int main()
{
int i, j, c, t;
for (scanf("%d", &t); t-- > 0;) {
for (i = 1, n = 32; i <= n; i++) {
for (j = 1; j <= n;) {
c = getchar();
if (c == '0')
a[i][j++] = 1;
else if (c == '1')
a[i][j++] = 0;
else if (c == '\n' && i == 1 && j > 1)
n = j - 1;
else if (c == EOF)
return 0;
}
}
printf("%d\n", zeroes());
if (t != 0) printf("\n");
}
return 0;
}
void setZeroes(vector<vector<int> > &matrix) {
int n = matrix.size();
if(n < 1) return;
int m = matrix[0].size();
vector<int> zeroes(m + n, -1);
int count = 0;
for(int i = 0; i < n; ++i){
for(int j = 0; j < m; ++j){
if(matrix[i][j] == 0){
if(count >= m + n) break;
rec[count++] = i * m + j;
}
}
}
for(int i = 0; i < count; ++i){
int x = rec[i] / m;
int y = rec[i] % m;
for(int j = 0; j < m; ++j){
matrix[x][j] = 0;
}
for(int j = 0; j < n; ++j){
matrix[j][y] = 0;
}
}
}
void
GBitmap::init(int arows, int acolumns, int aborder)
{
size_t np = arows * (acolumns + aborder) + aborder;
if (arows != (unsigned short) arows ||
acolumns != (unsigned short) acolumns ||
acolumns + aborder != (unsigned short)(acolumns + aborder) ||
(arows > 0 && (np-aborder)/(size_t)arows!=(size_t)(acolumns+aborder)) )
G_THROW("GBitmap: image size exceeds maximum (corrupted file?)");
GMonitorLock lock(monitor());
destroy();
grays = 2;
nrows = arows;
ncolumns = acolumns;
border = aborder;
bytes_per_row = ncolumns + border;
int npixels = nrows * bytes_per_row + border;
gzerobuffer=zeroes(bytes_per_row + border);
if (npixels > 0)
{
gbytes_data.resize(npixels);
gbytes_data.clear();
bytes = bytes_data;
}
}
void test_vector_magnitudes() {
printf("Testing vector magnitudes...\n");
TestStats stats = test_stats();
Vector test_vector;
double computed;
test_vector = zeroes(0);
computed = vector_mag(&test_vector);
assert_double(&stats, 0, computed,
"Zero element vectors should have zero magnitude");
int i;
for (i = -1; i < 3; i++) {
test_vector = linear(1, i, 0);
computed = vector_mag(&test_vector);
assert_double(&stats, abs(i), computed,
"One element vectors must have magnitude equal to their element.");
}
double quad_a[4] = {-.4, 0, .6, 1.2};
Vector quad = { 4, &quad_a[0] };
computed = vector_mag(&quad);
assert_double(&stats, 1.4, computed,
"Incorrectly computed vector magnitude");
print_state(&stats);
}
void SpeciesInfo::augmentDensityGridGrad(const ScalarFieldArray& E_n, std::vector<vector3<> >* forces)
{ static StopWatch watch("augmentDensityGridGrad"); watch.start();
augmentDensityGrid_COMMON_INIT
if(!nAug) augmentDensityInit();
const GridInfo &gInfo = e->gInfo;
double dGinv = 1./gInfo.dGradial;
matrix E_nAugRadial = zeroes(nCoeffHlf, e->eInfo.nDensities * atpos.size() * Nlm);
double* E_nAugRadialData = (double*)E_nAugRadial.dataPref();
matrix nAugRadial; const double* nAugRadialData=0;
if(forces)
{ matrix nAugTot = nAug; nAugTot.allReduce(MPIUtil::ReduceSum);
nAugRadial = QradialMat * nAugTot;
nAugRadialData = (const double*)nAugRadial.dataPref();
}
VectorFieldTilde E_atpos; if(forces) nullToZero(E_atpos, gInfo);
for(unsigned s=0; s<E_n.size(); s++)
{ ScalarFieldTilde ccE_n = Idag(E_n[s]);
for(unsigned atom=0; atom<atpos.size(); atom++)
{ int atomOffs = nCoeff * Nlm * (atom + atpos.size()*s);
if(forces) initZero(E_atpos);
callPref(nAugmentGrad)(Nlm, gInfo.S, gInfo.G, nCoeff, dGinv, forces? (nAugRadialData+atomOffs) :0, atpos[atom],
ccE_n->dataPref(), E_nAugRadialData+atomOffs, forces ? E_atpos.dataPref() : vector3<complex*>(), nagIndex, nagIndexPtr);
if(forces) for(int k=0; k<3; k++) (*forces)[atom][k] -= sum(E_atpos[k]);
}
}
E_nAug = dagger(QradialMat) * E_nAugRadial; //propagate from spline coeffs to radial functions
E_nAug.allReduce(MPIUtil::ReduceSum);
watch.stop();
}
void Field_solver::modify_equation_near_object_boundaries( Mat *A,
int nx, int ny, int nz,
double dx, double dy, double dz,
Inner_region &inner_region )
{
PetscErrorCode ierr;
int max_possible_neighbours = 6; // in 3d case; todo: make max_possible_nbr a property of Node_reference
std::vector<PetscScalar> zeroes( max_possible_neighbours, 0.0 );
for( auto &node : inner_region.near_boundary_nodes_not_at_domain_edge ){
PetscInt modify_single_row = 1;
PetscInt row_to_modify = node_global_index_in_matrix( node, nx, ny, nz );
std::vector<PetscInt> cols_to_modify =
adjacent_nodes_not_at_domain_edge_and_inside_inner_region( node, inner_region,
nx, ny, nz, dx, dy, dz );
PetscInt n_of_cols_to_modify = cols_to_modify.size();
if( n_of_cols_to_modify != 0 ){
PetscInt *col_indices = &cols_to_modify[0];
ierr = MatSetValues( *A,
modify_single_row, &row_to_modify,
n_of_cols_to_modify, col_indices,
&zeroes[0], INSERT_VALUES );
CHKERRXX( ierr );
}
}
ierr = MatAssemblyBegin( *A, MAT_FINAL_ASSEMBLY ); CHKERRXX( ierr );
ierr = MatAssemblyEnd( *A, MAT_FINAL_ASSEMBLY ); CHKERRXX( ierr );
}
int main() {
int N;
long n;
scanf("%d", &N);
for (int i = 0; i < N; i++) {
scanf("%ld", &n);
printf("%d\n", zeroes(n));
}
}
/**
* Default constructor creates an empty BezierRow, i.e. all entries are the zero vector.
*/
BezierRow::BezierRow()
{
//std::cout << "-->BezierRow::BezierRow()" << std::endl;
glm::vec3 zeroes(0.0f);
for (int i = 0; i < 4; ++i) this->controlpoints[i] = zeroes;
//std::cout << "<--BezierRow::BezierRow()" << std::endl;
}
/**
* Multiplication operator, right-multiplies a geometry vector by an ordinary matrix (a basis matrix).
* This can be used to right-multiply a Bezier geometry vector by an ordinary matrix (a basis matrix).
* \param geometryvector - The BezierVec4 that should be multiplied.
* \param matrix - The ordinary matrix to be right-multiplied (basis matrix) by the geometry vector.
* \return The product geometryvector * matrix.
