dd_MatrixPtr FromEigen (const cref_matrix_t& input)
{
if (dd_debug)
{
std::cout << "from eigen input " << input << std::endl;
}
dd_debug = false;
dd_MatrixPtr M=NULL;
dd_rowrange i;
dd_colrange j;
dd_rowrange m_input = (dd_rowrange)(input.rows());
dd_colrange d_input = (dd_colrange)(7);
dd_RepresentationType rep=dd_Generator;
mytype value;
dd_NumberType NT = dd_Real;;
dd_init(value);
M=dd_CreateMatrix(m_input, d_input);
M->representation=rep;
M->numbtype=NT;
for (i = 1; i <= input.rows(); i++)
{
dd_set_d(value, 0);
dd_set(M->matrix[i-1][0],value);
for (j = 2; j <= d_input; j++)
{
dd_set_d(value, input(i-1,j-2));
dd_set(M->matrix[i-1][j-1],value);
}
}
dd_clear(value);
return M;
}
void dd_MLSetMatrixWithString(dd_rowrange m, dd_colrange d, char line[], dd_MatrixPtr M)
{
dd_rowrange i=0;
dd_colrange j=0;
char *next,*copy;
const char ct[]=", {}\n"; /* allows separators ","," ","{","}". */
mytype value;
double dval;
dd_init(value);
copy=(char *)malloc(strlen(line) + 4048); /* some extra space as buffer. Somehow linux version needs this */
strcpy(copy,line);
next=strtok(copy,ct);
i=0; j=0;
do {
#if defined GMPRATIONAL
dd_sread_rational_value(next, value);
#else
dval=atof(next);
dd_set_d(value,dval);
#endif
dd_WriteNumber(stderr,value);
dd_set(M->matrix[i][j],value);
j++;
if (j == d) {
i++; j=0;
}
} while ((next=strtok(NULL,ct))!=NULL);
free(copy);
dd_clear(value);
return;
}
SEXP redundant(SEXP m, SEXP h)
{
GetRNGstate();
if (! isString(m))
error("'m' must be character");
if (! isMatrix(m))
error("'m' must be matrix");
if (! isLogical(h))
error("'h' must be logical");
if (LENGTH(h) != 1)
error("'h' must be scalar");
SEXP m_dim;
PROTECT(m_dim = getAttrib(m, R_DimSymbol));
int nrow = INTEGER(m_dim)[0];
int ncol = INTEGER(m_dim)[1];
UNPROTECT(1);
#ifdef WOOF
printf("nrow = %d\n", nrow);
printf("ncol = %d\n", ncol);
#endif /* WOOF */
if (nrow < 2)
error("less than 2 rows, cannot be redundant");
if (ncol <= 2)
error("no cols in m[ , - c(1, 2)]");
for (int i = 0; i < nrow; i++) {
const char *foo = CHAR(STRING_ELT(m, i));
if (strlen(foo) != 1)
error("column one of 'm' not zero-or-one valued");
if (! (foo[0] == '0' || foo[0] == '1'))
error("column one of 'm' not zero-or-one valued");
}
if (! LOGICAL(h)[0])
for (int i = nrow; i < 2 * nrow; i++) {
const char *foo = CHAR(STRING_ELT(m, i));
if (strlen(foo) != 1)
error("column two of 'm' not zero-or-one valued");
if (! (foo[0] == '0' || foo[0] == '1'))
error("column two of 'm' not zero-or-one valued");
}
dd_set_global_constants();
/* note actual type of "value" is mpq_t (defined in cddmp.h) */
mytype value;
dd_init(value);
dd_MatrixPtr mf = dd_CreateMatrix(nrow, ncol - 1);
/* note our matrix has one more column than Fukuda's */
/* representation */
if(LOGICAL(h)[0])
mf->representation = dd_Inequality;
else
mf->representation = dd_Generator;
mf->numbtype = dd_Rational;
/* linearity */
for (int i = 0; i < nrow; i++) {
const char *foo = CHAR(STRING_ELT(m, i));
if (foo[0] == '1')
set_addelem(mf->linset, i + 1);
/* note conversion from zero-origin to one-origin indexing */
}
