diff --git a/FunctionSpace/BasisScalar.cpp b/FunctionSpace/BasisScalar.cpp
index 3c00e67d27e3ccad70e86f46a1f82c769d944c12..ff7c5607d56c4638898570cd18592843d8ccebb2 100644
--- a/FunctionSpace/BasisScalar.cpp
+++ b/FunctionSpace/BasisScalar.cpp
@@ -15,25 +15,29 @@ string BasisScalar::toString(void) const{
stream << "Vertex Based:" << endl;
for(int i = 0; i < nVertex; i++)
- stream << " f(" << i << ") = "
+ stream << " # " << i + 1 << "\t"
+ << "f(" << i + 1 << ") = "
<< (*node)[i]->toString() << endl;
stream << "Edge Based:" << endl;
for(int i = 0; i < nEdge; i++)
for(int j = 0; j < nEdgeClosure; j++)
- stream << " f_" << j << "(" << i << ") = "
+ stream << " # " << i + 1 + nVertex << "\t"
+ << "f_" << j << "(" << i + 1 << ") = "
<< (*(*edge)[j])[i]->toString() << endl;
stream << "Face Based:" << endl;
for(int i = 0; i < nFace; i++)
for(int j = 0; j < nFaceClosure; j++)
- stream << " f_" << j << "(" << i << ") = "
- << (*(*face)[j])[i]->toString() << endl;
+ stream << " # " << i + 1 + nVertex + nEdge << "\t"
+ << "f_" << j << "(" << i + 1 << ") = "
+ << (*(*face)[j])[i]->toString() << endl;
stream << "Cell Based:" << endl;
for(int i = 0; i < nCell; i++)
- stream << " f(" << i << ") = "
- << (*cell)[i]->toString() << endl;
+ stream << " # " << i + 1 + nVertex + nEdge + nFace << "\t"
+ << "f(" << i + 1 << ") = "
+ << (*cell)[i]->toString() << endl;
return stream.str();
}
diff --git a/FunctionSpace/BasisVector.cpp b/FunctionSpace/BasisVector.cpp
index 7b13188de7c5a084fd5dc92efc84f358deb375cc..2b2649ebe6f659f4fed7d52a1d1d54facb547f07 100644
--- a/FunctionSpace/BasisVector.cpp
+++ b/FunctionSpace/BasisVector.cpp
@@ -15,33 +15,37 @@ string BasisVector::toString(void) const{
stream << "Vertex Based:" << endl;
for(int i = 0; i < nVertex; i++)
- stream << " f(" << i << ") = " << endl
- << " [ " <<(*(*node)[i])[0].toString() << " ]" << endl
- << " [ " <<(*(*node)[i])[1].toString() << " ]" << endl
- << " [ " <<(*(*node)[i])[2].toString() << " ]" << endl;
+ stream << " # " << i + 1 << "\t"
+ << "f(" << i + 1 << ") = " << endl
+ << "\t [ " <<(*(*node)[i])[0].toString() << " ]" << endl
+ << "\t [ " <<(*(*node)[i])[1].toString() << " ]" << endl
+ << "\t [ " <<(*(*node)[i])[2].toString() << " ]" << endl;
stream << "Edge Based:" << endl;
for(int i = 0; i < nEdge; i++)
for(int j = 0; j < nEdgeClosure; j++)
- stream << " f_" << j << "(" << i << ") = " << endl
- << " [ " << (*(*(*edge)[j])[i])[0].toString() << " ]" << endl
- << " [ " << (*(*(*edge)[j])[i])[1].toString() << " ]" << endl
- << " [ " << (*(*(*edge)[j])[i])[2].toString() << " ]" << endl;
+ stream << " # " << i + 1 + nVertex << "\t"
+ << " f_" << j << "(" << i + 1 << ") = " << endl
+ << "\t [ " << (*(*(*edge)[j])[i])[0].toString() << " ]" << endl
+ << "\t [ " << (*(*(*edge)[j])[i])[1].toString() << " ]" << endl
+ << "\t [ " << (*(*(*edge)[j])[i])[2].toString() << " ]" << endl;
stream << "Face Based:" << endl;
for(int i = 0; i < nFace; i++)
for(int j = 0; j < nFaceClosure; j++)