*/
BezierVec4 operator*(BezierVec4 const& geometryvector, glm::mat4x4 const& matrix)
{
glm::vec3 zeroes(0.0f);
BezierVec4 result(zeroes, zeroes, zeroes, zeroes);
for (int c = 0; c < 4; c++) {
glm::vec4 column(glm::column(matrix, c));
for (int i = 0; i < 4; ++i) {
result[c + 1] += geometryvector[i + 1] * column[i];
}
}
return result;
}
void test_vector_dot() {
printf("Testing vector dot product...\n");
TestStats stats = test_stats();
double computed;
Vector neg_vector = zeroes(0);
neg_vector.len = -1;
Vector empty_vector = zeroes(0);
Vector zero_vector = zeroes(5);
Vector some_vector = linear(5, -1.5, 1);
assert_isnan(&stats, vector_dot(&neg_vector, &empty_vector),
"Negative length vectors must return nan");
assert_isnan(&stats, vector_dot(&some_vector, &empty_vector),
"Differing length vectors must return nan");
assert_double(&stats, 0, vector_dot(&empty_vector, &empty_vector),
"Zero length vectors must have 0 value");
assert_double(&stats, 0, vector_dot(&zero_vector, &some_vector),
"Zero vectors must yield 0 dot product");
assert_double(&stats, 11.25, vector_dot(&some_vector, &some_vector),
"Dot product must actually work.");
print_state(&stats);
}
ColumnBundleTransform::ColumnBundleTransform(const vector3<>& kC, const Basis& basisC, const vector3<>& kD,
const ColumnBundleTransform::BasisWrapper& basisDwrapper, int nSpinor, const matrix3<int>& sym, int invert, const matrix3<int>& super)
: kC(kC), basisC(basisC), kD(kD), basisD(basisDwrapper.basis), nSpinor(nSpinor), invert(invert)
{
//Check k-point transformation and determine offset
const matrix3<>& metricC = basisC.gInfo->RTR;
myassert(nrm2(metricC - (~sym)*metricC*sym) < symmThreshold * nrm2(metricC)); //check symmetry
myassert(abs(invert) == 1); //check inversion
myassert(nrm2(basisC.gInfo->R * super - basisD.gInfo->R) < symmThreshold * nrm2(basisD.gInfo->R)); //check supercell
matrix3<int> affine = sym * invert * super; //net affine transformation
double offsetErr;
vector3<int> offset = round(kC * affine - kD, &offsetErr);
myassert(offsetErr < symmThreshold);
//Initialize index map:
index.resize(basisC.nbasis);
for(size_t n=0; n<basisC.nbasis; n++)
{ const vector3<int>& iG_C = basisC.iGarr[n]; //C recip lattice coords
vector3<int> iG_D = iG_C * affine + offset; //corresponding D recip lattice coords
index[n] = basisDwrapper.table[dot(basisDwrapper.pitch, iG_D + basisDwrapper.iGbox)]; //use lookup table to get D index
}
myassert(*std::min_element(index.begin(), index.end()) >= 0); //make sure all entries were found
#ifdef GPU_ENABLED
cudaMalloc(&indexGpu, sizeof(int)*index.size()); gpuErrorCheck();
cudaMemcpy(indexGpu, index.data(), sizeof(int)*index.size(), cudaMemcpyHostToDevice); gpuErrorCheck();
indexPref = indexGpu;
#else
indexPref = index.data();
#endif
//Initialize spinor transformation:
switch(nSpinor)
{ case 1: spinorRot = eye(1); break;
case 2:
{ spinorRot = Symmetries::getSpinorRotation(~(basisC.gInfo->R * sym * inv(basisC.gInfo->R)));
if(invert<0)
{ matrix sInvert = zeroes(2,2);
sInvert.set(0,1, 1.);
sInvert.set(1,0, -1.);
spinorRot = conj(sInvert * spinorRot);
}
break;
}
default: myassert(!"Invalid value for nSpinor");
}
}
void
GBitmap::init(int arows, int acolumns, int aborder)
{
GMonitorLock lock(monitor());
destroy();
grays = 2;
nrows = arows;
ncolumns = acolumns;
border = aborder;
bytes_per_row = ncolumns + border;
int npixels = nrows * bytes_per_row + border;
gzerobuffer=zeroes(bytes_per_row + border);
if (npixels > 0)
{
gbytes_data.resize(npixels);
gbytes_data.clear();
bytes = bytes_data;
}
}
string smallMultiplyWithDigits(int small, string large, int digits) {
int step = 0;
int l = large.size();
string ans;
for(int i = l - 1; i >= 0; i --) {
int temp = (large[i] - '0') * small + step;
step = temp / 10;
temp %= 10;
ans += (temp + '0');
}
while(step > 0) {
int temp = step;
step = temp / 10;
temp %= 10;
ans += (temp + '0');
}
reverse(ans.begin(), ans.end());
string zeroes(digits, '0');
return (ans.size() == 0 && ans[0] == '0')? ans: ans + zeroes;
}
void
GBitmap::minborder(int minimum)
{
if (border < minimum)
{
GMonitorLock lock(monitor());
if (border < minimum)
{
if (bytes)
{
GBitmap tmp(*this, minimum);
bytes_per_row = tmp.bytes_per_row;
tmp.gbytes_data.swap(gbytes_data);
bytes = bytes_data;
tmp.bytes = 0;
}
border = minimum;
gzerobuffer=zeroes(border + ncolumns + border);
}
}
}
void Field_solver::set_rhs_at_nodes_occupied_by_objects( Spatial_mesh &spat_mesh,
Inner_region &inner_region )
{
int nx = spat_mesh.x_n_nodes;
int ny = spat_mesh.y_n_nodes;
int nz = spat_mesh.z_n_nodes;
std::vector<PetscInt> indices_of_inner_nodes_not_at_domain_edge;
indices_of_inner_nodes_not_at_domain_edge =
list_of_nodes_global_indices_in_matrix( inner_region.inner_nodes_not_at_domain_edge, nx, ny, nz );
PetscErrorCode ierr;
PetscInt num_of_elements = indices_of_inner_nodes_not_at_domain_edge.size();
if( num_of_elements != 0 ){
PetscInt *global_indices = &indices_of_inner_nodes_not_at_domain_edge[0];
std::vector<PetscScalar> zeroes( num_of_elements, 0.0 );
ierr = VecSetValues( rhs, num_of_elements, global_indices, &zeroes[0], INSERT_VALUES );
CHKERRXX( ierr );
ierr = VecAssemblyBegin( rhs ); CHKERRXX( ierr );
ierr = VecAssemblyEnd( rhs ); CHKERRXX( ierr );
}
}
std::vector<ElectronScattering::Event> ElectronScattering::getEvents(bool chiMode, size_t ik, size_t iq, size_t& jk, matrix& nij, ElectronScattering::CEDA* ceda) const
{ static StopWatch watchI("ElectronScattering::getEventsI"), watchJ("ElectronScattering::getEventsJ"), watchCEDA("ElectronScattering::CEDA");
//Find target k-point:
const vector3<>& ki = supercell->kmesh[ik];
const vector3<> kj = ki + qmesh[iq].k;
jk = plook->find(kj);
myassert(jk != string::npos);
//Compile list of events:
int iReduced = supercell->kmeshTransform[ik].iReduced;
int jReduced = supercell->kmeshTransform[jk].iReduced;
const diagMatrix &Ei = E[iReduced], &Fi = F[iReduced];
const diagMatrix &Ej = E[jReduced], &Fj = F[jReduced];
std::vector<Event> events, eventsCEDA; events.reserve((nBands*nBands)/2);
std::vector<bool> iUsed(nBands,false), jUsed(nBands,false); //sets of i and j actually referenced
Event event;
for(event.i=0; event.i<nBands; event.i++)
for(event.j=0; event.j<nBands; event.j++)
{ event.fWeight = chiMode ? 0.5*(Fi[event.i] - Fj[event.j]) : (1. - Fi[event.i] - Fj[event.j]);
double Eii = Ei[event.i];
double Ejj = Ej[event.j];
event.Eji = Ejj - Eii;
if(!chiMode)
{ if(Eii<Emin || Eii>Emax) event.fWeight = 0.; //state out of relevant range
if(event.fWeight * (Eii-Ejj) <= 0) event.fWeight = 0; //wrong sign for energy transfer
}
bool needEvent = (fabs(event.fWeight) > fCut);
bool needCEDA = ceda && ((Fi[event.i]>fCut) || (Fj[event.j]>fCut)); //additionally need occupied-occupied combinations for CEDA
if(needEvent || needCEDA)
{ (needEvent ? events : eventsCEDA).push_back(event);
iUsed[event.i] = true;
jUsed[event.j] = true;
}
}
if(!events.size()) return events;
std::vector<Event> eventsAll = events;
eventsAll.insert(eventsAll.end(), eventsCEDA.begin(), eventsCEDA.end());
//Get wavefunctions in real space:
ColumnBundle Ci = getWfns(ik, ki), Cj = getWfns(jk, kj);
std::vector< std::vector<complexScalarField> > conjICi(nBands), ICj(nBands);
watchI.start();
for(int i=0; i<nBands; i++) if(iUsed[i])
{ conjICi[i].resize(nSpinor);
for(int s=0; s<nSpinor; s++)
conjICi[i][s] = conj(I(Ci.getColumn(i,s)));
}
for(int j=0; j<nBands; j++) if(jUsed[j])
{ ICj[j].resize(nSpinor);
for(int s=0; s<nSpinor; s++)
ICj[j][s] = I(Cj.getColumn(j,s));
}
watchI.stop();
//Initialize pair densities:
watchJ.start();
const Basis& basis_q = basisChi[iq];
int nbasis = basis_q.nbasis;
nij = zeroes(nbasis, eventsAll.size());
complex* nijData = nij.dataPref();
for(const Event& event: eventsAll)
{ complexScalarField Inij;
for(int s=0; s<nSpinor; s++)
Inij += conjICi[event.i][s] * ICj[event.j][s];
callPref(eblas_gather_zdaxpy)(nbasis, 1., basis_q.indexPref, J(Inij)->dataPref(), nijData);
nijData += nbasis;
}
watchJ.stop();
