/*
* Find the extreme vertices between lower_bound and upper_bound of the convex
* hull of ineqs.
*
* ineqs: row-major order matrix of total length nrow*ncols
* nrows: Number of rows in matrix
* ncols: Number of columns in matrix
* lower_bound: lower bound of solution space on x-axis
* upper_bound: upper bound of solution space on y-axis
* output size: Set to size of result
*
* Returns array representing 3 by (output_size/3) matrix, where each row is:
* x_i, y_i, l_i
* Where x_i, y_i are the coordinates of the vertex, and l_i is the index of
* the input inequality that constrains the solution space *to the right* of
* vertex i.
*/
double *extreme_vertices(const double *ineqs, const size_t nrows,
const size_t ncols, float lower_bound,
float upper_bound, /*OUT*/ size_t * output_size)
{
/* Preconditions */
assert(ineqs != NULL);
assert(ncols == 3);
assert(output_size != NULL);
/* Check for approx equal lower and upper bound */
if (abs(lower_bound - upper_bound) < EPS)
return NULL;
assert(lower_bound <= upper_bound);
/*
* Initialize library
* TODO: Do we want to do this on every call?
*/
dd_set_global_constants();
dd_ErrorType err;
dd_MatrixPtr generators;
dd_MatrixPtr m =
init_ineq_doubles(ineqs, nrows, ncols, lower_bound, upper_bound);
dd_SetFamilyPtr incidence;
/* Outputs */
dd_PolyhedraPtr poly = dd_DDMatrix2Poly(m, &err);
if (err != dd_NoError) {
return NULL;
}
/* Get generators */
generators = dd_CopyGenerators(poly);
/* Get incidence */
incidence = dd_CopyIncidence(poly);
double *result =
list_extreme_vertices(generators, incidence, nrows, m->rowsize - 1,
output_size);
dd_FreeMatrix(m);
dd_FreeMatrix(generators);
dd_FreePolyhedra(poly);
dd_FreeSetFamily(incidence);
dd_free_global_constants();
return result;
}
int main(int argc, char *argv[])
{
/* The original LP data m x n matrix
= | b -A |
| c0 c^T |,
where the LP to be solved is to
maximize c^T x + c0
subj. to
A x <= b.
*/
dd_ErrorType err=dd_NoError;
dd_LPSolverType solver=dd_DualSimplex;
/* either DualSimplex or CrissCross */
dd_LPPtr lp,lp1;
/* pointer to LP data structure that is not visible by user. */
dd_LPSolutionPtr lps,lps1;
/* pointer to LP solution data that is visible by user. */
dd_MatrixPtr M;
dd_colrange j;
dd_DataFileType inputfile;
dd_set_global_constants();
printf("\n--- Solving an LP with dd_LPSolve, and Finding an Interior Point ---\n");
/* Input an LP using the cdd library */
dd_SetInputFile(&reading,inputfile,&err);
if (err!=dd_NoError) goto _L99;
M=dd_PolyFile2Matrix(reading, &err);
if (err!=dd_NoError) goto _L99;
/* dd_WriteMatrix(stdout, M); */
lp=dd_Matrix2LP(M, &err);
if (err!=dd_NoError) goto _L99;
/* Solve the LP by cdd LP solver. */
printf("\n--- Running dd_LPSolve ---\n");
solver=dd_DualSimplex;
dd_LPSolve(lp, solver, &err); /* Solve the LP */
if (err!=dd_NoError) goto _L99;
/* Write the LP solutions by cdd LP reporter. */
/* dd_WriteLPResult(stdout, lp, err); */
/* dd_WriteLPResult(writing, lp, err); */
/* One can access the solutions by loading them. See dd_WriteLPResult
for outputing the results correctly. */
lps=dd_CopyLPSolution(lp);
if (lps->LPS==dd_Optimal){
