diff --git a/FunctionSpace/HexEdgeBasis.cpp b/FunctionSpace/HexEdgeBasis.cpp
index 7ebbbdee4101e8be34135ecf1fff54d4a65fb1b4..34f607aab48f4e01ba67df137da5507220448ab6 100644
--- a/FunctionSpace/HexEdgeBasis.cpp
+++ b/FunctionSpace/HexEdgeBasis.cpp
@@ -8,7 +8,7 @@ HexEdgeBasis::HexEdgeBasis(int order){
/*
// Set Basis Type //
this->order = order;
-
+
type = 1;
dim = 3;
@@ -60,43 +60,43 @@ HexEdgeBasis::HexEdgeBasis(int order){
int edge2[12] = {1, 2, 3, 0, 5, 6, 7, 4, 4, 5, 6, 7};
- // Lagrange //
- lagrange[0] =
+ // Lagrange //
+ lagrange[0] =
(Polynomial(1, 0, 0, 0) - Polynomial(1, 1, 0, 0)) *
(Polynomial(1, 0, 0, 0) - Polynomial(1, 0, 1, 0)) *
(Polynomial(1, 0, 0, 0) - Polynomial(1, 0, 0, 1));
- lagrange[1] =
+ lagrange[1] =
(Polynomial(1, 1, 0, 0)) *
(Polynomial(1, 0, 0, 0) - Polynomial(1, 0, 1, 0)) *
(Polynomial(1, 0, 0, 0) - Polynomial(1, 0, 0, 1));
- lagrange[2] =
+ lagrange[2] =
(Polynomial(1, 1, 0, 0)) *
(Polynomial(1, 0, 1, 0)) *
(Polynomial(1, 0, 0, 0) - Polynomial(1, 0, 0, 1));
- lagrange[3] =
+ lagrange[3] =
(Polynomial(1, 0, 0, 0) - Polynomial(1, 1, 0, 0)) *
(Polynomial(1, 0, 1, 0)) *
(Polynomial(1, 0, 0, 0) - Polynomial(1, 0, 0, 1));
- lagrange[4] =
+ lagrange[4] =
(Polynomial(1, 0, 0, 0) - Polynomial(1, 1, 0, 0)) *
(Polynomial(1, 0, 0, 0) - Polynomial(1, 0, 1, 0)) *
Polynomial(1, 0, 0, 1);
- lagrange[5] =
+ lagrange[5] =
(Polynomial(1, 1, 0, 0)) *
(Polynomial(1, 0, 0, 0) - Polynomial(1, 0, 1, 0)) *
Polynomial(1, 0, 0, 1);
- lagrange[6] =
+ lagrange[6] =
(Polynomial(1, 1, 0, 0)) *
(Polynomial(1, 0, 1, 0)) *
Polynomial(1, 0, 0, 1);
- lagrange[7] =
+ lagrange[7] =
(Polynomial(1, 0, 0, 0) - Polynomial(1, 1, 0, 0)) *
(Polynomial(1, 0, 1, 0)) *
Polynomial(1, 0, 0, 1);
@@ -105,44 +105,44 @@ HexEdgeBasis::HexEdgeBasis(int order){
for(int i = 0; i < 12; i++)
lagrangeSum[i] = lagrange[edge1[i]] + lagrange[edge2[i]];
-
+
// Lifting //
- lifting[0] =
+ lifting[0] =
(Polynomial(1, 0, 0, 0) - Polynomial(1, 1, 0, 0)) +
(Polynomial(1, 0, 0, 0) - Polynomial(1, 0, 1, 0)) +
(Polynomial(1, 0, 0, 0) - Polynomial(1, 0, 0, 1));
- lifting[1] =
+ lifting[1] =
(Polynomial(1, 1, 0, 0)) +
(Polynomial(1, 0, 0, 0) - Polynomial(1, 0, 1, 0)) +
(Polynomial(1, 0, 0, 0) - Polynomial(1, 0, 0, 1));
- lifting[2] =
+ lifting[2] =
(Polynomial(1, 1, 0, 0)) +
(Polynomial(1, 0, 1, 0)) +
(Polynomial(1, 0, 0, 0) - Polynomial(1, 0, 0, 1));
- lifting[3] =
+ lifting[3] =
(Polynomial(1, 0, 0, 0) - Polynomial(1, 1, 0, 0)) +
(Polynomial(1, 0, 1, 0)) +
(Polynomial(1, 0, 0, 0) - Polynomial(1, 0, 0, 1));
- lifting[4] =
+ lifting[4] =
(Polynomial(1, 0, 0, 0) - Polynomial(1, 1, 0, 0)) +
(Polynomial(1, 0, 0, 0) - Polynomial(1, 0, 1, 0)) +
Polynomial(1, 0, 0, 1);
- lifting[5] =
+ lifting[5] =
(Polynomial(1, 1, 0, 0)) +
(Polynomial(1, 0, 0, 0) - Polynomial(1, 0, 1, 0)) +
Polynomial(1, 0, 0, 1);
- lifting[6] =
+ lifting[6] =
(Polynomial(1, 1, 0, 0)) +
(Polynomial(1, 0, 1, 0)) +
Polynomial(1, 0, 0, 1);
- lifting[7] =
+ lifting[7] =
(Polynomial(1, 0, 0, 0) - Polynomial(1, 1, 0, 0)) +
(Polynomial(1, 0, 1, 0)) +
Polynomial(1, 0, 0, 1);
@@ -156,14 +156,14 @@ HexEdgeBasis::HexEdgeBasis(int order){
std::vector<std::vector<Polynomial>*> basis(size);
- // Edge Based (Nedelec) //
+ // Edge Based (Nedelec) //
int i = 0; // Function Counter
Polynomial oneHalf(0.5, 0, 0, 0);
for(int e = 0; e < 12; e++){
- basis[i] =
+ basis[i] =
new std::vector<Polynomial>((liftingSub[e]).gradient());
-
+
basis[i]->at(0).mul(lagrangeSum[e]);
basis[i]->at(1).mul(lagrangeSum[e]);
basis[i]->at(2).mul(lagrangeSum[e]);
@@ -179,9 +179,9 @@ HexEdgeBasis::HexEdgeBasis(int order){
// Edge Based (High Order) //
for(int l = 1; l < orderPlus; l++){
for(int e = 0; e < 12; e++){
- basis[i] =
+ basis[i] =
new std::vector<Polynomial>((intLegendre[l].compose(liftingSub[e]) * lagrangeSum[e]).gradient());
-
+
i++;
}
}
@@ -204,12 +204,12 @@ HexEdgeBasis::HexEdgeBasis(int order){
// 'Lambda' Functions
for(int f = 0; f < 6; f++)
- lambda[f] =
+ lambda[f] =
lagrange[face1[f]] +
lagrange[face2[f]] +
lagrange[face3[f]] +
lagrange[face4[f]];
-
+
// Gradients
for(int f = 0; f < 6; f++){
grXi[f] = xi[f].gradient();
@@ -219,26 +219,26 @@ HexEdgeBasis::HexEdgeBasis(int order){
// Compositions
for(int l = 0; l < orderPlus; l++){
iLegendreXi[l] = new Polynomial[6];
- iLegendreEta[l] = new Polynomial[6];
-
- legendreXi[l] = new Polynomial[6];
+ iLegendreEta[l] = new Polynomial[6];
+
+ legendreXi[l] = new Polynomial[6];
legendreEta[l] = new Polynomial[6];
for(int f = 0; f < 6; f++){
iLegendreXi[l][f] = intLegendre[l].compose(xi[f]);
iLegendreEta[l][f] = intLegendre[l].compose(eta[f]);
-
+
legendreXi[l][f] = legendre[l].compose(xi[f]);
legendreEta[l][f] = legendre[l].compose(eta[f]);
}
}
-
+
// Face Based (Type 1) //
for(int l1 = 1; l1 < orderPlus; l1++){
for(int l2 = 1; l2 < orderPlus; l2++){
for(int f = 0; f < 6; f++){
- basis[i] = new std::vector<Polynomial>((iLegendreXi[l1][f] *
+ basis[i] = new std::vector<Polynomial>((iLegendreXi[l1][f] *
iLegendreEta[l2][f] *
lambda[f]).gradient());
@@ -254,10 +254,10 @@ HexEdgeBasis::HexEdgeBasis(int order){
for(int f = 0; f < 6; f++){
basis[i] = new std::vector<Polynomial>(3);
- Polynomial tmp1 =
- legendreXi[l1][f] *
+ Polynomial tmp1 =
+ legendreXi[l1][f] *
iLegendreEta[l2][f];
-
+
Polynomial tmp2 =
iLegendreXi[l1][f] *
legendreEta[l2][f];
@@ -270,8 +270,8 @@ HexEdgeBasis::HexEdgeBasis(int order){
vector<Polynomial> gr2 = grEta[f];
gr2[0].mul(tmp2);
gr2[1].mul(tmp2);
- gr2[2].mul(tmp2);
-
+ gr2[2].mul(tmp2);
+
basis[i]->at(0) = (gr1[0] - gr2[0]) * lambda[f];
basis[i]->at(1) = (gr1[1] - gr2[1]) * lambda[f];
basis[i]->at(2) = (gr1[2] - gr2[2]) * lambda[f];
@@ -286,14 +286,14 @@ HexEdgeBasis::HexEdgeBasis(int order){
for(int l = 1; l < orderPlus; l++){
for(int f = 0; f < 6; f++){
Polynomial tmp = iLegendreEta[l][f] * lambda[f];
-
+
basis[i] = new std::vector<Polynomial>(grXi[f]);
-
+
basis[i]->at(0).mul(tmp);
basis[i]->at(1).mul(tmp);
basis[i]->at(2).mul(tmp);
-
- i++;
+
+ i++;
}
}
@@ -302,24 +302,24 @@ HexEdgeBasis::HexEdgeBasis(int order){
for(int l = 1; l < orderPlus; l++){
for(int f = 0; f < 6; f++){
Polynomial tmp = iLegendreXi[l][f] * lambda[f];
-
+
basis[i] = new std::vector<Polynomial>(grEta[f]);
-
+
basis[i]->at(0).mul(tmp);
basis[i]->at(1).mul(tmp);
basis[i]->at(2).mul(tmp);
-
- i++;
+
+ i++;
}
}
-
+
// Cell Based (Preliminary) //
Polynomial px = Polynomial(2, 1, 0, 0);
Polynomial py = Polynomial(2, 0, 1, 0);
Polynomial pz = Polynomial(2, 0, 0, 1);
Polynomial zero = Polynomial(0, 0, 0, 0);
-
+
px = px - Polynomial(1, 0, 0, 0);
py = py - Polynomial(1, 0, 0, 0);
pz = pz - Polynomial(1, 0, 0, 0);
@@ -338,7 +338,7 @@ HexEdgeBasis::HexEdgeBasis(int order){
for(int l1 = 1; l1 < orderPlus; l1++){
for(int l2 = 1; l2 < orderPlus; l2++){
for(int l3 = 1; l3 < orderPlus; l3++){
- basis[i] = new std::vector<Polynomial>((iLegendreX[l1] *
+ basis[i] = new std::vector<Polynomial>((iLegendreX[l1] *
iLegendreY[l2] *
iLegendreZ[l3]).gradient());
@@ -347,16 +347,16 @@ HexEdgeBasis::HexEdgeBasis(int order){
}
}
}
-
+
// Cell Based (Type 2 -- First Part) //
for(int j = 0; j < cellNumber; j++){
basis[i] = new std::vector<Polynomial>(3);
int off = j + cellStart;
-
+
basis[i]->at(0) = basis[off]->at(0);
- basis[i]->at(1) = basis[off]->at(1) * Polynomial(-1, 0, 0, 0);
+ basis[i]->at(1) = basis[off]->at(1) * Polynomial(-1, 0, 0, 0);
basis[i]->at(2) = basis[off]->at(2);
i++;
@@ -370,7 +370,7 @@ HexEdgeBasis::HexEdgeBasis(int order){
