int schwartz_screening(PFock_t pfock, BasisSet_t basis)
{
int myrank;
MPI_Comm_rank(MPI_COMM_WORLD, &myrank);
// create shell pairs values
ERD_t erd;
int nthreads = omp_get_max_threads();
CInt_createERD(basis, &erd, nthreads);
int nshells = pfock->nshells;
// create global arrays for screening
int dims[2];
int nprow = pfock->nprow;
int npcol = pfock->npcol;
int block[2];
int map[nprow + npcol];
for (int i = 0; i < nprow; i++) {
map[i] = pfock->rowptr_sh[i];
}
for (int i = 0; i < npcol; i++) {
map[i + nprow] = pfock->colptr_sh[i];
}
block[0] = nprow;
block[1] = npcol;
dims[0] = nshells;
dims[1] = nshells;
#if defined(USE_ELEMENTAL)
ElGlobalArraysCreateIrreg_d( eldga, 2, dims, "array Screening", block, map, &pfock->ga_screening);
#else
pfock->ga_screening =
NGA_Create_irreg(C_DBL, 2, dims, "array Screening", block, map);
if (0 == pfock->ga_screening) {
return -1;
}
#endif
// compute the max shell value
double *sq_values = (double *)PFOCK_MALLOC(sizeof(double) *
pfock->nshells_row * pfock->nshells_col);
if (NULL == sq_values) {
return -1;
}
int startM = pfock->sshell_row;
int startN = pfock->sshell_col;
int endM = pfock->eshell_row;
int endN = pfock->eshell_col;
double maxtmp = 0.0;
#pragma omp parallel
{
int tid = omp_get_thread_num();
#pragma omp for reduction(max:maxtmp)
for (int M = startM; M <= endM; M++) {
int dimM = CInt_getShellDim(basis, M);
for (int N = startN; N <= endN; N++) {
int dimN = CInt_getShellDim(basis, N);
int nints;
double *integrals;
CInt_computeShellQuartet(basis, erd, tid, M, N, M, N,
&integrals, &nints);
double maxvalue = 0.0;
if (nints != 0) {
for (int iM = 0; iM < dimM; iM++) {
for (int iN = 0; iN < dimN; iN++) {
int index =
iM * (dimN*dimM*dimN+dimN) + iN * (dimM*dimN+1);
if (maxvalue < fabs(integrals[index])) {
maxvalue = fabs(integrals[index]);
}
}
}
}
sq_values[(M - startM) * (endN - startN + 1) + (N - startN)]
= maxvalue;
if (maxvalue > maxtmp) {
maxtmp = maxvalue;
}
}
}
}
int lo[2];
int hi[2];
lo[0] = startM;
lo[1] = startN;
hi[0] = endM;
hi[1] = endN;
int ld = endN - startN + 1;
#if defined(USE_ELEMENTAL)
ElGlobalArraysPut_d( eldga, pfock->ga_screening, lo, hi,
sq_values, &ld );
#else
NGA_Put(pfock->ga_screening, lo, hi, sq_values, &ld);
#endif
// max value
MPI_Allreduce(&maxtmp, &(pfock->maxvalue), 1,
MPI_DOUBLE, MPI_MAX, MPI_COMM_WORLD);
CInt_destroyERD(erd);
PFOCK_FREE(sq_values);
// init shellptr
sq_values = (double *)PFOCK_MALLOC(sizeof(double) * nshells);
if (NULL == sq_values) {
return -1;
}
int nnz = 0;
double eta = pfock->tolscr2 / pfock->maxvalue;
pfock->shellptr = (int *)PFOCK_MALLOC(sizeof(int) * (nshells + 1));
pfock->mem_cpu += 1.0 * sizeof(int) * (nshells + 1);
if (NULL == pfock->shellptr) {
return -1;
}
memset(pfock->shellptr, 0, sizeof(int) * (nshells + 1));
for (int M = 0; M < nshells; M++) {
pfock->shellptr[M] = nnz;
lo[0] = M;
hi[0] = M;
lo[1] = 0;
hi[1] = nshells - 1;
ld = nshells;
#if defined(USE_ELEMENTAL)
ElGlobalArraysGet_d( eldga, pfock->ga_screening, lo, hi,
