int main(int argc, char ** argv)
{
if (argc != 3) {
std::cerr << "Usage: chol <num_threads> <matrix_size>" << std::endl;
return 1;
}
omp_set_num_threads(atoi(argv[1]));
double L = 1.0;
unsigned int N = atoi(argv[2]);
double dx = (double) L / (N - 1);
double * A = (double *)malloc(N * N * sizeof(double));
for (unsigned int i = 0; i < N; i++) {
for (unsigned int j = 0; j < N; j++) {
A[i*N+j] = cov(i*dx, j*dx);
}
}
double start = omp_get_wtime();
// We're letting MKL choose the workspace array at runtime
// Assume unsigned int N converts to lapack_int
int info = LAPACKE_dpotrf(LAPACK_ROW_MAJOR, 'U', N, A, N);
double time = omp_get_wtime() - start;
std::cout << "LAPACKE_dpotrf executed in " << time << " secs." << std::endl;
std::cout << "LAPACKE_dpotrf return value is: " << info << std::endl;
free(A);
return info;
}
// This task computes the Cholesky factorization of a symmetric positive definite matrix...
// This is the first step in the tile Cholesky factorization.
ocrGuid_t lapacke_dpotrf_task ( u32 paramc, u64* paramv, u32 depc, ocrEdtDep_t depv[]) {
u32 info;
u64 *func_args = paramv;
u32 k = (u32) func_args[0];
u32 tileSize = (u32) func_args[1];
ocrGuid_t out_lkji_kkkp1_event_guid = (ocrGuid_t) func_args[2];
double* aBlock = (double*) (depv[0].ptr);
// PRINTF("RUNNING sequential_cholesky %d with 0x%llx to satisfy\n", k, (u64)(out_lkji_kkkp1_event_guid));
ocrGuid_t out_lkji_kkkp1_db_guid;
ocrGuid_t out_lkji_kkkp1_db_affinity = NULL_GUID;
info = LAPACKE_dpotrf(LAPACK_ROW_MAJOR, 'L', tileSize, aBlock, tileSize );
if (info != 0)
{
if (info > 0) PRINTF("Matrix A is not Symmetric Positive Definite (SPD)");
else PRINTF("i-th parameter had an illegal value.");
ASSERT(0);
ocrShutdown();
return NULL_GUID;
}
ocrEventSatisfy(out_lkji_kkkp1_event_guid, depv[0].guid);
return NULL_GUID;
}
static int Choleski_decompose(double *X, double *L, int n, int lapack){
int i,j,error_code;
char upper = 'U';
for (i=0; i < n; i++){
for (j=0; j < n; j++){
if (i > j)
L[j*n+i] = 0.0;
else {
L[j*n+i] = X[j*n + i];
}
}
}
#if 0
if (!lapack){
dpofa_(L,&n,&n,&error_code);
} else {
dpotrf_(&upper,&n,L,&n,&error_code);
}
#endif
error_code = LAPACKE_dpotrf( LAPACK_COL_MAJOR, upper, n, L, n );
return error_code;
}
int CholeskyFactorization::factorize() {
if (m_matrix_type == Matrix::MATRIX_SPARSE) {
/* Cholesky decomposition of a SPARSE matrix: */
if (m_matrix->m_sparse == NULL) {
m_matrix->_createSparse();
}
/* analyze */
m_factor = cholmod_analyze(m_matrix->m_sparse, Matrix::cholmod_handle());
/* factorize */
cholmod_factorize(m_matrix->m_sparse, m_factor, Matrix::cholmod_handle());
/* Success: status = 0, else 1*/
return (m_factor->minor == m_matrix->m_nrows) ? ForBESUtils::STATUS_OK : ForBESUtils::STATUS_NUMERICAL_PROBLEMS;
} else { /* If this is any non-sparse matrix: */
memcpy(m_L, m_matrix->getData(), m_matrix->length() * sizeof (double)); /* m_L := m_matrix.m_data */
int info = ForBESUtils::STATUS_OK;
if (m_matrix_type == Matrix::MATRIX_DENSE) { /* This is a dense matrix */
info = LAPACKE_dpotrf(LAPACK_COL_MAJOR, 'L', m_matrix_nrows, m_L, m_matrix_nrows);
#ifdef SET_L_OFFDIAG_TO_ZERO
for (size_t i = 0; i < m_matrix_nrows; i++) {
for (size_t j = i + 1; j < m_matrix_nrows; j++) {
L.set(i, j, 0.0);
}
}
#endif
} else if (m_matrix_type == Matrix::MATRIX_SYMMETRIC) { /* This is a symmetric matrix */
info = LAPACKE_dpptrf(LAPACK_COL_MAJOR, 'L', m_matrix_nrows, m_L);
}
return info;
}
}
GP_LKonly::GP_LKonly(int d, int n, double* Xin, double* Yin, double* Sin, int* Din, int kindex, double* hyp, double* R){
D=d;
N=n;
K=kindex;
//lk = 0.;
