/*
* 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) */
/*----------------------------------------------------------------------------------------------------------------------------
------------------------------------------------------------------------------------------------------------------------------
MAIN FUNCTION
------------------------------------------------------------------------------------------------------------------------------
------------------------------------------------------------------------------------------------------------------------------ */
SEXP local_poly_estimator(SEXP X, SEXP Y, SEXP points, SEXP band, SEXP grid1, SEXP degree_poly, SEXP kernel_type1, SEXP deriv1)
{
int i, j;
i = 0;j = 0;
/* Digest the datastructures (SEXPs) from R */
double *xptr, *yptr, *grid;
int kernel_type = INTEGER_VALUE(kernel_type1);
int degree_pol = INTEGER_VALUE(degree_poly);
int deriv = INTEGER_VALUE(deriv1);
PROTECT(grid1 = coerceVector (grid1, REALSXP) ) ;
grid = REAL(grid1);
SEXP dimgrid = coerceVector(getAttrib(grid1, R_DimSymbol), INTSXP);
int n_grid = INTEGER(dimgrid)[1];
// get dimensions of matrix X
SEXP dimX = coerceVector(getAttrib(X, R_DimSymbol), INTSXP);
d = INTEGER(dimX)[0];
n = INTEGER(dimX)[1];
// get dimensions of matrix points
double *pontos;
int n_pontos, d_pontos;
SEXP dimpoints = coerceVector(getAttrib(points, R_DimSymbol), INTSXP);
d_pontos = INTEGER(dimpoints)[0];
n_pontos = INTEGER(dimpoints)[1];
if ((d > 1) && (d_pontos == 1)) // X is a matrix n by d and points is a vector
{ // then, points is one point of d dimension
n_pontos = 1;
d_pontos = d;
}
PROTECT(X = coerceVector (X, REALSXP) ) ;
xptr = REAL(X);
PROTECT(Y = coerceVector (Y, REALSXP) ) ;
yptr = REAL(Y);
PROTECT(points = coerceVector (points, REALSXP) ) ;
pontos = REAL(points);
// aux is at each step the point x at which we predict y
double aux[d];
int k;
// pred is the predicted values that will be returned
SEXP pred;
double *p_pred;
PROTECT(pred = NEW_NUMERIC(n_pontos));
p_pred = NUMERIC_POINTER(pred);
PROTECT(band = coerceVector (band, REALSXP) ) ;
double * banda = REAL(band);
// banda must have dimensions: n_points by d
SEXP bandwidth;
double *p_bandwidth;
PROTECT(bandwidth = NEW_NUMERIC(d*n_pontos));
p_bandwidth = NUMERIC_POINTER(bandwidth);
// ------------------------------------------------------------- Cross Validation or GCV
if ((banda[0] == 0) || (banda[0] == -1))
{
GCV(xptr, yptr, n , d , kernel_type, grid, n_grid, degree_pol, deriv, p_bandwidth);
for (i = 1; i < n_pontos; i++)
for (j = 0; j < d; j++)
p_bandwidth[i*d + j] = p_bandwidth[j];
} else
// ------------------------------------------------------------- Cross Validation or GCV multidimensional
if ((banda[0] == -2) || (banda[0] == -3))
{
GCV_each_dimens(xptr, yptr, n , d , kernel_type, grid, n_grid, degree_pol, deriv, p_bandwidth);
for (i = 1; i < n_pontos; i++)
for (j = 0; j < d; j++)
p_bandwidth[i*d + j] = p_bandwidth[j];
} else
// -------------------------------------------------------------
{ // if no cross-validation, I still need to fill the matrix of bandwidths
// where each row correspond to a point in 'points' sent by the user here
for (i = 0; i < n_pontos; i++)
for (j = 0; j < d; j++)
p_bandwidth[i*d + j] = banda[i*d + j];
}
// variables used to solve (X'X)^-1X'Y
const int m = n;
int n2;
if (degree_pol == 1)
n2 = 1 + d;
else if (degree_pol == 2)
n2 = 1+d + d*(d+1)/2;
else
n2 = degree_pol + 1;
double a[n2*n]; // this will be X
double b[n]; // this will be Y
const int nrhs = 1;
const int lda = n;
const int ldb = n;
int lwork;
int mn = m;
if (n2 < m)
mn = n2;
if (mn == 1)
lwork = mn + 1;
else
lwork = mn + mn;
int info = 0;
double work[lwork];
for(i = 0; i < lwork; i++)
work[i] = 0;
// ------------------------------------------------------------------------------------------------- Prediction
for (i = 0; i < n_pontos; i++)
{
// ------------------------------------ construct aux
//aux is the point where m1 is to be estimated
if (d == 1)
aux[0] = pontos[i];
else
if (n_pontos == 1) // here, X is a matrix n by d (d>1)
for (j = 0; j < d; j++) //and points is a vector size d, thus there is 1 point
aux[j] = pontos[j];
else
{
for (j = 0; j < d; j++)
aux[j] = pontos[i*d + j];
}
// for each observation in X construct a and obtain beta_hat_0 = m_hat(aux)
for (j = 0; j < n; j++)
{
// construct a = sqrt(W)XX
a[j] = 1;
for (k = 1; k <= d; k++)
a[j] = a[j]*sqrt(K(kernel_type, (xptr[j*d + k-1]-aux[k-1])/p_bandwidth[i*d + k-1])); // for a vector of bandwidths
if ((degree_pol == 1) || (degree_pol == 2)) // add columns X1-x, X2-x,... Xd-x
for (k = 1; k <= d; k++)
a[j+n*k] = (xptr[j*d + k-1]-aux[k-1])*a[j]; // note that a is transpose manner
if (degree_pol == 2) // include columns of half vectorization: VECH
{
int l, ind_vech;
ind_vech = 1;
for (k = 1; k <= d; k++)
for (l = k; l <= d; l++)
{
a[j+n*d+n*ind_vech] = (xptr[j*d + k-1]-aux[k-1])*(xptr[j*d + l-1]-aux[l-1])*a[j];
ind_vech = ind_vech + 1;
}
}
if ((degree_pol > 2) && (d == 1)) // works only for d == 1
for (k = 1; k <= degree_pol; k++)
a[j+n*k] = pow((xptr[j]-aux[0]),k)*a[j];
b[j] = yptr[j]*a[j]; // b = sqrt(W)Y
}
// reg does (a'a)^-1a'b
reg(&m, &n2, &nrhs, a, &lda, b, &ldb, work, &lwork, &info);
p_pred[i] = factorial(deriv)*b[deriv];
}
// -------------------------------------------------------------------------------------------------- Prediction
SEXP list, list_names;
char *names[2] = {"predicted", "bandwidth"};
PROTECT(list_names = allocVector(STRSXP,2));
PROTECT(list = allocVector(VECSXP, 2));
for(i = 0; i < 2; i++)
SET_STRING_ELT(list_names,i,mkChar(names[i]));
SET_VECTOR_ELT(list, 0, pred);
SET_VECTOR_ELT(list, 1, bandwidth);
setAttrib(list, R_NamesSymbol, list_names);
UNPROTECT( 9 ) ;
return(list);
}
/*
* 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 */