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graphtheory.cc
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graphtheory.cc
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/*
* graphtheory.cc
*
* (c) 2018 Luka Marohnić
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation; either version 3 of the License, or
* (at your option) any later version.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program. If not, see <http://www.gnu.org/licenses/>.
*/
#include "giacPCH.h"
#include "giac.h"
#include "graphtheory.h"
#include "optimization.h"
#include "signalprocessing.h"
using namespace std;
#ifndef NO_NAMESPACE_GIAC
namespace giac {
#endif // ndef NO_NAMESPACE_GIAC
bool is_graphe(const gen &g) {
return graphe::from_gen(g)!=NULL;
}
inline bool is_seq_vect(const gen &g) {
return g.type==_VECT && g.subtype==_SEQ__VECT;
}
/* error messages */
static const char *gt_error_messages[] = {
gettext("Unknown error"), // 0
gettext("Argument is not a graph"), // 1
gettext("Weighted graph is required"), // 2
gettext("Unweighted graph is required"), // 3
gettext("Directed graph is required"), // 4
gettext("Undirected graph is required"), // 5
gettext("does not specify an edge"), // 6
gettext("Mixing edges and arcs not allowed"), // 7
gettext("Weight/adjacency matrix must be symmetric for undirected graphs"), // 8
gettext("Failed to read graph from file"), // 9
gettext("Edge not found"), // 10
gettext("Vertex not found"), // 11
gettext("Graph is not a tree"), // 12
gettext("Exactly one root node must be specified per connected component"), // 13
gettext("Invalid root node specification"), // 14
gettext("Graph is not planar"), // 15
gettext("Connected graph required"), // 16
gettext("Invalid drawing method specification"), // 17
gettext("does not specify a cycle in the given graph"), // 18
gettext("No cycle found"), // 19
gettext("Graph name is not recognized"), // 20
gettext("Argument is not a subgraph"), // 21
gettext("Graph is null"), // 22
gettext("Expected \"tag\"=value pair"), // 23
gettext("Argument is not a valid graphic sequence"), // 24
gettext("Graph is not acyclic"), // 25
gettext("Biconnected graph required"), // 26
gettext("Graph is not bipartite"), // 27
gettext("Wrong number of arguments"), // 28
gettext("Positive integer required"), // 29
gettext("Invalid vertex specification"), // 30
gettext("Expected an identifier"), // 31
};
gen gt_err(int code) {
return generr(gt_error_messages[code]);
}
gen gt_err(const gen &g,int code) {
string str;
str+=gen2string(g);
str+=": ";
str+=gt_error_messages[code];
return generr(str.c_str());
}
bool is_unassigned_identifier(const gen &g,GIAC_CONTEXT) {
return g.type==_IDNT && _eval(g,contextptr)==g;
}
void identifier_assign(const identificateur &var,const gen &value,GIAC_CONTEXT) {
_eval(symbolic(at_sto,makesequence(value,var)),contextptr);
}
bool has_suffix(const string &str,const string &suffix)
{
return str.size()>=suffix.size() &&
str.compare(str.size()-suffix.size(),suffix.size(),suffix)==0;
}
string strip_string(const string &str) {
string res(str);
int i=0;
for (;res[i]==' ';++i);
res=res.substr(i);
#if 1
i=int(res.size())-1;
for (;i>=0;--i){
if (res[i]!=' ')
break;
}
res=res.substr(0,i+1);
#else
while (res.back()==' ') {
res.pop_back();
}
#endif
return res;
}
string make_absolute_file_path(const string &relative_path) {
#ifdef _WIN32
return relative_path;
#else
if (relative_path[0]=='/')
return relative_path;
#ifdef HAVE_NO_CWD
string path="/"+relative_path;
#else
string path=string(getcwd(0,0))+"/"+relative_path;
#endif
vector<string> tokens;
size_t lastpos=0,pos;
while ((pos=path.find_first_of('/',lastpos))!=string::npos) {
tokens.push_back(path.substr(lastpos,pos-lastpos));
lastpos=pos+1;
}
tokens.push_back(path.substr(lastpos));
vector<string>::iterator it;
for (it=tokens.begin();it!=tokens.end();++it) {