//hyp process
std::vector<double> ih = std::vector<double>(numhyp(kindex,d));
hypconvert(&hyp[0], K, D, &ih[0]);
//buildK
std::vector<double>Kxx = std::vector<double>(N*N);
double smodel = 0;
for (int i=0; i<N; i++){
Kxx[i*N+i] = kern[K](&Xin[i*D], &Xin[i*D],Din[i],Din[i],D,&ih[0],&smodel);
for (int j=0; j<i; j++){
Kxx[i*N+j] = Kxx[i+N*j] = kern[K](&Xin[i*D], &Xin[j*D],Din[i],Din[j],D,&ih[0],&smodel);
//if (i<10){printf("%f %f %d %d %d %f %f %f %f _ ",Xin[i*D], Xin[j*D],Din[i],Din[j],D,ih[0],ih[1],ih[2],k(&Xin[i*D], &Xin[j*D],Din[i],Din[j],D,&ih[0]));}
}
Kxx[i*N+i]+=Sin[i]+smodel;
}
//cho factor
int c = LAPACKE_dpotrf(LAPACK_ROW_MAJOR,'L',N,&Kxx[0],N);
if (c!=0){
printf("failed to cho fac Kxx %d with hyp [",c);
for (int i=0; i<numhyp(kindex,d);i++){printf("%f ",hyp[i]);}
printf("]");
R[0]=-1e22; return;
}
std::vector<double>Yd = std::vector<double>(N);
for (int i=0; i<N; i++){
Yd[i]= Yin[i];
}
//solve agains Y
LAPACKE_dpotrs(LAPACK_ROW_MAJOR,'L',N,1,&Kxx[0],N,&Yd[0],1);
//calc the llk
R[0] = - 0.5*N*L2PI;
//printf("\n1 %f\n",R[0]);
for (int i=0; i<N; i++){
R[0]-=log(Kxx[i*(N+1)]);
}
//printf("2 %f\n",R[0]);
R[0] -= 0.5*cblas_ddot(N,&Yin[0],1,&Yd[0],1);
//printf("3 %f\n",R[0]);
return;
}
void GeneticAlgorithm::initialiseMatrices(){
_emat = calcEmat(_R, _basis);
int address = 0;
int addresses[8];
for(int i = 0; i < 8; i ++){
addresses[i] = address;
address += (_basisPop[i])*(_R+1);
}
for(int i = 0; i < 8; i++){
int ch0 = LAPACKE_dpotrf(LAPACK_ROW_MAJOR, 'U', _basisPop[i], &_emat[addresses[i]], _R);
}
_gradientCalcs = calcGradient(_R,_basis);
return;
}
int cholesky_tiled(double *mat, int tile_size, int num_tiles, int mat_size,
int niter, int max_log_str, bool layRow, int verify, int num_doms, int use_host, int num_mics,
int host_ht_offset)
{
//verification result
bool result;
//total number of tiles
int tot_tiles = num_tiles * num_tiles;
//memory allocation for matrix for tiled-Cholesky
double *A_my = (double *)malloc(mat_size * mat_size * sizeof(double));
//memory allocation for matrix for MKL cholesky (for comparison)
double *A_MKL = (double *)malloc(mat_size * mat_size * sizeof(double));
//memory allocation for tiled matrix
double **Asplit = new double* [tot_tiles];
int mem_size_tile = tile_size * tile_size * sizeof(double);
#define HSTR_BUFFER_PROPS_VALUES { \
HSTR_MEM_TYPE_NORMAL, \
HSTR_MEM_ALLOC_PREFERRED, \
HSTR_BUF_PROP_ALIASED}
HSTR_BUFFER_PROPS buffer_props = HSTR_BUFFER_PROPS_VALUES;
for (int i = 0; i < tot_tiles; ++i) {
//Buffer per tile, host allocation
Asplit[i] = (double *)_mm_malloc(mem_size_tile, 64);
//Buffer creation and allocation on the card
//hStreams_app_create_buf((void *)Asplit[i], mem_size_tile);
CHECK_HSTR_RESULT(hStreams_Alloc1DEx(
(void *)Asplit[i],
mem_size_tile,
&buffer_props,
-1,
NULL));
}
double tbegin, tend;
int iter;
int info;
//Events are needed for various synchronizations to enforce
//data dependence between and among data-transfers/computes
HSTR_EVENT *eventcpyto = new HSTR_EVENT[tot_tiles];
HSTR_EVENT *eventcpyto_trsm = new HSTR_EVENT[tot_tiles * num_doms];
HSTR_EVENT *eventcpyfr = new HSTR_EVENT[tot_tiles];
HSTR_EVENT *eventpotrf = new HSTR_EVENT[tot_tiles];
HSTR_EVENT *eventtrsm = new HSTR_EVENT[tot_tiles];
HSTR_EVENT *eventsyrk = new HSTR_EVENT[tot_tiles];
HSTR_EVENT *eventgemm = new HSTR_EVENT[tot_tiles];
//for timing tiled cholesky
double *totTimeMsec = new double [niter];
//for timing MKL cholesky
double *totTimeMsecMKL = new double [niter];
mkl_mic_disable();
//these queues are used for queining up compute on the card and
//data transfers to/from the card.
