Csparse.c

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                        /* Sparse matrices in compressed column-oriented form */

#include "Csparse.h"
#include "Tsparse.h"
#include "chm_common.h"

Rboolean isValid_Csparse(SEXP x)
{
    /* NB: we do *NOT* check a potential 'x' slot here, at all */
    SEXP pslot = GET_SLOT(x, Matrix_pSym),
        islot = GET_SLOT(x, Matrix_iSym);
    int *dims = INTEGER(GET_SLOT(x, Matrix_DimSym)), j,
        nrow = dims[0],
        ncol = dims[1],
        *xp = INTEGER(pslot),
        *xi = INTEGER(islot);

    if (length(pslot) != dims[1] + 1)
        return FALSE;
    if (xp[0] != 0)
        return FALSE;
    if (length(islot) < xp[ncol]) /* allow larger slots from over-allocation!*/
        return FALSE;
    for (j = 0; j < xp[ncol]; j++) {
        if (xi[j] < 0 || xi[j] >= nrow)
            return FALSE;
    }
    for (j = 0; j < ncol; j++) {
        if (xp[j] > xp[j + 1])
            return FALSE;
    }
    return TRUE;
}

SEXP Csparse_validate(SEXP x) {
    return Csparse_validate_(x, FALSE);
}

SEXP Csparse_validate2(SEXP x, SEXP maybe_modify) {
    return Csparse_validate_(x, asLogical(maybe_modify));
}

SEXP Csparse_validate_(SEXP x, Rboolean maybe_modify)
{
    /* NB: we do *NOT* check a potential 'x' slot here, at all */
    SEXP pslot = GET_SLOT(x, Matrix_pSym),
        islot = GET_SLOT(x, Matrix_iSym);
    Rboolean sorted, strictly;
    int j, k,
        *dims = INTEGER(GET_SLOT(x, Matrix_DimSym)),
        nrow = dims[0],
        ncol = dims[1],
        *xp = INTEGER(pslot),
        *xi = INTEGER(islot);

    if (length(pslot) != dims[1] + 1)
        return mkString(_("slot p must have length = ncol(.) + 1"));
    if (xp[0] != 0)
        return mkString(_("first element of slot p must be zero"));
    if (length(islot) < xp[ncol]) /* allow larger slots from over-allocation!*/
        return
            mkString(_("last element of slot p must match length of slots i and x"));
    for (j = 0; j < xp[ncol]; j++) {
        if (xi[j] < 0 || xi[j] >= nrow)
            return mkString(_("all row indices must be between 0 and nrow-1"));
    }
    sorted = TRUE; strictly = TRUE;
    for (j = 0; j < ncol; j++) {
        if (xp[j] > xp[j + 1])
            return mkString(_("slot p must be non-decreasing"));
        if(sorted) /* only act if >= 2 entries in column j : */
            for (k = xp[j] + 1; k < xp[j + 1]; k++) {
                if (xi[k] < xi[k - 1])
                    sorted = FALSE;
                else if (xi[k] == xi[k - 1])
                    strictly = FALSE;
            }
    }
    if (!sorted) {
        if(maybe_modify) {
            CHM_SP chx = (CHM_SP) alloca(sizeof(cholmod_sparse));
            R_CheckStack();
            as_cholmod_sparse(chx, x, FALSE, TRUE);/*-> cholmod_l_sort() ! */
            /* as chx = AS_CHM_SP__(x)  but  ^^^^ sorting x in_place !!! */

            /* Now re-check that row indices are *strictly* increasing
             * (and not just increasing) within each column : */
            for (j = 0; j < ncol; j++) {
                for (k = xp[j] + 1; k < xp[j + 1]; k++)
                    if (xi[k] == xi[k - 1])
                        return mkString(_("slot i is not *strictly* increasing inside a column (even after cholmod_l_sort)"));
            }
        } else { /* no modifying sorting : */
            return mkString(_("row indices are not sorted within columns"));
        }
    } else if(!strictly) {  /* sorted, but not strictly */
        return mkString(_("slot i is not *strictly* increasing inside a column"));
    }
    return ScalarLogical(1);
}

SEXP Rsparse_validate(SEXP x)
{
    /* NB: we do *NOT* check a potential 'x' slot here, at all */
    SEXP pslot = GET_SLOT(x, Matrix_pSym),
        jslot = GET_SLOT(x, Matrix_jSym);
    Rboolean sorted, strictly;
    int i, k,
        *dims = INTEGER(GET_SLOT(x, Matrix_DimSym)),
        nrow = dims[0],
        ncol = dims[1],
        *xp = INTEGER(pslot),
        *xj = INTEGER(jslot);

