// betasp => n x q
// Xsp => N x q
// XB => N x 1
void comb_XB_sp(int *n, int *r, int *T, int *q, double *Xsp, double *betasp,
int *constant, double *XB)
{
int i, j, l, t, n1, r1, T1, q1;
n1=*n;
r1=*r;
T1=*T;
q1=*q;
double *XB1, *dump, *I;
XB1 = (double *) malloc((size_t)((n1*n1)*sizeof(double)));
dump = (double *) malloc((size_t)((n1)*sizeof(double)));
I = (double *) malloc((size_t)((n1)*sizeof(double)));
for(l=0; l<r1; l++){
for(t=0; t<T1; t++){
for(i=0; i<n1; i++){
I[i] = 0.0;
}
for(j=0; j<q1; j++){
extract_X_sp2(t, l, j, n, r, T, Xsp, XB1); // n x n
for(i=0; i<n1; i++){
dump[i] = betasp[i+j*n1]; // n x 1
}
MProd(dump, constant, n, XB1, n, dump); // n x 1
MAdd(I, n, constant, dump, I); // n x 1
}
put_together1(l, t, n, r, T, XB, I);
}
}
free(XB1); free(dump); free(I);
return;
}
// betatp => T x p ??
// Xtp => N x p
// XB => N x 1
void comb_XB_tp(int *n, int *r, int *T, int *p, double *Xtp, double *betatp,
int *constant, double *XB)
{
int t, l, n1, r1, T1, p1;
n1 =*n;
r1 =*r;
T1 =*T;
p1 =*p;
double *X1, *beta, *XB1;
X1 = (double *) malloc((size_t)((n1*p1)*sizeof(double)));
beta = (double *) malloc((size_t)((p1)*sizeof(double)));
XB1 = (double *) malloc((size_t)((n1)*sizeof(double)));
for(l=0; l<r1; l++){
for(t=0; t<T1; t++){
extract_X(t, l, n, r, T, p, Xtp, X1); // nrT x p into n x p
extract_beta_t(t, T, p, betatp, beta); // p x T into p x 1
MProd(beta, constant, p, X1, n, XB1); // n x 1
put_together1(l, t, n, r, T, XB, XB1);
// int i;
// for(i=0; i< n1*p1; i++){
// Rprintf(" X1: %4.4f, \n", X1[i]);
// }
// for(i=0; i< p1; i++){
// Rprintf(" beta: %4.4f, \n", beta[i]);
// }
// for(i=0; i< n1; i++){
// Rprintf(" XB: %4.4f, \n", XB1[i]);
// }
}
}
free(X1); free(beta); free(XB1);
return;
}
// K-step Forecasts without its
void zlt_fore_gpp(int *cov, int *K, int *n, int *m, int *r, int *p, int *rT, int *T,
int *rK, int *nrK, double *dnm, double *dm, double *phi, double *nu, double *sig_e,
double *sig_eta, double *beta, double *rho, double *wp, double *foreX,
int *constant, double *foreZ)
{
int l, k, t, i, T1, K1, r1, n1, m1, col;
T1 =*T;
K1 =*K;
r1 =*r;
n1 =*n;
m1 =*m;
col =*constant;
double *C, *det, *I, *A, *mu, *XB, *XB1;
double *wp1, *Aw, *eta, *eps, *zfore;
C = (double *) malloc((size_t)((n1*m1)*sizeof(double)));
// Sigeta = (double *) malloc((size_t)((m1*m1)*sizeof(double)));
// Sinv = (double *) malloc((size_t)((m1*m1)*sizeof(double)));
det = (double *) malloc((size_t)((col)*sizeof(double)));
I = (double *) malloc((size_t)((m1*col)*sizeof(double)));
A = (double *) malloc((size_t)((m1*n1)*sizeof(double)));
mu = (double *) malloc((size_t)((col)*sizeof(double)));
XB = (double *) malloc((size_t)((n1*r1*K1*col)*sizeof(double)));
XB1 = (double *) malloc((size_t)((n1*col)*sizeof(double)));
wp1 = (double *) malloc((size_t)((m1*col)*sizeof(double)));
