int traceV(int i, int j) {
int a, b, c, d, Vij;
if (j-i < TURN) return INFINITY_;
a = canHairpin(i,j)?eH(i, j):INFINITY_;
b = canStack(i,j)?eS(i, j) + V(i + 1, j - 1):INFINITY_;
c = canStack(i,j)?VBI(i,j):INFINITY_;
d = canStack(i,j)?VM(i,j):INFINITY_;
Vij = V(i,j);
structure[i] = j;
structure[j] = i;
if (Vij == a ) {
if (print_energy_decompose == 1) fprintf(energy_decompose_outfile, "i %5d j %5d Hairpin %12.2f\n", i, j, eH(i, j)/100.00);
total_en += eH(i,j);
return Vij;
} else if (Vij == b) {
if (print_energy_decompose == 1) fprintf(energy_decompose_outfile, "i %5d j %5d Stack %12.2f\n", i, j, eS(i, j)/100.00);
total_en += eS(i,j);
traceV(i + 1, j - 1);
return Vij;
} else if (Vij == c) {
if (print_energy_decompose == 1) fprintf(energy_decompose_outfile, "i %5d j %5d IntLoop ", i, j);
traceVBI(i, j);
return Vij;
} else if (Vij == d) {
int eVM = traceVM(i, j);
if (print_energy_decompose ==1) fprintf(energy_decompose_outfile, "i %5d j %5d MultiLoop %12.2f\n", i, j, (Vij-eVM)/100.0);
total_en += (Vij-eVM);
return Vij;
}
return 0;
}
int traceV(int i, int j) {
int a, b, c, d, Vij;
if (j-i < TURN) return INFINITY_;
a = eH(i, j);
b = eS(i, j) + V(i + 1, j - 1);
if (eS(i, j) == 0) b = INFINITY_;
c = VBI(i,j);
d = VM(i,j);
Vij = MIN(MIN(a, b), MIN(c, d));
if (Vij == a && Vij != b && Vij != c && Vij != d) {
if (verbose == 1)
printf("i %5d j %5d Hairpin %12.2f\n", i, j, eH(i, j)/100.00);
total_en += eH(i,j);
return Vij;
} else if (Vij == b) {
if (verbose == 1)
printf("i %5d j %5d Stack %12.2f\n", i, j, eS(i, j)/100.00);
total_en += eS(i,j);
structure[i + 1] = j - 1;
structure[j - 1] = i + 1;
traceV(i + 1, j - 1);
return Vij;
} else if (Vij == c) {
if (verbose == 1)
printf("i %5d j %5d IntLoop ", i, j);
traceVBI(i, j);
return Vij;
} else if (Vij == d && Vij != a && Vij != b && Vij != c) {
int eVM = traceVM(i, j);
if (verbose ==1)
printf("i %5d j %5d MultiLoop %12.2f\n", i, j, (Vij-eVM)/100.0);
total_en += (Vij-eVM);
return Vij;
}
return 0;
}
void omxComputeNumericDeriv::computeImpl(FitContext *fc)
{
if (fc->fitUnits == FIT_UNITS_SQUARED_RESIDUAL ||
fc->fitUnits == FIT_UNITS_SQUARED_RESIDUAL_CHISQ) { // refactor TODO
numParams = 0;
if (verbose >= 1) mxLog("%s: derivatives %s units are meaningless",
name, fitUnitsToName(fc->fitUnits));
return; //Possible TODO: calculate Hessian anyway?
