void AssocEntropy::Calc(int ** nn, int ni, int nj)
{
int i, j;
double p;
Vector sumi(ni), sumj(nj);
sumi.Zero();
sumj.Zero();
sum = 0.0;
// Get the row totals
for (i = 0; i < ni; i++)
for ( j = 0; j < nj; j++)
{
sumi[i] += nn[i][j];
sum += nn[i][j];
}
// Get the column totals
for (j = 0; j < nj; j++)
for ( i = 0; i < ni; i++ )
sumj[j] += nn[i][j];
// Entropy of the x distribution
hx = 0.0;
for (i = 0; i < ni; i++)
if (sumi[i] > FPMIN)
{
p = sumi[i] / sum;
hx -= p * log(p);
}
// Entropy of the y distribution
hy = 0.0;
for (j = 0; j < nj; j++)
if (sumj[j] > FPMIN)
{
p = sumj[j] / sum;
hx -= p * log(p);
}
// Total entropy for the table
h = 0.0;
for (i = 0; i < ni; i++)
for (j = 0; j < nj; j++)
if (nn[i][j] > 0)
{
p = nn[i][j] / sum;
h -= p * log ( p );
}
hygx = h - hx;
hxgy = h - hy;
uygx = (hy - hygx) / ( hy + TINY );
uxgy = (hx - hxgy) / ( hx + TINY );
uxy = 2.0 * ( hx + hy - h ) / ( hx + hy + TINY );
isValid = 1;
}
void AssocChi::Calc(int ** nn, int ni, int nj)
{
int nnj, nni, j, i, minij;
double expected, temp;
Vector sumi(ni), sumj(nj);
sumi.Zero();
sumj.Zero();
sum = 0.0;
nni = ni;
nnj = nj;
// Get the row totals
for (i = 0; i < ni; i++)
{
for ( j = 0; j < nj; j++)
{
sumi[i] += nn[i][j];
sum += nn[i][j];
}
if ( sumi[i] < FPMIN) --nni; // eliminate zero rows by reducing number
}
// Get the column totals
for (j = 0; j < nj; j++)
{
for ( i = 0; i < ni; i++ )
sumj[j] += nn[i][j];
if ( sumj[j] < FPMIN) --nnj; // eliminated any zero columns
}
df = nni * nnj - nni - nnj + 1; // corrected degrees of freedom
chisq = 0.0;
for (i = 0; i < ni; i++)
{
for (j = 0; j < nj; j++)
{
expected = sumj[j] * sumi[i] / sum;
temp = nn[i][j] - expected;
chisq += temp * temp / (expected + TINY);
}
}
prob = df ? gammq ( 0.5 * df, 0.5 * chisq ) : 1.0;
lop = prob > 1e-100 ? -log10(prob) : 99.999;
minij = nni < nnj ? nni - 1 : nnj - 1;
cramrv = minij ? sqrt ( chisq / ( sum * minij ) ) : 0.0;
ccc = sum ? sqrt ( chisq / ( chisq + sum) ) : 0.0;
isValid = 1;
}
void Tri2dFCBlockSolver::gradSetupQuadratic()
{
// form quadratic sub elements
int nElemQ = 3*nElem;
int nneQ = 6; //quadratic elements
int nngQ = 4; //quadratic elements
Array2D<int> elemQ(nElemQ,nneQ),gNode(nElemQ,nngQ);
int m=0;
for (int n=0; n<nElem; n++){
elemQ(m ,0) = elem(n,0);
elemQ(m ,1) = elem(n,4);
elemQ(m ,2) = elem(n,7);
elemQ(m ,3) = elem(n,3);
elemQ(m ,4) = elem(n,9);
elemQ(m ,5) = elem(n,8);
gNode(m ,0) = 0;
gNode(m ,1) = 3;
gNode(m ,2) = 4;
gNode(m++,3) = 5;
elemQ(m ,0) = elem(n,3);
elemQ(m ,1) = elem(n,1);
elemQ(m ,2) = elem(n,6);
elemQ(m ,3) = elem(n,4);
elemQ(m ,4) = elem(n,5);
elemQ(m ,5) = elem(n,9);
gNode(m ,0) = 1;
gNode(m ,1) = 4;
gNode(m ,2) = 5;
gNode(m++,3) = 3;
elemQ(m ,0) = elem(n,8);
elemQ(m ,1) = elem(n,5);
elemQ(m ,2) = elem(n,2);
elemQ(m ,3) = elem(n,9);
elemQ(m ,4) = elem(n,6);
elemQ(m ,5) = elem(n,7);
gNode(m ,0) = 2;
gNode(m ,1) = 5;
gNode(m ,2) = 3;
gNode(m++,3) = 4;
}
/*
for (int n=0; n<nElemQ; n++){
cout << n << " ";
for (int j=0; j<nneQ; j++) cout << elemQ(n,j) << " ";
cout << endl;
}
exit(0);
*/
// Jacobian terms