//q_trsm for dtrsm, q_potrf for dportf, q_syrk_gemm for both dsyrk and dgemm.
//The queues are incremented by one for every compute queued and wrap
//around the max_log_str available. This ensures good load-balancing.
int q_trsm, q_potrf;
int q_syrk_gemm[10];
CBLAS_ORDER blasLay;
int lapackLay;
if (layRow) {
blasLay = CblasRowMajor;
lapackLay = LAPACK_ROW_MAJOR;
} else {
blasLay = CblasColMajor;
lapackLay = LAPACK_COL_MAJOR;
}
for (iter = 0; iter < niter; ++iter) {
//copying matrices into separate variables for tiled cholesky (A_my)
//and MKL cholesky (A_MKL)
//The output overwrites the matrices and hence the need to copy
//for each iteration
copy_mat(mat, A_my, mat_size);
copy_mat(mat, A_MKL, mat_size);
unsigned int m, n, k;
printf("\nIteration = %d\n", iter);
//splitting time included in the timing
//This splits the input matrix into tiles (or blocks)
split_into_blocks(A_my, Asplit, num_tiles, tile_size, mat_size, layRow);
//beginning of timing
tbegin = dtimeGet();
int ic;
int is_mic;
for (ic = 0; ic < num_doms; ++ic) {
q_syrk_gemm[ic] = 0;
}
q_potrf = 0;
q_trsm = 0;
for (k = 0; k < num_tiles; ++k) {
//POTRF
//dpotrf is executed on the host on the diagonal tile
if (mach_wide_league) {
q_potrf = 0;
} else {
q_potrf = q_syrk_gemm[0];
}
int qindex = (int)q_potrf % max_log_str;
if (use_host) {
if (k == 0) {
if (loc_verbose > 0)
printf("Sending tile[%d][%d] to host in queue %d, triggering event eventcpyto[%d][%d]\n",
k, k, (int)(qindex), k, k);
hStreams_app_xfer_memory((int)(qindex),
Asplit[k * num_tiles + k],
Asplit[k * num_tiles + k], mem_size_tile,
HSTR_SRC_TO_SINK,
&eventcpyto[k * num_tiles + k]);
}
}
if (k > 0) {
if (use_host) {
hStreams_app_event_wait_in_stream(qindex, 1, &eventcpyfr[k * num_tiles + k], 0, NULL, NULL);
} else {
hStreams_app_event_wait(1, &eventcpyfr[k * num_tiles + k]);
}
if (loc_verbose > 0) {
printf("Waiting on eventcpyfr[%d]\n", k * num_tiles + k);
}
}
if (loc_verbose > 0)
printf("Executing potrf on host for tile[%d][%d], in queue (if use_host) %d, triggerring eventpotrf[%d][%d]\n",
k, k, qindex, k, k);
if (use_host) {
CHECK_HSTR_RESULT(hStreams_custom_dpotrf(lapackLay, 'L', tile_size,
Asplit[k * num_tiles + k], tile_size, qindex, &eventpotrf[k * num_tiles + k]));
} else {
info = LAPACKE_dpotrf(lapackLay, 'L', tile_size,
Asplit[k * num_tiles + k], tile_size);
}
if (mach_wide_league) {
q_trsm = q_syrk_gemm[0];
} else {
q_potrf++;
q_trsm = q_potrf;
}
for (m = k + 1; m < num_tiles; ++m) {
if (mach_wide_league) {
qindex = (int)(q_trsm % max_log_str + 1);
} else {
qindex = (int)(q_trsm % max_log_str);
}
if (use_host) {
if (k == 0) {
if (loc_verbose > 0)
printf("Sending tile[%d][%d] to host in queue %d, triggering event eventcpyto[%d][%d]\n",
m, k, (int)(qindex), m, k);
hStreams_app_xfer_memory((int)(qindex),
Asplit[m * num_tiles + k],
Asplit[m * num_tiles + k], mem_size_tile,
HSTR_SRC_TO_SINK,
&eventcpyto[m * num_tiles + k]);
}
}
if (k > 0) {
if (use_host) {
hStreams_app_event_wait_in_stream(qindex, 1, &eventcpyfr[m * num_tiles + k], 0, NULL, NULL);
} else {
hStreams_app_event_wait(1, &eventcpyfr[m * num_tiles + k]);
}
if (loc_verbose > 0) {
printf("Waiting on eventcpyfr[%d]\n", m * num_tiles + k);
}
}
if (use_host)
//hStreams_app_event_wait(1, &eventpotrf[k*num_tiles + k]);
{
hStreams_app_event_wait_in_stream(qindex, 1, &eventpotrf[k * num_tiles + k], 0, NULL, NULL);