}
int newWanted = fc->wanted | FF_COMPUTE_GRADIENT;
if (wantHessian) newWanted |= FF_COMPUTE_HESSIAN;
int nf = fc->calcNumFree();
if (numParams != 0 && numParams != nf) {
mxThrow("%s: number of parameters changed from %d to %d",
name, numParams, nf);
}
numParams = nf;
if (numParams <= 0) { complainNoFreeParam(); return; }
optima.resize(numParams);
fc->copyEstToOptimizer(optima);
paramMap.resize(numParams);
for (int px=0,ex=0; px < numParams; ++ex) {
if (fc->profiledOut[ex]) continue;
paramMap[px++] = ex;
}
omxAlgebraPreeval(fitMat, fc);
fc->createChildren(fitMat); // allow FIML rowwiseParallel even when parallel=false
fc->state->countNonlinearConstraints(fc->state->numEqC, fc->state->numIneqC, false);
int c_n = fc->state->numEqC + fc->state->numIneqC;
fc->constraintFunVals.resize(c_n);
fc->constraintJacobian.resize(c_n, numParams);
if(c_n){
omxCalcFinalConstraintJacobian(fc, numParams);
}
// TODO: Allow more than one hessian value for calculation
int numChildren = 1;
if (parallel && !fc->openmpUser && fc->childList.size()) numChildren = fc->childList.size();
if (!fc->haveReferenceFit(fitMat)) return;
minimum = fc->fit;
hessWorkVector = new hess_struct[numChildren];
if (numChildren == 1) {
omxPopulateHessianWork(hessWorkVector, fc);
} else {
for(int i = 0; i < numChildren; i++) {
omxPopulateHessianWork(hessWorkVector + i, fc->childList[i]);
}
}
if(verbose >= 1) mxLog("Numerical Hessian approximation (%d children, ref fit %.2f)",
numChildren, minimum);
hessian = NULL;
if (wantHessian) {
hessian = fc->getDenseHessUninitialized();
Eigen::Map< Eigen::MatrixXd > eH(hessian, numParams, numParams);
eH.setConstant(NA_REAL);
if (knownHessian) {
int khSize = int(khMap.size());
Eigen::Map< Eigen::MatrixXd > kh(knownHessian, khSize, khMap.size());
for (int rx=0; rx < khSize; ++rx) {
for (int cx=0; cx < khSize; ++cx) {
if (khMap[rx] < 0 || khMap[cx] < 0) continue;
eH(khMap[rx], khMap[cx]) = kh(rx, cx);
}
}
}
}
if (detail) {
recordDetail = false; // already done it once
} else {
Rf_protect(detail = Rf_allocVector(VECSXP, 4));
SET_VECTOR_ELT(detail, 0, Rf_allocVector(LGLSXP, numParams));
for (int gx=0; gx < 3; ++gx) {
SET_VECTOR_ELT(detail, 1+gx, Rf_allocVector(REALSXP, numParams));
}
SEXP detailCols;
Rf_protect(detailCols = Rf_allocVector(STRSXP, 4));
Rf_setAttrib(detail, R_NamesSymbol, detailCols);
SET_STRING_ELT(detailCols, 0, Rf_mkChar("symmetric"));
SET_STRING_ELT(detailCols, 1, Rf_mkChar("forward"));
SET_STRING_ELT(detailCols, 2, Rf_mkChar("central"));
SET_STRING_ELT(detailCols, 3, Rf_mkChar("backward"));
SEXP detailRowNames;
Rf_protect(detailRowNames = Rf_allocVector(STRSXP, numParams));
Rf_setAttrib(detail, R_RowNamesSymbol, detailRowNames);
for (int nx=0; nx < int(numParams); ++nx) {
SET_STRING_ELT(detailRowNames, nx, Rf_mkChar(fc->varGroup->vars[nx]->name));
}
markAsDataFrame(detail);
}
gforward = REAL(VECTOR_ELT(detail, 1));
gcentral = REAL(VECTOR_ELT(detail, 2));
gbackward = REAL(VECTOR_ELT(detail, 3));
Eigen::Map< Eigen::ArrayXd > Gf(gforward, numParams);
Eigen::Map< Eigen::ArrayXd > Gc(gcentral, numParams);
Eigen::Map< Eigen::ArrayXd > Gb(gbackward, numParams);
Gf.setConstant(NA_REAL);
Gc.setConstant(NA_REAL);
Gb.setConstant(NA_REAL);
calcHessianEntry che(this);
CovEntrywiseParallel(numChildren, che);
for(int i = 0; i < numChildren; i++) {
struct hess_struct *hw = hessWorkVector + i;
totalProbeCount += hw->probeCount;
}
delete [] hessWorkVector;
if (isErrorRaised()) return;
Eigen::Map< Eigen::ArrayXi > Gsymmetric(LOGICAL(VECTOR_ELT(detail, 0)), numParams);