int off = j + cellStart;
basis[i]->at(0) = basis[off]->at(0);
- basis[i]->at(1) = basis[off]->at(1) * Polynomial(-1, 0, 0, 0);
+ basis[i]->at(1) = basis[off]->at(1) * Polynomial(-1, 0, 0, 0);
basis[i]->at(2) = basis[off]->at(2) * Polynomial(-1, 0, 0, 0);
i++;
@@ -379,13 +379,13 @@ HexEdgeBasis::HexEdgeBasis(int order){
// Cell Based (Type 3 -- First Part) //
for(int l2 = 1; l2 < orderPlus; l2++){
- for(int l3 = 1; l3 < orderPlus; l3++){
+ for(int l3 = 1; l3 < orderPlus; l3++){
basis[i] = new std::vector<Polynomial>(3);
basis[i]->at(0) = iLegendreY[l2] * iLegendreZ[l3];
basis[i]->at(1) = zero;
basis[i]->at(2) = zero;
-
+
i++;
}
}
@@ -393,30 +393,30 @@ HexEdgeBasis::HexEdgeBasis(int order){
// Cell Based (Type 3 -- Second Part) //
for(int l1 = 1; l1 < orderPlus; l1++){
- for(int l3 = 1; l3 < orderPlus; l3++){
+ for(int l3 = 1; l3 < orderPlus; l3++){
basis[i] = new std::vector<Polynomial>(3);
-
+
basis[i]->at(0) = zero;
basis[i]->at(1) = iLegendreX[l1] * iLegendreZ[l3];
basis[i]->at(2) = zero;
-
+
i++;
}
- }
+ }
// Cell Based (Type 3 -- Thrid Part) //
for(int l1 = 1; l1 < orderPlus; l1++){
for(int l2 = 1; l2 < orderPlus; l2++){
basis[i] = new std::vector<Polynomial>(3);
-
+
basis[i]->at(0) = zero;
basis[i]->at(1) = zero;
basis[i]->at(2) = iLegendreX[l1] * iLegendreY[l2];
-
+
i++;
}
- }
+ }
// Free Temporary Sapce //
@@ -438,21 +438,21 @@ HexEdgeBasis::HexEdgeBasis(int order){
for(int l = 0; l < orderPlus; l++){
delete[] iLegendreXi[l];
- delete[] iLegendreEta[l];
- delete[] legendreXi[l];
+ delete[] iLegendreEta[l];
+ delete[] legendreXi[l];
delete[] legendreEta[l];
}
delete[] iLegendreXi;
- delete[] iLegendreEta;
- delete[] legendreXi;
+ delete[] iLegendreEta;
+ delete[] legendreXi;
delete[] legendreEta;
delete[] iLegendreX;
delete[] iLegendreY;
delete[] iLegendreZ;
-
+
// Set Basis //
this->basis = new std::vector<const std::vector<Polynomial>*>
(basis.begin(), basis.end());
diff --git a/FunctionSpace/HexNodeBasis.cpp b/FunctionSpace/HexNodeBasis.cpp
index 5cc68e7f0cc0401270948fc6a9edcb035dee1375..6bb1691e6366aaad091b167b2366df5d362f39c4 100644
--- a/FunctionSpace/HexNodeBasis.cpp
+++ b/FunctionSpace/HexNodeBasis.cpp
@@ -33,16 +33,16 @@ HexNodeBasis::HexNodeBasis(int order){
Legendre::integrated(legendre, order);
// Vertices definig Edges & Permutations //
- const int edgeV[2][12][2] =
+ const int edgeV[2][12][2] =
{
- { {0, 1}, {0, 3}, {0, 4}, {1, 2}, {1, 5}, {2, 3},
+ { {0, 1}, {0, 3}, {0, 4}, {1, 2}, {1, 5}, {2, 3},
{2, 6}, {3, 7}, {4, 5}, {4, 7}, {5, 6}, {6, 7} },
- { {1, 0}, {3, 0}, {4, 0}, {2, 1}, {5, 1}, {3, 2},
+ { {1, 0}, {3, 0}, {4, 0}, {2, 1}, {5, 1}, {3, 2},
{6, 2}, {7, 3}, {5, 4}, {7, 4}, {6, 5}, {7, 6} },
};
- const int faceV[6][4] =
+ const int faceV[6][4] =
{
{0, 3, 2, 1},
{0, 1, 5, 4},
@@ -52,44 +52,44 @@ HexNodeBasis::HexNodeBasis(int order){
{4, 5, 6, 7}
};
-
+
// Lifting //
- lifting[0] =
+ lifting[0] =
(Polynomial(1, 0, 0, 0) - Polynomial(1, 1, 0, 0)) +
(Polynomial(1, 0, 0, 0) - Polynomial(1, 0, 1, 0)) +
(Polynomial(1, 0, 0, 0) - Polynomial(1, 0, 0, 1));
- lifting[1] =
+ lifting[1] =
(Polynomial(1, 1, 0, 0)) +
(Polynomial(1, 0, 0, 0) - Polynomial(1, 0, 1, 0)) +
(Polynomial(1, 0, 0, 0) - Polynomial(1, 0, 0, 1));
- lifting[2] =
+ lifting[2] =
(Polynomial(1, 1, 0, 0)) +
(Polynomial(1, 0, 1, 0)) +
(Polynomial(1, 0, 0, 0) - Polynomial(1, 0, 0, 1));
- lifting[3] =
+ lifting[3] =
(Polynomial(1, 0, 0, 0) - Polynomial(1, 1, 0, 0)) +
(Polynomial(1, 0, 1, 0)) +
(Polynomial(1, 0, 0, 0) - Polynomial(1, 0, 0, 1));
- lifting[4] =
+ lifting[4] =
(Polynomial(1, 0, 0, 0) - Polynomial(1, 1, 0, 0)) +
(Polynomial(1, 0, 0, 0) - Polynomial(1, 0, 1, 0)) +
Polynomial(1, 0, 0, 1);
- lifting[5] =
+ lifting[5] =
(Polynomial(1, 1, 0, 0)) +
(Polynomial(1, 0, 0, 0) - Polynomial(1, 0, 1, 0)) +
Polynomial(1, 0, 0, 1);
- lifting[6] =
+ lifting[6] =
(Polynomial(1, 1, 0, 0)) +
(Polynomial(1, 0, 1, 0)) +
Polynomial(1, 0, 0, 1);
- lifting[7] =
+ lifting[7] =
(Polynomial(1, 0, 0, 0) - Polynomial(1, 1, 0, 0)) +
(Polynomial(1, 0, 1, 0)) +
Polynomial(1, 0, 0, 1);
@@ -99,48 +99,48 @@ HexNodeBasis::HexNodeBasis(int order){
basis = new std::vector<const Polynomial*>(size);
- // Vertex Based (Lagrange) //
- (*basis)[0] =
+ // Vertex Based (Lagrange) //
+ (*basis)[0] =
new Polynomial((Polynomial(1, 0, 0, 0) - Polynomial(1, 1, 0, 0)) *
(Polynomial(1, 0, 0, 0) - Polynomial(1, 0, 1, 0)) *
(Polynomial(1, 0, 0, 0) - Polynomial(1, 0, 0, 1)));
- (*basis)[1] =
+ (*basis)[1] =
new Polynomial((Polynomial(1, 1, 0, 0)) *
(Polynomial(1, 0, 0, 0) - Polynomial(1, 0, 1, 0)) *
(Polynomial(1, 0, 0, 0) - Polynomial(1, 0, 0, 1)));
- (*basis)[2] =
+ (*basis)[2] =
new Polynomial((Polynomial(1, 1, 0, 0)) *
(Polynomial(1, 0, 1, 0)) *
(Polynomial(1, 0, 0, 0) - Polynomial(1, 0, 0, 1)));
- (*basis)[3] =
+ (*basis)[3] =
new Polynomial((Polynomial(1, 0, 0, 0) - Polynomial(1, 1, 0, 0)) *
(Polynomial(1, 0, 1, 0)) *
(Polynomial(1, 0, 0, 0) - Polynomial(1, 0, 0, 1)));
- (*basis)[4] =
+ (*basis)[4] =
new Polynomial((Polynomial(1, 0, 0, 0) - Polynomial(1, 1, 0, 0)) *
(Polynomial(1, 0, 0, 0) - Polynomial(1, 0, 1, 0)) *
Polynomial(1, 0, 0, 1));
- (*basis)[5] =
+ (*basis)[5] =
new Polynomial((Polynomial(1, 1, 0, 0)) *
(Polynomial(1, 0, 0, 0) - Polynomial(1, 0, 1, 0)) *
Polynomial(1, 0, 0, 1));
- (*basis)[6] =
+ (*basis)[6] =
new Polynomial((Polynomial(1, 1, 0, 0)) *
(Polynomial(1, 0, 1, 0)) *
Polynomial(1, 0, 0, 1));
- (*basis)[7] =
+ (*basis)[7] =
new Polynomial((Polynomial(1, 0, 0, 0) - Polynomial(1, 1, 0, 0)) *
(Polynomial(1, 0, 1, 0)) *
Polynomial(1, 0, 0, 1));
-
+
// Edge Based //
// Keep counting
int i = 8;
@@ -152,14 +152,14 @@ HexNodeBasis::HexNodeBasis(int order){
for(int l = 1; l < order; l++){
for(int e = 0; e < 12; e++){
(*basis)[i] = new Polynomial(
- legendre[l].compose(lifting[edge1[e]] - lifting[edge2[e]]) *
+ legendre[l].compose(lifting[edge1[e]] - lifting[edge2[e]]) *
(*(*basis)[edge1[e]] + *(*basis)[edge2[e]]));
-
+
i++;
}
}
-
+
// Face Based (Preliminary) //
// Points definig Faces
const int face1[6] = {0, 3, 2, 1, 5, 4};
@@ -177,7 +177,7 @@ HexNodeBasis::HexNodeBasis(int order){
// 'Lambda' Functions
for(int f = 0; f < 6; f++)
- lambda[f] =
+ lambda[f] =
*(*basis)[face1[f]] +
*(*basis)[face2[f]] +
*(*basis)[face3[f]] +
@@ -187,18 +187,18 @@ HexNodeBasis::HexNodeBasis(int order){
// Face Based //
for(int l1 = 1; l1 < order; l1++){
for(int l2 = 1; l2 < order; l2++){
- for(int f = 0; f < 6; f++){
+ for(int f = 0; f < 6; f++){
(*basis)[i] = new Polynomial(
legendre[l1].compose(xi[f]) *
legendre[l2].compose(eta[f]) *
lambda[f]);
-
+
i++;
}
}
}
-
-
+
+
// Cell Based //
Polynomial px = Polynomial(2, 1, 0, 0);
Polynomial py = Polynomial(2, 0, 1, 0);
@@ -211,11 +211,11 @@ HexNodeBasis::HexNodeBasis(int order){
for(int l1 = 1; l1 < order; l1++){
for(int l2 = 1; l2 < order; l2++){
for(int l3 = 1; l3 < order; l3++){
- (*basis)[i] =
- new Polynomial(legendre[l1].compose(px) *
+ (*basis)[i] =
+ new Polynomial(legendre[l1].compose(px) *
legendre[l2].compose(py) *
legendre[l3].compose(pz));
-
+
i++;
}
}
@@ -237,7 +237,7 @@ HexNodeBasis::~HexNodeBasis(void){
// Vertex Based //
for(int i = 0; i < nVertex; i++)
delete (*node)[i];
-
+
delete node;
@@ -245,10 +245,10 @@ HexNodeBasis::~HexNodeBasis(void){
for(int c = 0; c < 2; c++){
for(int i = 0; i < nEdge; i++)
delete (*(*edge)[c])[i];
-
+
delete (*edge)[c];
}
-
+
delete edge;
@@ -256,7 +256,7 @@ HexNodeBasis::~HexNodeBasis(void){
for(int c = 0; c < 6; c++){
for(int i = 0; i < nFace; i++)