}
//dtrsm is executed on the host
if (loc_verbose > 0)
printf("Executing trsm for tile[%d][%d] on host, in queue (if use_host) %d, triggering eventtrsm[%d][%d]\n",
m, k, qindex, m, k);
if (use_host) {
CHECK_HSTR_RESULT(hStreams_custom_dtrsm(blasLay, CblasRight, CblasLower,
CblasTrans, CblasNonUnit, tile_size, tile_size, 1.0,
Asplit[k * num_tiles + k], tile_size, Asplit[m * num_tiles + k],
tile_size, qindex,
&eventtrsm[m * num_tiles + k]));
} else {
cblas_dtrsm(blasLay, CblasRight, CblasLower,
CblasTrans, CblasNonUnit, tile_size, tile_size, 1.0,
Asplit[k * num_tiles + k], tile_size, Asplit[m * num_tiles + k],
tile_size);
}
//transfer to all cards
for (ic = 0; ic < num_doms; ++ic) {
if ((use_host == 1) && (num_mics >= 1)) {
if (ic == 0) {
is_mic = 0; //this is host
} else {
is_mic = 1;
}
} else {
is_mic = 0;
}
if (mach_wide_league) {
qindex = (int)q_trsm % max_log_str + ic * max_log_str + 1 + is_mic * host_ht_offset;
} else {
qindex = (int)q_trsm % max_log_str + ic * max_log_str + is_mic * host_ht_offset;
}
if (use_host)
//hStreams_app_event_wait(1, &eventtrsm[m*num_tiles + k]);
{
hStreams_app_event_wait_in_stream(qindex, 1, &eventtrsm[m * num_tiles + k], 0, NULL, NULL);
}
if (loc_verbose > 0)
printf("Sending tile[%d][%d] to card %d in queue %d, triggering event eventcpyto_trsm[%d]\n",
m, k, ic, (int)(qindex), m * num_tiles + k + ic * tot_tiles);
hStreams_app_xfer_memory((int)(qindex),
Asplit[m * num_tiles + k],
Asplit[m * num_tiles + k], mem_size_tile,
HSTR_SRC_TO_SINK,
&eventcpyto_trsm[m * num_tiles + k + ic * tot_tiles]);
}
q_trsm++;
}
if (use_host) {
q_syrk_gemm[0] = q_trsm;
for (ic = 1; ic < num_doms; ++ic) {
q_syrk_gemm[ic] = 0;
}
} else {
for (ic = 0; ic < num_doms; ++ic) {
q_syrk_gemm[ic] = 0;
}
}
for (n = k + 1; n < num_tiles; ++n) {
ic = n % num_doms; //round-robin rows across num_doms
if ((use_host == 1) && (num_mics >= 1)) {
if (ic == 0) {
is_mic = 0; //this is host
} else {
is_mic = 1;
}
} else {
is_mic = 0;
}
if (mach_wide_league) {
qindex = q_syrk_gemm[ic] % max_log_str + ic * max_log_str + 1 + is_mic * host_ht_offset;
} else {
qindex = q_syrk_gemm[ic] % max_log_str + ic * max_log_str + is_mic * host_ht_offset;
}
if (k == 0) {
if (loc_verbose > 0)
printf("Sending tile[%d][%d] to card in queue %d\n",
n, n, (int)(qindex));
hStreams_app_xfer_memory((int)(qindex),
Asplit[n * num_tiles + n],
Asplit[n * num_tiles + n], mem_size_tile,
HSTR_SRC_TO_SINK,
&eventcpyto[n * num_tiles + n]);
}
//DSYRK
//hStreams_app_event_wait(1, &eventcpyto_trsm[n*num_tiles + k + ic*tot_tiles]);
hStreams_app_event_wait_in_stream(qindex, 1, &eventcpyto_trsm[n * num_tiles + k + ic * tot_tiles], 0, NULL, NULL);
if (loc_verbose > 0) {
printf("Waiting on eventcpyto_trsm[%d]\n", n * num_tiles + k + ic * tot_tiles);
}
if (k > 0) {
//hStreams_app_event_wait(1, &eventsyrk[n*num_tiles + n]);
hStreams_app_event_wait_in_stream(qindex, 1, &eventsyrk[n * num_tiles + n], 0, NULL, NULL);
if (loc_verbose > 0) {
printf("Waiting on eventsyrk[%d]\n", n * num_tiles + n);
}
}
//dsyrk is executed on the card
if (loc_verbose > 0)
printf("Executing syrk for tile[%d][%d] on card in queue %d, triggering event eventsyrk[%d]\n",
n, n, (int)(qindex), n * num_tiles + n);
CHECK_HSTR_RESULT(hStreams_custom_dsyrk(blasLay, CblasLower, CblasNoTrans,
tile_size, tile_size, -1.0, Asplit[n * num_tiles + k],
