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cuPC-S.cu
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#include <time.h>
#include <stdlib.h>
#include <math.h>
#include "gpuerrors.h"
#include "cuPC-S.h"
//========================> Main Function Parameter <========================
//Description : this function just calculate one Stage of PC stable algorithm
//@param C = Correlation matrix
//@param VarSize = Number of Nodes in Dataset
//@param Stage = Number of Neighbor in each dimension of Neighbor Matrix
//@param G = Is the Graph array
//@param TH = The Th for deleting each edge
//@param Nbr = Neighbor Matrix with format of:
//[i , j , |Neighbor idx 1|,|Neighbor idx 2| , ...]
//@param Nrow = Number Of row in Nbr matrix
//@param Ncol = Number of Col in Nbr matrix
//============================================================================
void Skeleton(double* C, int *P, int *G, double *Th, int *l, int *maxlevel, double *pMax, int* SepSet)
{
double *C_cuda; //Copy of C array in GPU
double *pMax_cuda;
int *G_cuda; //Copy of G Array in GPU
int *nprime_cuda;
int *SepSet_cuda;
int *GPrime_cuda;
int *mutex_cuda;
int n = *P;
int nprime = 0;
dim3 BLOCKS_PER_GRID;
dim3 THREADS_PER_BLOCK;
bool FinishFlag = false;
*l = 0;
HANDLE_ERROR( cudaMalloc((void**)&mutex_cuda, n * n * sizeof(int)) );
HANDLE_ERROR( cudaMalloc((void**)&nprime_cuda, 1 * sizeof(int)) );
HANDLE_ERROR( cudaMalloc((void**)&SepSet_cuda, n * n * ML * sizeof(int)) );
HANDLE_ERROR( cudaMalloc((void**)&GPrime_cuda, n * n * sizeof(int)) );
HANDLE_ERROR( cudaMalloc((void**)&C_cuda, n * n * sizeof(double)) );
HANDLE_ERROR( cudaMalloc((void**)&G_cuda, n * n * sizeof(int)) );
HANDLE_ERROR( cudaMalloc((void**)&pMax_cuda, n * n * sizeof(double)) );
//copy correlation matrix from CPU to GPU
HANDLE_ERROR( cudaMemcpy(C_cuda, C, n * n * sizeof(double), cudaMemcpyHostToDevice) );
//initialize a 0 matrix
HANDLE_ERROR( cudaMemset(mutex_cuda, 0, n * n * sizeof(int)) );
CudaCheckError();
//----------------------------------------------------------
for (*l = 0; *l <= ML && !FinishFlag && *l <= *maxlevel; *l = *l + 1){
if (*l == 0){
if ( (n * n) < 1024) {
BLOCKS_PER_GRID = dim3( 1, 1 ,1);
THREADS_PER_BLOCK = dim3(32, 32, 1);
cal_Indepl0 <<< BLOCKS_PER_GRID, THREADS_PER_BLOCK >>> (C_cuda, G_cuda, Th[0], pMax_cuda, n);
CudaCheckError();
}
else {
BLOCKS_PER_GRID = dim3(ceil( ( (double) (n)) / 32.0), ceil( ( (double) (n)) / 32.0), 1);
THREADS_PER_BLOCK = dim3(32, 32, 1);
cal_Indepl0 <<< BLOCKS_PER_GRID, THREADS_PER_BLOCK >>> (C_cuda, G_cuda, Th[0], pMax_cuda, n);
CudaCheckError();
}
BLOCKS_PER_GRID = dim3(n * n, 1, 1);
THREADS_PER_BLOCK = dim3(ML, 1, 1);
SepSet_initialize<<< BLOCKS_PER_GRID, THREADS_PER_BLOCK >>>(SepSet_cuda, n);
CudaCheckError();
} else {
//================================> Start Scan Process <===============================
HANDLE_ERROR( cudaMemset(nprime_cuda, 0, 1 * sizeof(int)) );
BLOCKS_PER_GRID = dim3(1, n, 1);
THREADS_PER_BLOCK = dim3(1024, 1, 1);
scan_compact <<< BLOCKS_PER_GRID, THREADS_PER_BLOCK, n * sizeof(int) >>> (GPrime_cuda, G_cuda, n, nprime_cuda);
CudaCheckError();
HANDLE_ERROR( cudaMemcpy(&nprime, nprime_cuda, 1 * sizeof(int), cudaMemcpyDeviceToHost) );
//================================> Begin The Gaussian CI Test <==============================
// CHeck whether a CI test is possible
if (nprime - 1 < *l){//if not:
*l = *l - 1;
FinishFlag = true;
break;
}
if (*l == 1){
BLOCKS_PER_GRID = dim3(NumOfBlockForEachNodeL1, n, 1);