delete (*(*face)[c])[i];
-
+
delete (*face)[c];
}
diff --git a/FunctionSpace/Legendre.cpp b/FunctionSpace/Legendre.cpp
index e7ad4f9bbb1a8bebf5ed6d70bc0d910491c832bb..a4e7f72620511fa1763bb3cd524548150e692abe 100644
--- a/FunctionSpace/Legendre.cpp
+++ b/FunctionSpace/Legendre.cpp
@@ -1,6 +1,6 @@
#include "Legendre.h"
-Polynomial Legendre::legendre(const int n, const Polynomial& l,
+Polynomial Legendre::legendre(const int n, const Polynomial& l,
const Polynomial& lMinus){
const double nPlus = n + 1;
@@ -8,16 +8,16 @@ Polynomial Legendre::legendre(const int n, const Polynomial& l,
l * Polynomial(1, 1, 0, 0) * ((2 * n + 1) / nPlus) - lMinus * (n / nPlus);
}
-Polynomial Legendre::scaled(const int n, const Polynomial& l,
+Polynomial Legendre::scaled(const int n, const Polynomial& l,
const Polynomial& lMinus){
const double nPlus = n + 1;
return
- l * Polynomial(1, 1, 0, 0) * ((2 * n + 1) / nPlus) -
+ l * Polynomial(1, 1, 0, 0) * ((2 * n + 1) / nPlus) -
lMinus * Polynomial(1, 0, 2, 0) * (( n ) / nPlus);
}
-Polynomial Legendre::integrated(const int n, const Polynomial& l,
+Polynomial Legendre::integrated(const int n, const Polynomial& l,
const Polynomial& lMinus){
const double nPlus = n + 1;
@@ -25,12 +25,12 @@ Polynomial Legendre::integrated(const int n, const Polynomial& l,
l * Polynomial(1, 1, 0, 0) * ((2 * n - 1) / nPlus) - lMinus * ((n - 2) / nPlus);
}
-Polynomial Legendre::intScaled(const int n, const Polynomial& l,
+Polynomial Legendre::intScaled(const int n, const Polynomial& l,
const Polynomial& lMinus){
const double nPlus = n + 1;
return
- l * Polynomial(1, 1, 0, 0) * ((2 * n - 1) / nPlus) -
+ l * Polynomial(1, 1, 0, 0) * ((2 * n - 1) / nPlus) -
lMinus * Polynomial(1, 0, 2, 0) * (( n - 2) / nPlus);
}
@@ -41,7 +41,7 @@ void Legendre::legendre(Polynomial* polynomial, const int order){
if(order >= 0)
polynomial[0] = Polynomial(1, 0, 0, 0);
-
+
if(order >= 1)
polynomial[1] = Polynomial(1, 1, 0, 0);
@@ -49,7 +49,7 @@ void Legendre::legendre(Polynomial* polynomial, const int order){
for(k = 2; k <= order; k++){
i = k - 1;
j = k - 2;
-
+
polynomial[k] = legendre(i, polynomial[i], polynomial[j]);
}
}
@@ -68,7 +68,7 @@ void Legendre::integrated(Polynomial* polynomial, const int order){
for(k = 2; k < order; k++){
i = k - 1;
j = k - 2;
-
+
polynomial[k] = integrated(k, polynomial[i], polynomial[j]);
}
}
@@ -79,7 +79,7 @@ void Legendre::scaled(Polynomial* polynomial, const int order){
if(order >= 0)
polynomial[0] = Polynomial(1, 0, 0, 0);
-
+
if(order >= 1)
polynomial[1] = Polynomial(1, 1, 0, 0);
@@ -87,7 +87,7 @@ void Legendre::scaled(Polynomial* polynomial, const int order){
for(k = 2; k <= order; k++){
i = k - 1;
j = k - 2;
-
+
polynomial[k] = scaled(i, polynomial[i], polynomial[j]);
}
}
@@ -106,7 +106,7 @@ void Legendre::intScaled(Polynomial* polynomial, const int order){
for(k = 2; k < order; k++){
i = k - 1;
j = k - 2;
-
+
polynomial[k] = intScaled(k, polynomial[i], polynomial[j]);
}
}
diff --git a/FunctionSpace/Legendre.h b/FunctionSpace/Legendre.h
index 4120b65adfcdbe50af71b773a5bb354915f21550..25924558f094f6cc74e3e3dc9e218962f6286c86 100644
--- a/FunctionSpace/Legendre.h
+++ b/FunctionSpace/Legendre.h
@@ -6,8 +6,8 @@
/**
@class Legendre
@brief Generators for legendre Polynomial%s
-
- This class handles the generation of legendre
+
+ This class handles the generation of legendre
Polynomial%s of many types:
@li Classical legendre (Legendre::legendre)
@li Integrated legendre (Legendre::integrated)
@@ -29,50 +29,50 @@ class Legendre{
private:
static Polynomial legendre(const int n,
- const Polynomial& l,
+ const Polynomial& l,
const Polynomial& lMinus);
-
+
static Polynomial integrated(const int n,
- const Polynomial& l,
+ const Polynomial& l,
const Polynomial& lMinus);
static Polynomial scaled(const int n,
- const Polynomial& l,
+ const Polynomial& l,
const Polynomial& lMinus);
static Polynomial intScaled(const int n,
- const Polynomial& l,
+ const Polynomial& l,
const Polynomial& lMinus);
};
/**
@fn void Legendre::legendre(Polynomial*, const int)
- @param polynomial An @em allocated array (of size @c 'order' @c + @c 1)
+ @param polynomial An @em allocated array (of size @c 'order' @c + @c 1)
for storing the requested legendre Polynomial%s
@param order The @em maximal order of the requested Polynomial%s
@return Stores in @c 'polynomial' all the @em classical legendre Polynomial%s
- of order [@c 0, @c 'order']
+ of order [@c 0, @c 'order']
@fn void Legendre::integrated(Polynomial*, const int)
@param polynomial An @em allocated array (of size @c 'order')
for storing the requested legendre Polynomial%s
@param order The @em maximal order of the requested Polynomial%s
@return Stores in @c 'polynomial' all the @em integrated legendre Polynomial%s
- of order [@c 1, @c 'order']
+ of order [@c 1, @c 'order']
@fn void Legendre::scaled(Polynomial*, const int)
- @param polynomial An @em allocated array (of size @c 'order' @c + @c 1)
+ @param polynomial An @em allocated array (of size @c 'order' @c + @c 1)
for storing the requested legendre Polynomial%s
@param order The @em maximal order of the requested Polynomial%s
@return Stores in @c 'polynomial' all the @em scaled legendre Polynomial%s
- of order [@c 0, @c 'order']
+ of order [@c 0, @c 'order']
@fn void Legendre::intScaled(Polynomial*, const int)
@param polynomial An @em allocated array (of size @c 'order')
for storing the requested legendre Polynomial%s
@param order The @em maximal order of the requested Polynomial%s
- @return Stores in @c 'polynomial' all the @em scaled @em integrated
- legendre Polynomial%s of order [@c 1, @c 'order']
+ @return Stores in @c 'polynomial' all the @em scaled @em integrated
+ legendre Polynomial%s of order [@c 1, @c 'order']
*/
#endif
diff --git a/FunctionSpace/LineNodeBasis.cpp b/FunctionSpace/LineNodeBasis.cpp
index 6e9c8933f0978c9afbcd56de8240ca23bafc8a11..3839f9b0fc6c8da00a4d2457938e452a2c2fc11e 100644
--- a/FunctionSpace/LineNodeBasis.cpp
+++ b/FunctionSpace/LineNodeBasis.cpp
@@ -14,7 +14,7 @@ LineNodeBasis::LineNodeBasis(unsigned int order){
// Set Basis Type //
this->order = order;
-
+
type = 0;
dim = 1;
@@ -43,23 +43,23 @@ LineNodeBasis::LineNodeBasis(unsigned int order){
// Vertex Based (Lagrange) //
for(unsigned int s = 0; s < nRefSpace; s++){
- basis[s][0] =
- new Polynomial(Polynomial(0.5, 0, 0, 0) -
+ basis[s][0] =
+ new Polynomial(Polynomial(0.5, 0, 0, 0) -
Polynomial(0.5, 1, 0, 0));
-
- basis[s][1] =
- new Polynomial(Polynomial(0.5, 0, 0, 0) +
+
+ basis[s][1] =
+ new Polynomial(Polynomial(0.5, 0, 0, 0) +
Polynomial(0.5, 1, 0, 0));
}
// Edge Based //
for(unsigned int s = 0; s < nRefSpace; s++){
unsigned int i = nVertex;
-
+
for(unsigned int l = 1; l < order; l++){
- basis[s][i] =
+ basis[s][i] =
new Polynomial(intLegendre[l].compose(x[(*(*edgeV[s])[0])[0]]));
-
+
i++;
}
}
diff --git a/FunctionSpace/LineReferenceSpace.cpp b/FunctionSpace/LineReferenceSpace.cpp
index 4b2be2283b293487998ca9c4064305463ae0ccff..d4d41069dd02ad999328ea232a3f37a2400363b6 100644
--- a/FunctionSpace/LineReferenceSpace.cpp
+++ b/FunctionSpace/LineReferenceSpace.cpp
@@ -19,7 +19,7 @@ LineReferenceSpace::LineReferenceSpace(void){
// Face Definition //
nFace = 0;
refFace = NULL;
-
+
// Init All //
init();
}
@@ -28,7 +28,7 @@ LineReferenceSpace::~LineReferenceSpace(void){
// Delete Ref Edge //
for(unsigned int i = 0; i < nEdge; i++)
delete[] refEdge[i];
-
+
delete[] refEdge;
}