tile_size, 1.0, Asplit[n * num_tiles + n], tile_size,
(int)(qindex), &eventsyrk[n * num_tiles + n]));
//send tile to host (only if n = k+1)
if (n == k + 1) {
if (loc_verbose > 0)
printf("Sending tile[%d][%d] from card to host in queue %d, triggering event eventcpyfr[%d]\n",
n, n, (int)(qindex), n * num_tiles + n);
hStreams_app_xfer_memory((int)(qindex),
Asplit[n * num_tiles + n],
Asplit[n * num_tiles + n], mem_size_tile,
HSTR_SINK_TO_SRC,
&eventcpyfr[n * num_tiles + n]);
}
q_syrk_gemm[ic]++;
for (m = n + 1; m < num_tiles; ++m) {
ic = m % num_doms; //round-robin rows across num_doms
if ((use_host == 1) && (num_mics >= 1)) {
if (ic == 0) {
is_mic = 0; //this is host
} else {
is_mic = 1;
}
} else {
is_mic = 0;
}
if (mach_wide_league) {
qindex = q_syrk_gemm[ic] % max_log_str + ic * max_log_str + 1 + is_mic * host_ht_offset;
} else {
qindex = q_syrk_gemm[ic] % max_log_str + ic * max_log_str + is_mic * host_ht_offset;
}
if (k == 0) {
if (loc_verbose > 0)
printf("Sending tile[%d][%d] to card in queue %d\n",
m, n, (int)(qindex));
hStreams_app_xfer_memory((int)(qindex),
Asplit[m * num_tiles + n],
Asplit[m * num_tiles + n], mem_size_tile,
HSTR_SRC_TO_SINK,
&eventcpyto[m * num_tiles + n]);
}
//DGEMM
if (loc_verbose > 0) {
printf("Waiting on eventcpyto_trsm[%d]\n", m * num_tiles + k + ic * tot_tiles);
}
//hStreams_app_event_wait(1, &eventcpyto_trsm[m*num_tiles + k + ic*tot_tiles]);
hStreams_app_event_wait_in_stream(qindex, 1, &eventcpyto_trsm[m * num_tiles + k + ic * tot_tiles], 0, NULL, NULL);
if (loc_verbose > 0) {
printf("Waiting on eventcpyto_trsm[%d]\n", n * num_tiles + k + ic * tot_tiles);
}
//hStreams_app_event_wait(1, &eventcpyto_trsm[n*num_tiles + k + ic*tot_tiles]);
hStreams_app_event_wait_in_stream(qindex, 1, &eventcpyto_trsm[n * num_tiles + k + ic * tot_tiles], 0, NULL, NULL);
if (k > 0) {
//hStreams_app_event_wait(1, &eventgemm[m*num_tiles + n]);
hStreams_app_event_wait_in_stream(qindex, 1, &eventgemm[m * num_tiles + n], 0, NULL, NULL);
if (loc_verbose > 0) {
printf("Waiting on eventgemm[%d]\n", m * num_tiles + n);
}
}
//dgemm is executed on the card
if (loc_verbose > 0)
printf("Executing gemm for tile[%d][%d] on card in queue %d, triggering event eventgemm[%d]\n",
m, n, (int)(qindex), m * num_tiles + n);
CHECK_HSTR_RESULT(hStreams_app_dgemm((int)(qindex),
blasLay, CblasNoTrans, CblasTrans,
tile_size, tile_size, tile_size, -1.0, Asplit[m * num_tiles + k],
tile_size, Asplit[n * num_tiles + k], tile_size, 1.0,
Asplit[m * num_tiles + n], tile_size,
&eventgemm[m * num_tiles + n]));
//send tile to host (only if n = k+1)
if (n == k + 1) {
if (loc_verbose > 0)
printf("Sending tile[%d][%d] from card to host in queue %d, triggering event eventcpyfr[%d]\n",
m, n, (int)(qindex), m * num_tiles + n);
hStreams_app_xfer_memory(
(int)(qindex),
Asplit[m * num_tiles + n],
Asplit[m * num_tiles + n], mem_size_tile,
HSTR_SINK_TO_SRC,
&eventcpyfr[m * num_tiles + n]);
}
q_syrk_gemm[ic]++;
}
}
}
//syncrhonizing all the streams
hStreams_app_thread_sync();
//end of timing
tend = dtimeGet();
totTimeMsec[iter] = 1e3 * (tend - tbegin);
printf("time for Tiled hstreams Cholesky for iteration %d = %.2f msec\n",
iter, totTimeMsec[iter]);
//assembling of tiles back into full matrix
assemble(Asplit, A_my, num_tiles, tile_size, mat_size, layRow);
//calling mkl cholesky for verification and timing comparison.
