// Prediction for all sites for all time point "XB"
void z_pr_ar(int *cov, int *nsite, int *n, int *r, int *rT, int *T, int *p,
int *N, double *d, double *d12, double *phip, double *nup,
double *sig_ep, double *sig_etap, double *sig_l0p, double *rhop,
double *betap, double *mu_lp, double *X, double *valX,
double *op, int *constant, double *zpred)
{
int i, j, l, t, r1, col, rT1, n1, nn, ns, p1, N1;
col = *constant;
r1 = *r;
rT1 = *rT;
n1 = *n;
nn = n1*n1;
ns = *nsite;
p1 = *p;
N1 = *N;
int *T1, *T2;
T1 = (int *) malloc((size_t)((r1)*sizeof(int)));
T2 = (int *) malloc((size_t)((r1+1)*sizeof(int)));
for(i=0; i<r1; i++){
T1[i] = T[i];
}
cumsumint(r, T, T2);
double *S_eta, *Si_eta, *S_eta12, *S_eta12c, *det;
S_eta = (double *) malloc((size_t)((n1*n1)*sizeof(double)));
Si_eta = (double *) malloc((size_t)((n1*n1)*sizeof(double)));
S_eta12 = (double *) malloc((size_t)((n1*ns)*sizeof(double)));
S_eta12c = (double *) malloc((size_t)((n1)*sizeof(double)));
det = (double *) malloc((size_t)((col)*sizeof(double)));
covF(cov, n, n, phip, nup, d, S_eta);
MInv(S_eta, Si_eta, n, det);
covF(cov, n, nsite, phip, nup, d12, S_eta12);
double *S, *m1, *O11, *O_l0, *XB;
S = (double *) malloc((size_t)((n1*n1)*sizeof(double)));
m1 = (double *) malloc((size_t)((n1)*sizeof(double)));
O11 = (double *) malloc((size_t)((n1)*sizeof(double)));
O_l0 = (double *) malloc((size_t)((n1*r1*col)*sizeof(double)));
XB = (double *) malloc((size_t)((N1*col)*sizeof(double)));
for(l=0; l<r1; l++){
for(i=0; i<nn; i++){
S[i] = sig_l0p[l]*Si_eta[i];
}
for(i=0; i<n1; i++) {
m1[i] = mu_lp[l];
}
mvrnormal(constant, m1, S, n, O11);
for(i=0; i<n1; i++) {
O_l0[i+l*n1] = O11[i];
}
}
MProd(betap, constant, p, X, N, XB);
double *s21, *sig, *m, *sig_0;
s21 = (double *) malloc((size_t)((col)*sizeof(double)));
sig = (double *) malloc((size_t)((col)*sizeof(double)));
m = (double *) malloc((size_t)((col)*sizeof(double)));
sig_0 = (double *) malloc((size_t)((col)*sizeof(double)));
double *O1, *opp, *XB1, *valX1, *valXB1;
O1 = (double *) malloc((size_t)((col)*sizeof(double)));
opp = (double *) malloc((size_t)((n1)*sizeof(double)));
XB1 = (double *) malloc((size_t)((n1)*sizeof(double)));
valX1 = (double *) malloc((size_t)((p1*ns)*sizeof(double)));
valXB1 = (double *) malloc((size_t)((ns)*sizeof(double)));
double *opp1, *oox, *part2, *out, *out1, *mu, *opre;
opp1 = (double *) malloc((size_t)((n1)*sizeof(double)));
oox = (double *) malloc((size_t)((n1)*sizeof(double)));
part2 = (double *) malloc((size_t)((col)*sizeof(double)));
out = (double *) malloc((size_t)((col)*sizeof(double)));
out1 = (double *) malloc((size_t)((col)*sizeof(double)));
mu = (double *) malloc((size_t)((col)*sizeof(double)));
opre = (double *) malloc((size_t)((rT1*col)*sizeof(double)));
for(j=0; j < ns; j++) {
extn_12(j, n, S_eta12,S_eta12c);
xTay(S_eta12c, Si_eta, S_eta12c, n, s21);
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_etap[0] * (1.0 - s21[0]);
for(l=0; l < r1; l++) {
t=0;
m[0] = mu_lp[l];
sig_0[0] = sig_l0p[l];
mvrnormal(constant, m, sig_0, constant, O1);
extract_alt_uneqT(l, t, n, r, T, rT, op, opp);
extract_alt_uneqT(l, t, n, r, T, rT, XB, XB1);
extract_X21_uneqT(l, t, nsite, rT, r, T, p, valX, valX1);
// extract_alt2(l, t, n, rT, T, op, opp);
// extract_alt2(l, t, n, rT, T, XB, XB1);
// extract_X21(l, t, nsite, rT, T, p, valX, valX1); // X1 = p x n
MProd(valX1, nsite, p, betap, constant, valXB1);
for(i=0; i < n1; i++){
opp1[i] = O_l0[i+l*n1];
}
for(i=0; i < n1; i++) {
oox[i] = opp[i]-rhop[0]*opp1[i]-XB1[i];
}
xTay(S_eta12c, Si_eta, oox, n, part2);
mu[0] = 0.0;
mvrnormal(constant, mu, sig, constant, out);
mu[0] = 0.0;
mvrnormal(constant, mu, sig_ep, constant, out1);
opre[t+T2[l]]=rhop[0]*O1[0]+valXB1[j]+part2[0];
zpred[t+T2[l]+j*(rT1)]=opre[t+T2[l]]+out[0]+out1[0];
//rhop[0]*O1[0]+valXB1[j]+part2[0]+out[0]+out1[0];
for(t=1; t < T1[l]; t++) {
extract_alt_uneqT(l, t-1, n, r, T, rT, op, opp1);
extract_alt_uneqT(l, t, n, r, T, rT, op, opp);
extract_alt_uneqT(l, t, n, r, T, rT, XB, XB1);
extract_X21_uneqT(l, t, nsite, rT, r, T, p, valX, valX1);
// extract_alt2(l, t-1, n, rT, T, op, opp1);
// extract_alt2(l, t, n, rT, T, op, opp);
// extract_alt2(l, t, n, rT, T, XB, XB1);
// extract_X21(l, t, nsite, rT, T, p, valX, valX1); // X1 = p x n
MProd(valX1, nsite, p, betap, constant, valXB1); // 1 x n
for(i=0; i < n1; i++) {
oox[i] = opp[i]-rhop[0]*opp1[i]-XB1[i];
}
xTay(S_eta12c, Si_eta, oox, n, part2);
mu[0] = 0.0;
mvrnormal(constant, mu, sig, constant, out);
mu[0] = 0.0;
mvrnormal(constant, mu, sig_ep, constant, out1);
opre[t+T2[l]] = rhop[0]*opre[(t-1)+T2[l]]+valXB1[j]+part2[0];
zpred[t+T2[l]+j*(rT1)]=opre[t+T2[l]] + out[0]+ out1[0];
// zpred[t+T2[l]+j*(rT1)]=rhop[0]*zpred[t+T2[l]+j*(rT1)]+valXB1[j]+part2[0] + out[0]+ out1[0];
}
}
}
free(opre);
free(T1); free(T2);
free(mu); free(out1); free(out); free(part2); free(oox); free(opp1);
free(valXB1); free(valX1); free(XB1); free(opp); free(O1); free(sig_0);
free(m); free(sig); free(s21); free(XB); free(O_l0); free(O11); free(m1);
free(S); free(det); free(S_eta12c); free(S_eta12); free(Si_eta); free(S_eta);
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;
}