sq_values, &ld );
#else
NGA_Get(pfock->ga_screening, lo, hi, sq_values, &ld);
#endif
for (int N = 0; N < nshells; N++) {
double maxvalue = sq_values[N];
if (maxvalue > eta) {
if (M > N && (M + N) % 2 == 1 || M < N && (M + N) % 2 == 0) {
continue;
} else {
nnz++;
}
}
}
pfock->shellptr[M + 1] = nnz;
}
pfock->nnz = nnz;
double maxvalue;
pfock->shellvalue = (double *)PFOCK_MALLOC(sizeof(double) * nnz);
pfock->shellid = (int *)PFOCK_MALLOC(sizeof(int) * nnz);
pfock->shellrid = (int *)PFOCK_MALLOC(sizeof(int) * nnz);
pfock->mem_cpu += 1.0 * sizeof(double) * nnz + 2.0 * sizeof(int) * nnz;
nshells = pfock->nshells;
if (pfock->shellvalue == NULL ||
pfock->shellid == NULL ||
pfock->shellrid == NULL) {
return -1;
}
nnz = 0;
for (int A = 0; A < nshells; A++) {
pfock->shellptr[A] = nnz;
lo[0] = A;
hi[0] = A;
lo[1] = 0;
hi[1] = nshells - 1;
ld = nshells;
#if defined(USE_ELEMENTAL)
ElGlobalArraysGet_d( eldga, pfock->ga_screening, lo, hi,
sq_values, &ld );
#else
NGA_Get(pfock->ga_screening, lo, hi, sq_values, &ld);
#endif
for (int B = 0; B < nshells; B++) {
maxvalue = sq_values[B];
if (maxvalue > eta) {
if (A > B && (A + B) % 2 == 1 || A < B && (A + B) % 2 == 0)
continue;
if (A == B) {
pfock->shellvalue[nnz] = maxvalue;
} else {
pfock->shellvalue[nnz] = -maxvalue;
}
pfock->shellid[nnz] = B;
pfock->shellrid[nnz] = A;
nnz++;
}
}
}
PFOCK_FREE(sq_values);
#if defined(USE_ELEMENTAL)
ElGlobalArraysDestroy_d( eldga, pfock->ga_screening );
#else
GA_Destroy(pfock->ga_screening);
#endif
return 0;
}
int main (int argc, char **argv)
{
if (argc != 4) {
printf ("Usage: %s <basisset> <xyz>\n", argv[0]);
return -1;
}
const uint64_t freq = get_cpu_frequency();
const int nthreads = atoi(argv[3]);
/*
#ifdef _OPENMP
omp_set_num_threads(nthreads);
#else
assert(nthreads == 1);
#endif
*/
// load basis set
BasisSet_t basis;
CInt_createBasisSet(&basis);
CInt_loadBasisSet(basis, argv[1], argv[2]);
printf("Molecule info:\n");
printf(" #Atoms\t= %d\n", CInt_getNumAtoms(basis));
printf(" #Shells\t= %d\n", CInt_getNumShells(basis));
printf(" #Funcs\t= %d\n", CInt_getNumFuncs(basis));
printf(" #OccOrb\t= %d\n", CInt_getNumOccOrb(basis));
ERD_t erd;
CInt_createERD(basis, &erd, nthreads);
printf("Computing Lazy Evaluation Cholesky of ERIs\n");
// reset profiler
// erd_reset_profile();
int n = CInt_getNumFuncs(basis);
int n2 = n * n;
int n3 = n2 * n;
int n4 = n3 * n;
double* G_ERI;
double tol = 1e-6;
int max_rank = n2;
//int max_rank = (1-floor(log10(tol)))*n;
int rank;
const uint64_t start_clock = __rdtsc();
cholERI(basis, erd, &G_ERI, tol, max_rank, &rank);
const uint64_t end_clock = __rdtsc();
const uint64_t total_ticks = end_clock - start_clock;
const double timepass = ((double) total_ticks) / freq;
printf("Done\n");
printf("Total GigaTicks: %.3lf, freq = %.3lf GHz\n", (double) (total_ticks) * 1.0e-9, (double)freq/1.0e9);
printf("Total time: %.4lf secs\n", timepass);
printf("n: %d, rank: %d, 7n: %d, n2: %d\n",n,rank,7*n,n2);
double* diag = (double*) malloc(n2*sizeof(double));