//Using auto-offload feature of MKL
tbegin = dtimeGet();
//calling MKL dpotrf on the full matrix
info = LAPACKE_dpotrf(lapackLay, 'L', mat_size, A_MKL, mat_size);
tend = dtimeGet();
totTimeMsecMKL[iter] = 1e3 * (tend - tbegin);
printf("time for MKL Cholesky (AO) for iteration %d = %.2f msec\n",
iter, totTimeMsecMKL[iter]);
if (info != 0) {
printf("error with dpotrf\n");
}
mkl_mic_disable();
if (verify == 1) {
result = verify_results(A_my, A_MKL, mat_size * mat_size);
if (result == true) {
printf("Tiled Cholesky successful\n");
} else {
printf("Tiled Chloesky failed\n");
}
}
}
double meanTimeMsec, stdDevMsec;
double meanTimeMsecMKL, stdDevMsecMKL;
mean_and_stdev(totTimeMsec, meanTimeMsec, stdDevMsec, niter);
mean_and_stdev(totTimeMsecMKL, meanTimeMsecMKL, stdDevMsecMKL, niter);
double gflops = pow(mat_size, 3.0) / 3.0 * 1e-9;
printf("\nMatrix size = %d\n", mat_size);
printf("Tiled hStreams Cholesky: for %d iterations (ignoring first),\n"
"mean Time = %.2f msec, stdDev Time = %.2f msec,\n"
"Mean Gflops (using mean Time) = %.2f\n",
niter - 1, meanTimeMsec, stdDevMsec, gflops / (meanTimeMsec * 1e-3));
printf("\nMKL AO Cholesky: for %d iterations (ignoring first),\n"
"mean Time = %.2f msec, stdDev Time = %.2f msec,\n"
"Mean Gflops (using meanTime) = %.2f\n\n",
niter - 1, meanTimeMsecMKL, stdDevMsecMKL, gflops / (meanTimeMsecMKL * 1e-3));
//Free
free(A_my);
free(A_MKL);
for (int i = 0; i < tot_tiles; ++i) {
_mm_free(Asplit[i]);
}
delete [] Asplit;
delete [] eventcpyto;
delete [] eventcpyto_trsm;
delete [] eventcpyfr;
delete [] eventpotrf;
delete [] eventtrsm;
delete [] eventsyrk;
delete [] eventgemm;
delete [] totTimeMsec;
delete [] totTimeMsecMKL;
// true result indicates all OK
if (result) {
return 0;
}
return 1;
}
int GP::fac(){
return LAPACKE_dpotrf(LAPACK_ROW_MAJOR,'L',N,&Kxx[0],N);
}
void cholesky_tiled(double *mat, int tile_size, int num_tiles, int mat_size,
int niter, int max_log_str, bool layRow, int verify)
{
//total number of tiles
int tot_tiles = num_tiles * num_tiles;
//memory allocation for matrix for tiled-Cholesky
double *A_my = (double *)malloc(mat_size * mat_size * sizeof(double));
//memory allocation for matrix for MKL cholesky (for comparison)
double *A_MKL = (double *)malloc(mat_size * mat_size * sizeof(double));
//memory allocation for tiled matrix
double **Asplit = new double* [tot_tiles];
int mem_size_tile = tile_size * tile_size * sizeof(double);
for (int i = 0; i < tot_tiles; ++i) {
//Buffer per tile, host allocation
Asplit[i] = (double *)_mm_malloc(mem_size_tile, 64);
//Buffer creation and allocation on the card
hStreams_app_create_buf((void *)Asplit[i], mem_size_tile);
}
double tbegin, tend;
int iter;
int info;
//Events are needed for various synchronizations to enforce
//data dependence between and among data-transfers/computes
HSTR_EVENT *eventcpyto = new HSTR_EVENT[tot_tiles];
HSTR_EVENT *eventcpyfr = new HSTR_EVENT[tot_tiles];
HSTR_EVENT *eventpotrf = new HSTR_EVENT[tot_tiles];
HSTR_EVENT *eventtrsm = new HSTR_EVENT[tot_tiles];
HSTR_EVENT *eventsyrk = new HSTR_EVENT[tot_tiles];
HSTR_EVENT *eventgemm = new HSTR_EVENT[tot_tiles];
//for timing tiled cholesky
double *totTimeMsec = new double [niter];
//for timing MKL cholesky
double *totTimeMsecMKL = new double [niter];
HSTR_RESULT res;
//these queues are used for queining up compute on the card and
//data transfers to/from the card.
//q_trsm for dtrsm, q_potrf for dportf, q_syrk_gemm for both dsyrk and dgemm.