- stream << " f_" << j << "(" << i << ") = " << endl
- << " [ " << (*(*(*face)[j])[i])[0].toString() << " ]" << endl
- << " [ " << (*(*(*face)[j])[i])[1].toString() << " ]" << endl
- << " [ " << (*(*(*face)[j])[i])[2].toString() << " ]" << endl;
+ stream << " # " << i + 1 + nVertex + nEdge << "\t"
+ << " f_" << j << "(" << i + 1 << ") = " << endl
+ << "\t [ " << (*(*(*face)[j])[i])[0].toString() << " ]" << endl
+ << "\t [ " << (*(*(*face)[j])[i])[1].toString() << " ]" << endl
+ << "\t [ " << (*(*(*face)[j])[i])[2].toString() << " ]" << endl;
stream << "Cell Based:" << endl;
for(int i = 0; i < nCell; i++)
- stream << " f(" << i << ") = "
- << " [ " << (*(*cell)[i])[0].toString() << " ]" << endl
- << " [ " << (*(*cell)[i])[1].toString() << " ]" << endl
- << " [ " << (*(*cell)[i])[2].toString() << " ]" << endl;
+ stream << " # " << i + 1 + nVertex + nEdge << "\t"
+ << " f(" << i + 1 << ") = " << endl
+ << "\t [ " << (*(*cell)[i])[0].toString() << " ]" << endl
+ << "\t [ " << (*(*cell)[i])[1].toString() << " ]" << endl
+ << "\t [ " << (*(*cell)[i])[2].toString() << " ]" << endl;
return stream.str();
}
diff --git a/FunctionSpace/ReferenceSpace.cpp b/FunctionSpace/ReferenceSpace.cpp
new file mode 100644
index 0000000000000000000000000000000000000000..8ef1f20a6c09d63cdf4fdbd5ab34ec2079dde2b6
--- /dev/null
+++ b/FunctionSpace/ReferenceSpace.cpp
@@ -0,0 +1,232 @@
+#include <sstream>
+#include "ReferenceSpace.h"
+
+using namespace std;
+
+ReferenceSpace::ReferenceSpace(void){
+}
+
+ReferenceSpace::~ReferenceSpace(void){
+ // Destroy Tree //
+ destroy(&pTreeRoot);
+ delete[] perm;
+
+ // Delete Permutated Edge //
+ for(unsigned int p = 0; p < nPerm; p++){
+ for(unsigned int i = 0; i < nEdge; i++)
+ delete (*(*edge)[p])[i];
+
+ delete (*edge)[p];
+ }
+
+ delete edge;
+
+ // Delete Permutated Face //
+ for(unsigned int p = 0; p < nPerm; p++){
+ for(unsigned int i = 0; i < nFace; i++)
+ delete (*(*face)[p])[i];
+
+ delete (*face)[p];
+ }
+
+ delete face;
+}
+
+void ReferenceSpace::init(void){
+ // Init Root //
+ nPerm = 0;
+
+ pTreeRoot.depth = 0;
+ pTreeRoot.last = NULL;
+ pTreeRoot.number = nVertex;
+ pTreeRoot.possible = new unsigned int[pTreeRoot.number];
+ pTreeRoot.next = NULL;
+
+ for(unsigned int i = 0; i < pTreeRoot.number; i++)
+ pTreeRoot.possible[i] = i;
+
+ // Generate Tree //
+ lPerm = new list<unsigned int*>;
+ generate(&pTreeRoot);
+
+ perm = new unsigned int*[nPerm];
+ for(unsigned int i = 0; i < nPerm; i++){
+ perm[i] = lPerm->front();
+ lPerm->pop_front();
+ }
+
+ delete lPerm;
+
+ // Get Edges & Faces //
+ getEdge();
+ getFace();
+}
+
+void ReferenceSpace::generate(node* pTreeRoot){
+ const unsigned int number = pTreeRoot->number;
+ const unsigned int depth = pTreeRoot->depth;
+
+ if(!number){
+ pTreeRoot->next = NULL;
+ nPerm++;
+ lPerm->push_back(pTreeRoot->last);
+ }
+
+ else{
+ pTreeRoot->next = new node[number];
+
+ for(unsigned int i = 0; i < number; i++){
+ unsigned int nextDepth = pTreeRoot->depth + 1;