@@ -36,7 +36,7 @@ string LineReferenceSpace::toLatex(void) const{
stringstream stream;
stream << "\\documentclass{article}" << endl << endl
-
+
<< "\\usepackage{longtable}" << endl
<< "\\usepackage{tikz}" << endl
<< "\\usetikzlibrary{arrows}" << endl << endl
@@ -52,10 +52,10 @@ string LineReferenceSpace::toLatex(void) const{
<< "\\node[vertex] (n0) at(0, 0) {$0$};" << endl
<< "\\node[vertex] (n1) at(3, 0) {$1$};" << endl << endl
-
- << "\\path[line]"
+
+ << "\\path[line]"
<< " (n" << (*(*(*edge)[p])[0])[0] << ")"
- << " -- "
+ << " -- "
<< " (n" << (*(*(*edge)[p])[0])[1] << ");"
<< endl
@@ -64,6 +64,6 @@ string LineReferenceSpace::toLatex(void) const{
stream << "\\end{longtable}" << endl
<< "\\end{document}" << endl;
-
+
return stream.str();
}
diff --git a/FunctionSpace/LineReferenceSpace.h b/FunctionSpace/LineReferenceSpace.h
index 9059d23ff07162dcb494e96168bf505a76bf3062..ab613949acc073fd1c0e6dc5a170f506e2c15df3 100644
--- a/FunctionSpace/LineReferenceSpace.h
+++ b/FunctionSpace/LineReferenceSpace.h
@@ -16,7 +16,7 @@ class LineReferenceSpace: public ReferenceSpace{
LineReferenceSpace(void);
virtual ~LineReferenceSpace(void);
- virtual std::string toLatex(void) const;
+ virtual std::string toLatex(void) const;
};
/**
diff --git a/FunctionSpace/Polynomial.cpp b/FunctionSpace/Polynomial.cpp
index fe952cc856924a8b60542b38924673aa2378b4b0..c5a3ca8ee24082007b80c26ecca10e752db41547 100644
--- a/FunctionSpace/Polynomial.cpp
+++ b/FunctionSpace/Polynomial.cpp
@@ -13,16 +13,16 @@ Polynomial::Polynomial(const double coef, const int powerX,
const int powerZ){
nMon = 1;
mon = new monomial_t[1];
-
+
mon[0].coef = coef;
mon[0].power[0] = powerX;
mon[0].power[1] = powerY;
mon[0].power[2] = powerZ;
}
-
+
Polynomial::Polynomial(const Polynomial& other){
nMon = other.nMon;
- mon = copyMonomial(other.mon, nMon);
+ mon = copyMonomial(other.mon, nMon);
}
Polynomial::Polynomial(void){
@@ -35,7 +35,7 @@ Polynomial::~Polynomial(void){
delete[] mon;
}
-void Polynomial::derivative(const int dim){
+void Polynomial::derivative(const int dim){
// Take derivative //
for(int i = 0; i < nMon; i++){
mon[i].coef *= mon[i].power[dim];
@@ -56,19 +56,19 @@ void Polynomial::derivative(const int dim){
// If no monomial any more ---> return zero polynomial
if(!N){
delete[] mon;
-
+
mon = zeroPolynomial();
nMon = 1;
return;
}
-
+
// If no zero found ---> return;
- if(N == nMon)
+ if(N == nMon)
return;
// Else, remove them //
monomial_t* tmp = mon;
-
+
mon = new monomial_t[N];
nMon = N;
@@ -79,7 +79,7 @@ void Polynomial::derivative(const int dim){
delete[] tmp;
- // Sort resulting monomial and return //
+ // Sort resulting monomial and return //
sort(mon, nMon);
return;
@@ -97,7 +97,7 @@ vector<Polynomial> Polynomial::gradient(void) const{
grad[0].derivative(0);
grad[1].derivative(1);
grad[2].derivative(2);
-
+
return grad;
}
@@ -144,11 +144,11 @@ Polynomial Polynomial::divergence(const vector<Polynomial>& p){
double Polynomial::at
(const double x, const double y, const double z) const{
-
+
double val = 0;
for(int i = 0; i < nMon; i++){
- val += mon[i].coef * pow(x, mon[i].power[0])
- * pow(y, mon[i].power[1])
+ val += mon[i].coef * pow(x, mon[i].power[0])
+ * pow(y, mon[i].power[1])
* pow(z, mon[i].power[2]);
}
@@ -160,7 +160,7 @@ fullVector<double> Polynomial::at(const vector<Polynomial>& P,
const double y,
const double z){
fullVector<double> val(3);
-
+
val(0) = P[0].at(x, y, z);
val(1) = P[1].at(x, y, z);
val(2) = P[2].at(x, y, z);
@@ -171,7 +171,7 @@ fullVector<double> Polynomial::at(const vector<Polynomial>& P,
Polynomial Polynomial::operator+(const Polynomial& other) const{
Polynomial newP;
-
+
newP.nMon = mergeMon(mon, nMon, other.mon, other.nMon, &newP.mon);
return newP;
@@ -179,11 +179,11 @@ Polynomial Polynomial::operator+(const Polynomial& other) const{
Polynomial Polynomial::operator-(const Polynomial& other) const{
const int otherNMon = other.nMon;
- monomial_t* otherMinus = copyMonomial(other.mon, otherNMon);
-
+ monomial_t* otherMinus = copyMonomial(other.mon, otherNMon);
+
Polynomial newP;
- mult(otherMinus, otherNMon, -1);
+ mult(otherMinus, otherNMon, -1);
newP.nMon = mergeMon(mon, nMon, otherMinus, otherNMon, &newP.mon);
delete[] otherMinus;
@@ -192,7 +192,7 @@ Polynomial Polynomial::operator-(const Polynomial& other) const{
Polynomial Polynomial::operator*(const Polynomial& other) const{
Polynomial newP;
-
+
newP.nMon = mult(mon, nMon, other.mon, other.nMon, &newP.mon);
return newP;
@@ -200,7 +200,7 @@ Polynomial Polynomial::operator*(const Polynomial& other) const{
Polynomial Polynomial::operator*(const double alpha) const{
Polynomial newP;
-
+
newP.mon = copyMonomial(mon, nMon);
newP.nMon = nMon;
@@ -212,7 +212,7 @@ Polynomial Polynomial::operator*(const double alpha) const{
void Polynomial::add(const Polynomial& other){
monomial_t* tmp = mon;
-
+
nMon = mergeMon(mon, nMon, other.mon, other.nMon, &mon);
delete[] tmp;
@@ -220,10 +220,10 @@ void Polynomial::add(const Polynomial& other){
void Polynomial::sub(const Polynomial& other){
const int otherNMon = other.nMon;
- monomial_t* otherMinus = copyMonomial(other.mon, otherNMon);
+ monomial_t* otherMinus = copyMonomial(other.mon, otherNMon);
monomial_t* tmp = mon;
-
- mult(otherMinus, otherNMon, -1);
+
+ mult(otherMinus, otherNMon, -1);
nMon = mergeMon(mon, nMon, otherMinus, otherNMon, &mon);
delete[] otherMinus;
@@ -232,7 +232,7 @@ void Polynomial::sub(const Polynomial& other){
void Polynomial::mul(const Polynomial& other){
monomial_t* tmp = mon;
-
+
nMon = mult(mon, nMon, other.mon, other.nMon, &mon);
delete[] tmp;
@@ -250,21 +250,21 @@ void Polynomial::power(const int n){
switch(n){
case 0:
delete[] mon;
-
+
mon = unitPolynomial();
nMon = 1;
-
+
break;
-
+
case 1:
break;
default:
Polynomial old = *this;
-
+
for(int i = 1; i < n; i++)
mul(old);
-
+
break;
}
}
@@ -291,7 +291,7 @@ Polynomial Polynomial::compose(const Polynomial& otherA,
void Polynomial::operator=(const Polynomial& other){
if(mon)
delete[] mon;
-
+
nMon = other.nMon;
mon = copyMonomial(other.mon, nMon);
}
@@ -308,7 +308,7 @@ string Polynomial::toString(const Polynomial::monomial_t* mon, const bool isAbs)
}
// If we're here, we do not have a constant term
-
+
// If we have a coefficient of '1', we don't display it
if(notUnitCoef && isAbs)
stream << abs(mon->coef);
@@ -328,7 +328,7 @@ string Polynomial::toString(const Polynomial::monomial_t* mon, const bool isAbs)
stream << " * ";
stream << coefName[i];
-
+
if(mon->power[i] != 1)
stream << "^" << mon->power[i];
@@ -344,7 +344,7 @@ string Polynomial::toString(void) const{
bool isAbs = false;
stream << toString(&mon[0], isAbs);
-
+
for(int i = 1; i < nMon; i++){
if(mon[i].coef < 0.0){
stream << " - ";
@@ -362,17 +362,17 @@ string Polynomial::toString(void) const{
return stream.str();
}
-bool Polynomial::isSmaller(const Polynomial::monomial_t* a,
+bool Polynomial::isSmaller(const Polynomial::monomial_t* a,
const Polynomial::monomial_t* b){
- // GRevLex order:
+ // GRevLex order:
// http://www.math.uiuc.edu/Macaulay2/doc/Macaulay2-1.4/share/doc/Macaulay2/Macaulay2Doc/html/___G__Rev__Lex.html
-
+
int dif[3];
int last = 0;
if(isSmallerPower(a, b))
return true;
-
+
if(isEqualPower(a, b)){
for(int i = 0, j = 2; i < 3; i++, j--)
dif[i] = b->power[j] - a->power[j];
@@ -383,11 +383,11 @@ bool Polynomial::isSmaller(const Polynomial::monomial_t* a,
if(last < 0)
return true;
-
+
else
return false;
}
-
+
return false;
}