//The queues are incremented by one for every compute queued and wrap
//around the max_log_str available. This ensures good load-balancing.
int q_trsm, q_potrf, q_syrk_gemm;
CBLAS_ORDER blasLay;
int lapackLay;
if (layRow) {
blasLay = CblasRowMajor;
lapackLay = LAPACK_ROW_MAJOR;
} else {
blasLay = CblasColMajor;
lapackLay = LAPACK_COL_MAJOR;
}
for (iter = 0; iter < niter; ++iter) {
//copying matrices into separate variables for tiled cholesky (A_my)
//and MKL cholesky (A_MKL)
//The output overwrites the matrices and hence the need to copy
//for each iteration
copy_mat(mat, A_my, mat_size);
copy_mat(mat, A_MKL, mat_size);
unsigned int m, n, k;
printf("\nIteration = %d\n", iter);
split_into_blocks(A_my, Asplit, num_tiles, tile_size, mat_size, layRow);
//beginning of timing
tbegin = dtimeGet();
//splitting time included in the timing
//This splits the input matrix into tiles (or blocks)
//split_into_blocks(A_my, Asplit, num_tiles, tile_size, mat_size, layRow);
q_potrf = 0;
for (k = 0; k < num_tiles; ++k) {
//POTRF
//dpotrf is executed on the host on the diagonal tile
//the results are then sent to the card
if (k > 0) {
hStreams_app_event_wait(1, &eventsyrk[k * num_tiles + k]);
if (loc_verbose > 0)
printf("Sending tile[%d][%d] to host in queue %d\n",
k, k, (int)(q_potrf % max_log_str)) ;
hStreams_app_xfer_memory(Asplit[k * num_tiles + k],
Asplit[k * num_tiles + k], mem_size_tile,
(int)(q_potrf % max_log_str), HSTR_SINK_TO_SRC,
&eventcpyfr[k * num_tiles + k]);
hStreams_app_event_wait(1, &eventcpyfr[k * num_tiles + k]);
}
if (loc_verbose > 0) {
printf("Executing potrf on host for tile[%d][%d]\n", k, k);
}
info = LAPACKE_dpotrf(lapackLay, 'L', tile_size,
Asplit[k * num_tiles + k], tile_size);
if (k < num_tiles - 1) {
if (loc_verbose > 0)
printf("Sending tile[%d][%d] to card in queue %d\n",
k, k, (int)(q_potrf % max_log_str));
hStreams_app_xfer_memory(Asplit[k * num_tiles + k],
Asplit[k * num_tiles + k], mem_size_tile,
(int)(q_potrf % max_log_str), HSTR_SRC_TO_SINK,
&eventcpyto[k * num_tiles + k]);
}
q_potrf++;
q_trsm = 0;
for (m = k + 1; m < num_tiles; ++m) {
if (k == 0) {
if (loc_verbose > 0)
printf("Sending tile[%d][%d] to card in queue %d\n",
m, k, (int)(q_trsm % max_log_str));
hStreams_app_xfer_memory(Asplit[m * num_tiles + k],
Asplit[m * num_tiles + k], mem_size_tile,
(int)(q_trsm % max_log_str), HSTR_SRC_TO_SINK,
&eventcpyto[m * num_tiles + k]);
}
//DTRSM
hStreams_app_event_wait(1, &eventcpyto[k * num_tiles + k]);
if (k > 0) {
hStreams_app_event_wait(1, &eventgemm[m * num_tiles + k]);
}
//dtrsm is executed on the card
if (loc_verbose > 0)
printf("Executing trsm for tile[%d][%d] on card in queue %d\n",
m, k, (int)(q_trsm % max_log_str));
res = hStreams_custom_dtrsm(blasLay, CblasRight, CblasLower,
CblasTrans, CblasNonUnit, tile_size, tile_size, 1.0,
Asplit[k * num_tiles + k], tile_size, Asplit[m * num_tiles + k],
tile_size, (int)(q_trsm % max_log_str),
&eventtrsm[m * num_tiles + k]);
if (loc_verbose > 0)
printf("Sending tile[%d][%d] back to host in queue %d\n",
m, k, (int)(q_trsm % max_log_str));
hStreams_app_xfer_memory(Asplit[m * num_tiles + k],
Asplit[m * num_tiles + k], mem_size_tile,
(int)(q_trsm % max_log_str), HSTR_SINK_TO_SRC,
&eventcpyfr[m * num_tiles + k]);
q_trsm++;
}
q_syrk_gemm = 0;
for (n = k + 1; n < num_tiles; ++n) {
if (k == 0) {
if (loc_verbose > 0)
printf("Sending tile[%d][%d] to card in queue %d\n",
n, n, (int)(q_syrk_gemm % max_log_str));
hStreams_app_xfer_memory(Asplit[n * num_tiles + n],
Asplit[n * num_tiles + n], mem_size_tile,
(int)(q_syrk_gemm % max_log_str), HSTR_SRC_TO_SINK,
&eventcpyto[n * num_tiles + n]);
}
//DSYRK
hStreams_app_event_wait(1, &eventtrsm[n * num_tiles + k]);