double gradNorm = 0.0;
double feasibilityTolerance = Global->feasibilityTolerance;
for (int px=0; px < numParams; ++px) {
// factor out simliar code in ComputeNR
omxFreeVar &fv = *fc->varGroup->vars[ paramMap[px] ];
if ((fabs(optima[px] - fv.lbound) < feasibilityTolerance && Gc[px] > 0) ||
(fabs(optima[px] - fv.ubound) < feasibilityTolerance && Gc[px] < 0)) {
Gsymmetric[px] = false;
continue;
}
gradNorm += Gc[px] * Gc[px];
double relsym = 2 * fabs(Gf[px] + Gb[px]) / (Gb[px] - Gf[px]);
Gsymmetric[px] = (Gf[px] < 0 && 0 < Gb[px] && relsym < 1.5);
if (checkGradient && verbose >= 2 && !Gsymmetric[px]) {
mxLog("%s: param[%d] %d %f", name, px, Gsymmetric[px], relsym);
}
}
fc->grad.resize(fc->numParam);
fc->grad.setZero();
fc->copyGradFromOptimizer(Gc);
if(c_n){
fc->inequality.resize(fc->state->numIneqC);
fc->analyticIneqJacTmp.resize(fc->state->numIneqC, numParams);
fc->myineqFun(true, verbose, omxConstraint::LESS_THAN, false);
}
gradNorm = sqrt(gradNorm);
double gradThresh = Global->getGradientThreshold(minimum);
//The gradient will generally not be near zero at a local minimum if there are equality constraints
//or active inequality constraints:
if ( checkGradient && gradNorm > gradThresh && !(fc->state->numEqC || fc->inequality.array().sum()) ) {
if (verbose >= 1) {
mxLog("Some gradient entries are too large, norm %f", gradNorm);
}
if (fc->getInform() < INFORM_NOT_AT_OPTIMUM) fc->setInform(INFORM_NOT_AT_OPTIMUM);
}
fc->setEstFromOptimizer(optima);
// auxillary information like per-row likelihoods need a refresh
ComputeFit(name, fitMat, FF_COMPUTE_FIT, fc);
fc->wanted = newWanted;
}
//Shel: Function for scoring a node (recursive)
int ScoreNode(TreeNode* node, int* RNA, nndb_constants* param, int length){
int result;
result = 0;
int *pairedChildren;
pairedChildren = NULL;
int numPairedChildren;
numPairedChildren = 0;
int i;
for (i = 0 ; i < node->numChildren ; i++){
// find location and number of paired children
//and add scores of associated loops
if ((node->children[i])->isPair) {
//Manoj: Changed the code to generate warnings in case of pairing in structure which are not valid
/*Base lb = (node->children[i])->lowBase.base;
char lbChar;
if(lb==1)lbChar='A';else if(lb==2)lbChar='C';else if(lb==4)lbChar='G';else if(lb==8)lbChar='U';else lbChar="X";
Base hb = (node->children[i])->highBase.base;
char hbChar;
if(hb==1)hbChar='A';else if(hb==2)hbChar='C';else if(hb==4)hbChar='G';else if(hb==8)hbChar='U';else hbChar="X";
printf("CHECKING: bases %d and %d (%c%c) if they can pair!\n",(node->children[i])->lowBase.index, (node->children[i])->highBase.index,lbChar, hbChar);*/
if(!canPair((node->children[i])->lowBase.base, (node->children[i])->highBase.base)){
Base lb = (node->children[i])->lowBase.base;
char lbChar;
if(lb==1)lbChar='A';else if(lb==2)lbChar='C';else if(lb==4)lbChar='G';else if(lb==8)lbChar='U';else lbChar='X';
Base hb = (node->children[i])->highBase.base;
char hbChar;
if(hb==1)hbChar='A';else if(hb==2)hbChar='C';else if(hb==4)hbChar='G';else if(hb==8)hbChar='U';else hbChar='X';
printf("WARNING: bases %d and %d (%c%c) can't pair; structure cannot be scored. Exiting.\n",(node->children[i])->lowBase.index, (node->children[i])->highBase.index,lbChar, hbChar);
exit(-1);
//continue;
}
//printf("Yes they can pair\n");
result += ScoreNode(node->children[i], RNA, param, length);
numPairedChildren += 1;
pairedChildren = realloc(pairedChildren, sizeof(int) * numPairedChildren);
pairedChildren[numPairedChildren - 1] = i;
}
}
if (node->lowBase.index != 0)
{
if (numPairedChildren == 0) // must be a hairpin
