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[matrix] Diff of /pkg/Matrix/src/Csparse.c
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Diff of /pkg/Matrix/src/Csparse.c

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pkg/src/Csparse.c revision 2540, Tue May 18 08:53:43 2010 UTC pkg/Matrix/src/Csparse.c revision 3020, Tue Oct 14 16:14:02 2014 UTC
# Line 1  Line 1 
1                          /* Sparse matrices in compressed column-oriented form */                          /* Sparse matrices in compressed column-oriented form */
2    
3  #include "Csparse.h"  #include "Csparse.h"
4  #include "Tsparse.h"  #include "Tsparse.h"
5  #include "chm_common.h"  #include "chm_common.h"
# Line 36  Line 37 
37      return Csparse_validate_(x, FALSE);      return Csparse_validate_(x, FALSE);
38  }  }
39    
 SEXP Csparse_validate2(SEXP x, SEXP maybe_modify) {  
     return Csparse_validate_(x, asLogical(maybe_modify));  
 }  
40    
41  SEXP Csparse_validate_(SEXP x, Rboolean maybe_modify)  #define _t_Csparse_validate
42  {  #include "t_Csparse_validate.c"
     /* 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);  
43    
44      if (length(pslot) != dims[1] + 1)  #define _t_Csparse_sort
45          return mkString(_("slot p must have length = ncol(.) + 1"));  #include "t_Csparse_validate.c"
     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 !!! */  
46    
47              /* Now re-check that row indices are *strictly* increasing  // R: .validateCsparse(x, sort.if.needed = FALSE) :
48               * (and not just increasing) within each column : */  SEXP Csparse_validate2(SEXP x, SEXP maybe_modify) {
49              for (j = 0; j < ncol; j++) {      return Csparse_validate_(x, asLogical(maybe_modify));
                 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"));  
50      }      }
51      return ScalarLogical(1);  
52    // R: Matrix:::.sortCsparse(x) :
53    SEXP Csparse_sort (SEXP x) {
54       int ok = Csparse_sort_2(x, TRUE); // modifying x directly
55       if(!ok) warning(_("Csparse_sort(x): x is not a valid (apart from sorting) CsparseMatrix"));
56       return x;
57  }  }
58    
59  SEXP Rsparse_validate(SEXP x)  SEXP Rsparse_validate(SEXP x)
# Line 136  Line 93 
93              }              }
94      }      }
95      if (!sorted)      if (!sorted)
96          /* cannot easily use cholmod_l_sort(.) ... -> "error out" :*/          /* cannot easily use cholmod_sort(.) ... -> "error out" :*/
97          return mkString(_("slot j is not increasing inside a column"));          return mkString(_("slot j is not increasing inside a column"));
98      else if(!strictly) /* sorted, but not strictly */      else if(!strictly) /* sorted, but not strictly */
99          return mkString(_("slot j is not *strictly* increasing inside a column"));          return mkString(_("slot j is not *strictly* increasing inside a column"));
# Line 154  Line 111 
111      /* This loses the symmetry property, since cholmod_dense has none,      /* This loses the symmetry property, since cholmod_dense has none,
112       * BUT, much worse (FIXME!), it also transforms CHOLMOD_PATTERN ("n") matrices       * BUT, much worse (FIXME!), it also transforms CHOLMOD_PATTERN ("n") matrices
113       * to numeric (CHOLMOD_REAL) ones : */       * to numeric (CHOLMOD_REAL) ones : */
114      CHM_DN chxd = cholmod_l_sparse_to_dense(chxs, &c);      CHM_DN chxd = cholmod_sparse_to_dense(chxs, &c);
115      int Rkind = (chxs->xtype == CHOLMOD_PATTERN)? -1 : Real_kind(x);      int Rkind = (chxs->xtype == CHOLMOD_PATTERN)? -1 : Real_kind(x);
116      R_CheckStack();      R_CheckStack();
117    
118      return chm_dense_to_SEXP(chxd, 1, Rkind, GET_SLOT(x, Matrix_DimNamesSym));      return chm_dense_to_SEXP(chxd, 1, Rkind, GET_SLOT(x, Matrix_DimNamesSym));
119  }  }
120    
121    // FIXME: do not go via CHM (should not be too hard, to just *drop* the x-slot, right?
122  SEXP Csparse_to_nz_pattern(SEXP x, SEXP tri)  SEXP Csparse_to_nz_pattern(SEXP x, SEXP tri)
123  {  {
124      CHM_SP chxs = AS_CHM_SP__(x);      CHM_SP chxs = AS_CHM_SP__(x);
125      CHM_SP chxcp = cholmod_l_copy(chxs, chxs->stype, CHOLMOD_PATTERN, &c);      CHM_SP chxcp = cholmod_copy(chxs, chxs->stype, CHOLMOD_PATTERN, &c);
126      int tr = asLogical(tri);      int tr = asLogical(tri);
127      R_CheckStack();      R_CheckStack();
128    
# Line 174  Line 132 
132                                GET_SLOT(x, Matrix_DimNamesSym));                                GET_SLOT(x, Matrix_DimNamesSym));
133  }  }
134    
135  SEXP Csparse_to_matrix(SEXP x)  // n.CMatrix --> [dli].CMatrix  (not going through CHM!)
136    SEXP nz_pattern_to_Csparse(SEXP x, SEXP res_kind)
137  {  {
138      return chm_dense_to_matrix(cholmod_l_sparse_to_dense(AS_CHM_SP__(x), &c),      return nz2Csparse(x, asInteger(res_kind));
139    }
140    // n.CMatrix --> [dli].CMatrix  (not going through CHM!)
