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Compute E_L before moving, and fix bug in Python code

This commit is contained in:
Anthony Scemama 2021-02-02 14:23:54 +01:00
parent dbf3f108a0
commit 4df30f51c0
2 changed files with 27 additions and 24 deletions

49
QMC.org
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@ -1424,13 +1424,13 @@ gfortran hydrogen.f90 qmc_stats.f90 qmc_uniform.f90 -o qmc_uniform
The algorithm is summarized as follows:
1) Compute $\Psi$ at a new position $\mathbf{r'} = \mathbf{r}_n +
\delta L\, \mathbf{u}$
2) Compute the ratio $A = \frac{\left|\Psi(\mathbf{r'})\right|^2}{\left|\Psi(\mathbf{r}_{n})\right|^2}$
3) Draw a uniform random number $v \in [0,1]$
4) if $v \le A$, accept the move : set $\mathbf{r}_{n+1} = \mathbf{r'}$
5) else, reject the move : set $\mathbf{r}_{n+1} = \mathbf{r}_n$
6) evaluate the local energy at $\mathbf{r}_{n+1}$
1) Evaluate the local energy at $\mathbf{r}_n$ and accumulate it
2) Compute a new position $\mathbf{r'} = \mathbf{r}_n + \delta L\, \mathbf{u}$
3) Evaluate $\Psi(\mathbf{r}')$ at the new position
4) Compute the ratio $A = \frac{\left|\Psi(\mathbf{r'})\right|^2}{\left|\Psi(\mathbf{r}_{n})\right|^2}$
5) Draw a uniform random number $v \in [0,1]$
6) if $v \le A$, accept the move : set $\mathbf{r}_{n+1} = \mathbf{r'}$
7) else, reject the move : set $\mathbf{r}_{n+1} = \mathbf{r}_n$
#+begin_note
A common error is to remove the rejected samples from the
@ -1742,7 +1742,7 @@ gfortran hydrogen.f90 qmc_stats.f90 qmc_metropolis.f90 -o qmc_metropolis
Furthermore, to sample the density even better, we can "push" the electrons
into in the regions of high probability, and "pull" them away from
the low-probability regions. This will ncrease the
the low-probability regions. This will increase the
acceptance ratios and improve the sampling.
To do this, we can use the gradient of the probability density
@ -1761,7 +1761,7 @@ gfortran hydrogen.f90 qmc_stats.f90 qmc_metropolis.f90 -o qmc_metropolis
\Psi(\mathbf{r}_n)}{\Psi(\mathbf{r}_n)} \right)^2}{2\,\delta t} \right]\,.
\]
The corrsponding move is proposed as
The corresponding move is proposed as
\[
\mathbf{r}_{n+1} = \mathbf{r}_{n} + \delta t\, \frac{\nabla
@ -1775,15 +1775,14 @@ gfortran hydrogen.f90 qmc_stats.f90 qmc_metropolis.f90 -o qmc_metropolis
The algorithm of the previous exercise is only slighlty modified as:
1) Compute a new position $\mathbf{r'} = \mathbf{r}_n +
1) Evaluate the local energy at $\mathbf{r}_{n}$ and accumulate it
2) Compute a new position $\mathbf{r'} = \mathbf{r}_n +
\delta t\, \frac{\nabla \Psi(\mathbf{r})}{\Psi(\mathbf{r})} + \chi$
Evaluate $\Psi$ and $\frac{\nabla \Psi(\mathbf{r})}{\Psi(\mathbf{r})}$ at the new position
2) Compute the ratio $A = \frac{T(\mathbf{r}_{n+1} \rightarrow \mathbf{r}_{n}) P(\mathbf{r}_{n+1})}{T(\mathbf{r}_{n} \rightarrow \mathbf{r}_{n+1}) P(\mathbf{r}_{n})}$
3) Draw a uniform random number $v \in [0,1]$
4) if $v \le A$, accept the move : set $\mathbf{r}_{n+1} = \mathbf{r'}$
5) else, reject the move : set $\mathbf{r}_{n+1} = \mathbf{r}_n$
6) evaluate the local energy at $\mathbf{r}_{n+1}$
3) Evaluate $\Psi(\mathbf{r}')$ and $\frac{\nabla \Psi(\mathbf{r'})}{\Psi(\mathbf{r'})}$ at the new position
4) Compute the ratio $A = \frac{T(\mathbf{r}' \rightarrow \mathbf{r}_{n}) P(\mathbf{r}')}{T(\mathbf{r}_{n} \rightarrow \mathbf{r}') P(\mathbf{r}_{n})}$
5) Draw a uniform random number $v \in [0,1]$
6) if $v \le A$, accept the move : set $\mathbf{r}_{n+1} = \mathbf{r'}$
7) else, reject the move : set $\mathbf{r}_{n+1} = \mathbf{r}_n$
*** Gaussian random number generator
@ -1840,6 +1839,11 @@ end subroutine random_gauss
*** Exercise 1
#+begin_exercise
If you use Fortran, copy/paste the ~random_gauss~ function in
a Fortran file.
#+end_exercise
#+begin_exercise
Write a function to compute the drift vector $\frac{\nabla \Psi(\mathbf{r})}{\Psi(\mathbf{r})}$.
#+end_exercise
@ -2014,13 +2018,13 @@ def MonteCarlo(a,nmax,dt):
d2_old = d2_new
psi_old = psi_new
return energy/nmax, accep_rate/nmax
return energy/nmax, N_accep/nmax
# Run simulation
a = 1.2
nmax = 100000
dt = 1.3
dt = 1.0
X0 = [ MonteCarlo(a,nmax,dt) for i in range(30)]
@ -2036,8 +2040,6 @@ print(f"A = {A} +/- {deltaA}")
#+END_SRC
#+RESULTS:
: E = -0.4951317910667116 +/- 0.00014045774335059988
: A = 0.7200673333333333 +/- 0.00045942791345632793
*Fortran*
#+BEGIN_SRC f90
@ -2144,8 +2146,8 @@ gfortran hydrogen.f90 qmc_stats.f90 vmc_metropolis.f90 -o vmc_metropolis
#+end_src
#+RESULTS:
: E = -0.49497258331144794 +/- 1.0973395750688713E-004
: A = 0.78839866666666658 +/- 3.2503783452043152E-004
: E = -0.47940635575542706 +/- 5.5613594433433764E-004
: A = 0.62037333333333333 +/- 4.8970160591451110E-004
* Diffusion Monte Carlo :solution:
@ -3099,4 +3101,5 @@ gfortran hydrogen.f90 qmc_stats.f90 vmc.f90 -o vmc
| <2021-02-04 Thu 14:00-14:10> | 3.1 |
| <2021-02-04 Thu 14:10-14:30> | 3.2 |
| <2021-02-04 Thu 14:30-15:30> | 3.3 |
| <2021-02-04 Thu 15:30-16:30> | 3.4 |
|------------------------------+---------|

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@ -45,7 +45,7 @@ def MonteCarlo(a,nmax,dt):
# Run simulation
a = 1.2
nmax = 100000
dt = 1.3
dt = 1.0
X0 = [ MonteCarlo(a,nmax,dt) for i in range(30)]