Restart work on code. Fix changes of last period.
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J.-S. Caux
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ABACUS.org
11
ABACUS.org
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@ -32,6 +32,7 @@ Type your description here
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TIP: Search for the string BUGRISK in the codebase
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* Priority :ABACUS:Dev:Priority:
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:PROPERTIES:
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:ARCHIVE: %s_archive::* Priority
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@ -45,6 +46,16 @@ TIP: Search for the string BUGRISK in the codebase
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:CUSTOM_ID: ImplementationQueue
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:END:
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** CONCEPT Unittests for integration functions
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- State "CONCEPT" from "" [2018-02-20 Tue 07:01]
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Select a number of standard functions with known definite integrals:
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- polynomial
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- rational
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- exponential
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- sinusoidal
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Write a unittest aiming to reproduce the exact result, and displaying the accuracy.
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** CONCEPT Complex integration
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- State "CONCEPT" from "" [2018-02-10 Sat 06:28]
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@ -6,7 +6,7 @@ Copyright (c) J.-S. Caux
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-----------------------------------------------------------
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File: ABACUS+_Usage_Example_Heis.cc
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File: ABACUS_Usage_Example_Heis.cc
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Purpose: illustrates basic use of ABACUS for spin chains.
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@ -22,20 +22,21 @@ int main()
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{
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clock_t StartTime = clock();
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// Refer to include/JSC_Heis.h for all class definitions
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// Refer to include/ABACUS_Heis.h for all class definitions
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// and to src/HEIS/ for the actual implementations.
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// Set basic system parameters:
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DP Delta = 1.0; // anisotropy
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int N = 64; // chain length
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int M = 32; // number of downturned spins as compared to all spins up; must be <= N/2 (on or above equator)
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int M = 32; // number of downturned spins; must be <= N/2 (on or above equator)
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// Define the chain: J, Delta, h, Nsites
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Heis_Chain chain(1.0, Delta, 0.0, N);
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// The Heis_Chain class so constructed contains information about all types of strings:
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cout << "Delta = " << Delta << endl << "Possible string lengths and parities: ";
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for (int j = 0; j < chain.Nstrings; ++j) cout << "(" << chain.Str_L[j] << ", " << chain.par[j] << ")" << "\t";
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for (int j = 0; j < chain.Nstrings; ++j)
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cout << "(" << chain.Str_L[j] << ", " << chain.par[j] << ")" << "\t";
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cout << endl;
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@ -64,22 +65,26 @@ int main()
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// Now define some excited state.
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// First method:
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// Start with defining a base using a base constructor with a vector of numbers of rapidities of each type as argument:
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// Start with defining a base using a base constructor with a vector of
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// numbers of rapidities of each type as argument:
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// First define Nrapidities vector:
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Vect<int> Nrapidities(0, chain.Nstrings);
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// Assigning the numbers that follow, you have to ensure (yourself!) the \sum_j M_j n_j = M (where n_j is the length of type j).
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// Assigning the numbers that follow, you have to ensure (yourself!) that
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// the \sum_j M_j n_j = M (where n_j is the length of type j).
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Nrapidities[0] = M-2; // number of one-strings
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Nrapidities[1] = 1; // one two-string
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// Define the base:
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Heis_Base ebase(chain, Nrapidities);
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// Once the base is defined, the limiting quantum numbers are automatically computed:
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cout << "ebase defined, data is (Mdown, Nrap, Nraptot, Ix2_infty, Ix2_min, Ix2_max, baselabel):"
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<< ebase.Mdown << endl << ebase.Nrap << endl << ebase.Nraptot << endl << ebase.Ix2_infty << endl
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<< ebase.Mdown << endl << ebase.Nrap << endl << ebase.Nraptot << endl
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<< ebase.Ix2_infty << endl
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<< ebase.Ix2_min << endl << ebase.Ix2_max << endl << ebase.baselabel << endl;
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// An excited state can then be defined using this new base:
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XXX_Bethe_State estate(chain, ebase);
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// Individual quantum numbers can be manipulated: this will NOT update the state label or verify range of Ix2
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// Individual quantum numbers can be manipulated: this will NOT update the
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// state label or verify range of Ix2
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estate.Ix2[0][0] = M+1;
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estate.Compute_All(true);
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cout << endl << "estate: " << estate << endl;
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@ -91,11 +96,12 @@ int main()
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// Construct a new Bethe state
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XXX_Bethe_State estateref (chain, ebase2); // this will contain the lowest-energy quantum numbers for this base
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XXX_Bethe_State estateref (chain, ebase2); // defaults to the lowest-energy state for this base
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XXX_Bethe_State estate2 (chain, ebase2); // yet another state
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// Setting a state to a given label:
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estate2.Set_to_Label ("31_1_nh", estateref.Ix2); // The base of estate must coincide with the base in the label. Label is relative to estateref.Ix2
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// The base of estate must coincide with the base in label. Label is relative to estateref.Ix2.
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estate2.Set_to_Label ("31_1_nh", estateref.Ix2);
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estate2.Compute_All(true);
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cout << "estate2: " << estate2 << endl;
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@ -106,7 +112,8 @@ int main()
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cout << "Excitation momentum (mod 2 pi) = estate.K - gstate.K = " << estate.K - gstate.K << endl;
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// Computing matrix elements: CAREFUL: magnetizations must be consistent with operator (error is flagged).