141    SEXP nz2Csparse(SEXP x, enum x_slot_kind r_kind)
142    {
143        const char *cl_x = class_P(x);
144        if(cl_x[0] != 'n') error(_("not a 'n.CMatrix'"));
145        if(cl_x[2] != 'C') error(_("not a CsparseMatrix"));
146        int nnz = LENGTH(GET_SLOT(x, Matrix_iSym));
147        SEXP ans;
148        char *ncl = alloca(strlen(cl_x) + 1); /* not much memory required */
149        strcpy(ncl, cl_x);
150        double *dx_x; int *ix_x;
151        ncl[0] = (r_kind == x_double ? 'd' :
152                  (r_kind == x_logical ? 'l' :
153                   /* else (for now):  r_kind == x_integer : */ 'i'));
154        PROTECT(ans = NEW_OBJECT(MAKE_CLASS(ncl)));
155        // create a correct 'x' slot:
156        switch(r_kind) {
157            int i;
158        case x_double: // 'd'
159            dx_x = REAL(ALLOC_SLOT(ans, Matrix_xSym, REALSXP, nnz));
160            for (i=0; i < nnz; i++) dx_x[i] = 1.;
161            break;
162        case x_logical: // 'l'
163            ix_x = LOGICAL(ALLOC_SLOT(ans, Matrix_xSym, LGLSXP, nnz));
164            for (i=0; i < nnz; i++) ix_x[i] = TRUE;
165            break;
166        case x_integer: // 'i'
167            ix_x = INTEGER(ALLOC_SLOT(ans, Matrix_xSym, INTSXP, nnz));
168            for (i=0; i < nnz; i++) ix_x[i] = 1;
169            break;
170    
171        default:
172            error(_("nz2Csparse(): invalid/non-implemented r_kind = %d"),
173                  r_kind);
174        }
175    
176        // now copy all other slots :
177        slot_dup(ans, x, Matrix_iSym);
178        slot_dup(ans, x, Matrix_pSym);
179        slot_dup(ans, x, Matrix_DimSym);
180        slot_dup(ans, x, Matrix_DimNamesSym);
181        if(ncl[1] != 'g') { // symmetric or triangular ...
182            slot_dup_if_has(ans, x, Matrix_uploSym);
183            slot_dup_if_has(ans, x, Matrix_diagSym);
184        }
185        UNPROTECT(1);
186        return ans;
187    }
188    
189    SEXP Csparse_to_matrix(SEXP x, SEXP chk)
190    {
191        return chm_dense_to_matrix(cholmod_sparse_to_dense(AS_CHM_SP2(x, asLogical(chk)), &c),
192                                 1 /*do_free*/, GET_SLOT(x, Matrix_DimNamesSym));                                 1 /*do_free*/, GET_SLOT(x, Matrix_DimNamesSym));
193  }  }
194    SEXP Csparse_to_vector(SEXP x)
195    {
196        return chm_dense_to_vector(cholmod_sparse_to_dense(AS_CHM_SP__(x), &c), 1);
197    }
198    
199  SEXP Csparse_to_Tsparse(SEXP x, SEXP tri)  SEXP Csparse_to_Tsparse(SEXP x, SEXP tri)
200  {  {
201      CHM_SP chxs = AS_CHM_SP__(x);      CHM_SP chxs = AS_CHM_SP__(x);
202      CHM_TR chxt = cholmod_l_sparse_to_triplet(chxs, &c);      CHM_TR chxt = cholmod_sparse_to_triplet(chxs, &c);
203      int tr = asLogical(tri);      int tr = asLogical(tri);
204      int Rkind = (chxs->xtype != CHOLMOD_PATTERN) ? Real_kind(x) : 0;      int Rkind = (chxs->xtype != CHOLMOD_PATTERN) ? Real_kind(x) : 0;
205      R_CheckStack();      R_CheckStack();
# Line 203  Line 219 
219    
220      if (!(chx->stype))      if (!(chx->stype))
221          error(_("Nonsymmetric matrix in Csparse_symmetric_to_general"));          error(_("Nonsymmetric matrix in Csparse_symmetric_to_general"));
222      chgx = cholmod_l_copy(chx, /* stype: */ 0, chx->xtype, &c);      chgx = cholmod_copy(chx, /* stype: */ 0, chx->xtype, &c);
223      /* xtype: pattern, "real", complex or .. */      /* xtype: pattern, "real", complex or .. */
224      return chm_sparse_to_SEXP(chgx, 1, 0, Rkind, "",      return chm_sparse_to_SEXP(chgx, 1, 0, Rkind, "",
225                                GET_SLOT(x, Matrix_DimNamesSym));                                GET_SLOT(x, Matrix_DimNamesSym));
# Line 211  Line 227 
227    
228  SEXP Csparse_general_to_symmetric(SEXP x, SEXP uplo)  SEXP Csparse_general_to_symmetric(SEXP x, SEXP uplo)
229  {  {
230        int *adims = INTEGER(GET_SLOT(x, Matrix_DimSym)), n = adims[0];
231        if(n != adims[1]) {
232            error(_("Csparse_general_to_symmetric(): matrix is not square!"));
233            return R_NilValue; /* -Wall */
234        }
235      CHM_SP chx = AS_CHM_SP__(x), chgx;      CHM_SP chx = AS_CHM_SP__(x), chgx;
236      int uploT = (*CHAR(STRING_ELT(uplo,0)) == 'U') ? 1 : -1;      int uploT = (*CHAR(asChar(uplo)) == 'U') ? 1 : -1;
237      int Rkind = (chx->xtype != CHOLMOD_PATTERN) ? Real_kind(x) : 0;      int Rkind = (chx->xtype != CHOLMOD_PATTERN) ? Real_kind(x) : 0;
238      R_CheckStack();      R_CheckStack();
239        chgx = cholmod_copy(chx, /* stype: */ uploT, chx->xtype, &c);
240    
241      chgx = cholmod_l_copy(chx, /* stype: */ uploT, chx->xtype, &c);      /* need _symmetric_ dimnames */
242        SEXP dns = PROTECT(duplicate(GET_SLOT(x, Matrix_DimNamesSym))),
243            nms_dns = getAttrib(dns, R_NamesSymbol);
244        if(!equal_string_vectors(VECTOR_ELT(dns, 0),
245                                 VECTOR_ELT(dns, 1))) {
246            if(uploT == 1)
247                SET_VECTOR_ELT(dns, 0, VECTOR_ELT(dns,1));
248            else
249                SET_VECTOR_ELT(dns, 1, VECTOR_ELT(dns,0));
250        }
251        if(!isNull(nms_dns) &&  // names(dimnames(.)) :
252           !R_compute_identical(STRING_ELT(nms_dns, 0),
253                                STRING_ELT(nms_dns, 1), 15)) {
254            if(uploT == 1)
255                SET_STRING_ELT(nms_dns, 0, STRING_ELT(nms_dns,1));
256            else
