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Update Discretized_LiebLin_Bethe_State (copy from abacus-dev)

This commit is contained in:
Jean-Sébastien Caux 2023-04-23 10:04:12 +02:00
parent 6ea82da104
commit 28f3db1979
1 changed files with 35 additions and 14 deletions
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49
src/TBA/TBA_LiebLin.cc
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@ -643,37 +643,55 @@ namespace ABACUS {
return(sbar);
}
LiebLin_Bethe_State Discretized_LiebLin_Bethe_State (DP c_int, DP L, int N, const Root_Density& rho)
{
// This function returns the Bethe state at finite size which is
// the closest approximation to the continuum density rho(lambda)
// Each time N \int_{-\infty}^\lambda d\lambda' \rho(\lambda') crosses a half integer, add a particle:
// Check that the provided rho has the expected filling
DP rho_check = 0.0;
for (int i = 0; i < rho.Npts; ++i) rho_check += L * rho.value[i] * rho.dlambda[i];
// The integral of rho should be between N - 0.5 and N + 0.5 for the algorithm to work
if (fabs(rho_check - N) > 0.5)
cout << "WARNING: integral of rho != N in Discretized_LiebLin_Bethe_State, "
<< "consistent discretization is impossible. \int rho dlambda = "
<< rho_check << ", N = " << N << ", L = " << L << ", N/L = " << N/L << endl;
// Using the counting function
// c(\lambda) \equiv L \int_{-\infty}^\lambda d\lambda' \rho(\lambda'),
// we seek to find lambda[i] such that c(lambda[i]) = i + 0.5, i = 0...N-1
DP integral = 0.0;
DP integral_prev = 0.0;
int Nfound = 0;
Vect<DP> lambda_found(0.0, 2*N);
Vect<DP> lambda_found(0.0, N);
int nr_to_set = 0;
for (int i = 0; i < rho.Npts; ++i) {
// Note: integral_prev is the counting function
// at rapidity rho.lambda[i-1] + 0.5* rho.dlambda[i-1]
// which equals rho.lambda[i] - 0.5* rho.dlambda[i]
integral_prev = integral;
// Note: integral gives the value of the counting function
// at rapidity rho.lambda[i] + 0.5* rho.dlambda[i]
integral += L * rho.value[i] * rho.dlambda[i];
if (integral > Nfound + 0.5) {
// Subtle error: if the rho is too discontinuous, i.e. if more than one rapidity is found, must correct for this.
if (integral > Nfound + 1.5 && integral < Nfound + 2.5) { // found two rapidities
lambda_found[Nfound++] = 0.25 * (3.0 * rho.lambda[i-1] + rho.lambda[i]);
lambda_found[Nfound++] = 0.25 * (rho.lambda[i-1] + 3.0 * rho.lambda[i]);
}
else {
// Better: center the lambda_found between these points:
lambda_found[Nfound] = 0.5 * (rho.lambda[i-1] + rho.lambda[i]);
Nfound++;
}
// We already have filled the RHS of the counting equation up to Nfound - 0.5.
// Therefore, the additional number found is
nr_to_set = floor(integral + 0.5 - Nfound);
// if (nr_to_set > 1)
// cout << "WARNING: setting " << nr_to_set << " rapidities in one step in Discretized_LiebLin_Bethe_State" << endl;
for (int n = 1; n <= nr_to_set; ++n) {
// Solve c(lambda[Nfound]) = Nfound + 0.5 for lambda[Nfound],
// namely (using linear interpolation)
// integral_prev + (lambda - rho.lambda[i-1] - 0.5*rho.dlambda[i-1]) * (integral - integra_prev)/rho.dlambda[i] = Nfound + 0.5
lambda_found[Nfound] = rho.lambda[i-1] + 0.5*rho.dlambda[i-1] + (Nfound + 0.5 - integral_prev) * rho.dlambda[i]/(integral - integral_prev);
Nfound++;
}
}
Vect<DP> lambda(N);
// Fill up the found rapidities:
for (int il = 0; il < ABACUS::min(N, Nfound); ++il) lambda[il] = lambda_found[il];
for (int il = 0; il < abacus::min(N, Nfound); ++il) lambda[il] = lambda_found[il];
// If there are missing ones, put them at the end; ideally, this should never be called
for (int il = Nfound; il < N; ++il) lambda[il] = lambda_found[Nfound-1] + (il - Nfound + 1) * (lambda_found[Nfound-1] - lambda_found[Nfound-2]);
@ -687,6 +705,9 @@ namespace ABACUS {
Ix2[i] = 2.0 * floor((L* lambda[i] + sum)/twoPI + 0.5 * (N%2 ? 1 : 2)) + (N%2) - 1;
}
// Check that the Ix2 are all ordered
for (int i = 0; i < N-1; ++i) if (Ix2[i] >= Ix2[i+1]) cout << "Alert: Ix2 not ordered around index i = " << i << ": Ix2[i] = " << Ix2[i] << "\tIx2[i+1] = " << Ix2[i+1] << endl;
// Check that the quantum numbers are all distinct:
bool allOK = false;
while (!allOK) {