THREADS_PER_BLOCK = dim3(ParGivenL1, 1, 1);
// HANDLE_ERROR( cudaMalloc((void**)&SepSet_cuda, n * n * 1 * sizeof(int)) );
cal_Indepl1 <<< BLOCKS_PER_GRID, THREADS_PER_BLOCK, nprime * sizeof(int) >>> (C_cuda, G_cuda, GPrime_cuda, mutex_cuda, SepSet_cuda, pMax_cuda, Th[1], n);
// HANDLE_ERROR( cudaFree(SepSet_cuda) );
CudaCheckError();
HANDLE_ERROR( cudaDeviceSynchronize() ) ;
CudaCheckError();
}
else if (*l == 2){
BLOCKS_PER_GRID = dim3(NumOfBlockForEachNodeL2, n, 1);
THREADS_PER_BLOCK = dim3(ParGivenL2, 1, 1);
// HANDLE_ERROR( cudaMalloc((void**)&SepSet_cuda, n * n * 1 * sizeof(int)) );
cal_Indepl2 <<< BLOCKS_PER_GRID, THREADS_PER_BLOCK, nprime * sizeof(int) >>> (C_cuda, G_cuda, GPrime_cuda, mutex_cuda, SepSet_cuda, pMax_cuda,n, Th[2]);
// HANDLE_ERROR( cudaFree(SepSet_cuda) );
CudaCheckError();
}
else if(*l == 3){
BLOCKS_PER_GRID = dim3(NumOfBlockForEachNodeL3, n, 1);
THREADS_PER_BLOCK = dim3(ParGivenL3, 1, 1);
// HANDLE_ERROR( cudaMalloc((void**)&SepSet_cuda, n * n * 1 * sizeof(int)) );
cal_Indepl3 <<< BLOCKS_PER_GRID, THREADS_PER_BLOCK, nprime * sizeof(int) >>> (C_cuda, G_cuda, GPrime_cuda, mutex_cuda, SepSet_cuda, pMax_cuda,n, Th[3]);
// HANDLE_ERROR( cudaFree(SepSet_cuda) );
CudaCheckError();
}
else if(*l == 4){
BLOCKS_PER_GRID = dim3(NumOfBlockForEachNodeL4, n, 1);
THREADS_PER_BLOCK = dim3(ParGivenL4, 1, 1);
cal_Indepl4 <<< BLOCKS_PER_GRID, THREADS_PER_BLOCK, nprime * sizeof(int) >>> (C_cuda, G_cuda, GPrime_cuda, mutex_cuda, SepSet_cuda, pMax_cuda,n, Th[4]);
CudaCheckError();
}
else if(*l == 5){
BLOCKS_PER_GRID = dim3(NumOfBlockForEachNodeL5, n, 1);
THREADS_PER_BLOCK = dim3(ParGivenL5, 1, 1);
cal_Indepl5 <<< BLOCKS_PER_GRID, THREADS_PER_BLOCK, nprime * sizeof(int) >>> (C_cuda, G_cuda, GPrime_cuda, mutex_cuda, SepSet_cuda, pMax_cuda,n, Th[5]);
CudaCheckError();
}
else if(*l == 6){
BLOCKS_PER_GRID = dim3(NumOfBlockForEachNodeL6, n, 1);
THREADS_PER_BLOCK = dim3(ParGivenL6, 1, 1);
cal_Indepl6 <<< BLOCKS_PER_GRID, THREADS_PER_BLOCK, nprime * sizeof(int) >>> (C_cuda, G_cuda, GPrime_cuda, mutex_cuda, SepSet_cuda, pMax_cuda,n, Th[6]);
CudaCheckError();
}
else if(*l == 7){
BLOCKS_PER_GRID = dim3(NumOfBlockForEachNodeL7, n, 1);
THREADS_PER_BLOCK = dim3(ParGivenL7, 1, 1);
cal_Indepl7 <<< BLOCKS_PER_GRID, THREADS_PER_BLOCK, nprime * sizeof(int) >>> (C_cuda, G_cuda, GPrime_cuda, mutex_cuda, SepSet_cuda, pMax_cuda,n, Th[7]);
CudaCheckError();
}
else if(*l == 8){
BLOCKS_PER_GRID = dim3(NumOfBlockForEachNodeL8, n, 1);
THREADS_PER_BLOCK = dim3(ParGivenL8, 1, 1);
cal_Indepl8 <<< BLOCKS_PER_GRID, THREADS_PER_BLOCK, nprime * sizeof(int) >>> (C_cuda, G_cuda, GPrime_cuda, mutex_cuda, SepSet_cuda, pMax_cuda,n, Th[8]);
CudaCheckError();
}
else if(*l == 9){
BLOCKS_PER_GRID = dim3(NumOfBlockForEachNodeL9, n, 1);
THREADS_PER_BLOCK = dim3(ParGivenL9, 1, 1);
cal_Indepl9 <<< BLOCKS_PER_GRID, THREADS_PER_BLOCK, nprime * sizeof(int) >>> (C_cuda, G_cuda, GPrime_cuda, mutex_cuda, SepSet_cuda, pMax_cuda,n, Th[9]);
CudaCheckError();
}
else if(*l == 10){
BLOCKS_PER_GRID = dim3(NumOfBlockForEachNodeL10, n, 1);
THREADS_PER_BLOCK = dim3(ParGivenL10, 1, 1);
cal_Indepl10 <<< BLOCKS_PER_GRID, THREADS_PER_BLOCK, nprime * sizeof(int) >>> (C_cuda, G_cuda, GPrime_cuda, mutex_cuda, SepSet_cuda, pMax_cuda,n, Th[10]);
CudaCheckError();
}
else if(*l == 11){
BLOCKS_PER_GRID = dim3(NumOfBlockForEachNodeL11, n, 1);
THREADS_PER_BLOCK = dim3(ParGivenL11, 1, 1);
cal_Indepl11 <<< BLOCKS_PER_GRID, THREADS_PER_BLOCK, nprime * sizeof(int) >>> (C_cuda, G_cuda, GPrime_cuda, mutex_cuda, SepSet_cuda, pMax_cuda,n, Th[11]);
