void approximatedNormals(const pointSet& mesh, vector<int> neighb, int pnb, double& nx_out, double& ny_out)
{
if (mesh.getBND(pnb)==0)
throw mfpmExcept(0);
int NP = neighb.size();
double sl2 = mesh.getSL(pnb);
// New approach
double sumX = 0, sumY = 0;
double nx, ny;
int count = 0;
for (int i=0; i<NP; i++)
{
if (pnb!=neighb[i] )
{
nx = (mesh.y(pnb)-mesh.y(neighb[i]));
ny = -(mesh.x(pnb)-mesh.x(neighb[i]));
double weight = exp(-5.0* (nx*nx+ny*ny) / sl2);
double length = sqrt(nx*nx+ny*ny);
nx /= length;
ny /= length;
if ( nx*mesh.getNormal(0,pnb) + ny*mesh.getNormal(1,pnb) < 0)
{
nx *= -1.0;
ny *= -1.0;
}
sumX += nx*weight;
sumY += ny*weight;
}
}
sumX /= NP-1;
sumY /= NP-1;
double length = sqrt(sumX*sumX+sumY*sumY);
if (length==0)
throw mfpmExcept(1000);
nx_out = sumX / length;
ny_out = sumY / length;
}
int partialNeumannMatEntry(const pointSet& mesh, int pnb, const Array& active, Array& entries, bool forceLowOrder)
{
int NP = mesh.getNIDX(pnb);
double b[NP];
double A[6*NP];
double weight[NP];
int arrayEntry[NP];
if (NP < 4)
throw mfpmExcept(20);
double sl2 = pow(mesh.getSL(pnb),2);
b[0] = 0*3.0 / mesh.getSL(pnb);
b[1] = 0.0;
b[2] = mesh.getNormal(0,pnb);
b[3] = mesh.getNormal(1,pnb);
b[4] = 0.0;
b[5] = 0.0;
b[6] = 0.0;
int orderFac = 6;
if (NP<6 | forceLowOrder)
orderFac = 4;
int idx, mi;
int diagEntry=0;
double h, k;
int cnt = 0;
// Store matrix in Fortran format
for (int i=0; i<NP; i++)
{
idx = mesh.getIDX(pnb,i);
mi = orderFac*cnt;
if (idx!=pnb)
{
if (active(i) > 0.5)
{
h = mesh.x(idx) - mesh.x(pnb);
k = mesh.y(idx) - mesh.y(pnb);
weight[cnt] = exp(-2.0 * (h*h+k*k)/sl2 );
A[mi+0] = 0.0;
A[mi+1] = 1.0 * weight[cnt];
A[mi+2] = h * weight[cnt];
A[mi+3] = k * weight[cnt];
if (orderFac>4)
{
A[mi+4] = h*h * weight[cnt];
A[mi+5] = h*k * weight[cnt];
A[mi+6] = k*k * weight[cnt];
}
arrayEntry[cnt] = i;
cnt++;
}
}
else
{
weight[cnt] = 1.0;
A[mi+0] = 1.0;
A[mi+1] = 1.0;
A[mi+2] = 0.0;
A[mi+3] = 0.0;
if (orderFac>4)
{
A[mi+4] = 0.0;
A[mi+5] = 0.0;
}
arrayEntry[cnt] = i;
cnt++;
}
}
int n = orderFac;
int m = cnt;
double work[2*(m+n)];
int info, workl = 2*(m+n);
int one = 1;
char TN[] ="N";
dgels_(TN, &n, &m, &one, A, &n, b, &m, work, &workl, &info);
if (info!=0)
{
cout << "Error solving least squares: laplaceMatEntry!" << endl;
throw mfpmExcept(27);
}
entries = 0.0;
for (int i=0; i<cnt; i++)
{
entries(arrayEntry[i]) = b[i]*weight[i];
}
//~ // Test operator:
//~ double tmp = entries(diagEntry);
//~ for (int i=0; i<NP; i++)
//~ {
//~ if (abs(entries(i))>tmp)
//~ {
//~ //cout << "Invalid Neumann matrix entries!!" << endl;
//~ //return -1;
//~ }
//~ }
//~ double sum = 0;
//~ for (int i=0; i<NP; i++)
//~ {
//~ idx = mesh.getIDX(pnb,i);
//~ sum += entries(i)*(mesh.x(idx)+mesh.y(idx));
//~ }
//~ if ( (sum - mesh.getNormal(0,pnb) - mesh.getNormal(1,pnb)) > 1e-7 )
//~ {
//~ //cout << "Invalid Neumann matrix entries!!" << endl;
//~ return -2;
//~ }
return 0;
}
int neumannMatEntry(const pointSet& mesh, int pnb, Array& entries, bool forceLowOrder)
{
int NP = mesh.getNIDX(pnb);
double b[NP];
double A[6*NP];
double weight[NP];
if (NP < 4)
throw mfpmExcept(20);
double sl2 = pow(mesh.getSL(pnb),2);
b[0] = 3.0 / mesh.getSL(pnb);
b[1] = 0.0;
b[2] = mesh.getNormal(0,pnb);
b[3] = mesh.getNormal(1,pnb);
b[4] = 0.0;
b[5] = 0.0;
int orderFac = 6;
if (NP<6 | forceLowOrder)
orderFac = 4;
int idx, mi;
int diagEntry=0;
double h, k;
// Store matrix in Fortran format
for (int i=0; i<NP; i++)
{
idx = mesh.getIDX(pnb,i);
mi = orderFac*i;
if (idx!=pnb)
{
h = mesh.x(idx) - mesh.x(pnb);
k = mesh.y(idx) - mesh.y(pnb);
weight[i] = exp(-2.0 * (h*h+k*k)/sl2 );
A[mi+0] = 0.0;
A[mi+1] = 1.0 * weight[i];
A[mi+2] = h * weight[i];
A[mi+3] = k * weight[i];
if (orderFac>4)
{
A[mi+4] = h*h * weight[i];
A[mi+5] = k*k * weight[i];
}
}
else
{
diagEntry = i;
weight[i] = 1.0;
A[mi+0] = 1.0;
A[mi+1] = 1.0;
A[mi+2] = 0.0;
A[mi+3] = 0.0;
if (orderFac>4)
{
A[mi+4] = 0.0;
A[mi+5] = 0.0;
}
}
}
int n = orderFac;
int m = NP;
double work[m+n];
int info, workl = m+n;
int one = 1;
char TN[] ="N";
dgels_(TN, &n, &m, &one, A, &n, b, &m, work, &workl, &info);
if (info!=0)
{
cout << "Error solving least squares: laplaceMatEntry!" << endl;
throw mfpmExcept(27);
}
for (int i=0; i<NP; i++)
{
entries(i) = b[i]*weight[i];
}
// Test operator:
double tmp = entries(diagEntry);
for (int i=0; i<NP; i++)
{
if (abs(entries(i))>tmp)
{
//cout << "Invalid Neumann matrix entries!!" << endl;
//return -1;
}
}
double sum = 0;
for (int i=0; i<NP; i++)
{
idx = mesh.getIDX(pnb,i);
sum += entries(i)*(mesh.x(idx)+mesh.y(idx));
}
if ( (sum - mesh.getNormal(0,pnb) - mesh.getNormal(1,pnb)) > 1e-7 )
{
//cout << "Invalid Neumann matrix entries!!" << endl;
return -2;
}
return 0;
}