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Feature: Quasiatomic Orbital (QO) implement - immediate (deepmodeling…
…#3236) * building two center overlap * 20231120 * 20231121 * 20231124 * serial implementation done * because rcut_max is not set in previous, after addition, the corresponding unit test is forgotten to update. * full implementation of QO analysis, next is to improve accuracy of associated Laguerre Polynomial * Accurancy improved. C++-side in principle no problem for use anymore * provide python-end qo analysis into tools folder. In readme.md the usage is introduced. * recover changed INPUT files * support strategy full, use filter in postprocessing to select basis to reconstruct hamiltonian * - add new derived class pswfc_radials - extend strategy of derived class hydrogen_radials (but tested to perform ill) * implement qo_basis = pswfc * update python-end * Oops! update Makefile.Objects * add ceil() when computing supercell * update documentation * change kvec_c to kvec_d when folding * add integrated test and support output of HqoR matrix * correct CMakeLists.txt * correct CMakeLists.txt * correct CMakeLists.txt * reduce number of hydrogen-like orbitals generated with "energy" strategy * update reference value of hydrogen_radials unittest * update example and debugging the unfolding_Hk function, not completed yet * correct the method to find supercells * recover example/scf/lcao_Cu * recover examples/scf/lcao_Cu * complete necessary annotations * support the use of qo_thr for qo_basis = pswfc, flexibly controls the rcut of pswfc * add more unittest to test the symmetrical-kpoints cancellation on imaginary parts * update unittest on toqo class * complement zero_out before every so-called folding_Hk * update debugged python-end analysis package and correct CMakeLists.txt * update README.md of QO in tools/qo * Update INPUT in tools/qo/examples/abacus_input * delete redundant example files * update docs according to the newest implementation * remove commented out codes accordint to code review * provide example and update more detailed README.md * change default strategy to `minimal` for memory save concern --------- Co-authored-by: wqzhou <[email protected]>
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@@ -18,4 +18,6 @@ build | |
| dist | ||
| .idea | ||
| toolchain.tar.gz | ||
| time.json | ||
| time.json | ||
| *.pyc | ||
| __pycache__ | ||
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,137 @@ | ||
| #include "module_base/assoc_laguerre.h" | ||
| #include "module_base/global_function.h" | ||
| //#include <tr1/cmath> // use cmath the factorial function | ||
| #include <cmath> | ||
| Assoc_Laguerre::Assoc_Laguerre() | ||
| { | ||
| } | ||
|
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||
| Assoc_Laguerre::~Assoc_Laguerre() | ||
| { | ||
| } | ||
|
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| void Assoc_Laguerre::generate(const int &n, const int &l, const double ns, double* const &s, double* L) | ||
| { | ||
| for(int i = 0; i < ns; i++) | ||
| { | ||
| L[i] = this->value(n, l, s[i]); | ||
| } | ||
| } | ||
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| void Assoc_Laguerre::generate(const int &n, const int &l, std::vector<double> &x, std::vector<double> &y) | ||
| { | ||
| for(int i = 0; i < x.size(); i++) | ||
| { | ||
| y[i] = this->value(n, l, x[i]); | ||
| } | ||
| } | ||
|
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| double Assoc_Laguerre::laguerre(const int &n, const double x) | ||
| { | ||
| if(n == 0) | ||
| { | ||
| return 1; | ||
| } | ||
| else if(n == 1) | ||
| { | ||
| return -x + 1; | ||
| } | ||
| else if(n == 2) | ||
| { | ||
| return 0.5 * x * x - 2 * x + 1; | ||
| } | ||
| else if(n == 3) | ||
| { | ||
| return -x * x * x / 6.0 + 3.0 * x * x / 2.0 - 3.0 * x + 1; | ||
| } | ||
| else if(n >= 4) | ||
| { | ||
| double n_ = static_cast<double>(n); | ||
| double first = (2*n_ - 1 - x)/n_ * Assoc_Laguerre::laguerre(n-1, x); | ||
| double second = (n_ - 1)/n_ * Assoc_Laguerre::laguerre(n-2, x); | ||
| return first - second; | ||
| } | ||
| else | ||
| { | ||
| ModuleBase::WARNING_QUIT("Assoc_Laguerre::laguerre", "n is out of range"); | ||
| return 0; | ||
| } | ||
| } | ||
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| double Assoc_Laguerre::associate_laguerre(const int &n, const double x, const int &a) | ||