/* matrix */
for (int j = 1, k = nrow; j < ncol; j++)
for (int i = 0; i < nrow; i++, k++) {
const char *rat_str = CHAR(STRING_ELT(m, k));
if (mpq_set_str(value, rat_str, 10) == -1)
ERROR_WITH_CLEANUP_3("error converting string to GMP rational");
mpq_canonicalize(value);
dd_set(mf->matrix[i][j - 1], value);
/* note our matrix has one more column than Fukuda's */
}
dd_rowset impl_linset, redset;
dd_rowindex newpos;
dd_ErrorType err = dd_NoError;
dd_MatrixCanonicalize(&mf, &impl_linset, &redset, &newpos, &err);
if (err != dd_NoError) {
rr_WriteErrorMessages(err);
ERROR_WITH_CLEANUP_6("failed");
}
int mrow = mf->rowsize;
int mcol = mf->colsize;
if (mcol + 1 != ncol)
ERROR_WITH_CLEANUP_6("Cannot happen! computed matrix has"
" wrong number of columns");
#ifdef WOOF
printf("mrow = %d\n", mrow);
printf("mcol = %d\n", mcol);
#endif /* WOOF */
SEXP bar;
PROTECT(bar = allocMatrix(STRSXP, mrow, ncol));
/* linearity output */
for (int i = 0; i < mrow; i++)
if (set_member(i + 1, mf->linset))
SET_STRING_ELT(bar, i, mkChar("1"));
else
SET_STRING_ELT(bar, i, mkChar("0"));
/* note conversion from zero-origin to one-origin indexing */
/* matrix output */
for (int j = 1, k = mrow; j < ncol; j++)
for (int i = 0; i < mrow; i++, k++) {
dd_set(value, mf->matrix[i][j - 1]);
/* note our matrix has one more column than Fukuda's */
char *zstr = NULL;
zstr = mpq_get_str(zstr, 10, value);
SET_STRING_ELT(bar, k, mkChar(zstr));
free(zstr);
}
if (mf->representation == dd_Inequality) {
SEXP attr_name, attr_value;
PROTECT(attr_name = ScalarString(mkChar("representation")));
PROTECT(attr_value = ScalarString(mkChar("H")));
setAttrib(bar, attr_name, attr_value);
UNPROTECT(2);
}
if (mf->representation == dd_Generator) {
SEXP attr_name, attr_value;
PROTECT(attr_name = ScalarString(mkChar("representation")));
PROTECT(attr_value = ScalarString(mkChar("V")));
setAttrib(bar, attr_name, attr_value);
UNPROTECT(2);
}
int impl_size = set_card(impl_linset);
int red_size = set_card(redset);
int nresult = 1;
int iresult = 1;
SEXP baz = NULL;
if (impl_size > 0) {
PROTECT(baz = rr_set_fwrite(impl_linset));
nresult++;
}
SEXP qux = NULL;
if (red_size > 0) {
PROTECT(qux = rr_set_fwrite(redset));
nresult++;
}
SEXP fred = NULL;
{
PROTECT(fred = allocVector(INTSXP, nrow));
for (int i = 1; i <= nrow; i++)
INTEGER(fred)[i - 1] = newpos[i];
nresult++;
}
#ifdef WOOF
fprintf(stderr, "impl_size = %d\n", impl_size);
fprintf(stderr, "red_size = %d\n", red_size);
fprintf(stderr, "nresult = %d\n", nresult);
if (baz)
fprintf(stderr, "LENGTH(baz) = %d\n", LENGTH(baz));
if (qux)
fprintf(stderr, "LENGTH(qux) = %d\n", LENGTH(qux));
#endif /* WOOF */
SEXP result, resultnames;
PROTECT(result = allocVector(VECSXP, nresult));
PROTECT(resultnames = allocVector(STRSXP, nresult));
SET_STRING_ELT(resultnames, 0, mkChar("output"));
SET_VECTOR_ELT(result, 0, bar);
if (baz) {
SET_STRING_ELT(resultnames, iresult, mkChar("implied.linearity"));
SET_VECTOR_ELT(result, iresult, baz);
iresult++;
}
if (qux) {
SET_STRING_ELT(resultnames, iresult, mkChar("redundant"));
SET_VECTOR_ELT(result, iresult, qux);