CudaCheckError();
}
else if(*l == 12){
BLOCKS_PER_GRID = dim3(NumOfBlockForEachNodeL12, n, 1);
THREADS_PER_BLOCK = dim3(ParGivenL12, 1, 1);
cal_Indepl12 <<< BLOCKS_PER_GRID, THREADS_PER_BLOCK, nprime * sizeof(int) >>> (C_cuda, G_cuda, GPrime_cuda, mutex_cuda, SepSet_cuda, pMax_cuda,n, Th[12]);
CudaCheckError();
}
else if(*l == 13){
BLOCKS_PER_GRID = dim3(NumOfBlockForEachNodeL13, n, 1);
THREADS_PER_BLOCK = dim3(ParGivenL13, 1, 1);
cal_Indepl13 <<< BLOCKS_PER_GRID, THREADS_PER_BLOCK, nprime * sizeof(int) >>> (C_cuda, G_cuda, GPrime_cuda, mutex_cuda, SepSet_cuda, pMax_cuda,n, Th[13]);
CudaCheckError();
}
else if(*l == 14){
BLOCKS_PER_GRID = dim3(NumOfBlockForEachNodeL14, n, 1);
THREADS_PER_BLOCK = dim3(ParGivenL14, 1, 1);
cal_Indepl14 <<< BLOCKS_PER_GRID, THREADS_PER_BLOCK, nprime * sizeof(int) >>> (C_cuda, G_cuda, GPrime_cuda, mutex_cuda, SepSet_cuda, pMax_cuda,n, Th[14]);
CudaCheckError();
} else{
//TODO: add PC serial
}
}
}// if l > 0
// Copy Graph G from GPU to CPU
HANDLE_ERROR( cudaMemcpy(G, G_cuda, n * n * sizeof(int), cudaMemcpyDeviceToHost) );
// Copy separation set from GPU to CPU
HANDLE_ERROR( cudaMemcpy(SepSet, SepSet_cuda, n * n * ML * sizeof(int), cudaMemcpyDeviceToHost) );
// Copy Pmax from GPU to CPU
HANDLE_ERROR( cudaMemcpy(pMax, pMax_cuda, n * n * sizeof(double), cudaMemcpyDeviceToHost) );
//Preprocess pMax
double temp = 0;
for (int i = 0; i < n; i++){
pMax[i * n + i] = 1;
for(int j = (i + 1); j < n; j++){
if(G[i * n + j] == 0){
temp = fmax(pMax[j * n + i], pMax[i * n + j]);
pMax[j * n + i] = temp;
pMax[i * n + j] = temp;
}
else{
pMax[j * n + i] = -100000;
pMax[i * n + j] = -100000;
}
}
}
// Free allocated space
HANDLE_ERROR( cudaFree(SepSet_cuda) );
HANDLE_ERROR( cudaFree(C_cuda) );
HANDLE_ERROR( cudaFree(GPrime_cuda) );
HANDLE_ERROR( cudaFree(G_cuda) );
HANDLE_ERROR( cudaFree(mutex_cuda) );
HANDLE_ERROR( cudaFree(pMax_cuda) );
}// Skeleton
__global__ void SepSet_initialize(int *SepSet, int size){
int row = bx;
SepSet[row * ML + tx] = -1;
}
__global__ void cal_Indepl0(double *C, int *G, double th, double *pMax, int n)
{
int row = blockDim.x * bx + tx;
int col = blockDim.y * by + ty;
if(row < col && col < n){
double res = C[row * n + col];
res = abs( 0.5 * log( abs ( (1 + res) / (1 - res) ) ) );
if (res < th){
pMax[row * n + col] = res;
G[row * n + col] = 0;
G[col * n + row] = 0;
}
else {
G[row * n + col] = 1;
G[col * n + row] = 1;
}
}
if (row == col && col < n){
G[row * n + col] = 0;
G[col * n + row] = 0;
}
}
__global__ void cal_Indepl1(double *C, int *G, int *GPrime, int *mutex, int* Sepset, double* pMax, double th, int n)
{
int YIdx;
int XIdx = by;
int NbrIdxPointer;
int NbrIdx;
int SizeOfArr;
int NumberOfJump;
int NumOfGivenJump;
__shared__ int NoEdgeFlag;
double M0;
double H[2][2];
double M1[2];
double rho, Z;
extern __shared__ int G_Chunk[];
NoEdgeFlag = 0;
SizeOfArr = GPrime[XIdx * n + n - 1];
if( (SizeOfArr % ParGivenL1) == 0 ){
NumberOfJump = SizeOfArr / ParGivenL1;
}
else{
NumberOfJump = SizeOfArr / ParGivenL1 + 1;
}
//Copy Row Xid from GPrime to G_chunck
for (int cnt = 0; cnt < NumberOfJump; cnt++){
if( ( tx + cnt * ParGivenL1 ) < SizeOfArr){
G_Chunk[ tx + cnt * ParGivenL1 ] = GPrime[ XIdx * n + tx + cnt * ParGivenL1];
}
__syncthreads();
}
if( (SizeOfArr % (ParGivenL1 * NumOfBlockForEachNodeL1)) == 0 ){
NumOfGivenJump = SizeOfArr / (ParGivenL1 * NumOfBlockForEachNodeL1);
}
else{
NumOfGivenJump = SizeOfArr / (ParGivenL1 * NumOfBlockForEachNodeL1) + 1;
}
