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[matrix] View of /pkg/src/bCrosstab.c
 [matrix] / pkg / src / bCrosstab.c

View of /pkg/src/bCrosstab.c

Thu Jan 13 19:34:03 2005 UTC (15 years, 2 months ago) by bates
File size: 18831 byte(s)
```Use the AZERO macro
```
```#include "bCrosstab.h"
/* TODO:
* - Use the off-diagonal blocks of L
* - Remove the off-diagonal blocks of ZZpO
* - Only do a fill-reducing permutation on the first non-nested factor
*/

/**
* Allocate a 3-dimensional array
*
* @param TYP The R Type code (e.g. INTSXP)
* @param nr number of rows
* @param nc number of columns
* @param nf number of faces
*
* @return A 3-dimensional array of the indicated dimensions and type
*/
static
SEXP alloc3Darray(int TYP, int nr, int nc, int nf)
{
SEXP val, dd = PROTECT(allocVector(INTSXP, 3));

INTEGER(dd)[0] = nr; INTEGER(dd)[1] = nc; INTEGER(dd)[2] = nf;
val = allocArray(TYP, dd);
UNPROTECT(1);
return val;
}

/**
* Calculate the zero-based index in a row-wise packed lower
* triangular matrix.  This is used for the arrays of blocked sparse matrices.
*
* @param i row number (0-based)
* @param k column number (0-based)
*
* @return The 0-based index of the (i,k) element of a row-wise packed lower
* triangular matrix.
*/
static R_INLINE int
Lind(int i, int k)
{
return (i * (i + 1))/2 + k;
}

/**
* Apply a permutation to an index vector
*
* @param i vector of 0-based indices
* @param nnz length of vector i
* @param perm 0-based permutation vector of length max(i)
*/
static R_INLINE void
ind_permute(int i[], int nnz, const int perm[])
{
int j;
for (j = 0; j < nnz; j++) i[j] = perm[i[j]];
}

/**
* Force indices to be in the upper triangle of a matrix
*
* @param i vector of 0-based row indices
* @param j vector of 0-based column indices
* @param nnz length of index vectors
*/
static R_INLINE void
make_upper_triangular(int i[], int j[], int nnz)
{
int k;
for (k = 0; k < nnz; k++) {
if (i[k] > j[k]) {
int tmp = i[k];
i[k] = j[k];
j[k] = tmp;
}
}
}

/**
* Create a named vector of type TYP
*
* @param TYP a vector SEXP type (e.g. REALSXP)
* @param names names of list elements with null string appended
*
* @return pointer to a named vector of type TYP
*/
static SEXP
make_named(int TYP, char **names)
{
SEXP ans, nms;
int i, n;

for (n = 0; strlen(names[n]) > 0; n++) {}
ans = PROTECT(allocVector(TYP, n));
nms = PROTECT(allocVector(STRSXP, n));
for (i = 0; i < n; i++) SET_STRING_ELT(nms, i, mkChar(names[i]));
setAttrib(ans, R_NamesSymbol, nms);
UNPROTECT(2);
return ans;
}

/**
* Check for the existence of the (row, col) pair in a csc structure.
*
* @param p vector of column pointers
* @param i vector of row indices
* @param row row index
* @param col column index
*
* @return index of element at (row, col) if it exists, otherwise -1
*/
static R_INLINE int
check_csc_index(const int p[], const int i[], int row, int col)
{
int k, k2 = p[col + 1];
/* use a linear search for now */
/* perhaps replace by bsearch later */
for (k = p[col]; k < k2; k++) {
if (i[k] == row) return k;
}
return -1;
}

static int*
expand_column_pointers(int ncol, const int mp[], int mj[])
{
int j;