iresult++;
}
{
SET_STRING_ELT(resultnames, iresult, mkChar("new.position"));
SET_VECTOR_ELT(result, iresult, fred);
iresult++;
}
namesgets(result, resultnames);
set_free(redset);
set_free(impl_linset);
free(newpos);
dd_FreeMatrix(mf);
dd_clear(value);
dd_free_global_constants();
PutRNGstate();
UNPROTECT(nresult + 2);
return result;
}
SEXP allfaces(SEXP hrep)
{
GetRNGstate();
if (! isMatrix(hrep))
error("'hrep' must be matrix");
if (! isString(hrep))
error("'hrep' must be character");
SEXP hrep_dim;
PROTECT(hrep_dim = getAttrib(hrep, R_DimSymbol));
int nrow = INTEGER(hrep_dim)[0];
int ncol = INTEGER(hrep_dim)[1];
UNPROTECT(1);
if (nrow <= 0)
error("no rows in 'hrep'");
if (ncol <= 3)
error("three or fewer cols in hrep");
for (int i = 0; i < nrow; ++i) {
const char *foo = CHAR(STRING_ELT(hrep, i));
if (strlen(foo) != 1)
error("column one of 'hrep' not zero-or-one valued");
if (! (foo[0] == '0' || foo[0] == '1'))
error("column one of 'hrep' not zero-or-one valued");
}
dd_set_global_constants();
/* note actual type of "value" is mpq_t (defined in cddmp.h) */
mytype value;
dd_init(value);
dd_MatrixPtr mf = dd_CreateMatrix(nrow, ncol - 1);
/* note our matrix has one more column than Fukuda's */
mf->representation = dd_Inequality;
mf->numbtype = dd_Rational;
/* linearity */
for (int i = 0; i < nrow; ++i) {
const char *foo = CHAR(STRING_ELT(hrep, i));
if (foo[0] == '1')
set_addelem(mf->linset, i + 1);
/* note conversion from zero-origin to one-origin indexing */
}
/* matrix */
for (int j = 1, k = nrow; j < ncol; ++j)
for (int i = 0; i < nrow; ++i, ++k) {
const char *rat_str = CHAR(STRING_ELT(hrep, k));
if (mpq_set_str(value, rat_str, 10) == -1) {
dd_FreeMatrix(mf);
dd_clear(value);
dd_free_global_constants();
error("error converting string to GMP rational");
}
mpq_canonicalize(value);
dd_set(mf->matrix[i][j - 1], value);
/* note our matrix has one more column than Fukuda's */
}
SEXP result;
PROTECT(result = FaceEnum(mf));
dd_FreeMatrix(mf);
dd_clear(value);
dd_free_global_constants();
if (result == R_NilValue)
error("failed");
PutRNGstate();
UNPROTECT(1);
return result;
}
static dd_ErrorType FaceEnumHelper(dd_MatrixPtr M, dd_rowset R, dd_rowset S)
{
dd_ErrorType err;
dd_rowset LL, ImL, RR, SS, Lbasis;
dd_rowrange iprev = 0;
dd_colrange dim;
dd_LPSolutionPtr lps = NULL;
set_initialize(&LL, M->rowsize);
set_initialize(&RR, M->rowsize);
set_initialize(&SS, M->rowsize);
set_copy(LL, M->linset);
set_copy(RR, R);
set_copy(SS, S);
/* note actual type of "value" is mpq_t (defined in cddmp.h) */
mytype value;
dd_init(value);
err = dd_NoError;
dd_boolean foo = dd_ExistsRestrictedFace(M, R, S, &err);
if (err != dd_NoError) {
#ifdef MOO
fprintf(stderr, "err from dd_ExistsRestrictedFace\n");
fprintf(stderr, "err = %d\n", err);
#endif /* MOO */
set_free(LL);
set_free(RR);
set_free(SS);
dd_clear(value);
return err;
}
if (foo) {
set_uni(M->linset, M->linset, R);
err = dd_NoError;
dd_FindRelativeInterior(M, &ImL, &Lbasis, &lps, &err);
if (err != dd_NoError) {
#ifdef MOO
fprintf(stderr, "err from dd_FindRelativeInterior\n");