*it=strip_string(*it);
}
int i;
while ((it=find(tokens.begin(),tokens.end(),string("..")))!=tokens.end()) {
if (it==tokens.begin())
return path;
i=it-tokens.begin()-1;
tokens.erase(it);
tokens.erase(tokens.begin()+i);
}
string res;
for (it=tokens.begin();it!=tokens.end();++it) {
res=res+*it;
if (it+1!=tokens.end())
res=res+"/";
}
return res;
#endif // _WIN32
}
bool vertices_from_integer_or_vecteur(const gen &g,graphe &G) {
vecteur V;
int n;
if (g.is_integer()) {
n=g.val;
if (n<1)
return false;
G.make_default_labels(V,n);
} else if (g.type==_VECT) {
V=*g._VECTptr;
if (V.empty())
return false;
n=V.size();
} else return false;
G.add_nodes(V);
return true;
}
void parse_trail(graphe &G,const gen &g) {
assert(g.is_symb_of_sommet(at_trail));
const vecteur &trail=*g._SYMBptr->feuille._VECTptr;
int n=trail.size();
for (int i=0;i<n-1;++i) {
G.add_edge(trail[i],trail[i+1]);
}
}
bool parse_vertex_colors(graphe &G,const gen &g,const graphe::ivector &nodes=graphe::ivector(0)) {
if (g.type==_VECT) {
assert(int(g._VECTptr->size()==(nodes.empty()?G.node_count():int(nodes.size()))));
int k=0;
for (const_iterateur it=g._VECTptr->begin();it!=g._VECTptr->end();++it) {
if (!it->is_integer())
return false;
G.set_node_attribute(nodes.empty()?k:nodes[k],_GT_ATTRIB_COLOR,it->val);
++k;
}
} else if (g.is_integer()) {
if (g.val<0)
return false;
if (nodes.empty()) {
for (int k=G.node_count();k-->0;)
G.set_node_attribute(k,_GT_ATTRIB_COLOR,g.val);
} else {
for (graphe::ivector_iter it=nodes.begin();it!=nodes.end();++it)
G.set_node_attribute(*it,_GT_ATTRIB_COLOR,g.val);
}
} else return false;
return true;
}
bool parse_vertex_coordinates(graphe &G,const vecteur &v,bool &size_error) {
vecteur c;
int i=0,dim=-1;
for (const_iterateur it=v.begin();it!=v.end();++it) {
if (it->is_symb_of_sommet(at_point))
c=*it->_SYMBptr->feuille._VECTptr;
else if (it->type==_CPLX) {
c.resize(2);
c[0]=*it->_CPLXptr;
c[1]=*(it->_CPLXptr+1);
} else if (it->type==_VECT) {
c=*it->_VECTptr;
} else return false;
if (dim<0)
dim=c.size();
else if (dim!=int(c.size())) {
size_error=true;
return false;
}
G.set_node_attribute(i++,_GT_ATTRIB_POSITION,c);
}
return true;
}
bool parse_matrix(graphe &G,const matrice &m,bool is_weight_matrix,int mode,bool &size_error) {
int n=m.size();
size_error=false;
if (int(m.front()._VECTptr->size())!=n || (mode>0 && G.node_count()!=n)) {
size_error=true;
return false;
}
if (!has_num_coeff(_evalf(m,context0)))
return false;
bool isdir=G.is_directed() || m!=mtran(m),isweighted=is_weight_matrix;
if (mode==0) {
vecteur V;
G.make_default_labels(V,n);
G.add_nodes(V);
}
if (mode<2) {
G.set_directed(isdir);
for (int i=0;i<n;++i) {
for (int j=isdir?0:i+1;j<n;++j) {
if (i==j)
continue;
const gen &w=m[i][j];
if (!is_zero(w)) {
G.add_edge(i,j);
if (!is_one(w))
isweighted=true;
}
}
}
}
if (isweighted)
G.make_weighted(m);
return true;
}
bool parse_edge_with_weight(graphe &G,const vecteur &E) {
if (E.size()!=2)
return false;
const vecteur &e=*E.front()._VECTptr;
const gen &w=E.back();
if (e.size()!=2 || e.front()==e.back())
return false;
if (w.type==_MAP) { // a map of attributes is given instead of a weight
graphe::attrib a;
for (gen_map::const_iterator it=w._MAPptr->begin();it!=w._MAPptr->end();++it) {
if (it->first.type!=_STRNG)
return false;
a[G.tag2index(*it->first._STRNGptr)]=it->second;
}
G.add_edge(e.front(),e.back(),a);
} else {
if (!G.is_weighted())
G.set_weighted(true);
G.add_edge(e.front(),e.back(),w);
}
return true;
}
bool parse_edges(graphe &G,const vecteur &E,bool is_set,int &addc) {
if (is_set) {
for (const_iterateur it=E.begin();it!=E.end();++it) {
if (it->type!=_VECT || it->_VECTptr->size()!=2)
return false;
if (it->_VECTptr->front().type!=_VECT) {
if (it->_VECTptr->front()==it->_VECTptr->back())
return false;
if (G.add_edge(it->_VECTptr->front(),it->_VECTptr->back()))
++addc;
} else {
if (!parse_edge_with_weight(G,*it->_VECTptr))