    if (length(pslot) != dims[0] + 1)
        return mkString(_("slot p must have length = nrow(.) + 1"));
    if (xp[0] != 0)
        return mkString(_("first element of slot p must be zero"));
    if (length(jslot) < xp[nrow]) /* allow larger slots from over-allocation!*/
        return
            mkString(_("last element of slot p must match length of slots j and x"));
    for (i = 0; i < length(jslot); i++) {
        if (xj[i] < 0 || xj[i] >= ncol)
            return mkString(_("all column indices must be between 0 and ncol-1"));
    }
    sorted = TRUE; strictly = TRUE;
    for (i = 0; i < nrow; i++) {
        if (xp[i] > xp[i+1])
            return mkString(_("slot p must be non-decreasing"));
        if(sorted)
            for (k = xp[i] + 1; k < xp[i + 1]; k++) {
                if (xj[k] < xj[k - 1])
                    sorted = FALSE;
                else if (xj[k] == xj[k - 1])
                    strictly = FALSE;
            }
    }
    if (!sorted)
        /* cannot easily use cholmod_sort(.) ... -> "error out" :*/
        return mkString(_("slot j is not increasing inside a column"));
    else if(!strictly) /* sorted, but not strictly */
        return mkString(_("slot j is not *strictly* increasing inside a column"));

    return ScalarLogical(1);
}


/* Called from ../R/Csparse.R : */
/* Can only return [dln]geMatrix (no symm/triang);
 * FIXME: replace by non-CHOLMOD code ! */
SEXP Csparse_to_dense(SEXP x)
{
    CHM_SP chxs = AS_CHM_SP__(x);
    /* This loses the symmetry property, since cholmod_dense has none,
     * BUT, much worse (FIXME!), it also transforms CHOLMOD_PATTERN ("n") matrices
     * to numeric (CHOLMOD_REAL) ones : */
    CHM_DN chxd = cholmod_sparse_to_dense(chxs, &c);
    int Rkind = (chxs->xtype == CHOLMOD_PATTERN)? -1 : Real_kind(x);
    R_CheckStack();

    return chm_dense_to_SEXP(chxd, 1, Rkind, GET_SLOT(x, Matrix_DimNamesSym));
}

// FIXME: do not go via CHM (should not be too hard, to just *drop* the x-slot, right?
SEXP Csparse_to_nz_pattern(SEXP x, SEXP tri)
{
    CHM_SP chxs = AS_CHM_SP__(x);
    CHM_SP chxcp = cholmod_copy(chxs, chxs->stype, CHOLMOD_PATTERN, &c);
    int tr = asLogical(tri);
    R_CheckStack();

    return chm_sparse_to_SEXP(chxcp, 1/*do_free*/,
                              tr ? ((*uplo_P(x) == 'U') ? 1 : -1) : 0,
                              0, tr ? diag_P(x) : "",
                              GET_SLOT(x, Matrix_DimNamesSym));
}

// n.CMatrix --> [dli].CMatrix  (not going through CHM!)
SEXP nz_pattern_to_Csparse(SEXP x, SEXP res_kind)
{
    return nz2Csparse(x, asInteger(res_kind));
}
// n.CMatrix --> [dli].CMatrix  (not going through CHM!)
SEXP nz2Csparse(SEXP x, enum x_slot_kind r_kind)
{
    const char *cl_x = class_P(x);
    if(cl_x[0] != 'n') error(_("not a 'n.CMatrix'"));
    if(cl_x[2] != 'C') error(_("not a CsparseMatrix"));
    int nnz = LENGTH(GET_SLOT(x, Matrix_iSym));
    SEXP ans;
    char *ncl = strdup(cl_x);
    double *dx_x; int *ix_x;
    ncl[0] = (r_kind == x_double ? 'd' :
              (r_kind == x_logical ? 'l' :
               /* else (for now):  r_kind == x_integer : */ 'i'));
    PROTECT(ans = NEW_OBJECT(MAKE_CLASS(ncl)));
    // create a correct 'x' slot:
    switch(r_kind) {
        int i;
    case x_double: // 'd'
        dx_x = REAL(ALLOC_SLOT(ans, Matrix_xSym, REALSXP, nnz));
        for (i=0; i < nnz; i++) dx_x[i] = 1.;
        break;
    case x_logical: // 'l'
        ix_x = LOGICAL(ALLOC_SLOT(ans, Matrix_xSym, LGLSXP, nnz));
        for (i=0; i < nnz; i++) ix_x[i] = TRUE;
        break;
    case x_integer: // 'i'
        ix_x = INTEGER(ALLOC_SLOT(ans, Matrix_xSym, INTSXP, nnz));
        for (i=0; i < nnz; i++) ix_x[i] = 1;
        break;

    default:
        error(_("nz2Csparse(): invalid/non-implemented r_kind = %d"),
              r_kind);
    }

    // now copy all other slots :
    slot_dup(ans, x, Matrix_iSym);
    slot_dup(ans, x, Matrix_pSym);
    slot_dup(ans, x, Matrix_DimSym);
    slot_dup(ans, x, Matrix_DimNamesSym);
    if(ncl[1] != 'g') { // symmetric or triangular ...
        slot_dup_if_has(ans, x, Matrix_uploSym);
        slot_dup_if_has(ans, x, Matrix_diagSym);
    }
    UNPROTECT(1);
    return ans;
}