for (j = 0; j < ncol; j++) {
int j2 = mp[j+1], jj;
for (jj = mp[j]; jj < j2; jj++) mj[jj] = j;
}
return mj;
}

/**
* Replace the structure of C by the structure of CA
*
* @param A a unit lower triangular cscBlocked object
* @param C a cscBlocked object to be updated
*/
static void
symbolic_right_unit_mm(SEXP A, SEXP C)
{
SEXP aip = GET_SLOT(A, Matrix_iSym),
app = GET_SLOT(A, Matrix_pSym),
cip = GET_SLOT(C, Matrix_iSym),
cpp = GET_SLOT(C, Matrix_pSym);
int *Flag,
*ai = INTEGER(aip),
*ap = INTEGER(app),
*ci = INTEGER(cip),
*cp = INTEGER(cpp),
*ncp,
anc = length(app) - 1,
anz = length(aip),
cnr, cnz = length(cip),
i, j;

if ((length(cpp) - 1) != anc) /* A is square so can compare no of cols */
error("No. of rows in A (%d) does not match no. of cols in C (%d)",
anc, length(cpp) - 1);
if (anz < 1) return;	/* A is the identity */
cnr = -1;			/* number of rows in C is max(ci + 1) */
for (i = 0; i < cnz; i++) {
int ri = ci[i] + 1;
if (cnr < ri) cnr = ri;
}
Flag = Calloc(cnr, int);
ncp = Calloc(anc + 1, int);	/* new column pointers */

ncp[0] = 0;
for (j = 0; j < anc; j++) {
int aj2 = ap[j + 1], cj2 = cp[j + 1], ka, kc;
for (i = 0; i < cnr; i++) Flag[i] = 0;
ncp[j+1] = ncp[j] + cj2 - cp[j];
/* positions of current column j of C */
for (kc = cp[j]; kc < cj2; kc++) Flag[ci[kc]] = 1;
/* other positions in column j of product */
for (ka = ap[j]; ka < aj2; ka++) {
int kk = ai[ka], kk2 = cp[kk + 1];
for (kc = cp[kk]; kc < kk2; kc++) {
if (!Flag[ci[kc]]) {
ncp[j+1]++;
Flag[ci[kc]] = 1;
}
}
}
}
if (ncp[anc] > cp[anc]) {
int *dims, *nci, nnz = ncp[anc], pos = 0;
double *ncx;

SET_SLOT(C, Matrix_iSym, allocVector(INTSXP,  nnz));
nci = INTEGER(GET_SLOT(C, Matrix_iSym));
dims = INTEGER(getAttrib(GET_SLOT(C, Matrix_xSym), R_DimSymbol));
SET_SLOT(C, Matrix_xSym, alloc3Darray(REALSXP, dims[0], dims[1], nnz));
ncx = REAL(GET_SLOT(C, Matrix_xSym));
for (i = 0; i < nnz; i++) ncx[i] = 1.;
/* As Diana Krall said, "Just do it again." */
for (j = 0; j < anc; j++) {
int aj2 = ap[j + 1], cj2 = cp[j + 1], ka, kc;
for (i = 0; i < cnr; i++) Flag[i] = 0;
for (kc = cp[j]; kc < cj2; kc++) Flag[ci[kc]] = 1;
for (ka = ap[j]; ka < aj2; ka++) {
int kk = ai[ka], kk2 = cp[kk + 1];
for (kc = cp[kk]; kc < kk2; kc++) Flag[ci[kc]] = 1;
}
for (i = 0; i < cnr; i++) if (Flag[i]) nci[pos++] = i;
}
Memcpy(cp, ncp, anc + 1);
}
Free(Flag); Free(ncp);
}

/**
* Replace the structure of C by the structure of CA'
*
* @param A a unit lower triangular cscBlocked object
* @param C a cscBlocked object to be updated
*/
static void
symbolic_right_unit_mm_trans(SEXP A, SEXP C)
{
SEXP aip = GET_SLOT(A, Matrix_iSym),
app = GET_SLOT(A, Matrix_pSym),
cip = GET_SLOT(C, Matrix_iSym),
cpp = GET_SLOT(C, Matrix_pSym);
int *ai = INTEGER(aip),
*ap = INTEGER(app),
*ci = INTEGER(cip),
*cp = INTEGER(cpp),
anc = length(app) - 1,
anz = length(aip),
cnz = length(cip),
j, nextra = 0;

if ((length(cpp) - 1) != anc)
error("No. of cols in A (%d) does not match no. of cols in C (%d)",
anc, length(cpp) - 1);
if (anz < 1) return;	/* A is the identity */
for (j = 0; j < anc; j++) { /* bound the number of extra triplets */
int aj2 = ap[j + 1], cj2 = cp[j + 1], ka, kc;