computeDiag(basis, erd, diag);
for (int i = 0; i < n2; i++) {
double aii = 0;
for (int j = 0; j < rank; j++) {
aii += G_ERI[i+j*n2] * G_ERI[i+j*n2];
}
double abserror2 = (diag[i] - aii)*(diag[i] - aii);
if (abserror2 > tol)
printf("i=%d, truth=%1.2e, approx=%1.2e, error: %1.2e\n", i, diag[i], aii, abserror2);
}
free(diag);
printf("Testing accuracy for each shell quartet\n");
double chol_time_total = 0;
double CInt_time_total = 0;
int nshell = CInt_getNumShells(basis);
int shellIndexM, shellIndexN, shellIndexP, shellIndexQ;
int correct = 1;
for (shellIndexM = 0; shellIndexM < nshell; shellIndexM++) {
for (shellIndexN = 0; shellIndexN < nshell; shellIndexN++) {
for (shellIndexP = 0; shellIndexP < nshell; shellIndexP++) {
for (shellIndexQ = 0; shellIndexQ < nshell; shellIndexQ++) {
int dimM = CInt_getShellDim (basis, shellIndexM);
int dimN = CInt_getShellDim (basis, shellIndexN);
int dimP = CInt_getShellDim (basis, shellIndexP);
int dimQ = CInt_getShellDim (basis, shellIndexQ);
// Compute shell with Cholesky
double *cholintegrals;
int cholnints;
const uint64_t chol_start = __rdtsc();
cholComputeShellQuartet(basis, G_ERI, rank, shellIndexM, shellIndexN, shellIndexP, shellIndexQ, &cholintegrals, &cholnints);
const uint64_t chol_end = __rdtsc();
chol_time_total += ((double) chol_end - chol_start) / freq;
// Compute the same shell quartet with CInt
double *integrals;
int nints;
const uint64_t CInt_start = __rdtsc();
CInt_computeShellQuartet(basis, erd, 0, shellIndexM, shellIndexN, shellIndexP, shellIndexQ, &integrals, &nints);
const uint64_t CInt_end = __rdtsc();
CInt_time_total += ((double) CInt_end - CInt_start) / freq;
// Compare each integral individually
for (int iM = 0; iM < dimM; iM++) {
for (int iN = 0; iN < dimN; iN++) {
for (int iP = 0; iP < dimP; iP++) {
for (int iQ = 0; iQ < dimQ; iQ++) {
int idx = iM + dimM * (iN + dimN * (iP + dimP *(iQ)));
double abserror2 = (integrals[idx] - cholintegrals[idx]);
abserror2 = abserror2*abserror2;
if (abserror2 > tol) {
correct = 0;
printf("Integral does not satisfy error tolerance: error = %1.2e\n",abserror2);
}
}
}
}
}
free(cholintegrals);
}
}
}
}
if (correct) {
printf("All integrals in all shell quartets satisfy error tolerance\n");
} else {
printf("Some integrals did not satisfy error tolerance\n");
}
printf("Total time to eval shells from Cholesky factor: %.4lf secs\n", chol_time_total);
printf("Total time to eval shells with CInt: %.4lf secs\n", CInt_time_total);
printf("Total time to compute Cholesky factor and eval shells from Cholesky factor: %.4lf secs\n", timepass+chol_time_total);
printf("Computing Structured Lazy Evaluation Cholesky of ERIs\n");
double* G_structERI;
max_rank = (n*(n+1))/2;
const uint64_t struct_start_clock = __rdtsc();
structcholERI(basis, erd, &G_structERI, tol, max_rank, &rank);
const uint64_t struct_end_clock = __rdtsc();
const uint64_t struct_total_ticks = struct_end_clock - struct_start_clock;
