// Posterior distribution for "sig_e"
void sig_e_gp(int *n, int *r, int *T, int *rT, int *N, double *shape,
double *prior_b, double *XB, double *o, double *z, double *sig_e,
int *constant, double *sig2e)
{
int i, t, l, n1, r1, T1, col;
n1 =*n;
r1 =*r;
T1 =*T;
col =*constant;
double *z1, *o1, *zo, *zzoo, *XB1, *tmp;
z1 = (double *) malloc((size_t)((n1*col)*sizeof(double)));
o1 = (double *) malloc((size_t)((n1*col)*sizeof(double)));
zo = (double *) malloc((size_t)((n1*col)*sizeof(double)));
zzoo = (double *) malloc((size_t)((col)*sizeof(double)));
XB1 = (double *) malloc((size_t)((n1*col)*sizeof(double)));
tmp = (double *) malloc((size_t)((col)*sizeof(double)));
double u, v, b, sige[1];
u = 0.0;
v = 0.0;
b = 0.0;
for(l=0; l<r1; l++){
for(t=0; t<T1; t++){
extract_alt2(l, t, n, rT, T, o, o1);
extract_alt2(l, t, n, rT, T, z, z1);
extract_alt2(l, t, n, rT, T, XB, XB1);
for(i=0; i<n1; i++){
// zzoo[0] = o1[i]-XB1[i];
zzoo[0] = z1[i]-o1[i];
tmp[0] = 0.005;
mvrnormal(constant, zzoo, tmp, constant, zzoo);
// zo[i] = z1[i]-(o1[i]+zzoo[0]);
zo[i] = zzoo[0];
}
MProd(zo, constant, n, zo, constant, zzoo);
u += zzoo[0];
}
}
b = *prior_b;
u = b + 0.5 * u;
v = *shape;
sige[0] = rigammaa(v, u);
*sig2e = sige[0];
free(z1); free(o1); free(zo); free(zzoo); free(XB1);free(tmp);
return;
}
void phidens_gp(double *phi, double *Qeta, double *det, int *n, int *r,
int *T, int *rT, int *N, double *prior_a, double *prior_b, double *XB,
double *o, int *constant, double *out)
{
int row, col, l, i, j, r1, T1, N1, rT1;
row = *n;
col = *constant;
r1 = *r;
T1 = *T;
N1 = *N;
rT1 = *rT;
double *ov, *o1, *XB1;
o1 = (double *) malloc((size_t)((row*col)*sizeof(double)));
ov = (double *) malloc((size_t)((row*col)*sizeof(double)));
XB1 = (double *) malloc((size_t)((row*col)*sizeof(double)));
double u, a, b;
u = 0.0;
for(l=0; l < r1; l++) {
for(i=0; i < T1; i++) {
extract_alt2(l, i, n, rT, T, o, o1);
extract_alt2(l, i, n, rT, T, XB, XB1);
for(j=0; j < row; j++) {
ov[j]=o1[j]-XB1[j];
}
u += xTay2(ov, Qeta, ov, row);
}
}
free(o1); free(ov); free(XB1);
a = *prior_a;
b = *prior_b;
u = 0.5 * u;
if(det[0] <= 0){
det[0] = pow(1,-320);
}
if(phi[0] <= 0){
phi[0] = pow(1,-320);
}
double tr;
tr = 0.0;
tr = (a-1.0)*log(phi[0])-b*phi[0]-0.5*rT1*log(det[0])-u;
out[0] = tr;
return;
}
// Posterior distribution for "sig_eta"
void sig_eta_gp(int *n, int *r, int *T, int *rT, double *shape,
double *prior_b, double *Sinv, double *XB, double *o, int *constant,
double *sig2eta)
{
double *ov, *o1, *out, u, b, sh, sig[1];
int row, col, l, i, j, r1, T1;
row = *n;
col = *constant;
r1 = *r;
T1 = *T;
o1 = (double *) malloc((size_t)((row*col)*sizeof(double)));
ov = (double *) malloc((size_t)((row*col)*sizeof(double)));
out = (double *) malloc((size_t)((row*col)*sizeof(double)));
double *XB1;
XB1 = (double *) malloc((size_t)((row*col)*sizeof(double)));
u = 0.0;
for(l=0; l < r1; l++) {
for(i=0; i < T1; i++) {
extract_alt2(l, i, n, rT, T, o, o1);
extract_alt2(l, i, n, rT, T, XB, XB1);
for(j=0; j < row; j++) {
ov[j]=o1[j]-XB1[j];
}
MProd(ov, constant, n, Sinv, n, out);
MProd(out, constant, n, ov, constant, out);
u += out[0];
// u += xTay2(ov, Sinv, ov, row);
}
}
b = *prior_b;
u = b + 0.5 * u;
sh = *shape;
sig[0] = rigammaa(sh, u);
*sig2eta = sig[0];
free(ov); free(o1); free(XB1); free(out);
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;
}
// Rnadom-walk metropolis for phi
void phi_gp_MH(double *Qeta1, double *Qeta2, double *det1, double *det2,
double *phi1, double *phi2, int *n, int *r, int *T, int *rT, int *N,
