/*
* n_vars is the number of variables to be considered,
* d is the data array of variables d[0],...,d[n_vars-1],
* pred determines which estimate is required: BLUE, BLUP, or BLP
*/
void gls(DATA **d /* pointer to DATA array */,
int n_vars, /* length of DATA array (to consider) */
enum GLS_WHAT pred, /* what type of prediction is requested */
DPOINT *where, /* prediction location */
double *est /* output: array that holds the predicted values and variances */)
{
GLM *glm = NULL; /* to be copied to/from d */
static MAT *X0 = MNULL, *C0 = MNULL, *MSPE = MNULL, *CinvC0 = MNULL,
*Tmp1 = MNULL, *Tmp2 = MNULL, *Tmp3 = MNULL, *R = MNULL;
static VEC *blup = VNULL, *tmpa = VNULL, *tmpb = VNULL;
PERM *piv = PNULL;
volatile unsigned int i, rows_C;
unsigned int j, k, l = 0, row, col, start_i, start_j, start_X, global,
one_nbh_empty;
VARIOGRAM *v = NULL;
static enum GLS_WHAT last_pred = GLS_INIT; /* the initial value */
double c_value, *X_ori;
int info;
if (d == NULL) { /* clean up */
if (X0 != MNULL) M_FREE(X0);
if (C0 != MNULL) M_FREE(C0);
if (MSPE != MNULL) M_FREE(MSPE);
if (CinvC0 != MNULL) M_FREE(CinvC0);
if (Tmp1 != MNULL) M_FREE(Tmp1);
if (Tmp2 != MNULL) M_FREE(Tmp2);
if (Tmp3 != MNULL) M_FREE(Tmp3);
if (R != MNULL) M_FREE(R);
if (blup != VNULL) V_FREE(blup);
if (tmpa != VNULL) V_FREE(tmpa);
if (tmpb != VNULL) V_FREE(tmpb);
last_pred = GLS_INIT;
return;
}
if (DEBUG_COV) {
printlog("we're at %s X: %g Y: %g Z: %g\n",
IS_BLOCK(where) ? "block" : "point",
where->x, where->y, where->z);
}
if (pred != UPDATE) /* it right away: */
last_pred = pred;
assert(last_pred != GLS_INIT);
if (d[0]->glm == NULL) { /* allocate and initialize: */
glm = new_glm();
d[0]->glm = (void *) glm;
} else
glm = (GLM *) d[0]->glm;
glm->mu0 = v_resize(glm->mu0, n_vars);
MSPE = m_resize(MSPE, n_vars, n_vars);
if (pred == GLS_BLP || UPDATE_BLP) {
X_ori = where->X;
for (i = 0; i < n_vars; i++) { /* mu(0) */
glm->mu0->ve[i] = calc_mu(d[i], where);
blup = v_copy(glm->mu0, v_resize(blup, glm->mu0->dim));
where->X += d[i]->n_X; /* shift to next x0 entry */
}
where->X = X_ori; /* ... and set back */
for (i = 0; i < n_vars; i++) { /* Cij(0,0): */
for (j = 0; j <= i; j++) {
v = get_vgm(LTI(d[i]->id,d[j]->id));
ME(MSPE, i, j) = ME(MSPE, j, i) = COVARIANCE0(v, where, where, d[j]->pp_norm2);
}
}
fill_est(NULL, blup, MSPE, n_vars, est); /* in case of empty neighbourhood */
}
/* xxx */
/*
logprint_variogram(v, 1);
*/
/*
* selection dependent problem dimensions:
*/
for (i = rows_C = 0, one_nbh_empty = 0; i < n_vars; i++) {
rows_C += d[i]->n_sel;
if (d[i]->n_sel == 0)
one_nbh_empty = 1;
}
if (rows_C == 0 /* all selection lists empty */
|| one_nbh_empty == 1) { /* one selection list empty */
if (pred == GLS_BLP || UPDATE_BLP)
debug_result(blup, MSPE, pred);
return;
}
for (i = 0, global = 1; i < n_vars && global; i++)
global = (d[i]->sel == d[i]->list
&& d[i]->n_list == d[i]->n_original
&& d[i]->n_list == d[i]->n_sel);
/*
* global things: enter whenever (a) first time, (b) local selections or