return false;
}
}
} else {
int n=E.size();
if (n<2)
return false;
if (E.front().type==_VECT) {
if (!parse_edge_with_weight(G,E))
return false;
} else {
for (int i=0;i<n-1;++i) {
if (E[i]==E[i+1])
return false;
if (G.add_edge(E[i],E[i+1]))
++addc;
}
}
}
return true;
}
void parse_lp_options(const_iterateur opt_start,const_iterateur opt_end,bool *store,int *k,int &tm_lim,double &gap_tol,bool &verbose,GIAC_CONTEXT) {
for (const_iterateur it=opt_start;it!=opt_end;++it) {
if (store!=NULL && *it==at_sto)
*store=true;
else if (it->is_integer() && it->val>0) {
if (is_mcint(*it,_LP_VERBOSE))
verbose=true;
else if (k!=NULL)
*k=it->val;
} else if (is_equal(*it)) {
const gen &lhs=it->_SYMBptr->feuille._VECTptr->front();
const gen &rhs=it->_SYMBptr->feuille._VECTptr->back();
if (is_mcint(lhs)) {
switch (lhs.val) {
case _LP_TIME_LIMIT:
if (!rhs.is_integer() || rhs.val<=0)
generr(gettext("Expected a positive integer"));
tm_lim=rhs.val;
break;
case _LP_GAP_TOLERANCE:
if (!is_real_number(rhs,contextptr) || !is_positive(to_real_number(rhs,contextptr),contextptr))
generr(gettext("Expected a nonnegative real number"));
gap_tol=to_real_number(rhs,contextptr).to_double(contextptr);
break;
default: gentypeerr(contextptr);
}
} else gentypeerr(contextptr);
} else gentypeerr(contextptr);
}
}
bool delete_edges(graphe &G,const vecteur &E,int &delc) {
if (ckmatrix(E)) {
if (E.front()._VECTptr->size()!=2)
return false;
for (const_iterateur it=E.begin();it!=E.end();++it) {
int i=G.node_index(it->_VECTptr->front()),j=G.node_index(it->_VECTptr->back());
if (G.remove_edge(i,j)) ++delc;
}
} else {
int n=E.size();
if (n<2)
return false;
for (int k=0;k<n-1;++k) {
int i=G.node_index(E[k]),j=G.node_index(E[k+1]);
if (G.remove_edge(i,j)) ++delc;
}
}
return true;
}
gen flights(const graphe &G,const gen vert,bool arrive,GIAC_CONTEXT) {
if (!G.is_directed())
return gt_err(_GT_ERR_DIRECTED_GRAPH_REQUIRED);
if (G.is_null())
return gt_err(_GT_ERR_GRAPH_IS_NULL);
int i=0;
if (!is_undef(vert)) {
i=G.node_index(vert);
if (i<0)
return gt_err(vert,_GT_ERR_VERTEX_NOT_FOUND);
}
vecteur res;
graphe::ivector adj;
do {
G.adjacent_nodes(i,adj);
vecteur v;
for (graphe::ivector::const_iterator it=adj.begin();it!=adj.end();++it) {
if (G.has_edge(arrive?*it:i,arrive?i:*it))
v.push_back(G.node_label(*it));
}
if (!is_undef(vert))
return sort_identifiers(v,contextptr);
res.push_back(sort_identifiers(v,contextptr));
} while (++i<G.node_count());
return change_subtype(res,_LIST__VECT);
}
gen randomgraph(const vecteur &gv,bool directed,GIAC_CONTEXT) {
graphe G(contextptr);
vecteur V;
if (gv.front().type==_VECT)
V=*gv.front()._VECTptr;
else if (gv.front().is_integer())
G.make_default_labels(V,gv.front().val);
else
return gentypeerr(contextptr);
int n=V.size();
G.reserve_nodes(n);
G.add_nodes(V);
if (gv.size()==2) {
gen p;
if (is_real_number(gv.back(),contextptr)) {
if (!is_strictly_positive(p=to_real_number(gv.back(),contextptr),contextptr))
return gentypeerr("Expected a positive constant");
G.set_directed(directed);
G.erdos_renyi(p.to_double(contextptr));
} else {
vecteur P;
if (directed)
return generr(gettext("This method cannot generate digraphs"));
if (gv.back().type==_VECT) {
P=*gv.back()._VECTptr;
} else if (gv.back().is_symb_of_sommet(at_program) || gv.back().type==_FUNC) {
vecteur L(n);
for (int i=0;i<n;++i) L[i]=i;
P=*_apply(makesequence(gv.back(),L),contextptr)._VECTptr;
}
for (iterateur it=P.begin();it!=P.end();++it) {
gen w;
if (!is_real_number(*it,contextptr) || !is_positive(w=to_real_number(*it,contextptr),contextptr))
return generr(gettext("Weights must be nonnegative real numbers"));
*it=w;
}
G.molloy_reed(P);
}
} else if (gv.size()==3) { // preferential attachment
if (directed)
return generr(gettext("This method cannot generate digraphs"));
if (!gv[1].is_integer() || !is_strictly_positive(gv[1],contextptr))
