int forkal(int ip,int iq,int id,double *phi,double*theta,double *delta,int N,double *W,double *resid,int il,double *Y,double *AMSE) {
int ifault,ir,np,k,nrbar,ird,irz;
double *A,*P,*V,*store,*xrow;
double zero, one, two,AA,del,sumlog,ssq,sigma,A1,dt,phij,phijdt,phii,AMS;
int i, j, ll, nt, nj, idk, iid,iupd,nit,iter,ind,irj;
int ir2, ir1, id2r, id2r1, id1,idd1,idd2,i45,idrr1,iddr,jkl,jkl1,id2r2,ibc,l,iri1,jj;
int lk, lk1,jklj,iri,kk1,k1,kk,kkk,ind1,ind2,jrj,j1,jrk;
/*
C C Translation of Fortran routine
C ALGORITHM AS 182 APPL. STATIST. (1982) VOL.31, NO.2
C
C Finite sample prediction from ARIMA processes.
C
C Auxiliary routines required: KARMA & STARMA from AS 154 and
C routines called by them: INCLU2 from ASR 17 (a slight variant on
C AS 75, and REGRES from AS 75.
C*/
ir = iq + 1;
if (ir < ip) {
ir = ip;
}
np = (ir * (ir + 1)) / 2;
nrbar = (np * (np - 1)) / 2;
ird = ir + id;
irz = (ird * (ird + 1)) / 2;
zero = 0.0;
one = 1.0;
two = 2.0;
ifault = 0;
if (ip < 0) {
ifault = 1;
}
if (iq < 0) {
ifault = ifault + 2;
}
if (ip*ip + iq*iq == 0) {
ifault = 4;
}
if (id < 0) {
ifault = 8;
}
if (il < 1) {
ifault = 11;
}
if (ifault != 0) {
return ifault;
}
A = (double*)malloc(sizeof(double)* ird);
P = (double*)malloc(sizeof(double)* irz);
V = (double*)malloc(sizeof(double)* np);
store = (double*)malloc(sizeof(double)* ird);
xrow = (double*)malloc(sizeof(double)* np);
//Initial Conditions for Kalman Filter
for (i = 0; i < ird; ++i) {
A[i] = zero;
store[i] = zero;
}
for (i = 0; i < irz; ++i) {
P[i] = zero;
}
for (i = 0; i < np; ++i) {
V[i] = zero;
xrow[i] = zero;
}
A[0] = zero;
V[0] = one;
/*
if (np != 1) {
for (i = 2; i <= np; ++i) {
V[i-1] = zero;
}
if (iq != 0) {
iq1 = iq + 1;
for (i = 2; i <= iq1; ++i) {
V[i-1] = theta[i - 2];
}
for (j = 1; j <= iq; ++j) {
ll = j * (2 * ir + 1 - j) / 2;
for (i = j; i <= iq; ++i) {
lli = ll + i;
V[lli-1] = theta[i-1] * theta[j-1]; // Error
}
}
}
}//130
*/
//Find initial likelihood conditions.
if (ir == 1) {
*P = 1.0 / (1.0 - phi[0] * phi[0]);
}
else {
starma(ip, iq, phi, theta,A, P, V);
}
//Calculate Data Transformations
nt = N - id;
if (id != 0) {
for (j = 1; j <= id; ++j) {
nj = N - j;
store[j-1] = W[nj-1];
}
for (i = 1; i <= nt; ++i) {
AA = zero;
for (k = 1; k <= id; ++k) {
idk = id + i - k;
AA -= delta[k - 1] * W[idk - 1];
}
iid = i + id;
W[i - 1] = W[iid - 1] + AA;
}
}//170
//Evaluate likelihood to obtain final KF conditions
sumlog = ssq = zero;
del = -1.0;
iupd = 1;
nit = 0;
iter = 0;
karma(ip, iq, phi, theta, A, P, V, nt, W, resid, &sumlog, &ssq, iupd, del,&iter, &nit);
//Calculate M.L.E. of sigma squared
sigma = zero;
for (j = 0; j < nt; ++j) {
sigma += resid[j] * resid[j];
}
sigma = sigma / nt;
//mdisplay(resid, 1, N);
//Reset the initial A and P when differencing occurs
if (id != 0) {
