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.github/workflows/gh-pages.yml
vendored
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.github/workflows/gh-pages.yml
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name: github pages
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on:
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push:
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branches:
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- master
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jobs:
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deploy:
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runs-on: ubuntu-latest
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steps:
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- uses: actions/checkout@v2
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- name: install extra repository
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run: sudo add-apt-repository ppa:kelleyk/emacs
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- name: refresh apt
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run: sudo apt-get update
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- name: install dependencies
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run: sudo apt-get install emacs26
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- name: install htmlize
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run: git clone https://github.com/hniksic/emacs-htmlize && cp emacs-htmlize/htmlize.el docs/
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- name: make
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run: cd docs ; ./create.sh ../QMC.org
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- name: Deploy
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uses: peaceiris/actions-gh-pages@v3
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with:
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github_token: ${{ secrets.GITHUB_TOKEN }}
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publish_dir: ./docs
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158
QMC.org
158
QMC.org
@ -1253,7 +1253,7 @@ gfortran hydrogen.f90 qmc_stats.f90 vmc.f90 -o vmc
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that the acceptance rate is around 0.5 for a good efficiency of
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that the acceptance rate is around 0.5 for a good efficiency of
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the simulation.
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the simulation.
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**** TODO Exercise
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**** Exercise
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#+begin_exercise
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#+begin_exercise
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Modify the previous program to introduce the accept/reject step.
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Modify the previous program to introduce the accept/reject step.
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@ -1303,11 +1303,12 @@ tau = 1.0
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X = [MonteCarlo(a,tau,nmax) for i in range(30)]
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X = [MonteCarlo(a,tau,nmax) for i in range(30)]
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E, deltaE = ave_error([x[0] for x in X])
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E, deltaE = ave_error([x[0] for x in X])
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A, deltaA = ave_error([x[1] for x in X])
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A, deltaA = ave_error([x[1] for x in X])
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print(f"E = {E} +/- {deltaE} {A} +/- {deltaA}")
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print(f"E = {E} +/- {deltaE}\nA = {A} +/- {deltaA}")
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#+END_SRC
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#+END_SRC
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#+RESULTS:
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#+RESULTS:
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: E = -0.49387078389332206 +/- 0.0033326460286729792 0.4983000000000001 +/- 0.006825097363627021
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: E = -0.4949730317138491 +/- 0.00012478601801760644
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: A = 0.7887163333333334 +/- 0.00026834549840347617
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*Fortran*
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*Fortran*
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#+BEGIN_SRC f90
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#+BEGIN_SRC f90
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@ -1400,6 +1401,157 @@ gfortran hydrogen.f90 qmc_stats.f90 vmc_metropolis.f90 -o vmc_metropolis
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:header-args:f90: :tangle dmc.f90
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:header-args:f90: :tangle dmc.f90
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:END:
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:END:
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** Hydrogen atom
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**** Exercise
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#+begin_exercise
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Modify the Metropolis VMC program to introduce the PDMC weight.
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In the limit $\tau \rightarrow 0$, you should recover the exact
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energy of H for any value of $a$.
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#+end_exercise
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*Python*
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#+BEGIN_SRC python :results output
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from hydrogen import *
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from qmc_stats import *
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def MonteCarlo(a,tau,nmax,Eref):
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E = 0.
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N = 0.
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accep_rate = 0.