return generr(gettext("Expected a positive integer"));
if (!gv[2].is_integer() || !is_positive(gv[2],contextptr))
return generr(gettext("Expected a nonnegative integer"));
int d=gv[1].val,o=gv[2].val;
G.preferential_attachment(d,o);
} else return gt_err(_GT_ERR_WRONG_NUMBER_OF_ARGS);
return G;
}
bool compute_product_of_graphs(const vecteur &gv,graphe &P,bool cartesian,GIAC_CONTEXT) {
stack<graphe*> Gs;
for (const_iterateur it=gv.begin();it!=gv.end();++it) {
Gs.push(graphe::from_gen(*it));
if (Gs.top()==NULL)
return false;
}
P=*Gs.top();
Gs.pop();
while (!Gs.empty()) {
graphe G(P);
if (cartesian)
Gs.top()->cartesian_product(G,P); // compute Cartesian product
else Gs.top()->tensor_product(G,P); // compute tensor product
Gs.pop();
}
return true;
}
void add_prefix_to_vertex_label(gen &label,int prefix) {
string str;
str+=graphe::int2string(prefix);
str+=":";
str+=label.type==_STRNG?graphe::genstring2str(label):giac::gen2string(label);
label=graphe::str2gen(str,true);
}
int graphunion(graphe &G,const vecteur &gv,bool disjoint) {
bool have_properties=false;
int k=0,i,j;
graphe::ipairs E;
for (const_iterateur it=gv.begin();it!=gv.end();++it) {
++k;
graphe *Gk=graphe::from_gen(*it);
if (Gk==NULL)
return _GT_ERR_NOT_A_GRAPH;
if (have_properties) {
if (G.is_directed()!=Gk->is_directed())
return G.is_directed()?_GT_ERR_DIRECTED_GRAPH_REQUIRED:_GT_ERR_UNDIRECTED_GRAPH_REQUIRED;
if (G.is_weighted()!=Gk->is_weighted())
return G.is_weighted()?_GT_ERR_WEIGHTED_GRAPH_REQUIRED:_GT_ERR_UNWEIGHTED_GRAPH_REQUIRED;
} else {
G.set_directed(Gk->is_directed());
G.set_weighted(Gk->is_weighted());
have_properties=true;
}
vecteur V=Gk->vertices();
for (iterateur it=V.begin();it!=V.end();++it) {
if (disjoint)
add_prefix_to_vertex_label(*it,k);
G.add_node(*it,Gk->node_attributes(it-V.begin()));
}
Gk->get_edges_as_pairs(E);
for (graphe::ipairs_iter it=E.begin();it!=E.end();++it) {
const gen &v=V[it->first],&w=V[it->second];
i=G.node_index(v); j=G.node_index(w);
assert(i>=0 && j>=0);
if (!disjoint && G.is_weighted() && G.has_edge(i,j))
G.set_edge_attribute(i,j,_GT_ATTRIB_WEIGHT,G.weight(i,j)+Gk->weight(it->first,it->second));
if (!G.has_edge(i,j))
G.add_edge(v,w,Gk->edge_attributes(it->first,it->second));
}
}
return -1;
}
gen count_spanning_trees(const graphe &G) {
matrice L;
G.laplacian_matrix(L);
const context *ctx=G.giac_context();
return _det(_delcols(makesequence(_delrows(makesequence(L,0),ctx),0),ctx),ctx);
}
// +--------------------------------------------------------------------------+
// | GIAC COMMANDS |
// +--------------------------------------------------------------------------+
/* USAGE: foldl(op,id,r1,r2,...)
*
* Returns the composition of the binary operator or function op, with identity
* or initial value id onto its arguments r1, r2, ..., associating from the
* left. For example, given three arguments a, b and c and an initial value id,
* foldl(op,id,a,b,c) is equivalent to op(op(op(id,a),b),c).
*/
gen _foldl(const gen &g,GIAC_CONTEXT) {
if (g.type==_STRNG && g.subtype==-1) return g;
if (g.type!=_VECT || g.subtype!=_SEQ__VECT)
return gentypeerr(contextptr);
const vecteur &gv=*g._VECTptr;
if (gv.size()<3)
return gt_err(_GT_ERR_WRONG_NUMBER_OF_ARGS);
const gen &op=gv.front();
gen arg=gv[1];
for (const_iterateur it=gv.begin()+2;it!=gv.end();++it) {
arg=symb_of(op,makesequence(arg,*it));
}
return _eval(arg,contextptr);
}
static const char _foldl_s[]="foldl";
static define_unary_function_eval(__foldl,&_foldl,_foldl_s);
define_unary_function_ptr5(at_foldl,alias_at_foldl,&__foldl,0,true)
/* USAGE: foldr(op,id,r1,r2,...)
*
* Returns the composition of the binary operator or function op, with identity
* or initial value id onto its arguments r1, r2, ..., associating from the
* right. For example, given three arguments a, b and c and an initial value id,
* foldl(op,id,a,b,c) is equivalent to op(a,op(b,op(c,id))).
