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(root)/tags/Matrix-pre-lmer-move/src/lmer.c – Rev 1579
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#include "lmer.h"/*** Check validity of an lmer object.** @param x Pointer to an lmer object** @return TRUE if the object is a valid lmer object, else a string* describing the nature of the violation.*/SEXP lmer_validate(SEXP x){SEXP/* ZZxP = GET_SLOT(x, Matrix_ZZxSym), */ZtXP = GET_SLOT(x, Matrix_ZtXSym),XtXP = GET_SLOT(x, Matrix_XtXSym),RZXP = GET_SLOT(x, Matrix_RZXSym),RXXP = GET_SLOT(x, Matrix_RXXSym)/* , cnames = GET_SLOT(x, Matrix_cnamesSym) */;int *ZtXd = INTEGER(getAttrib(ZtXP, R_DimSymbol)),*XtXd = INTEGER(getAttrib(XtXP, R_DimSymbol));if (!(isReal(ZtXP) && isReal(XtXP) && isReal(RZXP) && isReal(RXXP) ))return mkString(_("Slots ZtX, XtX, RZX, and RXX must be real matrices"));if (!match_mat_dims(ZtXd, INTEGER(getAttrib(RZXP, R_DimSymbol))))return mkString(_("Dimensions of slots ZtX and RZX must match"));if (!match_mat_dims(XtXd, INTEGER(getAttrib(RXXP, R_DimSymbol))))return mkString(_("Dimensions of slots XtX and RXX must match"));if (ZtXd[1] != XtXd[0] || XtXd[0] != XtXd[1])return mkString(_("Slots XtX must be a square matrix with same no. of cols as ZtX"));return ScalarLogical(1);}/*** Create the pairwise crosstabulation of the elements of flist.** @param flist pointer to the factor list.* @param nobs number of observations.* @param nc number of columns in the model matrices.** @return the pairwise crosstabulation in the form of the ZtZ array.* This version does not fill in the counts as they are not needed.*/static SEXPlmer_crosstab(SEXP flist, int nobs, const int nc[]){int i, nf = length(flist);int npairs = (nf * (nf + 1))/2;SEXP val = PROTECT(allocVector(VECSXP, npairs));SEXP cscbCl = PROTECT(MAKE_CLASS("dgBCMatrix"));int *Ti = Calloc(nobs, int),*nlevs = Calloc(nf, int),**zb = Calloc(nf, int*); /* zero-based indices */for (i = 0; i < nf; i++) { /* populate the zb vectors */SEXP fi = VECTOR_ELT(flist, i);int j;zb[i] = Calloc(nobs, int);nlevs[i] = length(getAttrib(fi, R_LevelsSymbol));for (j = 0; j < nobs; j++) zb[i][j] = INTEGER(fi)[j] - 1;for (j = 0; j <= i; j++) {int *ijp, ind = Lind(i, j), nnz;SEXP ZZij;SET_VECTOR_ELT(val, ind, ZZij = NEW_OBJECT(cscbCl));ijp = INTEGER(ALLOC_SLOT(ZZij, Matrix_pSym,INTSXP, nlevs[j] + 1));triplet_to_col(nlevs[i], nlevs[j], nobs,zb[i], zb[j], (double *) NULL,ijp, Ti, (double *) NULL);nnz = ijp[nlevs[j]];Memcpy(INTEGER(ALLOC_SLOT(ZZij, Matrix_iSym, INTSXP, nnz)),Ti, nnz);}}for (i = 0; i < nf; i++) Free(zb[i]);Free(zb); Free(nlevs); Free(Ti);UNPROTECT(2);return val;}/*** Allocate the x slot in an dgBCMatrix object** mm Pointer to a dgBCMatrix object* nr number of rows per block* nc number of columns per block*/#define ALLOC_X_SLOT(mm, nr, nc) \SET_SLOT(mm, Matrix_xSym, alloc3Darray(REALSXP, nr, nc, \length(GET_SLOT(mm, Matrix_iSym))))/*** Permute the levels of one of the grouping factors in a bCrosstab object** @param ctab Pointer to a bCrosstab object* @param nf number of factors in ctab* @param jj index (0-based) of the factor levels to permute* @param nlev number of levels of the grouping factors* @param iperm inverse of the permutation*/static voidbCrosstab_permute(SEXP ctab, int nf, int jj,const int nlev[], const int iperm[]){int j;for (j = 0; j < nf; j++) {int ind = (j < jj ? Lind(jj, j) : Lind(j, jj)),ncol = (j < jj ? nlev[j] : nlev[jj]),nrow = (j < jj ? nlev[jj] : nlev[j]);SEXP cscb = VECTOR_ELT(ctab, ind),cscbi = GET_SLOT(cscb, Matrix_iSym);int *cp = INTEGER(GET_SLOT(cscb, Matrix_pSym)),nnz = length(cscbi);int *mj = expand_cmprPt(ncol, cp, Calloc(nnz, int));int *mi = Memcpy(Calloc(nnz, int), INTEGER(cscbi), nnz);if (j <= jj) int_permute(mi, nnz, iperm);if (j >= jj) int_permute(mj, nnz, iperm);if (j == jj) make_upper_triangular(mi, mj, nnz);triplet_to_col(nrow, ncol, nnz, mi, mj, (double *) NULL,cp, INTEGER(cscbi), (double *) NULL);Free(mi); Free(mj);}}/*** Apply a permutation of the rows and columns to a sparse symmetric* matrix object.** @param A A sparse, symmetric matrix object stored in the upper* triangle* @param nlev order of A* @param iperm A 0-based permutation of length nlev*/static voidsymmetric_permute(int Ap[], int Ai[], int n, const int iperm[]){int nnz = Ap[n];int *mj = expand_cmprPt(n, Ap, Calloc(nnz, int));int *mi = Memcpy(Calloc(nnz, int), Ai, nnz);int_permute(mi, nnz, iperm);int_permute(mj, nnz, iperm);make_upper_triangular(mi, mj, nnz);triplet_to_col(n, n, nnz, mi, mj, (double *) NULL,Ap, Ai, (double *) NULL);Free(mi); Free(mj);}/*** Apply a permutation vector to the levels of a factor.** The dest pointer is assumed to point to a copy of the src pointer's* contents.** @param dest pointer to the destination factor* @param src pointer to the source factor* @param perm permutation vector (0-based)* @param iperm inverse permutation vector (0-based)*/static voidfactor_levels_permute(SEXP dest, SEXP src, const int perm[],const int iperm[]){SEXP dlev = getAttrib(dest, R_LevelsSymbol),slev = getAttrib(src, R_LevelsSymbol);int nlev = length(dlev), flen = length(dest);int *d = INTEGER(dest), *s = INTEGER(src), i;if (length(slev) != nlev)error(_("number of levels in src and dest must match"));if (length(src) != flen)error(_("length of src and dest must match"));for (i = 0; i < nlev; i++)SET_STRING_ELT(dlev, i, STRING_ELT(slev, perm[i]));for (i = 0; i < flen; i++)d[i] = 1 + iperm[s[i]-1];}/*** Create and populate slots in an lmer object from the blocked crosstabulation.** @param val Pointer to an lmer object*/voidlmer_populate(SEXP val){SEXP D, L, Parent, ZZpO,flist = GET_SLOT(val, Matrix_flistSym),perm, Omega, ZtZ = GET_SLOT(val, Matrix_ZtZSym);SEXP fnms = getAttrib(flist, R_NamesSymbol);int j, k, nf = length(flist);int *nc = INTEGER(GET_SLOT(val, Matrix_ncSym)), *Gp,*nlev = Calloc(nf, int), npairs = (nf * (nf + 1))/2;char *statnms[] = {"factored", "inverted", ""},*devnms[] = {"ML", "REML", ""},*pnms[] = {"index", "block", ""};/* Allocate fixed-sized slots */SET_SLOT(val, Matrix_statusSym, Matrix_make_named(LGLSXP, statnms));SET_SLOT(val, Matrix_devianceSym, Matrix_make_named(REALSXP, devnms));SET_SLOT(val, Matrix_devCompSym, allocVector(REALSXP, 4));/* Allocate slots that are lists of length nf */ZZpO = ALLOC_SLOT(val, Matrix_ZZpOSym, VECSXP, nf);setAttrib(ZZpO, R_NamesSymbol, duplicate(fnms));D = ALLOC_SLOT(val, Matrix_DSym, VECSXP, nf);setAttrib(D, R_NamesSymbol, duplicate(fnms));perm = ALLOC_SLOT(val, Matrix_permSym, VECSXP, nf);setAttrib(perm, R_NamesSymbol, duplicate(fnms));Parent = ALLOC_SLOT(val, Matrix_ParentSym, VECSXP, nf);setAttrib(Parent, R_NamesSymbol, duplicate(fnms));Omega = ALLOC_SLOT(val, Matrix_OmegaSym, VECSXP, nf);setAttrib(Omega, R_NamesSymbol, duplicate(fnms));/* Allocate peculiar length slots */L = ALLOC_SLOT(val, Matrix_LSym, VECSXP, npairs);Gp = INTEGER(ALLOC_SLOT(val, Matrix_GpSym, INTSXP, nf + 1));Gp[0] = 0;for (j = 0; j < nf; j++) {nlev[j] = length(getAttrib(VECTOR_ELT(flist, j), R_LevelsSymbol));Gp[j + 1] = Gp[j] + nc[j] * nlev[j];SET_VECTOR_ELT(D, j, alloc3Darray(REALSXP, nc[j], nc[j], nlev[j]));AZERO(REAL(VECTOR_ELT(D, j)), nc[j] * nc[j] * nlev[j]);SET_VECTOR_ELT(Omega, j, allocMatrix(REALSXP, nc[j], nc[j]));SET_VECTOR_ELT(ZZpO, j, duplicate(VECTOR_ELT(ZtZ, Lind(j, j))));for (k = j; k < nf; k++)SET_VECTOR_ELT(L, Lind(k, j),duplicate(VECTOR_ELT(ZtZ, Lind(k, j))));}SET_SLOT(val, Matrix_XtXSym, allocMatrix(REALSXP, nc[nf], nc[nf]));AZERO(REAL(GET_SLOT(val, Matrix_XtXSym)), nc[nf] * nc[nf]);SET_SLOT(val, Matrix_RXXSym, allocMatrix(REALSXP, nc[nf], nc[nf]));AZERO(REAL(GET_SLOT(val, Matrix_RXXSym)), nc[nf] * nc[nf]);SET_SLOT(val, Matrix_ZtXSym, allocMatrix(REALSXP, Gp[nf], nc[nf]));SET_SLOT(val, Matrix_RZXSym, allocMatrix(REALSXP, Gp[nf], nc[nf]));for (j = 0; j < nf; j++) {int dind = Lind(j, j), i;SEXP ctd = VECTOR_ELT(ZZpO, j); /* diagonal in crosstab */SEXP Ljj = VECTOR_ELT(L, dind),cpp = GET_SLOT(ctd, Matrix_pSym),cip = GET_SLOT(ctd, Matrix_iSym), parent;int *Lp = INTEGER(GET_SLOT(Ljj, Matrix_pSym)), *Perm,*cp = INTEGER(cpp),*ci = INTEGER(cip),ncj = length(cpp) - 1,nnz = length(cip);SET_VECTOR_ELT(Parent, j, Matrix_make_named(VECSXP, pnms));parent = VECTOR_ELT(Parent, j);SET_VECTOR_ELT(parent, 0, allocVector(INTSXP, ncj));SET_VECTOR_ELT(parent, 1, allocVector(INTSXP, ncj));SET_VECTOR_ELT(perm, j, allocVector(INTSXP, ncj));Perm = INTEGER(VECTOR_ELT(perm, j));if (nnz > ncj) { /* calculate fill-reducing permutation */SEXP fac = VECTOR_ELT(flist, j);SEXP fcp = PROTECT(duplicate(fac));int *iPerm = Calloc(ncj, int);ssc_metis_order(ncj, cp, ci, Perm, iPerm);/* apply to the crosstabulation, L, and ZZpO */bCrosstab_permute(ZtZ, nf, j, nlev, iPerm);bCrosstab_permute(L, nf, j, nlev, iPerm);symmetric_permute(cp, ci, nlev[j], iPerm);/* apply to the factor */factor_levels_permute(fac, fcp, Perm, iPerm);/* symbolic analysis to get Parent */R_ldl_symbolic(ncj, cp, ci, Lp, INTEGER(VECTOR_ELT(parent, 0)),(int *) NULL, (int *) NULL);for (i = 0; i < ncj; i++)INTEGER(VECTOR_ELT(parent, 1))[i] =(INTEGER(VECTOR_ELT(parent, 0))[i] < 0) ? -1 : j;nnz = Lp[ncj];SET_SLOT(Ljj, Matrix_iSym, allocVector(INTSXP, nnz));Free(iPerm); UNPROTECT(1);} else {for (i = 0; i < ncj; i++) {Lp[i] = 0;INTEGER(VECTOR_ELT(parent,0))[i] = -1;INTEGER(VECTOR_ELT(parent,1))[i] = -1;Perm[i] = i;}Lp[ncj] = 0;SET_SLOT(Ljj, Matrix_iSym, allocVector(INTSXP, 0));}for (k = j+1; k < nf; k++) { /* Update other blocks in this column */SEXP Lkj = VECTOR_ELT(L, Lind(k,j));SET_SLOT(Lkj, Matrix_iSym,lCholClgCsm(RGT, TRN, nlev[k], nlev[j],INTEGER(VECTOR_ELT(parent, 0)),GET_SLOT(Lkj, Matrix_iSym),INTEGER(GET_SLOT(Lkj, Matrix_pSym))));}for (k = j + 1; k < nf; k++) { /* Update remaining columns */SEXP db = VECTOR_ELT(ZZpO, k), Lkj = VECTOR_ELT(L, Lind(k, j));int *Lkji = INTEGER(GET_SLOT(Lkj, Matrix_iSym)),*Lkjp = INTEGER(GET_SLOT(Lkj, Matrix_pSym));SET_SLOT(db, Matrix_iSym,Matrix_lgCsyrk(1, 0, nlev[k], nlev[j], Lkji, Lkjp,1, GET_SLOT(db, Matrix_iSym),INTEGER(GET_SLOT(db, Matrix_pSym))));for (i = k + 1; i < nf; i++) {SEXP Lij = VECTOR_ELT(L, Lind(i, j)),Lik = VECTOR_ELT(L, Lind(i, k));SET_SLOT(Lik, Matrix_iSym,Matrix_lgClgCmm(0, 1, nlev[i], nlev[k], nlev[j],INTEGER(GET_SLOT(Lij, Matrix_iSym)),INTEGER(GET_SLOT(Lij, Matrix_pSym)),Lkji, Lkjp,1, GET_SLOT(Lik, Matrix_iSym),INTEGER(GET_SLOT(Lik, Matrix_pSym))));}}}for (j = 0; j < nf; j++) { /* allocate x slots in dgBCMatrix objects */ALLOC_X_SLOT(VECTOR_ELT(ZZpO, j), nc[j], nc[j]);for (k = j; k < nf; k++) {int indkj = Lind(k,j);ALLOC_X_SLOT(VECTOR_ELT(L, indkj), nc[k], nc[j]);ALLOC_X_SLOT(VECTOR_ELT(ZtZ, indkj), nc[k], nc[j]);}}/* FIXME: Use these macros from Tim Davis instead */#define EMPTY -1#define FLIP(i) (-(i)-2)#define UNFLIP(i) (((i) < EMPTY) ? FLIP(i) : (i))/* Convert blockwise Parent arrays to extended Parent arrays */for (j = 0; j < (nf - 1); j++) { /* Parent[nf] does not need conversion */SEXP Ljp1j = VECTOR_ELT(L, Lind(j + 1, j)),LpP = GET_SLOT(Ljp1j, Matrix_pSym);int *Li = INTEGER(GET_SLOT(Ljp1j, Matrix_iSym)),*Lp = INTEGER(LpP),*block = INTEGER(VECTOR_ELT(VECTOR_ELT(Parent, j), 1)),*parent = INTEGER(VECTOR_ELT(VECTOR_ELT(Parent, j), 0)),i, nlev = length(LpP) - 1;for (i = 0; i < nlev; i++) {if (block[i] < 0) {block[i] = j + 1;parent[i] = Li[Lp[i]];}}}Free(nlev);}/*** Update the arrays ZtZ, ZtX, and XtX in an lme object* according to a list of model matrices.** @param x pointer to an lmer object* @param mmats pointer to a list of model matrices** @return NULL*/SEXP lmer_update_mm(SEXP x, SEXP mmats){SEXPZtZP = GET_SLOT(x, Matrix_ZtZSym),ZtXP = GET_SLOT(x, Matrix_ZtXSym),flist = GET_SLOT(x, Matrix_flistSym);int *Gp = INTEGER(GET_SLOT(x, Matrix_GpSym)),*dims = INTEGER(getAttrib(ZtXP, R_DimSymbol)),*nc = INTEGER(GET_SLOT(x, Matrix_ncSym)),*status = LOGICAL(GET_SLOT(x, Matrix_statusSym)),nf = length(flist), nfp1 = nf + 1,i, ione = 1,nobs = nc[nfp1],pp1 = nc[nf];double*X,*XtX = REAL(GET_SLOT(x, Matrix_XtXSym)),*ZtX = REAL(ZtXP),one = 1.0, zero = 0.0;if (!isNewList(mmats) || length(mmats) != nfp1)error(_("mmats must be a list of %d model matrices"), nfp1);for (i = 0; i <= nf; i++) {SEXP mmat = VECTOR_ELT(mmats, i);int *mdims = INTEGER(getAttrib(mmat, R_DimSymbol));if (!isMatrix(mmat) || !isReal(mmat))error(_("element %d of mmats is not a numeric matrix"), i + 1);if (nobs != mdims[0])error(_("Expected %d rows in the %d'th model matrix. Got %d"),nobs, i+1, mdims[0]);if (nc[i] != mdims[1])error(_("Expected %d columns in the %d'th model matrix. Got %d"),nc[i], i+1, mdims[1]);}/* Create XtX */X = REAL(VECTOR_ELT(mmats, nf));F77_CALL(dsyrk)("U", "T", &pp1, &nobs, &one, X, &nobs, &zero, XtX, nc + nf);/* Zero an accumulator */AZERO(ZtX, pp1 * Gp[nf]);for (i = 0; i < nf; i++) {int *fac = INTEGER(VECTOR_ELT(flist, i)),j, k, nci = nc[i], ZtXrows = Gp[i+1] - Gp[i];int ncisqr = nci * nci, nlev = ZtXrows/nci;double *Z = REAL(VECTOR_ELT(mmats, i)), *ZZx;for (k = 0; k < i; k++) {SEXP ZZxM = VECTOR_ELT(ZtZP, Lind(i, k));int *rowind = INTEGER(GET_SLOT(ZZxM, Matrix_iSym)),*colptr = INTEGER(GET_SLOT(ZZxM, Matrix_pSym));int *f2 = INTEGER(VECTOR_ELT(flist, k)), nck = nc[k];double *Zk = REAL(VECTOR_ELT(mmats, k));ZZx = REAL(GET_SLOT(ZZxM, Matrix_xSym));AZERO(ZZx, length(GET_SLOT(ZZxM, Matrix_xSym)));for (j = 0; j < nobs; j++) {F77_CALL(dgemm)("T", "N", nc + i, nc + k, &ione, &one,Z + j, &nobs, Zk + j, &nobs, &one,ZZx + check_csc_index(colptr, rowind,fac[j] - 1, f2[j] - 1, 0)* (nci * nck), &nci);}}ZZx = REAL(GET_SLOT(VECTOR_ELT(ZtZP, Lind(i, i)), Matrix_xSym));AZERO(ZZx, nci * nci * nlev);if (nci == 1) { /* single column in Z */for (j = 0; j < nobs; j++) {int fj = fac[j] - 1; /* factor indices are 1-based */ZZx[fj] += Z[j] * Z[j];F77_CALL(daxpy)(&pp1, Z + j, X + j, &nobs, ZtX + fj, dims);}} else {for (j = 0; j < nobs; j++) {int fj = fac[j] - 1; /* factor indices are 1-based */F77_CALL(dsyr)("U", nc + i, &one, Z + j, &nobs,ZZx + fj * ncisqr, nc + i);F77_CALL(dgemm)("T", "N", nc + i, &pp1, &ione,&one, Z + j, &nobs,X + j, &nobs, &one,ZtX + fj * nci, dims);}}ZtX += ZtXrows;}status[0] = status[1] = 0;return R_NilValue;}/*** Create an lmer object from a list of grouping factors and a list of model* matrices. There is one more model matrix than grouping factor. The last* model matrix is the fixed effects and the response.** @param flist pointer to a list of grouping factors* @param mmats pointer to a list of model matrices** @return pointer to an lmer object*/SEXP lmer_create(SEXP flist, SEXP mmats, SEXP method){SEXP val = PROTECT(NEW_OBJECT(MAKE_CLASS("mer")));SEXP ZtZ, cnames, fnms, nms;int *nc, i, nf = length(flist), nobs;/* Check validity of flist */if (!(nf > 0 && isNewList(flist)))error(_("flist must be a non-empty list"));nobs = length(VECTOR_ELT(flist, 0));if (nobs < 1) error(_("flist[[0]] must be a non-null factor"));for (i = 0; i < nf; i++) {SEXP fi = VECTOR_ELT(flist, i);if (!(isFactor(fi) && length(fi) == nobs))error(_("flist[[%d]] must be a factor of length %d"),i + 1, nobs);}SET_SLOT(val, Matrix_flistSym, duplicate(flist));/* Check mmats; allocate and populate nc */if (!(isNewList(mmats) && length(mmats) == (nf + 1)))error(_("mmats must be a list of length %d"), nf + 1);nc = INTEGER(ALLOC_SLOT(val, Matrix_ncSym, INTSXP, nf + 2));nc[nf + 1] = nobs;for (i = 0; i <= nf; i++) {SEXP mi = VECTOR_ELT(mmats, i);int *dims;if (!(isMatrix(mi) && isReal(mi)))error(_("mmats[[%d]] must be a numeric matrix"), i + 1);dims = INTEGER(getAttrib(mi, R_DimSymbol));if (dims[0] != nobs)error(_("mmats[[%d]] must have %d rows"), i + 1, nobs);if (dims[1] < 1)error(_("mmats[[%d]] must have at least 1 column"), i + 1);nc[i] = dims[1];} /* Arguments have now been checked for type, dimension, etc. *//* Create pairwise crosstabulation in ZtZ */SET_SLOT(val, Matrix_ZtZSym, lmer_crosstab(flist, nobs, nc));SET_SLOT(val, Matrix_methodSym, duplicate(method));lmer_populate(val);ZtZ = GET_SLOT(val, Matrix_ZtZSym);/* FIXME: Check for possible reordering of the factors to maximize the* number of levels (columns?) in the leading nested sequence. */fnms = getAttrib(flist, R_NamesSymbol);/* Allocate and populate cnames */cnames = ALLOC_SLOT(val, Matrix_cnamesSym, VECSXP, nf + 1);setAttrib(cnames, R_NamesSymbol, allocVector(STRSXP, nf + 1));nms = getAttrib(cnames, R_NamesSymbol);for (i = 0; i <= nf; i++) {SEXP mi = VECTOR_ELT(mmats, i);SET_VECTOR_ELT(cnames, i,duplicate(VECTOR_ELT(getAttrib(mi, R_DimNamesSymbol),1)));SET_STRING_ELT(nms, i, (i < nf) ? duplicate(STRING_ELT(fnms, i)) :mkChar(".fixed"));}lmer_update_mm(val, mmats);SET_SLOT(val, Matrix_bVarSym, duplicate(GET_SLOT(val, Matrix_DSym)));UNPROTECT(1);return val;}/*** Create and insert initial values for Omega.