+ unsigned int nextLast = pTreeRoot->possible[i];
+ unsigned int nextNumber = number - 1;
+ unsigned int offset = 0;
+
+ pTreeRoot->next[i].depth = nextDepth;
+ pTreeRoot->next[i].last = new unsigned int[nextDepth];
+ pTreeRoot->next[i].last[depth] = nextLast;
+
+ for(unsigned int j = 0; j < depth; j++)
+ pTreeRoot->next[i].last[j] = pTreeRoot->last[j];
+
+ pTreeRoot->next[i].number = nextNumber;
+ pTreeRoot->next[i].possible = new unsigned int[nextNumber];
+
+ for(unsigned int j = 0; j < nextNumber; j++){
+ if(pTreeRoot->possible[j] == nextLast)
+ offset = 1;
+
+ pTreeRoot->next[i].possible[j] = pTreeRoot->possible[j + offset];
+ }
+
+ generate(&pTreeRoot->next[i]);
+ }
+ }
+}
+
+void ReferenceSpace::destroy(node* node){
+ const unsigned int number = node->number;
+
+ for(unsigned int i = 0; i < number; i++){
+ destroy(&node->next[i]);
+ node->number--;
+ }
+
+ delete[] node->possible;
+ delete[] node->last;
+ delete[] node->next;
+}
+
+void ReferenceSpace::getEdge(void){
+ vector<const vector<unsigned int>*>* tmp;
+ edge = new vector<const vector<const vector<unsigned int>*>*>(nPerm);
+
+ for(unsigned int p = 0; p < nPerm; p++){
+ tmp = new vector<const vector<unsigned int>*>(nEdge);
+
+ for(unsigned int i = 0; i < nEdge; i++)
+ (*tmp)[i] = inOrder(p,
+ refEdge[i][0],
+ refEdge[i][1]);
+ (*edge)[p] = tmp;
+ }
+}
+
+void ReferenceSpace::getFace(void){
+ vector<const vector<unsigned int>*>* tmp;
+ face = new vector<const vector<const vector<unsigned int>*>*>(nPerm);
+
+ for(unsigned int p = 0; p < nPerm; p++){
+ tmp = new vector<const vector<unsigned int>*>(nFace);
+
+ for(unsigned int i = 0; i < nFace; i++)
+ (*tmp)[i] = inOrder(p,
+ refFace[i][0],
+ refFace[i][1],
+ refFace[i][2]);
+ (*face)[p] = tmp;
+ }
+}
+
+const vector<unsigned int>* ReferenceSpace::
+inOrder(unsigned int permutation,
+ unsigned int a,
+ unsigned int b){
+
+ unsigned int v;
+ unsigned int k = 0;
+ vector<unsigned int>* inorder =
+ new vector<unsigned int>(2);
+
+ for(unsigned int i = 0; i < nVertex; i++){
+ v = perm[permutation][i];
+
+ if(v == a || v == b){
+ (*inorder)[k] = v;
+ k++;
+ }
+ }
+
+ return inorder;
+}
+
+const std::vector<unsigned int>* ReferenceSpace::
+inOrder(unsigned int permutation,
+ unsigned int a,
+ unsigned int b,
+ unsigned int c){
+
+ unsigned int v;
+ unsigned int k = 0;
+ vector<unsigned int>* inorder =
+ new vector<unsigned int>(3);
+
+ for(unsigned int i = 0; i < nVertex; i++){
+ v = perm[permutation][i];
+
+ if(v == a || v == b || v == c){
+ (*inorder)[k] = v;
+ k++;
+ }
+ }
+
+ return inorder;
+}
+
+string ReferenceSpace::toString(void) const{
+ stringstream stream;
+
+ // Tree //
+ stream << "Tree:" << endl;
+ stream << toString(&pTreeRoot) << endl;
+
+ // ReferenceSpaces //
+ stream << "ReferenceSpace:" << endl;
+
+ for(unsigned int i = 0; i < nPerm; i++){
+ stream << " * ";
+
+ for(unsigned int j = 0; j < nVertex; j++)
+ stream << perm[i][j] << " ";
+
+ stream << " (# " << i + 1 << ")" << endl;
+ }
+
+ return stream.str();
+}
+