fprintf(stderr, "err = %d\n", err);
#endif /* MOO */
dd_FreeLPSolution(lps);
set_free(ImL);
set_free(Lbasis);
set_free(LL);
set_free(RR);
set_free(SS);
dd_clear(value);
return err;
}
dim = M->colsize - set_card(Lbasis) - 1;
set_uni(M->linset, M->linset, ImL);
SEXP mydim, myactive, myrip;
PROTECT(mydim = ScalarInteger(dim));
PROTECT(myactive = rr_set_fwrite(M->linset));
int myd = (lps->d) - 2;
PROTECT(myrip = allocVector(STRSXP, myd));
for (int j = 1; j <= myd; j++) {
dd_set(value, lps->sol[j]);
char *zstr = NULL;
zstr = mpq_get_str(zstr, 10, value);
SET_STRING_ELT(myrip, j - 1, mkChar(zstr));
free(zstr);
}
REPROTECT(dimlist = CONS(mydim, dimlist), dimidx);
REPROTECT(riplist = CONS(myrip, riplist), ripidx);
REPROTECT(activelist = CONS(myactive, activelist), activeidx);
UNPROTECT(3);
dd_FreeLPSolution(lps);
set_free(ImL);
set_free(Lbasis);
if (dim > 0) {
for (int i = 1; i <= M->rowsize; i++) {
if ((! set_member(i, M->linset)) && (! set_member(i, S))) {
set_addelem(RR, i);
if (iprev) {
set_delelem(RR, iprev);
set_delelem(M->linset, iprev);
set_addelem(SS, iprev);
}
iprev = i;
err = FaceEnumHelper(M, RR, SS);
if (err != dd_NoError) {
#ifdef MOO
fprintf(stderr, "err from FaceEnumHelper\n");
fprintf(stderr, "err = %d\n", err);
#endif /* MOO */
set_copy(M->linset, LL);
set_free(LL);
set_free(RR);
set_free(SS);
dd_clear(value);
return err;
}
}
}
}
}
set_copy(M->linset, LL);
set_free(LL);
set_free(RR);
set_free(SS);
dd_clear(value);
return dd_NoError;
}
dd_MatrixPtr dd_BlockElimination(dd_MatrixPtr M, dd_colset delset, dd_ErrorType *error)
/* Eliminate the variables (columns) delset by
the Block Elimination with dd_DoubleDescription algorithm.
Given (where y is to be eliminated):
c1 + A1 x + B1 y >= 0
c2 + A2 x + B2 y = 0
1. First construct the dual system: z1^T B1 + z2^T B2 = 0, z1 >= 0.
2. Compute the generators of the dual.
3. Then take the linear combination of the original system with each generator.
4. Remove redundant inequalies.
*/
{
dd_MatrixPtr Mdual=NULL, Mproj=NULL, Gdual=NULL;
dd_rowrange i,h,m,mproj,mdual,linsize;
dd_colrange j,k,d,dproj,ddual,delsize;
dd_colindex delindex;
mytype temp,prod;
dd_PolyhedraPtr dualpoly;
dd_ErrorType err=dd_NoError;
dd_boolean localdebug=dd_FALSE;
*error=dd_NoError;
m= M->rowsize;
d= M->colsize;
delindex=(long*)calloc(d+1,sizeof(long));
dd_init(temp);
dd_init(prod);
k=0; delsize=0;
for (j=1; j<=d; j++){
if (set_member(j, delset)){
k++; delsize++;
delindex[k]=j; /* stores the kth deletion column index */
}
}
if (localdebug) dd_WriteMatrix(stdout, M);
linsize=set_card(M->linset);
ddual=m+1;
mdual=delsize + m - linsize; /* #equalitions + dimension of z1 */
/* setup the dual matrix */
Mdual=dd_CreateMatrix(mdual, ddual);
Mdual->representation=dd_Inequality;
for (i = 1; i <= delsize; i++){
set_addelem(Mdual->linset,i); /* equality */
for (j = 1; j <= m; j++) {
dd_set(Mdual->matrix[i-1][j], M->matrix[j-1][delindex[i]-1]);
}
}
k=0;
for (i = 1; i <= m; i++){
if (!set_member(i, M->linset)){
/* set nonnegativity for the dual variable associated with
each non-linearity inequality. */