| { | ||
| // formula from https://en.wikipedia.org/wiki/Laguerre_polynomials | ||
| double n_ = static_cast<double>(n); | ||
| double a_ = static_cast<double>(a); | ||
| if(n == 0) | ||
| { | ||
| return 1; | ||
| } | ||
| else if(n == 1) | ||
| { | ||
| return -x + 1 + a_; | ||
| } | ||
| else if(n == 2) | ||
| { | ||
| return 0.5 * (x*x - 2*(a_+2)*x + (a_+1)*(a_+2)); | ||
| } | ||
| else if(n == 3) | ||
| { | ||
| return -x*x*x/6.0 + (a_+3)*x*x/2.0 - (a_+2)*(a_+3)*x/2.0 + (a_+1)*(a_+2)*(a_+3)/6.0; | ||
| } | ||
| else if(n >= 4) | ||
| { | ||
| double first = (2*n_ - 1 + a_ - x)/n_ * this->associate_laguerre(n-1, x, a); | ||
| double second = (n_ + a_ - 1)/n_ * this->associate_laguerre(n-2, x, a); | ||
| return first - second; | ||
| } | ||
| else | ||
| { | ||
| ModuleBase::WARNING_QUIT("Assoc_Laguerre::associate_laguerre", "n is out of range"); | ||
| return 0; | ||
| } | ||
| } | ||
|
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| int Assoc_Laguerre::factorial(const int &n) | ||
| { | ||
| if(n == 0) | ||
| { | ||
| return 1; | ||
| } | ||
| else if(n > 0) | ||
| { | ||
| return n * this->factorial(n-1); | ||
| } | ||
| else | ||
| { | ||
| ModuleBase::WARNING_QUIT("Assoc_Laguerre::factorial", "n is out of range"); | ||
| return 0; | ||
| } | ||
| } | ||
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| double Assoc_Laguerre::value(const int &n, const int &l, const double &s) | ||
| { | ||
| int k_ = 2*l + 1; | ||
| int n_ = n - l - 1; | ||
| if(k_ < 0) | ||
| { | ||
| ModuleBase::WARNING_QUIT("Assoc_Laguerre::value", "k is out of range"); | ||
| return 0; | ||
| } | ||
| if(n_ < 0) | ||
| { | ||
| ModuleBase::WARNING_QUIT("Assoc_Laguerre::value", "n is out of range"); | ||
| return 0; | ||
| } | ||
| double L = 0; | ||
| for(int iq = 0; iq <= n_; iq++) | ||
| { | ||
| L += std::pow(-s, iq) * | ||
| static_cast<double>(this->factorial(n_ + k_)) / | ||
| static_cast<double>(this->factorial(n_ - iq)) / | ||
| static_cast<double>(this->factorial(k_ + iq)) / | ||
| static_cast<double>(this->factorial(iq)); | ||
| } | ||
| //L = std::tr1::assoc_laguerre(n_, k_, s); // use standard library | ||
| return L; | ||
| } |
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,47 @@ | ||
| #ifndef ASSOC_LAGUEERRE_H | ||
| #define ASSOC_LAGUEERRE_H | ||
|
|
||
| #include <vector> | ||
| #include <string> | ||
|
|
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| class Assoc_Laguerre | ||
| { | ||
| public: | ||
| Assoc_Laguerre(); | ||
| ~Assoc_Laguerre(); | ||
| /// @brief generate the associated Laguerre polynomial (overloaded for double*) | ||
| /// @param n principal quantum number | ||
| /// @param l orbital quantum number | ||
| /// @param ns number of x-coordinates | ||
| /// @param s x-coordinates | ||
| /// @param L y-coordinates | ||
| void generate(const int &n, const int &l, const double ns, double* const &s, double* L); | ||
| /// @brief generate the associated Laguerre polynomial (overloaded for std::vector) | ||
| /// @param n principal quantum number | ||
| /// @param l orbital quantum number | ||
| /// @param x x-coordinates in std::vector | ||
| /// @param y y-coordinates in std::vector | ||
| void generate(const int &n, const int &l, std::vector<double> &x, std::vector<double> &y); | ||
| /// @brief Laguerre polynomial | ||
| /// @param n degree of the polynomial | ||
| /// @param x radial coordinate | ||
| /// @return L_n(x) | ||
| double laguerre(const int &n, const double x); | ||
| /// @brief recursive relationship to find the associated Laguerre polynomial | ||
| /// @param n degree of the polynomial | ||
| /// @param x radial coordinate | ||
| /// @param a order of the polynomial | ||
| /// @return L^(a)_n(x) | ||
| double associate_laguerre(const int &n, const double x, const int &a); | ||
| /// @brief wrapper for associate_laguerre | ||
| /// @param n principal quantum number | ||
| /// @param l orbital quantum number | ||
| /// @param s radial coordinate | ||
| /// @return L^(2l+1)_(n-l-1)(s) | ||
| double value(const int &n, const int &l, const double &s); | ||
| /// @brief factorial function | ||
| /// @param n | ||
| /// @return n! | ||
| int factorial(const int &n); | ||
| }; | ||
| #endif // ASSOC_LAGUEERRE_H |
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