257                SET_STRING_ELT(nms_dns, 1, STRING_ELT(nms_dns,0));
258            setAttrib(dns, R_NamesSymbol, nms_dns);
259        }
260    
261        UNPROTECT(1);
262      /* xtype: pattern, "real", complex or .. */      /* xtype: pattern, "real", complex or .. */
263      return chm_sparse_to_SEXP(chgx, 1, 0, Rkind, "",      return chm_sparse_to_SEXP(chgx, 1, 0, Rkind, "", dns);
                               GET_SLOT(x, Matrix_DimNamesSym));  
264  }  }
265    
266  SEXP Csparse_transpose(SEXP x, SEXP tri)  SEXP Csparse_transpose(SEXP x, SEXP tri)
# Line 228  Line 269 
269       *       since cholmod (& cs) lacks sparse 'int' matrices */       *       since cholmod (& cs) lacks sparse 'int' matrices */
270      CHM_SP chx = AS_CHM_SP__(x);      CHM_SP chx = AS_CHM_SP__(x);
271      int Rkind = (chx->xtype != CHOLMOD_PATTERN) ? Real_kind(x) : 0;      int Rkind = (chx->xtype != CHOLMOD_PATTERN) ? Real_kind(x) : 0;
272      CHM_SP chxt = cholmod_l_transpose(chx, chx->xtype, &c);      CHM_SP chxt = cholmod_transpose(chx, chx->xtype, &c);
273      SEXP dn = PROTECT(duplicate(GET_SLOT(x, Matrix_DimNamesSym))), tmp;      SEXP dn = PROTECT(duplicate(GET_SLOT(x, Matrix_DimNamesSym))), tmp;
274      int tr = asLogical(tri);      int tr = asLogical(tri);
275      R_CheckStack();      R_CheckStack();
# Line 236  Line 277 
277      tmp = VECTOR_ELT(dn, 0);    /* swap the dimnames */      tmp = VECTOR_ELT(dn, 0);    /* swap the dimnames */
278      SET_VECTOR_ELT(dn, 0, VECTOR_ELT(dn, 1));      SET_VECTOR_ELT(dn, 0, VECTOR_ELT(dn, 1));
279      SET_VECTOR_ELT(dn, 1, tmp);      SET_VECTOR_ELT(dn, 1, tmp);
280        if(!isNull(tmp = getAttrib(dn, R_NamesSymbol))) { // swap names(dimnames(.)):
281            SEXP nms_dns = PROTECT(allocVector(VECSXP, 2));
282            SET_VECTOR_ELT(nms_dns, 1, STRING_ELT(tmp, 0));
283            SET_VECTOR_ELT(nms_dns, 0, STRING_ELT(tmp, 1));
284            setAttrib(dn, R_NamesSymbol, nms_dns);
285            UNPROTECT(1);
286        }
287      UNPROTECT(1);      UNPROTECT(1);
288      return chm_sparse_to_SEXP(chxt, 1, /* SWAP 'uplo' for triangular */      return chm_sparse_to_SEXP(chxt, 1, /* SWAP 'uplo' for triangular */
289                                tr ? ((*uplo_P(x) == 'U') ? -1 : 1) : 0,                                tr ? ((*uplo_P(x) == 'U') ? -1 : 1) : 0,
# Line 247  Line 295 
295      CHM_SP      CHM_SP
296          cha = AS_CHM_SP(a),          cha = AS_CHM_SP(a),
297          chb = AS_CHM_SP(b),          chb = AS_CHM_SP(b),
298          chc = cholmod_l_ssmult(cha, chb, /*out_stype:*/ 0,          chc = cholmod_ssmult(cha, chb, /*out_stype:*/ 0,
299                                 /* values:= is_numeric (T/F) */ cha->xtype > 0,                                 /* values:= is_numeric (T/F) */ cha->xtype > 0,
300                                 /*out sorted:*/ 1, &c);                                 /*out sorted:*/ 1, &c);
301      const char *cl_a = class_P(a), *cl_b = class_P(b);      const char *cl_a = class_P(a), *cl_b = class_P(b);
# Line 298  Line 346 
346      SEXP dn = PROTECT(allocVector(VECSXP, 2));      SEXP dn = PROTECT(allocVector(VECSXP, 2));
347      R_CheckStack();      R_CheckStack();
348    
349      chTr = cholmod_l_transpose((tr) ? chb : cha, chb->xtype, &c);      chTr = cholmod_transpose((tr) ? chb : cha, chb->xtype, &c);
350      chc = cholmod_l_ssmult((tr) ? cha : chTr, (tr) ? chTr : chb,      chc = cholmod_ssmult((tr) ? cha : chTr, (tr) ? chTr : chb,
351                           /*out_stype:*/ 0, cha->xtype, /*out sorted:*/ 1, &c);                           /*out_stype:*/ 0, cha->xtype, /*out sorted:*/ 1, &c);
352      cholmod_l_free_sparse(&chTr, &c);      cholmod_free_sparse(&chTr, &c);
353    
354      /* Preserve triangularity and unit-triangularity if appropriate;      /* Preserve triangularity and unit-triangularity if appropriate;
355       * see Csparse_Csparse_prod() for comments */       * see Csparse_Csparse_prod() for comments */
# Line 325  Line 373 
373  SEXP Csparse_dense_prod(SEXP a, SEXP b)  SEXP Csparse_dense_prod(SEXP a, SEXP b)
374  {  {
375      CHM_SP cha = AS_CHM_SP(a);      CHM_SP cha = AS_CHM_SP(a);
376      SEXP b_M = PROTECT(mMatrix_as_dgeMatrix(b));      SEXP b_M = PROTECT(mMatrix_as_dgeMatrix2(b, // transpose_if_vector =
377                                                 cha->ncol == 1));
378      CHM_DN chb = AS_CHM_DN(b_M);      CHM_DN chb = AS_CHM_DN(b_M);
379      CHM_DN chc = cholmod_l_allocate_dense(cha->nrow, chb->ncol, cha->nrow,      CHM_DN chc = cholmod_allocate_dense(cha->nrow, chb->ncol, cha->nrow,
380                                          chb->xtype, &c);                                          chb->xtype, &c);
381      SEXP dn = PROTECT(allocVector(VECSXP, 2));      SEXP dn = PROTECT(allocVector(VECSXP, 2));
382      double one[] = {1,0}, zero[] = {0,0};      double one[] = {1,0}, zero[] = {0,0};
383        int nprot = 2;
384      R_CheckStack();      R_CheckStack();
385        /* Tim Davis, please FIXME:  currently (2010-11) *fails* when  a  is a pattern matrix:*/
386      cholmod_l_sdmult(cha, 0, one, zero, chb, chc, &c);      if(cha->xtype == CHOLMOD_PATTERN) {
387            /* warning(_("Csparse_dense_prod(): cholmod_sdmult() not yet implemented for pattern./ ngCMatrix" */
388            /*        " --> slightly inefficient coercion")); */
389    
390            // This *fails* to produce a CHOLMOD_REAL ..