for (i = 1; i <= np; ++i) {
xrow[i-1] = P[i-1];
}
for (i = 1; i <= irz; ++i) {
P[i-1] = zero;
}
ind = 0;
for (j = 1; j <= ir; ++j) {
k = (j - 1) * (id + ir + 1) - (j - 1) * j / 2;
for (i = j; i <= ir; ++i) {
ind++;
k++;
P[k - 1] = xrow[ind-1];
}
}
for (j = 1; j <= id; ++j) {
irj = ir + j;
A[irj-1] = store[j-1];
}
}//250
//Set up constants
ir2 = ir + 1;
ir1 = ir - 1;
id1 = id - 1;
id2r = 2 * ird;
id2r1 = id2r - 1;
idd1 = 2 * id + 1;
idd2 = idd1 + 1;
i45 = id2r + 1;
idrr1 = ird + 1;
iddr = 2 * id + ir;
jkl = ir * (iddr + 1) / 2;
jkl1 = jkl + 1;
id2r2 = id2r + 2;
ibc = ir * (i45 - ir) / 2;
for (l = 1; l <= il; ++l) {
//Predict A
A1 = A[0];
if (ir != 1) {
for (i = 1; i <= ir1; ++i) {
A[i-1] = A[i];
}
}//310
A[ir-1] = zero;
if (ip != 0) {
for (j = 1; j <= ip; ++j) {
A[j-1] += phi[j-1] * A1;
}
}//330
if (id != 0) {
for (j = 1; j <= id; ++j) {
irj = ir + j;
A1 += delta[j-1] * A[irj-1];
}//340
if (id >= 2) {
for (i = 1; i <= id1; ++i) {
iri1 = ird - i;
A[iri1] = A[iri1-1];
}
}//360
A[ir2 - 1] = A1;
}//360
//A[ir2-1] = A1;
//Predict P
if (id != 0) {
for (i = 1; i <= id; ++i) {
store[i-1] = zero;
for (j = 1; j <= id; ++j) {
ll = imax(i, j);
k = imin(i, j);
jj = jkl + (ll - k) + 1 + (k - 1) * (idd2 - k) / 2;
store[i-1] += delta[j-1] * P[jj-1];
}
}//370
if (id != 1) {
for (j = 1; j <= id1; ++j) {
jj = id - j;
lk = (jj - 1) * (idd2 - jj) / 2 + jkl;
lk1 = jj * (idd1 - jj) / 2 + jkl;
for (i = 1; i <= j; ++i) {
lk = lk + 1;
lk1 = lk1 + 1;
P[lk1-1] = P[lk-1];
}
}//380
for (j = 1; j <= id1; ++j) {
jklj = jkl1 + j;
irj = ir + j;
P[jklj - 1] = store[j - 1] + P[irj-1];
}
}//400
P[jkl1 - 1] = P[0];
for (i = 1; i <= id; ++i) {
iri = ir + i;
P[jkl1 - 1] += delta[i - 1] * (store[i - 1] + two * P[iri - 1]);
}
for (i = 1; i <= id; ++i) {
iri = ir + i;
store[i - 1] = P[iri - 1];
}
for (j = 1; j <= ir; ++j) {
kk1 = j * (id2r1 - j) / 2 + ir;
k1 = (j - 1) * (id2r - j) / 2 + ir;
for (i = 1; i <= id; ++i) {
kk = kk1 + i;
k = k1 + i;
P[k - 1] = phi[j - 1] * store[i - 1];
if (j != ir) {
P[k - 1] += P[kk - 1];
}
}
}
for (j = 1; j <= ir; ++j) {
store[j - 1] = zero;
kkk = j * (i45 - j) / 2 - id;
for (i = 1; i <= id; ++i) {
kkk++;
store[j - 1] += delta[i - 1] * P[kkk - 1];
}
}//440
if (id != 1) {
for (j = 1; j <= ir; ++j) {
k = j * idrr1 - j * (j + 1) / 2 + 1;
for (i = 1; i <= id1; ++i) {
k--;
P[k - 1] = P[k - 2];
}
}
}//460
for (j = 1; j <= ir; ++j) {
k = (j - 1) * (id2r - j) / 2 + ir + 1;
P[k - 1] = store[j - 1] + phi[j - 1] * P[0];
if (j < ir) {
P[k - 1] += P[j];
}
}
}//480
for (i = 0; i < ir; ++i) {
store[i] = P[i];
}
ind = 0;
dt = P[0];
for (j = 1; j <= ir; ++j) {
phij = phi[j - 1];
phijdt = phij * dt;
ind2 = (j - 1) * (id2r2 - j) / 2;
ind1 = j * (i45 - j) / 2;
for (i = j; i <= ir; ++i) {
ind++;
ind2++;
phii = phi[i - 1];
P[ind2 - 1] = V[ind - 1] + phii * phijdt;