const double struct_timepass = ((double) struct_total_ticks) / freq;
printf("Done\n");
printf("Total GigaTicks: %.3lf, freq = %.3lf GHz\n", (double) (struct_total_ticks) * 1.0e-9, (double)freq/1.0e9);
printf("Total time: %.4lf secs\n", struct_timepass);
double* structdiag = (double*) malloc(max_rank*sizeof(double));
computeStructDiag(basis, erd, structdiag);
for (int i = 0; i < max_rank; i++) {
double aii = 0;
for (int j = 0; j < rank; j++) {
aii += G_structERI[i+j*max_rank] * G_structERI[i+j*max_rank];
}
double abserror2 = (structdiag[i] - aii)*(structdiag[i] - aii);
if (abserror2 > tol)
printf("i=%d, truth=%1.2e, approx=%1.2e, error: %1.2e\n", i, structdiag[i], aii, abserror2);
}
free(structdiag);
printf("Testing accuracy for each shell quartet\n");
double struct_chol_time_total = 0;
CInt_time_total = 0;
correct = 1;
for (shellIndexM = 0; shellIndexM < nshell; shellIndexM++) {
for (shellIndexN = 0; shellIndexN < nshell; shellIndexN++) {
for (shellIndexP = 0; shellIndexP < nshell; shellIndexP++) {
for (shellIndexQ = 0; shellIndexQ < nshell; shellIndexQ++) {
int dimM = CInt_getShellDim (basis, shellIndexM);
int dimN = CInt_getShellDim (basis, shellIndexN);
int dimP = CInt_getShellDim (basis, shellIndexP);
int dimQ = CInt_getShellDim (basis, shellIndexQ);
// Compute shell with structured Cholesky
double *cholintegrals;
int cholnints;
const uint64_t struct_chol_start = __rdtsc();
structcholComputeShellQuartet(basis, G_structERI, rank, shellIndexM, shellIndexN, shellIndexP, shellIndexQ, &cholintegrals, &cholnints);
const uint64_t struct_chol_end = __rdtsc();
struct_chol_time_total += ((double) struct_chol_end - struct_chol_start) / freq;
// Compute the same shell quartet with CInt
double *integrals;
int nints;
const uint64_t CInt_start = __rdtsc();
CInt_computeShellQuartet(basis, erd, 0, shellIndexM, shellIndexN, shellIndexP, shellIndexQ, &integrals, &nints);
const uint64_t CInt_end = __rdtsc();
CInt_time_total += ((double) CInt_end - CInt_start) / freq;
// Compare each integral individually
for (int iM = 0; iM < dimM; iM++) {
for (int iN = 0; iN < dimN; iN++) {
for (int iP = 0; iP < dimP; iP++) {
for (int iQ = 0; iQ < dimQ; iQ++) {
int idx = iM + dimM * (iN + dimN * (iP + dimP *(iQ)));
double abserror2 = (integrals[idx] - cholintegrals[idx]);
abserror2 = abserror2*abserror2;
if (abserror2 > tol) {
correct = 0;
printf("Integral does not satisfy error tolerance: error = %1.2e\n",abserror2);
}
}
}
}
}
free(cholintegrals);
}
}
}
}
if (correct) {
printf("All integrals in all shell quartets satisfy error tolerance\n");
} else {
printf("Some integrals did not satisfy error tolerance\n");
}
printf("Total time to eval shells from structured Cholesky factor: %.4lf secs\n", struct_chol_time_total);
printf("Total time to eval shells with CInt: %.4lf secs\n", CInt_time_total);
printf("Total time to compute Cholesky factor and eval shells from Cholesky factor: %.4lf secs\n", struct_timepass+struct_chol_time_total);
free(G_structERI);
free(G_ERI);
return 0;
}