*/
gen _foldr(const gen &g,GIAC_CONTEXT) {
if (g.type==_STRNG && g.subtype==-1) return g;
if (g.type!=_VECT || g.subtype!=_SEQ__VECT)
return gentypeerr(contextptr);
vecteur &gv=*g._VECTptr;
if (gv.size()<3)
return gt_err(_GT_ERR_WRONG_NUMBER_OF_ARGS);
const gen &op=gv.front();
gen arg=gv[1];
for (int i=gv.size();i-->2;) {
arg=symb_of(op,makesequence(gv[i],arg));
}
return _eval(arg,contextptr);
}
static const char _foldr_s[]="foldr";
static define_unary_function_eval(__foldr,&_foldr,_foldr_s);
define_unary_function_ptr5(at_foldr,alias_at_foldr,&__foldr,0,true)
bool is_density(const gen &g,const gen &d) {
if (d==at_normal)
return g==at_normal || g==at_normald || g==at_NORMALD || g==at_randNorm || g==at_randnormald;
if (d==at_uniform)
return g==at_uniform || g==at_uniformd;
if (d==at_exp)
return g==at_exp || g==at_exponential || g==at_exponentiald || g==at_EXP;
if (d==at_poisson)
return g==at_poisson || g==at_POISSON;
if (d==at_weibull)
return g==at_weibull || g==at_weibulld;
if (d==at_Gamma)
return g==at_Gamma || g==at_gammad;
if (d==at_Beta)
return g==at_Beta || g==at_betad;
if (d==at_binomial)
return g==at_binomial || g==at_BINOMIAL;
return g==d;
}
/* USAGE: randvar(f,[params])
* random_variable(f,[params])
* randvar(f,[range=]a..b,[V])
* randvar(L,[V])
*
* Returns a random variable with the specified probability distribution.
*/
gen _randvar(const gen &g,GIAC_CONTEXT) {
if (g.type==_STRNG && g.subtype==-1) return g;
if (g.is_symb_of_sommet(at_program) || g.type==_FUNC) {
if (is_density(g,at_normal))
return symbolic(at_normald,makesequence(0.0,1.0));
if (is_density(g,at_uniform))
return symbolic(at_uniformd,makesequence(0.0,1.0));
if (is_density(g,at_exp))
return symbolic(at_exponentiald,1.0);
return g;
}
if (g.type!=_VECT)
return gentypeerr(contextptr);
vecteur items,weights,categories;
if (g.subtype==_SEQ__VECT) {
const vecteur &gv=*g._VECTptr;
if (gv.front().type==_FUNC) {
const_iterateur it=gv.begin()+1;
for (;it!=gv.end();++it) {
if (!is_real_number(*it,contextptr) && it->type!=_IDNT) break;
}
if (it==gv.end()) {
gen args=change_subtype(vecteur(gv.begin()+1,gv.end()),_SEQ__VECT);
if (is_density(gv.front(),at_exp)) {
if (args._VECTptr->size()==1)
return symbolic(at_exponentiald,args._VECTptr->front());
return gensizeerr(contextptr);
}
if (is_density(gv.front(),at_poisson)) {
if (args._VECTptr->size()==1)
return symbolic(at_poisson,args._VECTptr->front());
return gensizeerr(contextptr);
}
if (is_density(gv.front(),at_geometric)) {
if (args._VECTptr->size()==1)
return symbolic(at_geometric,args._VECTptr->front());
return gensizeerr(contextptr);
}
if (is_density(gv.front(),at_normal)) {
if (args._VECTptr->size()==2)
return symbolic(at_normald,args);
return gensizeerr(contextptr);
}
gen dist=symbolic(gv.front()._SYMBptr->sommet,args);
int nd=is_distribution(dist);
if (nd==0) return gensizeerr(contextptr);
return symbolic(distribution(nd)._SYMBptr->sommet,args);
}
}
if (gv.size()<2)
return generrdim(gettext("Too few input arguments"));
gen mean(undef),sdev(undef),a(undef),b(undef);
const gen &f=gv.front();
int cnt=1,samples=0;
for (const_iterateur it=gv.begin()+1;it!=gv.end();++it,++cnt) {
if (is_equal(*it)) {
const gen &lh=it->_SYMBptr->feuille._VECTptr->front();
const gen &rh=it->_SYMBptr->feuille._VECTptr->back();
if (lh==at_mean)
mean=rh;
else if (lh==at_stddev)
sdev=rh;
else if (lh==at_variance) {
if (!is_positive(rh,contextptr)) return generr(gettext("Variance must be nonnegative"));
sdev=sqrt(rh,contextptr);
} else if (lh==at_range) {
if (rh.type==_VECT) {
if (rh._VECTptr->size()!=2)
return gensizeerr(contextptr);
a=rh._VECTptr->front();
b=rh._VECTptr->back();
} else if (rh.is_symb_of_sommet(at_interval)) {
a=rh._SYMBptr->feuille._VECTptr->front();
b=rh._SYMBptr->feuille._VECTptr->back();
} else return generr(gettext("Invalid range specification"));
} else return generr(gettext("Unknown distribution parameter"));
} else if (it->is_symb_of_sommet(at_interval)) {
a=it->_SYMBptr->feuille._VECTptr->front();
b=it->_SYMBptr->feuille._VECTptr->back();
} else if (it->type==_VECT) {