for(int d1 = 0; d1 < NumOfGivenJump; d1++){
__syncthreads();
if(NoEdgeFlag == 1){
return;
}
__syncthreads();
NbrIdxPointer = tx + bx * ParGivenL1 + d1 * ParGivenL1 * NumOfBlockForEachNodeL1;
NoEdgeFlag = 1;
__syncthreads();
if( NbrIdxPointer < SizeOfArr){
NbrIdx = G_Chunk[NbrIdxPointer];
M1[0] = C[XIdx * n + NbrIdx];
for(int d2 = 0; d2 < SizeOfArr; d2++){
if( d2 == NbrIdxPointer ){
continue;
}
YIdx = G_Chunk[d2];
if (G[XIdx * n + YIdx] == 1) {
NoEdgeFlag = 0;
M0 = C[XIdx * n + YIdx];
M1[1] = C[YIdx * n + NbrIdx];
H[0][0] = 1 - (M1[0] * M1[0]);
H[0][1] = M0 - (M1[0] * M1[1]);
H[1][1] = 1 - (M1[1] * M1[1]);
rho = H[0][1] / (sqrt(fabs(H[0][0])) * sqrt(fabs(H[1][1])));
Z = fabs( 0.5 * (log( fabs((1 + rho))) - log(fabs(1 - rho)) ) );
if (Z < th){
if(atomicCAS(&mutex[XIdx * n + YIdx], 0, 1) == 0){
G[XIdx * n + YIdx] = 0;
G[YIdx * n + XIdx] = 0;
pMax[XIdx * n + YIdx] = Z;
Sepset[(XIdx * n + YIdx) * ML] = NbrIdx;
}
}
}
}
}
}
}
__global__ void cal_Indepl2(double *C, int *G, int* GPrime, int *mutex, int* Sepset, double* pMax, int n, double th)
{
int YIdx;
int XIdx = by;
int NbrIdxPointer[2];
int NbrIdx[2];
int SizeOfArr;
int NumberOfJump;
int NumOfGivenJump;
int NumOfComb;
__shared__ int NoEdgeFlag;
double M0;
double M1[2][2];
double M2[2][2];
double M2Inv[2][2];
double M1MulM2Inv[2][2];
double H[2][2];
double rho;
double Z;
//Lock WriteSepSetLock;
extern __shared__ int G_Chunk[];
NoEdgeFlag = 0;
SizeOfArr = GPrime[XIdx * n + n - 1];
if (SizeOfArr <= 2){
return;
}
if( (SizeOfArr % ParGivenL2) == 0 ){
NumberOfJump = SizeOfArr / ParGivenL2;
}
else{
NumberOfJump = SizeOfArr / ParGivenL2 + 1;
}
//Copy Row Xid from GPrime to G_chunck
for (int cnt = 0; cnt < NumberOfJump; cnt++){
if( ( tx + cnt * ParGivenL2 ) < SizeOfArr){
G_Chunk[ tx + cnt * ParGivenL2 ] = GPrime[ XIdx * n + tx + cnt * ParGivenL2];
}
__syncthreads();
}
BINOM(SizeOfArr, 2, &NumOfComb);
if( (NumOfComb % (ParGivenL2 * NumOfBlockForEachNodeL2)) == 0 ){
NumOfGivenJump = NumOfComb / (ParGivenL2 * NumOfBlockForEachNodeL2);
}
else{
NumOfGivenJump = NumOfComb / (ParGivenL2 * NumOfBlockForEachNodeL2) + 1;
}
for(int d1 = 0; d1 < NumOfGivenJump; d1++){
__syncthreads();
if(NoEdgeFlag == 1){
return;
}
if( (tx + bx * ParGivenL2 + d1 * ParGivenL2 * NumOfBlockForEachNodeL2) < NumOfComb){
__syncthreads();
NoEdgeFlag = 1;
__syncthreads();
IthCombination(NbrIdxPointer, SizeOfArr, 2, tx + bx * ParGivenL2 + d1 * ParGivenL2 * NumOfBlockForEachNodeL2 + 1);
NbrIdx[0] = G_Chunk[NbrIdxPointer[0] - 1];
NbrIdx[1] = G_Chunk[NbrIdxPointer[1] - 1];
M2[0][1] = C[ NbrIdx[0] * n + NbrIdx[1] ];
M2[1][0] = M2[0][1];
M2[1][1] = 1;
M2[0][0] = 1;
M1[0][1] = C[ XIdx * n + NbrIdx[1] ];
M1[0][0] = C[ XIdx * n + NbrIdx[0] ];
pseudoinversel2(M2, M2Inv);
for(int d2 = 0; d2 < SizeOfArr; d2++){
if( (d2 == (NbrIdxPointer[0] - 1)) || (d2 == (NbrIdxPointer[1] - 1)) ){
continue;
}
YIdx = G_Chunk[d2];
if (G[XIdx * n + YIdx] == 1) {
NoEdgeFlag = 0;
M0 = C[XIdx * n + YIdx];
M1[1][0] = C[ YIdx * n + NbrIdx[0] ];
M1[1][1] = C[ YIdx * n + NbrIdx[1] ];
for (int c1 = 0; c1 < 2; c1++)
{
for (int c2 = 0; c2 < 2; c2++)
{
M1MulM2Inv[c1][c2] = 0;
for (int c3 = 0; c3 < 2; c3++)
M1MulM2Inv[c1][c2] += M1[c1][c3] * M2Inv[c3][c2];
}
}
H[0][0] = 1 - (M1MulM2Inv[0][0] * M1[0][0] + M1MulM2Inv[0][1] * M1[0][1]);
H[0][1] = M0 - (M1MulM2Inv[0][0] * M1[1][0] + M1MulM2Inv[0][1] * M1[1][1]);
H[1][1] = 1 - (M1MulM2Inv[1][0] * M1[1][0] + M1MulM2Inv[1][1] * M1[1][1]);
rho = H[0][1] / ( sqrt( abs(H[0][0] * H[1][1]) ) );
Z = 0.5 * abs( log( abs( (1 + rho) / (1 - rho) ) ) );