printf("Optimal solution found:\n");
printf(" primal_solution\n");
for (j=1; j<lps->d; j++) {
printf(" %3ld : ",j);
dd_WriteNumber(stdout,lps->sol[j]);
printf("\n");
}
printf(" dual_solution\n");
for (j=1; j<lps->d; j++){
if (lps->nbindex[j+1]>0) {
printf(" %3ld : ",lps->nbindex[j+1]);
dd_WriteNumber(stdout,lps->dsol[j]); printf("\n");
}
}
printf(" optimal_value : "); dd_WriteNumber(stdout,lps->optvalue);
printf("\n");
}
/* Find an interior point with cdd LP library. */
printf("\n--- Running dd_FindInteriorPoint ---\n");
lp1=dd_MakeLPforInteriorFinding(lp);
printf("The LP to be solved for finding an interior point:\n");
dd_WriteLP(stdout,lp1);
dd_LPSolve(lp1,solver,&err);
if (err!=dd_NoError) goto _L99;
/* Write an interior point. */
lps1=dd_CopyLPSolution(lp1);
if (dd_Positive(lps1->optvalue)){
printf("\nAn interior point found: (");
for (j=1; j <(lps1->d)-1; j++) {
dd_WriteNumber(stdout,lps1->sol[j]);
}
printf(")\n");
}
if (dd_Negative(lps1->optvalue))
printf("\nThe feasible region is empty.\n");
if (dd_EqualToZero(lps1->optvalue))
printf("\nThe feasible region is nonempty but has no interior point.\n");
/* Free allocated spaces. */
dd_FreeLPSolution(lps);
dd_FreeLPData(lp);
dd_FreeLPSolution(lps1);
dd_FreeLPData(lp1);
dd_FreeMatrix(M);
_L99:;
if (err!=dd_NoError) dd_WriteErrorMessages(stdout, err);
dd_free_global_constants(); /* At the end, this should be called. */
return 0;
}
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;
}
int main(int argc, char *argv[])
{
dd_MatrixPtr M=NULL,M1=NULL,M2=NULL;
dd_colrange j,s,d;
dd_ErrorType err=dd_NoError;
dd_rowset redset,impl_linset;
dd_rowindex newpos;
mytype val;
dd_DataFileType inputfile;
FILE *reading=NULL;
dd_set_global_constants(); /* First, this must be called. */
dd_init(val);
if (argc>1) strcpy(inputfile,argv[1]);
if (argc<=1 || !SetInputFile(&reading,argv[1])){
dd_WriteProgramDescription(stdout);
fprintf(stdout,"\ncddlib test program to apply Fourier's Elimination to an H-polyhedron.\n");
dd_SetInputFile(&reading,inputfile, &err);
}
if (err==dd_NoError) {
M=dd_PolyFile2Matrix(reading, &err);
}
else {
fprintf(stderr,"Input file not found\n");
goto _L99;
}
if (err!=dd_NoError) goto _L99;
d=M->colsize;
M2=dd_CopyMatrix(M);
printf("How many variables to elminate? (max %ld): ",d-1);
scanf("%ld",&s);
if (s>0 && s < d){
for (j=1; j<=s; j++){
M1=dd_FourierElimination(M2, &err);
printf("\nRemove the variable %ld. The resulting redundant system.\n",d-j);
dd_WriteMatrix(stdout, M1);
dd_MatrixCanonicalize(&M1, &impl_linset, &redset, &newpos, &err);
if (err!=dd_NoError) goto _L99;
fprintf(stdout, "\nRedundant rows: ");
set_fwrite(stdout, redset);
dd_FreeMatrix(M2);
M2=M1;
set_free(redset);
set_free(impl_linset);
free(newpos);
}
printf("\nNonredundant representation:\n");
dd_WriteMatrix(stdout, M1);
} else {
printf("Value out of range\n");
}
dd_FreeMatrix(M);
dd_FreeMatrix(M1);
dd_clear(val);
_L99:;
/* if (err!=dd_NoError) dd_WriteErrorMessages(stderr,err); */
dd_free_global_constants(); /* At the end, this should be called. */
return 0;
}
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;
}