{
int energy = eH(node->lowBase.index,node->highBase.index, RNA, param);
result += energy;
if(printOn2)printf("%d \t %d: Hairpin Loop with energy %.2f\n", node->lowBase.index, node->highBase.index, (double)energy/100);
}
else if (numPairedChildren == 1) // must be stack, bulge, or internal
{
if (node->numChildren == 1) // must be stack
{
int energy = eS(node->lowBase.index, node->highBase.index, RNA, param);
result += energy;
if(printOn2)printf("%d \t %d: Stacked pair with energy %.2f\n", node->lowBase.index, node->highBase.index, (double)energy/100);
}
else
{ // must be bulge or internal
int energy = eL(node->lowBase.index, node->highBase.index,
node->children[pairedChildren[0]]->lowBase.index,
node->children[pairedChildren[0]]->highBase.index,
RNA, param);
result += energy;
if(printOn2)printf("%d \t %d: Bulge or Inernal Loop with energy %.2f\n", node->lowBase.index, node->highBase.index, (double)energy/100);
}
}
else // must be a multi-loop
{
int energy = eM(node, pairedChildren, numPairedChildren, RNA, param);
result += energy;
if(printOn2)printf("%d \t %d: Multi-loop with energy %.2f\n", node->lowBase.index, node->highBase.index, (double)energy/100);
}
}
else { // must be external
int energy = eE(node, pairedChildren, numPairedChildren, RNA, param, length);
result += energy;
if(printOn2)printf("%d \t %d: External loop with energy %.2f\n", node->lowBase.index, node->highBase.index, (double)energy/100);
}
return result;
}
int calculate(int len, int nThreads) {
int b, i, j;
#ifdef _OPENMP
if (nThreads>0) omp_set_num_threads(nThreads);
#endif
#ifdef _OPENMP
#pragma omp parallel
#pragma omp master
fprintf(stdout,"Thread count: %3d \n",omp_get_num_threads());
#endif
for (b = TURN+1; b <= len-1; b++) {
#ifdef _OPENMP
#pragma omp parallel for private (i,j) schedule(guided)
#endif
for (i = 1; i <= len - b; i++) {
j = i + b;
int flag = 0, newWM = INFINITY_;
if (canPair(RNA[i], RNA[j])) {
flag = 1;
int eh = canHairpin(i,j)?eH(i,j):INFINITY_; //hair pin
int es = canStack(i,j)?eS(i,j)+getShapeEnergy(i)+getShapeEnergy(j)+V(i+1,j-1):INFINITY_; // stack
if (j-i > 6) { // Internal Loop BEGIN
int p=0, q=0;
int VBIij = INFINITY_;
for (p = i+1; p <= MIN(j-2-TURN,i+MAXLOOP+1) ; p++) {
int minq = j-i+p-MAXLOOP-2;
if (minq < p+1+TURN) minq = p+1+TURN;
int maxq = (p==i+1)?(j-2):(j-1);
for (q = minq; q <= maxq; q++) {
if (!canPair(RNA[p], RNA[q])) continue;
if (!canILoop(i,j,p,q)) continue;
VBIij = MIN(eL(i, j, p, q) + V(p,q), VBIij);
}
}
VBI(i,j) = VBIij;
V(i,j) = V(i,j) + getShapeEnergy(i) + getShapeEnergy(j);
} // Internal Loop END
if (j-i > 10) { // Multi Loop BEGIN
int h;
int VMij, VMijd, VMidj, VMidjd;
VMij = VMijd = VMidj = VMidjd = INFINITY_;
for (h = i+TURN+1; h <= j-1-TURN; h++) {
VMij = MIN(VMij, WMU(i+1,h-1) + WML(h,j-1));
VMidj = MIN(VMidj, WMU(i+2,h-1) + WML(h,j-1));
VMijd = MIN(VMijd, WMU(i+1,h-1) + WML(h,j-2));
VMidjd = MIN(VMidjd, WMU(i+2,h-1) + WML(h,j-2));
}
int d3 = canSS(j-1)?Ed3(i,j,j-1):INFINITY_;
int d5 = canSS(i+1)?Ed5(i,j,i+1):INFINITY_;
VMij = MIN(VMij, (VMidj + d5 +Ec)) ;
VMij = MIN(VMij, (VMijd + d3 +Ec));
VMij = MIN(VMij, (VMidjd + d5 + d3+ 2*Ec));
VMij = VMij + Ea + Eb + auPenalty(i,j);
VM(i,j) = canStack(i,j)?VMij:INFINITY_;
} // Multi Loop END
V(i,j) = MIN4(eh,es,VBI(i,j),VM(i,j));
}
else V(i,j) = INFINITY_;
if (j-i > 4) { // WM BEGIN
int h;
for (h = i+TURN+1 ; h <= j-TURN-1; h++) {
//ZS: This sum corresponds to when i,j are NOT paired with each other.
//So we need to make sure only terms where i,j aren't pairing are considered.