@@ -405,7 +405,7 @@ void Polynomial::swap(monomial_t* mon, const int i, const int j){
}
-int Polynomial::mergeMon(monomial_t* sourceA, const int sizeA,
+int Polynomial::mergeMon(monomial_t* sourceA, const int sizeA,
monomial_t* sourceB, const int sizeB,
monomial_t** dest){
stack<monomial_t> s;
@@ -421,20 +421,20 @@ int Polynomial::mergeMon(monomial_t* sourceA, const int sizeA,
else if(sourceB[j].coef == 0.0)
j++;
-
+
else if(isEqual(&sourceA[i], &sourceB[j])){
tmp = sourceA[i];
- tmp.coef += sourceB[j].coef;
-
+ tmp.coef += sourceB[j].coef;
+
if(tmp.coef != 0.0){
s.push(tmp);
N++;
}
-
+
i++;
j++;
}
-
+
else if(isSmaller(&sourceA[i], &sourceB[j])){
s.push(sourceA[i]);
i++;
@@ -488,11 +488,11 @@ int Polynomial::mult(const monomial_t* sourceA, const int sizeA,
if(sizeA < sizeB){
a = sourceA;
- b = sourceB;
+ b = sourceB;
nDist = sizeA;
size = sizeB;
}
-
+
else{
a = sourceB;
b = sourceA;
@@ -511,7 +511,7 @@ int Polynomial::mult(const monomial_t* sourceA, const int sizeA,
for(int i = 0; i < nDist; i++){
dist[i] = copyMonomial(b, size);
-
+
distribute(dist[i], size, &a[i]);
}
@@ -522,8 +522,8 @@ int Polynomial::mult(const monomial_t* sourceA, const int sizeA,
for(int i = 1, j = 0; i < nDist; i++, j++){
tmp[j] = dist[0];
-
- finalSize = mergeMon(dist[0], finalSize,
+
+ finalSize = mergeMon(dist[0], finalSize,
dist[i], size,
&dist[0]);
}
@@ -536,7 +536,7 @@ int Polynomial::mult(const monomial_t* sourceA, const int sizeA,
delete[] dist[i];
delete[] tmp[j];
}
-
+
delete[] dist;
delete[] tmp;
@@ -549,31 +549,31 @@ void Polynomial::mult(monomial_t* source, const int size, const double alpha){
}
-void Polynomial::distribute(monomial_t* src, const int size, const monomial_t* m){
+void Polynomial::distribute(monomial_t* src, const int size, const monomial_t* m){
for(int i = 0; i < size; i++){
src[i].coef *= m->coef;
-
+
src[i].power[0] += m->power[0];
src[i].power[1] += m->power[1];
- src[i].power[2] += m->power[2];
+ src[i].power[2] += m->power[2];
}
}
void Polynomial::compose(const Polynomial::monomial_t* src,
Polynomial comp,
stack<Polynomial::monomial_t>* stk){
-
+
comp.power(src->power[0]);
comp.mul(src->coef);
-
+
const int size = comp.nMon;
for(int i = 0; i < size; i++){
if(comp.mon[i].coef != 0){
-
+
comp.mon[i].power[1] += src->power[1];
comp.mon[i].power[2] += src->power[2];
-
+
stk->push(comp.mon[i]);
}
}
@@ -585,17 +585,17 @@ void Polynomial::compose(const Polynomial::monomial_t* src,
compA.power(src->power[0]);
compB.power(src->power[1]);
-
+
compA.mul(compB);
compA.mul(src->coef);
-
+
const int size = compA.nMon;
for(int i = 0; i < size; i++){
if(compA.mon[i].coef != 0){
-
+
compA.mon[i].power[2] += src->power[2];
-
+
stk->push(compA.mon[i]);
}
}
@@ -617,12 +617,12 @@ Polynomial Polynomial::polynomialFromStack(std::stack<Polynomial::monomial_t>& s
newMon[0] = stk.top();
newNMon = 1;
stk.pop();
-
+
while(!stk.empty()){
tmp = newMon;
newNMon = mergeMon(newMon, newNMon, &stk.top(), 1, &newMon);
stk.pop();
-
+
delete[] tmp;
}
}
@@ -648,23 +648,23 @@ Polynomial::monomial_t* Polynomial::copyMonomial(const monomial_t* src, const in
Polynomial::monomial_t* Polynomial::zeroPolynomial(void){
monomial_t* zero = new monomial_t[1];
-
+
zero->coef = 0;
zero->power[0] = 0;
zero->power[1] = 0;
zero->power[2] = 0;
-
+
return zero;
}
Polynomial::monomial_t* Polynomial::unitPolynomial(void){
monomial_t* unit = new monomial_t[1];
-
+
unit->coef = 1;
unit->power[0] = 0;
unit->power[1] = 0;
unit->power[2] = 0;
-
+
return unit;
}
@@ -705,7 +705,7 @@ int main(void){
Polynomial p4 = p3 * p3;
cout << "p3 = " << p3.toString() << endl;
cout << "p4 = " << p4.toString() << endl;
-
+
p3.mul(p3);
cout << "p3 = " << p3.toString() << endl;
@@ -715,10 +715,10 @@ int main(void){
cout << "p5 = " << p5.toString() << endl;
cout << "p6 = " << p6.toString() << endl;
cout << "p7 = " << p7.toString() << endl;
-
+
p6.sub(p6);
cout << "p6 = " << p6.toString() << endl;
-
+
Polynomial p8(p4);
Polynomial p9(p4);
diff --git a/FunctionSpace/Polynomial.h b/FunctionSpace/Polynomial.h
index 322f665fcd4d6b65b27b61cbd31bcf615db43037..ba52b8e75eef2cafb9ba259d7665884d151d69f2 100644
--- a/FunctionSpace/Polynomial.h
+++ b/FunctionSpace/Polynomial.h
@@ -16,14 +16,14 @@
// We suppose 3D Polynomial
class Polynomial{
- private:
+ private:
static const char coefName[3];
struct monomial_t{
double coef;
int power[3];
};
-
+
int nMon;
monomial_t* mon;
@@ -42,10 +42,10 @@ class Polynomial{
static Polynomial divergence(const std::vector<Polynomial>& p);
double operator()
- (const double x, const double y, const double z) const;
-
+ (const double x, const double y, const double z) const;
+
double at
- (const double x, const double y, const double z) const;
+ (const double x, const double y, const double z) const;
static fullVector<double> at(const std::vector<Polynomial>& P,
const double x,
@@ -65,7 +65,7 @@ class Polynomial{
void power(const int n);
Polynomial compose(const Polynomial& other) const;
- Polynomial compose(const Polynomial& otherA,
+ Polynomial compose(const Polynomial& otherA,
const Polynomial& otherB) const;
void operator=(const Polynomial& other);
@@ -75,31 +75,31 @@ class Polynomial{
private:
static std::string toString(const monomial_t* mon, const bool isAbs);
- static bool isSmaller(const monomial_t* a, const monomial_t*b);
- static bool isEqual(const monomial_t* a, const monomial_t*b);
- static bool isSmallerPower(const monomial_t* a, const monomial_t* b);
+ static bool isSmaller(const monomial_t* a, const monomial_t*b);
+ static bool isEqual(const monomial_t* a, const monomial_t*b);
+ static bool isSmallerPower(const monomial_t* a, const monomial_t* b);
static bool isEqualPower(const monomial_t* a, const monomial_t* b);
-
+
static void sort(monomial_t* mon, const int size);
static void swap(monomial_t* mon, const int i, const int j);
- static int mergeMon(monomial_t* sourceA, const int sizeA,
+ static int mergeMon(monomial_t* sourceA, const int sizeA,
monomial_t* sourceB, const int sizeB,
monomial_t** dest);
-
+
static int mult(const monomial_t* sourceA, const int sizeA,
const monomial_t* sourceB, const int sizeB,
monomial_t** dest);
-
+
static void mult(monomial_t* source, const int size, const double alpha);
static void distribute(monomial_t* src, const int size, const monomial_t* m);
- static void compose(const monomial_t* src,
+ static void compose(const monomial_t* src,
Polynomial comp,
std::stack<monomial_t>* stk);
- static void compose(const monomial_t* src,
+ static void compose(const monomial_t* src,
Polynomial compA, Polynomial compB,
std::stack<monomial_t>* stk);
@@ -114,11 +114,11 @@ class Polynomial{
/**
@fn Polynomial::Polynomial(const double, const int, const int, const int)
@param coef The coeficient of the futur monomial
- @param powerX The power of the '@c x' coordinate
+ @param powerX The power of the '@c x' coordinate
of the futur monomial
- @param powerY The power of the '@c y' coordinate
+ @param powerY The power of the '@c y' coordinate
of the futur monomial
- @param powerZ The power of the '@c z' coordinate
+ @param powerZ The power of the '@c z' coordinate
of the futur monomial
@return Returns a new Monomial with the given
parameters
@@ -140,7 +140,7 @@ class Polynomial{
@em with @em no @em monomials.@n
In particular, the empty Polynomial is @em not
the @em zero @em Polynomial.@n
- Indeed, the @em zero @em Polynomial has one monomial,
+ Indeed, the @em zero @em Polynomial has one monomial,
@em @c 0.
