/* Returns [ slope, constant, minLS ]
* where minLS = sum_i w_i res_i^2
*/
real_t * wLinearRegression( const real_t * w, const real_t * x, const real_t * y, const bool * allowed, const uint_fast32_t n, real_t *res){
if(NULL==w){ return NULL;}
if(NULL==x){ return NULL;}
if(NULL==y){ return NULL;}
if(n==0){return NULL;} // Matter of definition
if(NULL==res){ res = calloc(3,sizeof(real_t));}
if(NULL==res){ return NULL;}
real_t wmx = wmean(w,x,allowed,n);
real_t wmy = wmean(w,y,allowed,n);
real_t wmxx = wmeanxx(w,x,allowed,n); // Could be made more generic, to wmean(w,f(x),n);
real_t wmxy = wmeanxy(w,x,y,allowed,n);
real_t wmyy = wmeanxx(w,y,allowed,n);
real_t ws = sum(w,allowed,n);
res[0] = (wmxy-wmx*wmy)/(wmxx-wmx*wmx); // Solve LS problem for slope
res[1] = wmy - res[0]*wmx; // Error remaining
res[2] = ws*(wmyy - res[0] * wmxy - res[1] * wmy);
return res;
}
double wvar(double* x, double* w, long n){
long i;
double res=0.;
double nef=0.;
double mm = wmean(x, w, n);
for(i=0; i<n; i++){
if(isnan(x[i])==0){
res += w[i]*pow(x[i]-mm, 2.0);
nef += w[i];
}
}
return res/nef;
}
/* Weighted variance by compensated summation
*/
real_t wvariance( const real_t * w, const real_t * x, const bool * allowed, const uint_fast32_t n){
if(NULL==w || NULL==x){return NAN;}
const real_t m = wmean(x,w,allowed,n);
real_t v = 0.;
real_t c = 0.;
real_t wsum = 0.0;
uint_fast32_t nallowed = 0;
for ( uint_fast32_t i=0; i<n ; i++){
if(NULL!=allowed && !allowed[i]){ continue; }
volatile real_t y = w[i]*(x[i] - m)*(x[i]-m) - c;
volatile real_t t = v + y;
c = (t-v) - y;
v = t;
// Sum of weights not compensated
wsum += w[i];
nallowed++;
}
return v/(nallowed-1.) * nallowed/wsum;
}