k++;
dd_set(Mdual->matrix[delsize+k-1][i], dd_one);
}
}
/* 2. Compute the generators of the dual system. */
dualpoly=dd_DDMatrix2Poly(Mdual, &err);
Gdual=dd_CopyGenerators(dualpoly);
/* 3. Take the linear combination of the original system with each generator. */
dproj=d-delsize;
mproj=Gdual->rowsize;
Mproj=dd_CreateMatrix(mproj, dproj);
Mproj->representation=dd_Inequality;
set_copy(Mproj->linset, Gdual->linset);
for (i=1; i<=mproj; i++){
k=0;
for (j=1; j<=d; j++){
if (!set_member(j, delset)){
k++; /* new index of the variable x_j */
dd_set(prod, dd_purezero);
for (h = 1; h <= m; h++){
dd_mul(temp,M->matrix[h-1][j-1],Gdual->matrix[i-1][h]);
dd_add(prod,prod,temp);
}
dd_set(Mproj->matrix[i-1][k-1],prod);
}
}
}
if (localdebug) printf("Size of the projection system: %ld x %ld\n", mproj, dproj);
dd_FreePolyhedra(dualpoly);
free(delindex);
dd_clear(temp);
dd_clear(prod);
dd_FreeMatrix(Mdual);
dd_FreeMatrix(Gdual);
return Mproj;
}
dd_MatrixPtr dd_FourierElimination(dd_MatrixPtr M,dd_ErrorType *error)
/* Eliminate the last variable (column) from the given H-matrix using
the standard Fourier Elimination.
*/
{
dd_MatrixPtr Mnew=NULL;
dd_rowrange i,inew,ip,in,iz,m,mpos=0,mneg=0,mzero=0,mnew;
dd_colrange j,d,dnew;
dd_rowindex posrowindex, negrowindex,zerorowindex;
mytype temp1,temp2;
dd_boolean localdebug=dd_FALSE;
*error=dd_NoError;
m= M->rowsize;
d= M->colsize;
if (d<=1){
*error=dd_ColIndexOutOfRange;
if (localdebug) {
printf("The number of column is too small: %ld for Fourier's Elimination.\n",d);
}
goto _L99;
}
if (M->representation==dd_Generator){
*error=dd_NotAvailForV;
if (localdebug) {
printf("Fourier's Elimination cannot be applied to a V-polyhedron.\n");
}
goto _L99;
}
if (set_card(M->linset)>0){
*error=dd_CannotHandleLinearity;
if (localdebug) {
printf("The Fourier Elimination function does not handle equality in this version.\n");
}
goto _L99;
}
/* Create temporary spaces to be removed at the end of this function */
posrowindex=(long*)calloc(m+1,sizeof(long));
negrowindex=(long*)calloc(m+1,sizeof(long));
zerorowindex=(long*)calloc(m+1,sizeof(long));
dd_init(temp1);
dd_init(temp2);
for (i = 1; i <= m; i++) {
if (dd_Positive(M->matrix[i-1][d-1])){
mpos++;
posrowindex[mpos]=i;
} else if (dd_Negative(M->matrix[i-1][d-1])) {
mneg++;
negrowindex[mneg]=i;
} else {
mzero++;
zerorowindex[mzero]=i;
}
} /*of i*/
if (localdebug) {
dd_WriteMatrix(stdout, M);
printf("No of (+ - 0) rows = (%ld, %ld, %ld)\n", mpos,mneg, mzero);
}
/* The present code generates so many redundant inequalities and thus
is quite useless, except for very small examples
*/
mnew=mzero+mpos*mneg; /* the total number of rows after elimination */
dnew=d-1;
Mnew=dd_CreateMatrix(mnew, dnew);
dd_CopyArow(Mnew->rowvec, M->rowvec, dnew);
/* set_copy(Mnew->linset,M->linset); */
Mnew->numbtype=M->numbtype;
Mnew->representation=M->representation;
Mnew->objective=M->objective;
/* Copy the inequalities independent of x_d to the top of the new matrix. */
for (iz = 1; iz <= mzero; iz++){
for (j = 1; j <= dnew; j++) {