//CEDA plasma-frequency sum rule contributions:
if(ceda)
{ myassert(chiMode);
watchCEDA.start();
//Single loop quantities:
for(int i=0; i<nBands; i++)
{ ceda->Fsum[i] += Fi[i];
ceda->FEsum[i] += Fi[i] * Ei[i];
}
//Double loop quantities:
const complex* nijData = nij.data();
for(const Event& event: eventsAll)
{ //Compute elementwise nij^2:
diagMatrix nijSq(nbasis, 0.);
eblas_accumNorm(nbasis, 1., nijData, nijSq.data());
nijData += nbasis;
//Accumulate to appropriate entries of oNum and oDen:
double numWeight = 0.5*(Fi[event.i]*Ej[event.j] + Fj[event.j]*Ei[event.i]);
double denWeight = 0.5*(Fi[event.i] + Fj[event.j]);
int ijMax = std::max(event.i,event.j);
ceda->oNum[ijMax] += numWeight * nijSq;
ceda->oDen[ijMax] += denWeight * nijSq;
}
//Nonlocal corrections:
//--- get DFT+U matrices:
std::vector<matrix> Urho;
std::vector<ColumnBundle> psi;
if(e->eInfo.hasU)
e->iInfo.rhoAtom_getV(Cj, e->eVars.U_rhoAtom, psi, Urho); //get atomic orbitals at kj
for(size_t sp=0; sp<e->iInfo.species.size(); sp++)
{ //get nonlocal psp matrices and projectors:
matrix Mnl;
std::shared_ptr<ColumnBundle> V = e->iInfo.species[sp]->getV(Cj, &Mnl); //get projectors at kj
bool hasNL = Mnl.nRows();
bool hasU = e->eInfo.hasU && Urho[sp].nRows();
if(!(hasNL || hasU)) continue;
//Put projectors and orbitals in real space:
std::vector<complexScalarField> IV;
std::vector< std::vector<complexScalarField> > Ipsi;
diagMatrix diagNL, diagU; //(q+G)-diagonal contributions
if(hasNL)
{ myassert(Mnl.nRows() == V->nCols()*nSpinor);
IV.resize(V->nCols());
for(int v=0; v<V->nCols(); v++)
IV[v] = I(V->getColumn(v,0)); //NL projectors are always non-spinorial
matrix CjDagV = Cj ^ (*V);
diagNL = diag(CjDagV * Mnl * dagger(CjDagV));
}
if(hasU)
{ myassert(Urho[sp].nRows() == psi[sp].nCols());
Ipsi.resize(psi[sp].nCols());
for(int n=0; n<psi[sp].nCols(); n++)
{ Ipsi[n].resize(nSpinor);
for(int s=0; s<nSpinor; s++)
Ipsi[n][s] = I(psi[sp].getColumn(n,s)); //atomic orbitals will be spinorial in noncollinear modes
}
matrix CjDagPsi = Cj ^ psi[sp];
diagU = diag(CjDagPsi * Urho[sp] * dagger(CjDagPsi));
}
//Diagonal terms (computed at j, since those projectors have been retrieved):
for(int j=0; j<nBands; j++) if(Fj[j] > fCut)
{ double diag_j = (hasNL ? diagNL[j] : 0.) + (hasU ? diagU[j] : 0.);
ceda->FNLsum[j] -= (Fj[j] * diag_j) * eye(nbasis);
}
//Off-diagonal terms (coupling i and j):
for(int i=0; i<nBands; i++) if(Fi[i] > fCut)
{ myassert(iUsed[i]);
if(hasNL)
{ //Put pair densities with projectors in reciprocal space:
matrix niV = zeroes(nbasis, Mnl.nRows()); //anologous to nij above, but with V instead
complex* niVdata = niV.dataPref();
for(int v=0; v<V->nCols(); v++)
for(int s=0; s<nSpinor; s++)
{ callPref(eblas_gather_zdaxpy)(nbasis, 1., basis_q.indexPref, J(conjICi[i][s] * IV[v])->dataPref(), niVdata);
niVdata += nbasis;
}
//Accumulate correction:
ceda->FNLsum[i] += Fi[i] * diagouter(niV * Mnl, niV);
}
if(hasU)
{ //Put pair densities with orbitals in reciprocal space:
matrix niPsi = zeroes(nbasis, Urho[sp].nRows()); //anologous to nij above, but with psi instead
complex* niPsiData = niPsi.dataPref();
for(int n=0; n<psi[sp].nCols(); n++)
{ complexScalarField IniPsi;
for(int s=0; s<nSpinor; s++)
IniPsi += conjICi[i][s] * Ipsi[n][s];
callPref(eblas_gather_zdaxpy)(nbasis, 1., basis_q.indexPref, J(IniPsi)->dataPref(), niPsiData);
niPsiData += nbasis;
}
//Accumulate correction:
ceda->FNLsum[i] += Fi[i] * diagouter(niPsi * Urho[sp], niPsi);
}
}
}
watchCEDA.stop();
}
//Trim extra columns in matrix (which were needed only for CEDA):
if(eventsCEDA.size())
nij = nij(0,nij.nRows(), 0,events.size());
return events;
}
void ElectronScattering::dump(const Everything& everything)
{ Everything& e = (Everything&)everything; //may modify everything to save memory / optimize
this->e = &everything;
nBands = e.eInfo.nBands;
nSpinor = e.eInfo.spinorLength();
logPrintf("\n----- Electron-electron scattering Im(Sigma) -----\n"); logFlush();
//Update default parameters:
if(!eta)
{ eta = e.eInfo.kT;
if(!eta) die("eta must be specified explicitly since electronic temperature is zero.\n");
}
if(!Ecut) Ecut = e.cntrl.Ecut;
double oMin = DBL_MAX, oMax = -DBL_MAX; //occupied energy range
double uMin = DBL_MAX, uMax = -DBL_MAX; //unoccupied energy range
for(int q=e.eInfo.qStart; q<e.eInfo.qStop; q++)
for(int b=0; b<nBands; b++)
{ double E = e.eVars.Hsub_eigs[q][b];
double f = e.eVars.F[q][b];
if(f > fCut) //sufficiently occupied
{ oMin = std::min(oMin, E);
oMax = std::max(oMax, E);
}
if(f < 1.-fCut) //sufficiently unoccupied
{ uMin = std::min(uMin, E);
uMax = std::max(uMax, E);
}
}
mpiUtil->allReduce(oMin, MPIUtil::ReduceMin);
mpiUtil->allReduce(oMax, MPIUtil::ReduceMax);
mpiUtil->allReduce(uMin, MPIUtil::ReduceMin);
mpiUtil->allReduce(uMax, MPIUtil::ReduceMax);
if(!omegaMax) omegaMax = std::max(uMax-uMin, oMax-oMin);
Emin = uMin - omegaMax;
Emax = oMax + omegaMax;
//--- print selected values after fixing defaults:
logPrintf("Frequency resolution: %lg\n", eta);
logPrintf("Dielectric matrix Ecut: %lg\n", Ecut);
logPrintf("Maximum energy transfer: %lg\n", omegaMax);
//Initialize frequency grid:
diagMatrix omegaGrid, wOmega;
omegaGrid.push_back(0.);
wOmega.push_back(0.5*eta); //integration weight (halved at endpoint)
while(omegaGrid.back()<omegaMax + 10*eta) //add margin for covering enough of the Lorentzians
{ omegaGrid.push_back(omegaGrid.back() + eta);
wOmega.push_back(eta);
}
int iOmegaStart, iOmegaStop; //split dielectric computation over frequency grid
TaskDivision omegaDiv(omegaGrid.size(), mpiUtil);
omegaDiv.myRange(iOmegaStart, iOmegaStop);
logPrintf("Initialized frequency grid with resolution %lg and %d points.\n", eta, omegaGrid.nRows());
//Make necessary quantities available on all processes:
C.resize(e.eInfo.nStates);
E.resize(e.eInfo.nStates);
F.resize(e.eInfo.nStates);
for(int q=0; q<e.eInfo.nStates; q++)
{ int procSrc = e.eInfo.whose(q);
if(procSrc == mpiUtil->iProcess())
{ std::swap(C[q], e.eVars.C[q]);
std::swap(E[q], e.eVars.Hsub_eigs[q]);
std::swap(F[q], e.eVars.F[q]);
}
else
{ C[q].init(nBands, e.basis[q].nbasis * nSpinor, &e.basis[q], &e.eInfo.qnums[q]);
E[q].resize(nBands);
F[q].resize(nBands);
}
C[q].bcast(procSrc);
E[q].bcast(procSrc);
F[q].bcast(procSrc);
}
//Randomize supercell to improve load balancing on k-mesh:
{ std::vector< vector3<> >& kmesh = e.coulombParams.supercell->kmesh;
std::vector<Supercell::KmeshTransform>& kmeshTransform = e.coulombParams.supercell->kmeshTransform;
for(size_t ik=0; ik<kmesh.size()-1; ik++)
{ size_t jk = ik + floor(Random::uniform(kmesh.size()-ik));
mpiUtil->bcast(jk);
if(jk !=ik && jk < kmesh.size())
{ std::swap(kmesh[ik], kmesh[jk]);
std::swap(kmeshTransform[ik], kmeshTransform[jk]);
}
}
}
//Report maximum nearest-neighbour eigenvalue change (to guide choice of eta)
supercell = e.coulombParams.supercell;
matrix3<> kBasisT = inv(supercell->Rsuper) * e.gInfo.R;
vector3<> kBasis[3]; for(int j=0; j<3; j++) kBasis[j] = kBasisT.row(j);
plook = std::make_shared< PeriodicLookup< vector3<> > >(supercell->kmesh, e.gInfo.GGT);
size_t ikStart, ikStop;
TaskDivision(supercell->kmesh.size(), mpiUtil).myRange(ikStart, ikStop);
double dEmax = 0.;
for(size_t ik=ikStart; ik<ikStop; ik++)
{ const diagMatrix& Ei = E[supercell->kmeshTransform[ik].iReduced];
for(int j=0; j<3; j++)
{ size_t jk = plook->find(supercell->kmesh[ik] + kBasis[j]);
myassert(jk != string::npos);
const diagMatrix& Ej = E[supercell->kmeshTransform[jk].iReduced];
for(int b=0; b<nBands; b++)
if(Emin <= Ei[b] && Ei[b] <= Emax)
dEmax = std::max(dEmax, fabs(Ej[b]-Ei[b]));
}
}
mpiUtil->allReduce(dEmax, MPIUtil::ReduceMax);
logPrintf("Maximum k-neighbour dE: %lg (guide for selecting eta)\n", dEmax);
//Initialize reduced q-Mesh:
//--- q-mesh is a k-point dfference mesh, which could differ from k-mesh for off-Gamma meshes
qmesh.resize(supercell->kmesh.size());
for(size_t iq=0; iq<qmesh.size(); iq++)
{ qmesh[iq].k = supercell->kmesh[iq] - supercell->kmesh[0]; //k-difference
qmesh[iq].weight = 1./qmesh.size(); //uniform mesh