if (k > 0) {
hStreams_app_event_wait(1, &eventsyrk[n * num_tiles + n]);
}
//dsyrk is executed on the card
if (loc_verbose > 0)
printf("Executing syrk for tile[%d][%d] on card in queue %d\n",
n, n, (int)(q_syrk_gemm % max_log_str));
res = hStreams_custom_dsyrk(blasLay, CblasLower, CblasNoTrans,
tile_size, tile_size, -1.0, Asplit[n * num_tiles + k],
tile_size, 1.0, Asplit[n * num_tiles + n], tile_size,
(int)(q_syrk_gemm % max_log_str), &eventsyrk[n * num_tiles + n]);
q_syrk_gemm++;
for (m = n + 1; m < num_tiles; ++m) {
if (k == 0) {
if (loc_verbose > 0)
printf("Sending tile[%d][%d] to card in queue %d\n",
m, n, (int)(q_syrk_gemm % max_log_str));
hStreams_app_xfer_memory(Asplit[m * num_tiles + n],
Asplit[m * num_tiles + n], mem_size_tile,
(int)(q_syrk_gemm % max_log_str),
HSTR_SRC_TO_SINK,
&eventcpyto[m * num_tiles + n]);
}
//DGEMM
hStreams_app_event_wait(1, &eventtrsm[m * num_tiles + k]);
hStreams_app_event_wait(1, &eventtrsm[n * num_tiles + k]);
if (k > 0) {
hStreams_app_event_wait(1, &eventgemm[m * num_tiles + n]);
}
//dgemm is executed on the card
if (loc_verbose > 0)
printf("Executing gemm for tile[%d][%d] on card in queue %d\n",
m, n, (int)(q_syrk_gemm % max_log_str));
res = hStreams_app_dgemm(blasLay, CblasNoTrans, CblasTrans,
tile_size, tile_size, tile_size, -1.0, Asplit[m * num_tiles + k],
tile_size, Asplit[n * num_tiles + k], tile_size, 1.0,
Asplit[m * num_tiles + n], tile_size,
(int)(q_syrk_gemm % max_log_str), &eventgemm[m * num_tiles + n]);
q_syrk_gemm++;
}
}
}
//syncrhonizing all the streams
hStreams_app_thread_sync();
//end of timing
tend = dtimeGet();
totTimeMsec[iter] = 1e3 * (tend - tbegin);
printf("time for Tiled hstreams Cholesky for iteration %d = %.2f msec\n",
iter, totTimeMsec[iter]);
//assembling of tiles back into full matrix
assemble(Asplit, A_my, num_tiles, tile_size, mat_size, layRow);
//calling mkl cholesky for verification and timing comparison.
//Using auto-offload feature of MKL
#ifndef _WIN32
//FIXME: calling this function causes a crash on Windows
mkl_mic_enable();
#endif
tbegin = dtimeGet();
//calling MKL dpotrf on the full matrix
info = LAPACKE_dpotrf(lapackLay, 'L', mat_size, A_MKL, mat_size);
tend = dtimeGet();
totTimeMsecMKL[iter] = 1e3 * (tend - tbegin);
printf("time for MKL Cholesky (AO) for iteration %d = %.2f msec\n",
iter, totTimeMsecMKL[iter]);
if (info != 0) {
printf("error with dpotrf\n");
}
mkl_mic_disable();
if (verify == 1) {
bool result = verify_results(A_my, A_MKL, mat_size * mat_size);
if (result == true) {
printf("Tiled Cholesky successful\n");
} else {
printf("Tiled Chloesky failed\n");
}
}
}
double meanTimeMsec, stdDevMsec;
double meanTimeMsecMKL, stdDevMsecMKL;
mean_and_stdev(totTimeMsec, meanTimeMsec, stdDevMsec, niter);
mean_and_stdev(totTimeMsecMKL, meanTimeMsecMKL, stdDevMsecMKL, niter);
double gflops = pow(mat_size, 3.0) / 3.0 * 1e-9;
printf("\nMatrix size = %d\n", mat_size);
printf("Tiled hStreams Cholesky: for %d iterations (ignoring first),\n"
"mean Time = %.2f msec, stdDev Time = %.2f msec,\n"
"Mean Gflops (using mean Time) = %.2f\n",
niter - 1, meanTimeMsec, stdDevMsec, gflops / (meanTimeMsec * 1e-3));
printf("\nMKL AO Cholesky: for %d iterations (ignoring first),\n"
"mean Time = %.2f msec, stdDev Time = %.2f msec,\n"
"Mean Gflops (using meanTime) = %.2f\n\n",
niter - 1, meanTimeMsecMKL, stdDevMsecMKL, gflops / (meanTimeMsecMKL * 1e-3));
//Free
free(A_my);
free(A_MKL);
for (int i = 0; i < tot_tiles; ++i) {
_mm_free(Asplit[i]);
}
delete [] Asplit;
delete [] eventcpyto;
delete [] eventcpyfr;
delete [] eventpotrf;
delete [] eventtrsm;
delete [] eventsyrk;
delete [] eventgemm;
delete [] totTimeMsec;
delete [] totTimeMsecMKL;
}