391            // CHM_SP chd = cholmod_l_copy(cha, cha->stype, CHOLMOD_REAL, &c);
392            // --> use our Matrix-classes
393            SEXP da = PROTECT(nz2Csparse(a, x_double)); nprot++;
394            cha = AS_CHM_SP(da);
395        }
396        cholmod_sdmult(cha, 0, one, zero, chb, chc, &c);
397      SET_VECTOR_ELT(dn, 0,       /* establish dimnames */      SET_VECTOR_ELT(dn, 0,       /* establish dimnames */
398                     duplicate(VECTOR_ELT(GET_SLOT(a, Matrix_DimNamesSym), 0)));                     duplicate(VECTOR_ELT(GET_SLOT(a, Matrix_DimNamesSym), 0)));
399      SET_VECTOR_ELT(dn, 1,      SET_VECTOR_ELT(dn, 1,
400                     duplicate(VECTOR_ELT(GET_SLOT(b_M, Matrix_DimNamesSym), 1)));                     duplicate(VECTOR_ELT(GET_SLOT(b_M, Matrix_DimNamesSym), 1)));
401      UNPROTECT(2);      UNPROTECT(nprot);
402      return chm_dense_to_SEXP(chc, 1, 0, dn);      return chm_dense_to_SEXP(chc, 1, 0, dn);
403  }  }
404    
405  SEXP Csparse_dense_crossprod(SEXP a, SEXP b)  SEXP Csparse_dense_crossprod(SEXP a, SEXP b)
406  {  {
407      CHM_SP cha = AS_CHM_SP(a);      CHM_SP cha = AS_CHM_SP(a);
408      SEXP b_M = PROTECT(mMatrix_as_dgeMatrix(b));      SEXP b_M = PROTECT(mMatrix_as_dgeMatrix2(b, // transpose_if_vector =
409                                                 cha->nrow == 1));
410      CHM_DN chb = AS_CHM_DN(b_M);      CHM_DN chb = AS_CHM_DN(b_M);
411      CHM_DN chc = cholmod_l_allocate_dense(cha->ncol, chb->ncol, cha->ncol,      CHM_DN chc = cholmod_allocate_dense(cha->ncol, chb->ncol, cha->ncol,
412                                          chb->xtype, &c);                                          chb->xtype, &c);
413      SEXP dn = PROTECT(allocVector(VECSXP, 2));      SEXP dn = PROTECT(allocVector(VECSXP, 2)); int nprot = 2;
414      double one[] = {1,0}, zero[] = {0,0};      double one[] = {1,0}, zero[] = {0,0};
415      R_CheckStack();      R_CheckStack();
416        // -- see Csparse_dense_prod() above :
417      cholmod_l_sdmult(cha, 1, one, zero, chb, chc, &c);      if(cha->xtype == CHOLMOD_PATTERN) {
418            SEXP da = PROTECT(nz2Csparse(a, x_double)); nprot++;
419            cha = AS_CHM_SP(da);
420        }
421        cholmod_sdmult(cha, 1, one, zero, chb, chc, &c);
422      SET_VECTOR_ELT(dn, 0,       /* establish dimnames */      SET_VECTOR_ELT(dn, 0,       /* establish dimnames */
423                     duplicate(VECTOR_ELT(GET_SLOT(a, Matrix_DimNamesSym), 1)));                     duplicate(VECTOR_ELT(GET_SLOT(a, Matrix_DimNamesSym), 1)));
424      SET_VECTOR_ELT(dn, 1,      SET_VECTOR_ELT(dn, 1,
425                     duplicate(VECTOR_ELT(GET_SLOT(b_M, Matrix_DimNamesSym), 1)));                     duplicate(VECTOR_ELT(GET_SLOT(b_M, Matrix_DimNamesSym), 1)));
426      UNPROTECT(2);      UNPROTECT(nprot);
427      return chm_dense_to_SEXP(chc, 1, 0, dn);      return chm_dense_to_SEXP(chc, 1, 0, dn);
428  }  }
429    
# Line 376  Line 441 
441  #endif  #endif
442      CHM_SP chcp, chxt,      CHM_SP chcp, chxt,
443          chx = (trip ?          chx = (trip ?