if (Z < th){
if(atomicCAS(&mutex[XIdx * n + YIdx], 0, 1) == 0){//lock
G[XIdx * n + YIdx] = 0;
G[YIdx * n + XIdx] = 0;
pMax[XIdx * n + YIdx] = Z;
Sepset[(XIdx * n + YIdx) * ML] = NbrIdx[0];
Sepset[(XIdx * n + YIdx) * ML + 1] = NbrIdx[1];
}
}
}
}
}
}
}
__global__ void cal_Indepl3(double *C, int *G, int* GPrime, int *mutex, int* Sepset, double* pMax, int n, double th)
{
int YIdx;
int XIdx = by;
int NbrIdxPointer[3];
int SizeOfArr;
int NumberOfJump;
int NumOfGivenJump;
int NumOfComb;
__shared__ int NoEdgeFlag;
int NbrIdx[3];
double M0;
double M1[2][3];
double M2[3][3];
double M2Inv[3][3];
double M1MulM2Inv[2][3];
double H[2][2];
double rho;
double Z;
//Lock WriteSepSetLock;
extern __shared__ int G_Chunk[];
NoEdgeFlag = 0;
SizeOfArr = GPrime[XIdx * n + n - 1];
if (SizeOfArr <= 3){
return;
}
if( (SizeOfArr % ParGivenL3) == 0 ){
NumberOfJump = SizeOfArr / ParGivenL3;
}
else{
NumberOfJump = SizeOfArr / ParGivenL3 + 1;
}
//Copy Row Xid from GPrime to G_chunck
for (int cnt = 0; cnt < NumberOfJump; cnt++){
if( ( tx + cnt * ParGivenL3 ) < SizeOfArr){
G_Chunk[ tx + cnt * ParGivenL3 ] = GPrime[ XIdx * n + tx + cnt * ParGivenL3];
}
__syncthreads();
}
BINOM(SizeOfArr, 3, &NumOfComb);
if( (NumOfComb % (ParGivenL3 * NumOfBlockForEachNodeL3)) == 0 ){
NumOfGivenJump = NumOfComb / (ParGivenL3 * NumOfBlockForEachNodeL3);
}
else{
NumOfGivenJump = NumOfComb / (ParGivenL3 * NumOfBlockForEachNodeL3) + 1;
}
__syncthreads();
for(int d1 = 0; d1 < NumOfGivenJump; d1++){
__syncthreads();
if(NoEdgeFlag == 1){
return;
}
if(tx + bx * ParGivenL3 + d1 * ParGivenL3 * NumOfBlockForEachNodeL3 < NumOfComb){
__syncthreads();
NoEdgeFlag = 1;
__syncthreads();
IthCombination(NbrIdxPointer, SizeOfArr, 3, tx + bx * ParGivenL3 + d1 * ParGivenL3 * NumOfBlockForEachNodeL3 + 1);
NbrIdx[0] = G_Chunk[NbrIdxPointer[0] - 1];
NbrIdx[1] = G_Chunk[NbrIdxPointer[1] - 1];
NbrIdx[2] = G_Chunk[NbrIdxPointer[2] - 1];
M2[0][0] = 1;
M2[0][1] = C[ NbrIdx[0] * n + NbrIdx[1] ];
M2[0][2] = C[ NbrIdx[0] * n + NbrIdx[2] ];
M2[1][0] = M2[0][1];
M2[1][1] = 1;
M2[1][2] = C[ NbrIdx[1] * n + NbrIdx[2] ];
M2[2][0] = M2[0][2];
M2[2][1] = M2[1][2];
M2[2][2] = 1;
M1[0][0] = C[ XIdx * n + NbrIdx[0] ];
M1[0][1] = C[ XIdx * n + NbrIdx[1] ];
M1[0][2] = C[ XIdx * n + NbrIdx[2] ];
pseudoinversel3(M2, M2Inv);
for(int d2 = 0; d2 < SizeOfArr; d2++){
if( (d2 == (NbrIdxPointer[0] - 1)) || (d2 == (NbrIdxPointer[1] - 1)) || (d2 == (NbrIdxPointer[2] - 1)) ){
continue;
}
YIdx = G_Chunk[d2];
if (G[XIdx * n + YIdx] == 1) {
NoEdgeFlag = 0;
M0 = C[XIdx * n + YIdx];
M1[1][0] = C[ YIdx * n + NbrIdx[0] ];
M1[1][1] = C[ YIdx * n + NbrIdx[1] ];
M1[1][2] = C[ YIdx * n + NbrIdx[2] ];
//Begin to calculate I2Inv Using pseudo-inverse
for (int c1 = 0; c1 < 2; c1++)
{
for (int c2 = 0; c2 < 3; c2++)
{
M1MulM2Inv[c1][c2] = 0;
for (int c3 = 0; c3 < 3; c3++)
M1MulM2Inv[c1][c2] += M1[c1][c3] * M2Inv[c3][c2];
}
}
for (int c1 = 0; c1 < 2; c1++)
{
for (int c2 = 0; c2 < 2; c2++)
{
H[c1][c2] = 0;
for (int c3 = 0; c3 < 3; c3++)
H[c1][c2] += M1MulM2Inv[c1][c3] * M1[c2][c3];
}
}
H[0][0] = 1 - H[0][0];
H[0][1] = M0 - H[0][1];
H[1][1] = 1 - H[1][1];
rho = H[0][1] / ( sqrt( abs(H[0][0] * H[1][1]) ) );
Z = abs( 0.5 * log( abs( (1 + rho) / (1 - rho) ) ) );
if (Z < th){
if(atomicCAS(&mutex[XIdx * n + YIdx], 0, 1) == 0){//lock
G[XIdx * n + YIdx] = 0;
G[YIdx * n + XIdx] = 0;
pMax[XIdx * n + YIdx] = Z;
Sepset[(XIdx * n + YIdx) * ML] = NbrIdx[0];
Sepset[(XIdx * n + YIdx) * ML + 1] = NbrIdx[1];
Sepset[(XIdx * n + YIdx) * ML + 2] = NbrIdx[2];
}
}