** @param x pointer to an lmer object** @return NULL*/SEXP lmer_initial(SEXP x){SEXP Omg = GET_SLOT(x, Matrix_OmegaSym);int *status = LOGICAL(GET_SLOT(x, Matrix_statusSym)), i, nf = length(Omg);for (i = 0; i < nf; i++) {SEXP ZZxP = GET_SLOT(VECTOR_ELT(GET_SLOT(x, Matrix_ZtZSym), Lind(i, i)),Matrix_xSym);int *dims = INTEGER(getAttrib(ZZxP, R_DimSymbol));int j, k, nzc = dims[0], nlev = dims[2];int nzcsqr = nzc * nzc, nzcp1 = nzc + 1;double *Omega = REAL(VECTOR_ELT(Omg, i)),mi = 0.375 / ((double) nlev);AZERO(Omega, nzc * nzc);for (j = 0; j < nlev; j ++) {for (k = 0; k < nzc; k++) {Omega[k * nzcp1] += REAL(ZZxP)[k * nzcp1 + j * nzcsqr] * mi;}}}status[0] = status[1] = 0;return R_NilValue;}/*** Copy ZtZ to ZZpO and L. Inflate diagonal blocks of ZZpO by Omega.* Update devComp[1].** @param x pointer to an lmer object*/SEXPlmer_inflate(SEXP x){SEXP Omg = GET_SLOT(x, Matrix_OmegaSym),ZZpO = GET_SLOT(x, Matrix_ZZpOSym),ZtZ = GET_SLOT(x, Matrix_ZtZSym),LP = GET_SLOT(x, Matrix_LSym);int *Gp = INTEGER(GET_SLOT(x, Matrix_GpSym)),*nc = INTEGER(GET_SLOT(x, Matrix_ncSym)),i, k, nf = length(Omg);double *dcmp = REAL(GET_SLOT(x, Matrix_devCompSym));for (i = 0; i < nf; i++) {SEXP ZZOel = VECTOR_ELT(ZZpO, i);SEXP ZZOm = GET_SLOT(ZZOel, Matrix_xSym);SEXP ZZel = VECTOR_ELT(ZtZ, Lind(i, i));int *Di = INTEGER(GET_SLOT(ZZOel, Matrix_iSym)),*Dp = INTEGER(GET_SLOT(ZZOel, Matrix_pSym)),*Si = INTEGER(GET_SLOT(ZZel, Matrix_iSym)),*Sp = INTEGER(GET_SLOT(ZZel, Matrix_pSym)),*dims = INTEGER(getAttrib(ZZOm, R_DimSymbol));int sz = dims[0] * dims[1];int ii, j, nci = nc[i], ncisqr = nci * nci;int nlev = (Gp[i + 1] - Gp[i])/nci;double *Omega = REAL(VECTOR_ELT(Omg, i)),*ZZ = REAL(GET_SLOT(ZZel, Matrix_xSym)),*tmp = Memcpy(Calloc(ncisqr, double), Omega, ncisqr);F77_CALL(dpotrf)("U", &nci, tmp, &nci, &j);if (j)error(_("Leading %d minor of Omega[[%d]] not positive definite"),j, i + 1);/* update dcmp[1] */for (j = 0; j < nci; j++) { /* nlev * logDet(Omega_i) */dcmp[1] += nlev * 2. * log(tmp[j * (nci + 1)]);}Free(tmp);AZERO(REAL(ZZOm), dims[0] * dims[1] * dims[2]);for (j = 0; j < nlev; j++) { /* copy diagonal block and inflate */double *ZZOkk = REAL(ZZOm) + check_csc_index(Dp, Di, j, j, 0) * sz;int kk, k2 = Sp[j + 1];for (kk = Sp[j]; kk < k2; kk++) {Memcpy(REAL(ZZOm) + check_csc_index(Dp, Di, Si[kk], j, 0) * sz,ZZ + kk * sz, sz);}for (kk = 0; kk < nci; kk++) {for (ii = 0; ii <= kk; ii++) {int ind = ii + kk * nci;ZZOkk[ind] += Omega[ind];}}}for (k = i + 1; k < nf; k++) {int ind = Lind(k, i);SEXP Lel = VECTOR_ELT(LP, ind),Lm = GET_SLOT(Lel, Matrix_xSym);double *L = REAL(Lm);dims = INTEGER(getAttrib(Lm, R_DimSymbol));ZZel = VECTOR_ELT(ZtZ, ind);ZZ = REAL(GET_SLOT(ZZel, Matrix_xSym));Di = INTEGER(GET_SLOT(Lel, Matrix_iSym));Dp = INTEGER(GET_SLOT(Lel, Matrix_pSym));Si = INTEGER(GET_SLOT(ZZel, Matrix_iSym));Sp = INTEGER(GET_SLOT(ZZel, Matrix_pSym));sz = dims[0] * dims[1];AZERO(L, sz * dims[2]); /* zero L */for (j = 0; j < nlev; j++) { /* copy src blocks to dest */int kk, k2 = Sp[j + 1];for (kk = Sp[j]; kk < k2; kk++) {Memcpy(L + check_csc_index(Dp, Di, Si[kk], j, 0) * sz,ZZ + kk * sz, sz);}}}}return R_NilValue;}/*** Convert the extended parent pair (Parent, Block) to a parent array* for the jth diagonal block of size n.** @param j index (0-based) of the diagonal outer block* @param n number of inner column blocks in the outer block* @param par array of length n to be filled with the parent array* @param ParP pointer to the extended parent structure** @return par*/static R_INLINEint *block_parent(int j, int n, int par[], SEXP ParP){SEXP Parj = VECTOR_ELT(ParP, j);int *Parent = INTEGER(VECTOR_ELT(Parj, 0)),*Block = INTEGER(VECTOR_ELT(Parj, 1)), i;for (i = 0; i < n; i++) par[i] = (Block[i] == j) ? Parent[i] : -1;return par;}/*** If status[["factored"]] is FALSE, create and factor Z'Z+Omega. Also* create RZX and RXX, the deviance components, and the value of the* deviance for both ML and REML.** @param x pointer to an lmer object** @return NULL*/SEXP lmer_factor(SEXP x){int *status = LOGICAL(GET_SLOT(x, Matrix_statusSym));if (!status[0]) {SEXP DP = GET_SLOT(x, Matrix_DSym),LP = GET_SLOT(x, Matrix_LSym),RZXP = GET_SLOT(x, Matrix_RZXSym),ZZOP = GET_SLOT(x, Matrix_ZZpOSym),Parent = GET_SLOT(x, Matrix_ParentSym);int *dims = INTEGER(getAttrib(RZXP, R_DimSymbol)),*nc = INTEGER(GET_SLOT(x, Matrix_ncSym)),*Gp = INTEGER(GET_SLOT(x, Matrix_GpSym)),i, j, nf = length(DP);int nml = nc[nf + 1], nreml = nml + 1 - nc[nf];double*RXX = REAL(GET_SLOT(x, Matrix_RXXSym)),*RZX = REAL(RZXP),*dcmp = REAL(GET_SLOT(x, Matrix_devCompSym)),*deviance = REAL(GET_SLOT(x, Matrix_devianceSym)),minus1 = -1., one = 1.;dcmp[0] = dcmp[1] = dcmp[2] = dcmp[3] = 0.;Memcpy(RZX, REAL(GET_SLOT(x, Matrix_ZtXSym)), dims[0] * dims[1]);lmer_inflate(x); /* initialize ZZpO and L */for (i = 0; i < nf; i++) {SEXP ZZOiP = VECTOR_ELT(ZZOP, i);SEXP DiP = VECTOR_ELT(DP, i);SEXP LiP = VECTOR_ELT(LP, Lind(i, i));int nlev = INTEGER(getAttrib(DiP, R_DimSymbol))[2];int jj, nci = nc[i], ncisqr = nci * nci;int *Pari = block_parent(i, nlev, Calloc(nlev, int), Parent);double *D = REAL(DiP);jj = cscb_ldl(ZZOiP, Pari, LiP, DiP);if (jj != nlev) error(_("cscb_ldl returned %d < nlev = %d"), jj, nlev);for (j = 0; j < nlev; j++) { /* accumulate dcmp[0] */double *Dj = D + j * ncisqr;for (jj = 0; jj < nci; jj++) /* accumulate determinant */dcmp[0] += 2. * log(Dj[jj * (nci + 1)]);}/* Solve L_{i,i} %*% RZX_i := RZX_i */cscb_trsm(LOW, NTR, UNT, 1., LiP,Gp[i+1] - Gp[i], dims[1], RZX + Gp[i], dims[0]);/* Solve D_i^{T/2} %*% RZX_i := RZX_i */for (jj = 0; jj < nlev; jj++) {F77_CALL(dtrsm)("L", "U", "T", "N", &nci, &dims[1],&one, D + jj * ncisqr, &nci,RZX + Gp[i] + jj * nci, dims);}for (j = i + 1; j < nf; j++) { /* further blocks */SEXP Lji = VECTOR_ELT(LP, Lind(j, i));SEXP Lx = GET_SLOT(Lji, Matrix_xSym);double *L = REAL(Lx);int *xdims = INTEGER(getAttrib(Lx, R_DimSymbol)),*Lp = INTEGER(GET_SLOT(Lji, Matrix_pSym));int ntot = xdims[0] * xdims[1];/* L_{j,i} := L_{j,i} %*% L_{i,i}^{-T} %*% D_i^{-1/2} */cscb_trcbsm(RGT, LOW, TRN, UNT, 1.0, LiP, Pari, Lji);for (jj = 0; jj < nlev; jj++) {int k, k2 = Lp[jj + 1];for (k = Lp[jj]; k < k2; k++)F77_CALL(dtrsm)("R", "U", "N", "N", xdims, xdims + 1,&one, D + jj * ncisqr, &nci,L + k * ntot, xdims);}/* RZX_j := RZX_j - (L_{j,i} %*% D_i^{T/2}) %*% RZX_i *//* At this point Lji contains L_{j,i} %*% D_i^{T/2} */cscb_mm(LFT, NTR, Gp[j + 1] - Gp[j], dims[1], Gp[i+1] - Gp[i],-1.0, Lji, RZX + Gp[i], dims[0],1.0, RZX + Gp[j], dims[0]);}for (j = i + 1; j < nf; j++) { /* block pairs and final update */SEXP Lji = VECTOR_ELT(LP, Lind(j, i));SEXP Lx = GET_SLOT(Lji, Matrix_xSym);double *L = REAL(Lx);int *xdims = INTEGER(getAttrib(Lx, R_DimSymbol)),*Lp = INTEGER(GET_SLOT(Lji, Matrix_pSym));int ntot = xdims[0] * xdims[1];/* ZZpO_{j,j} := ZZpO_{j,j} - L{j,i} %*% L_{j,i}^T */cscb_syrk(UPP, NTR, -1.0, Lji, 1.0, VECTOR_ELT(ZZOP, j));for (jj = j+1; jj < nf; jj++) {/* L_{jj,j} := L_{jj,j} - L{jj,i} %*% L_{j,i}^T */cscb_cscbm(NTR, TRN, -1.0, VECTOR_ELT(LP, Lind(jj, i)),Lji, 1.0, VECTOR_ELT(LP, Lind(jj, j)));}/* L_{j,i} := L_{j,i} %*% D_i^{-T/2} */for (jj = 0; jj < nlev; jj++) {int k, k2 = Lp[jj + 1];for (k = Lp[jj]; k < k2; k++)F77_CALL(dtrsm)("R", "U", "T", "N", xdims, xdims + 1,&one, D + jj * ncisqr, &nci,L + k * ntot, xdims);}}Free(Pari);}/* downdate and factor XtX */Memcpy(RXX, REAL(GET_SLOT(x, Matrix_XtXSym)), dims[1] * dims[1]);F77_CALL(dsyrk)("U", "T", &dims[1], &dims[0],&minus1, RZX, &dims[0], &one, RXX, dims + 1);F77_CALL(dpotrf)("U", &dims[1], RXX, &dims[1], &j);if (j) {warning(_("Leading minor of size %d of downdated X'X is indefinite"),j);dcmp[2] = dcmp[3] = deviance[0] = deviance[1] = NA_REAL;} else {for (j = 0; j < (dims[1] - 1); j++) /* 2 logDet(RXX) */dcmp[2] += 2 * log(RXX[j * (dims[1] + 1)]);dcmp[3] = 2. * log(RXX[dims[1] * dims[1] - 1]); /* 2 log(ryy) */deviance[0] = /* ML criterion */dcmp[0] - dcmp[1] + nml*(1.