double dlmvnorm_singular(double *x, int p, double *mu, double *LTsigma)
{
/* Calculates the p-variate Gaussian log-density at the p-variate point x
with mean mu and the lower triangle (px(p+1)/2) LTsigma of the
pxp-dimensional dispersion matrix Sigma.
Note that this function actually incorporates the case for singular
determinants
*/
double *eivec,*eival,value=0;
int i,ind=0;
MAKE_VECTOR(eivec,p*p);
MAKE_VECTOR(eival,p);
i=eigens(LTsigma,eivec,eival,p);
if (eival[0]==0) { /* only possible if LTsigma is all zero, which means
that the distribution is degenerate at mu */
for(i=0;((i<p) && (!ind));i++) if (x[i]!=mu[i]) ind =1;
if (ind) value=-Inf;
else value=0;
}
else {
int j,dmin;
double *y,*z,sum=0,sump=0;
for(i=0;i<p;i++) sum+=eival[i];
for(i=0;((i<p) && (sump<0.99));i++) {
sump+=eival[i]/sum;
value-=0.5*log(eival[i]);
}
dmin=i;
MAKE_VECTOR(y,p);
for(i=0;i<p;i++) y[i]=x[i]-mu[i];
MAKE_VECTOR(z,dmin);
for(i=0;i<dmin;i++) z[i]=0;
for(i=0;i<dmin;i++) {
for(j=0;j<p;j++) z[i]+=eivec[j*p+i]*y[j];
}
FREE_VECTOR(y);
for(i=0;i<dmin;i++) value-=0.5*z[i]*z[i]/eival[i];
FREE_VECTOR(z);
value-=0.5*dmin*log(2*PI);
}
FREE_VECTOR(eival);
FREE_VECTOR(eivec);
return value;
}
/**
* \ingroup eigen
* Eigenvectors
* \param m \f$m\f$
* \return a variable matrix with the
* eigenvectors of \f$m\f$ stored in its columns.
*/
dmatrix eigenvectors(const dmatrix &m)
{
if (m.rowsize() != m.colsize())
{
cerr <<
"error -- non square matrix passed to dmatrix eigenvectors(const dmatrix& m)\n";
ad_exit(1);
}
int rmin = m.rowmin();
int rmax = m.rowmax();
dmatrix evecs(rmin, rmax, rmin, rmax);
dvector evals(rmin, rmax);
eigens(m, evecs, evals);
return evecs;
}
int main() {
int testCount = 1;
int p = 1;
int low = -10;
int high = 10;
int fails = 0;
double eps = 1e-8;
for (int n = 2; n <= pow(2, p); n *= 2) {
for (int i = 0; i < testCount; i++) {
Mat_DP A(n, n);
Vec_CPLX_DP eigens(n);
ranmat2(A, low, high);
eigen(A, eigens);
if(testSum(&A, &eigens, eps)){
fails++;
cout << "FAIL! n = " << n << endl;
}
}
}
}