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// Computing matrix elements:
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// CAREFUL: magnetizations must be consistent with operator (error is flagged).
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cout << "Matrix elements: " << endl;
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// The logarithm of the matrix elements are computed as complex numbers:
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cout << "ln_Sz (gstate, estate) = " << ln_Sz_ME (gstate, estate) << endl;
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@ -294,6 +294,13 @@ namespace ABACUS {
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XXZ_Bethe_State Add_Particle_at_Center (const XXZ_Bethe_State& RefState);
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XXZ_Bethe_State Remove_Particle_at_Center (const XXZ_Bethe_State& RefState);
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// Defined in XXZ_Bethe_State.cc
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inline DP fbar_XXZ (DP lambda, int par, DP tannzetaover2);
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DP Theta_XXZ (DP lambda, int nj, int nk, int parj, int park, DP* tannzetaover2);
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DP hbar_XXZ (DP lambda, int n, int par, DP* si_n_anis_over_2);
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DP ddlambda_Theta_XXZ (DP lambda, int nj, int nk, int parj, int park, DP* si_n_anis_over_2);
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//****************************************************************************
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@ -422,17 +422,20 @@ namespace ABACUS {
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for (int k = 0; k < RefChain.Nstrings; ++k) {
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sum2 = 0.0;
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// sum2 = 0.0;
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sum2 += (RefChain.Str_L[j] == RefChain.Str_L[k]) ? 0.0 :
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2.0 * atan(tan(0.25 * PI * (1.0 + RefChain.par[j] * RefChain.par[k])
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- 0.5 * fabs(RefChain.Str_L[j] - RefChain.Str_L[k]) * RefChain.anis));
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sum2 += 2.0 * atan(tan(0.25 * PI * (1.0 + RefChain.par[j] * RefChain.par[k])
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- 0.5 * (RefChain.Str_L[j] + RefChain.Str_L[k]) * RefChain.anis));
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// sum2 += (RefChain.Str_L[j] == RefChain.Str_L[k]) ? 0.0 :
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// 2.0 * atan(tan(0.25 * PI * (1.0 + RefChain.par[j] * RefChain.par[k])
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// - 0.5 * fabs(RefChain.Str_L[j] - RefChain.Str_L[k]) * RefChain.anis));
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// sum2 += 2.0 * atan(tan(0.25 * PI * (1.0 + RefChain.par[j] * RefChain.par[k])
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// - 0.5 * (RefChain.Str_L[j] + RefChain.Str_L[k]) * RefChain.anis));
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for (int a = 1; a < ABACUS::min(RefChain.Str_L[j], RefChain.Str_L[k]); ++a)
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sum2 += 2.0 * 2.0 * atan(tan(0.25 * PI * (1.0 + RefChain.par[j] * RefChain.par[k])
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- 0.5 * (fabs(RefChain.Str_L[j] - RefChain.Str_L[k]) + 2.0*a) * RefChain.anis));
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// for (int a = 1; a < ABACUS::min(RefChain.Str_L[j], RefChain.Str_L[k]); ++a)
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// sum2 += 2.0 * 2.0 * atan(tan(0.25 * PI * (1.0 + RefChain.par[j] * RefChain.par[k])
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// - 0.5 * (fabs(RefChain.Str_L[j] - RefChain.Str_L[k]) + 2.0*a) * RefChain.anis));
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sum2 = Theta_XXZ(1.0, RefChain.Str_L[j], RefChain.Str_L[k], RefChain.par[j],
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RefChain.par[k], RefChain.ta_n_anis_over_2);
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sum1 += (Nrap[k] - ((j == k) ? 1 : 0)) * sum2;
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}
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@ -459,6 +462,10 @@ namespace ABACUS {
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if (!((Nrap[j] + Ix2_max[j]) % 2)) Ix2_max[j] -= 1;
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// If Ix2_max equals Ix2_infty, we reduce it by 2:
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if (Ix2_max[j] == int(Ix2_infty[j])) Ix2_max[j] -= 2;
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while (Ix2_max[j] > RefChain.Nsites) {
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Ix2_max[j] -= 2;
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}
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@ -20,10 +20,10 @@ namespace ABACUS {
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// Function prototypes
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inline DP fbar_XXZ (DP lambda, int par, DP tannzetaover2);
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DP Theta_XXZ (DP lambda, int nj, int nk, int parj, int park, DP* tannzetaover2);
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DP hbar_XXZ (DP lambda, int n, int par, DP* si_n_anis_over_2);
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DP ddlambda_Theta_XXZ (DP lambda, int nj, int nk, int parj, int park, DP* si_n_anis_over_2);
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// inline DP fbar_XXZ (DP lambda, int par, DP tannzetaover2);
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// DP Theta_XXZ (DP lambda, int nj, int nk, int parj, int park, DP* tannzetaover2);
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// DP hbar_XXZ (DP lambda, int n, int par, DP* si_n_anis_over_2);
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// DP ddlambda_Theta_XXZ (DP lambda, int nj, int nk, int parj, int park, DP* si_n_anis_over_2);
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//***************************************************************************************************
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