}
}
}
}
}
__global__ void cal_Indepl4(double *C, int *G, int* GPrime, int *mutex, int* Sepset, double* pMax, int n, double th)
{
int YIdx;
int XIdx = by;
int NbrIdxPointer[4];
int SizeOfArr;
int NumberOfJump;
int NumOfGivenJump;
int NumOfComb;
__shared__ int NoEdgeFlag;
int NbrIdx[4];
double M0;
double M1[2][4];
double M2[4][4];
double M2Inv[4][4];
double M1MulM2Inv[2][4];
double H[2][2];
double rho;
double Z;
double v[4][4];
double w[4], rv1[4];
double res1[4][4];
//Lock WriteSepSetLock;
extern __shared__ int G_Chunk[];
NoEdgeFlag = 0;
SizeOfArr = GPrime[XIdx * n + n - 1];
if (SizeOfArr <= 4){
return;
}
if( (SizeOfArr % ParGivenL4) == 0 ){
NumberOfJump = SizeOfArr / ParGivenL4;
}
else{
NumberOfJump = SizeOfArr / ParGivenL4 + 1;
}
//Copy Row Xid from GPrime to G_chunck
for (int cnt = 0; cnt < NumberOfJump; cnt++){
if( ( tx + cnt * ParGivenL4 ) < SizeOfArr){
G_Chunk[ tx + cnt * ParGivenL4 ] = GPrime[ XIdx * n + tx + cnt * ParGivenL4];
}
__syncthreads();
}
BINOM(SizeOfArr, 4, &NumOfComb);
if( (NumOfComb % (ParGivenL4 * NumOfBlockForEachNodeL4)) == 0 ){
NumOfGivenJump = NumOfComb / (ParGivenL4 * NumOfBlockForEachNodeL4);
}
else{
NumOfGivenJump = NumOfComb / (ParGivenL4 * NumOfBlockForEachNodeL4) + 1;
}
__syncthreads();
for(int d1 = 0; d1 < NumOfGivenJump; d1++){
__syncthreads();
if(NoEdgeFlag == 1){
return;
}
if(tx + bx * ParGivenL4 + d1 * ParGivenL4 * NumOfBlockForEachNodeL4 < NumOfComb){
__syncthreads();
NoEdgeFlag = 1;
__syncthreads();
IthCombination(NbrIdxPointer, SizeOfArr, 4, tx + bx * ParGivenL4 + d1 * ParGivenL4 * NumOfBlockForEachNodeL4 + 1);
NbrIdx[0] = G_Chunk[NbrIdxPointer[0] - 1];
NbrIdx[1] = G_Chunk[NbrIdxPointer[1] - 1];
NbrIdx[2] = G_Chunk[NbrIdxPointer[2] - 1];
NbrIdx[3] = G_Chunk[NbrIdxPointer[3] - 1];
M2[0][0] = 1;
M2[0][1] = C[ NbrIdx[0] * n + NbrIdx[1] ];
M2[0][2] = C[ NbrIdx[0] * n + NbrIdx[2] ];
M2[0][3] = C[ NbrIdx[0] * n + NbrIdx[3] ];
M2[1][0] = M2[0][1];
M2[1][1] = 1;
M2[1][2] = C[ NbrIdx[1] * n + NbrIdx[2] ];
M2[1][3] = C[ NbrIdx[1] * n + NbrIdx[3] ];
M2[2][0] = M2[0][2];
M2[2][1] = M2[1][2];
M2[2][2] = 1;
M2[2][3] = C[ NbrIdx[2] * n + NbrIdx[3] ];
M2[3][0] = M2[0][3];
M2[3][1] = M2[1][3];
M2[3][2] = M2[2][3];
M2[3][3] = 1;
M1[0][0] = C[ XIdx * n + NbrIdx[0] ];
M1[0][1] = C[ XIdx * n + NbrIdx[1] ];
M1[0][2] = C[ XIdx * n + NbrIdx[2] ];
M1[0][3] = C[ XIdx * n + NbrIdx[3] ];
pseudoinversel4(M2, M2Inv, v, rv1, w, res1 );
for(int d2 = 0; d2 < SizeOfArr; d2++){
if( (d2 == (NbrIdxPointer[0] - 1)) || (d2 == (NbrIdxPointer[1] - 1)) || (d2 == (NbrIdxPointer[2] - 1))
|| (d2 == (NbrIdxPointer[3] - 1))){
continue;
}
YIdx = G_Chunk[d2];
if (G[XIdx * n + YIdx] == 1) {
NoEdgeFlag = 0;
M0 = C[XIdx * n + YIdx];
M1[1][0] = C[ YIdx * n + NbrIdx[0] ];
M1[1][1] = C[ YIdx * n + NbrIdx[1] ];
M1[1][2] = C[ YIdx * n + NbrIdx[2] ];
M1[1][3] = C[ YIdx * n + NbrIdx[3] ];
//Begin to calculate I2Inv Using pseudo-inverse
for (int c1 = 0; c1 < 2; c1++)
{
for (int c2 = 0; c2 < 4; c2++)
{
M1MulM2Inv[c1][c2] = 0;
for (int c3 = 0; c3 < 4; c3++)
M1MulM2Inv[c1][c2] += M1[c1][c3] * M2Inv[c3][c2];
}
}
for (int c1 = 0; c1 < 2; c1++)
{
for (int c2 = 0; c2 < 2; c2++)
{
H[c1][c2] = 0;
for (int c3 = 0; c3 < 4; c3++)
H[c1][c2] += M1MulM2Inv[c1][c3] * M1[c2][c3];
}
}
H[0][0] = 1 - H[0][0];
H[0][1] = M0 - H[0][1];
H[1][1] = 1 - H[1][1];
rho = H[0][1] / ( sqrt( abs(H[0][0] * H[1][1]) ) );
Z = abs( 0.5 * log( abs( (1 + rho) / (1 - rho) ) ) );
if (Z < th){
if(atomicCAS(&mutex[XIdx * n + YIdx], 0, 1) == 0){//lock
G[XIdx * n + YIdx] = 0;