newWM = (!forcePair(i,j))?MIN(newWM, WMU(i,h-1) + WML(h,j)):newWM;
}
newWM = MIN(V(i,j) + auPenalty(i,j) + Eb, newWM);
newWM = canSS(i)?MIN(V(i+1,j) + Ed3(j,i+1,i) + auPenalty(i+1,j) + Eb + Ec, newWM):newWM; //i dangle
newWM = canSS(j)?MIN(V(i,j-1) + Ed5(j-1,i,j) + auPenalty(i,j-1) + Eb + Ec, newWM):newWM; //j dangle
newWM = (canSS(i)&&canSS(j))?MIN(V(i+1,j-1) + Ed3(j-1,i+1,i) + Ed5(j-1,i+1,j) + auPenalty(i+1,j-1) + Eb + 2*Ec, newWM):newWM; //i,j dangle
newWM = canSS(i)?MIN(WMU(i+1,j) + Ec, newWM):newWM; //i dangle
newWM = canSS(j)?MIN(WML(i,j-1) + Ec, newWM):newWM; //j dangle
WMU(i,j) = WML(i,j) = newWM;
} // WM END
}
}
for (j = TURN+2; j <= len; j++) {
int i, Wj, Widjd, Wijd, Widj, Wij, Wim1;
Wj = INFINITY_;
for (i = 1; i < j-TURN; i++) {
Wij = Widjd = Wijd = Widj = INFINITY_;
Wim1 = MIN(0, W[i-1]);
Wij = V(i, j) + auPenalty(i, j) + Wim1;
Widjd = (canSS(i)&&canSS(j))?V(i+1,j-1) + auPenalty(i+1,j-1) + Ed3(j-1,i + 1,i) + Ed5(j-1,i+1,j) + Wim1:Widjd;
Wijd = canSS(j)?V(i,j-1) + auPenalty(i,j-1) + Ed5(j-1,i,j) + Wim1:Wijd;
Widj = canSS(i)?V(i+1, j) + auPenalty(i+1,j) + Ed3(j,i + 1,i) + Wim1:Widj;
Wj = MIN(MIN4(Wij, Widjd, Wijd, Widj), Wj);
}
W[j] = canSS(j)?MIN(Wj, W[j-1]):Wj;
}
return W[len];
}
int main(int argc, char *argv[]) {
if(argc != 6 && argc != 7) {
printf("usage: rrg N n s D seed (id_string)\n");
return 1;
}
time_t t1,t2,tI,tF;
ITensor U,Dg,P,S;
Index ei;
// RRG structure parameters
const int N = atoi(argv[1]); // should be n*(power of 2)
const int n = atoi(argv[2]); // initial blocking size
int w = n; // block size (scales with m)
int ll = 0; // lambda block index
int m = 0; // RG scale factor
// AGSP and subspace parameters
const double t = 0.3; // Trotter temperature
const int M = 100; // num Trotter steps
const int k = 1; // power of Trotter op (just use 1)
const int s = atoi(argv[3]); // formal s param
const int D = atoi(argv[4]); // formal D param
// computational settings
const bool doI = true; // diag restricted Hamiltonian iteratively?
// setup random sampling
std::random_device r;
const int seed = atoi(argv[5]);
fprintf(stderr,"seed is %d\n",seed);
std::mt19937 gen(seed);
std::uniform_real_distribution<double> udist(0.0,1.0);
FILE *sxfl,*syfl,*szfl,*gsfl;
char id[128],sxnm[256],synm[256],sznm[256],gsnm[256];
if(argc == 6) sprintf(id,"rrg-L%d-s%d-D%d",N,s,D);
else sprintf(id,"%s",argv[6]);
strcat(sxnm,id); strcat(sxnm,"-sx.dat");
strcat(synm,id); strcat(synm,"-sy.dat");
strcat(sznm,id); strcat(sznm,"-sz.dat");
strcat(gsnm,id); strcat(gsnm,"-gs.dat");
sxfl = fopen(sxnm,"a");
syfl = fopen(synm,"a");
szfl = fopen(sznm,"a");
gsfl = fopen(gsnm,"a");
// initialize Hilbert subspaces for each level m = 0,...,log(N/n)
vector<SpinHalf> hsps;
for(int x = n ; x <= N ; x *= 2) hsps.push_back(SpinHalf(x));
SpinHalf hs = hsps.back();
// generate product basis over m=0 Hilbert space
auto p = int(pow(2,n));
vector<MPS> V1;
for(int i = 0 ; i < p ; ++i) {
InitState istate(hsps[0],"Dn");
for(int j = 1 ; j <= n ; ++j)
if(i/(int)pow(2,j-1)%2) istate.set(j,"Up");
V1.push_back(MPS(istate));
}
MPS bSpaceL(hsps[0]);