if (j < ir) {
P[ind2 - 1] += store[j] * phii;
}
if (i != ir) {
ind1++;
P[ind2 - 1] += store[i] * phij + P[ind1 - 1];
}//500
}
}//500
//Predict Y
Y[l - 1] = A[0];
if (id != 0) {
for (j = 1; j <= id; ++j) {
irj = ir + j;
Y[l - 1] += A[irj - 1] * delta[j - 1];
}
//Calculate MSE of Y
}//520
AMS = P[0];
if (id != 0) {
for (j = 1; j <= id; ++j) {
jrj = ibc + (j - 1) * (idd2 - j) / 2;
irj = ir + j;
AMS += (two * delta[j - 1] * P[irj - 1] + P[jrj] * delta[j - 1] * delta[j - 1]);
}
if (id != 1) {
for (j = 1; j <= id1; ++j) {
j1 = j + 1;
jrk = ibc + 1 + (j - 1) * (idd2 - j) / 2;
for (i = j1; i <= id; ++i) {
jrk++;
AMS += two * delta[i-1] * delta[j-1] * P[jrk-1];
}
}
}//550
}//550
AMSE[l - 1] = AMS * sigma;
}//560
/*
mdisplay(A, 1, ird);
mdisplay(P, 1, irz);
mdisplay(V, 1, np);
mdisplay(store, 1, ird);
mdisplay(xrow, 1, np);
*/
free(A);
free(P);
free(V);
free(store);
free(xrow);
return ifault;
}
double fas154_seas(double *b, int pq, void *params) {
double value, ssq, sumlog, delta;
int p, q, ps, qs,s,offset;
int ip, iq, ir, i,j, np, ifault, N, iupd, nit, iter;
double *phi, *theta, *A, *P, *V;
alik_seas_object obj = (alik_seas_object)params;
value = ssq = sumlog = 0.0;
ip = obj->p + (obj->s * obj->P);
iq = obj->q + (obj->s * obj->Q);
ir = obj->r;
N = obj->N;
p = obj->p;
ps = obj->P;
q = obj->q;
qs = obj->Q;
s = obj->s;
offset = obj->offset;
np = (ir * (ir + 1)) / 2;
phi = (double*)malloc(sizeof(double)* ir);
theta = (double*)malloc(sizeof(double)* ir);
A = (double*)malloc(sizeof(double)* ir);
P = (double*)malloc(sizeof(double)* np);
V = (double*)malloc(sizeof(double)* np);
for (i = 0; i < ir; ++i) {
phi[i] = 0.0;
theta[i] = 0.0;
}
for (i = 0; i < p; ++i) {
phi[i] = b[i];
}
for (i = 0; i < q; ++i) {
theta[i] = b[i + p];
}
/*
for (i = p; i < ip; ++i) {
phi[i] = 0.0;
}
for (i = q; i < iq; ++i) {
theta[i] = 0.0;
}
*/
for (j = 0; j < ps; ++j) {
phi[(j + 1)*s - 1] += b[p + q + j];
for (i = 0; i < p; ++i) {
phi[(j + 1)*s + i] -= b[i] * b[p + q + j];
}
}
for (j = 0; j < qs; ++j) {
theta[(j + 1)*s - 1] += b[p + q + ps + j];
for (i = 0; i < q; ++i) {
theta[(j + 1)*s + i] += b[i + p] * b[p + q + ps + j];
}
}
if (obj->M == 1) {
for (i = 0; i < N; ++i) {
obj->x[offset + i] = obj->x[offset + 2 * N + i] - b[p + q + ps + qs];
}
}
//mdisplay(phi, 1, ir);
//mdisplay(theta, 1, ir);
iupd = 0;
//mdisplay(b, 1, pq);
if (ip == 1 && iq == 0) {
*V = 1.0;
*A = 0.0;
*P = 1.0 / (1.0 - phi[0] * phi[0]);
}
else {
iupd = 1;
ifault = starma(ip, iq, phi, theta, A, P, V);
}
nit = 0;
delta = 0.001;
//mdisplay(P, 1, np);
karma(ip, iq, phi, theta, A, P, V, N, obj->x + offset, obj->x + offset + N, &sumlog, &ssq, iupd, delta, &iter, &nit);
obj->ssq = ssq;
//mdisplay(V, 1, np);
value = 0.5 * (sumlog / (double)iter + log(ssq / (double)iter));