G[YIdx * n + XIdx] = 0;
pMax[XIdx * n + YIdx] = Z;
Sepset[(XIdx * n + YIdx) * ML] = NbrIdx[0];
Sepset[(XIdx * n + YIdx) * ML + 1] = NbrIdx[1];
Sepset[(XIdx * n + YIdx) * ML + 2] = NbrIdx[2];
Sepset[(XIdx * n + YIdx) * ML + 3] = NbrIdx[3];
}
}
}
}
}
}
}
__global__ void cal_Indepl5(double *C, int *G, int* GPrime, int *mutex, int* Sepset, double* pMax, int n, double th)
{
int YIdx;
int XIdx = by;
int NbrIdxPointer[5];
int SizeOfArr;
int NumberOfJump;
int NumOfGivenJump;
int NumOfComb;
__shared__ int NoEdgeFlag;
int NbrIdx[5];
double M0;
double M1[2][5];
double M2[5][5];
double M2Inv[5][5];
double M1MulM2Inv[2][5];
double H[2][2];
double rho;
double Z;
extern __shared__ int G_Chunk[];
//pseudo-inverse parameter
double v[5][5];
double w[5], rv1[5];
double res1[5][5];
NoEdgeFlag = 0;
SizeOfArr = GPrime[XIdx * n + n - 1];
if (SizeOfArr <= 5){
return;
}
if( (SizeOfArr % ParGivenL5) == 0 ){
NumberOfJump = SizeOfArr / ParGivenL5;
}
else{
NumberOfJump = SizeOfArr / ParGivenL5 + 1;
}
//Copy Row Xid from GPrime to G_chunck
for (int cnt = 0; cnt < NumberOfJump; cnt++){
if( ( tx + cnt * ParGivenL5 ) < SizeOfArr){
G_Chunk[ tx + cnt * ParGivenL5 ] = GPrime[ XIdx * n + tx + cnt * ParGivenL5];
}
__syncthreads();
}
BINOM(SizeOfArr, 5, &NumOfComb);
if( (NumOfComb % (ParGivenL5 * NumOfBlockForEachNodeL5)) == 0 ){
NumOfGivenJump = NumOfComb / (ParGivenL5 * NumOfBlockForEachNodeL5);
}
else{
NumOfGivenJump = NumOfComb / (ParGivenL5 * NumOfBlockForEachNodeL5) + 1;
}
for(int d1 = 0; d1 < NumOfGivenJump; d1++){
__syncthreads();
if(NoEdgeFlag == 1){
return;
}
if(tx + bx * ParGivenL5 + d1 * ParGivenL5 * NumOfBlockForEachNodeL5 < NumOfComb){
__syncthreads();
NoEdgeFlag = 1;
__syncthreads();
IthCombination(NbrIdxPointer, SizeOfArr, 5, tx + bx * ParGivenL5 + d1 * ParGivenL5 * NumOfBlockForEachNodeL5 + 1);
for(int tmp = 0; tmp < 5; tmp++){
NbrIdx[tmp] = G_Chunk[NbrIdxPointer[tmp] - 1];
}
M2[0][0] = 1;
M2[0][1] = C[ NbrIdx[0] * n + NbrIdx[1] ];
M2[0][2] = C[ NbrIdx[0] * n + NbrIdx[2] ];
M2[0][3] = C[ NbrIdx[0] * n + NbrIdx[3] ];
M2[0][4] = C[ NbrIdx[0] * n + NbrIdx[4] ];
M2[1][0] = M2[0][1];
M2[1][1] = 1;
M2[1][2] = C[ NbrIdx[1] * n + NbrIdx[2] ];
M2[1][3] = C[ NbrIdx[1] * n + NbrIdx[3] ];
M2[1][4] = C[ NbrIdx[1] * n + NbrIdx[4] ];
M2[2][0] = M2[0][2];
M2[2][1] = M2[1][2];
M2[2][2] = 1;
M2[2][3] = C[ NbrIdx[2] * n + NbrIdx[3] ];
M2[2][4] = C[ NbrIdx[2] * n + NbrIdx[4] ];
M2[3][0] = M2[0][3];
M2[3][1] = M2[1][3];
M2[3][2] = M2[2][3];
M2[3][3] = 1;
M2[3][4] = C[ NbrIdx[3] * n + NbrIdx[4] ];
M2[4][0] = M2[0][4];
M2[4][1] = M2[1][4];
M2[4][2] = M2[2][4];
M2[4][3] = M2[3][4];
M2[4][4] = 1;
M1[0][0] = C[ XIdx * n + NbrIdx[0] ];
M1[0][1] = C[ XIdx * n + NbrIdx[1] ];
M1[0][2] = C[ XIdx * n + NbrIdx[2] ];
M1[0][3] = C[ XIdx * n + NbrIdx[3] ];
M1[0][4] = C[ XIdx * n + NbrIdx[4] ];
pseudoinversel5(M2, M2Inv, v, rv1, w, res1 );
for(int d2 = 0; d2 < SizeOfArr; d2++){
if( (d2 == (NbrIdxPointer[0] - 1)) || (d2 == (NbrIdxPointer[1] - 1)) || (d2 == (NbrIdxPointer[2] - 1))
|| (d2 == (NbrIdxPointer[3] - 1))
|| (d2 == (NbrIdxPointer[4] - 1))
){
continue;
}
YIdx = G_Chunk[d2];
if (G[XIdx * n + YIdx] == 1) {
NoEdgeFlag = 0;
M0 = C[XIdx * n + YIdx];
//Beginning Of the Indep Test Calculation
M1[1][0] = C[ YIdx * n + NbrIdx[0] ];
M1[1][1] = C[ YIdx * n + NbrIdx[1] ];
M1[1][2] = C[ YIdx * n + NbrIdx[2] ];
M1[1][3] = C[ YIdx * n + NbrIdx[3] ];
M1[1][4] = C[ YIdx * n + NbrIdx[4] ];
//Begin to calculate I2Inv Using pseudo-inverse
for (int c1 = 0; c1 < 2; c1++)
{
for (int c2 = 0; c2 < 5; c2++)
{