+dcmp[3]+log(2.*PI/nml));deviance[1] = dcmp[0] - dcmp[1] + /* REML */dcmp[2] + nreml*(1.+dcmp[3]+log(2.*PI/nreml));}status[0] = 1; status[1] = 0; /* factored but not inverted */}return R_NilValue;}/*** Solve one of the matrix equations op(L)*X=alpha*B or* X*op(L)=alpha*B where L is a sparse, blocked, unit lower triangular matrix.** @param side LFT or RGT for left or right* @param trans TRN or NTR for transpose or no transpose* @param nf number of grouping factors* @param Gp group pointers for the rows* @param n number of columns* @param alpha multiplier* @param L pointer to the L cscb object* @param B pointer to the matrix of right-hand sides* @param ldb leading dimension of array B as declared in the caller*/static voidlmer_sm(enum CBLAS_SIDE side, enum CBLAS_TRANSPOSE trans, int nf, const int Gp[],int n, double alpha, SEXP L, double B[], int ldb){int j, k;if (side == LFT) {if (trans == TRN) {for (j = nf - 1; j >= 0; j--) {int nrj = Gp[j + 1] - Gp[j];cscb_trsm(LOW, TRN, UNT, alpha, VECTOR_ELT(L, Lind(j, j)),nrj, n, B + Gp[j], ldb);for (k = 0; k < j; k++) {cscb_mm(LFT, TRN, Gp[k + 1] - Gp[k], n, nrj,-1., VECTOR_ELT(L, Lind(j, k)),B + Gp[j], ldb, alpha, B + Gp[k], ldb);}}} else error(_("Code for non-transpose case not yet written"));} else error(_("Code for right-side solutions not yet written"));}/*** Determine the maximum number of nonzero elements in a column and* allocate storage for the tmp and ind arrays.** @param j level* @param Parent Parent list** @return Maximum number of nonzero elements in a column*/static voidalloc_tmp_ind(int nf, const int nc[], const int nlevs[], SEXP Parent,double *tmp[], int *ind[]){int j, maxnc;for (maxnc = -1, j = 0; j < nf; j++) {SEXP lst = VECTOR_ELT(Parent, j);SEXP blk = VECTOR_ELT(lst, 1), par = VECTOR_ELT(lst, 0);int *nfj = Calloc(nlevs[j], int), i, val;if (nc[j] > maxnc) maxnc = nc[j];for (val = -1, i = nlevs[j] - 1; i >= 0; i--) {int thisnnz = (INTEGER(blk)[i] != j) ? 1 : nfj[INTEGER(par)[i]] + 1;if (thisnnz > val) val = thisnnz;nfj[i] = thisnnz;}ind[j] = Calloc(val, int);tmp[j] = Calloc(val * nc[j] * maxnc, double);Free(nfj);}}#define BLK(i,j) INTEGER(VECTOR_ELT(VECTOR_ELT(Parent, i), 1))[j]#define PAR(i,j) INTEGER(VECTOR_ELT(VECTOR_ELT(Parent, i), 0))[j]/*** Fill the nnz array with the number of nonzero inner blocks in each* outer block of the jth inner column block of the ith outer block of* L^{-1}. Also fill the ind array.** @param i outer block index* @param j inner block index within the ith outer block* @param nf number of factors* @param Parent pointer to the extended parent pairs* @param nc* @param nnz array of length nf* @param tmp array of length nf of pointers to doubles* @param ind array of length nf of pointers to ints**/staticvoid fill_ind(int i, int j, int nf, SEXP Parent, int nnz[], int *ind[]){int blk, k, par;AZERO(nnz, nf);for (blk = BLK(i,j), par = PAR(i,j); blk >= 0;k = BLK(blk,par), par = PAR(blk,par), blk = k) {ind[blk][nnz[blk]++] = par;}}static R_INLINEint fsrch(int target, const int vals[], int nvals){int i;for (i = 0; i < nvals; i++) if (vals[i] == target) return i;error(_("fsrch: unable to find target %d in nvals %d "), target, nvals);return -1; /* -Wall */}/*** If necessary, factor Z'Z+Omega, ZtX, and XtX then, if necessary,* replace the RZX and RXX slots by the corresponding parts of the* inverse of the Cholesky factor. Replace the elements of the D slot* by the blockwise inverses and evaluate bVar.** @param x pointer to an lmer object** @return NULL (x is updated in place)*/SEXP lmer_invert(SEXP x){int *status = LOGICAL(GET_SLOT(x, Matrix_statusSym));if (!status[0]) lmer_factor(x);if (!R_FINITE(REAL(GET_SLOT(x, Matrix_devianceSym))[0]))error(_("Unable to invert singular factor of downdated X'X"));if (!status[1]) {SEXP DP = GET_SLOT(x, Matrix_DSym),LP = GET_SLOT(x, Matrix_LSym),ParP = GET_SLOT(x, Matrix_ParentSym),RZXP = GET_SLOT(x, Matrix_RZXSym),bVarP = GET_SLOT(x, Matrix_bVarSym);int *Gp = INTEGER(GET_SLOT(x, Matrix_GpSym)),*dims = INTEGER(getAttrib(RZXP, R_DimSymbol)),*nc = INTEGER(GET_SLOT(x, Matrix_ncSym)),i, nf = length(DP);int **ind = Calloc(nf, int *),*nlevs = Calloc(nf, int),*nnz = Calloc(nf, int);double **tmp = Calloc(nf, double *),*RXX = REAL(GET_SLOT(x, Matrix_RXXSym)),*RZX = REAL(RZXP),minus1 = -1., one = 1., zero = 0.;/* RXX := RXX^{-1} */F77_CALL(dtrtri)("U", "N", &dims[1], RXX, &dims[1], &i);if (i)error(_("Leading minor of size %d of downdated X'X,is indefinite"),i + 1);/* RZX := - RZX %*% RXX */F77_CALL(dtrmm)("R", "U", "N", "N", &dims[0], &dims[1], &minus1,RXX, &dims[1], RZX, dims);for(i = 0; i < nf; i++) {int info, j, jj, nci = nc[i];int ncisqr = nci * nci;double *Di = REAL(VECTOR_ELT(DP, i)),*RZXi = RZX + Gp[i];nlevs[i] = (Gp[i+1] - Gp[i])/nci;/* D_i := D_i^{-1}; RZX_i := D_i %*% RZX_i */if (nci == 1) {for (j = 0; j < nlevs[i]; j++) {Di[j] = 1./Di[j];for (jj = 0; jj < dims[1]; jj++)RZXi[j + jj * dims[0]] *= Di[j];}} else {for (j = 0; j < nlevs[i]; j++) {F77_CALL(dtrtri)("U", "N", &nci, Di + j * ncisqr, &nci, &info);if (info)error(_("D[,,%d] for factor %d is singular"), j + 1, i + 1);F77_CALL(dtrmm)("L", "U", "N", "N", &nci, &dims[1], &one,Di + j * ncisqr, &nci, RZXi + j * nci, dims);}}}/* RZX := L^{-T} %*% RZX */lmer_sm(LFT, TRN, nf, Gp, dims[1], 1.0, LP, RZX, dims[0]);alloc_tmp_ind(nf, nc, nlevs, ParP, tmp, ind);/* Create bVar arrays as crossprod of column blocks of D^{-T/2}%*%L^{-1} */for (i = 0; i < nf; i++) { /* ith column of outer blocks */int j, k, kj, nci = nc[i];int ncisqr = nci * nci;double *Di = REAL(VECTOR_ELT(DP, i)),*bVi = REAL(VECTOR_ELT(bVarP, i));AZERO(bVi, ncisqr * nlevs[i]);for (j = 0; j < nlevs[i]; j++) {double *bVij = bVi + j * ncisqr, *Dij = Di + j * ncisqr;F77_CALL(dsyrk)("U", "N", &nci, &nci, &one, Dij,&nci, &zero, bVij, &nci);/* count non-zero blocks; allocate and zero storage */fill_ind(i, j, nf, ParP, nnz, ind);for (k = i; k < nf; k++) { /* kth row of outer blocks */SEXP Lki = VECTOR_ELT(LP, Lind(k, i));int *Lkii = INTEGER(GET_SLOT(Lki, Matrix_iSym)),*Lkip = INTEGER(GET_SLOT(Lki, Matrix_pSym));double *Lkix = REAL(GET_SLOT(Lki, Matrix_xSym));int kk, sz = nc[i] * nc[k];AZERO(tmp[k], sz * nnz[k]);/* initialize tmp from jth column of (k,i)th block *//* - sign in sol'n incorporated in dtrmm call below */for (kk = Lkip[j]; kk < Lkip[j + 1]; kk++)Memcpy(tmp[k] + fsrch(Lkii[kk], ind[k], nnz[k]) * sz,Lkix + kk * sz, sz);/* columns in ind[kk] for (k,kk)th block */for (kk = i; kk <= k; kk++) {int szk = nc[k] * nc[kk];/* skip getting slots if not using them */if (!nnz[kk]) continue;Lki = VECTOR_ELT(LP, Lind(k, kk));Lkii = INTEGER(GET_SLOT(Lki, Matrix_iSym));Lkip = INTEGER(GET_SLOT(Lki, Matrix_pSym));Lkix = REAL(GET_SLOT(Lki, Matrix_xSym));for (kj = 0; kj < nnz[kk]; kj++) {int col = ind[kk][kj], k1, szkk = nc[i] * nc[kk];for (k1 = Lkip[col]; k1 < Lkip[col + 1]; k1++) {if ((kk == k) && col >= Lkii[k1]) break;F77_CALL(dgemm)("N", "N", &nc[k], &nci, &nc[kk],&minus1, Lkix + k1 * szk,&nc[k], tmp[kk] + kj * szkk,&nc[kk], &one,tmp[k] +fsrch(Lkii[k1],ind[k],nnz[k])*sz,&nc[k]);}}}}for (k = 0; k < nf; k++) {for (kj = 0; kj < nnz[k]; kj++) {F77_CALL(dtrmm)("L", "U", "T", "N", nc + k, &nci, &minus1,REAL(VECTOR_ELT(DP, k))+ind[k][kj]*nc[k]*nc[k],nc + k, tmp[k] + kj * nc[i] * nc[k],nc + k);}if (nnz[k] > 0) {kj = nc[k] * nnz[k];F77_CALL(dsyrk)("U", "T", &nci, &kj, &one, tmp[k], &kj,&one, bVij, &nci);}}}}for (i = 0; i < nf; i++) {if (tmp[i]) Free(tmp[i]);if (ind[i]) Free(ind[i]);}Free(tmp); Free(nlevs); Free(nnz); Free(ind);status[1] = 1;}return R_NilValue;}/*** Extract the ML or REML conditional estimate of sigma** @param x pointer to an lme object* @param REML logical scalar - TRUE if REML estimates are requested** @return pointer to a numeric scalar*/SEXP lmer_sigma(SEXP x, SEXP REML){SEXP RXXsl = GET_SLOT(x, Matrix_RXXSym);int pp1 = INTEGER(getAttrib(RXXsl, R_DimSymbol))[1],nobs = INTEGER(GET_SLOT(x, Matrix_ncSym))[length(GET_SLOT(x, Matrix_OmegaSym)) + 1];lmer_invert(x);return ScalarReal(1./(REAL(RXXsl)[pp1*pp1 - 1] *sqrt((double)(asLogical(REML) ?nobs + 1 - pp1 : nobs))));}/*** Calculate the length of the parameter vector (historically called "coef"* even though these are not coefficients).