Gaussian sampling

energy_hydrogen.py

@@ -1,23 +1,23 @@
 import numpy as np
 from hydrogen import e_loc, psi
 
-interval = np.linspace(-5,5,num=50)
+ interval = np.linspace(-5,5,num=50)
-delta = (interval[1]-interval[0])**3
+ delta = (interval[1]-interval[0])**3
 
-r = np.array([0.,0.,0.])
+ r = np.array([0.,0.,0.])
 
-for a in [0.1, 0.2, 0.5, 0.9, 1., 1.5, 2.]:
+ for a in [0.1, 0.2, 0.5, 0.9, 1., 1.5, 2.]:
-      E = 0.
+     E = 0.
-      norm = 0.
+     norm = 0.
-      for x in interval:
+       for x in interval:
-            r[0] = x
+           r[0] = x
-            for y in interval:
+             for y in interval:
-                  r[1] = y
+                 r[1] = y
-                  for z in interval:
+                   for z in interval:
-                        r[2] = z
+                       r[2] = z
-                        w = psi(a,r)
+                       w = psi(a,r)
-                        w = w * w * delta
+                       w = w * w * delta
-                        E    += w * e_loc(a,r)
+                       E    += w * e_loc(a,r)
-                        norm += w 
+                       norm += w 
-      E = E / norm
+                       E = E / norm
-      print(f"a = {a} \t E = {E}")
+                       print(f"a = {a} \t E = {E}")

qmc_stats.f90

@@ -13,3 +13,31 @@ subroutine ave_error(x,n,ave,err)
      err = dsqrt(variance/dble(n))
   endif
 end subroutine ave_error
+
+subroutine random_gauss(z,n)
+  implicit none
+  integer, intent(in) :: n
+  double precision, intent(out) :: z(n)
+  double precision :: u(n+1)
+  double precision, parameter :: two_pi = 2.d0*dacos(-1.d0)
+  integer :: i
+
+  call random_number(u)
+  if (iand(n,1) == 0) then
+     ! n is even
+     do i=1,n,2
+        z(i)   = dsqrt(-2.d0*dlog(u(i))) 
+        z(i+1) = z(i) + dsin( two_pi*u(i+1) )
+        z(i)   = z(i) + dcos( two_pi*u(i+1) )
+     end do
+  else
+     ! n is odd
+     do i=1,n-1,2
+        z(i)   = dsqrt(-2.d0*dlog(u(i))) 
+        z(i+1) = z(i) + dsin( two_pi*u(i+1) )
+        z(i)   = z(i) + dcos( two_pi*u(i+1) )
+     end do
+     z(n)   = dsqrt(-2.d0*dlog(u(n))) 
+     z(n)   = z(n) + dcos( two_pi*u(n+1) )
+  end if
+end subroutine random_gauss

qmc_uniform.py

@@ -1,19 +1,19 @@
 from hydrogen  import *
 from qmc_stats import *
 
-def MonteCarlo(a, nmax):
+   def MonteCarlo(a, nmax):
-    E = 0.
+       E = 0.
-    N = 0.
+       N = 0.
-    for istep in range(nmax):
+       for istep in range(nmax):
-        r = np.random.uniform(-5., 5., (3))
+           r = np.random.uniform(-5., 5., (3))
-        w = psi(a,r)
+           w = psi(a,r)
-        w = w*w
+           w = w*w
-        N += w
+           N += w
-        E += w * e_loc(a,r)
+           E += w * e_loc(a,r)
-    return E/N
+       return E/N
 
-a = 0.9
+   a = 0.9
-nmax = 100000
+   nmax = 100000
-X = [MonteCarlo(a,nmax) for i in range(30)]
+   X = [MonteCarlo(a,nmax) for i in range(30)]
-E, deltaE = ave_error(X)
+   E, deltaE = ave_error(X)
-print(f"E = {E} +/- {deltaE}")
+   print(f"E = {E} +/- {deltaE}")

variance_hydrogen.py

@@ -20,8 +20,8 @@ for a in [0.1, 0.2, 0.5, 0.9, 1., 1.5, 2.]:
                 El = e_loc(a, r)
                 E  += w * El
                 norm += w 
-    E = E / norm
+                E = E / norm
-    s2 = 0.
+                s2 = 0.
     for x in interval:
         r[0] = x
         for y in interval:
@@ -32,5 +32,5 @@ for a in [0.1, 0.2, 0.5, 0.9, 1., 1.5, 2.]:
                 w = w * w * delta
                 El = e_loc(a, r)
                 s2 += w * (El - E)**2
-    s2 = s2 / norm
+                s2 = s2 / norm
-    print(f"a = {a} \t E = {E:10.8f}  \t  \sigma^2 = {s2:10.8f}")
+                print(f"a = {a} \t E = {E:10.8f}  \t  \sigma^2 = {s2:10.8f}")