Aw = (double *) malloc((size_t)((n1*col)*sizeof(double)));
eta = (double *) malloc((size_t)((m1*col)*sizeof(double)));
eps = (double *) malloc((size_t)((col)*sizeof(double)));
zfore = (double *) malloc((size_t)((n1*col)*sizeof(double)));
double *S, *C12c, *s21, *sig;
S = (double *) malloc((size_t)((m1*m1)*sizeof(double)));
C12c = (double *) malloc((size_t)((m1*col)*sizeof(double)));
s21 = (double *) malloc((size_t)((col)*sizeof(double)));
sig = (double *) malloc((size_t)((col)*sizeof(double)));
/*
// exponential covariance
if(cov[0] == 1){
for(i = 0; i < (m1*m1); i++){
S[i] = exp(-1.0*phi[0]*dm[i]);
// Sigeta[i] = sig_eta[0]*S[i];
}
// MInv(Sigeta, Sinv_eta, m, det);
for(i=0; i < m1*n1; i++){
C[i] = exp(-1.0*phi[0]*dnm[i]);
}
}
// gaussian covariance
if(cov[0] == 2){
for(i = 0; i < (m1*m1); i++){
S[i] = exp(-1.0*phi[0]*phi[0]*dm[i]*dm[i]);
// Sigeta[i] = sig_eta[0]*S[i];
}
// MInv(Sigeta, Sinv_eta, m, det);
for(i=0; i < m1*n1; i++){
C[i] = exp(-1.0*phi[0]*phi[0]*dnm[i]*dnm[i]);
}
}
// spherical covariance
if(cov[0] == 3){
for(i = 0; i < (m1*m1); i++){
if(dm[i] > 0 && dm[i] <= 1.0/phi[0]){
S[i] = (1.0-1.5*phi[0]*dm[i]+0.5*(phi[0]*dm[i])*(phi[0]*dm[i])*(phi[0]*dm[i]));
// Sigeta[i] = sig_eta[0]*S[i];
}
else if(dm[i] >= 1.0/phi[0]){
S[i] = 0.0;
// Sigeta[i] = 0.0;
}
else{
S[i] = 1.0;
// Sigeta[i] = 1.0*sig_eta[0];
}
}
// MInv(Sigeta, Sinv_eta, m, det);
for(i=0; i < m1*n1; i++){
if(dnm[i] > 0 && dnm[i] <= 1.0/phi[0]){
C[i] = 1.0-1.5*phi[0]*dnm[i]+0.5*(phi[0]*dnm[i])*(phi[0]*dnm[i])*(phi[0]*dnm[i]);
}
else if(dnm[i] >= 1.0/phi[0]){
C[i] = 0.0;
}
else{
C[i] = 1.0;
}
}
}
// matern covariance, nu = 3/2
if(cov[0] == 4){
for(i = 0; i < (m1*m1); i++){
S[i] = ((1.0+phi[0]*dm[i])*exp(-1.0*phi[0]*dm[i]));
// Sigeta[i] = sig_eta[0]*S[i];
}
// MInv(Sigeta, Sinv_eta, m, det);
for(i=0; i < m1*n1; i++){
C[i] = (1.0+phi[0]*dnm[i])*exp(-1.0*phi[0]*dnm[i]);
}
}
*/
covF(cov, m, m, phi, nu, dm, S);
covF(cov, n, m, phi, nu, dnm, C);
MInv(S, S, m, det); // m x m
MProd(S, m, m, C, n, A); // n x m
for(i=0; i<m1; i++){
I[i] = 0.0;
}
mu[0] = 0.0;
MProd(beta, constant, p, foreX, nrK, XB); // nrK x 1
for(l=0; l<r1; l++){
for(k=0; k<1; k++){
t = (T1-1);
extract_alt2(l, k, n, rK, K, XB, XB1); // n x 1
for(i=0; i<m1; i++){
wp1[i] = wp[i+t*m1+l*m1*T1];
}
MProd(wp1, constant, m, A, n, Aw); // n x 1
for(i=0; i<n1; i++){
extn_12(i, m, C, C12c); // m x 1
xTay(C12c, S, C12c, m, s21); // 1 x 1
if(s21[0] > 1.0){
s21[0] = 1.0-pow(1,-320);
}
if(s21[0] == 1.0){
s21[0] = 1.0-pow(1,-320);
}
sig[0] = sig_eta[0] * (1.0 - s21[0]);
mu[0] = 0.0;
mvrnormal(constant, mu, sig_e, constant, eps);
mu[0] = Aw[i];
mvrnormal(constant, mu, sig, constant, eta);
zfore[i] = XB1[i] + eta[0] + eps[0];
}
put_together1(l, k, n, r, K, foreZ, zfore);
}
for(k=1; k<K1; k++){