for (ka = ap[j]; ka < aj2; ka++) {
for (kc = cp[j]; kc < cj2; kc++) {
if (check_csc_index(cp, ci, ai[ka], ci[kc]) < 0) nextra++;
}
}
}
if (nextra) {
int cnr, ntot = cnz + nextra, pos;
int *dims = INTEGER(getAttrib(GET_SLOT(C, Matrix_xSym), R_DimSymbol)),
*Ti = Memcpy((int *) Calloc(ntot, int), ci, cnz),
*Tj = expand_column_pointers(anc, cp, Calloc(ntot, int)),
*Ci = Calloc(ntot, int);

for (j = 0, pos = cnz; j < anc; j++) {
int aj2 = ap[j + 1], cj2 = cp[j + 1], ka, kc;
for (ka = ap[j]; ka < aj2; ka++) {
for (kc = cp[j]; kc < cj2; kc++) {
if (check_csc_index(cp, ci, ci[kc], ai[ka]) < 0) {
Tj[pos] = ai[ka];
Ti[pos] = ci[kc];
pos++;
}
}
}
}
for (j = 0, cnr = -1; j < cnz; j++) {int rr = ci[j]; if (rr > cnr) cnr = rr;}
cnr++;			/* maximum index is 1 less than number of rows */
triplet_to_col(cnr, anc, ntot, Ti, Tj, (double *) NULL,
INTEGER(cpp), Ci, (double *) NULL);
cnz = cp[anc];
SET_SLOT(C, Matrix_iSym, allocVector(INTSXP, cnz));
SET_SLOT(C, Matrix_xSym, alloc3Darray(REALSXP, dims[0], dims[1], cnz));
Free(Ti); Free(Tj); Free(Ci);
}
}

/**
* Update a block of L in the blocked crosstabulation
*
* @param ctab pointer to a blocked crosstabulation object
* @param j index of updating column
* @param k column index of block to be updated
* @param i row index of block to be updated (j < k <= i)
*/
static void
block_update(SEXP ctab, int j, int k, int i)
{
SEXP tb = VECTOR_ELT(ctab, Lind(i, k)),
ib = VECTOR_ELT(ctab, Lind(i, j)),
kb = VECTOR_ELT(ctab, Lind(k, j));
SEXP tpp = GET_SLOT(tb, Matrix_pSym),
kpp = GET_SLOT(kb, Matrix_pSym);
int *ti = INTEGER(GET_SLOT(tb, Matrix_iSym)),
*tp = INTEGER(tpp),
*ii = INTEGER(GET_SLOT(ib, Matrix_iSym)),
*ip = INTEGER(GET_SLOT(ib, Matrix_pSym)),
*ki = INTEGER(GET_SLOT(kb, Matrix_iSym)),
*kp = INTEGER(kpp),
tnc = length(tpp) - 1,
knc = length(kpp) - 1;
int jj, extra;

if (k > i || j >= k)
error("i,j,k values of %d,%d,%d do not satisfy j < k <= i",
i, j, k);
/* bound the number of extra elements */
extra = 0;
for (jj = 0; jj < knc; jj++) {
int i1, kk, i2 = ip[jj + 1], k2 = kp[jj + 1];
for (kk = kp[jj]; kk < k2; kk++) {
for (i1 = ip[jj]; i1 < i2; i1++) {
if ((check_csc_index(tp, ti, ii[i1], ki[kk]) < 0) &&
/* only update upper triangle of
* diagonal blocks */
((k != i) || (ii[i1] <= ki[kk]))) extra++;
}
}
}
if (!extra) return;
{
int pos, nnz = tp[tnc];
int ntot = nnz + extra, tnr;
int *Ai = Calloc(ntot, int),
*Ti = Calloc(ntot, int),
*Tj = Calloc(ntot, int),
*dims;
double *Ax;

Memcpy(Ti, ti, nnz);	/* make a copy of the row indices */
for (pos = 0, jj = 0; jj < tnc; jj++) {	/* fill in the column indices */
int j2 = tp[jj + 1];
for (; pos < j2; pos++) Tj[pos] = jj;
}
/* add the extra elements */
for (jj = 0; jj < knc; jj++) {
int i1, kk, i2 = ip[jj + 1], k2 = kp[jj + 1];
for (kk = kp[jj]; kk < k2; kk++) {
for (i1 = ip[jj]; i1 < i2; i1++) {
if ((check_csc_index(tp, ti, ii[i1], ki[kk]) < 0) &&
((k != i) || (ii[i1] <= ki[kk]))) {
Ti[pos] = ii[i1];
Tj[pos] = ki[kk];
pos++;
}
}
}
}
/* Pass nlev instead of doing this.  The dimensions are nlev[i], nlev[k] */
/* Determine maximum row index in T */