qmesh[iq].spin = 0;
}
logPrintf("Symmetries reduced momentum transfers (q-mesh) from %d to ", int(qmesh.size()));
qmesh = e.symm.reduceKmesh(qmesh);
logPrintf("%d entries\n", int(qmesh.size())); logFlush();
//Initialize polarizability/dielectric bases corresponding to qmesh:
logPrintf("Setting up reduced polarizability bases at Ecut = %lg: ", Ecut); logFlush();
basisChi.resize(qmesh.size());
double avg_nbasis = 0.;
const GridInfo& gInfoBasis = e.gInfoWfns ? *e.gInfoWfns : e.gInfo;
logSuspend();
for(size_t iq=0; iq<qmesh.size(); iq++)
{ basisChi[iq].setup(gInfoBasis, e.iInfo, Ecut, qmesh[iq].k);
avg_nbasis += qmesh[iq].weight * basisChi[iq].nbasis;
}
logResume();
logPrintf("nbasis = %.2lf average, %.2lf ideal\n", avg_nbasis, pow(sqrt(2*Ecut),3)*(e.gInfo.detR/(6*M_PI*M_PI)));
logFlush();
//Initialize common wavefunction basis and ColumnBundle transforms for full k-mesh:
logPrintf("Setting up k-mesh wavefunction transforms ... "); logFlush();
double kMaxSq = 0;
for(const vector3<>& k: supercell->kmesh)
{ kMaxSq = std::max(kMaxSq, e.gInfo.GGT.metric_length_squared(k));
for(const QuantumNumber& qnum: qmesh)
kMaxSq = std::max(kMaxSq, e.gInfo.GGT.metric_length_squared(k + qnum.k));
}
double kWeight = double(e.eInfo.spinWeight) / supercell->kmesh.size();
double GmaxEff = sqrt(2.*e.cntrl.Ecut) + sqrt(kMaxSq);
double EcutEff = 0.5*GmaxEff*GmaxEff * (1.+symmThreshold); //add some margin for round-off error safety
logSuspend();
basis.setup(e.gInfo, e.iInfo, EcutEff, vector3<>());
logResume();
ColumnBundleTransform::BasisWrapper basisWrapper(basis);
std::vector<matrix3<int>> sym = e.symm.getMatrices();
for(size_t ik=ikStart; ik<ikStop; ik++)
{ const vector3<>& k = supercell->kmesh[ik];
for(const QuantumNumber& qnum: qmesh)
{ vector3<> k2 = k + qnum.k; double roundErr;
vector3<int> k2sup = round((k2 - supercell->kmesh[0]) * supercell->super, &roundErr);
myassert(roundErr < symmThreshold);
auto iter = transform.find(k2sup);
if(iter == transform.end())
{ size_t ik2 = plook->find(k2); myassert(ik2 != string::npos);
const Supercell::KmeshTransform& kTransform = supercell->kmeshTransform[ik2];
const Basis& basisC = e.basis[kTransform.iReduced];
const vector3<>& kC = e.eInfo.qnums[kTransform.iReduced].k;
transform[k2sup] = std::make_shared<ColumnBundleTransform>(kC, basisC, k2, basisWrapper,
nSpinor, sym[kTransform.iSym], kTransform.invert);
//Initialize corresponding quantum number:
QuantumNumber qnum;
qnum.k = k2;
qnum.spin = 0;
qnum.weight = kWeight;
qnumMesh[k2sup] = qnum;
}
}
}
logPrintf("done.\n"); logFlush();
//Main loop over momentum transfers:
diagMatrix ImKscrHead(omegaGrid.size(), 0.);
std::vector<diagMatrix> ImSigma(e.eInfo.nStates, diagMatrix(nBands,0.));
diagMatrix cedaNum(nBands, 0.), cedaDen(nBands, 0.);
for(size_t iq=0; iq<qmesh.size(); iq++)
{ logPrintf("\nMomentum transfer %d of %d: q = ", int(iq+1), int(qmesh.size()));
qmesh[iq].k.print(globalLog, " %+.5lf ");
int nbasis = basisChi[iq].nbasis;
//Construct Coulomb operator (regularizes G=0 using the tricks developed for EXX):
matrix invKq = inv(coulombMatrix(iq));
//Calculate chi_KS:
std::vector<matrix> chiKS(omegaGrid.nRows()); CEDA ceda(nBands, nbasis);
logPrintf("\tComputing chi_KS ... "); logFlush();
size_t nkMine = ikStop-ikStart;
int ikInterval = std::max(1, int(round(nkMine/20.))); //interval for reporting progress
for(size_t ik=ikStart; ik<ikStop; ik++)
{ //Report progress:
size_t ikDone = ik-ikStart+1;
if(ikDone % ikInterval == 0)
{ logPrintf("%d%% ", int(round(ikDone*100./nkMine)));
logFlush();
}
//Get events:
size_t jk; matrix nij;
std::vector<Event> events = getEvents(true, ik, iq, jk, nij, &ceda);
if(!events.size()) continue;
//Collect contributions for each frequency:
for(int iOmega=0; iOmega<omegaGrid.nRows(); iOmega++)
{ double omega = omegaGrid[iOmega];
complex omegaTilde(omega, 2*eta);
complex one(1,0);
std::vector<complex> Xks; Xks.reserve(events.size());
for(const Event& event: events)
Xks.push_back(-e.gInfo.detR * kWeight * event.fWeight
* (one/(event.Eji - omegaTilde) + one/(event.Eji + omegaTilde)) );
chiKS[iOmega] += (nij * Xks) * dagger(nij);
}
}
for(int iOmega=0; iOmega<omegaGrid.nRows(); iOmega++)
chiKS[iOmega].allReduce(MPIUtil::ReduceSum);
logPrintf("done.\n"); logFlush();
diagMatrix chiKS0diag = diag(chiKS[0]); //static neglecting local-fields (for CEDA)
//Figure out head entry index:
int iHead = -1;
for(int n=0; n<nbasis; n++)
if(!basisChi[iq].iGarr[n].length_squared())
{ iHead = n;
break;
}
myassert(iHead >= 0);
//Calculate Im(screened Coulomb operator):
logPrintf("\tComputing Im(Kscreened) ... "); logFlush();
std::vector<matrix> ImKscr(omegaGrid.nRows(), zeroes(nbasis, nbasis));
for(int iOmega=iOmegaStart; iOmega<iOmegaStop; iOmega++)
{ ImKscr[iOmega] = imag(inv(invKq - chiKS[iOmega]));
chiKS[iOmega] = 0; //free to save memory
ImKscrHead[iOmega] += qmesh[iq].weight * ImKscr[iOmega](iHead,iHead).real(); //accumulate head of ImKscr
}
for(int iOmega=0; iOmega<omegaGrid.nRows(); iOmega++)
ImKscr[iOmega].bcast(omegaDiv.whose(iOmega));
chiKS.clear();
logPrintf("done.\n"); logFlush();
//Collect CEDA contributions:
ceda.collect(*this, iq, chiKS0diag, cedaNum, cedaDen);
//Calculate ImSigma contributions:
logPrintf("\tComputing ImSigma ... "); logFlush();
for(size_t ik=ikStart; ik<ikStop; ik++)
{ //Report progress:
size_t ikDone = ik-ikStart+1;
if(ikDone % ikInterval == 0)
{ logPrintf("%d%% ", int(round(ikDone*100./nkMine)));
logFlush();
}
//Get events:
size_t jk; matrix nij;
std::vector<Event> events = getEvents(false, ik, iq, jk, nij);
if(!events.size()) continue;
//Integrate over frequency for event contributions to linewidth:
diagMatrix eventContrib(events.size(), 0);
for(int iOmega=0; iOmega<omegaGrid.nRows(); iOmega++)
{ //Construct energy conserving delta-function:
double omega = omegaGrid[iOmega];
complex omegaTilde(omega, 2*eta);
diagMatrix delta; delta.reserve(events.size());
for(const Event& event: events)
delta.push_back(e.gInfo.detR * event.fWeight //overlap and sign for electron / hole
* (2*eta/M_PI) * ( 1./(event.Eji - omegaTilde).norm() - 1./(event.Eji + omegaTilde).norm()) ); //Normalized Lorentzians
eventContrib += wOmega[iOmega] * delta * diag(dagger(nij) * ImKscr[iOmega] * nij);
}
//Accumulate contributions to linewidth:
int iReduced = supercell->kmeshTransform[ik].iReduced; //directly collect to reduced k-point
double symFactor = e.eInfo.spinWeight / (supercell->kmesh.size() * e.eInfo.qnums[iReduced].weight); //symmetrization factor = 1 / |orbit of iReduced|
double qWeight = qmesh[iq].weight;
for(size_t iEvent=0; iEvent<events.size(); iEvent++)
{ const Event& event = events[iEvent];
ImSigma[iReduced][event.i] += symFactor * qWeight * eventContrib[iEvent];
}
}
logPrintf("done.\n"); logFlush();
}
logPrintf("\n");
ImKscrHead.allReduce(MPIUtil::ReduceSum);
for(diagMatrix& IS: ImSigma)
IS.allReduce(MPIUtil::ReduceSum);
for(int q=0; q<e.eInfo.nStates; q++)
for(int b=0; b<nBands; b++)
{ double Eqb = E[q][b];
if(Eqb<Emin || Eqb>Emax)
ImSigma[q][b] = NAN; //clearly mark as invalid
}
string fname = e.dump.getFilename("ImSigma_ee");
logPrintf("Dumping %s ... ", fname.c_str()); logFlush();
e.eInfo.write(ImSigma, fname.c_str());
logPrintf("done.\n");
fname = e.dump.getFilename("ImKscrHead");
logPrintf("Dumping %s ... ", fname.c_str()); logFlush();
if(mpiUtil->isHead())
{ FILE* fp = fopen(fname.c_str(), "w");
for(int iOmega=0; iOmega<omegaGrid.nRows(); iOmega++)
fprintf(fp, "%lf %le\n", omegaGrid[iOmega], ImKscrHead[iOmega]);
fclose(fp);
}
logPrintf("done.\n");
fname = e.dump.getFilename("CEDA");
logPrintf("Dumping %s ... ", fname.c_str()); logFlush();
if(mpiUtil->isHead())
{ FILE* fp = fopen(fname.c_str(), "w");
if(!fp) die("Could not open '%s' for writing.\n", fname.c_str());
(cedaNum * inv(cedaDen)).print(fp, "%19.12le\n");
fclose(fp);
}
logPrintf("done.\n");
logPrintf("\n"); logFlush();
}
/* Function for calculating the probability density, BY SOME
* METRIC THAT'S STILL UNDER DEVELOPMENT.