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sq_tau = np.sqrt(tau)
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r_old = np.random.normal(loc=0., scale=1.0, size=(3))
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d_old = drift(a,r_old)
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d2_old = np.dot(d_old,d_old)
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psi_old = psi(a,r_old)
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w = 1.0
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for istep in range(nmax):
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chi = np.random.normal(loc=0., scale=1.0, size=(3))
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el = e_loc(a,r_old)
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w *= np.exp(-tau*(el - Eref))
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N += w
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E += w * el
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r_new = r_old + tau * d_old + sq_tau * chi
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d_new = drift(a,r_new)
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d2_new = np.dot(d_new,d_new)
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psi_new = psi(a,r_new)
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# Metropolis
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prod = np.dot((d_new + d_old), (r_new - r_old))
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argexpo = 0.5 * (d2_new - d2_old)*tau + prod
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q = psi_new / psi_old
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q = np.exp(-argexpo) * q*q
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# PDMC weight
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if np.random.uniform() < q:
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accep_rate += w
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r_old = r_new
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d_old = d_new
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d2_old = d2_new
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psi_old = psi_new
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return E/N, accep_rate/N
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a = 0.9
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nmax = 10000
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tau = .1
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X = [MonteCarlo(a,tau,nmax,-0.5) for i in range(30)]
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E, deltaE = ave_error([x[0] for x in X])
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A, deltaA = ave_error([x[1] for x in X])
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print(f"E = {E} +/- {deltaE}\nA = {A} +/- {deltaA}")
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#+END_SRC
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#+RESULTS:
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: E = -0.49654807434947584 +/- 0.0006868522447409156
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: A = 0.9876193891840709 +/- 0.00041857361650995804
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*Fortran*
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#+BEGIN_SRC f90
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subroutine variational_montecarlo(a,tau,nmax,energy,accep_rate)
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implicit none
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double precision, intent(in) :: a, tau
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integer*8 , intent(in) :: nmax
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double precision, intent(out) :: energy, accep_rate
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integer*8 :: istep
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double precision :: norm, sq_tau, chi(3), d2_old, prod, u
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double precision :: psi_old, psi_new, d2_new, argexpo, q
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double precision :: r_old(3), r_new(3)
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double precision :: d_old(3), d_new(3)
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double precision, external :: e_loc, psi
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sq_tau = dsqrt(tau)
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! Initialization
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energy = 0.d0
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norm = 0.d0
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accep_rate = 0.d0
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call random_gauss(r_old,3)
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call drift(a,r_old,d_old)
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d2_old = d_old(1)*d_old(1) + d_old(2)*d_old(2) + d_old(3)*d_old(3)
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psi_old = psi(a,r_old)
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do istep = 1,nmax
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call random_gauss(chi,3)
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r_new(:) = r_old(:) + tau * d_old(:) + chi(:)*sq_tau
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call drift(a,r_new,d_new)
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d2_new = d_new(1)*d_new(1) + d_new(2)*d_new(2) + d_new(3)*d_new(3)
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psi_new = psi(a,r_new)
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! Metropolis
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prod = (d_new(1) + d_old(1))*(r_new(1) - r_old(1)) + &
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(d_new(2) + d_old(2))*(r_new(2) - r_old(2)) + &
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(d_new(3) + d_old(3))*(r_new(3) - r_old(3))
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argexpo = 0.5d0 * (d2_new - d2_old)*tau + prod
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q = psi_new / psi_old
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q = dexp(-argexpo) * q*q
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call random_number(u)
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if (u<q) then
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accep_rate = accep_rate + 1.d0
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r_old(:) = r_new(:)
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d_old(:) = d_new(:)
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d2_old = d2_new
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psi_old = psi_new
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end if
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norm = norm + 1.d0
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energy = energy + e_loc(a,r_old)
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end do
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energy = energy / norm
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accep_rate = accep_rate / norm
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end subroutine variational_montecarlo
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program qmc
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implicit none
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double precision, parameter :: a = 0.9
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double precision, parameter :: tau = 1.0
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integer*8 , parameter :: nmax = 100000
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integer , parameter :: nruns = 30
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integer :: irun
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double precision :: X(nruns), accep(nruns)
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double precision :: ave, err
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do irun=1,nruns
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call variational_montecarlo(a,tau,nmax,X(irun),accep(irun))
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enddo
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call ave_error(X,nruns,ave,err)
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print *, 'E = ', ave, '+/-', err
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call ave_error(accep,nruns,ave,err)
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print *, 'A = ', ave, '+/-', err
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end program qmc
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#+END_SRC
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#+begin_src sh :results output :exports both
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gfortran hydrogen.f90 qmc_stats.f90 vmc_metropolis.f90 -o vmc_metropolis
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./vmc_metropolis
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#+end_src
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#+RESULTS:
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: E = -0.49499990423528023 +/- 1.5958250761863871E-004
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: A = 0.78861366666666655 +/- 3.5096729498002445E-004
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** Dihydrogen
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We will now consider the H_2 molecule in a minimal basis composed of the
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We will now consider the H_2 molecule in a minimal basis composed of the
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$1s$ orbitals of the hydrogen atoms:
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$1s$ orbitals of the hydrogen atoms:
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71
docs/config.el
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71
docs/config.el
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;; Thanks to Tobias's answer on Emacs Stack Exchange:
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;; https://emacs.stackexchange.com/questions/38437/org-mode-batch-export-missing-syntax-highlighting
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(package-initialize)
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(require 'htmlize)
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(require 'font-lock)
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(require 'subr-x) ;; for `when-let'
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(unless (boundp 'maximal-integer)
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(defconst maximal-integer (lsh -1 -1)
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"Maximal integer value representable natively in emacs lisp."))