MPS bSpaceR(hsps[0]);
makeVS(V1,bSpaceL,LEFT);
makeVS(V1,bSpaceR,RIGHT);
// Hamiltonian parameters
const double Gamma = 2.0;
vector<double> J(2*(N-1));
fprintf(stdout,"# Hamiltonian terms Jx1,Jy1,Jx2,... (seed=%d)\n",seed);
for(int i = 0 ; i < N-1 ; ++i) {
J[2*i+0] = pow(udist(gen),Gamma);
J[2*i+1] = pow(udist(gen),Gamma);
fprintf(stdout,"%16.14f,%16.14f",J[2*i],J[2*i+1]);
if(i != N-2) fprintf(stdout,",");
}
fprintf(stdout,"\n");
fflush(stdout);
// initialize H for full system and extract block Hamiltonians
AutoMPO autoH(hs);
std::stringstream sts;
auto out = std::cout.rdbuf(sts.rdbuf());
vector<vector<MPO> > Hs(hsps.size());
for(int i = 1 ; i < N ; ++i) {
autoH += (J[2*(i-1)]-J[2*(i-1)+1]),"S+",i,"S+",i+1;
autoH += (J[2*(i-1)]-J[2*(i-1)+1]),"S-",i,"S-",i+1;
autoH += (J[2*(i-1)]+J[2*(i-1)+1]),"S+",i,"S-",i+1;
autoH += (J[2*(i-1)]+J[2*(i-1)+1]),"S-",i,"S+",i+1;
}
auto H = toMPO<ITensor>(autoH,{"Exact",true});
std::cout.rdbuf(out);
for(auto i : args(hsps)) extractBlocks(autoH,Hs[i],hsps[i]);
vector<MPO> prodSz,prodSx,projSzUp,projSzDn,projSxUp,projSxDn;
for(auto& it : hsps) {
auto curSz = sysOp(it,"Sz",2.0).toMPO(); prodSz.push_back(curSz);
auto curSx = sysOp(it,"Sx",2.0).toMPO(); prodSx.push_back(curSx);
auto curSzUp = sysOp(it,"Id").toMPO(); curSzUp.plusEq(curSz); curSzUp /= 2.0;
auto curSzDn = sysOp(it,"Id").toMPO(); curSzDn.plusEq(-1.0*curSz); curSzDn /= 2.0;
auto curSxUp = sysOp(it,"Id").toMPO(); curSxUp.plusEq(curSx); curSxUp /= 2.0;
auto curSxDn = sysOp(it,"Id").toMPO(); curSxDn.plusEq(-1.0*curSx); curSxDn /= 2.0;
projSzUp.push_back(curSzUp); projSzDn.push_back(curSzDn);
projSxUp.push_back(curSxUp); projSxDn.push_back(curSxDn);
}
// approximate the thermal operator exp(-H/t)^k using Trotter
// and MPO multiplication; temperature of K is k/t
time(&tI);
MPO eH(hs);
twoLocalTrotter(eH,t,M,autoH);
auto K = eH;
for(int i = 1 ; i < k ; ++i) {
nmultMPO(eH,K,K,{"Cutoff",eps,"Maxm",MAXBD});
K.Aref(1) *= 1.0/norm(K.A(1));
}
// INITIALIZATION: reduce dimension by sampling from initial basis, either
// bSpaceL or bSpaceR depending on how the merge will work
vector<MPS> Spre;
for(ll = 0 ; ll < N/n ; ll++) {
auto xs = ll % 2 ? 1 : n; // location of dangling Select index
auto cur = ll % 2 ? bSpaceR : bSpaceL;
Index si("ext",s,Select);
// return orthonormal basis of evecs
auto eigs = diagHermitian(-overlapT(cur,Hs[0][ll],cur),P,S,{"Maxm",s});
cur.Aref(xs) *= P*delta(commonIndex(P,S),si);
regauge(cur,xs,{"Truncate",false});
Spre.push_back(cur);
}
time(&t2);
fprintf(stderr,"initialization: %.f s\n",difftime(t2,tI));
// ITERATION: proceed through RRG hierarchy, increasing the scale m
vector<MPS> Spost;
for(m = 0 ; (int)Spre.size() > 1 ; ++m,w*=2) {
fprintf(stderr,"Level %d (w = %d)\n",m,w);
auto hs = hsps[m];
auto DD = D;//max(4,D/(int(log2(N/n)-m)));
auto thr = 1e-8;
Spost.clear();
// EXPAND STEP: for each block, expand dimension of subspace with AGSP operators
for(ll = 0 ; ll < N/w ; ++ll) {
MPO A(hs) , Hc = Hs[m][ll];
MPS pre = Spre[ll] , ret(hs);
int xs = ll % 2 ? 1 : w;
// STEP 1: extract filtering operators A from AGSP K
