/**
* Compute relative weights based on sample size in m_O;
**/
void logistic_normal::compute_relative_weights()
{
m_dWy.allocate(m_y1,m_y2);
dvector dNy = rowsum(m_O);
double dN = mean(dNy);
m_dWy = sqrt( dN / dNy );
}
void ContingencyTable_entropies (ContingencyTable me, double *h, double *hx, double *hy, double *hygx, double *hxgy, double *uygx, double *uxgy, double *uxy) {
*h = *hx = *hy = *hxgy = *hygx = *uygx = *uxgy = *uxy = 0;
autoNUMvector<double> rowsum (1, my numberOfRows);
autoNUMvector<double> colsum (1, my numberOfColumns);
// row and column totals
double sum = 0.0;
for (long i = 1; i <= my numberOfRows; i++) {
for (long j = 1; j <= my numberOfColumns; j++) {
rowsum[i] += my data[i][j];
colsum[j] += my data[i][j];
}
sum += rowsum[i];
}
// Entropy of x distribution
for (long j = 1; j <= my numberOfColumns; j++) {
if (colsum[j] > 0.0) {
double p = colsum[j] / sum;
*hx -= p * NUMlog2 (p);
}
}
// Entropy of y distribution
for (long i = 1; i <= my numberOfRows; i++) {
if (rowsum[i] > 0.0) {
double p = rowsum[i] / sum;
*hy -= p * NUMlog2 (p);
}
}
// Total entropy
for (long i = 1; i <= my numberOfRows; i++) {
for (long j = 1; j <= my numberOfColumns; j++) {
if (my data[i][j] > 0.0) {
double p = my data[i][j] / sum;
*h -= p * NUMlog2 (p);
}
}
}
// Conditional entropies
*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);
}
/**
\ingroup matop
Matrix exponential.
The matrix exponential is calculated using the Pade approximation adapted from Moler, Cleve; Van Loan, Charles F. (2003), "Nineteen Dubious Ways to Compute the Exponential of a Matrix, Twenty-Five Years Later"
The main use of the matrix exponential is to solve linear ordinary differential equation (ODE) systems:
\f[
\frac{d}{dt}y(t) = Ay(t)\ , \ \mbox{with } y(0) = y_0
\f]
\item then the solution becomes
\f[
y(t) = e^{At}y_0
\f]
\param A square df1b2matrix
\returns The matrix exponential of A
*/
df1b2matrix expm(const df1b2matrix & A)
{
RETURN_ARRAYS_INCREMENT();
int rmin = A.rowmin();
int rmax = A.rowmax();
if(rmax != A.colmax())
{cout<<"Error: Not square matrix in expm."<<endl; ad_exit(1);}
if(rmin != A.colmin())
{cout<<"Error: Not square matrix in expm."<<endl; ad_exit(1);}
df1b2matrix I(rmin,rmax,rmin,rmax);
df1b2matrix AA(rmin,rmax,rmin,rmax);
df1b2matrix X(rmin,rmax,rmin,rmax);
df1b2matrix E(rmin,rmax,rmin,rmax);
df1b2matrix D(rmin,rmax,rmin,rmax);
df1b2matrix cX(rmin,rmax,rmin,rmax);
I.initialize();
for(int i = rmin; i<=rmax; ++i){I(i,i) = 1.0;}
df1b2variable log2NormInf;
log2NormInf = log(max(rowsum(fabs(value(A)))));
log2NormInf/=log(2.0);
int e = (int)value(log2NormInf) + 1;
int s = e+1;
s = (s<0) ? 0 : s;
AA = 1.0/pow(2.0,s)*A;
X = AA;
df1b2variable c = 0.5;
E = I+c*AA;
D = I-c*AA;
int q = 6, p = 1;
for(int k = 2; k<=q; ++k){
c*=((double)q-k+1.0)/((double)k*(2*q-k+1));
X = AA*X;
cX = c*X;
E+=cX;
if(p==1){D+=cX;}else{D-=cX;}
p = (p==1) ? 0 : 1;
}
// E = inv(D)*E;
E = solve(D,E);
for(int k = 1; k<=s; ++k){
E = E*E;
}
RETURN_ARRAYS_DECREMENT();
return E;
}
void ContingencyTable_chisq (ContingencyTable me, double *chisq, long *df) {
long nr = my numberOfRows, nc = my numberOfColumns;
*chisq = 0; *df = 0;
autoNUMvector<double> rowsum (1, nr);
autoNUMvector<double> colsum (1, nc);
/*
row and column marginals
*/
double sum = 0;
for (long i = 1; i <= my numberOfRows; i++) {
for (long j = 1; j <= my numberOfColumns; j++) {
rowsum[i] += my data[i][j];
colsum[j] += my data[i][j];
}
sum += rowsum[i];
}
for (long i = 1; i <= my numberOfRows; i++) {
if (rowsum[i] == 0) {
--nr;
}
}
for (long j = 1; j <= my numberOfColumns; j++) {
if (colsum[j] == 0) {
--nc;
}
}
*df = (nr - 1) * (nc - 1);
for (long i = 1; i <= my numberOfRows; i++) {
if (rowsum[i] == 0) {
continue;
}
for (long j = 1; j <= my numberOfColumns; j++) {
if (colsum[j] == 0) {
continue;
}
double expt = rowsum[i] * colsum[j] / sum;
double tmp = my data[i][j] - expt;
*chisq += tmp * tmp / expt;
}
}
}