tnr = -1; for (jj = 0; jj < ntot; jj++) if (Ti[jj] > tnr) tnr = Ti[jj];
tnr++;			/* increment by 1 to get number of rows */
triplet_to_col(tnr, tnc, ntot, Ti, Tj, (double *) NULL,
tp, Ai, (double *) NULL);
nnz = tp[tnc];
SET_SLOT(tb, Matrix_iSym, allocVector(INTSXP, nnz));
Memcpy(INTEGER(GET_SLOT(tb, Matrix_iSym)), Ai, nnz);
dims = INTEGER(getAttrib(GET_SLOT(tb, Matrix_xSym), R_DimSymbol));
SET_SLOT(tb, Matrix_xSym, alloc3Darray(REALSXP, dims[0], dims[1], nnz));
Ax = REAL(GET_SLOT(tb, Matrix_xSym));
for (j = 0; j < nnz; j++) Ax[j] = 1.;
Free(Ai); Free(Ti); Free(Tj);
return;
}
}

/**
* 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 ncj number of columns in level jj
* @param perm permutation (0-based) to apply
* @param pperm inverse of the permutation
*/
static void
bCrosstab_permute(SEXP ctab, int nf, int jj, const int nlev[],
const int perm[], 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);
double *cx = REAL(GET_SLOT(cscb, Matrix_xSym));
int *mj = expand_column_pointers(ncol, cp, Calloc(nnz, int));
int *mi = Memcpy(Calloc(nnz, int), INTEGER(cscbi), nnz);
double *mx = Memcpy(Calloc(nnz, double), cx, nnz);

if (j <= jj) ind_permute(mi, nnz, iperm);
if (j >= jj) ind_permute(mj, nnz, iperm);
if (j == jj) make_upper_triangular(mi, mj, nnz);
triplet_to_col(nrow, ncol, nnz, mi, mj, mx, cp, INTEGER(cscbi), cx);
Free(mi); Free(mj); Free(mx);
}
}

/**
* 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 void
factor_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
*/
void
lmer_populate(SEXP val)
{
SEXP D, L, Linv, Parent, cscB = MAKE_CLASS("cscBlocked"), ZZpO,
flist = GET_SLOT(val, Matrix_flistSym), perm, Omega,
ZtZ = GET_SLOT(val, Matrix_ZtZSym);
int j, 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", ""};

/* Allocate fixed-sized slots */
SET_SLOT(val, Matrix_statusSym, make_named(LGLSXP, statnms ));
SET_SLOT(val, Matrix_devianceSym, make_named(REALSXP, devnms));
SET_SLOT(val, Matrix_devCompSym, allocVector(REALSXP, 4));
/* Copy ZtZ to ZZpO */
SET_SLOT(val, Matrix_ZZpOSym, duplicate(ZtZ));
ZZpO = GET_SLOT(val, Matrix_ZZpOSym);
/* Allocate slots that are lists of length nf */
SET_SLOT(val, Matrix_DSym, allocVector(VECSXP, nf));
D = GET_SLOT(val, Matrix_DSym);
setAttrib(D, R_NamesSymbol, duplicate(getAttrib(flist, R_NamesSymbol)));
SET_SLOT(val, Matrix_LinvSym, allocVector(VECSXP, nf));
Linv = GET_SLOT(val, Matrix_LinvSym);
setAttrib(Linv, R_NamesSymbol, duplicate(getAttrib(flist, R_NamesSymbol)));
SET_SLOT(val, Matrix_permSym, allocVector(VECSXP, nf));
perm = GET_SLOT(val, Matrix_permSym);
setAttrib(perm, R_NamesSymbol, duplicate(getAttrib(flist, R_NamesSymbol)));
SET_SLOT(val, Matrix_ParentSym, allocVector(VECSXP, nf));
Parent = GET_SLOT(val, Matrix_ParentSym);
setAttrib(Parent, R_NamesSymbol, duplicate(getAttrib(flist, R_NamesSymbol)));
SET_SLOT(val, Matrix_OmegaSym, allocVector(VECSXP, nf));
Omega = GET_SLOT(val, Matrix_OmegaSym);
setAttrib(Omega, R_NamesSymbol, duplicate(getAttrib(flist, R_NamesSymbol)));

/* Allocate peculiar length slots */
SET_SLOT(val, Matrix_LSym, allocVector(VECSXP, npairs));
L = GET_SLOT(val, Matrix_LSym);
SET_SLOT(val, Matrix_GpSym, allocVector(INTSXP, nf + 1));