** @param nf number of factors* @param nc number of columns in the model matrices for each factor** @return total length of the coefficient vector*/static R_INLINEint coef_length(int nf, const int nc[]){int i, ans = 0;for (i = 0; i < nf; i++) ans += (nc[i] * (nc[i] + 1))/2;return ans;}/*** Extract parameters from the Omega matrices. These aren't* "coefficients" but the extractor is called coef for historical* reasons. Within each group these values are in the order of the* diagonal entries first then the strict upper triangle in row* order.** The parameters can be returned in three forms:* 0 - nonlinearly constrained - elements of the relative precision matrix* 1 - unconstrained - from the LDL' decomposition - logarithms of* the diagonal elements of D* 2 - box constrained - also from the LDL' decomposition - inverses* of the diagonal elements of D** @param x pointer to an lme object* @param pType pointer to an integer scalar indicating the form of the* parameters to be returned.** @return numeric vector of the values in the upper triangles of the* Omega matrices*/SEXP lmer_coef(SEXP x, SEXP pType){SEXP Omega = GET_SLOT(x, Matrix_OmegaSym);int *nc = INTEGER(GET_SLOT(x, Matrix_ncSym)),i, nf = length(Omega), ptyp = asInteger(pType), vind;SEXP val = PROTECT(allocVector(REALSXP, coef_length(nf, nc)));double *vv = REAL(val);vind = 0; /* index in vv */for (i = 0; i < nf; i++) {int nci = nc[i], ncip1 = nci + 1;if (nci == 1) {double dd = REAL(VECTOR_ELT(Omega, i))[0];vv[vind++] = ptyp ? ((ptyp == 1) ? log(dd) : 1./dd) : dd;} else {if (ptyp) { /* L log(D) L' factor of Omega[,,i] */int j, k, ncisq = nci * nci;double *tmp = Memcpy(Calloc(ncisq, double),REAL(VECTOR_ELT(Omega, i)), ncisq);F77_CALL(dpotrf)("U", &nci, tmp, &nci, &j);if (j) /* should never happen */error(_("DPOTRF returned error code %d on Omega[[%d]]"),j, i+1);for (j = 0; j < nci; j++) {double diagj = tmp[j * ncip1];vv[vind++] = (ptyp == 1) ? (2. * log(diagj)) :1./(diagj * diagj);for (k = j + 1; k < nci; k++) {tmp[j + k * nci] /= diagj;}}for (j = 0; j < nci; j++) {for (k = j + 1; k < nci; k++) {vv[vind++] = tmp[j + k * nci];}}Free(tmp);} else { /* upper triangle of Omega[,,i] */int j, k, odind = vind + nci;double *omgi = REAL(VECTOR_ELT(Omega, i));for (j = 0; j < nci; j++) {vv[vind++] = omgi[j * ncip1];for (k = j + 1; k < nci; k++) {vv[odind++] = omgi[k*nci + j];}}vind = odind;}}}UNPROTECT(1);return val;}staticvoid lmer_cfGts(SEXP x, const double cc[], int ptyp){SEXP Omega = GET_SLOT(x, Matrix_OmegaSym);int *nc = INTEGER(GET_SLOT(x, Matrix_ncSym)),*status = LOGICAL(GET_SLOT(x, Matrix_statusSym)),cind, i, nf = length(Omega);cind = 0;for (i = 0; i < nf; i++) {int nci = nc[i];if (nci == 1) {double dd = cc[cind++];REAL(VECTOR_ELT(Omega, i))[0] =ptyp ? ((ptyp == 1) ? exp(dd) : 1./dd) : dd;} else {int odind = cind + nci, /* off-diagonal index */j, k,ncip1 = nci + 1,ncisq = nci * nci;double*omgi = REAL(VECTOR_ELT(Omega, i));if (ptyp) {double *tmp = Calloc(ncisq, double),diagj, one = 1., zero = 0.;AZERO(omgi, ncisq);for (j = 0; j < nci; j++) {double dd = cc[cind++];tmp[j * ncip1] = diagj =(ptyp == 1) ? exp(dd/2.) : sqrt(1./dd);for (k = j + 1; k < nci; k++) {tmp[k*nci + j] = cc[odind++] * diagj;}}F77_CALL(dsyrk)("U", "T", &nci, &nci, &one,tmp, &nci, &zero, omgi, &nci);Free(tmp);} else {for (j = 0; j < nci; j++) {omgi[j * ncip1] = cc[cind++];for (k = j + 1; k < nci; k++) {omgi[k*nci + j] = cc[odind++];}}}cind = odind;}}status[0] = status[1] = 0;}/*** Assign the upper triangles of the Omega matrices according to a* vector of parameters.** @param x pointer to an lme object* @param coef pointer to an numeric vector of appropriate length* @param pType pointer to an integer scalar** @return R_NilValue*/SEXP lmer_coefGets(SEXP x, SEXP coef, SEXP pType){int clen = coef_length(LENGTH(GET_SLOT(x, Matrix_flistSym)),INTEGER(GET_SLOT(x, Matrix_ncSym)));if (LENGTH(coef) != clen || !isReal(coef))error(_("coef must be a numeric vector of length %d"), clen);lmer_cfGts(x, REAL(coef), asInteger(pType));return x;}/*** Extract the conditional estimates of the fixed effects** @param x Pointer to an lme object** @return a numeric vector containing the conditional estimates of* the fixed effects*/SEXP lmer_fixef(SEXP x){SEXP RXXsl = GET_SLOT(x, Matrix_RXXSym),cnames = GET_SLOT(x, Matrix_cnamesSym);int j, pp1 = INTEGER(getAttrib(RXXsl, R_DimSymbol))[1];SEXP val = PROTECT(allocVector(REALSXP, pp1));double*beta = REAL(val),nryyinv; /* negative ryy-inverse */lmer_invert(x);Memcpy(beta, REAL(RXXsl) + pp1 * (pp1 - 1), pp1);nryyinv = -REAL(RXXsl)[pp1*pp1 - 1];for (j = 0; j < pp1; j++) beta[j] /= nryyinv;setAttrib(val, R_NamesSymbol,duplicate(VECTOR_ELT(cnames, length(cnames) - 1)));UNPROTECT(1);return val;}/*** Extract the conditional modes of the random effects.** @param x Pointer to an lme object** @return a list of matrices containing the conditional modes of the random effects*/SEXP lmer_ranef(SEXP x){SEXP RZXP = GET_SLOT(x, Matrix_RZXSym),cnames = GET_SLOT(x, Matrix_cnamesSym),flist = GET_SLOT(x, Matrix_flistSym);int *Gp = INTEGER(GET_SLOT(x, Matrix_GpSym)),*dims = INTEGER(getAttrib(RZXP, R_DimSymbol)),*nc = INTEGER(GET_SLOT(x, Matrix_ncSym)),i, ii, jj,nf = length(flist);SEXP val = PROTECT(allocVector(VECSXP, nf));double*b = REAL(RZXP) + dims[0] * (dims[1] - 1),nryyinv; /* negative ryy-inverse */lmer_invert(x);setAttrib(val, R_NamesSymbol,duplicate(getAttrib(flist, R_NamesSymbol)));nryyinv = -REAL(GET_SLOT(x, Matrix_RXXSym))[dims[1] * dims[1] - 1];for (i = 0; i < nf; i++) {SEXP nms, rnms = getAttrib(VECTOR_ELT(flist, i), R_LevelsSymbol);int nci = nc[i], mi = length(rnms);double *bi = b + Gp[i], *mm;SET_VECTOR_ELT(val, i, allocMatrix(REALSXP, mi, nci));setAttrib(VECTOR_ELT(val, i), R_DimNamesSymbol, allocVector(VECSXP, 2));nms = getAttrib(VECTOR_ELT(val, i), R_DimNamesSymbol);SET_VECTOR_ELT(nms, 0, duplicate(rnms));SET_VECTOR_ELT(nms, 1, duplicate(VECTOR_ELT(cnames, i)));mm = REAL(VECTOR_ELT(val, i));for (jj = 0; jj < nci; jj++)for(ii = 0; ii < mi; ii++)mm[ii + jj * mi] = bi[jj + ii * nci]/nryyinv;}UNPROTECT(1);return val;}/*** Fill in four symmetric matrices for each level, providing the* information to generate the gradient or the ECME step. The four* matrices are* 1) -m_i\bOmega_i^{-1}* 2) \bB_i\bB_i\trans* 3) \tr\left[\der_{\bOmega_i}\bOmega\left(\bZ\trans\bZ+\bOmega\right)\inv\right]* 4) The term added to 3) to get \tr\left[\der_{\bOmega_i}\bOmega\vb\right]** @param x pointer to an lme object* @param val pointer to a list of matrices of the correct sizes** @return val*//* static */SEXP lmer_firstDer(SEXP x, SEXP val){SEXP bVarP = GET_SLOT(x, Matrix_bVarSym),OmegaP = GET_SLOT(x, Matrix_OmegaSym),RZXP = GET_SLOT(x, Matrix_RZXSym);int *dims = INTEGER(getAttrib(RZXP, R_DimSymbol)),*Gp = INTEGER(GET_SLOT(x, Matrix_GpSym)),i, nf = length(OmegaP), p = dims[1] - 1;double *RZX = REAL(RZXP),*b = REAL(RZXP) + dims[0] * p;lmer_invert(x);/* FIXME: Why is this loop run backwards? It appears it could run forwards. */for (i = nf - 1; i >= 0; i--) {SEXP bVPi = VECTOR_ELT(bVarP, i);int *ddims = INTEGER(getAttrib(bVPi, R_DimSymbol)), j, k;int nci = ddims[0];int ncisqr = nci * nci, RZXrows = Gp[i + 1] - Gp[i];int nlev = RZXrows/nci;double *RZXi = RZX + Gp[i], *bVi = REAL(bVPi),*bi = b + Gp[i], *mm = REAL(VECTOR_ELT(val, i)),*tmp = Memcpy(Calloc(ncisqr, double),REAL(VECTOR_ELT(OmegaP, i)), ncisqr),dlev = (double) nlev,one = 1., zero = 0.;if (nci == 1) {int ione = 1;mm[0] = ((double) nlev)/tmp[0];mm[1] = F77_CALL(ddot)(&nlev, bi, &ione, bi, &ione);mm[2] = 0.;for (k = 0; k < nlev; k++) mm[2] += bVi[k];mm[3] = 0.;for (j = 0; j < p; j++) {mm[3] += F77_CALL(ddot)(&RZXrows, RZXi + j * dims[0], &ione,RZXi + j * dims[0], &ione);}} else {AZERO(mm, 4 * ncisqr);F77_CALL(dpotrf)("U", &nci, tmp, &nci, &j);if (j)error(_("Omega[[%d]] is not positive definite"), i + 1);F77_CALL(dtrtri)("U", "N", &nci, tmp, &nci, &j);if (j)error(_("Omega[[%d]] is not positive definite"), i + 1);F77_CALL(dsyrk)("U", "N", &nci, &nci, &dlev, tmp, &nci,&zero, mm, &nci);mm += ncisqr; /* \bB_i term */F77_CALL(dsyrk)("U", "N", &nci, &nlev, &one, bi, &nci,&zero, mm, &nci);mm += ncisqr; /* Sum of diagonal blocks of the inverse* (Z'Z+Omega)^{-1} */for (j = 0; j < ncisqr; j++) {for (k = 0; k < nlev; k++) mm[j] += bVi[j + k*ncisqr];}mm += ncisqr; /* Extra term for \vb */for (j = 0; j < p; j++) {F77_CALL(dsyrk)("U", "N", &nci, &nlev, &one,RZXi + j * dims[0], &nci,&one, mm, &nci);}}Free(tmp);}return val;}/*** Return a length nf list of arrays of dimension (nci, nci, 4). The* values of these arrays are assigned in lmer_firstDer.