*
* Approximated by drawing samples from pre-computed random
* sequences at each point and comparing to the native sequence.
*/
float EnergyFuncProposal::calcProbDensity(){
unsigned int i, j, middle;
float nativeEng = 0.0;
float density, dispersal, randomEng;
vector<float> parameters;
vector<float> randomEngs;
vector<float> decoyEngs( decoyTermVals.size(), 0.0);
vector<float> zeroes( decoyTermVals.size(), 0.0);
vector<float> quarts;
/* Convert current parameter set to floating point representation.
*/
for(i = 0; i < params.size(); i++){
parameters.push_back( params[i]->toFloat() );
}
/* Calculate the native sequence energy under these
* parameters.
*/
for(i = 0; i < parameters.size(); i++){
nativeEng += parameters[i]*natSeqTermVals[i];
}
/* And the respective decoy energies.
*/
for(i = 0; i < decoyTermVals.size(); i++){
for(j = 0; j < parameters.size(); j++){
decoyEngs[i] += parameters[i]*decoyTermVals[i][j];
}
}
/* Calculate the scaled version of the energy function for
* all random sequences. Note that random energy values are
* organized by column (one for each term in the function),
* not by row (one for each sequence).
*/
for(i = 0; i < randSeqTermVals[0].size(); i++){
randomEng = 0.0;
/* Get the scaled energy value for this random sequence.
*/
for(j = 0; j < parameters.size(); j++){
randomEng += parameters[j]*randSeqTermVals[j][i];
}
randomEngs.push_back(randomEng);
}
/* Calculate the quartiles of the distribution of random
* energies.
*/
quarts = quartiles(randomEngs);
dispersal = quarts[2] - quarts[1];
/* Calculate the enegy gap to the nearest explicit decoy
* conformation, or the energy gap to the middle of the distribution
* of random conformation.
*/
if(decoyEngs != zeroes){
sort(decoyEngs.begin(), decoyEngs.end());
/* Case 1: Best decoy is between native and random states,
* measure against it.
*/
if(randomEngs[0] > nativeEng && decoyEngs[0] > nativeEng && decoyEngs[0] < randomEngs[0]){
/* DEBUG
*
cerr << "A decoy is the closest misfold." << endl;
*/
density = (decoyEngs[0] - nativeEng) / dispersal;
}
/* Case 2: Best decoy is worse than best random state: measure
* against random.
*/
else if(randomEngs[0] > nativeEng && decoyEngs[0] > randomEngs[0]){
/* DEBUG
*
cerr << "A random sequence is the closest misfold." << endl;
*/
density = (randomEngs[0] - nativeEng) / dispersal;
}
/* Either the best decoy or best random is better than native:
* not cool, sign should switch to negative to get out of this
* situation.
*/
else if(decoyEngs[0] < nativeEng || randomEngs[0] < nativeEng){
/* DEBUG
*
cerr << "DANGER: native not the most stable state, ";
*/
if(decoyEngs[0] < randomEngs[0]){
/* DEBUG
*
cout << "a decoy is!" << endl;
*/
density = (decoyEngs[0] - nativeEng) / dispersal;
}
else{
/* DEBUG
*
cout << "a random sequence is!" << endl;
*/
density = (randomEngs[0] - nativeEng) / dispersal;
}
}
}
else{
density = -1.0*( (nativeEng - quarts[2]) / (quarts[2]-quarts[1]) );
}
return density;
}
void Phonon::setup(bool printDefaults)
{
//Parse input to initialize unit cell:
parse(input, e, printDefaults);
logSuspend();
parse(input, eSupTemplate); //silently create a copy by re-parsing input (Everything is not trivially copyable)
logResume();
//Ensure phonon command specified:
if(!sup.length())
die("phonon supercell must be specified using the phonon command.\n");
if(!e.gInfo.S.length_squared())
die("Manual fftbox setting required for phonon. If supercell grid\n"
"initialization fails, specify slightly larger manual fftbox.\n");
//Check kpoint and supercell compatibility:
if(e.eInfo.qnums.size()>1 || e.eInfo.qnums[0].k.length_squared())
die("phonon requires a Gamma-centered uniform kpoint mesh.\n");
for(int j=0; j<3; j++)
{ if(!sup[j] || e.eInfo.kfold[j] % sup[j])
{ die("kpoint folding %d is not a multiple of supercell count %d for lattice direction %d.\n",
e.eInfo.kfold[j], sup[j], j);
}
eSupTemplate.eInfo.kfold[j] = e.eInfo.kfold[j] / sup[j];
}
logPrintf("########### Unit cell calculation #############\n");
SpeciesInfo::Constraint constraintFull;
constraintFull.moveScale = 0;
constraintFull.type = SpeciesInfo::Constraint::None;
for(size_t sp=0; sp<e.iInfo.species.size(); sp++)
e.iInfo.species[sp]->constraints.assign(e.iInfo.species[sp]->atpos.size(), constraintFull);
e.setup();
if(!e.coulombParams.supercell) e.updateSupercell(true); //force supercell generation
nSpins = e.eInfo.spinType==SpinZ ? 2 : 1;
nSpinor = e.eInfo.spinorLength();
//Initialize state of unit cell:
if(e.cntrl.dumpOnly)
{ //Single energy calculation so that all dependent quantities have been initialized:
logPrintf("\n----------- Energy evaluation at fixed state -------------\n"); logFlush();
e.eVars.elecEnergyAndGrad(e.ener, 0, 0, true);
}
else elecFluidMinimize(e);
logPrintf("# Energy components:\n"); e.ener.print(); logPrintf("\n");
//Determine optimum number of bands for supercell calculation:
nBandsOpt = 0;
for(int q=e.eInfo.qStart; q<e.eInfo.qStop; q++)
{ int nBands_q = std::upper_bound(e.eVars.F[q].begin(), e.eVars.F[q].end(), Fcut, std::greater<double>()) - e.eVars.F[q].begin();
nBandsOpt = std::max(nBandsOpt, nBands_q);
}
mpiUtil->allReduce(nBandsOpt, MPIUtil::ReduceMax);
logPrintf("Fcut=%lg reduced nBands from %d to %d per unit cell.\n", Fcut, e.eInfo.nBands, nBandsOpt);
//Make unit cell state available on all processes
//(since MPI division of qSup and q are different and independent of the map)
for(int q=0; q<e.eInfo.nStates; q++)
{ //Allocate:
if(!e.eInfo.isMine(q))
{ e.eVars.C[q].init(e.eInfo.nBands, e.basis[q].nbasis * e.eInfo.spinorLength(), &e.basis[q], &e.eInfo.qnums[q]);
e.eVars.F[q].resize(e.eInfo.nBands);
e.eVars.Hsub_eigs[q].resize(e.eInfo.nBands);
if(e.eInfo.fillingsUpdate==ElecInfo::FermiFillingsAux)
e.eVars.B[q].init(e.eInfo.nBands, e.eInfo.nBands);
}
//Broadcast from owner:
int qSrc = e.eInfo.whose(q);
e.eVars.C[q].bcast(qSrc);
e.eVars.F[q].bcast(qSrc);
e.eVars.Hsub_eigs[q].bcast(qSrc);
if(e.eInfo.fillingsUpdate==ElecInfo::FermiFillingsAux)
e.eVars.B[q].bcast(qSrc);
}
logPrintf("\n------- Configuring supercell and perturbation modes -------\n");
//Grid:
eSupTemplate.gInfo.S = Diag(sup) * e.gInfo.S; //ensure exact supercell
eSupTemplate.gInfo.R = e.gInfo.R * Diag(sup);
prodSup = sup[0] * sup[1] * sup[2];
//Replicate atoms (and related properties):
for(size_t sp=0; sp<e.iInfo.species.size(); sp++)
{ const SpeciesInfo& spIn = *(e.iInfo.species[sp]);
SpeciesInfo& spOut = *(eSupTemplate.iInfo.species[sp]);