if (f.type==_VECT) {
if (cnt!=1) return gensizeerr(contextptr);
items=*(it->_VECTptr);
} else if (cnt==1)
categories=*(it->_VECTptr);
else items=*(it->_VECTptr);
} else if (it->is_integer() && it->val>1 && cnt==2) {
samples=it->val;
} else return generr(gettext("Invalid distribution specification"));
}
if (!is_undef(sdev) && !is_strictly_positive(sdev,contextptr))
return generr(gettext("Standard deviation must be positive"));
if (f.type==_VECT) { // custom discrete distribution
weights=*f._VECTptr;
} else if (is_density(f,at_normal)) {
if (is_undef(mean)) mean=0;
if (is_undef(sdev)) sdev=1;
mean=_evalf(mean,contextptr);
sdev=_evalf(sdev,contextptr);
return symbolic(at_normald,makesequence(mean,sdev));
} else if (is_density(f,at_uniform)) {
if (!is_undef(a) && !is_undef(b)) {
if (!is_real_number(a,contextptr) || !is_real_number(b,contextptr) ||
!is_strictly_greater(b=to_real_number(b,contextptr),a=to_real_number(a,contextptr),contextptr))
return generr(gettext("Invalid distribution parameter(s)"));
return makesequence(at_uniformd,a,b);
} else if (!is_undef(mean) && !is_undef(sdev)) {
gen sqrt3=sqrt(3,contextptr);
return symbolic(at_uniformd,makesequence(mean-sqrt3*sdev,mean+sqrt3*sdev));
} else return gensizeerr(contextptr);
} else if (is_density(f,at_poisson)) {
gen lambda;
if (!is_undef(mean)) {
if (!is_undef(sdev) && !is_zero(_ratnormal(sq(sdev)-mean,contextptr)))
return gensizeerr(contextptr);
lambda=mean;
} else if (!is_undef(sdev)) {
lambda=sq(sdev);
} else return gensizeerr(contextptr);
if (!is_strictly_positive(lambda,contextptr))
return gensizeerr(contextptr);
if (!is_strictly_positive(lambda,contextptr))
return generr(gettext("Invalid distribution parameter"));
return symbolic(at_poisson,lambda);
} else if (is_density(f,at_exp)) {
gen lambda;
if (!is_undef(mean)) {
if (!is_undef(sdev) && !is_zero(_ratnormal(sdev-mean,contextptr)))
return gensizeerr(contextptr);
if (!is_strictly_positive(mean,contextptr))
return gensizeerr(contextptr);
lambda=_inv(mean,contextptr);
} else if (!is_undef(sdev)) {
lambda=_inv(sdev,contextptr);
} else return gensizeerr(contextptr);
if (!is_strictly_positive(lambda,contextptr))
return gensizeerr(contextptr);
if (!is_strictly_positive(lambda,contextptr))
return generr(gettext("Invalid distribution parameter"));
return symbolic(at_exponentiald,lambda);
} else if (is_density(f,at_weibull)) {
if (is_undef(mean) || is_undef(sdev) || !is_strictly_positive(mean,contextptr))
return gensizeerr(contextptr);
gen var=sq(sdev);
if (is_zero(var))
return gensizeerr(contextptr);
identificateur tmp(" k");
gen e=_Gamma(1+gen(2)/tmp,contextptr)/_Gamma(1+gen(1)/tmp,contextptr)-var/sq(mean)-1;
gen k=_solve(makesequence(e,symb_equal(tmp,max(1,_inv(var,contextptr),contextptr)),_NEWTON_SOLVER),contextptr);
gen lambda=mean/_Gamma(1+_inv(k,contextptr),contextptr);
if (!is_strictly_positive(k,contextptr) || !is_strictly_positive(lambda,contextptr))
return generr(gettext("Invalid distribution parameter(s)"));
return symbolic(at_weibulld,makesequence(k,lambda));
} else if (is_density(f,at_Gamma)) {
if (is_undef(mean) || is_undef(sdev) || !is_strictly_positive(mean,contextptr))
return gensizeerr(contextptr);
gen var=sq(sdev);
return symbolic(at_gammad,makesequence(sq(mean)/var,mean/var));
} else if (is_density(f,at_Beta)) {
if (is_undef(mean) || is_undef(sdev) || !is_strictly_positive(mean,contextptr) ||
!is_strictly_greater(1,mean,contextptr))
return gensizeerr(contextptr);
gen var=sq(sdev),fac=(var+sq(mean)-mean)/var;
gen par1=-mean*fac,par2=(mean-1)*fac;
if (!is_strictly_positive(par1,contextptr) || !is_strictly_positive(par2,contextptr))
return generr(gettext("Invalid distribution parameter(s)"));
return symbolic(at_betad,makesequence(par1,par2));
} else if (is_density(f,at_geometric)) {
gen p;
if (!is_undef(mean)) {
if (!is_strictly_positive(mean,contextptr) ||
(!is_undef(sdev) && !is_zero(_ratnormal(sq(sdev)-sq(mean)-mean,contextptr))))
return gensizeerr(contextptr);
p=_inv(mean,contextptr);
} else if (!is_undef(sdev)) {
gen var=sq(sdev);