dd_set(Mnew->matrix[iz-1][j-1], M->matrix[zerorowindex[iz]-1][j-1]);
}
}
/* Create the new inequalities by combining x_d positive and negative ones. */
inew=mzero; /* the index of the last x_d zero inequality */
for (ip = 1; ip <= mpos; ip++){
for (in = 1; in <= mneg; in++){
inew++;
dd_neg(temp1, M->matrix[negrowindex[in]-1][d-1]);
for (j = 1; j <= dnew; j++) {
dd_LinearComb(temp2,M->matrix[posrowindex[ip]-1][j-1],temp1,\
M->matrix[negrowindex[in]-1][j-1],\
M->matrix[posrowindex[ip]-1][d-1]);
dd_set(Mnew->matrix[inew-1][j-1],temp2);
}
dd_Normalize(dnew,Mnew->matrix[inew-1]);
}
}
free(posrowindex);
free(negrowindex);
free(zerorowindex);
dd_clear(temp1);
dd_clear(temp2);
_L99:
return Mnew;
}
SEXP impliedLinearity(SEXP m, SEXP h)
{
GetRNGstate();
if (! isMatrix(m))
error("'m' must be matrix");
if (! isLogical(h))
error("'h' must be logical");
if (LENGTH(h) != 1)
error("'h' must be scalar");
if (! isString(m))
error("'m' must be character");
SEXP m_dim;
PROTECT(m_dim = getAttrib(m, R_DimSymbol));
int nrow = INTEGER(m_dim)[0];
int ncol = INTEGER(m_dim)[1];
UNPROTECT(1);
if (nrow <= 1)
error("no use if only one row");
if (ncol <= 3)
error("no use if only one col");
for (int i = 0; i < nrow; i++) {
const char *foo = CHAR(STRING_ELT(m, i));
if (strlen(foo) != 1)
error("column one of 'm' not zero-or-one valued");
if (! (foo[0] == '0' || foo[0] == '1'))
error("column one of 'm' not zero-or-one valued");
}
if (! LOGICAL(h)[0])
for (int i = nrow; i < 2 * nrow; i++) {
const char *foo = CHAR(STRING_ELT(m, i));
if (strlen(foo) != 1)
error("column two of 'm' not zero-or-one valued");
if (! (foo[0] == '0' || foo[0] == '1'))
error("column two of 'm' not zero-or-one valued");
}
dd_set_global_constants();
/* note actual type of "value" is mpq_t (defined in cddmp.h) */
mytype value;
dd_init(value);
dd_MatrixPtr mf = dd_CreateMatrix(nrow, ncol - 1);
/* note our matrix has one more column than Fukuda's */
/* representation */
if(LOGICAL(h)[0])
mf->representation = dd_Inequality;
else
mf->representation = dd_Generator;
mf->numbtype = dd_Rational;
/* linearity */
for (int i = 0; i < nrow; i++) {
const char *foo = CHAR(STRING_ELT(m, i));
if (foo[0] == '1')
set_addelem(mf->linset, i + 1);
/* note conversion from zero-origin to one-origin indexing */
}
/* matrix */
for (int j = 1, k = nrow; j < ncol; j++)
for (int i = 0; i < nrow; i++, k++) {
const char *rat_str = CHAR(STRING_ELT(m, k));
if (mpq_set_str(value, rat_str, 10) == -1) {
dd_FreeMatrix(mf);
dd_clear(value);
dd_free_global_constants();
error("error converting string to GMP rational");
}
mpq_canonicalize(value);
dd_set(mf->matrix[i][j - 1], value);
/* note our matrix has one more column than Fukuda's */
}
dd_ErrorType err = dd_NoError;
dd_rowset out = dd_ImplicitLinearityRows(mf, &err);
if (err != dd_NoError) {
rr_WriteErrorMessages(err);
set_free(out);
dd_FreeMatrix(mf);
dd_clear(value);
dd_free_global_constants();
error("failed");
}
SEXP foo;
PROTECT(foo = rr_set_fwrite(out));
set_free(out);
dd_FreeMatrix(mf);
dd_clear(value);
dd_free_global_constants();
PutRNGstate();
UNPROTECT(1);
return foo;
}