spOut.atpos.clear();
spOut.initialMagneticMoments.clear();
matrix3<> invSup = inv(Diag(vector3<>(sup)));
vector3<int> iR;
for(iR[0]=0; iR[0]<sup[0]; iR[0]++)
for(iR[1]=0; iR[1]<sup[1]; iR[1]++)
for(iR[2]=0; iR[2]<sup[2]; iR[2]++)
{ for(vector3<> pos: spIn.atpos)
spOut.atpos.push_back(invSup * (pos + iR));
for(vector3<> M: spIn.initialMagneticMoments)
spOut.initialMagneticMoments.push_back(M); //needed only to determine supercell symmetries
}
spOut.constraints.assign(spOut.atpos.size(), constraintFull);
}
//Supercell symmetries:
eSupTemplate.symm.setup(eSupTemplate);
const std::vector< matrix3<int> >& symSup = eSupTemplate.symm.getMatrices();
symSupCart.clear();
eSupTemplate.gInfo.invR = inv(eSupTemplate.gInfo.R);
for(const matrix3<int>& m: symSup)
symSupCart.push_back(eSupTemplate.gInfo.R * m * eSupTemplate.gInfo.invR);
//Pick maximally symmetric orthogonal basis:
logPrintf("\nFinding maximally-symmetric orthogonal basis for displacements:\n");
std::vector< vector3<> > dirBasis;
{ std::multimap<int, vector3<> > dirList; //directions indexed by their stabilizer group cardinality
vector3<int> iR;
for(iR[0]=0; iR[0]<=+1; iR[0]++)
for(iR[1]=-1; iR[1]<=+1; iR[1]++)
for(iR[2]=-1; iR[2]<=+1; iR[2]++)
if(iR.length_squared())
{ //Try low-order lattice vector linear combination:
vector3<> n = eSupTemplate.gInfo.R * iR; n *= (1./n.length());
dirList.insert(std::make_pair(nStabilizer(n, symSupCart), n));
//Try low-order reciprocal lattice vector linear combination:
n = iR * eSupTemplate.gInfo.invR; n *= (1./n.length());
dirList.insert(std::make_pair(nStabilizer(n, symSupCart), n));
}
dirBasis.push_back(dirList.rbegin()->second);
//Pick second driection orthogonal to first:
std::multimap<int, vector3<> > dirList2;
for(auto entry: dirList)
{ vector3<> n = entry.second;
n -= dot(n, dirBasis[0]) * dirBasis[0];
if(n.length_squared() < symmThresholdSq) continue;
n *= (1./n.length());
dirList2.insert(std::make_pair(nStabilizer(n, symSupCart), n));
}
dirBasis.push_back(dirList2.rbegin()->second);
dirBasis.push_back(cross(dirBasis[0], dirBasis[1])); //third direction constrained by orthogonality
}
for(const vector3<>& n: dirBasis)
logPrintf(" [ %+lf %+lf %+lf ] |Stabilizer|: %d\n", n[0], n[1], n[2], nStabilizer(n,symSupCart));
//List all modes:
modes.clear();
for(size_t sp=0; sp<e.iInfo.species.size(); sp++)
for(size_t at=0; at<e.iInfo.species[sp]->atpos.size(); at++) //only need to move atoms in first unit cell
for(int iDir=0; iDir<3; iDir++)
{ Mode mode;
mode.sp = sp;
mode.at = at;
mode.dir[iDir] = 1.;
modes.push_back(mode);
}
//Find irreducible modes:
perturbations.clear();
for(unsigned sp=0; sp<e.iInfo.species.size(); sp++)
{ int nAtoms = e.iInfo.species[sp]->atpos.size();
int nPert = nAtoms * dirBasis.size();
//generate all perturbations first:
std::vector<Perturbation> pertSp(nPert); //perturbations of this species
std::vector<matrix> proj(nPert); //projection operator into subspace spanned by star of current perturbation
matrix projTot;
const auto& atomMap = eSupTemplate.symm.getAtomMap()[sp];
for(int iPert=0; iPert<nPert; iPert++)
{ pertSp[iPert].sp = sp;
pertSp[iPert].at = iPert / dirBasis.size();
pertSp[iPert].dir = dirBasis[iPert % dirBasis.size()];
pertSp[iPert].weight = 1./symSupCart.size();
for(unsigned iSym=0; iSym<symSupCart.size(); iSym++)
{ int at = atomMap[pertSp[iPert].at][iSym] % nAtoms; //map back to first cell
vector3<> dir = symSupCart[iSym] * pertSp[iPert].dir;
matrix nHat = zeroes(nPert,1);
for(int iDir=0; iDir<3; iDir++)
nHat.set(at*3+iDir,0, dir[iDir]);
proj[iPert] += pertSp[iPert].weight * nHat * dagger(nHat);
}
projTot += proj[iPert];
}
myassert(nrm2(projTot - eye(nPert)) < symmThreshold);
//only select perturbations with distinct subspace projections:
std::vector<bool> irred(nPert, true); //whether each perturbation is in irreducible set
for(int iPert=0; iPert<nPert; iPert++)
{ for(int jPert=0; jPert<iPert; jPert++)
if(irred[jPert] && nrm2(proj[iPert]-proj[jPert])<symmThreshold)
{ pertSp[jPert].weight += pertSp[iPert].weight; //send weight of current mode to its image in irreducible set
irred[iPert] = false; //this mode will be accounted for upon symmetrization
break;
}
}
for(int iPert=0; iPert<nPert; iPert++)
if(irred[iPert])
perturbations.push_back(pertSp[iPert]);
}
logPrintf("\n%d perturbations of the unit cell reduced to %d under symmetries:\n", int(modes.size()), int(perturbations.size()));
for(const Perturbation& pert: perturbations)
logPrintf("%s %d [ %+lf %+lf %+lf ] %lf\n", e.iInfo.species[pert.sp]->name.c_str(),
pert.at, pert.dir[0], pert.dir[1], pert.dir[2], pert.weight*symSupCart.size());
//Determine wavefunction unitary rotations:
logPrintf("\nCalculating unitary rotations of unit cell states under symmetries:\n");
stateRot.resize(nSpins);
double unitarityErr = 0.;
for(int iSpin=0; iSpin<nSpins; iSpin++)
{ //Find states involved in the supercell Gamma-point:
struct Kpoint : public Supercell::KmeshTransform
{ vector3<> k; //also store k-point for convenience (KmeshTransform doesn't have it)
};
std::vector<Kpoint> kpoints; kpoints.reserve(prodSup);
const Supercell& supercell = *(e.coulombParams.supercell);
for(unsigned ik=0; ik<supercell.kmesh.size(); ik++)
{ double kSupErr; round(matrix3<>(Diag(sup)) * supercell.kmesh[ik], &kSupErr);
if(kSupErr < symmThreshold) //maps to Gamma point
{ Kpoint kpoint;
(Supercell::KmeshTransform&)kpoint = supercell.kmeshTransform[ik]; //copy base class
kpoint.k = supercell.kmesh[ik];
kpoint.iReduced += iSpin*(e.eInfo.nStates/nSpins); //point to source k-point with appropriate spin
kpoints.push_back(kpoint);
}
}
myassert(int(kpoints.size()) == prodSup);
//Initialize basis and qnum for these states:
std::vector<QuantumNumber> qnums(prodSup);
std::vector<Basis> basis(prodSup);
logSuspend();
for(int ik=0; ik<prodSup; ik++)
{ qnums[ik].k = kpoints[ik].k;
qnums[ik].spin = (nSpins==1 ? 0 : (iSpin ? +1 : -1));
qnums[ik].weight = 1./prodSup;
basis[ik].setup(e.gInfo, e.iInfo, e.cntrl.Ecut, kpoints[ik].k);
}
logResume();
//Get wavefunctions for all these k-points:
#define whose_ik(ik) (((ik) * mpiUtil->nProcesses())/prodSup) //local MPI division
std::vector<ColumnBundle> C(prodSup);
std::vector<std::shared_ptr<ColumnBundleTransform::BasisWrapper> > basisWrapper(prodSup);
auto sym = e.symm.getMatrices(); //unit cell symmetries
for(int ik=0; ik<prodSup; ik++)
{ C[ik].init(e.eInfo.nBands, basis[ik].nbasis*nSpinor, &basis[ik], &qnums[ik], isGpuEnabled());