SEXP Csparse_to_matrix(SEXP x)
{
    return chm_dense_to_matrix(cholmod_sparse_to_dense(AS_CHM_SP__(x), &c),
                               1 /*do_free*/, GET_SLOT(x, Matrix_DimNamesSym));
}

SEXP Csparse_to_Tsparse(SEXP x, SEXP tri)
{
    CHM_SP chxs = AS_CHM_SP__(x);
    CHM_TR chxt = cholmod_sparse_to_triplet(chxs, &c);
    int tr = asLogical(tri);
    int Rkind = (chxs->xtype != CHOLMOD_PATTERN) ? Real_kind(x) : 0;
    R_CheckStack();

    return chm_triplet_to_SEXP(chxt, 1,
                               tr ? ((*uplo_P(x) == 'U') ? 1 : -1) : 0,
                               Rkind, tr ? diag_P(x) : "",
                               GET_SLOT(x, Matrix_DimNamesSym));
}

/* this used to be called  sCMatrix_to_gCMatrix(..)   [in ./dsCMatrix.c ]: */
SEXP Csparse_symmetric_to_general(SEXP x)
{
    CHM_SP chx = AS_CHM_SP__(x), chgx;
    int Rkind = (chx->xtype != CHOLMOD_PATTERN) ? Real_kind(x) : 0;
    R_CheckStack();

    if (!(chx->stype))
        error(_("Nonsymmetric matrix in Csparse_symmetric_to_general"));
    chgx = cholmod_copy(chx, /* stype: */ 0, chx->xtype, &c);
    /* xtype: pattern, "real", complex or .. */
    return chm_sparse_to_SEXP(chgx, 1, 0, Rkind, "",
                              GET_SLOT(x, Matrix_DimNamesSym));
}

SEXP Csparse_general_to_symmetric(SEXP x, SEXP uplo)
{
    CHM_SP chx = AS_CHM_SP__(x), chgx;
    int uploT = (*CHAR(STRING_ELT(uplo,0)) == 'U') ? 1 : -1;
    int Rkind = (chx->xtype != CHOLMOD_PATTERN) ? Real_kind(x) : 0;
    R_CheckStack();

    chgx = cholmod_copy(chx, /* stype: */ uploT, chx->xtype, &c);
    /* xtype: pattern, "real", complex or .. */
    return chm_sparse_to_SEXP(chgx, 1, 0, Rkind, "",
                              GET_SLOT(x, Matrix_DimNamesSym));
}

SEXP Csparse_transpose(SEXP x, SEXP tri)
{
    /* TODO: lgCMatrix & igC* currently go via double prec. cholmod -
     *       since cholmod (& cs) lacks sparse 'int' matrices */
    CHM_SP chx = AS_CHM_SP__(x);
    int Rkind = (chx->xtype != CHOLMOD_PATTERN) ? Real_kind(x) : 0;
    CHM_SP chxt = cholmod_transpose(chx, chx->xtype, &c);
    SEXP dn = PROTECT(duplicate(GET_SLOT(x, Matrix_DimNamesSym))), tmp;
    int tr = asLogical(tri);
    R_CheckStack();

    tmp = VECTOR_ELT(dn, 0);    /* swap the dimnames */
    SET_VECTOR_ELT(dn, 0, VECTOR_ELT(dn, 1));
    SET_VECTOR_ELT(dn, 1, tmp);
    UNPROTECT(1);
    return chm_sparse_to_SEXP(chxt, 1, /* SWAP 'uplo' for triangular */
                              tr ? ((*uplo_P(x) == 'U') ? -1 : 1) : 0,
                              Rkind, tr ? diag_P(x) : "", dn);
}

SEXP Csparse_Csparse_prod(SEXP a, SEXP b)
{
    CHM_SP
        cha = AS_CHM_SP(a),
        chb = AS_CHM_SP(b),
        chc = cholmod_ssmult(cha, chb, /*out_stype:*/ 0,
                               /* values:= is_numeric (T/F) */ cha->xtype > 0,
                               /*out sorted:*/ 1, &c);
    const char *cl_a = class_P(a), *cl_b = class_P(b);
    char diag[] = {'\0', '\0'};
    int uploT = 0;
    SEXP dn = PROTECT(allocVector(VECSXP, 2));
    R_CheckStack();

#ifdef DEBUG_Matrix_verbose
    Rprintf("DBG Csparse_C*_prod(%s, %s)\n", cl_a, cl_b);
#endif

    /* Preserve triangularity and even unit-triangularity if appropriate.
     * Note that in that case, the multiplication itself should happen
     * faster.  But there's no support for that in CHOLMOD */