time(&t1);
restrictMPO(K,A,w*ll+1,DD,ll%2);
time(&t2);
fprintf(stderr,"trunc AGSP: %.f s\n",difftime(t2,t1));
// STEP 2: expand subspace using the mapping A:pre->ret
time(&t1);
ret = applyMPO(A,pre,ll%2,{"Cutoff",eps,"Maxm",MAXBD});
time(&t2);
fprintf(stderr,"apply AGSP: %.f s\n",difftime(t2,t1));
// rotate into principal components of subspace, poxsibly reducing dimension
// and stabilizing numerics, then store subspace in eigenbasis of block H
time(&t1);
diagHermitian(overlapT(ret,ret),U,Dg,{"Cutoff",thr});
time(&t2);
ei = Index("ext",int(commonIndex(Dg,U)),Select);
Dg.apply(invsqrt);
ret.Aref(xs) *= dag(U)*Dg*delta(prime(commonIndex(Dg,U)),ei);
fprintf(stderr,"rotate MPS: %.f s\n",difftime(t2,t1));
auto eigs = diagHermitian(-overlapT(ret,Hs[m][ll],ret),P,S);
ret.Aref(xs) *= P*delta(commonIndex(P,S),ei);
ret.Aref(xs) *= 1.0/sqrt(overlapT(ret,ret).real(ei(1),prime(ei)(1)));
regauge(ret,xs,{"Cutoff",eps});
fprintf(stderr,"max m: %d\n",maxM(ret));
Spost.push_back(ret);
}
// MERGE/REDUCE STEP: construct tensor subspace, sample to reduce dimension
Spre.clear();
for(ll = 0 ; ll < N/w ; ll+=2) {
auto spL = Spost[ll]; // L subspace
auto spR = Spost[ll+1]; // R subspace
// STEP 1: find s lowest eigenpairs of restricted H
time(&t1);
auto tpH = tensorProdContract(spL,spR,Hs[m+1][ll/2]);
tensorProdH<ITensor> resH(tpH);
resH.diag(s,doI);
P = resH.eigenvectors();
time(&t2);
fprintf(stderr,"diag restricted H: %.f s\n",difftime(t2,t1));
// STEP 2: tensor viable sets on each side and reduce dimension
MPS ret(hsps[m+1]);
time(&t1);
tensorProduct(spL,spR,ret,P,(ll/2)%2);
time(&t2);
fprintf(stderr,"tensor product (ll=%d): %.f s\n",ll,difftime(t2,t1));
Spre.push_back(ret);
}
}
// EXIT: extract two lowest energy candidate states to determine gap
auto res = Spre[0];
auto fi = Index("ext",s/2,Select);
vector<MPS> resSz = {res,res};
// project to Sz sectors of the eigenspace
diagHermitian(overlapT(res,prodSz[m],res),U,Dg);
resSz[0].Aref(N) *= U*delta(commonIndex(U,Dg),fi);
diagHermitian(overlapT(res,-1.0*prodSz[m],res),U,Dg);
resSz[1].Aref(N) *= U*delta(commonIndex(U,Dg),fi);
vector<MPS> evecs(2);
for(int i : range(2)) {
auto fc = resSz[i];
// diagonalize H within the Sz sectors
auto eigs = diagHermitian(-overlapT(fc,H,fc),P,S);
fc.Aref(N) *= (P*setElt(commonIndex(P,S)(1)));
fc.orthogonalize({"Cutoff",epx,"Maxm",MAXBD});
fc.normalize();
if(i == 0)
fprintf(stderr,"RRG gs energy: %17.14f\n",overlap(fc,H,fc));
evecs[i] = fc;
}
time(&t2);
Real vz,vx;
vz = overlap(evecs[0],prodSz[m],evecs[0]); vx = overlap(evecs[0],prodSx[m],evecs[0]);
fprintf(stderr,"Vz,vx of 0 is: %17.14f,%17.14f\n",vz,vx);
vz = overlap(evecs[1],prodSz[m],evecs[1]); vx = overlap(evecs[1],prodSx[m],evecs[1]);
fprintf(stderr,"Vz,vx of 1 is: %17.14f,%17.14f\n",vz,vx);
int x1_up = (vx > 0.0 ? 1 : 0);
evecs[0] = exactApplyMPO(evecs[0],projSzUp[m],{"Cutoff",epx});
evecs[0] = exactApplyMPO(evecs[0],projSxUp[m],{"Cutoff",epx});
evecs[1] = exactApplyMPO(evecs[1],projSzDn[m],{"Cutoff",epx});
evecs[1] = exactApplyMPO(evecs[1],(x1_up?projSxUp[m]:projSxDn[m]),{"Cutoff",epx});