obj->loglik = value;
//printf("sumlog ssq %g %g %d \n", sumlog,value,iter);
free(phi);
free(theta);
free(A);
free(P);
free(V);
return value;
}
SEXP arma0fa(SEXP pG, SEXP inparams)
{
int i, j, ifault = 0, it, streg;
double sumlog, ssq, tmp, ans;
GET_STARMA;
dotrans(G, REAL(inparams), G->params, G->trans);
if(G->ns > 0) {
/* expand out seasonal ARMA models */
for(i = 0; i < G->mp; i++) G->phi[i] = G->params[i];
for(i = 0; i < G->mq; i++) G->theta[i] = G->params[i + G->mp];
for(i = G->mp; i < G->p; i++) G->phi[i] = 0.0;
for(i = G->mq; i < G->q; i++) G->theta[i] = 0.0;
for(j = 0; j < G->msp; j++) {
G->phi[(j + 1)*G->ns - 1] += G->params[j + G->mp + G->mq];
for(i = 0; i < G->mp; i++)
G->phi[(j + 1)*G->ns + i] -= G->params[i]*
G->params[j + G->mp + G->mq];
}
for(j = 0; j < G->msq; j++) {
G->theta[(j + 1)*G->ns - 1] +=
G->params[j + G->mp + G->mq + G->msp];
for(i = 0; i < G->mq; i++)
G->theta[(j + 1)*G->ns + i] += G->params[i + G->mp]*
G->params[j + G->mp + G->mq + G->msp];
}
} else {
for(i = 0; i < G->mp; i++) G->phi[i] = G->params[i];
for(i = 0; i < G->mq; i++) G->theta[i] = G->params[i + G->mp];
}
streg = G->mp + G->mq + G->msp + G->msq;
if(G->m > 0) {
for(i = 0; i < G->n; i++) {
tmp = G->wkeep[i];
for(j = 0; j < G->m; j++)
tmp -= G->reg[i + G->n*j] * G->params[streg + j];
G->w[i] = tmp;
}
}
if(G->method == 1) {
int p = G->mp + G->ns * G->msp, q = G->mq + G->ns * G->msq, nu = 0;
ssq = 0.0;
for(i = 0; i < G->ncond; i++) G->resid[i] = 0.0;
for(i = G->ncond; i < G->n; i++) {
tmp = G->w[i];
for(j = 0; j < min(i - G->ncond, p); j++)
tmp -= G->phi[j] * G->w[i - j - 1];
for(j = 0; j < min(i - G->ncond, q); j++)
tmp -= G->theta[j] * G->resid[i - j - 1];
G->resid[i] = tmp;
if(!ISNAN(tmp)) {
nu++;
ssq += tmp * tmp;
}
}
G->s2 = ssq/(double)(nu);
ans = 0.5 * log(G->s2);
} else {
starma(G, &ifault);
if(ifault) error(_("starma error code %d"), ifault);
sumlog = 0.0;
ssq = 0.0;
it = 0;
karma(G, &sumlog, &ssq, 1, &it);
G->s2 = ssq/(double)G->nused;
ans = 0.5*(log(ssq/(double)G->nused) + sumlog/(double)G->nused);
}
return ScalarReal(ans);
}
double fas154(double *b,int pq,void *params) {
double value,ssq,sumlog,delta;
int ip, iq, ir,i,np,ifault,N,iupd,nit,iter;
double *phi, *theta, *A,*P,*V;
alik_object obj = (alik_object)params;
value = ssq = sumlog = 0.0;
ip = obj->p;
iq = obj->q;
ir = obj->r;
N = obj->N;
np = (ir * (ir + 1)) / 2;
phi = (double*)malloc(sizeof(double)* ir);
theta = (double*)malloc(sizeof(double)* ir);
A = (double*)malloc(sizeof(double)* ir);
P = (double*)malloc(sizeof(double)* np);
V = (double*)malloc(sizeof(double)* np);
//bt = (double*)malloc(sizeof(double)* (ip+iq));
/*
for (i = 0; i < ip + iq; ++i) {
bt[i] = b[i];
}
pdlreg(ip, bt, b);
pdlreg(iq, bt + ip, b + ip);
*/
for (i = 0; i < ip; ++i) {
phi[i] = b[i];
}