444                 cholmod_l_triplet_to_sparse(cht, cht->nnz, &c) :                 cholmod_triplet_to_sparse(cht, cht->nnz, &c) :
445                 AS_CHM_SP(x));                 AS_CHM_SP(x));
446      SEXP dn = PROTECT(allocVector(VECSXP, 2));      SEXP dn = PROTECT(allocVector(VECSXP, 2));
447      R_CheckStack();      R_CheckStack();
448    
449      if (!tr) chxt = cholmod_l_transpose(chx, chx->xtype, &c);      if (!tr) chxt = cholmod_transpose(chx, chx->xtype, &c);
450      chcp = cholmod_l_aat((!tr) ? chxt : chx, (int *) NULL, 0, chx->xtype, &c);      chcp = cholmod_aat((!tr) ? chxt : chx, (int *) NULL, 0, chx->xtype, &c);
451      if(!chcp) {      if(!chcp) {
452          UNPROTECT(1);          UNPROTECT(1);
453          error(_("Csparse_crossprod(): error return from cholmod_l_aat()"));          error(_("Csparse_crossprod(): error return from cholmod_aat()"));
454      }      }
455      cholmod_l_band_inplace(0, chcp->ncol, chcp->xtype, chcp, &c);      cholmod_band_inplace(0, chcp->ncol, chcp->xtype, chcp, &c);
456      chcp->stype = 1;      chcp->stype = 1;
457      if (trip) cholmod_l_free_sparse(&chx, &c);      if (trip) cholmod_free_sparse(&chx, &c);
458      if (!tr) cholmod_l_free_sparse(&chxt, &c);      if (!tr) cholmod_free_sparse(&chxt, &c);
459      SET_VECTOR_ELT(dn, 0,       /* establish dimnames */      SET_VECTOR_ELT(dn, 0,       /* establish dimnames */
460                     duplicate(VECTOR_ELT(GET_SLOT(x, Matrix_DimNamesSym),                     duplicate(VECTOR_ELT(GET_SLOT(x, Matrix_DimNamesSym),
461                                          (tr) ? 0 : 1)));                                          (tr) ? 0 : 1)));
# Line 403  Line 468 
468      return chm_sparse_to_SEXP(chcp, 1, 0, 0, "", dn);      return chm_sparse_to_SEXP(chcp, 1, 0, 0, "", dn);
469  }  }
470    
471    /* Csparse_drop(x, tol):  drop entries with absolute value < tol, i.e,
472    *  at least all "explicit" zeros */
473  SEXP Csparse_drop(SEXP x, SEXP tol)  SEXP Csparse_drop(SEXP x, SEXP tol)
474  {  {
475      const char *cl = class_P(x);      const char *cl = class_P(x);
476      /* dtCMatrix, etc; [1] = the second character =?= 't' for triangular */      /* dtCMatrix, etc; [1] = the second character =?= 't' for triangular */
477      int tr = (cl[1] == 't');      int tr = (cl[1] == 't');
478      CHM_SP chx = AS_CHM_SP__(x);      CHM_SP chx = AS_CHM_SP__(x);
479      CHM_SP ans = cholmod_l_copy(chx, chx->stype, chx->xtype, &c);      CHM_SP ans = cholmod_copy(chx, chx->stype, chx->xtype, &c);
480      double dtol = asReal(tol);      double dtol = asReal(tol);
481      int Rkind = (chx->xtype != CHOLMOD_PATTERN) ? Real_kind(x) : 0;      int Rkind = (chx->xtype != CHOLMOD_PATTERN) ? Real_kind(x) : 0;
482      R_CheckStack();      R_CheckStack();
483    
484      if(!cholmod_l_drop(dtol, ans, &c))      if(!cholmod_drop(dtol, ans, &c))
485          error(_("cholmod_l_drop() failed"));          error(_("cholmod_drop() failed"));
486      return chm_sparse_to_SEXP(ans, 1,      return chm_sparse_to_SEXP(ans, 1,
487                                tr ? ((*uplo_P(x) == 'U') ? 1 : -1) : 0,                                tr ? ((*uplo_P(x) == 'U') ? 1 : -1) : 0,
488                                Rkind, tr ? diag_P(x) : "",                                Rkind, tr ? diag_P(x) : "",
# Line 431  Line 498 
498      R_CheckStack();      R_CheckStack();
499    
500      /* TODO: currently drops dimnames - and we fix at R level */      /* TODO: currently drops dimnames - and we fix at R level */
501      return chm_sparse_to_SEXP(cholmod_l_horzcat(chx, chy, 1, &c),      return chm_sparse_to_SEXP(cholmod_horzcat(chx, chy, 1, &c),
502                                1, 0, Rkind, "", R_NilValue);                                1, 0, Rkind, "", R_NilValue);
503  }  }
504    
# Line 444  Line 511 
511      R_CheckStack();      R_CheckStack();
512    
513      /* TODO: currently drops dimnames - and we fix at R level */      /* TODO: currently drops dimnames - and we fix at R level */
514      return chm_sparse_to_SEXP(cholmod_l_vertcat(chx, chy, 1, &c),      return chm_sparse_to_SEXP(cholmod_vertcat(chx, chy, 1, &c),
515                                1, 0, Rkind, "", R_NilValue);                                1, 0, Rkind, "", R_NilValue);
516  }  }
517    
# Line 452  Line 519 
519  {  {
520      CHM_SP chx = AS_CHM_SP__(x);      CHM_SP chx = AS_CHM_SP__(x);
521      int Rkind = (chx->xtype != CHOLMOD_PATTERN) ? Real_kind(x) : 0;      int Rkind = (chx->xtype != CHOLMOD_PATTERN) ? Real_kind(x) : 0;
522      CHM_SP ans = cholmod_l_band(chx, asInteger(k1), asInteger(k2), chx->xtype, &c);      CHM_SP ans = cholmod_band(chx, asInteger(k1), asInteger(k2), chx->xtype, &c);
523      R_CheckStack();      R_CheckStack();
524    
525      return chm_sparse_to_SEXP(ans, 1, 0, Rkind, "",      return chm_sparse_to_SEXP(ans, 1, 0, Rkind, "",
# Line 470  Line 537 
537      }      }
538      else { /* unit triangular (diag='U'): "fill the diagonal" & diag:= "N" */      else { /* unit triangular (diag='U'): "fill the diagonal" & diag:= "N" */
539          CHM_SP chx = AS_CHM_SP__(x);          CHM_SP chx = AS_CHM_SP__(x);
540          CHM_SP eye = cholmod_l_speye(chx->nrow, chx->ncol, chx->xtype, &c);          CHM_SP eye = cholmod_speye(chx->nrow, chx->ncol, chx->xtype, &c);
541          double one[] = {1, 0};          double one[] = {1, 0};
542          CHM_SP ans = cholmod_l_add(chx, eye, one, one, TRUE, TRUE, &c);          CHM_SP ans = cholmod_add(chx, eye, one, one, TRUE, TRUE, &c);
543          int uploT = (*uplo_P(x) == 'U') ? 1 : -1;          int uploT = (*uplo_P(x) == 'U') ? 1 : -1;