+string ReferenceSpace::toString(const node* node) const{
+ const unsigned int number = node->number;
+ stringstream stream;
+
+ if(node->last)
+ stream << "(" << node->last[node->depth - 1] << " ";
+ else
+ stream << "(root ";
+
+ for(unsigned int i = 0; i < number; i++)
+ stream << toString(&node->next[i]);
+
+ stream << ")";
+
+ return stream.str();
+}
diff --git a/FunctionSpace/ReferenceSpace.h b/FunctionSpace/ReferenceSpace.h
new file mode 100644
index 0000000000000000000000000000000000000000..59d28e65f384971e980cd2f8676081bd0bc95e94
--- /dev/null
+++ b/FunctionSpace/ReferenceSpace.h
@@ -0,0 +1,96 @@
+#ifndef _REFERENCESPACE_H_
+#define _REFERENCESPACE_H_
+
+#include <vector>
+#include <list>
+#include <string>
+
+class ReferenceSpace{
+ protected:
+ // Permuation Tree Structure //
+ struct node_s{
+ unsigned int depth; // Depth
+ unsigned int* last; // Last Choises
+ unsigned int number; // Number of Next Choise
+ unsigned int* possible; // Possible Next Choise
+ node_s* next; // Next Choise
+ };
+
+ typedef node_s node;
+
+ // Permutation (Tree + Leaf) //
+ unsigned int nVertex;
+ unsigned int nPerm;
+ unsigned int** perm;
+ node pTreeRoot;
+
+ mutable std::list<unsigned int*>* lPerm;
+
+ // Edge Permutation //
+ unsigned int nEdge;
+ unsigned int** refEdge;
+ std::vector<const std::vector<const std::vector<unsigned int>*>*>* edge;
+
+ // Face Permutation //
+ unsigned int nFace;
+ unsigned int** refFace;
+ std::vector<const std::vector<const std::vector<unsigned int>*>*>* face;
+
+ public:
+ virtual ~ReferenceSpace(void);
+
+ unsigned int getNReferenceSpace(void) const;
+
+ std::vector<const std::vector<const std::vector<unsigned int>*>*>&
+ getAllEdge(void) const;
+
+ std::vector<const std::vector<const std::vector<unsigned int>*>*>&
+ getAllFace(void) const ;
+
+ std::string toString(void) const;
+
+ protected:
+ ReferenceSpace(void);
+
+ void init(void);
+ void generate(node* pTreeRoot);
+ void destroy(node* node);
+
+ void getEdge(void);
+ void getFace(void);
+
+ const std::vector<unsigned int>* inOrder(unsigned int permutation,
+ unsigned int a,
+ unsigned int b);
+
+ const std::vector<unsigned int>* inOrder(unsigned int permutation,
+ unsigned int a,
+ unsigned int b,
+ unsigned int c);
+
+ std::string toString(const node* node) const;
+};
+
+//////////////////////
+// Inline Functions //
+//////////////////////
+
+inline
+unsigned int
+ReferenceSpace::getNReferenceSpace(void) const{
+ return nPerm;
+}
+
+inline
+std::vector<const std::vector<const std::vector<unsigned int>*>*>&
+ReferenceSpace::getAllEdge(void) const{
+ return *edge;
+}
+
+inline
+std::vector<const std::vector<const std::vector<unsigned int>*>*>&
+ReferenceSpace::getAllFace(void) const{
+ return *face;
+}
+
+#endif
diff --git a/FunctionSpace/TetReferenceSpace.cpp b/FunctionSpace/TetReferenceSpace.cpp
new file mode 100644
index 0000000000000000000000000000000000000000..14835bb5b0fc07863025b605d2d774b3381a6f7b
--- /dev/null
+++ b/FunctionSpace/TetReferenceSpace.cpp