for (i = ip; i < ir; ++i) {
phi[i] = 0.0;
}
for (i = 0; i < iq; ++i) {
theta[i] = b[i+ip];
}
for (i = iq; i < ir; ++i) {
theta[i] = 0.0;
}
if (obj->M == 1) {
for (i = 0; i < N; ++i) {
obj->x[i] = obj->x[2 * N + i] - b[ip + iq];
}
}
iupd = 0;
if (ip == 1 && iq == 0) {
*V = 1.0;
*A = 0.0;
*P = 1.0 / (1.0 - phi[0] * phi[0]);
}
else {
iupd = 1;
ifault = starma(ip, iq, phi, theta, A, P, V);
}
nit = 0;
delta = 0.001;
//mdisplay(P, 1, np);
karma(ip, iq, phi, theta, A, P, V, N, obj->x, obj->x + N, &sumlog, &ssq, iupd, delta,&iter, &nit);
obj->ssq = ssq;
//mdisplay(phi, 1, ip);
value = 0.5 * (sumlog/(double)iter + log(ssq/(double) iter));
obj->loglik = value;
//printf("sumlog ssq %g %g %d \n", sumlog,value,iter);
free(phi);
free(theta);
free(A);
free(P);
free(V);
//free(bt);
return value;
}
/* start of AS 182 */
void
forkal(Starma G, int d, int il, double *delta, double *y, double *amse,
int *ifault)
{
int p = G->p, q = G->q, r = G->r, n = G->n, np = G->np;
double *phi = G->phi, *V = G->V, *w = G->w, *xrow = G->xrow;
double *a, *P, *store;
int rd = r + d, rz = rd*(rd + 1)/2;
double phii, phij, sigma2, a1, aa, dt, phijdt, ams, tmp;
int i, j, k, l, nu = 0;
int k1;
int i45, jj, kk, lk, ll;
int nt;
int kk1, lk1;
int ind, jkl, kkk;
int ind1, ind2;
/* Finite sample prediction from ARIMA processes. */
/* This routine will calculate the finite sample predictions
and their conditional mean square errors for any ARIMA process. */
/* invoking this routine will calculate the finite sample predictions */
/* and their conditional mean square errors for any arima process. */
store = (double *) R_alloc(rd, sizeof(double));
Free(G->a); G->a = a = Calloc(rd, double);
Free(G->P); G->P = P = Calloc(rz, double);
/* check for input faults. */
*ifault = 0;
if (p < 0) *ifault = 1;
if (q < 0) *ifault += 2;
if (p * p + q * q == 0) *ifault = 4;
if (r != max(p, q + 1)) *ifault = 5;
if (np != r * (r + 1) / 2) *ifault = 6;
if (d < 0) *ifault = 8;
if (il < 1) *ifault = 11;
if (*ifault != 0) return;
/* Find initial likelihood conditions. */
if (r == 1) {
a[0] = 0.0;
V[0] = 1.0;
P[0] = 1.0 / (1.0 - phi[0] * phi[0]);
} else starma(G, ifault);
/* Calculate data transformations */
nt = n - d;
if (d > 0) {
for (j = 0; j < d; j++) {
store[j] = w[n - j - 2];
if(ISNAN(store[j]))
error(_("missing value in last %d observations"), d);
}
for (i = 0; i < nt; i++) {
aa = 0.0;
for (k = 0; k < d; ++k) aa -= delta[k] * w[d + i - k - 1];
w[i] = w[i + d] + aa;
}
}
/* Evaluate likelihood to obtain final Kalman filter conditions */
{
double sumlog = 0.0, ssq = 0.0;
int nit = 0;
G->n = nt;
karma(G, &sumlog, &ssq, 1, &nit);
}
/* Calculate m.l.e. of sigma squared */
sigma2 = 0.0;
for (j = 0; j < nt; j++) {
/* MacOS X/gcc 3.5 does/didn't have isnan defined properly */
tmp = G->resid[j];