544          int Rkind = (chx->xtype != CHOLMOD_PATTERN) ? Real_kind(x) : 0;          int Rkind = (chx->xtype != CHOLMOD_PATTERN) ? Real_kind(x) : 0;
545    
546          R_CheckStack();          R_CheckStack();
547          cholmod_l_free_sparse(&eye, &c);          cholmod_free_sparse(&eye, &c);
548          return chm_sparse_to_SEXP(ans, 1, uploT, Rkind, "N",          return chm_sparse_to_SEXP(ans, 1, uploT, Rkind, "N",
549                                    GET_SLOT(x, Matrix_DimNamesSym));                                    GET_SLOT(x, Matrix_DimNamesSym));
550      }      }
# Line 494  Line 561 
561      }      }
562      else { /* triangular with diag='N'): now drop the diagonal */      else { /* triangular with diag='N'): now drop the diagonal */
563          /* duplicate, since chx will be modified: */          /* duplicate, since chx will be modified: */
564          CHM_SP chx = AS_CHM_SP__(duplicate(x));          SEXP xx = PROTECT(duplicate(x));
565            CHM_SP chx = AS_CHM_SP__(xx);
566          int uploT = (*uplo_P(x) == 'U') ? 1 : -1,          int uploT = (*uplo_P(x) == 'U') ? 1 : -1,
567              Rkind = (chx->xtype != CHOLMOD_PATTERN) ? Real_kind(x) : 0;              Rkind = (chx->xtype != CHOLMOD_PATTERN) ? Real_kind(x) : 0;
568          R_CheckStack();          R_CheckStack();
569    
570          chm_diagN2U(chx, uploT, /* do_realloc */ FALSE);          chm_diagN2U(chx, uploT, /* do_realloc */ FALSE);
571    
572          return chm_sparse_to_SEXP(chx, /*dofree*/ 0/* or 1 ?? */,          SEXP ans = chm_sparse_to_SEXP(chx, /*dofree*/ 0/* or 1 ?? */,
573                                    uploT, Rkind, "U",                                    uploT, Rkind, "U",
574                                    GET_SLOT(x, Matrix_DimNamesSym));                                    GET_SLOT(x, Matrix_DimNamesSym));
575            UNPROTECT(1);// only now !
576            return ans;
577      }      }
578  }  }
579    
# Line 529  Line 599 
599      if (csize >= 0 && !isInteger(j))      if (csize >= 0 && !isInteger(j))
600          error(_("Index j must be NULL or integer"));          error(_("Index j must be NULL or integer"));
601    
602      if (chx->stype) /* symmetricMatrix */  #define CHM_SUB(_M_, _i_, _j_)                                  \
603        cholmod_submatrix(_M_,                                      \
604                          (rsize < 0) ? NULL : INTEGER(_i_), rsize, \
605                          (csize < 0) ? NULL : INTEGER(_j_), csize, \
606                          TRUE, TRUE, &c)
607        CHM_SP ans;
608        if (!chx->stype) {/* non-symmetric Matrix */
609            ans = CHM_SUB(chx, i, j);
610        }
611        else {
612          /* for now, cholmod_submatrix() only accepts "generalMatrix" */          /* for now, cholmod_submatrix() only accepts "generalMatrix" */
613          chx = cholmod_l_copy(chx, /* stype: */ 0, chx->xtype, &c);          CHM_SP tmp = cholmod_copy(chx, /* stype: */ 0, chx->xtype, &c);
614            ans = CHM_SUB(tmp, i, j);
615            cholmod_free_sparse(&tmp, &c);
616        }
617    
618      return chm_sparse_to_SEXP(cholmod_l_submatrix(chx,      // "FIXME": currently dropping dimnames, and adding them afterwards in R :
619                                  (rsize < 0) ? NULL : INTEGER(i), rsize,      /* // dimnames: */
620                                  (csize < 0) ? NULL : INTEGER(j), csize,      /* SEXP x_dns = GET_SLOT(x, Matrix_DimNamesSym), */
621                                                    TRUE, TRUE, &c),      /*  dn = PROTECT(allocVector(VECSXP, 2)); */
622                                1, 0, Rkind, "",      return chm_sparse_to_SEXP(ans, 1, 0, Rkind, "", /* dimnames: */ R_NilValue);
                               /* FIXME: drops dimnames */ R_NilValue);  
623  }  }
624    
625    #define _d_Csp_
626    #include "t_Csparse_subassign.c"
627    
628    #define _l_Csp_
629    #include "t_Csparse_subassign.c"
630    
631    #define _i_Csp_
632    #include "t_Csparse_subassign.c"
633    
634    #define _n_Csp_
635    #include "t_Csparse_subassign.c"
636    
637    #define _z_Csp_
638    #include "t_Csparse_subassign.c"
639    
640    
641    
642  SEXP Csparse_MatrixMarket(SEXP x, SEXP fname)  SEXP Csparse_MatrixMarket(SEXP x, SEXP fname)
643  {  {
644      FILE *f = fopen(CHAR(asChar(fname)), "w");      FILE *f = fopen(CHAR(asChar(fname)), "w");
# Line 548  Line 646 
646      if (!f)      if (!f)
647          error(_("failure to open file \"%s\" for writing"),          error(_("failure to open file \"%s\" for writing"),
648                CHAR(asChar(fname)));                CHAR(asChar(fname)));
649      if (!cholmod_l_write_sparse(f, AS_CHM_SP(x),      if (!cholmod_write_sparse(f, AS_CHM_SP(x),
650                                (CHM_SP)NULL, (char*) NULL, &c))                                (CHM_SP)NULL, (char*) NULL, &c))
651          error(_("cholmod_l_write_sparse returned error code"));          error(_("cholmod_write_sparse returned error code"));
652      fclose(f);      fclose(f);
653      return R_NilValue;      return R_NilValue;
654  }  }
# Line 568  Line 666 
666   *   *
667   * @return  a SEXP, either a (double) number or a length n-vector of diagonal entries   * @return  a SEXP, either a (double) number or a length n-vector of diagonal entries
668   */   */
669  SEXP diag_tC_ptr(int n, int *x_p, double *x_x, int *perm, SEXP resultKind)  SEXP diag_tC_ptr(int n, int *x_p, double *x_x, Rboolean is_U, int *perm,
670  /*                                ^^^^^^ FIXME[Generalize] to int / ... */  /*                                ^^^^^^ FIXME[Generalize] to int / ... */