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(defun face-spec-default (spec)
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"Get list containing at most the default entry of face SPEC.
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Return nil if SPEC has no default entry."
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(let* ((first (car-safe spec))
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(display (car-safe first)))
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(when (eq display 'default)
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(list (car-safe spec)))))
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(defun face-spec-min-color (display-atts)
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"Get min-color entry of DISPLAY-ATTS pair from face spec."
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(let* ((display (car-safe display-atts)))
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(or (car-safe (cdr (assoc 'min-colors display)))
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maximal-integer)))
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(defun face-spec-highest-color (spec)
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"Search face SPEC for highest color.
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That means the DISPLAY entry of SPEC
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with class 'color and highest min-color value."
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(let ((color-list (cl-remove-if-not
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(lambda (display-atts)
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(when-let ((display (car-safe display-atts))
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(class (and (listp display)
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(assoc 'class display)))
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(background (assoc 'background display)))
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(and (member 'light (cdr background))
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(member 'color (cdr class)))))
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spec)))
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(cl-reduce (lambda (display-atts1 display-atts2)
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(if (> (face-spec-min-color display-atts1)
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(face-spec-min-color display-atts2))
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display-atts1
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display-atts2))
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(cdr color-list)
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:initial-value (car color-list))))
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(defun face-spec-t (spec)
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"Search face SPEC for fall back."
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(cl-find-if (lambda (display-atts)
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(eq (car-safe display-atts) t))
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spec))
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(defun my-face-attribute (face attribute &optional frame inherit)
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"Get FACE ATTRIBUTE from `face-user-default-spec' and not from `face-attribute'."
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(let* ((face-spec (face-user-default-spec face))
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(display-attr (or (face-spec-highest-color face-spec)
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(face-spec-t face-spec)))
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(attr (cdr display-attr))
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(val (or (plist-get attr attribute) (car-safe (cdr (assoc attribute attr))))))
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;; (message "attribute: %S" attribute) ;; for debugging
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(when (and (null (eq attribute :inherit))
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(null val))
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(let ((inherited-face (my-face-attribute face :inherit)))
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(when (and inherited-face
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(null (eq inherited-face 'unspecified)))
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(setq val (my-face-attribute inherited-face attribute)))))
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;; (message "face: %S attribute: %S display-attr: %S, val: %S" face attribute display-attr val) ;; for debugging
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(or val 'unspecified)))
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(advice-add 'face-attribute :override #'my-face-attribute)
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14
docs/create.sh
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14
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#!/bin/bash
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INPUT=$1
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if [[ -f ../docs/htmlize.el ]]
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then
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emacs --batch --load ../docs/htmlize.el --load ../docs/config.el $INPUT -f org-html-export-to-html
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else
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emacs --batch --load ../docs/config.el $INPUT -f org-html-export-to-html
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fi
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mv ../QMC.html index.html
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