** @param nf number of factors* @param nc vector of number of columns per factor** @return pointer to a list of REAL arrays*/staticSEXP EM_grad_array(int nf, const int nc[]){SEXP val = PROTECT(allocVector(VECSXP, nf));int i;for (i = 0; i < nf; i++) {SET_VECTOR_ELT(val, i, alloc3Darray(REALSXP, nc[i], nc[i], 4));}UNPROTECT(1);return val;}/*** Fill in the 4-dimensional vector of linear combinations of the* firstDer array according to whether ECME steps or the gradient are* needed and to whether or not REML is being used.** @param cc coefficient vector to be filled in* @param EM non-zero for ECME steps, zero for gradient* @param REML non-zero for REML, zero for ML* @param ns ns[0] is p+1, ns[1] is n** @return cc with the coefficients filled in*/static R_INLINEdouble *EM_grad_lc(double *cc, int EM, int REML, int ns[]){cc[0] = EM ? 0. : -1.;cc[1] = (double)(ns[1] - (REML ? ns[0] - 1 : 0));cc[2] = 1.;cc[3] = REML ? 1. : 0.;return cc;}/*** Print the verbose output in the ECME iterations** @param x pointer to an ssclme object* @param iter iteration number* @param REML non-zero for REML, zero for ML* @param firstDer arrays for calculating ECME steps and the first derivative* @param val Pointer to a list of arrays to receive the calculated values*/staticvoid EMsteps_verbose_print(SEXP x, int iter, int REML, SEXP firstDer, SEXP val){SEXP Omega = GET_SLOT(x, Matrix_OmegaSym),pMat = VECTOR_ELT(val, 2);int *nc = INTEGER(GET_SLOT(x, Matrix_ncSym)),*Its = INTEGER(VECTOR_ELT(val, 0)),i, ifour = 4, ii, ione = 1, jj, nf = length(Omega),niter = INTEGER(getAttrib(pMat, R_DimSymbol))[0];double*dev = REAL(GET_SLOT(x, Matrix_devianceSym)),*cc = EM_grad_lc(Calloc(4, double), 0, REML, nc + nf),*Devs = REAL(VECTOR_ELT(val, 1)),*pars = REAL(pMat) + iter,*grds = REAL(VECTOR_ELT(val, 3)) + iter,one = 1., zero = 0.;lmer_factor(x);if (iter == 0) Rprintf(" EM iterations\n");Rprintf("%3d %.3f", Its[iter] = iter, Devs[iter] = dev[REML ? 1 : 0]);for (i = 0; i < nf; i++) {int nci = nc[i], ncip1 = nci + 1, ncisqr = nci * nci;double*Omgi = REAL(VECTOR_ELT(Omega, i)),*Grad = Calloc(ncisqr, double);/* diagonals */Rprintf(" (%#8g", *pars = Omgi[0]);pars += niter;for (jj = 1; jj < nci; jj++, pars += niter) {Rprintf(" %#8g", *pars = Omgi[jj * ncip1]);}for (jj = 1; jj < nci; jj++) /* offdiagonals */for (ii = 0; ii < jj; ii++, pars += niter)Rprintf(" %#8g", *pars = Omgi[ii + jj * nci]);/* Evaluate and print the gradient */F77_CALL(dgemv)("N", &ncisqr, &ifour, &one,REAL(VECTOR_ELT(firstDer, i)), &ncisqr,cc, &ione, &zero, Grad, &ione);Rprintf(":%#8.3g", *grds = Grad[0]);grds += niter;/* diagonals */for (jj = 1; jj < nci; jj++, grds += niter) {Rprintf(" %#8.3g", *grds = Grad[jj * ncip1]);}for (jj = 1; jj < nci; jj++) /* offdiagonals */for (ii = 0; ii < jj; ii++, grds += niter)Rprintf(" %#8.3g", *grds = Grad[ii + jj * nci]);Rprintf(")");Free(Grad);}Rprintf("\n");Free(cc);}/*** Perform ECME steps for the REML or ML criterion.** @param x pointer to an ssclme object* @param nsteps pointer to an integer scalar - the number of ECME steps to perform* @param Verbp pointer to a logical scalar indicating verbose output** @return R_NilValue if verb == FALSE, otherwise a list of iteration*numbers, deviances, parameters, and gradients.*/SEXP lmer_ECMEsteps(SEXP x, SEXP nsteps, SEXP Verbp){SEXP Omega = GET_SLOT(x, Matrix_OmegaSym),flist = GET_SLOT(x, Matrix_flistSym),val = R_NilValue;int *nc = INTEGER(GET_SLOT(x, Matrix_ncSym)),*status = LOGICAL(GET_SLOT(x, Matrix_statusSym)),REML = !strcmp(CHAR(asChar(GET_SLOT(x, Matrix_methodSym))), "REML"),i, ifour = 4, info, ione = 1, iter,nEM = asInteger(nsteps),nf = length(Omega),verb = asLogical(Verbp);double*cc = EM_grad_lc(Calloc(4, double), 1, REML, nc + nf),zero = 0.0;SEXP firstDer = PROTECT(EM_grad_array(nf, nc));lmer_firstDer(x, firstDer);if (verb) {int nEMp1 = nEM + 1, npar = coef_length(nf, nc);val = PROTECT(allocVector(VECSXP, 4));SET_VECTOR_ELT(val, 0, allocVector(INTSXP, nEMp1));SET_VECTOR_ELT(val, 1, allocVector(REALSXP, nEMp1));SET_VECTOR_ELT(val, 2, allocMatrix(REALSXP, nEMp1, npar));SET_VECTOR_ELT(val, 3, allocMatrix(REALSXP, nEMp1, npar));EMsteps_verbose_print(x, 0, REML, firstDer, val);}for (iter = 0; iter < nEM; iter++) {for (i = 0; i < nf; i++) {int nci = nc[i], ncisqr = nci * nci;double *Omgi = REAL(VECTOR_ELT(Omega, i)),mult = 1./((double) length(getAttrib(VECTOR_ELT(flist, i),R_LevelsSymbol)));F77_CALL(dgemm)("N", "N", &ncisqr, &ione, &ifour, &mult,REAL(VECTOR_ELT(firstDer, i)), &ncisqr,cc, &ifour, &zero, Omgi, &ncisqr);F77_CALL(dpotrf)("U", &nci, Omgi, &nci, &info);if (info)error(_("DPOTRF in ECME update gave code %d"), info);F77_CALL(dpotri)("U", &nci, Omgi, &nci, &info);if (info)error(_("Matrix inverse in ECME update gave code %d"), info);}status[0] = status[1] = 0;lmer_firstDer(x, firstDer);if (verb) EMsteps_verbose_print(x, iter + 1, REML, firstDer, val);}lmer_factor(x);if (verb) UNPROTECT(1);UNPROTECT(1);return val;}/*** Evaluate the gradient vector** @param x Pointer to an lmer object* @param pType Pointer to an integer indicator of the parameterization being used** @return pointer to a gradient vector*/SEXP lmer_gradient(SEXP x, SEXP pType){SEXP Omega = GET_SLOT(x, Matrix_OmegaSym);int *nc = INTEGER(GET_SLOT(x, Matrix_ncSym)),dind, i, ifour = 4, info, ione = 1, nf = length(Omega),odind, ptyp = asInteger(pType);SEXPfirstDer = lmer_firstDer(x, PROTECT(EM_grad_array(nf, nc))),val = PROTECT(allocVector(REALSXP, coef_length(nf, nc)));double*cc = EM_grad_lc(Calloc(4, double), 0,!strcmp(CHAR(asChar(GET_SLOT(x, Matrix_methodSym))),"REML"), nc + nf),one = 1.0, zero = 0.0;dind = 0; /* index into val for diagonals */for (i = 0; i < nf; i++) {int nci = nc[i], ncisqr = nci * nci;double*Omgi = REAL(VECTOR_ELT(Omega, i)),*tmp = Calloc(ncisqr, double);F77_CALL(dgemm)("N", "N", &ncisqr, &ione, &ifour, &one,REAL(VECTOR_ELT(firstDer, i)), &ncisqr,cc, &ifour, &zero, tmp, &ncisqr);if (nci == 1) {REAL(val)[dind++] =(ptyp?((ptyp == 1)?Omgi[0]: -Omgi[0] * Omgi[0]) : 1) * tmp[0];} else {int ii, j, ncip1 = nci + 1;odind = dind + nci; /* index into val for off-diagonals */if (ptyp) {double *chol = Memcpy(Calloc(ncisqr, double),REAL(VECTOR_ELT(Omega, i)), ncisqr),*tmp2 = Calloc(ncisqr, double);/* Overwrite the gradient with respect to positions in* Omega[[i]] by the gradient with respect to the* unconstrained parameters.*/F77_CALL(dpotrf)("U", &nci, chol, &nci, &info);if (info)error(_("Omega[[%d]] is not positive definite"), i + 1);/* tmp2 := chol %*% tmp using only upper triangle of tmp */F77_CALL(dsymm)("R", "U", &nci, &nci, &one, tmp, &nci,chol, &nci, &zero, tmp2, &nci);/* full symmetric product gives diagonals */F77_CALL(dtrmm)("R", "U", "T", "N", &nci, &nci, &one, chol, &nci,Memcpy(tmp, tmp2, ncisqr), &nci);/* overwrite upper triangle with gradients for positions in L' */for (ii = 1; ii < nci; ii++) {for (j = 0; j < ii; j++) {tmp[j + ii*nci] = chol[j*ncip1] * tmp2[j + ii*nci];tmp[ii + j*nci] = 0.;}}if (ptyp > 1)for (ii = 0; ii < nci; ii++) {int ind = ii * ncip1;double sqrtd = chol[ind];tmp[ind] *= -(sqrtd*sqrtd);}}for (j = 0; j < nci; j++) {REAL(val)[dind + j] = tmp[j * ncip1];for (ii = 0; ii < j; ii++) /* offdiagonals count twice */REAL(val)[odind++] = 2. * tmp[ii + j * nci];}dind = odind;}Free(tmp);}UNPROTECT(2);Free(cc);return val;}/*** Fill in five symmetric matrices, providing the* information to generate the Hessian.