Gp = INTEGER(GET_SLOT(val, Matrix_GpSym));
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]));
SET_VECTOR_ELT(Omega, j, allocMatrix(REALSXP, nc[j], nc[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, k;
SEXP ctd = VECTOR_ELT(ZZpO, dind); /* diagonal in crosstab */
SEXP Linvj, Ljj, cpp = GET_SLOT(ctd, Matrix_pSym),
cip = GET_SLOT(ctd, Matrix_iSym);
int *Lp, *Linvp, *Perm, *cp = INTEGER(cpp),
*ci = INTEGER(cip), *dims, *parent,
ncj = length(cpp) - 1,
nnz = length(cip);
double *dtmp;

SET_VECTOR_ELT(Parent, j, allocVector(INTSXP, ncj));
parent = INTEGER(VECTOR_ELT(Parent, j));
SET_VECTOR_ELT(perm, j, allocVector(INTSXP, ncj));
Perm = INTEGER(VECTOR_ELT(perm, j));
SET_VECTOR_ELT(L, dind, NEW_OBJECT(cscB));
Ljj = VECTOR_ELT(L, dind);
SET_VECTOR_ELT(Linv, j, NEW_OBJECT(cscB));
Linvj = VECTOR_ELT(Linv, j);
SET_SLOT(Ljj, Matrix_pSym, allocVector(INTSXP, ncj + 1));
SET_SLOT(Linvj, Matrix_pSym, allocVector(INTSXP, ncj + 1));
Lp = INTEGER(GET_SLOT(Ljj, Matrix_pSym));
Linvp = INTEGER(GET_SLOT(Linvj, Matrix_pSym));
dims = INTEGER(getAttrib(GET_SLOT(ctd, Matrix_xSym), R_DimSymbol));
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 and ZZpO */
bCrosstab_permute(ZtZ, nf, j, nlev, Perm, iPerm);
bCrosstab_permute(ZZpO, nf, j, nlev, Perm, iPerm);
/* apply to the factor */
factor_levels_permute(fac, fcp, Perm, iPerm);
/* symbolic analysis to get Parent */
R_ldl_symbolic(ncj, cp, ci, Lp, parent,
(int *) NULL, (int *) NULL);
/* decompose the identity to get the row pointers */
dtmp = REAL(GET_SLOT(ctd, Matrix_xSym));
for (i = 0; i < nnz; i++) dtmp[i] = 0.; /* initialize */
/* diagonal el is last element in the column */
for (i = 0; i < ncj; i++) dtmp[cp[i+1] - 1] = 1.;
nnz = Lp[ncj];
SET_SLOT(Ljj, Matrix_iSym, allocVector(INTSXP, nnz));
SET_SLOT(Ljj, Matrix_xSym, alloc3Darray(REALSXP, dims[0], dims[1], nnz));
i = R_ldl_numeric(ncj, cp, ci, dtmp, Lp, parent,
INTEGER(GET_SLOT(Ljj, Matrix_iSym)),
REAL(GET_SLOT(Ljj, Matrix_xSym)),
(double *) R_alloc(ncj, sizeof(double)),	/* D */
(int *) NULL, (int *) NULL);
if (i < ncj) error("identity matrix is not positive definite?");
Free(iPerm); UNPROTECT(1);
} else {
for (i = 0; i <= ncj; i++) {
Lp[i] = 0;
parent[i] = -1;
Perm[i] = i;
}
SET_SLOT(Ljj, Matrix_iSym, allocVector(INTSXP, 0));
SET_SLOT(Ljj, Matrix_xSym, alloc3Darray(REALSXP, dims[0], dims[1], 0));
}
/* Derive the diagonal block of Linv */
nnz = parent_inv_ap(ncj, 0, parent, Linvp);
SET_SLOT(Linvj, Matrix_iSym, allocVector(INTSXP, nnz));
parent_inv_ai(ncj, 0, parent, INTEGER(GET_SLOT(Linvj, Matrix_iSym)));
SET_SLOT(Linvj, Matrix_xSym, alloc3Darray(REALSXP, dims[0], dims[1], nnz));
dtmp = REAL(GET_SLOT(Linvj, Matrix_xSym));
for (i = 0; i < nnz; i++) dtmp[i] = 1.;
for (k = j+1; k < nf; k++) { /* Update other blocks in this column */
symbolic_right_unit_mm_trans(Linvj, VECTOR_ELT(ZZpO, Lind(k,j)));
}
for (k = j+1; k < nf; k++) { /* Update remaining columns */
for (i = k; i < nf; i++) block_update(ZZpO, j, k, i);
}
for (i= 0; i < j; i++) { /* copy blocks to the left */
SET_VECTOR_ELT(L, Lind(j,i), duplicate(VECTOR_ELT(ZZpO, Lind(j,i))));
}
}
Free(nlev);
}
```