**
@@ -151,7 +151,7 @@ class Polynomial{
@fn Polynomial::derivative
@param dim The dimention to use for the
derivation
- @returns Derivates this Polynomial with
+ @returns Derivates this Polynomial with
respect to the given dimention
@note
Dimention:
@@ -161,16 +161,16 @@ class Polynomial{
**
@fn Polynomial::gradient
- @return Returns a Vector with the gradient
+ @return Returns a Vector with the gradient
of this Polynomial
**
-
+
@fn Polynomial::curl
@param p A vector of Polynomial%s
@return Returns the @em curl of the given
vector of Polynomial%s
**
-
+
@fn Polynomial::divergence
@param p A vector of Polynomial%s
@return Returns the @em divergence of the given
@@ -222,35 +222,35 @@ class Polynomial{
@fn Polynomial Polynomial::operator*(const double) const
@param alpha A value
- @return Returns a @em new Polynomial,
+ @return Returns a @em new Polynomial,
which is this Polynomial @em multiplied by @c alpha
**
@fn Polynomial::add
@param other An other Polynomial
- @return The given Polynomial is
+ @return The given Polynomial is
@em added to this Polynomial
@note
- The result of this operation is stored in
- this Polynomial
+ The result of this operation is stored in
+ this Polynomial
**
@fn Polynomial::sub
@param other An other Polynomial
- @return The given Polynomial is
+ @return The given Polynomial is
@em substracted to this Polynomial
@note
- The result of this operation is stored in
- this Polynomial
+ The result of this operation is stored in
+ this Polynomial
**
@fn void Polynomial::mul(const Polynomial&)
@param other An other Polynomial
- @return The given Polynomial is
+ @return The given Polynomial is
@em multiplied with this Polynomial
@note
- The result of this operation is stored in
- this Polynomial
+ The result of this operation is stored in
+ this Polynomial
**
@fn void Polynomial::mul(const double)
@@ -258,8 +258,8 @@ class Polynomial{
@return This Polynomial is @em multiplied
by the given value
@note
- The result of this operation is stored in
- this Polynomial
+ The result of this operation is stored in
+ this Polynomial
**
@fn Polynomial::power
@@ -268,7 +268,7 @@ class Polynomial{
**
@fn Polynomial Polynomial::compose(const Polynomial&) const
- @param other An other Polynomial,
+ @param other An other Polynomial,
called @c Q(x, @c y, @c z)
@return
Let this Polynomial be @c P(x, @c y, @c z).@n
@@ -277,13 +277,13 @@ class Polynomial{
**
@fn Polynomial Polynomial::compose(const Polynomial&, const Polynomial&) const
- @param otherA An other Polynomial,
+ @param otherA An other Polynomial,
called @c Q(x, @c y, @c z)
- @param otherB An other Polynomial,
+ @param otherB An other Polynomial,
called @c R(x, @c y, @c z)
@return
Let this Polynomial be @c P(x, @c y, @c z).@n
- This method returns a @em new Polynomial, representing
+ This method returns a @em new Polynomial, representing
@c P(Q(x, @c y, @c z), @c R(x, @c y, @c z), @c z)
**
@@ -301,8 +301,8 @@ class Polynomial{
// Inline Functions //
//////////////////////
-inline double Polynomial::operator() (const double x,
- const double y,
+inline double Polynomial::operator() (const double x,
+ const double y,
const double z) const{
return at(x, y, z);
}
@@ -316,20 +316,20 @@ inline bool Polynomial::isEqual(const Polynomial::monomial_t* a,
inline bool Polynomial::isSmallerPower(const Polynomial::monomial_t* a,
const Polynomial::monomial_t* b){
-
- return
- a->power[0] + a->power[1] + a->power[2]
- <
- b->power[0] + b->power[1] + b->power[2] ;
+
+ return
+ a->power[0] + a->power[1] + a->power[2]
+ <
+ b->power[0] + b->power[1] + b->power[2] ;
}
inline bool Polynomial::isEqualPower(const Polynomial::monomial_t* a,
const Polynomial::monomial_t* b){
-
- return
- a->power[0] + a->power[1] + a->power[2]
+
+ return
+ a->power[0] + a->power[1] + a->power[2]
==
- b->power[0] + b->power[1] + b->power[2] ;
+ b->power[0] + b->power[1] + b->power[2] ;
}
#endif
diff --git a/FunctionSpace/ReferenceSpace.cpp b/FunctionSpace/ReferenceSpace.cpp
index a56ab022bd65b9dc8b33ad9c8f448e6006763a6a..fca8c8cfac571f54361c7b4e38e144aba22a0af8 100644
--- a/FunctionSpace/ReferenceSpace.cpp
+++ b/FunctionSpace/ReferenceSpace.cpp
@@ -16,25 +16,25 @@ 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])[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])[i];
+
delete (*face)[p];
}
-
+
delete face;
}
@@ -44,11 +44,11 @@ void ReferenceSpace::init(void){
nextLeafId = 0;
pTreeRoot.depth = 0;
- pTreeRoot.last = NULL;
+ 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;
@@ -64,7 +64,7 @@ void ReferenceSpace::init(void){
perm[i] = lPerm->front();
lPerm->pop_front();
}
-
+
delete lPerm;
// Get Edges & Faces //
@@ -88,12 +88,12 @@ void ReferenceSpace::populate(node* pTreeRoot){
// Init Permutation
pTreeRoot->next = NULL;
pTreeRoot->leafId = nextLeafId;
-
+
// Value for Next Permutation
nextLeafId++;
nPerm++;
-
- // Put this Permutation in queue
+
+ // Put this Permutation in queue
// (AND IN ORDER)
lPerm->push_back(pTreeRoot->last);
}
@@ -103,27 +103,27 @@ void ReferenceSpace::populate(node* pTreeRoot){
// We got 'number' child nodes
pTreeRoot->next = new node[number];
- // Init each child node
+ // Init each child node
for(unsigned int i = 0; i < number; i++){
nextLast = pTreeRoot->possible[i];
offset = 0;
-
+
// Depth and Last Choices of child nodes
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];
// Possibilities of child node
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];
}
@@ -140,7 +140,7 @@ void ReferenceSpace::destroy(node* node){
destroy(&node->next[i]);
node->number--;
}
-
+
delete[] node->possible;
delete[] node->last;
delete[] node->next;
@@ -154,9 +154,9 @@ void ReferenceSpace::getEdge(void){
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]);
+ (*tmp)[i] = inOrder(p,
+ refEdge[i][0],
+ refEdge[i][1]);
(*edge)[p] = tmp;
}
}
@@ -169,57 +169,57 @@ void ReferenceSpace::getFace(void){
tmp = new vector<const vector<unsigned int>*>(nFace);
for(unsigned int i = 0; i < nFace; i++)
- (*tmp)[i] = inOrder(p,
- refFace[i][0],
+ (*tmp)[i] = inOrder(p,
+ refFace[i][0],
refFace[i][1],
- refFace[i][2]);
+ refFace[i][2]);
(*face)[p] = tmp;
}
}
const vector<unsigned int>* ReferenceSpace::
-inOrder(unsigned int permutation,
- unsigned int a,
+inOrder(unsigned int permutation,
+ unsigned int a,
unsigned int b){
-
+
unsigned int v;
unsigned int k = 0;
- vector<unsigned int>* inorder =
+ 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){
+
+ if(v == a || v == b){
(*inorder)[k] = v;
k++;
}
}
-
+
return inorder;
}
const std::vector<unsigned int>* ReferenceSpace::
-inOrder(unsigned int permutation,
- unsigned int a,
+inOrder(unsigned int permutation,
+ unsigned int a,
unsigned int b,
unsigned int c){
-
+
unsigned int v;
unsigned int k = 0;
- vector<unsigned int>* inorder =
+ 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){
+
+ if(v == a || v == b || v == c){
(*inorder)[k] = v;
k++;
}
}
-
- return inorder;
+
+ return inorder;
}
unsigned int ReferenceSpace::getPermutation(const MElement& elem) const{
@@ -232,12 +232,12 @@ unsigned int ReferenceSpace::getPermutation(const MElement& elem) const{
for(int i = 0; i < nVertex; i++){
vertex[i].first = i;
- vertex[i].second = element.getVertex(i);
+ vertex[i].second = element.getVertex(i);
}
-
- // Sort Them with repsect to Vertex Global ID //
+
+ // Sort Them with repsect to Vertex Global ID //