@@ -0,0 +1,106 @@
+#include <sstream>
+#include "TetReferenceSpace.h"
+
+using namespace std;
+
+TetReferenceSpace::TetReferenceSpace(void){
+ // Vertex Definition //
+ nVertex = 4;
+
+ // Edge Definition //
+ nEdge = 6;
+ refEdge = new unsigned int*[nEdge];
+
+ for(unsigned int i = 0; i < nEdge; i++)
+ refEdge[i] = new unsigned int[2];
+
+ refEdge[0][0] = 0; refEdge[0][1] = 1;
+ refEdge[1][0] = 1; refEdge[1][1] = 2;
+ refEdge[2][0] = 2; refEdge[2][1] = 0;
+ refEdge[3][0] = 0; refEdge[3][1] = 3;
+ refEdge[4][0] = 1; refEdge[4][1] = 3;
+ refEdge[5][0] = 2; refEdge[5][1] = 3;
+
+ // Face Definition //
+ nFace = 4;
+ refFace = new unsigned int*[nFace];
+
+ for(unsigned int i = 0; i < nFace; i++)
+ refFace[i] = new unsigned int[3];
+
+ refFace[0][0] = 0; refFace[0][1] = 1; refFace[0][2] = 2;
+ refFace[1][0] = 0; refFace[1][1] = 1; refFace[1][2] = 3;
+ refFace[2][0] = 1; refFace[2][1] = 2; refFace[2][2] = 3;
+ refFace[3][0] = 2; refFace[3][1] = 0; refFace[3][2] = 3;
+
+ // Init All //
+ init();
+}
+
+TetReferenceSpace::~TetReferenceSpace(void){
+ // Delete Ref Edge //
+ for(unsigned int i = 0; i < nEdge; i++)
+ delete[] refEdge[i];
+
+ delete[] refEdge;
+
+ // Delete Ref Face //
+ for(unsigned int i = 0; i < nFace; i++)
+ delete[] refFace[i];
+
+ delete[] refFace;
+}
+
+string TetReferenceSpace::toLatex(void) const{
+ stringstream stream;
+
+ stream << "\\documentclass{article}" << endl << endl
+
+ << "\\usepackage{longtable}" << endl
+ << "\\usepackage{tikz}" << endl
+ << "\\usetikzlibrary{arrows}" << endl << endl
+
+ << "\\begin{document}" << endl
+ << "\\tikzstyle{vertex} = [circle, fill = black!25]" << endl
+ << "\\tikzstyle{line} = [draw, thick, black, -latex']" << endl << endl
+
+ << "\\begin{longtable}{ccc}" << endl << endl;
+
+ for(unsigned int p = 0; p < nPerm; p++){
+ stream << "\\begin{tikzpicture}" << endl
+
+ << "\\node[vertex] (n0) at(0, 0) {$0$};" << endl
+ << "\\node[vertex] (n1) at(3, 0) {$1$};" << endl
+ << "\\node[vertex] (n2) at(0, 3) {$2$};" << endl
+ << "\\node[vertex] (n3) at(1, 1) {$3$};" << endl << endl;
+
+ for(unsigned int i = 0; i < 6; i++)
+ stream << "\\path[line]"
+ << " (n" << (*(*(*edge)[p])[i])[0] << ")"
+ << " -- "
+ << " (n" << (*(*(*edge)[p])[i])[1] << ");"
+ << endl;
+
+ if((p + 1) % 3)
+ stream << "\\end{tikzpicture} & " << endl << endl;
+
+ else
+ stream << "\\end{tikzpicture} \\\\ \\\\" << endl << endl;
+ }
+
+ stream << "\\end{longtable}" << endl
+ << "\\end{document}" << endl;
+
+ return stream.str();
+}
+
+/*
+#include <iostream>
+int main(void){
+ TetReferenceSpace p;
+
+ cout << p.toLatex() << endl;
+
+ return 0;
+}
+*/
diff --git a/FunctionSpace/TetReferenceSpace.h b/FunctionSpace/TetReferenceSpace.h
new file mode 100644
index 0000000000000000000000000000000000000000..53532863d49f5a66f9b3fe74e65558163e6f7ed1
--- /dev/null
+++ b/FunctionSpace/TetReferenceSpace.h
@@ -0,0 +1,15 @@
+#ifndef _TETREFERENCESPACE_H_
+#define _TETREFERENCESPACE_H_
+
+#include <string>