Array2D <double> xr(nElemQ,nngQ),yr(nElemQ,nngQ),xs(nElemQ,nngQ),
ys(nElemQ,nngQ),jac(nElemQ,nngQ),rs(nneQ,3),lc(nneQ,nneQ);
xr.set(0.);
yr.set(0.);
xs.set(0.);
ys.set(0.);
jac.set(0.);
int orderE=2; //quadratic elements
solutionPoints(orderE,
spacing,
&rs(0,0));
bool test=true;
lagrangePoly(test,
orderE,
&rs(0,0),
&lc(0,0));
int j,km,lm;
double lrm,lsm,ri,si;
for (int n=0; n<nElemQ; n++){
// evaluate the Jacobian terms at the mesh points
for (int i=0; i<nngQ; i++){ //ith mesh point
ri = rs(gNode(n,i),0);
si = rs(gNode(n,i),1);
for (int m=0; m<nneQ; m++){ //mth Lagrange polynomial
j = 0;
lrm = 0.;
lsm = 0.;
for (int k=0; k<=orderE; k++)
for (int l=0; l<=orderE-k; l++){
km = max(0,k-1);
lm = max(0,l-1);
lrm +=((double)k)*pow(ri,km)*pow(si,l )*lc(m,j );
lsm +=((double)l)*pow(ri,k )*pow(si,lm)*lc(m,j++);
}
xr(n,i) += lrm*x(elemQ(n,m),0);
yr(n,i) += lrm*x(elemQ(n,m),1);
xs(n,i) += lsm*x(elemQ(n,m),0);
ys(n,i) += lsm*x(elemQ(n,m),1);
}
jac(n,i) = xr(n,i)*ys(n,i)-yr(n,i)*xs(n,i);
}}
// lr(i,j) = (dl_j/dr)_i (a row is all Lagrange polynomials (derivatives)
// evaluated at a single mesh point i, same with the other derivatives)
Array2D<double> lr(nneQ,nneQ),ls(nneQ,nneQ),lrr(nneQ,nneQ),
lss(nneQ,nneQ),lrs(nneQ,nneQ);
lr.set(0.);
ls.set(0.);
lrr.set(0.);
lss.set(0.);
lrs.set(0.);
int kmm,lmm;
for (int n=0; n<nneQ; n++) // nth Lagrange polynomial
for (int i=0; i<nneQ; i++){ // ith mesh point
j = 0;
ri = rs(i,0);
si = rs(i,1);
for (int k=0; k<=orderE; k++)
for (int l=0; l<=orderE-k; l++){
km = max(0,k-1);
lm = max(0,l-1);
kmm = max(0,k-2);
lmm = max(0,l-2);
lr (i,n) +=((double)k)*pow(ri,km)*pow(si,l )*lc(n,j);
ls (i,n) +=((double)l)*pow(ri,k )*pow(si,lm)*lc(n,j);
lrr(i,n) +=((double)(k*km))*pow(ri,kmm)*pow(si,l )*lc(n,j );
lss(i,n) +=((double)(l*lm))*pow(ri,k )*pow(si,lmm)*lc(n,j );
lrs(i,n) +=((double)(k*l ))*pow(ri,km )*pow(si,lm )*lc(n,j++);
}}
// compute averaged quadratic FEM gradient coefficients
Array1D<double> sumj(nNode);
sumj.set(0.);
for (int n=0; n<nElemQ; n++)
for (int i=0; i<nngQ; i++){
m = gNode(n,i);
sumj(elemQ(n,m)) += jac(n,i);
}
for (int n=0; n<nNode; n++) sumj(n) = 1./sumj(n);
int k1,k2;
double xri,yri,xsi,ysi;
Array2D<double> ax(nNode,2);
ax.set(0.);
gxQ.set(0.);
for (int n=0; n<nElemQ; n++)
for (int i=0; i<nngQ; i++){
m = gNode(n,i);
k1 = elemQ(n,m);
xri = xr(n,i);
yri = yr(n,i);
xsi = xs(n,i);
ysi = ys(n,i);
for (int j=0; j<nneQ; j++){
k2 = elemQ(n,j);
ax(k2,0) = lr(m,j)*ysi-ls(m,j)*yri;
ax(k2,1) =-lr(m,j)*xsi+ls(m,j)*xri;
}
for(int j=psp2(k1); j<psp2(k1+1); j++){
k2 = psp1(j);
gxQ(j,0) += ax(k2,0);
gxQ(j,1) += ax(k2,1);
}
for (int j=0; j<nneQ; j++){
k2 = elemQ(n,j);
ax(k2,0) = 0.;
ax(k2,1) = 0.;
}}
for (int n=0; n<nNode; n++)
for (int i=psp2(n); i<psp2(n+1); i++){
gxQ(i,0) *= sumj(n);
gxQ(i,1) *= sumj(n);
}
// deallocate work arrays
elemQ.deallocate();
gNode.deallocate();
xr.deallocate();
yr.deallocate();
xs.deallocate();
ys.deallocate();
jac.deallocate();
rs.deallocate();
lc.deallocate();
lr.deallocate();
ls.deallocate();
lrr.deallocate();
lss.deallocate();
lrs.deallocate();
sumj.deallocate();
ax.deallocate();
}