671                     SEXP resultKind)
672  {  {
673      const char* res_ch = CHAR(STRING_ELT(resultKind,0));      const char* res_ch = CHAR(STRING_ELT(resultKind,0));
674      enum diag_kind { diag, diag_backpermuted, trace, prod, sum_log      enum diag_kind { diag, diag_backpermuted, trace, prod, sum_log, min, max, range
675      } res_kind = ((!strcmp(res_ch, "trace")) ? trace :      } res_kind = ((!strcmp(res_ch, "trace")) ? trace :
676                    ((!strcmp(res_ch, "sumLog")) ? sum_log :                    ((!strcmp(res_ch, "sumLog")) ? sum_log :
677                     ((!strcmp(res_ch, "prod")) ? prod :                     ((!strcmp(res_ch, "prod")) ? prod :
678                        ((!strcmp(res_ch, "min")) ? min :
679                         ((!strcmp(res_ch, "max")) ? max :
680                          ((!strcmp(res_ch, "range")) ? range :
681                      ((!strcmp(res_ch, "diag")) ? diag :                      ((!strcmp(res_ch, "diag")) ? diag :
682                       ((!strcmp(res_ch, "diagBack")) ? diag_backpermuted :                       ((!strcmp(res_ch, "diagBack")) ? diag_backpermuted :
683                        -1)))));                           -1))))))));
684      int i, n_x, i_from = 0;      int i, n_x, i_from;
685      SEXP ans = PROTECT(allocVector(REALSXP,      SEXP ans = PROTECT(allocVector(REALSXP,
686  /*                                 ^^^^  FIXME[Generalize] */  /*                                 ^^^^  FIXME[Generalize] */
687                                     (res_kind == diag ||                                     (res_kind == diag ||
688                                      res_kind == diag_backpermuted) ? n : 1));                                      res_kind == diag_backpermuted) ? n :
689                                       (res_kind == range ? 2 : 1)));
690      double *v = REAL(ans);      double *v = REAL(ans);
691  /*  ^^^^^^      ^^^^  FIXME[Generalize] */  /*  ^^^^^^      ^^^^  FIXME[Generalize] */
692    
693        i_from = (is_U ? -1 : 0);
694    
695  #define for_DIAG(v_ASSIGN)                                              \  #define for_DIAG(v_ASSIGN)                                              \
696      for(i = 0; i < n; i++, i_from += n_x) {                             \      for(i = 0; i < n; i++) {                                    \
697          /* looking at i-th column */                                    \          /* looking at i-th column */                                    \
698          n_x = x_p[i+1] - x_p[i];/* #{entries} in this column */ \          n_x = x_p[i+1] - x_p[i];/* #{entries} in this column */ \
699            if( is_U) i_from += n_x;                                \
700          v_ASSIGN;                                                       \          v_ASSIGN;                                                       \
701            if(!is_U) i_from += n_x;                                \
702      }      }
703    
704      /* NOTA BENE: we assume  -- uplo = "L" i.e. lower triangular matrix      /* NOTA BENE: we assume  -- uplo = "L" i.e. lower triangular matrix
705       *            for uplo = "U" (makes sense with a "dtCMatrix" !),       *            for uplo = "U" (makes sense with a "dtCMatrix" !),
706       *            should use  x_x[i_from + (nx - 1)] instead of x_x[i_from],       *            should use  x_x[i_from + (n_x - 1)] instead of x_x[i_from],
707       *            where nx = (x_p[i+1] - x_p[i])       *            where n_x = (x_p[i+1] - x_p[i])
708       */       */
709    
710      switch(res_kind) {      switch(res_kind) {
711      case trace:      case trace: // = sum
712          v[0] = 0.;          v[0] = 0.;
713          for_DIAG(v[0] += x_x[i_from]);          for_DIAG(v[0] += x_x[i_from]);
714          break;          break;
# Line 616  Line 723 
723          for_DIAG(v[0] *= x_x[i_from]);          for_DIAG(v[0] *= x_x[i_from]);
724          break;          break;
725    
726        case min:
727            v[0] = R_PosInf;
728            for_DIAG(if(v[0] > x_x[i_from]) v[0] = x_x[i_from]);
729            break;
730    
731        case max:
732            v[0] = R_NegInf;
733            for_DIAG(if(v[0] < x_x[i_from]) v[0] = x_x[i_from]);
734            break;
735    
736        case range:
737            v[0] = R_PosInf;
738            v[1] = R_NegInf;
739            for_DIAG(if(v[0] > x_x[i_from]) v[0] = x_x[i_from];
740                     if(v[1] < x_x[i_from]) v[1] = x_x[i_from]);
741            break;
742    
743      case diag:      case diag:
744          for_DIAG(v[i] = x_x[i_from]);          for_DIAG(v[i] = x_x[i_from]);
745          break;          break;
# Line 623  Line 747 
747      case diag_backpermuted:      case diag_backpermuted:
748          for_DIAG(v[i] = x_x[i_from]);          for_DIAG(v[i] = x_x[i_from]);
749    
750          warning(_("resultKind = 'diagBack' (back-permuted) is experimental"));          warning(_("%s = '%s' (back-permuted) is experimental"),
751                    "resultKind", "diagBack");
752          /* now back_permute : */          /* now back_permute : */
753          for(i = 0; i < n; i++) {          for(i = 0; i < n; i++) {
754              double tmp = v[i]; v[i] = v[perm[i]]; v[perm[i]] = tmp;              double tmp = v[i]; v[i] = v[perm[i]]; v[perm[i]] = tmp;
# Line 644  Line 769 
769   * Extract the diagonal entries from *triangular* Csparse matrix  __or__ a   * Extract the diagonal entries from *triangular* Csparse matrix  __or__ a
770   * cholmod_sparse factor (LDL = TRUE).   * cholmod_sparse factor (LDL = TRUE).