if(whose_ik(ik) == mpiUtil->iProcess())
{ int q = kpoints[ik].iReduced;
C[ik].zero();
basisWrapper[ik] = std::make_shared<ColumnBundleTransform::BasisWrapper>(basis[ik]);
ColumnBundleTransform(e.eInfo.qnums[q].k, e.basis[q], qnums[ik].k, *(basisWrapper[ik]),
nSpinor, sym[kpoints[ik].iSym], kpoints[ik].invert).scatterAxpy(1., e.eVars.C[q], C[ik],0,1);
}
}
for(int ik=0; ik<prodSup; ik++) C[ik].bcast(whose_ik(ik)); //make available on all processes
//Determine max eigenvalue:
int nBands = e.eInfo.nBands;
double Emax = -INFINITY;
for(int q=e.eInfo.qStart; q<e.eInfo.qStop; q++)
Emax = std::max(Emax, e.eVars.Hsub_eigs[q].back());
mpiUtil->allReduce(Emax, MPIUtil::MPIUtil::ReduceMax);
double EmaxValid = +INFINITY;
//Loop over supercell symmetry operations:
PeriodicLookup<QuantumNumber> plook(qnums, e.gInfo.GGT);
stateRot[iSpin].resize(symSupCart.size());
for(size_t iSym=0; iSym<symSupCart.size(); iSym++)
{ matrix3<> symUnitTmp = e.gInfo.invR * symSupCart[iSym] * e.gInfo.R; //in unit cell lattice coordinates
#define SymmErrMsg \
"Supercell symmetries do not map unit cell k-point mesh onto itself.\n" \
"This implies that the supercell is more symmetric than the unit cell!\n" \
"Please check to make sure that you have used the minimal unit cell.\n\n"
matrix3<int> symUnit;
for(int j1=0; j1<3; j1++)
for(int j2=0; j2<3; j2++)
{ symUnit(j1,j2) = round(symUnitTmp(j1,j2));
if(fabs(symUnit(j1,j2) - symUnitTmp(j1,j2)) > symmThreshold)
die(SymmErrMsg)
}
//Find image kpoints under rotation: (do this for all k-points so that all processes exit together if necessary)
std::vector<int> ikRot(prodSup);
for(int ik=0; ik<prodSup; ik++)
{ size_t ikRotCur = plook.find(qnums[ik].k * symUnit);
if(ikRotCur==string::npos) die(SymmErrMsg)
ikRot[ik] = ikRotCur;
}
#undef SymmErrMsg
//Calculate unitary transformation matrix:
stateRot[iSpin][iSym].init(prodSup, nBands);
for(int ik=0; ik<prodSup; ik++)
if(whose_ik(ikRot[ik]) == mpiUtil->iProcess()) //MPI division by target k-point
{ ColumnBundle Crot = C[ikRot[ik]].similar();
Crot.zero();
ColumnBundleTransform(qnums[ik].k, basis[ik], qnums[ikRot[ik]].k, *(basisWrapper[ikRot[ik]]),
nSpinor, symUnit, +1).scatterAxpy(1., C[ik], Crot,0,1);
matrix Urot = Crot ^ O(C[ikRot[ik]]); //will be unitary if Crot is a strict unitary rotation of C[ikRot[ik]]
//Check maximal subspace that is unitary: (remiander must be incomplete degenerate subspace)
int nBandsValid = nBands;
while(nBandsValid && !isUnitary(Urot(0,nBandsValid, 0,nBandsValid)))
nBandsValid--;
if(nBandsValid<nBands)
{ //Update energy range of validity:
EmaxValid = std::min(EmaxValid, e.eVars.Hsub_eigs[kpoints[ik].iReduced][nBandsValid]);
//Make valid subspace exactly unitary:
matrix UrotSub = Urot(0,nBandsValid, 0,nBandsValid);
matrix UrotOverlap = dagger(UrotSub) * UrotSub;
UrotSub = UrotSub * invsqrt(UrotOverlap); //make exactly unitary
unitarityErr += std::pow(nrm2(UrotOverlap - eye(nBandsValid)), 2);
//Zero out invalid subspace:
Urot.zero();
Urot.set(0,nBandsValid, 0,nBandsValid, UrotSub);
}
stateRot[iSpin][iSym].set(ik, ikRot[ik], Urot);
}
stateRot[iSpin][iSym].allReduce();
}
#undef whose_ik
mpiUtil->allReduce(EmaxValid, MPIUtil::ReduceMin);
if(nSpins>1) logPrintf("\tSpin %+d: ", iSpin ? +1 : -1); else logPrintf("\t");
logPrintf("Matrix elements valid for ");
if(std::isfinite(EmaxValid)) logPrintf("E < %+.6lf (Emax = %+.6lf) due to incomplete degenerate subspaces.\n", EmaxValid, Emax);
else logPrintf("all available states (all degenerate subspaces are complete).\n");
}
mpiUtil->allReduce(unitarityErr, MPIUtil::ReduceSum);
unitarityErr = sqrt(unitarityErr / (nSpins * prodSup * symSupCart.size()));
logPrintf("\tRMS unitarity error in valid subspaces: %le\n", unitarityErr);
}
static void lib_dtoa(FAR struct lib_outstream_s *obj, int fmt, int prec,
uint8_t flags, double value)
{
FAR char *digits; /* String returned by __dtoa */
FAR char *digalloc; /* Copy of digits to be freed after usage */
FAR char *rve; /* Points to the end of the return value */
int expt; /* Integer value of exponent */
int numlen; /* Actual number of digits returned by cvt */
int nchars; /* Number of characters to print */
int dsgn; /* Unused sign indicator */
int i;
/* Special handling for NaN and Infinity */
if (isnan(value))
{
lib_dtoa_string(obj, "NaN");
return;
}
if (isinf(value))
{
if (value < 0.0)
{
obj->put(obj, '-');
}
lib_dtoa_string(obj, "Infinity");
return;
}
/* Non-zero... positive or negative */
if (value < 0)
{
value = -value;
SET_NEGATE(flags);
}
/* Perform the conversion */
digits = __dtoa(value, 3, prec, &expt, &dsgn, &rve);
digalloc = digits;
numlen = rve - digits;
if (IS_NEGATE(flags))
{
obj->put(obj, '-');
}
else if (IS_SHOWPLUS(flags))
{
obj->put(obj, '+');
}
/* Special case exact zero or the case where the number is smaller than
* the print precision.
*/
if (value == 0 || expt < -prec)
{
/* kludge for __dtoa irregularity */
obj->put(obj, '0');
/* A decimal point is printed only in the alternate form or if a
* particular precision is requested.
*/
if (prec > 0 || IS_ALTFORM(flags))
{
obj->put(obj, '.');
/* Always print at least one digit to the right of the decimal point. */
prec = MAX(1, prec);
}
}
/* A non-zero value will be printed */
else
{
/* Handle the case where the value is less than 1.0 (in magnitude) and
* will need a leading zero.
*/
if (expt <= 0)
{
/* Print a single zero to the left of the decimal point */
obj->put(obj, '0');
/* Print the decimal point */
obj->put(obj, '.');
/* Print any leading zeros to the right of the decimal point */
if (expt < 0)
{
nchars = MIN(-expt, prec);
zeroes(obj, nchars);
prec -= nchars;
}
}
/* Handle the general case where the value is greater than 1.0 (in
* magnitude).
*/
else
{
/* Print the integer part to the left of the decimal point */
for (i = expt; i > 0; i--)
{
if (*digits != '\0')
{
obj->put(obj, *digits);
digits++;
}
else
{
obj->put(obj, '0');
}
}
/* Get the length of the fractional part */
numlen -= expt;
/* If there is no fractional part, then a decimal point is printed
* only in the alternate form or if a particular precision is
* requested.
*/
if (numlen > 0 || prec > 0 || IS_ALTFORM(flags))
{
/* Print the decimal point */
obj->put(obj, '.');
/* Always print at least one digit to the right of the decimal
* point.
*/
prec = MAX(1, prec);
}
}
/* If a precision was specified, then limit the number digits to the
* right of the decimal point.