M1MulM2Inv[c1][c2] = 0;
for (int c3 = 0; c3 < 5; c3++)
M1MulM2Inv[c1][c2] += M1[c1][c3] * M2Inv[c3][c2];
}
}
for (int c1 = 0; c1 < 2; c1++)
{
for (int c2 = 0; c2 < 2; c2++)
{
H[c1][c2] = 0;
for (int c3 = 0; c3 < 5; c3++)
H[c1][c2] += M1MulM2Inv[c1][c3] * M1[c2][c3];
}
}
H[0][0] = 1 - H[0][0];
H[0][1] = M0 - H[0][1];
H[1][1] = 1 - H[1][1];
rho = H[0][1] / ( sqrt( abs(H[0][0] * H[1][1]) ) );
Z = abs( 0.5 * log( abs( (1 + rho) / (1 - rho) ) ) );
if (Z < th){
if(atomicCAS(&mutex[XIdx * n + YIdx], 0, 1) == 0){//lock
G[XIdx * n + YIdx] = 0;
G[YIdx * n + XIdx] = 0;
pMax[XIdx * n + YIdx] = Z;
Sepset[(XIdx * n + YIdx) * ML] = NbrIdx[0];
Sepset[(XIdx * n + YIdx) * ML + 1] = NbrIdx[1];
Sepset[(XIdx * n + YIdx) * ML + 2] = NbrIdx[2];
Sepset[(XIdx * n + YIdx) * ML + 3] = NbrIdx[3];
Sepset[(XIdx * n + YIdx) * ML + 4] = NbrIdx[4];
}
}
}
}
}
}
}
__global__ void cal_Indepl6(double *C, int *G, int* GPrime, int *mutex, int* Sepset, double* pMax, int n, double th)
{
int YIdx;
int XIdx = by;
int NbrIdxPointer[6];
int SizeOfArr;
int NumberOfJump;
int NumOfGivenJump;
int NumOfComb;
__shared__ int NoEdgeFlag;
int NbrIdx[6];
double M0;
double M1[2][6];
double M2[6][6];
double M2Inv[6][6];
double M1MulM2Inv[2][6];
double H[2][2];
double rho;
double Z;
extern __shared__ int G_Chunk[];
//pseudo-inverse parameter
double v[6][6];
double w[6], rv1[6];
double res1[6][6];
NoEdgeFlag = 0;
SizeOfArr = GPrime[XIdx * n + n - 1];
if (SizeOfArr <= 6){
return;
}
if( (SizeOfArr % ParGivenL6) == 0 ){
NumberOfJump = SizeOfArr / ParGivenL6;
}
else{
NumberOfJump = SizeOfArr / ParGivenL6 + 1;
}
//Copy Row Xid from GPrime to G_chunck
for (int cnt = 0; cnt < NumberOfJump; cnt++){
if( ( tx + cnt * ParGivenL6 ) < SizeOfArr){
G_Chunk[ tx + cnt * ParGivenL6 ] = GPrime[ XIdx * n + tx + cnt * ParGivenL6];
}
__syncthreads();
}
BINOM(SizeOfArr, 6, &NumOfComb);
if( (NumOfComb % (ParGivenL6 * NumOfBlockForEachNodeL6)) == 0 ){
NumOfGivenJump = NumOfComb / (ParGivenL6 * NumOfBlockForEachNodeL6);
}
else{
NumOfGivenJump = NumOfComb / (ParGivenL6 * NumOfBlockForEachNodeL6) + 1;
}
for(int d1 = 0; d1 < NumOfGivenJump; d1++){
__syncthreads();
if(NoEdgeFlag == 1){
return;
}
if(tx + bx * ParGivenL6 + d1 * ParGivenL6 * NumOfBlockForEachNodeL6 < NumOfComb){
__syncthreads();
NoEdgeFlag = 1;
__syncthreads();
IthCombination(NbrIdxPointer, SizeOfArr, 6, tx + bx * ParGivenL6 + d1 * ParGivenL6 * NumOfBlockForEachNodeL6 + 1);
for(int tmp = 0; tmp < 6; tmp++){
NbrIdx[tmp] = G_Chunk[NbrIdxPointer[tmp] - 1];
}
M2[0][0] = 1;
M2[0][1] = C[ NbrIdx[0] * n + NbrIdx[1] ];
M2[0][2] = C[ NbrIdx[0] * n + NbrIdx[2] ];
M2[0][3] = C[ NbrIdx[0] * n + NbrIdx[3] ];
M2[0][4] = C[ NbrIdx[0] * n + NbrIdx[4] ];
M2[0][5] = C[ NbrIdx[0] * n + NbrIdx[5] ];
M2[1][0] = M2[0][1];
M2[1][1] = 1;
M2[1][2] = C[ NbrIdx[1] * n + NbrIdx[2] ];
M2[1][3] = C[ NbrIdx[1] * n + NbrIdx[3] ];
M2[1][4] = C[ NbrIdx[1] * n + NbrIdx[4] ];
M2[1][5] = C[ NbrIdx[1] * n + NbrIdx[5] ];
M2[2][0] = M2[0][2];
M2[2][1] = M2[1][2];
M2[2][2] = 1;
M2[2][3] = C[ NbrIdx[2] * n + NbrIdx[3] ];
M2[2][4] = C[ NbrIdx[2] * n + NbrIdx[4] ];
M2[2][5] = C[ NbrIdx[2] * n + NbrIdx[5] ];
M2[3][0] = M2[0][3];
M2[3][1] = M2[1][3];
M2[3][2] = M2[2][3];
M2[3][3] = 1;
M2[3][4] = C[ NbrIdx[3] * n + NbrIdx[4] ];
M2[3][5] = C[ NbrIdx[3] * n + NbrIdx[5] ];
M2[4][0] = M2[0][4];
M2[4][1] = M2[1][4];
M2[4][2] = M2[2][4];
M2[4][3] = M2[3][4];
M2[4][4] = 1;
M2[4][5] = C[ NbrIdx[4] * n + NbrIdx[5] ];
M2[5][0] = M2[0][5];
M2[5][1] = M2[1][5];
M2[5][2] = M2[2][5];
M2[5][3] = M2[3][5];