p=_ratnormal((sqrt(4*var+1,contextptr)-1)/(2*var),contextptr);
} else return gensizeerr(contextptr);
if (is_strictly_positive(-p,contextptr) || is_strictly_greater(p,1,contextptr))
return generr(gettext("Invalid distribution parameter(s)"));
return symbolic(at_geometric,p);
} else if (f==at_fisher || f==at_fisherd || f==at_snedecor || f==at_chisquare || f==at_chisquared ||
f==at_cauchy || f==at_cauchyd || f==at_student || f==at_studentd) {
return generr(gettext("Specifying moments is not supported for this distribution"));
} else if (is_density(f,at_multinomial)) {
if (categories.empty())
return gensizeerr(contextptr);
if (items.empty())
return makesequence(at_multinomial,categories);
return makesequence(at_multinomial,categories,items);
} else if (is_density(f,at_binomial)) {
if (is_undef(mean) || is_undef(sdev) || !is_strictly_positive(mean,contextptr) ||
is_zero(ratnormal(mean-sq(sdev),contextptr)))
return gensizeerr(contextptr);
gen tmp=mean-sq(sdev),N=_ratnormal(sq(mean)/tmp,contextptr),p=tmp/mean;
if (!is_zero(N-_floor(N,contextptr))) {
N=_round(N,contextptr);
if (is_zero(N))
return generr(gettext("Invalid distribution parameter(s)"));
p=mean/N;
} else N=_round(N,contextptr);
if (!is_greater(p,0,contextptr) || is_strictly_greater(p,1,contextptr))
return generr(gettext("Invalid distribution parameter(s)"));
return symbolic(at_binomial,makesequence(N,_ratnormal(p,contextptr)));
} else if (is_density(f,at_negbinomial)) {
if (is_undef(mean) || is_undef(sdev) || !is_strictly_positive(mean,contextptr) ||
is_zero(ratnormal(mean-sq(sdev),contextptr)))
return gensizeerr(contextptr);
gen N=_round(sq(mean)/(sq(sdev)-mean),contextptr),p=mean/sq(sdev);
if (!is_greater(N,1,contextptr) || is_strictly_positive(-p,contextptr) || is_strictly_greater(p,1,contextptr))
return generr(gettext("Invalid distribution parameter(s)"));
return symbolic(at_negbinomial,makesequence(N,_ratnormal(p,contextptr)));
} else if (f.type==_FUNC || f.is_symb_of_sommet(at_program)) { // custom discrete distribution
if (!is_integer(a) || !is_integer(b) || b.val<=a.val)
return gensizeerr(contextptr);
if (samples>0) {
identificateur k(" k");
gen support=_seq(makesequence(k,symb_equal(k,symb_interval(a,b)),
_evalf((b-a)/gen(samples),contextptr)),contextptr);
gen values=_apply(makesequence(f,support),contextptr);
return _randvar(makesequence(values,support),contextptr);
}
int lb=a.val,ub=b.val;
vecteur rng(ub-lb+1);
for (iterateur it=rng.begin();it!=rng.end();++it) {
*it=lb+int(it-rng.begin());
}
weights=*_apply(makesequence(gv.front(),rng),contextptr)._VECTptr;
if (items.empty()) items=rng;
}
} else if (ckmatrix(g)) {
if (g._VECTptr->front()._VECTptr->size()!=2)
return generrdim(gettext("Expected a two-column matrix"));
int n=g._VECTptr->size();
weights.reserve(n);
items.reserve(n);
for (int i=0;i<n;++i) {
items.push_back(g._VECTptr->at(i)._VECTptr->front());
weights.push_back(g._VECTptr->at(i)._VECTptr->back());
}
} else weights=*g._VECTptr;
if (weights.empty())
return gensizeerr(contextptr);
if (!items.empty() && items.size()!=weights.size())
return generrdim(gettext("Items and weights sizes do not match"));
for (const_iterateur it=weights.begin();it!=weights.end();++it) {
if (!is_real_number(*it,contextptr) || !is_positive(to_real_number(*it,contextptr),contextptr))
return gensizeerr(contextptr);
}
graphe::ransampl rs(weights,contextptr);
gen ret=rs.data();
if (!items.empty())
ret=mergevecteur(*ret._VECTptr,items);
return symbolic(at_discreted,change_subtype(ret,_SEQ__VECT));
}
static const char _randvar_s[]="randvar";
static define_unary_function_eval(__randvar,&_randvar,_randvar_s);
define_unary_function_ptr5(at_randvar,alias_at_randvar,&__randvar,0,true)
static const char _random_variable_s[]="random_variable";
static define_unary_function_eval(__random_variable,&_randvar,_random_variable_s);
define_unary_function_ptr5(at_random_variable,alias_at_random_variable,&__random_variable,0,true)
/* USAGE: trail(V)
*
* Returns a trail of vertices from sequence V (this is a dummy command, it
* returns itself).
