// Generate a random real from normal distribution N(0,1).
RealT genGaussianRandom(){
// Use Box-Muller transform to generate a point from normal
// distribution.
RealT x1, x2;
do{
x1 = genUniformRandom(0.0, 1.0);
} while (x1 == 0); // cannot take log of 0.
x2 = genUniformRandom(0.0, 1.0);
RealT z;
z = SQRT(-2.0 * LOG(x1)) * COS(2.0 * M_PI * x2);
return z;
}
// Creates the LSH hash functions for the R-near neighbor structure
// <nnStruct>. The functions fills in the corresponding field of
// <nnStruct>.
void initHashFunctions(PRNearNeighborStructT nnStruct){
ASSERT(nnStruct != NULL);
LSHFunctionT **lshFunctions;
// allocate memory for the functions
FAILIF(NULL == (lshFunctions = (LSHFunctionT**)MALLOC(nnStruct->nHFTuples * sizeof(LSHFunctionT*))));
for(IntT i = 0; i < nnStruct->nHFTuples; i++){
FAILIF(NULL == (lshFunctions[i] = (LSHFunctionT*)MALLOC(nnStruct->hfTuplesLength * sizeof(LSHFunctionT))));
for(IntT j = 0; j < nnStruct->hfTuplesLength; j++){
FAILIF(NULL == (lshFunctions[i][j].a = (RealT*)MALLOC(nnStruct->dimension * sizeof(RealT))));
}
}
// initialize the LSH functions
for(IntT i = 0; i < nnStruct->nHFTuples; i++){
for(IntT j = 0; j < nnStruct->hfTuplesLength; j++){
// vector a
for(IntT d = 0; d < nnStruct->dimension; d++){
#ifdef USE_L1_DISTANCE
lshFunctions[i][j].a[d] = genCauchyRandom();
#else
lshFunctions[i][j].a[d] = genGaussianRandom();
#endif
}
// b
lshFunctions[i][j].b = genUniformRandom(0, nnStruct->parameterW);
}
}
nnStruct->lshFunctions = lshFunctions;
}
int main(int nargs, char **args){
if (nargs < 5){
usage(args[0]);
exit(1);
}
IntT dimension = atoi(args[1]);
RealT M = atof(args[2]);
IntT nPoints = atoi(args[3]);
RealT R = atof(args[4]);
//IntT nExpNNs = atoi(args[4]);
RealT probability = atof(args[5]);
// for d even, Vol_d = pi^{d/2} / (d/2)!
// RealT vol_d_const = 1.0 / SQRT(M_PI * (RealT)dimension);
// RealT R = 2.0 * M * POW((RealT)nExpNNs / (RealT)nPoints / vol_d_const, 1.0/(RealT)dimension) / SQRT(M_PI) * SQRT((RealT)dimension / 2.0 / M_E);
// RealT vol_d_const = 1;
// for(IntT i = 1; i <= dimension / 2; i++)
// vol_d_const = vol_d_const * M_PI / (RealT)i;
// RealT R = 2.0 * M * POW((RealT)nExpNNs / (RealT)nPoints / vol_d_const, 1.0/(RealT)dimension);
//printf("%Lf %Lf \n", POW(R/2.0/M, dimension), (RealT)nExpNNs / (RealT)nPoints / vol_d_const);
printf("%d %d ", nPoints, dimension);
FPRINTF_REAL(stdout, R);
printf(" ");
FPRINTF_REAL(stdout, probability);
printf("\n");
for(IntT d = 0; d < dimension; d++){
FPRINTF_REAL(stdout, 0.99 * R / SQRT(dimension));
printf(" ");
}
printf("\n");
for(IntT i = 0; i < nPoints - 1; i++){
for(IntT d = 0; d < dimension; d++){
FPRINTF_REAL(stdout, genUniformRandom(-M, M));
printf(" ");
}
printf("\n");
}
}
// Creates the LSH hash functions for the R-near neighbor structure
// <nnStruct>. The functions fills in the corresponding field of
// <nnStruct>.
void initHashFunctions(PRNearNeighborStructT nnStruct)
{ /*按照 nHFTuples个 组，hfTuplesLength个最终的维度
产生高斯分布的随机值： a向量和 b，付给 nnStruct->lshFunctions【】【】
用于第一步的点积降维
*/
//按照gi hi 两层函数族的格式，初始化nnStruct->lshFunctions所指向的二维指针
//nHFTuples组hash函数g，每个组有hfTuplesLength个hi，每个hi就是一个向量a和一个b
//按照a。v+b 的格式，初始化结构体中的随机向量和空间
//nnStruct结构体中，初始化nnStruct->lshFunctions 所指向的二维随机矩阵
ASSERT(nnStruct != NULL);//编程技巧： asssert来判断条件执行： __line__ --file__显示位置
LSHFunctionT **lshFunctions;//LSHFunctionT结构体就两个元素：一个指针+一个double
// allocate memory for the functions
FAILIF(NULL == (lshFunctions = (LSHFunctionT**)MALLOC(nnStruct->nHFTuples * sizeof(LSHFunctionT*))));
for(IntT i = 0; i < nnStruct->nHFTuples; i++)
{
FAILIF(NULL == (lshFunctions[i] = (LSHFunctionT*)MALLOC(nnStruct->hfTuplesLength * sizeof(LSHFunctionT))));
for(IntT j = 0; j < nnStruct->hfTuplesLength; j++)
{
FAILIF(NULL == (lshFunctions[i][j].a = (RealT*)MALLOC(nnStruct->dimension * sizeof(RealT))));
}
}
// initialize the LSH functions
//这里开始构造算法中的一组“位置敏感”的Hash函数。
for(IntT i = 0; i < nnStruct->nHFTuples; i++)
{
for(IntT j = 0; j < nnStruct->hfTuplesLength; j++)
{
// vector a
for(IntT d = 0; d < nnStruct->dimension; d++)
{
#ifdef USE_L1_DISTANCE
lshFunctions[i][j].a[d] = genCauchyRandom();//L1距离有柯西分布
#else
lshFunctions[i][j].a[d] = genGaussianRandom(); //L2使用高斯分布 公式中a就是一组d维的正态分布随机数
#endif
}
// b
lshFunctions[i][j].b = genUniformRandom(0, nnStruct->parameterW);
}
}
nnStruct->lshFunctions = lshFunctions;
}