// (vertex[i].second->getNum) //
- std::sort(vertex.begin(), vertex.end(), sortPredicate);
+ std::sort(vertex.begin(), vertex.end(), sortPredicate);
// Tree Lookup //
try{
@@ -251,7 +251,7 @@ unsigned int ReferenceSpace::getPermutation(const MElement& elem) const{
}
unsigned int ReferenceSpace::treeLookup(const node* root,
- vector<pair<unsigned int, MVertex*> >&
+ vector<pair<unsigned int, MVertex*> >&
sortedArray){
// Temp Data //
unsigned int choice;
@@ -277,22 +277,22 @@ unsigned int ReferenceSpace::treeLookup(const node* root,
// Else: Return Leaf ID //
else
- return root->leafId;
+ return root->leafId;
}
string ReferenceSpace::toString(void) const{
stringstream stream;
-
+
// Tree //
stream << "Tree:" << endl;
stream << toString(&pTreeRoot) << endl;
// ReferenceSpaces //
stream << "Reference Spaces:" << endl;
-
+
for(unsigned int i = 0; i < nPerm; i++){
stream << " * ";
-
+
for(unsigned int j = 0; j < nVertex; j++)
stream << perm[i][j] << " ";
@@ -300,23 +300,23 @@ string ReferenceSpace::toString(void) const{
}
stream << "Edges Permutations:" << endl;
-
+
for(unsigned int i = 0; i < nPerm; i++){
stream << " * RefSpace #" << i + 1 << ":" << endl;
-
+
for(unsigned int j = 0; j < nEdge; j++)
- stream << " -- ["
+ stream << " -- ["
<< edge->at(i)->at(j)->at(0) << ", "
<< edge->at(i)->at(j)->at(1) << "]" << endl;
}
stream << "Faces Permutations:" << endl;
-
+
for(unsigned int i = 0; i < nPerm; i++){
stream << " * RefSpace #" << i + 1 << ":" << endl;
-
+
for(unsigned int j = 0; j < nFace; j++)
- stream << " -- ["
+ stream << " -- ["
<< face->at(i)->at(j)->at(0) << ", "
<< face->at(i)->at(j)->at(1) << ", "
<< face->at(i)->at(j)->at(2) << "]" << endl;
@@ -338,6 +338,6 @@ string ReferenceSpace::toString(const node* node) const{
stream << toString(&node->next[i]);
stream << ")";
-
+
return stream.str();
}
diff --git a/FunctionSpace/ReferenceSpace.h b/FunctionSpace/ReferenceSpace.h
index 580d56239f7c2c474f04134dac109e692eb4eabf..88e86a097839f6ce35fc3ec08bb0aac00bc19cfa 100644
--- a/FunctionSpace/ReferenceSpace.h
+++ b/FunctionSpace/ReferenceSpace.h
@@ -25,7 +25,7 @@ class ReferenceSpace{
unsigned int number; // Number of Next Choise
unsigned int* possible; // Possible Next Choise
node_s* next; // Next Choise
-
+
unsigned int leafId; // If leaf: this leaf number
// (from 0 to nLeaf - 1)
// Else: no meaning
@@ -57,12 +57,12 @@ class ReferenceSpace{
virtual ~ReferenceSpace(void);
unsigned int getNPermutation(void) const;
-
+
unsigned int getPermutation(const MElement& element) 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 ;
@@ -76,24 +76,24 @@ class ReferenceSpace{
void init(void);
void populate(node* pTreeRoot);
void destroy(node* node);
-
+
void getEdge(void);
void getFace(void);
- const std::vector<unsigned int>* inOrder(unsigned int permutation,
- unsigned int a,
+ 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,
+ const std::vector<unsigned int>* inOrder(unsigned int permutation,
+ unsigned int a,
unsigned int b,
unsigned int c);
- static bool sortPredicate(const std::pair<unsigned int, MVertex*>& a,
+ static bool sortPredicate(const std::pair<unsigned int, MVertex*>& a,
const std::pair<unsigned int, MVertex*>& b);
static unsigned int treeLookup(const node* root,
- std::vector<std::pair<unsigned int, MVertex*> >&
+ std::vector<std::pair<unsigned int, MVertex*> >&
sortedArray);
std::string toString(const node* node) const;
@@ -110,7 +110,7 @@ class ReferenceSpace{
@fn ReferenceSpace::~ReferenceSpace
Deletes this ReferenceSpace
**
-
+
@fn ReferenceSpace::getNPermutation
@returns Returns the number of permutation of this
ReferenceSpace
@@ -118,35 +118,35 @@ class ReferenceSpace{
@fn ReferenceSpace::getPermutation
@param element A MElement
- @returns Returns the a natural number defining
+ @returns Returns the a natural number defining
the permutation of the given element
-
+
@note If no permutation is found (e.g. the given
- element does not belong the @em same @em geometrical
+ element does not belong the @em same @em geometrical
entity as this ReferenceSpace) an Exception is thrown
**
@fn ReferenceSpace::getAllEdge
@return Returns every Edge permutation of this ReferenceSpace
-
+
@note
- @li The fisrt vector represents a particular permutation
+ @li The fisrt vector represents a particular permutation
(see ReferenceSpace::getPermutation())
- @li The second vector represents a particular edge
- (for a given permutation)
- @li The last vector represents the Vertex @c IDs of
+ @li The second vector represents a particular edge
+ (for a given permutation)
+ @li The last vector represents the Vertex @c IDs of
the given edge (in the @em geometrical reference space)
**
@fn ReferenceSpace::getAllFace
@return Returns every Face permutation of this ReferenceSpace
-
+
@note
- @li The fisrt vector represents a particular permutation
+ @li The fisrt vector represents a particular permutation
(see ReferenceSpace::getPermutation())
- @li The second vector represents a particular face
- (for a given permutation)
- @li The last vector represents the Vertex @c IDs of
+ @li The second vector represents a particular face
+ (for a given permutation)
+ @li The last vector represents the Vertex @c IDs of
the given face (in the @em geometrical reference space)
**
@@ -155,21 +155,21 @@ class ReferenceSpace{
**
@fn ReferenceSpace::toLatex
- @return Returns a string (of a Latex file)
- describing this ReferenceSpace
+ @return Returns a string (of a Latex file)
+ describing this ReferenceSpace
*/
//////////////////////
// Inline Functions //
//////////////////////
-inline
-unsigned int
+inline
+unsigned int
ReferenceSpace::getNPermutation(void) const{
return nPerm;
}
-
-inline
+
+inline
std::vector<const std::vector<const std::vector<unsigned int>*>*>&
ReferenceSpace::getAllEdge(void) const{
return *edge;
@@ -181,9 +181,9 @@ ReferenceSpace::getAllFace(void) const{
return *face;
}
-inline
-bool
-ReferenceSpace::sortPredicate(const std::pair<unsigned int, MVertex*>& a,
+inline
+bool
+ReferenceSpace::sortPredicate(const std::pair<unsigned int, MVertex*>& a,
const std::pair<unsigned int, MVertex*>& b){
return a.second->getNum() < b.second->getNum();
}
diff --git a/FunctionSpace/TetNodeBasis.cpp b/FunctionSpace/TetNodeBasis.cpp
index 4f36f7a8d21a31d6da279e9c48bbe3eaa86a7a61..37971f323cde740a0898ed833b8bd1674a104789 100644
--- a/FunctionSpace/TetNodeBasis.cpp
+++ b/FunctionSpace/TetNodeBasis.cpp
@@ -17,7 +17,7 @@ TetNodeBasis::TetNodeBasis(unsigned int order){
// Set Basis Type //
this->order = order;
-
+
type = 0;
dim = 3;
@@ -42,17 +42,17 @@ TetNodeBasis::TetNodeBasis(unsigned int order){
Legendre::intScaled(intLegendre, order);
// Lagrange Polynomial //
- const Polynomial lagrange[4] =
+ const Polynomial lagrange[4] =
{
- Polynomial(Polynomial(1, 0, 0, 0) -
- Polynomial(1, 1, 0, 0) -
- Polynomial(1, 0, 1, 0) -
+ Polynomial(Polynomial(1, 0, 0, 0) -
+ Polynomial(1, 1, 0, 0) -
+ Polynomial(1, 0, 1, 0) -
Polynomial(1, 0, 0, 1)),
-
+
Polynomial(Polynomial(1, 1, 0, 0)),
Polynomial(Polynomial(1, 0, 1, 0)),
-
+
Polynomial(Polynomial(1, 0, 0, 1))
};
@@ -77,12 +77,12 @@ TetNodeBasis::TetNodeBasis(unsigned int order){
for(int e = 0; e < 6; e++){
for(unsigned int l = 1; l < order; l++){
- basis[s][i] =
+ basis[s][i] =
new Polynomial(intLegendre[l].compose
- (lagrange[(*(*edgeV[s])[e])[0]] -
+ (lagrange[(*(*edgeV[s])[e])[0]] -