    /* UGLY hack -- rather should have (fast!) C-level version of
     *       is(a, "triangularMatrix") etc */
    if (cl_a[1] == 't' && cl_b[1] == 't')
        /* FIXME: fails for "Cholesky","BunchKaufmann"..*/
        if(*uplo_P(a) == *uplo_P(b)) { /* both upper, or both lower tri. */
            uploT = (*uplo_P(a) == 'U') ? 1 : -1;
            if(*diag_P(a) == 'U' && *diag_P(b) == 'U') { /* return UNIT-triag. */
                /* "remove the diagonal entries": */
                chm_diagN2U(chc, uploT, /* do_realloc */ FALSE);
                diag[0]= 'U';
            }
            else diag[0]= 'N';
        }
    SET_VECTOR_ELT(dn, 0,       /* establish dimnames */
                   duplicate(VECTOR_ELT(GET_SLOT(a, Matrix_DimNamesSym), 0)));
    SET_VECTOR_ELT(dn, 1,
                   duplicate(VECTOR_ELT(GET_SLOT(b, Matrix_DimNamesSym), 1)));
    UNPROTECT(1);
    return chm_sparse_to_SEXP(chc, 1, uploT, /*Rkind*/0, diag, dn);
}

SEXP Csparse_Csparse_crossprod(SEXP a, SEXP b, SEXP trans)
{
    int tr = asLogical(trans);
    CHM_SP
        cha = AS_CHM_SP(a),
        chb = AS_CHM_SP(b),
        chTr, chc;
    const char *cl_a = class_P(a), *cl_b = class_P(b);
    char diag[] = {'\0', '\0'};
    int uploT = 0;
    SEXP dn = PROTECT(allocVector(VECSXP, 2));
    R_CheckStack();

    chTr = cholmod_transpose((tr) ? chb : cha, chb->xtype, &c);
    chc = cholmod_ssmult((tr) ? cha : chTr, (tr) ? chTr : chb,
                         /*out_stype:*/ 0, cha->xtype, /*out sorted:*/ 1, &c);
    cholmod_free_sparse(&chTr, &c);

    /* Preserve triangularity and unit-triangularity if appropriate;
     * see Csparse_Csparse_prod() for comments */
    if (cl_a[1] == 't' && cl_b[1] == 't')
        if(*uplo_P(a) != *uplo_P(b)) { /* one 'U', the other 'L' */
            uploT = (*uplo_P(b) == 'U') ? 1 : -1;
            if(*diag_P(a) == 'U' && *diag_P(b) == 'U') { /* return UNIT-triag. */
                chm_diagN2U(chc, uploT, /* do_realloc */ FALSE);
                diag[0]= 'U';
            }
            else diag[0]= 'N';
        }
    SET_VECTOR_ELT(dn, 0,       /* establish dimnames */
                   duplicate(VECTOR_ELT(GET_SLOT(a, Matrix_DimNamesSym), (tr) ? 0 : 1)));
    SET_VECTOR_ELT(dn, 1,
                   duplicate(VECTOR_ELT(GET_SLOT(b, Matrix_DimNamesSym), (tr) ? 0 : 1)));
    UNPROTECT(1);
    return chm_sparse_to_SEXP(chc, 1, uploT, /*Rkind*/0, diag, dn);
}

SEXP Csparse_dense_prod(SEXP a, SEXP b)
{
    CHM_SP cha = AS_CHM_SP(a);
    SEXP b_M = PROTECT(mMatrix_as_dgeMatrix(b));
    CHM_DN chb = AS_CHM_DN(b_M);
    CHM_DN chc = cholmod_allocate_dense(cha->nrow, chb->ncol, cha->nrow,
                                        chb->xtype, &c);
    SEXP dn = PROTECT(allocVector(VECSXP, 2));
    double one[] = {1,0}, zero[] = {0,0};
    int nprot = 2;
    R_CheckStack();
    /* Tim Davis, please FIXME:  currently (2010-11) *fails* when  a  is a pattern matrix:*/
    if(cha->xtype == CHOLMOD_PATTERN) {
        /* warning(_("Csparse_dense_prod(): cholmod_sdmult() not yet implemented for pattern./ ngCMatrix" */
        /*        " --> slightly inefficient coercion")); */

        // This *fails* to produce a CHOLMOD_REAL ..
        // CHM_SP chd = cholmod_l_copy(cha, cha->stype, CHOLMOD_REAL, &c);
        // --> use our Matrix-classes
        SEXP da = PROTECT(nz2Csparse(a, x_double)); nprot++;
        cha = AS_CHM_SP(da);
    }
    cholmod_sdmult(cha, 0, one, zero, chb, chc, &c);
    SET_VECTOR_ELT(dn, 0,       /* establish dimnames */
                   duplicate(VECTOR_ELT(GET_SLOT(a, Matrix_DimNamesSym), 0)));
    SET_VECTOR_ELT(dn, 1,
                   duplicate(VECTOR_ELT(GET_SLOT(b_M, Matrix_DimNamesSym), 1)));
    UNPROTECT(nprot);
    return chm_dense_to_SEXP(chc, 1, 0, dn);
}