* (c) the size of the problem grew since the last call (e.g. simulation)
*/
if (glm->C == NULL || !global || rows_C > glm->C->m) {
/*
* fill y:
*/
glm->y = get_y(d, glm->y, n_vars);
if (pred != UPDATE) {
glm->C = m_resize(glm->C, rows_C, rows_C);
if (gl_choleski == 0) /* use LDL' decomposition, allocate piv: */
piv = px_resize(piv, rows_C);
m_zero(glm->C);
glm->X = get_X(d, glm->X, n_vars);
M_DEBUG(glm->X, "X");
glm->CinvX = m_resize(glm->CinvX, rows_C, glm->X->n);
glm->XCinvX = m_resize(glm->XCinvX, glm->X->n, glm->X->n);
glm->beta = v_resize(glm->beta, glm->X->n);
for (i = start_X = start_i = 0; i < n_vars; i++) { /* row var */
/* fill C, mu: */
for (j = start_j = 0; j <= i; j++) { /* col var */
v = get_vgm(LTI(d[i]->id,d[j]->id));
for (k = 0; k < d[i]->n_sel; k++) { /* rows */
row = start_i + k;
for (l = 0, col = start_j; col <= row && l < d[j]->n_sel; l++, col++) {
if (pred == GLS_BLUP)
c_value = GCV(v, d[i]->sel[k], d[j]->sel[l]);
else
c_value = COVARIANCE(v, d[i]->sel[k], d[j]->sel[l]);
/* on the diagonal, if necessary, add measurement error variance */
if (d[i]->colnvariance && i == j && k == l)
c_value += d[i]->sel[k]->variance;
ME(glm->C, col, row) = c_value; /* fill upper */
if (col != row)
ME(glm->C, row, col) = c_value; /* fill all */
} /* for l */
} /* for k */
start_j += d[j]->n_sel;
} /* for j */
start_i += d[i]->n_sel;
if (d[i]->n_sel > 0)
start_X += d[i]->n_X - d[i]->n_merge;
} /* for i */
/*
if (d[0]->colnvmu)
glm->C = convert_vmuC(glm->C, d[0]);
*/
if (d[0]->variance_fn) {
glm->mu = get_mu(glm->mu, glm->y, d, n_vars);
convert_C(glm->C, glm->mu, d[0]->variance_fn);
}
if (DEBUG_COV && pred == GLS_BLUP)
printlog("[using generalized covariances: max_val - semivariance()]");
M_DEBUG(glm->C, "Covariances (x_i, x_j) matrix C (upper triangle)");
/*
* factorize C:
*/
CHfactor(glm->C, piv, &info);
if (info != 0) { /* singular: */
pr_warning("Covariance matrix singular at location [%g,%g,%g]: skipping...",
where->x, where->y, where->z);
m_free(glm->C);
glm->C = MNULL; /* assure re-entrance if global */
P_FREE(piv);
return;
}
if (piv == NULL)
M_DEBUG(glm->C, "glm->C, Choleski decomposed:")
else
M_DEBUG(glm->C, "glm->C, LDL' decomposed:")
} /* if (pred != UPDATE) */
/*
* n_vars is the number of variables to be considered,
* d is the data array of variables d[0],...,d[n_vars-1],
* pred determines which estimate is required: BLUE, BLUP, or BLP
*/
void gls(DATA **d /* pointer to DATA array */,
int n_vars, /* length of DATA array (to consider) */
enum GLS_WHAT pred, /* what type of prediction is requested */
DPOINT *where, /* prediction location */
double *est /* output: array that holds the predicted values and variances */)
{
GLM *glm = NULL; /* to be copied to/from d */
static MAT *X0 = MNULL, *C0 = MNULL, *MSPE = MNULL, *CinvC0 = MNULL,
*Tmp1 = MNULL, *Tmp2 = MNULL, *Tmp3, *R = MNULL;
static VEC *blup = VNULL, *tmpa = VNULL, *tmpb = VNULL;
volatile unsigned int i, rows_C;
unsigned int j, k, l = 0, row, col, start_i, start_j, start_X, global;
VARIOGRAM *v = NULL;