lagrange[(*(*edgeV[s])[e])[1]]
- ,
- lagrange[(*(*edgeV[s])[e])[0]] +
+ ,
+ lagrange[(*(*edgeV[s])[e])[0]] +
lagrange[(*(*edgeV[s])[e])[1]]));
i++;
}
@@ -96,23 +96,23 @@ TetNodeBasis::TetNodeBasis(unsigned int order){
for(int f = 0; f < 4; f++){
for(int l1 = 1; l1 < orderMinus; l1++){
for(int l2 = 0; l1 + l2 - 1 < orderMinusTwo; l2++){
- Polynomial sum =
- lagrange[(*(*faceV[s])[f])[0]] +
- lagrange[(*(*faceV[s])[f])[1]] +
- lagrange[(*(*faceV[s])[f])[2]];
-
- basis[s][i] =
+ Polynomial sum =
+ lagrange[(*(*faceV[s])[f])[0]] +
+ lagrange[(*(*faceV[s])[f])[1]] +
+ lagrange[(*(*faceV[s])[f])[2]];
+
+ basis[s][i] =
new Polynomial(intLegendre[l1].compose
- (lagrange[(*(*faceV[s])[f])[0]] -
+ (lagrange[(*(*faceV[s])[f])[0]] -
lagrange[(*(*faceV[s])[f])[1]]
- ,
- lagrange[(*(*faceV[s])[f])[0]] +
- lagrange[(*(*faceV[s])[f])[1]])
-
- *
-
- lagrange[(*(*faceV[s])[f])[2]]
- *
+ ,
+ lagrange[(*(*faceV[s])[f])[0]] +
+ lagrange[(*(*faceV[s])[f])[1]])
+
+ *
+
+ lagrange[(*(*faceV[s])[f])[2]]
+ *
sclLegendre[l2].compose
(lagrange[(*(*faceV[s])[f])[2]] * 2 - sum, sum));
i++;
@@ -120,7 +120,7 @@ TetNodeBasis::TetNodeBasis(unsigned int order){
}
}
}
-
+
// Cell Based //
const Polynomial oneMinusFour = Polynomial(1, 0, 0, 0) - lagrange[3];
const Polynomial twoThreeOneMinusFour = lagrange[2] * 2 - oneMinusFour;
@@ -131,14 +131,14 @@ TetNodeBasis::TetNodeBasis(unsigned int order){
for(unsigned int s = 0; s < nRefSpace; s++){
unsigned int i = nVertex + nEdge + nFace;
-
+
for(int l1 = 1; l1 < orderMinusTwo; l1++){
for(int l2 = 0; l2 + l1 - 1 < orderMinusThree; l2++){
for(int l3 = 0; l3 + l2 + l1 - 1 < orderMinusThree; l3++){
- basis[s][i] =
- new Polynomial(intLegendre[l1].compose(sub, add) *
- lagrange[2] *
- sclLegendre[l2].compose(twoThreeOneMinusFour,
+ basis[s][i] =
+ new Polynomial(intLegendre[l1].compose(sub, add) *
+ lagrange[2] *
+ sclLegendre[l2].compose(twoThreeOneMinusFour,
oneMinusFour) *
lagrange[3] *
legendre[l3].compose(twoFourMinusOne));
diff --git a/FunctionSpace/TetReferenceSpace.cpp b/FunctionSpace/TetReferenceSpace.cpp
index dc8d039c3a1a87b8f9e59f1dc9e2d27260348a5d..247172bb05bf39fdf8b7d2f61e7aec9cc9f128d7 100644
--- a/FunctionSpace/TetReferenceSpace.cpp
+++ b/FunctionSpace/TetReferenceSpace.cpp
@@ -15,17 +15,17 @@ TetReferenceSpace::TetReferenceSpace(void){
for(unsigned int i = 0; i < nEdge; i++){
refEdge[i] = new unsigned int[2];
refEdge[i][0] = MTetrahedron::edges_tetra(i, 0);
- refEdge[i][1] = MTetrahedron::edges_tetra(i, 1);
+ refEdge[i][1] = MTetrahedron::edges_tetra(i, 1);
}
-
+
// Face Definition //
nFace = 4;
refFace = new unsigned int*[nFace];
for(unsigned int i = 0; i < nFace; i++){
refFace[i] = new unsigned int[3];
- refFace[i][0] = MTetrahedron::faces_tetra(i, 0);
- refFace[i][1] = MTetrahedron::faces_tetra(i, 1);
+ refFace[i][0] = MTetrahedron::faces_tetra(i, 0);
+ refFace[i][1] = MTetrahedron::faces_tetra(i, 1);
refFace[i][2] = MTetrahedron::faces_tetra(i, 2);
}
@@ -37,13 +37,13 @@ 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;
}
@@ -51,7 +51,7 @@ string TetReferenceSpace::toLatex(void) const{
stringstream stream;
stream << "\\documentclass{article}" << endl << endl
-
+
<< "\\usepackage{longtable}" << endl
<< "\\usepackage{tikz}" << endl
<< "\\usetikzlibrary{arrows}" << endl << endl
@@ -67,26 +67,26 @@ string TetReferenceSpace::toLatex(void) const{
<< "\\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] (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]"
+ 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();
}
@@ -96,7 +96,7 @@ int main(void){
TetReferenceSpace p;
cout << p.toLatex() << endl;
-
+
return 0;
}
*/
diff --git a/FunctionSpace/TetReferenceSpace.h b/FunctionSpace/TetReferenceSpace.h
index 4895fa849091d7c619d7f33cca208c9533894dd0..cec36e26ad534d90a6eec4859492b293ad891da3 100644
--- a/FunctionSpace/TetReferenceSpace.h
+++ b/FunctionSpace/TetReferenceSpace.h
@@ -16,7 +16,7 @@ class TetReferenceSpace: public ReferenceSpace{
TetReferenceSpace(void);
virtual ~TetReferenceSpace(void);
- virtual std::string toLatex(void) const;
+ virtual std::string toLatex(void) const;
};
/**
diff --git a/FunctionSpace/TriLagrangeBasis.h b/FunctionSpace/TriLagrangeBasis.h
index a008a69fb29911515050d6bb1fbea7671cafd163..272a21f32d84e27dea05dbe852389e507260aa40 100644
--- a/FunctionSpace/TriLagrangeBasis.h
+++ b/FunctionSpace/TriLagrangeBasis.h
@@ -6,11 +6,11 @@
/**
@class TriLagrangeBasis
@brief Lagrange Basis for Triangles
-
- This class can instantiate a @em Lagrange @em Basis
+
+ This class can instantiate a @em Lagrange @em Basis
for a Triangle and for a given Order.@n
-
- It uses
+
+ It uses
<a href="http://geuz.org/gmsh/">gmsh</a> Basis.
*/
@@ -18,21 +18,21 @@ class TriLagrangeBasis: public BasisLagrange{
public:
//! @param order A natural number
//!
- //! Returns a new TriLagrangeBasis
+ //! Returns a new TriLagrangeBasis
//! of the given Order
TriLagrangeBasis(unsigned int order);
-
+
//! Deletes this Basis
//!
virtual ~TriLagrangeBasis(void);
- private:
+ private:
//! @param order A natural number
- //! @return Returns the @em tag of a @em Triangle of
- //! the given order
+ //! @return Returns the @em tag of a @em Triangle of
+ //! the given order
static unsigned int getTag(unsigned int order);
- //! @param order A natural number
+ //! @param order A natural number
//! @return Returns Lagrangian Points on a Triangle
//! for the given Order
static fullMatrix<double> triPoint(unsigned int order);
diff --git a/FunctionSpace/TriReferenceSpace.cpp b/FunctionSpace/TriReferenceSpace.cpp
index f3b40cd9b598ae136da7d4653f189d75e2f7ab26..e4a1d15850f16d43224d50b872964812253f13b5 100644
--- a/FunctionSpace/TriReferenceSpace.cpp
+++ b/FunctionSpace/TriReferenceSpace.cpp
@@ -15,13 +15,13 @@ TriReferenceSpace::TriReferenceSpace(void){
for(unsigned int i = 0; i < nEdge; i++){
refEdge[i] = new unsigned int[2];
refEdge[i][0] = MTriangle::edges_tri(i, 0);
- refEdge[i][1] = MTriangle::edges_tri(i, 1);
+ refEdge[i][1] = MTriangle::edges_tri(i, 1);
}
// Face Definition //
nFace = 0;
refFace = NULL;
-
+
// Init All //
init();
}
@@ -30,7 +30,7 @@ TriReferenceSpace::~TriReferenceSpace(void){
// Delete Ref Edge //
for(unsigned int i = 0; i < nEdge; i++)
delete[] refEdge[i];
-
+
delete[] refEdge;
}
@@ -38,7 +38,7 @@ string TriReferenceSpace::toLatex(void) const{
stringstream stream;
stream << "\\documentclass{article}" << endl << endl
-
+
<< "\\usepackage{longtable}" << endl
<< "\\usepackage{tikz}" << endl
<< "\\usetikzlibrary{arrows}" << endl << endl
@@ -57,22 +57,22 @@ string TriReferenceSpace::toLatex(void) const{
<< "\\node[vertex] (n2) at(0, 3) {$2$};" << endl << endl;
for(unsigned int i = 0; i < 3; i++)
- stream << "\\path[line]"
+ 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();
}
@@ -82,7 +82,7 @@ int main(void){
TriReferenceSpace p;
cout << p.toLatex() << endl;
-
+
return 0;
}
*/
diff --git a/FunctionSpace/TriReferenceSpace.h b/FunctionSpace/TriReferenceSpace.h
index 0ac863a4162c7704c8d10033f13e54b2cdaf2bae..9f52b5d64eb9fe56dd5fff7e840c95d15bc77b25 100644
--- a/FunctionSpace/TriReferenceSpace.h
+++ b/FunctionSpace/TriReferenceSpace.h
@@ -16,7 +16,7 @@ class TriReferenceSpace: public ReferenceSpace{
TriReferenceSpace(void);
virtual ~TriReferenceSpace(void);
- virtual std::string toLatex(void) const;
+ virtual std::string toLatex(void) const;
};
/**