771   *   *
772     * @param obj -- now a cholmod_sparse factor or a dtCMatrix
773   * @param pslot  'p' (column pointer)   slot of Csparse matrix/factor   * @param pslot  'p' (column pointer)   slot of Csparse matrix/factor
774   * @param xslot  'x' (non-zero entries) slot of Csparse matrix/factor   * @param xslot  'x' (non-zero entries) slot of Csparse matrix/factor
775   * @param perm_slot  'perm' (= permutation vector) slot of corresponding CHMfactor;   * @param perm_slot  'perm' (= permutation vector) slot of corresponding CHMfactor;
# Line 652  Line 778 
778   *   *
779   * @return  a SEXP, either a (double) number or a length n-vector of diagonal entries   * @return  a SEXP, either a (double) number or a length n-vector of diagonal entries
780   */   */
781  SEXP diag_tC(SEXP pslot, SEXP xslot, SEXP perm_slot, SEXP resultKind)  SEXP diag_tC(SEXP obj, SEXP resultKind)
782  {  {
783    
784        SEXP
785            pslot = GET_SLOT(obj, Matrix_pSym),
786            xslot = GET_SLOT(obj, Matrix_xSym);
787        Rboolean is_U = (R_has_slot(obj, Matrix_uploSym) &&
788                         *CHAR(asChar(GET_SLOT(obj, Matrix_uploSym))) == 'U');
789      int n = length(pslot) - 1, /* n = ncol(.) = nrow(.) */      int n = length(pslot) - 1, /* n = ncol(.) = nrow(.) */
790          *x_p  = INTEGER(pslot),          *x_p  = INTEGER(pslot), pp = -1, *perm;
         *perm = INTEGER(perm_slot);  
791      double *x_x = REAL(xslot);      double *x_x = REAL(xslot);
792  /*  ^^^^^^        ^^^^ FIXME[Generalize] to INTEGER(.) / LOGICAL(.) / ... xslot !*/  /*  ^^^^^^        ^^^^ FIXME[Generalize] to INTEGER(.) / LOGICAL(.) / ... xslot !*/
793    
794      return diag_tC_ptr(n, x_p, x_x, perm, resultKind);      if(R_has_slot(obj, Matrix_permSym))
795            perm = INTEGER(GET_SLOT(obj, Matrix_permSym));
796        else perm = &pp;
797    
798        return diag_tC_ptr(n, x_p, x_x, is_U, perm, resultKind);
799  }  }
800    
801    
802  /**  /**
803   * Create a Csparse matrix object from indices and/or pointers.   * Create a Csparse matrix object from indices and/or pointers.
804   *   *
# Line 764  Line 900 
900      if (cls[1] != 'g')      if (cls[1] != 'g')
901          error(_("Only 'g'eneral sparse matrix types allowed"));          error(_("Only 'g'eneral sparse matrix types allowed"));
902                                  /* allocate and populate the triplet */                                  /* allocate and populate the triplet */
903      T = cholmod_l_allocate_triplet((size_t)nrow, (size_t)ncol, (size_t)nnz, 0,      T = cholmod_allocate_triplet((size_t)nrow, (size_t)ncol, (size_t)nnz, 0,
904                                      xtype, &c);                                      xtype, &c);
905      T->x = x;      T->x = x;
906      tri = (int*)T->i;      tri = (int*)T->i;
# Line 774  Line 910 
910          trj[ii] = j[ii] - ((!mj && index1) ? 1 : 0);          trj[ii] = j[ii] - ((!mj && index1) ? 1 : 0);
911      }      }
912                                  /* create the cholmod_sparse structure */                                  /* create the cholmod_sparse structure */
913      A = cholmod_l_triplet_to_sparse(T, nnz, &c);      A = cholmod_triplet_to_sparse(T, nnz, &c);
914      cholmod_l_free_triplet(&T, &c);      cholmod_free_triplet(&T, &c);
915                                  /* copy the information to the SEXP */                                  /* copy the information to the SEXP */
916      ans = PROTECT(NEW_OBJECT(MAKE_CLASS(cls)));      ans = PROTECT(NEW_OBJECT(MAKE_CLASS(cls)));
917  /* FIXME: This has been copied from chm_sparse_to_SEXP in chm_common.c */  /* FIXME: This has been copied from chm_sparse_to_SEXP in chm_common.c */
918                                  /* allocate and copy common slots */                                  /* allocate and copy common slots */
919      nnz = cholmod_l_nnz(A, &c);      nnz = cholmod_nnz(A, &c);
920      dims = INTEGER(ALLOC_SLOT(ans, Matrix_DimSym, INTSXP, 2));      dims = INTEGER(ALLOC_SLOT(ans, Matrix_DimSym, INTSXP, 2));
921      dims[0] = A->nrow; dims[1] = A->ncol;      dims[0] = A->nrow; dims[1] = A->ncol;
922      Memcpy(INTEGER(ALLOC_SLOT(ans, Matrix_pSym, INTSXP, A->ncol + 1)), (int*)A->p, A->ncol + 1);      Memcpy(INTEGER(ALLOC_SLOT(ans, Matrix_pSym, INTSXP, A->ncol + 1)), (int*)A->p, A->ncol + 1);
# Line 792  Line 928 
928      case 'l':      case 'l':
929          error(_("code not yet written for cls = \"lgCMatrix\""));          error(_("code not yet written for cls = \"lgCMatrix\""));
930      }      }
931      cholmod_l_free_sparse(&A, &c);  /* FIXME: dimnames are *NOT* put there yet (if non-NULL) */
932        cholmod_free_sparse(&A, &c);
933      UNPROTECT(1);      UNPROTECT(1);
934      return ans;      return ans;
935  }  }

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