*/
if (prec > 0)
{
nchars = MIN(numlen, prec);
}
else
{
nchars = numlen;
}
/* Print the fractional part to the right of the decimal point */
for (i = nchars; i > 0; i--)
{
obj->put(obj, *digits);
digits++;
}
/* Decremnt to get the number of trailing zeroes to print */
prec -= nchars;
}
/* Finally, print any trailing zeroes */
zeroes(obj, prec);
/* Is this memory supposed to be freed or not? */
#if 0
if (digalloc)
{
lib_free(digalloc);
}
#endif
}
//Extract imaginary part:
matrix imag(const matrix& m)
{ matrix out = zeroes(m.nRows(), m.nCols());
callPref(eblas_daxpy)(m.nData(), 1., ((const double*)m.dataPref())+1,2, (double*)out.dataPref(),2); //copy with stride of 2 to extract imaginary part
return out;
}
void SpeciesInfo::augmentDensitySphericalGrad(const QuantumNumber& qnum, const diagMatrix& Fq, const matrix& VdagCq, matrix& HVdagCq) const
{ static StopWatch watch("augmentDensitySphericalGrad"); watch.start();
augmentDensity_COMMON_INIT
int nProj = MnlAll.nRows();
const GridInfo &gInfo = e->gInfo;
const complex* E_nAugData = E_nAug.data();
matrix E_RhoVdagC(VdagCq.nRows(),VdagCq.nCols(),isGpuEnabled());
//Loop over atoms:
for(unsigned atom=0; atom<atpos.size(); atom++)
{
//Prepare gradient w.r.t density matrix in basis of current atom's projectors (split by spinor components, if any)
std::vector<matrix> E_Rho(e->eInfo.nDensities);
if(e->eInfo.isNoncollinear()) E_Rho.assign(E_Rho.size(), zeroes(nProj/2, nProj/2));
else E_Rho[qnum.index()] = zeroes(nProj, nProj);
//Propagate gradients from spherical functions to density matrix:
for(size_t s=0; s<E_Rho.size(); s++) if(E_Rho[s])
{ int atomOffs = Nlm*(atom + s*atpos.size());
//Triple loop over first projector:
int i1 = 0;
for(int l1=0; l1<int(VnlRadial.size()); l1++)
for(int p1=0; p1<int(VnlRadial[l1].size()); p1++)
for(int m1=-l1; m1<=l1; m1++)
{ //Triple loop over second projector:
int i2 = 0;
for(int l2=0; l2<int(VnlRadial.size()); l2++)
for(int p2=0; p2<int(VnlRadial[l2].size()); p2++)
for(int m2=-l2; m2<=l2; m2++)
{ if(i2<=i1) //rest handled by i1<->i2 symmetry
{ std::vector<YlmProdTerm> terms = expandYlmProd(l1,m1, l2,m2);
double E_Rho_i1i2sum = 0.;
for(const YlmProdTerm& term: terms)
{ QijIndex qIndex = { l1, p1, l2, p2, term.l };
auto Qijl = Qradial.find(qIndex);
if(Qijl==Qradial.end()) continue; //no entry at this l
E_Rho_i1i2sum += term.coeff * E_nAugData[E_nAug.index(Qijl->first.index, atomOffs + term.l*(term.l+1) + term.m)].real();
}
complex E_Rho_i1i2 = E_Rho_i1i2sum * (1./gInfo.detR) * cis(0.5*M_PI*(l2-l1));
E_Rho[s].data()[E_Rho[s].index(i2,i1)] += E_Rho_i1i2.conj();
if(i1!=i2) E_Rho[s].data()[E_Rho[s].index(i1,i2)] += E_Rho_i1i2;
}
i2++;
}
i1++;
}
}
//Collate density matrix from spinor components (if necessary)
matrix E_RhoAll;
if(e->eInfo.isNoncollinear())
{ E_RhoAll = zeroes(nProj, nProj);
E_RhoAll.set(0,2,nProj, 0,2,nProj, E_Rho[0]);
E_RhoAll.set(1,2,nProj, 1,2,nProj, E_Rho[E_Rho.size()>1 ? 1 : 0]);
if(E_Rho.size()>1) //full noncollinear mode (with magnetization)
{ E_RhoAll.set(0,2,nProj, 1,2,nProj, 0.5*E_Rho[2] + complex(0,0.5)*E_Rho[3]);
E_RhoAll.set(1,2,nProj, 0,2,nProj, 0.5*E_Rho[2] - complex(0,0.5)*E_Rho[3]);
}
}
else std::swap(E_RhoAll, E_Rho[qnum.index()]);
//Propagate gradients from densiy matrix to projections:
if(isRelativistic()) E_RhoAll = fljAll * E_RhoAll * fljAll; //transformation for relativistic pseudopotential
matrix atomVdagC = VdagCq(atom*nProj,(atom+1)*nProj, 0,VdagCq.nCols());
matrix E_atomRhoVdagC = E_RhoAll * atomVdagC;
E_RhoVdagC.set(atom*nProj,(atom+1)*nProj, 0,VdagCq.nCols(), E_atomRhoVdagC);
}
HVdagCq += E_RhoVdagC;
watch.stop();
}
/*! One possible version of the GFO problem.
Given a matrix of joint torques applied to the robot joints, this will check
if there exists a set of legal contact forces that balance them. If so, it
will compute the set of contact forces that adds up to the wrench of least
magnitude on the object.
For now, this output of this function is to set the computed contact forces
on each contact as dynamic forces, and also to accumulate the resulting
wrench on the object in its external wrench accumulator.
Return codes: 0 is success, >0 means finger slip, no legal contact forces
exist; <0 means error in computation
*/
int
Grasp::computeQuasistaticForces(const Matrix &robotTau)
{
//WARNING: for now, this ignores contacts on the palm. That might change in the future
//for now, if the hand is touching anything other then the object, abort
for (int c=0; c<hand->getNumChains(); c++) {
if ( hand->getChain(c)->getNumContacts(NULL) !=
hand->getChain(c)->getNumContacts(object) ) {
DBGA("Hand contacts not on object");
return 1;
}
}
std::list<Contact*> contacts;
std::list<Joint*> joints;
bool freeChainForces = false;
for(int c=0; c<hand->getNumChains(); c++) {
//for now, we look at all contacts
std::list<Contact*> chainContacts = hand->getChain(c)->getContacts(object);
contacts.insert(contacts.end(), chainContacts.begin(), chainContacts.end());
if (!chainContacts.empty()) {
std::list<Joint*> chainJoints = hand->getChain(c)->getJoints();
joints.insert(joints.end(), chainJoints.begin(), chainJoints.end());
} else {
//the chain has no contacts
//check if any joint forces are not 0
Matrix chainTau = hand->getChain(c)->jointTorquesVector(robotTau);
//torque units should be N * 1.0e6 * mm
if (chainTau.absMax() > 1.0e3) {
DBGA("Joint torque " << chainTau.absMax() << " on chain " << c
<< " with no contacts");
freeChainForces = true;
}
}
}
//if there are no contacts, nothing to compute!
if (contacts.empty()) return 0;
//assemble the joint forces matrix
Matrix tau((int)joints.size(), 1);
int jc; std::list<Joint*>::iterator jit;
for (jc=0, jit = joints.begin(); jit!=joints.end(); jc++,jit++) {
tau.elem(jc,0) = robotTau.elem( (*jit)->getNum(), 0 );
}
//if all the joint forces we care about are zero, do an early exit
//as zero contact forces are guaranteed to balance the chain
//we should probably be able to use a much larger threshold here, if
//units are what I think they are
if (tau.absMax() < 1.0e-3) {
return 0;
}
//if there are forces on chains with no contacts, we have no hope to balance them
if (freeChainForces) {
return 1;
}
Matrix J(contactJacobian(joints, contacts));
Matrix D(Contact::frictionForceBlockMatrix(contacts));
Matrix F(Contact::frictionConstraintsBlockMatrix(contacts));
Matrix R(Contact::localToWorldWrenchBlockMatrix(contacts));
//grasp map G = S*R*D
Matrix G(graspMapMatrix(R, D));
//left-hand equality matrix JTD = JTran * D
Matrix JTran(J.transposed());
Matrix JTD(JTran.rows(), D.cols());
matrixMultiply(JTran, D, JTD);
//matrix of zeroes for right-hand of friction inequality
Matrix zeroes(Matrix::ZEROES<Matrix>(F.rows(), 1));
//matrix of unknowns
Matrix c_beta(D.cols(), 1);
//bounds: all variables greater than 0
Matrix lowerBounds(Matrix::ZEROES<Matrix>(D.cols(),1));
Matrix upperBounds(Matrix::MAX_VECTOR(D.cols()));
//solve QP
double objVal;
int result = factorizedQPSolver(G, JTD, tau, F, zeroes, lowerBounds, upperBounds,
c_beta, &objVal);
if (result) {
if( result > 0) {
DBGP("Grasp: problem unfeasible");
} else {
DBGA("Grasp: QP solver error");
}
return result;
}
//retrieve contact wrenchs in local contact coordinate systems
Matrix cWrenches(D.rows(), 1);
matrixMultiply(D, c_beta, cWrenches);
DBGP("Contact wrenches:\n" << cWrenches);
//compute wrenches relative to object origin and expressed in world coordinates
Matrix objectWrenches(R.rows(), cWrenches.cols());
matrixMultiply(R, cWrenches, objectWrenches);
DBGP("Object wrenches:\n" << objectWrenches);
//display them on the contacts and accumulate them on the object
displayContactWrenches(&contacts, cWrenches);
accumulateAndDisplayObjectWrenches(&contacts, objectWrenches);
//simple sanity check: JT * c = tau
Matrix fCheck(tau.rows(), 1);
matrixMultiply(JTran, cWrenches, fCheck);
for (int j=0; j<tau.rows(); j++) {
//I am not sure this works well for universal and ball joints
double err = fabs(tau.elem(j, 0) - fCheck.elem(j,0));
//take error as a percentage of desired force, if force is non-zero
if ( fabs(tau.elem(j,0)) > 1.0e-2) {
err = err / fabs(tau.elem(j, 0));
} else {
//for zero desired torque, out of thin air we pull an error threshold of 1.0e2
//which is 0.1% of the normal range of torques at 1.0e6
if (err < 1.0e2) err = 0;
}
// 0.1% error is considered too much
if ( err > 1.0e-1) {
DBGA("Desired torque not obtained on joint " << j << ", error " << err <<
" out of " << fabs(tau.elem(j, 0)) );
return -1;
}
}
//complex sanity check: is object force same as QP optimization result?
//this is only expected to work if all contacts are on the same object
double* extWrench = object->getExtWrenchAcc();
vec3 force(extWrench[0], extWrench[1], extWrench[2]);
vec3 torque(extWrench[3], extWrench[4], extWrench[5]);
//take into account the scaling that has taken place
double wrenchError = objVal*1.0e-6 - (force.len_sq() + torque.len_sq()) * 1.0e6;
//units here are N * 1.0e-6; errors should be in the range on miliN
if (wrenchError > 1.0e3) {
DBGA("Wrench sanity check error: " << wrenchError);
return -1;
}
return 0;
}
// ===================================================================
// gets the filename from a movie id number
// ===================================================================
std::string getFilename(std::string movie_id){
// used to get the appropriate name for the file that we want to open
std::string zeroes(7 - int(movie_id.length()),'0');
return "files/mv_" + zeroes + movie_id + ".txt";
}