double *prior_a, double *prior_b, double *XB, double *o, int *constant,
double *accept, double *phip)
{
int row, col, l, i, j, r1, T1, N1, rT1;
row = *n;
col = *constant;
r1 = *r;
T1 = *T;
N1 = row*r1*T1;
rT1 = *rT;
double *ov, *o1, *XB1, *ratio, *U;
o1 = (double *) malloc((size_t)((row*col)*sizeof(double)));
ov = (double *) malloc((size_t)((row*col)*sizeof(double)));
XB1 = (double *) malloc((size_t)((row*col)*sizeof(double)));
ratio = (double *) malloc((size_t)((col)*sizeof(double)));
U = (double *) malloc((size_t)((col)*sizeof(double)));
double u, v, a, b;
u = 0.0;
v = 0.0;
for(l=0; l < r1; l++) {
for(i=0; i < T1; i++) {
extract_alt2(l, i, n, rT, T, o, o1);
extract_alt2(l, i, n, rT, T, XB, XB1);
for(j=0; j < row; j++) {
ov[j]=o1[j]-XB1[j];
}
u += xTay2(ov, Qeta1, ov, row);
v += xTay2(ov, Qeta2, ov, row);
}
}
a = *prior_a;
b = *prior_b;
u = 0.5 * u;
v = 0.5 * v;
double tr1, tr2;
tr1 = 0.0;
tr2 = 0.0;
if(det1[0] <= 0){
det1[0] = pow(1,-320);
}
if(det2[0] <= 0){
det2[0] = pow(1,-320);
}
if(phi1[0] <= 0){
phi1[0] = pow(1,-320);
}
if(phi2[0] <= 0){
phi2[0] = pow(1,-320);
}
if(phi2[0] < 0.0010){
phip[0] = phi1[0];
accept[0] = 0.0;
}
else if(phi2[0] > 0.9999){
phip[0] = phi1[0];
accept[0] = 0.0;
}
else{
tr1 = (a-1.0)*log(phi1[0])-b*phi1[0]-0.5*rT1*log(det1[0])- u;
tr2 = (a-1.0)*log(phi2[0])-b*phi2[0]-0.5*rT1*log(det2[0])- v;
ratio[0] = exp(tr2 + exp(tr2) - tr1 - exp(tr1));
ratio_fnc(ratio, constant, U);
if(U[0] < ratio[0]){
phip[0] = phi2[0];
accept[0] = 1.0;
}
else {
phip[0] = phi1[0];
accept[0] = 0.0;
}
}
free(o1); free(ov); free(XB1); free(ratio); free(U);
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;
}
// Posterior distribution for "theta"
void beta_gp(int *n, int *r, int *T, int *rT, int *p, double *prior_mu,
double *prior_sig, double *Qeta, double *X, double *o, int *constant,
double *betap)
{
int t, l, i, n1, p1, r1, T1, col;
n1 =*n;
p1 =*p;
r1 =*r;
T1 =*T;
col =*constant;
double *del, *chi, *ot1, *X1, *tX1, *out, *tX1QX1, *tX1Qo, *det, *mu, *I;
del = (double *) malloc((size_t)((p1*p1)*sizeof(double)));
chi = (double *) malloc((size_t)((p1*col)*sizeof(double)));
ot1 = (double *) malloc((size_t)((n1*col)*sizeof(double)));
X1 = (double *) malloc((size_t)((n1*p1)*sizeof(double)));
tX1 = (double *) malloc((size_t)((n1*p1)*sizeof(double)));
out = (double *) malloc((size_t)((n1*p1)*sizeof(double)));
tX1QX1 = (double *) malloc((size_t)((p1*p1)*sizeof(double)));
tX1Qo = (double *) malloc((size_t)((p1*col)*sizeof(double)));
det = (double *) malloc((size_t)((col)*sizeof(double)));
mu = (double *) malloc((size_t)((p1*col)*sizeof(double)));
I = (double *) malloc((size_t)((p1*p1)*sizeof(double)));
for(i=0; i<p1*p1; i++){
del[i] = 0.0;
}
for(i=0; i<p1; i++){
chi[i] = 0.0;
}
for(l=0; l<r1; l++){
for(t=0; t<T1; t++){
extract_X(t, l, n, r, T, p, X, X1); // n x p
MTranspose(X1, p, n, tX1); // p x n
MProd(X1, p, n, Qeta, n, out); // n x p
MProd(out, p, n, tX1, p, tX1QX1); // pxp
MAdd(del, p, p, tX1QX1, del); // pxp
extract_alt2(l, t, n, rT, T, o, ot1); // n x 1
MProd(ot1, constant, n, Qeta, n, out); // n x 1
MProd(out, constant, n, tX1, p, tX1Qo); // p x 1
MAdd(chi, p, constant, tX1Qo, chi); // p x 1
}
}
IdentityM(p, I);
for(i=0; i<p1*p1; i++){
del[i] = del[i] + I[i]*(1.0/prior_sig[0]);
}
free(I);
for(i=0; i<p1; i++){
chi[i] = chi[i] + prior_mu[0]/prior_sig[0];
}
MInv(del, del, p, det);
MProd(chi, constant, p, del, p, mu); // p x 1
mvrnormal(constant, mu, del, p, betap);
free(del); free(chi); free(ot1); free(X1); free(tX1);
free(out); free(tX1QX1); free(tX1Qo); free(det); free(mu);
return;
}