*/
gen _trail(const gen &g,GIAC_CONTEXT) {
if (g.type==_STRNG && g.subtype==-1) return g;
return symbolic(at_trail,g);
}
static const char _trail_s[]="trail";
static define_unary_function_eval(__trail,&_trail,_trail_s);
define_unary_function_ptr5(at_trail,alias_at_trail,&__trail,0,true)
/* USAGE: graph(V,[opts])
* graph(V,E,[opts])
* graph(V,E,A,[opts])
* graph(V,A,[opts])
* graph(A,[opts])
* graph("name")
*
* Create an (un)directed (un)weighted graph from list of vertices V, set of edges
* E, and/or adjacency matrix A containing edge weights. All parameters are
* optional.
*
* 'opts' is a sequence of options containing weighted=true/false,
* directed=true/false, color=c or coordinates=p. Here c is
* integer or list of integers (color(s) to be assigned to vertices (in order))
* and p is list of coordinates to assign to vertices (used for drawing).
*
* A special may be created by specifying its name as a string. Supported names
* are: clebsch - coxeter - desargues - dodecahedron - durer - dyck - grinberg
* - grotzsch - harries - harries-wong - heawood - herschel - icosahedron -
* levi - ljubljana - mcgee - mobius-kantor - nauru - octahedron - pappus -
* petersen - robertson - soccerball - shrikhande - tehtrahedron
*/
gen _graph(const gen &g,GIAC_CONTEXT) {
if (g.type==_STRNG) {
if (g.subtype==-1) return g;
// construct special graph
string name=graphe::genstring2str(g);
graphe G(name,contextptr);
if (G.is_null())
return gt_err(_GT_ERR_NAME_NOT_RECOGNIZED);
return G;
}
graphe G(contextptr);
if (g.is_integer() && g.val>=0) {
vecteur V;
G.make_default_labels(V,g.val);
G.add_nodes(V);
} else if (is_squarematrix(g) && g._VECTptr->size()>2) {
// adjacency matrix is given
bool size_err;
if (!parse_matrix(G,*g._VECTptr,false,0,size_err))
return size_err?generrdim(gettext("Bad matrix size")):gentypeerr(contextptr);
} else if (g.type==_VECT && g.subtype!=_SEQ__VECT) {
// list of vertices or set of edges is given
int addc=0;
if (g.subtype==_SET__VECT) {
if (!parse_edges(G,*g._VECTptr,true,addc))
return generrtype(gettext("Failed to parse edges"));
} else G.add_nodes(*g._VECTptr);
} else if (g.is_symb_of_sommet(at_trail)) {
// a trail is given
parse_trail(G,g);
} else {
if (g.type!=_VECT || g.subtype!=_SEQ__VECT)
return gentypeerr(contextptr);
const vecteur &args=*g._VECTptr;
int nargs=args.size(),n=nargs-1;
// parse options first
bool size_err;
while(is_equal(args[n])) {
const vecteur &sides=*args[n]._SYMBptr->feuille._VECTptr;
if (sides.front().is_integer() && sides.front().subtype!=_INT_MAPLECONVERSION) {
switch(sides.front().val) {
case _GT_DIRECTED:
if (!sides.back().is_integer())
return generr(gettext("Option value not supported"));
G.set_directed((bool)sides.back().val);
break;
case _GT_WEIGHTED:
if (!sides.back().is_integer())
return generr(gettext("Option value not supported"));
G.set_weighted((bool)sides.back().val);
break;
}
} else if (sides.front().type==_STRNG) {
// graph attribute is given
G.set_graph_attribute(G.tag2index(*sides.front()._STRNGptr),sides.back());
} else return generr(gettext("Unknown option"));
n--;
}
// parse other arguments
for (int i=0;i<nargs;++i) {
const gen &arg=args[i];
if (i<=n && ckmatrix(arg) && arg.subtype!=_SET__VECT) {
// adjacency or weight matrix
matrice &m=*arg._VECTptr;
if (!G.is_directed() && m!=mtran(m))
return gt_err(_GT_ERR_MATRIX_NOT_SYMMETRIC);
if (!parse_matrix(G,m,i==2 || G.is_weighted(),i,size_err))
return size_err?generrdim(gettext("Bad matrix size")):generrtype(gettext("Failed to parse matrix"));
} else if (i==0 && arg.is_integer()) {
int nv=arg.val;
if (nv<0)
return generr(gettext("Number of vertices must be positive"));
vecteur V;
G.make_default_labels(V,nv);
G.add_nodes(V);
} else if (i<2 && arg.type==_VECT) {
int permu_size;
graphe::ivector permu_int;
const vecteur &argv=*arg._VECTptr;
if (arg.subtype==_SET__VECT) {
// set of edges
int addc=0;
if (!parse_edges(G,argv,true,addc))
return generrtype(gettext("Failed to parse edges"));
} else if (i==1 && is_permu(argv,permu_int,contextptr) && (permu_size=argv.size())>0) {
if (permu_size!=G.node_count())
return generr(gettext("Permutation size does not match the number of vertices"));
// directed cycle
G.set_directed(true);
int offset=array_start(contextptr);
graphe::ivector_iter it=permu_int.begin(),itend=permu_int.end();