static enum GLS_WHAT last_pred = GLS_INIT; /* the initial value */
double c_value, *X_ori;
if (d == NULL) { /* clean up */
if (X0 != MNULL) M_FREE(X0);
if (C0 != MNULL) M_FREE(C0);
if (MSPE != MNULL) M_FREE(MSPE);
if (CinvC0 != MNULL) M_FREE(CinvC0);
if (Tmp1 != MNULL) M_FREE(Tmp1);
if (Tmp2 != MNULL) M_FREE(Tmp2);
if (Tmp3 != MNULL) M_FREE(Tmp3);
if (R != MNULL) M_FREE(R);
if (blup != VNULL) V_FREE(blup);
if (tmpa != VNULL) V_FREE(tmpa);
if (tmpb != VNULL) V_FREE(tmpb);
last_pred = GLS_INIT;
return;
}
#ifndef HAVE_SPARSE
if (gl_sparse) {
pr_warning("sparse matrices not supported: compile with --with-sparse");
gl_sparse = 0;
}
#endif
if (DEBUG_COV) {
printlog("we're at %s X: %g Y: %g Z: %g\n",
IS_BLOCK(where) ? "block" : "point",
where->x, where->y, where->z);
}
if (pred != UPDATE) /* it right away: */
last_pred = pred;
assert(last_pred != GLS_INIT);
if (d[0]->glm == NULL) { /* allocate and initialize: */
glm = new_glm();
d[0]->glm = (void *) glm;
} else
glm = (GLM *) d[0]->glm;
glm->mu0 = v_resize(glm->mu0, n_vars);
MSPE = m_resize(MSPE, n_vars, n_vars);
if (pred == GLS_BLP || UPDATE_BLP) {
X_ori = where->X;
for (i = 0; i < n_vars; i++) { /* mu(0) */
glm->mu0->ve[i] = calc_mu(d[i], where);
blup = v_copy(glm->mu0, v_resize(blup, glm->mu0->dim));
where->X += d[i]->n_X; /* shift to next x0 entry */
}
where->X = X_ori; /* ... and set back */
for (i = 0; i < n_vars; i++) { /* Cij(0,0): */
for (j = 0; j <= i; j++) {
v = get_vgm(LTI(d[i]->id,d[j]->id));
MSPE->me[i][j] = MSPE->me[j][i] = COVARIANCE0(v, where, where, d[j]->pp_norm2);
}
}
fill_est(NULL, blup, MSPE, n_vars, est); /* in case of empty neighbourhood */
}
/* xxx */
/*
logprint_variogram(v, 1);
*/
/*
* selection dependent problem dimensions:
*/
for (i = rows_C = 0; i < n_vars; i++)
rows_C += d[i]->n_sel;
if (rows_C == 0) { /* empty selection list(s) */
if (pred == GLS_BLP || UPDATE_BLP)
debug_result(blup, MSPE, pred);
return;
}
for (i = 0, global = 1; i < n_vars && global; i++)
global = (d[i]->sel == d[i]->list && d[i]->n_list == d[i]->n_original);
/*
* global things: enter whenever (a) first time, (b) local selections or
* (c) the size of the problem grew since the last call (e.g. simulation)
*/
if ((glm->C == NULL && glm->spC == NULL) || !global || rows_C > glm->C->m) {
/*
* fill y:
*/
glm->y = get_y(d, glm->y, n_vars);
if (pred != UPDATE) {
if (! gl_sparse) {
glm->C = m_resize(glm->C, rows_C, rows_C);
m_zero(glm->C);
}
#ifdef HAVE_SPARSE
else {
if (glm->C == NULL) {
glm->spC = sp_get(rows_C, rows_C, gl_sparse);
/* d->spLLT = spLLT = sp_get(rows_C, rows_C, gl_sparse); */
} else {
glm->spC = sp_resize(glm->spC, rows_C, rows_C);
/* d->spLLT = spLLT = sp_resize(spLLT, rows_C, rows_C); */
}
sp_zero(glm->spC);
}
#endif
glm->X = get_X(d, glm->X, n_vars);
M_DEBUG(glm->X, "X");
glm->CinvX = m_resize(glm->CinvX, rows_C, glm->X->n);
glm->XCinvX = m_resize(glm->XCinvX, glm->X->n, glm->X->n);
glm->beta = v_resize(glm->beta, glm->X->n);
for (i = start_X = start_i = 0; i < n_vars; i++) { /* row var */
/* fill C, mu: */