SEXP Csparse_dense_crossprod(SEXP a, SEXP b)
{
    CHM_SP cha = AS_CHM_SP(a);
    SEXP b_M = PROTECT(mMatrix_as_dgeMatrix(b));
    CHM_DN chb = AS_CHM_DN(b_M);
    CHM_DN chc = cholmod_allocate_dense(cha->ncol, chb->ncol, cha->ncol,
                                        chb->xtype, &c);
    SEXP dn = PROTECT(allocVector(VECSXP, 2)); int nprot = 2;
    double one[] = {1,0}, zero[] = {0,0};
    R_CheckStack();
    // -- see Csparse_dense_prod() above :
    if(cha->xtype == CHOLMOD_PATTERN) {
        SEXP da = PROTECT(nz2Csparse(a, x_double)); nprot++;
        cha = AS_CHM_SP(da);
    }
    cholmod_sdmult(cha, 1, one, zero, chb, chc, &c);
    SET_VECTOR_ELT(dn, 0,       /* establish dimnames */
                   duplicate(VECTOR_ELT(GET_SLOT(a, Matrix_DimNamesSym), 1)));
    SET_VECTOR_ELT(dn, 1,
                   duplicate(VECTOR_ELT(GET_SLOT(b_M, Matrix_DimNamesSym), 1)));
    UNPROTECT(nprot);
    return chm_dense_to_SEXP(chc, 1, 0, dn);
}

/* Computes   x'x  or  x x' -- *also* for Tsparse (triplet = TRUE)
   see Csparse_Csparse_crossprod above for  x'y and x y' */
SEXP Csparse_crossprod(SEXP x, SEXP trans, SEXP triplet)
{
    int trip = asLogical(triplet),
        tr   = asLogical(trans); /* gets reversed because _aat is tcrossprod */
#ifdef AS_CHM_DIAGU2N_FIXED_FINALLY
    CHM_TR cht = trip ? AS_CHM_TR(x) : (CHM_TR) NULL;
#else /* workaround needed:*/
    SEXP xx = PROTECT(Tsparse_diagU2N(x));
    CHM_TR cht = trip ? AS_CHM_TR__(xx) : (CHM_TR) NULL;
#endif
    CHM_SP chcp, chxt,
        chx = (trip ?
               cholmod_triplet_to_sparse(cht, cht->nnz, &c) :
               AS_CHM_SP(x));
    SEXP dn = PROTECT(allocVector(VECSXP, 2));
    R_CheckStack();

    if (!tr) chxt = cholmod_transpose(chx, chx->xtype, &c);
    chcp = cholmod_aat((!tr) ? chxt : chx, (int *) NULL, 0, chx->xtype, &c);
    if(!chcp) {
        UNPROTECT(1);
        error(_("Csparse_crossprod(): error return from cholmod_aat()"));
    }
    cholmod_band_inplace(0, chcp->ncol, chcp->xtype, chcp, &c);
    chcp->stype = 1;
    if (trip) cholmod_free_sparse(&chx, &c);
    if (!tr) cholmod_free_sparse(&chxt, &c);
    SET_VECTOR_ELT(dn, 0,       /* establish dimnames */
                   duplicate(VECTOR_ELT(GET_SLOT(x, Matrix_DimNamesSym),
                                        (tr) ? 0 : 1)));
    SET_VECTOR_ELT(dn, 1, duplicate(VECTOR_ELT(dn, 0)));
#ifdef AS_CHM_DIAGU2N_FIXED_FINALLY
    UNPROTECT(1);
#else
    UNPROTECT(2);
#endif
    return chm_sparse_to_SEXP(chcp, 1, 0, 0, "", dn);
}

/* Csparse_drop(x, tol):  drop entries with absolute value < tol, i.e,
*  at least all "explicit" zeros */
SEXP Csparse_drop(SEXP x, SEXP tol)
{
    const char *cl = class_P(x);
    /* dtCMatrix, etc; [1] = the second character =?= 't' for triangular */
    int tr = (cl[1] == 't');
    CHM_SP chx = AS_CHM_SP__(x);
    CHM_SP ans = cholmod_copy(chx, chx->stype, chx->xtype, &c);
    double dtol = asReal(tol);
    int Rkind = (chx->xtype != CHOLMOD_PATTERN) ? Real_kind(x) : 0;
    R_CheckStack();

    if(!cholmod_drop(dtol, ans, &c))
        error(_("cholmod_drop() failed"));
    return chm_sparse_to_SEXP(ans, 1,
                              tr ? ((*uplo_P(x) == 'U') ? 1 : -1) : 0,
                              Rkind, tr ? diag_P(x) : "",
                              GET_SLOT(x, Matrix_DimNamesSym));
}