for(i=0; i<m1; i++){
wp1[i] = wp1[i]; // m x 1
}
MProd(wp1, constant, m, A, n, Aw); // n x 1
extract_alt2(l, k, n, rK, K, XB, XB1); // n x 1
mvrnormal(constant, mu, sig_e, constant, eps);
for(i=0; i<n1; i++){
extn_12(i, m, C, C12c); // m x 1
xTay(C12c, S, C12c, m, s21); // 1 x 1
if(s21[0] > 1.0){
s21[0] = 1.0-pow(1,-320);
}
if(s21[0] == 1.0){
s21[0] = 1.0-pow(1,-320);
}
sig[0] = sig_eta[0] * (1.0 - s21[0]);
mu[0] = 0.0;
mvrnormal(constant, mu, sig_e, constant, eps);
mu[0] = Aw[i];
mvrnormal(constant, mu, sig, constant, eta);
zfore[i] = XB1[i] + eta[0] + eps[0];
}
put_together1(l, k, n, r, K, foreZ, zfore);
}
}
free(S); free(det);
free(C); free(I);
free(A); free(mu); free(XB); free(XB1); free(wp1); free(Aw);
free(eta); free(eps); free(zfore);
free(C12c); free(s21); free(sig);
return;
}
// conditional posterior for o_lt
void o_gp(int *n, int *r, int *T, int *rT, int *p, double *prior_omu,
double *prior_osig, double *sig_e, double *sig_eta, double *S,
double *Qeta, double *XB, double *z, int *constant, double *opost)
{
int i, l, t, r1, nn, row, T1, col, p1;
r1 = *r; row = *n; T1 = *T; nn = row * row; col = *constant;
p1 = *p;
double *o_1, *de_tT, *det1, *chi_tT, *mean1, *XB1, *QXB1, *zT;
o_1 = (double *) malloc((size_t)((row)*sizeof(double)));
de_tT = (double *) malloc((size_t)((nn)*sizeof(double)));
det1 = (double *) malloc((size_t)((col)*sizeof(double)));
chi_tT = (double *) malloc((size_t)((row)*sizeof(double)));
mean1 = (double *) malloc((size_t)((row)*sizeof(double)));
XB1 = (double *) malloc((size_t)((row)*sizeof(double)));
QXB1 = (double *) malloc((size_t)((row)*sizeof(double)));
zT = (double *) malloc((size_t)((row)*sizeof(double)));
// for 1 <= t <= T, the delta part
for(i=0; i < nn; i++) {
de_tT[i] = (1.0/sig_e[0]) + Qeta[i] + 1.0/prior_osig[0];
}
MInv(de_tT, de_tT, n, det1); // n x n
double *term1, *I, *term2, *zt;
term1 = (double *) malloc((size_t)((nn)*sizeof(double)));
I = (double *) malloc((size_t)((row)*sizeof(double)));
term2 = (double *) malloc((size_t)((row)*sizeof(double)));
zt = (double *) malloc((size_t)((row)*sizeof(double)));
// term1 and term2
for(i=0; i < nn; i++) {
term1[i] = (sig_eta[0]/sig_e[0])* S[i];
}
for(i=0; i < row; i++) {
I[i]= 1.0;
}
MProd(I, constant, n, term1, n, term2);
for(l=0; l < r1; l++) {
for(t=0; t < T1; t++) {
extract_alt2(l, t, n, rT, T, XB, XB1);
extract_alt2(l, t, n, rT, T, z, zT);
MProd(zT, constant, n, term1, n, zt);
for(i=0; i < row; i++) {
mean1[i] = (XB1[i]+zt[i])/(1+term2[i]) + prior_omu[0];
}
mvrnormal(constant, mean1, de_tT, n, o_1); // random generator
put_together1(l, t, n, r, T, opost, o_1);
}
} // End of loop year
free(o_1); free(de_tT); free(det1); free(chi_tT);
free(mean1); free(XB1); free(QXB1); free(zT);
free(term1); free(I); free(term2); free(zt);
return;
}