for (j = start_j = 0; j <= i; j++) { /* col var */
v = get_vgm(LTI(d[i]->id,d[j]->id));
for (k = 0; k < d[i]->n_sel; k++) { /* rows */
row = start_i + k;
for (l = 0, col = start_j; col <= row && l < d[j]->n_sel; l++, col++) {
if (pred == GLS_BLUP)
c_value = GCV(v, d[i]->sel[k], d[j]->sel[l]);
else
c_value = COVARIANCE(v, d[i]->sel[k], d[j]->sel[l]);
/* on the diagonal, if necessary, add measurement error variance */
if (d[i]->colnvariance && i == j && k == l)
c_value += d[i]->sel[k]->variance;
if (! gl_sparse)
glm->C->me[row][col] = c_value;
#ifdef HAVE_SPARSE
else {
if (c_value != 0.0)
sp_set_val(glm->spC, row, col, c_value);
}
#endif
} /* for l */
} /* for k */
start_j += d[j]->n_sel;
} /* for j */
start_i += d[i]->n_sel;
if (d[i]->n_sel > 0)
start_X += d[i]->n_X - d[i]->n_merge;
} /* for i */
/*
if (d[0]->colnvmu)
glm->C = convert_vmuC(glm->C, d[0]);
*/
if (d[0]->variance_fn) {
glm->mu = get_mu(glm->mu, glm->y, d, n_vars);
convert_C(glm->C, glm->mu, d[0]->variance_fn);
}
if (DEBUG_COV && pred == GLS_BLUP)
printlog("[using generalized covariances: max_val - semivariance()]");
if (! gl_sparse) {
M_DEBUG(glm->C, "Covariances (x_i, x_j) matrix C (lower triangle only)");
}
#ifdef HAVE_SPARSE
else {
SM_DEBUG(glm->spC, "Covariances (x_i, x_j) sparse matrix C (lower triangle only)")
}
#endif
/* check for singular C: */
if (! gl_sparse && gl_cn_max > 0.0) {
for (i = 0; i < rows_C; i++) /* row */
for (j = i+1; j < rows_C; j++) /* col > row */
glm->C->me[i][j] = glm->C->me[j][i]; /* fill symmetric */
if (is_singular(glm->C, gl_cn_max)) {
pr_warning("Covariance matrix (nearly) singular at location [%g,%g,%g]: skipping...",
where->x, where->y, where->z);
m_free(glm->C); glm->C = MNULL; /* assure re-entrance if global */
return;
}
}
/*
* factorize C:
*/
if (! gl_sparse)
LDLfactor(glm->C);
#ifdef HAVE_SPARSE
else {
sp_compact(glm->spC, 0.0);
spCHfactor(glm->spC);
}
#endif
} /* if (pred != UPDATE) */
if (pred != GLS_BLP && !UPDATE_BLP) { /* C-1 X and X'C-1 X, beta */
/*
* calculate CinvX:
*/
tmpa = v_resize(tmpa, rows_C);
for (i = 0; i < glm->X->n; i++) {
tmpa = get_col(glm->X, i, tmpa);
if (! gl_sparse)
tmpb = LDLsolve(glm->C, tmpa, tmpb);
#ifdef HAVE_SPARSE
else
tmpb = spCHsolve(glm->spC, tmpa, tmpb);
#endif
set_col(glm->CinvX, i, tmpb);
}
/*
* calculate X'C-1 X:
*/
glm->XCinvX = mtrm_mlt(glm->X, glm->CinvX, glm->XCinvX); /* X'C-1 X */
M_DEBUG(glm->XCinvX, "X'C-1 X");
if (gl_cn_max > 0.0 && is_singular(glm->XCinvX, gl_cn_max)) {
pr_warning("X'C-1 X matrix (nearly) singular at location [%g,%g,%g]: skipping...",
where->x, where->y, where->z);
m_free(glm->C); glm->C = MNULL; /* assure re-entrance if global */
return;
}
m_inverse(glm->XCinvX, glm->XCinvX);
/*
* calculate beta:
*/
tmpa = vm_mlt(glm->CinvX, glm->y, tmpa); /* X'C-1 y */
glm->beta = vm_mlt(glm->XCinvX, tmpa, glm->beta); /* (X'C-1 X)-1 X'C-1 y */
V_DEBUG(glm->beta, "beta");
M_DEBUG(glm->XCinvX, "Cov(beta), (X'C-1 X)-1");
M_DEBUG(R = get_corr_mat(glm->XCinvX, R), "Corr(beta)");
} /* if pred != GLS_BLP */
} /* if redo the heavy part */