SEXP Csparse_horzcat(SEXP x, SEXP y)
{
    CHM_SP chx = AS_CHM_SP__(x), chy = AS_CHM_SP__(y);
    int Rk_x = (chx->xtype != CHOLMOD_PATTERN) ? Real_kind(x) : 0,
        Rk_y = (chy->xtype != CHOLMOD_PATTERN) ? Real_kind(y) : 0,
        Rkind = /* logical if both x and y are */ (Rk_x == 1 && Rk_y == 1) ? 1 : 0;
    R_CheckStack();

    /* TODO: currently drops dimnames - and we fix at R level */
    return chm_sparse_to_SEXP(cholmod_horzcat(chx, chy, 1, &c),
                              1, 0, Rkind, "", R_NilValue);
}

SEXP Csparse_vertcat(SEXP x, SEXP y)
{
    CHM_SP chx = AS_CHM_SP__(x), chy = AS_CHM_SP__(y);
    int Rk_x = (chx->xtype != CHOLMOD_PATTERN) ? Real_kind(x) : 0,
        Rk_y = (chy->xtype != CHOLMOD_PATTERN) ? Real_kind(y) : 0,
        Rkind = /* logical if both x and y are */ (Rk_x == 1 && Rk_y == 1) ? 1 : 0;
    R_CheckStack();

    /* TODO: currently drops dimnames - and we fix at R level */
    return chm_sparse_to_SEXP(cholmod_vertcat(chx, chy, 1, &c),
                              1, 0, Rkind, "", R_NilValue);
}

SEXP Csparse_band(SEXP x, SEXP k1, SEXP k2)
{
    CHM_SP chx = AS_CHM_SP__(x);
    int Rkind = (chx->xtype != CHOLMOD_PATTERN) ? Real_kind(x) : 0;
    CHM_SP ans = cholmod_band(chx, asInteger(k1), asInteger(k2), chx->xtype, &c);
    R_CheckStack();

    return chm_sparse_to_SEXP(ans, 1, 0, Rkind, "",
                              GET_SLOT(x, Matrix_DimNamesSym));
}

SEXP Csparse_diagU2N(SEXP x)
{
    const char *cl = class_P(x);
    /* dtCMatrix, etc; [1] = the second character =?= 't' for triangular */
    if (cl[1] != 't' || *diag_P(x) != 'U') {
        /* "trivially fast" when not triangular (<==> no 'diag' slot),
           or not *unit* triangular */
        return (x);
    }
    else { /* unit triangular (diag='U'): "fill the diagonal" & diag:= "N" */
        CHM_SP chx = AS_CHM_SP__(x);
        CHM_SP eye = cholmod_speye(chx->nrow, chx->ncol, chx->xtype, &c);
        double one[] = {1, 0};
        CHM_SP ans = cholmod_add(chx, eye, one, one, TRUE, TRUE, &c);
        int uploT = (*uplo_P(x) == 'U') ? 1 : -1;
        int Rkind = (chx->xtype != CHOLMOD_PATTERN) ? Real_kind(x) : 0;

        R_CheckStack();
        cholmod_free_sparse(&eye, &c);
        return chm_sparse_to_SEXP(ans, 1, uploT, Rkind, "N",
                                  GET_SLOT(x, Matrix_DimNamesSym));
    }
}

SEXP Csparse_diagN2U(SEXP x)
{
    const char *cl = class_P(x);
    /* dtCMatrix, etc; [1] = the second character =?= 't' for triangular */
    if (cl[1] != 't' || *diag_P(x) != 'N') {
        /* "trivially fast" when not triangular (<==> no 'diag' slot),
           or already *unit* triangular */
        return (x);
    }
    else { /* triangular with diag='N'): now drop the diagonal */
        /* duplicate, since chx will be modified: */
        CHM_SP chx = AS_CHM_SP__(duplicate(x));
        int uploT = (*uplo_P(x) == 'U') ? 1 : -1,
            Rkind = (chx->xtype != CHOLMOD_PATTERN) ? Real_kind(x) : 0;
        R_CheckStack();

        chm_diagN2U(chx, uploT, /* do_realloc */ FALSE);

        return chm_sparse_to_SEXP(chx, /*dofree*/ 0/* or 1 ?? */,
                                  uploT, Rkind, "U",
                                  GET_SLOT(x, Matrix_DimNamesSym));
    }
}

SEXP Csparse_submatrix(SEXP x, SEXP i, SEXP j)
{
    CHM_SP chx = AS_CHM_SP(x); /* << does diagU2N() when needed */
    int rsize = (isNull(i)) ? -1 : LENGTH(i),
        csize = (isNull(j)) ? -1 : LENGTH(j);
    int Rkind = (chx->xtype != CHOLMOD_PATTERN) ? Real_kind(x) : 0;
    R_CheckStack();

    if (rsize >= 0 && !isInteger(i))
        error(_("Index i must be NULL or integer"));
    if (csize >= 0 && !isInteger(j))
        error(_("Index j must be NULL or integer"));

    if (chx->stype) /* symmetricMatrix */
        /* for now, cholmod_submatrix() only accepts "generalMatrix" */
        chx = cholmod_copy(chx, /* stype: */ 0, chx->xtype, &c);

    return chm_sparse_to_SEXP(cholmod_submatrix(chx,
                                (rsize < 0) ? NULL : INTEGER(i), rsize,
                                (csize < 0) ? NULL : INTEGER(j), csize,
                                                  TRUE, TRUE, &c),
                              1, 0, Rkind, "",
                              /* FIXME: drops dimnames */ R_NilValue);
}