+#include "ReferenceSpace.h"
+
+class TetReferenceSpace: public ReferenceSpace{
+ public:
+ TetReferenceSpace(void);
+ virtual ~TetReferenceSpace(void);
+
+ std::string toLatex(void) const;
+};
+
+#endif
diff --git a/FunctionSpace/TriReferenceSpace.cpp b/FunctionSpace/TriReferenceSpace.cpp
new file mode 100644
index 0000000000000000000000000000000000000000..a339a07c6ab6b8028bca4c0b22812ea96c45ceaa
--- /dev/null
+++ b/FunctionSpace/TriReferenceSpace.cpp
@@ -0,0 +1,88 @@
+#include <sstream>
+#include "TriReferenceSpace.h"
+
+using namespace std;
+
+TriReferenceSpace::TriReferenceSpace(void){
+ // Vertex Definition //
+ nVertex = 3;
+
+ // Edge Definition //
+ nEdge = 3;
+ refEdge = new unsigned int*[nEdge];
+
+ for(unsigned int i = 0; i < nEdge; i++)
+ refEdge[i] = new unsigned int[2];
+
+ refEdge[0][0] = 0; refEdge[0][1] = 1;
+ refEdge[1][0] = 1; refEdge[1][1] = 2;
+ refEdge[2][0] = 2; refEdge[2][1] = 0;
+
+ // Face Definition //
+ nFace = 0;
+ refFace = NULL;
+
+ // Init All //
+ init();
+}
+
+TriReferenceSpace::~TriReferenceSpace(void){
+ // Delete Ref Edge //
+ for(unsigned int i = 0; i < nEdge; i++)
+ delete[] refEdge[i];
+
+ delete[] refEdge;
+}
+
+string TriReferenceSpace::toLatex(void) const{
+ stringstream stream;
+
+ stream << "\\documentclass{article}" << endl << endl
+
+ << "\\usepackage{longtable}" << endl
+ << "\\usepackage{tikz}" << endl
+ << "\\usetikzlibrary{arrows}" << endl << endl
+
+ << "\\begin{document}" << endl
+ << "\\tikzstyle{vertex} = [circle, fill = black!25]" << endl
+ << "\\tikzstyle{line} = [draw, thick, black, -latex']" << endl << endl
+
+ << "\\begin{longtable}{ccc}" << endl << endl;
+
+ for(unsigned int p = 0; p < nPerm; p++){
+ stream << "\\begin{tikzpicture}" << endl
+
+ << "\\node[vertex] (n0) at(0, 0) {$0$};" << endl
+ << "\\node[vertex] (n1) at(3, 0) {$1$};" << endl
+ << "\\node[vertex] (n2) at(0, 3) {$2$};" << endl << endl;
+
+ for(unsigned int i = 0; i < 3; i++)
+ stream << "\\path[line]"
+ << " (n" << (*(*(*edge)[p])[i])[0] << ")"
+ << " -- "
+ << " (n" << (*(*(*edge)[p])[i])[1] << ");"
+ << endl;
+
+ if((p + 1) % 3)
+ stream << "\\end{tikzpicture} & " << endl << endl;
+
+ else
+ stream << "\\end{tikzpicture} \\\\ \\\\" << endl << endl;
+ }
+
+ stream << "\\end{longtable}" << endl
+ << "\\end{document}" << endl;
+
+ return stream.str();
+}
+
+/*
+#include <iostream>
+int main(void){
+ TriReferenceSpace p;
+
+ cout << p.toLatex() << endl;
+
+ return 0;
+}
+*/
diff --git a/FunctionSpace/TriReferenceSpace.h b/FunctionSpace/TriReferenceSpace.h
new file mode 100644
index 0000000000000000000000000000000000000000..9866c8e48b84d907c6689d8f5833ea6cda1d6f26
--- /dev/null
+++ b/FunctionSpace/TriReferenceSpace.h
@@ -0,0 +1,15 @@
+#ifndef _TRIREFERENCESPACE_H_
+#define _TRIREFERENCESPACE_H_
+
+#include <string>
+#include "ReferenceSpace.h"
+
+class TriReferenceSpace: public ReferenceSpace{
+ public:
+ TriReferenceSpace(void);
+ virtual ~TriReferenceSpace(void);
+
+ std::string toLatex(void) const;
+};
+
+#endif