for(auto& it : evecs) it.normalize();
fprintf(stderr,"gs candidate energy: %17.14f\nRRG BD ",overlap(evecs[0],H,evecs[0]));
for(const auto& it : evecs) fprintf(stderr,"%d ",maxM(it));
fprintf(stderr,"\telapsed: %.f s\n",difftime(t2,tI));
// CLEANUP: use DMRG to improve discovered evecs
vector<Real> evals(2),e_prev(2);
int max_iter = 30 , used_max = 0;
Real flr = 1e-13 , over_conv = 1e-1 , gap = 1.0 , conv = over_conv*gap , max_conv = 1.0;
for(int i = 0 ; i < (int)evecs.size() ; ++i) evals[i] = overlap(evecs[i],H,evecs[i]);
for(int i = 0 ; (i < 2 || conv < max_conv) && i < max_iter ; ++i) {
e_prev = evals;
time(&t1);
evals = dmrgMPO(H,evecs,8,{"Penalty",0.1,"Cutoff",epx});
time(&t2);
gap = evals[1]-evals[0];
max_conv = 0.0;
for(auto& j : range(2))
if(fabs(e_prev[j]-evals[j]) > max_conv) max_conv = e_prev[j]-evals[j];
fprintf(stderr,"DMRG BD ");
for(const auto& it : evecs) fprintf(stderr,"%3d ",maxM(it));
fprintf(stderr,"\tgap: %e\tconv=%9.2e,%9.2e\telapsed: %.f s\n",gap,
e_prev[0]-evals[0],e_prev[1]-evals[1],difftime(t2,t1));
conv = max(over_conv*gap,flr);
if(i == max_iter) used_max = 1;
}
for(int i = 0 ; i < (int)evecs.size() ; ++i) {
vz = overlap(evecs[i],prodSz[m],evecs[i]); vx = overlap(evecs[i],prodSx[m],evecs[i]);
fprintf(stderr,"Vz,vx of %d is: %12.9f,%12.9f\n",i,vz,vx);
}
evecs[0] = exactApplyMPO(evecs[0],projSzUp[m],{"Cutoff",1e-16});
evecs[0] = exactApplyMPO(evecs[0],projSxUp[m],{"Cutoff",1e-16});
evecs[1] = exactApplyMPO(evecs[1],projSzDn[m],{"Cutoff",1e-16});
evecs[1] = exactApplyMPO(evecs[1],(x1_up?projSxUp[m]:projSxDn[m]),{"Cutoff",1e-16});
for(auto& it : evecs) it.normalize();
for(auto i : range(evecs.size())) evals[i] = overlap(evecs[i],H,evecs[i]);
time(&tF);
auto gsR = evecs[0];
auto ee = measEE(gsR,N/2);
gap = evals[1]-evals[0];
fprintf(stderr,"gs: %17.14f gap: %15.9e ee: %10.8f\n",evals[0],gap,ee);
fprintf(gsfl,"# GS data (L=%d s=%d D=%d seed=%d time=%.f)\n",N,s,D,seed,difftime(tF,tI));
if(used_max) fprintf(gsfl,"# WARNING max iterations reached\n");
fprintf(gsfl,"%17.14f\t%15.9e\t%10.8f\n",evals[0],gap,ee);
// Compute two-point correlation functions in ground state via usual MPS method
fprintf(sxfl,"# SxSx corr matrix (L=%d s=%d D=%d seed=%d)\n",N,s,D,seed);
fprintf(syfl,"# SySy corr matrix (L=%d s=%d D=%d seed=%d)\n",N,s,D,seed);
fprintf(szfl,"# SzSz corr matrix (L=%d s=%d D=%d seed=%d)\n",N,s,D,seed);
for(int i = 1 ; i <= N ; ++i) {
gsR.position(i,{"Cutoff",0.0});
auto SxA = hs.op("Sx",i); auto SyA = hs.op("Sy",i); auto SzA = hs.op("Sz",i);
for(int j = 1 ; j <= N ; ++j) {
if(j <= i) {
fprintf(sxfl,"%15.12f\t",0.0);
fprintf(syfl,"%15.12f\t",0.0);
fprintf(szfl,"%15.12f\t",0.0);
} else {
auto SxB = hs.op("Sx",j); auto SyB = hs.op("Sy",j); auto SzB = hs.op("Sz",j);
fprintf(sxfl,"%15.12f\t",measOp(gsR,SxA,i,SxB,j));
fprintf(syfl,"%15.12f\t",measOp(gsR,SyA,i,SyB,j));
fprintf(szfl,"%15.12f\t",measOp(gsR,SzA,i,SzB,j));
}
}
fprintf(sxfl,"\n");
fprintf(syfl,"\n");
fprintf(szfl,"\n");
}
fclose(sxfl);
fclose(syfl);
fclose(szfl);
fclose(gsfl);
return 0;
}