#define _d_Csp_
#include "t_Csparse_subassign.c"

#define _l_Csp_
#include "t_Csparse_subassign.c"

#define _i_Csp_
#include "t_Csparse_subassign.c"

#define _n_Csp_
#include "t_Csparse_subassign.c"

#define _z_Csp_
#include "t_Csparse_subassign.c"



SEXP Csparse_MatrixMarket(SEXP x, SEXP fname)
{
    FILE *f = fopen(CHAR(asChar(fname)), "w");

    if (!f)
        error(_("failure to open file \"%s\" for writing"),
              CHAR(asChar(fname)));
    if (!cholmod_write_sparse(f, AS_CHM_SP(x),
                              (CHM_SP)NULL, (char*) NULL, &c))
        error(_("cholmod_write_sparse returned error code"));
    fclose(f);
    return R_NilValue;
}


SEXP diag_tC_ptr(int n, int *x_p, double *x_x, int *perm, SEXP resultKind)
/*                                ^^^^^^ FIXME[Generalize] to int / ... */
{
    const char* res_ch = CHAR(STRING_ELT(resultKind,0));
    enum diag_kind { diag, diag_backpermuted, trace, prod, sum_log
    } res_kind = ((!strcmp(res_ch, "trace")) ? trace :
                  ((!strcmp(res_ch, "sumLog")) ? sum_log :
                   ((!strcmp(res_ch, "prod")) ? prod :
                    ((!strcmp(res_ch, "diag")) ? diag :
                     ((!strcmp(res_ch, "diagBack")) ? diag_backpermuted :
                      -1)))));
    int i, n_x, i_from = 0;
    SEXP ans = PROTECT(allocVector(REALSXP,
/*                                 ^^^^  FIXME[Generalize] */
                                   (res_kind == diag ||
                                    res_kind == diag_backpermuted) ? n : 1));
    double *v = REAL(ans);
/*  ^^^^^^      ^^^^  FIXME[Generalize] */

#define for_DIAG(v_ASSIGN)                                              \
    for(i = 0; i < n; i++, i_from += n_x) {                             \
        /* looking at i-th column */                                    \
        n_x = x_p[i+1] - x_p[i];/* #{entries} in this column */ \
        v_ASSIGN;                                                       \
    }

    /* NOTA BENE: we assume  -- uplo = "L" i.e. lower triangular matrix
     *            for uplo = "U" (makes sense with a "dtCMatrix" !),
     *            should use  x_x[i_from + (nx - 1)] instead of x_x[i_from],
     *            where nx = (x_p[i+1] - x_p[i])
     */

    switch(res_kind) {
    case trace:
        v[0] = 0.;
        for_DIAG(v[0] += x_x[i_from]);
        break;

    case sum_log:
        v[0] = 0.;
        for_DIAG(v[0] += log(x_x[i_from]));
        break;

    case prod:
        v[0] = 1.;
        for_DIAG(v[0] *= x_x[i_from]);
        break;

    case diag:
        for_DIAG(v[i] = x_x[i_from]);
        break;

    case diag_backpermuted:
        for_DIAG(v[i] = x_x[i_from]);

        warning(_("resultKind = 'diagBack' (back-permuted) is experimental"));
        /* now back_permute : */
        for(i = 0; i < n; i++) {
            double tmp = v[i]; v[i] = v[perm[i]]; v[perm[i]] = tmp;
            /*^^^^ FIXME[Generalize] */
        }
        break;

    default: /* -1 from above */
        error(_("diag_tC(): invalid 'resultKind'"));
        /* Wall: */ ans = R_NilValue; v = REAL(ans);
    }

    UNPROTECT(1);
    return ans;
}

SEXP diag_tC(SEXP pslot, SEXP xslot, SEXP perm_slot, SEXP resultKind)
{
    int n = length(pslot) - 1, /* n = ncol(.) = nrow(.) */
        *x_p  = INTEGER(pslot),
        *perm = INTEGER(perm_slot);
    double *x_x = REAL(xslot);
/*  ^^^^^^        ^^^^ FIXME[Generalize] to INTEGER(.) / LOGICAL(.) / ... xslot !*/

    return diag_tC_ptr(n, x_p, x_x, perm, resultKind);
}

SEXP create_Csparse(char* cls, int* i, int* j, int* p, int np,
                    void* x, int nnz, int* dims, SEXP dimnames,
                    int index1)
{
    SEXP ans;
    int *ij = (int*)NULL, *tri, *trj,
        mi, mj, mp, nrow = -1, ncol = -1;
    int xtype = -1;             /* -Wall */
    CHM_TR T;
    CHM_SP A;