if(!ISNAN(tmp)) { nu++; sigma2 += tmp * tmp; }
}
sigma2 /= nu;
/* reset the initial a and P when differencing occurs */
if (d > 0) {
for (i = 0; i < np; i++) xrow[i] = P[i];
for (i = 0; i < rz; i++) P[i] = 0.0;
ind = 0;
for (j = 0; j < r; j++) {
k = j * (rd + 1) - j * (j + 1) / 2;
for (i = j; i < r; i++) P[k++] = xrow[ind++];
}
for (j = 0; j < d; j++) a[r + j] = store[j];
}
i45 = 2*rd + 1;
jkl = r * (2*d + r + 1) / 2;
for (l = 0; l < il; ++l) {
/* predict a */
a1 = a[0];
for (i = 0; i < r - 1; i++) a[i] = a[i + 1];
a[r - 1] = 0.0;
for (j = 0; j < p; j++) a[j] += phi[j] * a1;
if (d > 0) {
for (j = 0; j < d; j++) a1 += delta[j] * a[r + j];
for (i = rd - 1; i > r; i--) a[i] = a[i - 1];
a[r] = a1;
}
/* predict P */
if (d > 0) {
for (i = 0; i < d; i++) {
store[i] = 0.0;
for (j = 0; j < d; j++) {
ll = max(i, j);
k = min(i, j);
jj = jkl + (ll - k) + k * (2*d + 2 - k - 1) / 2;
store[i] += delta[j] * P[jj];
}
}
if (d > 1) {
for (j = 0; j < d - 1; j++) {
jj = d - j - 1;
lk = (jj - 1) * (2*d + 2 - jj) / 2 + jkl;
lk1 = jj * (2*d + 1 - jj) / 2 + jkl;
for (i = 0; i <= j; i++) P[lk1++] = P[lk++];
}
for (j = 0; j < d - 1; j++)
P[jkl + j + 1] = store[j] + P[r + j];
}
P[jkl] = P[0];
for (i = 0; i < d; i++)
P[jkl] += delta[i] * (store[i] + 2.0 * P[r + i]);
for (i = 0; i < d; i++) store[i] = P[r + i];
for (j = 0; j < r; j++) {
kk1 = (j+1) * (2*rd - j - 2) / 2 + r;
k1 = j * (2*rd - j - 1) / 2 + r;
for (i = 0; i < d; i++) {
kk = kk1 + i;
k = k1 + i;
P[k] = phi[j] * store[i];
if (j < r - 1) P[k] += P[kk];
}
}
for (j = 0; j < r; j++) {
store[j] = 0.0;
kkk = (j + 1) * (i45 - j - 1) / 2 - d;
for (i = 0; i < d; i++) store[j] += delta[i] * P[kkk++];
}
for (j = 0; j < r; j++) {
k = (j + 1) * (rd + 1) - (j + 1) * (j + 2) / 2;
for (i = 0; i < d - 1; i++) {
--k;
P[k] = P[k - 1];
}
}
for (j = 0; j < r; j++) {
k = j * (2*rd - j - 1) / 2 + r;
P[k] = store[j] + phi[j] * P[0];
if (j < r - 1) P[k] += P[j + 1];
}
}
for (i = 0; i < r; i++) store[i] = P[i];
ind = 0;
dt = P[0];
for (j = 0; j < r; j++) {
phij = phi[j];
phijdt = phij * dt;
ind2 = j * (2*rd - j + 1) / 2 - 1;
ind1 = (j + 1) * (i45 - j - 1) / 2 - 1;
for (i = j; i < r; i++) {
++ind2;
phii = phi[i];
P[ind2] = V[ind++] + phii * phijdt;
if (j < r - 1) P[ind2] += store[j + 1] * phii;
if (i < r - 1)
P[ind2] += store[i + 1] * phij + P[++ind1];
}
}
/* predict y */
y[l] = a[0];
for (j = 0; j < d; j++) y[l] += a[r + j] * delta[j];
/* calculate m.s.e. of y */
ams = P[0];
if (d > 0) {
for (j = 0; j < d; j++) {
k = r * (i45 - r) / 2 + j * (2*d + 1 - j) / 2;
tmp = delta[j];
ams += 2.0 * tmp * P[r + j] + P[k] * tmp * tmp;
}
for (j = 0; j < d - 1; j++) {
k = r * (i45 - r) / 2 + 1 + j * (2*d + 1 - j) / 2;
for (i = j + 1; i < d; i++)
ams += 2.0 * delta[i] * delta[j] * P[k++];
}
}
amse[l] = ams * sigma2;
}
return;
}
