nt, int);
R_CheckStack();
if (ST_nc_nlev(GET_SLOT(x, lme4_STSym), Gp, st, nc, nlev) < 2) return;
error("Code for non-trivial theta_T not yet written");
}
static double prior_u_Gp(int gn, SEXP da){
SEXP V = GET_SLOT(da, install("Sigma"));
int *Gp = Gp_SLOT(da), *nc = NCOL_SLOT(da), *nlev = NLEV_SLOT(da) ;
double *v = REAL(VECTOR_ELT(V, gn)), *u = U_SLOT(da), ans = 0.0;
if (nc[gn] == 1) { /* univariate normal */
for (int j = 0; j < nlev[gn]; j++)
ans += -0.5 * u[Gp[gn] + j] * u[Gp[gn] + j] / v[0];
return ans ;
}
else { /* multivariate normal */
double *xv = Alloca(nc[gn], double),
*iv = Alloca(nc[gn] * nc[gn], double);
R_CheckStack() ;
solve_po(nc[gn], v, iv) ;
for (int j = 0; j < nlev[gn]; j++){
for (int i = 0; i < nc[gn]; i++)
xv[i] = u[Gp[gn] + i * nlev[gn] + j] ;
ans += dmvnorm(nc[gn], xv, (double*) NULL, iv) ;
}
return ans ;
}
}
static void sim_Sigma(SEXP da){
SEXP V = GET_SLOT(da, install("Sigma")) ;
int *dm = DIMS_SLOT(da), *Gp = Gp_SLOT(da),
*nc = NCOL_SLOT(da), *nlev = NLEV_SLOT(da);
int nT = dm[nT_POS], mc = imax(nc, nT);
double *v, su, *u = U_SLOT(da),
*scl = Alloca(mc * mc, double);
R_CheckStack();
for (int i = 0; i < nT; i++){
v = REAL(VECTOR_ELT(V, i));
if (nc[i] == 1){ /* simulate from the inverse-Gamma */
su = sqr_length(u + Gp[i], nlev[i]);
v[0] = 1/rgamma(0.5 * nlev[i] + IG_SHAPE, 1.0/(su * 0.5 + IG_SCALE));
}
else { /* simulate from the inverse-Wishart */
mult_xtx(nlev[i], nc[i], u + Gp[i], scl); /* t(x) * (x) */
for (int j = 0; j < nc[i]; j++) scl[j * j] += 1.0; /* add prior (identity) scale matrix */
solve_po(nc[i], scl, v);
rwishart(nc[i], (double) (nlev[i] + nc[i]), v, scl);
solve_po(nc[i], scl, v);
}
}
}
/**
* Update the theta_S parameters from the ST arrays in place.
*
* @param x an mer object
* @param sigma current standard deviation of the per-observation
* noise terms.
*/
static void MCMC_S(SEXP x, double sigma)
{
CHM_SP A = A_SLOT(x), Zt = Zt_SLOT(x);
int *Gp = Gp_SLOT(x), *ai = (int*)(A->i),
*ap = (int*)(A->p), *dims = DIMS_SLOT(x), *perm = PERM_VEC(x);
int annz = ap[A->ncol], info, i1 = 1, n = dims[n_POS],
nt = dims[nt_POS], ns, p = dims[p_POS], pos,
q = dims[q_POS], znnz = ((int*)(Zt->p))[Zt->ncol];
double *R, *ax = (double*)(A->x), *b = RANEF_SLOT(x),
*eta = ETA_SLOT(x), *offset = OFFSET_SLOT(x),
*rr, *ss, one = 1, *u = U_SLOT(x), *y = Y_SLOT(x);
int *nc = Alloca(nt, int), *nlev = Alloca(nt, int),
*spt = Alloca(nt + 1, int);
double **st = Alloca(nt, double*);
R_CheckStack();
ST_nc_nlev(GET_SLOT(x, lme4_STSym), Gp, st, nc, nlev);
ns = 0; /* ns is length(theta_S) */
spt[0] = 0; /* pointers into ss for terms */
for (int i = 0; i < nt; i++) {
ns += nc[i];
spt[i + 1] = spt[i] + nc[i];
}
if (annz == znnz) { /* Copy Z' to A unless A has new nonzeros */
Memcpy(ax, (double*)(Zt->x), znnz);
} else error("Code not yet written for MCMC_S with NLMMs");
/* Create T'Zt in A */
Tt_Zt(A, Gp, nc, nlev, st, nt);
/* Create P'u in ranef slot */
for (int i = 0; i < q; i++) b[perm[i]] = u[i];
/* Create X\beta + offset in eta slot */
for (int i = 0; i < n; i++) eta[i] = offset ? offset[i] : 0;
F77_CALL(dgemv)("N", &n, &p, &one, X_SLOT(x), &n,
FIXEF_SLOT(x), &i1, &one, eta, &i1);
/* Allocate R, rr and ss */
R = Alloca(ns * ns, double); /* crossproduct matrix then factor */
rr = Alloca(ns, double); /* row of model matrix for theta_S */
ss = Alloca(ns, double); /* right hand side, then theta_S */
R_CheckStack();
AZERO(R, ns * ns);
AZERO(ss, ns);
/* Accumulate crossproduct from pseudo-data part of model matrix */
for (int i = 0; i < q; i++) {
int sj = theta_S_ind(i, nt, Gp, nlev, spt);
AZERO(rr, ns);
rr[sj] = b[i];
F77_CALL(dsyr)("U", &ns, &one, rr, &i1, R, &ns);
}
/* Accumulate crossproduct and residual product of the model matrix. */
/* This is done one row at a time. Rows of the model matrix
* correspond to columns of T'Zt */
for (int j = 0; j < n; j++) { /* jth column of T'Zt */
AZERO(rr, ns);
for (int p = ap[j]; p < ap[j + 1]; p++) {
int i = ai[p]; /* row in T'Zt */
int sj = theta_S_ind(i, nt, Gp, nlev, spt);
rr[sj] += ax[p] * b[i];
ss[sj] += rr[sj] * (y[j] - eta[j]);
}
F77_CALL(dsyr)("U", &ns, &one, rr, &i1, R, &ns);
}
F77_CALL(dposv)("U", &ns, &i1, R, &ns, ss, &ns, &info);
if (info)
error(_("Model matrix for theta_S is not positive definite, %d."), info);
for (int j = 0; j < ns; j++) rr[j] = sigma * norm_rand();
/* Sample from the conditional Gaussian distribution */
F77_CALL(dtrsv)("U", "N", "N", &ns, R, &ns, rr, &i1);
for (int j = 0; j < ns; j++) ss[j] += rr[j];
/* Copy positive part of solution onto diagonals of ST */
pos = 0;
for (int i = 0; i < nt; i++) {
for (int j = 0; j < nc[i]; j++) {
st[i][j * (nc[i] + 1)] = (ss[pos] > 0) ? ss[pos] : 0;
pos++;
}
}
update_A(x);
}
