RealT estimateNDistinctCollisionsFromDSPoint(IntT nPoints, IntT dim, PPointT *dataSet, IntT queryIndex, BooleanT useUfunctions, IntT k, IntT LorM, RealT R){
RealT sumCollisions = 0;
for(IntT i = 0; i < nPoints; i++){
if (queryIndex != i) {
RealT dist = distance(dim, dataSet[queryIndex], dataSet[i]);
if (!useUfunctions){
// Pi:
if ( R < Pi_EPSILON )
sumCollisions += 1-POW(1-POW(computeFunctionP(PARAMETER_W_DEFAULT, dist), k), LorM);
else
sumCollisions += 1-POW(1-POW(computeFunctionP(PARAMETER_W_DEFAULT, dist / R), k), LorM);
}else{
RealT mu;
RealT x;
// Pi:
if ( R < Pi_EPSILON )
mu = 1 - POW(computeFunctionP(PARAMETER_W_DEFAULT, dist), k / 2);
else
mu = 1 - POW(computeFunctionP(PARAMETER_W_DEFAULT, dist / R), k / 2);
x = POW(mu, LorM - 1);
sumCollisions += 1 - mu * x - LorM * (1 - mu) * x;
}
}
}
return sumCollisions;
}
RealT estimateNCollisionsFromDSPoint(IntT nPoints, IntT dim, PPointT *dataSet, IntT queryIndex, IntT k, IntT L, RealT R){
RealT sumCollisions = 0;
for(IntT i = 0; i < nPoints; i++){
if (queryIndex != i) {
RealT dist = distance(dim, dataSet[queryIndex], dataSet[i]);
// Pi:
if ( R < Pi_EPSILON )
sumCollisions += POW(computeFunctionP(PARAMETER_W_DEFAULT, dist), k);
else
sumCollisions += POW(computeFunctionP(PARAMETER_W_DEFAULT, dist / R), k);
}
}
return L * sumCollisions;
}
//estimateNDistinctCollisions(nPoints, dimension, dataSet, sampleQueries[i], TRUE, k, m, R);
RealT estimateNDistinctCollisions(IntT nPoints, IntT dim, PPointT *dataSet, PPointT query, BooleanT useUfunctions, IntT k, IntT LorM, RealT R){
RealT sumCollisions = 0;
for(IntT i = 0; i < nPoints; i++){
if (query != dataSet[i]) {
RealT dist = distance(dim, query, dataSet[i]);
if (!useUfunctions){
sumCollisions += 1-POW(1-POW(computeFunctionP(PARAMETER_W_DEFAULT, dist / R), k), LorM); //1-（1-p1^k）^L，两点冲突的概率
}else{
RealT mu = 1 - POW(computeFunctionP(PARAMETER_W_DEFAULT, dist / R), k / 2);
RealT x = POW(mu, LorM - 1);
sumCollisions += 1 - mu * x - LorM * (1 - mu) * x; //查询点与数据集点冲突的概率总和，为能查询到的近邻点的数目
}
}
}
return sumCollisions;
}
RealT estimateNCollisions(IntT nPoints, IntT dim, PPointT *dataSet, PPointT query, IntT k, IntT L, RealT R){
RealT sumCollisions = 0;
for(IntT i = 0; i < nPoints; i++){
if (query != dataSet[i]) {
RealT dist = distance(dim, query, dataSet[i]); //计算在桶中查询点与数据集中点的距离
sumCollisions += POW(computeFunctionP(PARAMETER_W_DEFAULT, dist / R), k); // dist很有可能就是表示r2，dist越大算出来的概率越小。
}
}
return L * sumCollisions; //求冲突的期望值 //sumCollosions是在所有桶中的冲突点的数目
}
RealT estimateNCollisions(IntT nPoints, IntT dim, PPointT *dataSet, PPointT query, IntT k, IntT L, RealT R){
RealT sumCollisions = 0;
for(IntT i = 0; i < nPoints; i++){
if (query != dataSet[i]) {
RealT dist = distance(dim, query, dataSet[i]);
sumCollisions += POW(computeFunctionP(PARAMETER_W_DEFAULT, dist / R), k);
}
}
return L * sumCollisions;
}
// Computes the parameter <m> of the algorithm, given the parameter
// <k> and the desired success probability <successProbability>. Only
// meaningful when functions <g> are interdependent (pairs of
// functions <u>, where the <m> functions <u> are each k/2-tuples of
// independent LSH functions). //g函数是相关时，有用！ 为了减少计算时间
IntT computeMForULSH(IntT k, RealT successProbability){
ASSERT((k & 1) == 0); // k should be even in order to use ULSH.
RealT mu = 1 - POW(computeFunctionP(PARAMETER_W_DEFAULT, 1), k / 2); //1-p1^(k/2) ，为1 说明c=1
RealT P = successProbability;
RealT d = (1-mu)/(1-P)*1/LOG(1/mu) * POW(mu, -1/(1-mu)); //(p1^k/2)/delta*log(1/(p1^k/2))*((1-p1^k/2)^(-1/(p1^(k/2))))
RealT y = LOG(d);
IntT m = CEIL(1 - y/LOG(mu) - 1/(1-mu));
while (POW(mu, m-1) * (1 + m * (1-mu)) > 1 - P){ //13
m++;
}
return m;
}
// Computes the parameter <L> of the algorithm, given the parameter
// <k> and the desired success probability
// <successProbability>. Functions <g> are considered all independent
// (original scheme).
IntT computeLfromKP(IntT k, RealT successProbability){
return CEIL(LOG(1 - successProbability) / LOG(1 - POW(computeFunctionP(PARAMETER_W_DEFAULT, 1), k))); //向上取整,LOG=ln ，公式6，返回L的值
}