    if (np < 0 || nnz < 0)
        error(_("negative vector lengths not allowed: np = %d, nnz = %d"),
              np, nnz);
    if (1 != ((mi = (i == (int*)NULL)) +
              (mj = (j == (int*)NULL)) +
              (mp = (p == (int*)NULL))))
        error(_("exactly 1 of 'i', 'j' or 'p' must be NULL"));
    if (mp) {
        if (np) error(_("np = %d, must be zero when p is NULL"), np);
    } else {
        if (np) {               /* Expand p to form i or j */
            if (!(p[0])) error(_("p[0] = %d, should be zero"), p[0]);
            for (int ii = 0; ii < np; ii++)
                if (p[ii] > p[ii + 1])
                    error(_("p must be non-decreasing"));
            if (p[np] != nnz)
                error("p[np] = %d != nnz = %d", p[np], nnz);
            ij = Calloc(nnz, int);
            if (mi) {
                i = ij;
                nrow = np;
            } else {
                j = ij;
                ncol = np;
            }
            /* Expand p to 0-based indices */
            for (int ii = 0; ii < np; ii++)
                for (int jj = p[ii]; jj < p[ii + 1]; jj++) ij[jj] = ii;
        } else {
            if (nnz)
                error(_("Inconsistent dimensions: np = 0 and nnz = %d"),
                      nnz);
        }
    }
    /* calculate nrow and ncol */
    if (nrow < 0) {
        for (int ii = 0; ii < nnz; ii++) {
            int i1 = i[ii] + (index1 ? 0 : 1); /* 1-based index */
            if (i1 < 1) error(_("invalid row index at position %d"), ii);
            if (i1 > nrow) nrow = i1;
        }
    }
    if (ncol < 0) {
        for (int jj = 0; jj < nnz; jj++) {
            int j1 = j[jj] + (index1 ? 0 : 1);
            if (j1 < 1) error(_("invalid column index at position %d"), jj);
            if (j1 > ncol) ncol = j1;
        }
    }
    if (dims != (int*)NULL) {
        if (dims[0] > nrow) nrow = dims[0];
        if (dims[1] > ncol) ncol = dims[1];
    }
    /* check the class name */
    if (strlen(cls) != 8)
        error(_("strlen of cls argument = %d, should be 8"), strlen(cls));
    if (!strcmp(cls + 2, "CMatrix"))
        error(_("cls = \"%s\" does not end in \"CMatrix\""), cls);
    switch(cls[0]) {
    case 'd':
    case 'l':
        xtype = CHOLMOD_REAL;
    break;
    case 'n':
        xtype = CHOLMOD_PATTERN;
        break;
    default:
        error(_("cls = \"%s\" must begin with 'd', 'l' or 'n'"), cls);
    }
    if (cls[1] != 'g')
        error(_("Only 'g'eneral sparse matrix types allowed"));
    /* allocate and populate the triplet */
    T = cholmod_allocate_triplet((size_t)nrow, (size_t)ncol, (size_t)nnz, 0,
                                 xtype, &c);
    T->x = x;
    tri = (int*)T->i;
    trj = (int*)T->j;
    for (int ii = 0; ii < nnz; ii++) {
        tri[ii] = i[ii] - ((!mi && index1) ? 1 : 0);
        trj[ii] = j[ii] - ((!mj && index1) ? 1 : 0);
    }
    /* create the cholmod_sparse structure */
    A = cholmod_triplet_to_sparse(T, nnz, &c);
    cholmod_free_triplet(&T, &c);
    /* copy the information to the SEXP */
    ans = PROTECT(NEW_OBJECT(MAKE_CLASS(cls)));
/* FIXME: This has been copied from chm_sparse_to_SEXP in chm_common.c */
    /* allocate and copy common slots */
    nnz = cholmod_nnz(A, &c);
    dims = INTEGER(ALLOC_SLOT(ans, Matrix_DimSym, INTSXP, 2));
    dims[0] = A->nrow; dims[1] = A->ncol;
    Memcpy(INTEGER(ALLOC_SLOT(ans, Matrix_pSym, INTSXP, A->ncol + 1)), (int*)A->p, A->ncol + 1);
    Memcpy(INTEGER(ALLOC_SLOT(ans, Matrix_iSym, INTSXP, nnz)), (int*)A->i, nnz);
    switch(cls[1]) {
    case 'd':
        Memcpy(REAL(ALLOC_SLOT(ans, Matrix_xSym, REALSXP, nnz)), (double*)A->x, nnz);
        break;
    case 'l':
        error(_("code not yet written for cls = \"lgCMatrix\""));
    }
/* FIXME: dimnames are *NOT* put there yet (if non-NULL) */
    cholmod_free_sparse(&A, &c);
    UNPROTECT(1);
    return ans;
}