* @param x pointer to an lme object* @param Valp ignored at present** @return Valp an array consisting of five symmetric faces*/staticSEXP lmer_secondDer(SEXP x, SEXP Valp){SEXPD = GET_SLOT(x, Matrix_DSym),Omega = GET_SLOT(x, Matrix_OmegaSym),RZXP = GET_SLOT(x, Matrix_RZXSym),levels = GET_SLOT(x, R_LevelsSymbol),val;int *dRZX = INTEGER(getAttrib(RZXP, R_DimSymbol)),*nc = INTEGER(GET_SLOT(x, Matrix_ncSym)),Q, Qsqr, RZXpos, facepos,i, ione = 1, j, nf = length(Omega), p = dRZX[1] - 1, pos;SEXPfirstDer = lmer_firstDer(x, PROTECT(EM_grad_array(nf, nc)));double*RZX = REAL(RZXP),*b = REAL(RZXP) + dRZX[0] * p,*bbface, /* vec of second faces of firstDer elts */one = 1.,zero = 0.;Q = 0; /* number of rows and columns in the result */for (i = 0; i < nf; i++) Q += nc[i] * nc[i];Qsqr = Q * Q;bbface = Calloc(Q, double);val = PROTECT(alloc3Darray(REALSXP, Q, Q, 5));AZERO(REAL(val), Qsqr * 5);pos = 0;for (i = 0; i < nf; i++) {int nci = nc[i], ncisqr = nci * nci;double *fDi = REAL(VECTOR_ELT(firstDer, i)),mult = 1./((double) length(VECTOR_ELT(levels, i)));Memcpy(bbface + pos, fDi + ncisqr, ncisqr);/* outer product of the third face of firstDer on the diagonal* of the third face of val */F77_CALL(dsyr)("U", &ncisqr, &mult, fDi + 2 * ncisqr, &ione,REAL(val) + 2 * Qsqr + pos * Q, &Q);pos += ncisqr;}/* fifth face of val is outer product of bbface */F77_CALL(dsyr)("U", &Q, &one, bbface, &ione, REAL(val) + 4 * Qsqr, &Q);/* fourth face from \bb\trans\der\vb\der\bb */AZERO(REAL(val) + 3 * Qsqr, Qsqr); /* zero accumulator */RZXpos = 0;facepos = 0;for (i = 0; i < nf; i++) {int ii, jj, nci = nc[i], ncisqr = nci * nci, nctp = nci * p,nlev = length(VECTOR_ELT(levels, i));int maxpq = (p > nci) ? p : nci;double*Di = REAL(VECTOR_ELT(D, i)),*arr = Calloc(ncisqr * maxpq, double), /* tmp 3Darray */*face = REAL(val) + 3 * Qsqr,*mat = Calloc(nci * maxpq, double); /* tmp matrix */for (j = 0; j < nlev; j++) {F77_CALL(dgemm)("T", "T", &p, &nci, &nci,&one, RZX + j * nci, dRZX, Di + j * ncisqr, &nci,&zero, mat, &p);F77_CALL(dgemm)("N", "N", &nctp, &nci, &ione,&one, mat, &nctp, b + j * nci, &ione,&zero, arr, &nctp);F77_CALL(dsyrk)("U", "T", &ncisqr, &p, &one, arr, &p,&one, face + facepos, &Q);/* Add the D_{i,j}^{-T/2} term */Memcpy(mat, Di + j * ncisqr, ncisqr);for (jj = 1; jj < nci; jj++) { /* transpose mat */for (ii = 0; ii < jj; ii++) {mat[jj + ii * nci] = mat[ii + jj * nci];mat[ii + jj * nci] = 0.;}}F77_CALL(dgemm)("N", "N", &ncisqr, &nci, &ione,&one, mat, &ncisqr, b + j * nci, &ione,&zero, arr, &ncisqr);/* FIXME: Next call could be dsyr (it's rank one). */F77_CALL(dsyrk)("U", "T", &ncisqr, &nci, &one, arr, &nci,&one, face + facepos, &Q);}RZXpos += nci * nlev;facepos += ncisqr;Free(arr); Free(mat);}UNPROTECT(2);Free(bbface);return val;}/*** Symmetrize a matrix by copying the strict upper triangle into the* lower triangle.** @param a pointer to a matrix in Fortran storage mode* @param nc number of columns (and rows and leading dimension) in the matrix** @return a, symmetrized*/static double*lmer_symmetrize(double *a, const int nc){int i, j;for (i = 1; i < nc; i++)for (j = 0; j < i; j++)a[i + j*nc] = a[j + i*nc];return a;}/*** Return the unscaled variances** @param x pointer to an lmer object** @return a list similar to the Omega list with the unscaled variances*/SEXP lmer_variances(SEXP x){SEXP Omg = PROTECT(duplicate(GET_SLOT(x, Matrix_OmegaSym)));int *nc = INTEGER(GET_SLOT(x, Matrix_ncSym)),i, nf = length(Omg);for (i = 0; i < nf; i++) {double *mm = REAL(VECTOR_ELT(Omg, i));int j, nci = nc[i];F77_CALL(dpotrf)("U", &nci, mm, &nci, &j);if (j) /* shouldn't happen */error(_("DPOTRF returned error code %d on Omega[%d]"),j, i + 1);F77_CALL(dpotri)("U", &nci, mm, &nci, &j);if (j) /* shouldn't happen */error(_("DTRTRI returned error code %d on Omega[%d]"),j, i + 1);lmer_symmetrize(mm, nci);}UNPROTECT(1);return Omg;}/*** Calculate and return the fitted values.** @param x pointer to an lmer object* @param mmats list of model matrices* @param useRf pointer to a logical scalar indicating if the random* effects should be used** @return pointer to a numeric array of fitted values*/SEXP lmer_fitted(SEXP x, SEXP mmats, SEXP useRf){SEXP flist = GET_SLOT(x, Matrix_flistSym);int *nc = INTEGER(GET_SLOT(x, Matrix_ncSym)), ione = 1,nf = length(flist), nobs = length(VECTOR_ELT(flist, 0));int p = nc[nf] - 1;SEXP val = PROTECT(allocVector(REALSXP, nobs));double one = 1.0, zero = 0.0;if (p > 0) {F77_CALL(dgemm)("N", "N", &nobs, &ione, &p, &one,REAL(VECTOR_ELT(mmats, nf)), &nobs,REAL(PROTECT(lmer_fixef(x))), &p,&zero, REAL(val), &nobs);UNPROTECT(1);} else {AZERO(REAL(val), nobs);}if (asLogical(useRf)) {int i;SEXP b = PROTECT(lmer_ranef(x));for (i = 0; i < nf; i++) {SEXP bi = VECTOR_ELT(b, i);int mi = INTEGER(getAttrib(bi, R_DimSymbol))[0];int *ff = INTEGER(VECTOR_ELT(flist, i)), j, nci = nc[i];double *mm = REAL(VECTOR_ELT(mmats, i));for (j = 0; j < nobs; ) {int nn = 1, lev = ff[j];/* check for adjacent rows with same factor level */while ((j + nn) < nobs && ff[j + nn] == lev) nn++;F77_CALL(dgemm)("N", "T", &nn, &ione, &nci,&one, mm + j, &nobs,REAL(bi) + (lev - 1), &mi,&one, REAL(val) + j, &nobs);j += nn;}}UNPROTECT(1);}UNPROTECT(1);return val;}/*** Copy an lmer object collapsing the fixed effects slots to the response only.** @param x pointer to an lmer object** @return a duplicate of x with the fixed effects slots collapsed to the response only*/SEXP lmer_collapse(SEXP x){SEXPans = PROTECT(NEW_OBJECT(MAKE_CLASS("lmer"))),Omega = GET_SLOT(x, Matrix_OmegaSym),Dim = getAttrib(GET_SLOT(x, Matrix_ZtXSym), R_DimSymbol);intnf = length(Omega),nz = INTEGER(Dim)[0];slot_dup(ans, x, Matrix_flistSym);slot_dup(ans, x, Matrix_permSym);slot_dup(ans, x, Matrix_ParentSym);slot_dup(ans, x, Matrix_DSym);slot_dup(ans, x, Matrix_bVarSym);slot_dup(ans, x, Matrix_LSym);slot_dup(ans, x, Matrix_ZZpOSym);slot_dup(ans, x, Matrix_OmegaSym);slot_dup(ans, x, Matrix_methodSym);slot_dup(ans, x, Matrix_ZtZSym);slot_dup(ans, x, Matrix_cnamesSym);slot_dup(ans, x, Matrix_devCompSym);slot_dup(ans, x, Matrix_devianceSym);slot_dup(ans, x, Matrix_ncSym);slot_dup(ans, x, Matrix_GpSym);slot_dup(ans, x, Matrix_statusSym);INTEGER(GET_SLOT(ans, Matrix_ncSym))[nf] = 1;SET_SLOT(ans, Matrix_XtXSym, allocMatrix(REALSXP, 1, 1));REAL(GET_SLOT(ans, Matrix_XtXSym))[0] = NA_REAL;SET_SLOT(ans, Matrix_RXXSym, allocMatrix(REALSXP, 1, 1));REAL(GET_SLOT(ans, Matrix_RXXSym))[0] = NA_REAL;SET_SLOT(ans, Matrix_ZtXSym, allocMatrix(REALSXP, nz, 1));SET_SLOT(ans, Matrix_RZXSym, allocMatrix(REALSXP, nz, 1));LOGICAL(GET_SLOT(ans, Matrix_statusSym))[0] = 0;UNPROTECT(1);return ans;}/* Gauss-Hermite Quadrature x positions */static const doubleGHQ_x1[1] = {0},GHQ_w1[1] = {1},GHQ_x2[1] = {1},GHQ_w2[1] = {0.5},GHQ_x3[2] = {1.7320507779261, 0},GHQ_w3[2] = {0.166666666666667, 0.666666666666667},GHQ_x4[2] = {2.3344141783872, 0.74196377160456},GHQ_w4[2] = {0.0458758533899086, 0.454124131589555},GHQ_x5[3] = {2.85696996497785, 1.35562615677371, 0},GHQ_w5[3] = {0.0112574109895360, 0.222075915334214, 0.533333317311434},GHQ_x6[3] = {3.32425737665988, 1.88917584542184, 0.61670657963811},GHQ_w6[3] = {0.00255578432527774, 0.0886157433798025, 0.408828457274383},GHQ_x7[4] = {3.7504396535397, 2.36675937022918, 1.15440537498316, 0},GHQ_w7[4] = {0.000548268839501628, 0.0307571230436095, 0.240123171391455,0.457142843409801},GHQ_x8[4] = {4.14454711519499, 2.80248581332504, 1.63651901442728,0.539079802125417},GHQ_w8[4] = {0.000112614534992306, 0.0096352198313359, 0.117239904139746,0.373012246473389},GHQ_x9[5] = {4.51274578616743, 3.20542894799789, 2.07684794313409,1.02325564627686, 0},GHQ_w9[5] = {2.23458433364535e-05, 0.00278914123744297, 0.0499164052656755,0.244097495561989, 0.406349194142045},GHQ_x10[5] = {4.85946274516615, 3.58182342225163, 2.48432579912153,1.46598906930182, 0.484935699216176},GHQ_w10[5] = {4.31065250122166e-06, 0.000758070911538954, 0.0191115799266379,0.135483698910192, 0.344642324578594},GHQ_x11[6] = {5.18800113558601, 3.93616653976536, 2.86512311160915,1.87603498804787, 0.928868981484148, 0},GHQ_w11[6] = {8.12184954622583e-07, 0.000195671924393029, 0.0067202850336527,0.066138744084179, 0.242240292596812, 0.36940835831095};static const double*GHQ_x[12] = {(double *) NULL, GHQ_x1, GHQ_x2, GHQ_x3, GHQ_x4, GHQ_x5,GHQ_x6, GHQ_x7, GHQ_x8, GHQ_x9, GHQ_x10, GHQ_x11},*GHQ_w[12] = {(double *) NULL, GHQ_w1, GHQ_w2, GHQ_w3, GHQ_w4, GHQ_w5,GHQ_w6, GHQ_w7, GHQ_w8, GHQ_w9, GHQ_w10, GHQ_w11};/*** Compute certain components of the Laplace likelihood approximation** @param x pointer to an lmer object** @return log likelihood*/SEXP glmer_Laplace_devComp(SEXP x) {SEXPranef = PROTECT(lmer_ranef(x)),bVar = GET_SLOT(x, Matrix_bVarSym),Omg = GET_SLOT(x, Matrix_OmegaSym);int*nc = INTEGER(GET_SLOT(x, Matrix_ncSym)),*Gp = INTEGER(GET_SLOT(x, Matrix_GpSym)),i, ione = 1, nf = length(Omg);double ans = 0, one = 1, zero = 0;for (i = 0; i < nf; i++) {int j, k, nci = nc[i];int ncip1 = nci + 1, ncisqr = nci * nci,nlev = (Gp[i + 1] - Gp[i])/nci;int ntot = nlev * nci;double *bVi = REAL(VECTOR_ELT(bVar, i)),*tmp = Memcpy(Calloc(ncisqr, double),REAL(VECTOR_ELT(Omg, i)), ncisqr),*tmp2 = Calloc(ntot, double);F77_CALL(dpotrf)("U", &nci, tmp, &nci, &j);if (j)error(_("Leading %d minor of Omega[[%d]] not positive definite"),j, i + 1);for (j = 0; j < nci; j++) { /* 0.5 * nlev * logDet(Omega_i) */ans += nlev * log(tmp[j * ncip1]); /* (2 * 0.5) since factoring */}F77_CALL(dgemm)("N", "T", &nlev, &nci, &nci, &one,REAL(VECTOR_ELT(ranef, i)), &nlev,tmp, &nci, &zero, tmp2, &nlev);ans -= 0.5 * F77_CALL(ddot)(&ntot, tmp2, &ione, tmp2, &ione);for (k = 0; k < nlev; k++) {Memcpy(tmp, bVi + k * ncisqr, ncisqr);F77_CALL(dpotrf)("U", &nci, tmp, &nci, &j);if (j)error(_("Leading %d minor of bVar[[%d]][,,%d] not positive definite"),j, i + 1, k + 1);for (j = 0; j < nci; j++) {ans += log(tmp[j * ncip1]);}}Free(tmp); Free(tmp2);}UNPROTECT(1);return ScalarReal(ans);}/* R-callable drivers to test some utilities */SEXP lmer_Crosstab(SEXP flist){SEXP val;int i, nf = length(flist), nobs;int *nc = Calloc(nf, int);if (!(nf > 0 && isNewList(flist)))error(_("flist must be a non-empty list"));nobs = length(VECTOR_ELT(flist, 0));if (nobs < 1) error(_("flist[[1]] must be a non-null factor"));for (i = 0; i < nf; i++) {SEXP fi = VECTOR_ELT(flist, i);if (!(isFactor(fi) && length(fi) == nobs))error(_("flist[[%d]] must be a factor of length %d"),i + 1, nobs);nc[i] = 1;}val = lmer_crosstab(flist, nobs, nc);Free(nc);return val;}static voidglmer_wt_lst(SEXP MLin, double *wts, double *adjst, int n, SEXP MLout){int i, j, nf = LENGTH(MLin);SEXP lastM;for (i = 0; i < nf; i++) {SEXP Min = VECTOR_ELT(MLin, i),Mout = VECTOR_ELT(MLout, i);int *din, *dout, k, nc;if (!(isMatrix(Min) && isReal(Min)))error(_("component %d of MLin is not a numeric matrix"), i + 1);din = INTEGER(getAttrib(Min, R_DimSymbol));nc = din[1];if (din[0] != n)error(_("component %d of MLin has %d rows, expected %d"), i + 1,din[0], n);if (!(isMatrix(Mout) && isReal(Mout)))error(_("component %d of MLout is not a numeric matrix"), i + 1);dout = INTEGER(getAttrib(Mout, R_DimSymbol));if (dout[0] != n)error(_("component %d of MLout has %d rows, expected %d"), i + 1,dout[0], n);if (dout[1] != nc)error(_("component %d of MLout has %d columns, expected %d"), i + 1,dout[1], nc);for (k = 0; k < nc; k++) {for (j = 0; j < n; j++) {REAL(Mout)[j + k * n] = REAL(Min)[j + k * n] * wts[j];}}}lastM = VECTOR_ELT(MLout, nf - 1);j = INTEGER(getAttrib(lastM, R_DimSymbol))[1] - 1;for (i = 0; i < n; i++)REAL(lastM)[j*n + i] = adjst[i] * wts[i];}/*** Produce a weighted copy of the matrices in MLin in the storage* allocated to MLout** @param MLin input matrix list* @param wts real vector of weights* @param adjst adjusted response* @param MLout On input a list of matrices of the same dimensions as MLin.** @return MLout with its contents overwritten by a weighted copy of* MLin according to wts with adjst overwriting the response.*/SEXP glmer_weight_matrix_list(SEXP MLin, SEXP wts, SEXP adjst, SEXP MLout){int n, nf;if (!(isNewList(MLin) && isReal(wts) && isReal(adjst) && isNewList(MLout)))error(_("Incorrect argument type"));nf = LENGTH(MLin);if (LENGTH(MLout) != nf)error(_("Lengths of MLin (%d) and MLout (%d) must match"), nf,LENGTH(MLout));n = LENGTH(wts);if (LENGTH(adjst) != n)error(_("Expected adjst to have length %d, got %d"), n, LENGTH(adjst));glmer_wt_lst(MLin, REAL(wts), REAL(adjst), n, MLout);return MLout;}staticSEXP find_and_check(SEXP rho, SEXP nm, SEXPTYPE mode, int len){SEXP ans;if (R_NilValue == PROTECT(ans = findVarInFrame(rho, nm)))error(_("environment `rho' must contain an object `%s'"),CHAR(PRINTNAME(nm)));if (TYPEOF(ans) != mode)error(_("object `%s' of incorrect type"), CHAR(PRINTNAME(nm)));if (len && LENGTH(ans) != len)error(_("object `%s' must be of length `%d'"),CHAR(PRINTNAME(nm)), len);UNPROTECT(1);return ans;}staticSEXP eval_check_store(SEXP fcn, SEXP rho, SEXP vv){SEXP v = PROTECT(eval(fcn, rho));if (TYPEOF(v) != TYPEOF(vv) || LENGTH(v) != LENGTH(vv))error(_("fcn produced mode %d, length %d - wanted mode %d, length %d"),TYPEOF(v), LENGTH(v), TYPEOF(vv), LENGTH(vv));switch (TYPEOF(v)) {case LGLSXP:Memcpy(LOGICAL(vv), LOGICAL(v), LENGTH(vv));break;case INTSXP:Memcpy(INTEGER(vv), INTEGER(v), LENGTH(vv));break;case REALSXP:Memcpy(REAL(vv), REAL(v), LENGTH(vv));break;default:error(_("invalid type for eval_check_store"));}UNPROTECT(1);return vv;}staticSEXP eval_check(SEXP fcn, SEXP rho, SEXPTYPE mode, int len){SEXP v = PROTECT(eval(fcn, rho));if (TYPEOF(v) != mode || LENGTH(v) != len)error(_("fcn produced mode %d, length %d - wanted mode %d, length %d"),TYPEOF(v), LENGTH(v), mode, len);UNPROTECT(1);return v;}#define BHAT_NITER 20SEXP glmer_bhat_iterate(SEXP pars, SEXP tolp, SEXP rho){SEXP eta, fitted, linkinv, mu, mu_eta, offset, rdobj,unwtd, variance, wts, wtd, x, y, lTRUE = ScalarLogical(1);int conv, i, ii, ione = 1, n, *nc, nf, p;SEXP dmu_deta, var;double *etaold, *off, *w, *z,one = 1, tol = asReal(tolp), zero = 0;if (!isReal(pars) || LENGTH(pars) < 1)error(_("`%s' must be a nonempty, numeric vector"), "pars");if (!isEnvironment(rho))error(_("`rho' must be an environment"));y = find_and_check(rho, install("y"), REALSXP, 0);if ((n = LENGTH(y)) < 1)error(_("`%s' must be a nonempty, numeric vector"), "y");etaold = Calloc(n, double);off = Calloc(n, double);w = Calloc(n, double);z = Calloc(n, double);rdobj = find_and_check(rho, install("rdobj"), VECSXP, 0);nc = INTEGER(GET_SLOT(rdobj, Matrix_ncSym));nf = LENGTH(GET_SLOT(rdobj, Matrix_flistSym));p = LENGTH(pars) - coef_length(nf, nc);mu = find_and_check(rho, install("mu"), REALSXP, n);offset = find_and_check(rho, install("offset"), REALSXP, n);x = find_and_check(rho, install("x"), REALSXP, n * p);eta = find_and_check(rho, install("eta"), REALSXP, n);unwtd = find_and_check(rho, install("unwtd"), VECSXP, nf + 1);wts = find_and_check(rho, install("wts"), REALSXP, n);wtd = find_and_check(rho, install("wtd"), VECSXP, nf + 1);linkinv = find_and_check(rho, install("linkinv"), LANGSXP, 0);mu_eta = find_and_check(rho, install("mu.eta"), LANGSXP, 0);variance = find_and_check(rho, install("variance"), LANGSXP, 0);F77_CALL(dgemv)("N", &n, &p, &one, REAL(x), &n,REAL(pars), &ione, &zero, off, &ione);for (ii = 0; ii < n; ii++)REAL(eta)[ii] = (off[ii] += REAL(offset)[ii]);lmer_cfGts(rdobj, REAL(pars) + p, 2);conv = 0;Memcpy(etaold, REAL(eta), n);for (i = 0; i < BHAT_NITER && !conv; i++) {double max_eta, max_diff;eval_check_store(linkinv, rho, mu);dmu_deta = PROTECT(eval_check(mu_eta, rho, REALSXP, n));var = PROTECT(eval_check(variance, rho, REALSXP, n));for (ii = 0; ii < n; ii++) {w[ii] = REAL(wts)[ii] * REAL(dmu_deta)[ii]/sqrt(REAL(var)[ii]);z[ii] = REAL(eta)[ii] - off[ii] +(REAL(y)[ii] - REAL(mu)[ii])/REAL(dmu_deta)[ii];}UNPROTECT(2);glmer_wt_lst(unwtd, w, z, n, wtd);lmer_update_mm(rdobj, wtd);/* FIXME: Change this so it does not* allocate storage. That is, make a* stub for lmer_fitted. */fitted = PROTECT(lmer_fitted(rdobj, unwtd, lTRUE));max_eta = max_diff = -1.;for (ii = 0; ii < n; ii++) {double abs_eta, abs_diff;REAL(eta)[ii] = off[ii] + REAL(fitted)[ii];abs_eta = fabs(REAL(eta)[ii]);if (abs_eta > max_eta) max_eta = abs_eta;abs_diff = fabs(REAL(eta)[ii] - etaold[ii]);if (abs_diff > max_diff) max_diff = abs_diff;etaold[ii] = REAL(eta)[ii];}UNPROTECT(1);if (max_diff < (0.1 + max_eta) * tol) {conv = 1;break;}}if (!conv) warning(_("iterations for bhat did not converge"));Free(etaold); Free(off); Free(w); Free(z);return R_NilValue;}