added codes

doc/Programs/VariousCodes/hamiltonian-1.py

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+import scipy as scipy
+import scipy.special as special
+import numpy as np
+import itertools as it
+from pandas import *
+import matplotlib.pylab as plt
+from scipy.integrate import ode
+import time
+
+def unique_rows(a):
+    a = np.ascontiguousarray(a)
+    unique_a = np.unique(a.view([('', a.dtype)]*a.shape[1]))
+    return unique_a.view(a.dtype).reshape((unique_a.shape[0], a.shape[1]))
+
+def hamiltonian(n_pairs,n_basis,delta,g):
+	"""
+	n_pairs - Number of electron pairs
+	n_basis - Number of spacial basis states
+	"""
+	n_SD = int(special.binom(n_basis,n_pairs))
+	print("n = ", n_SD)
+	H_mat = np.zeros((n_SD,n_SD))
+	S = stateMatrix(n_pairs,n_basis)
+	for row in range(n_SD):
+		bra = S[row,:]
+		for col in range(n_SD):
+			ket = S[col,:]
+			if np.sum(np.equal(bra,ket)) == bra.shape:
+				H_mat[row,col] += 2*delta*np.sum(bra - 1) - 0.5*g*n_pairs
+			if n_pairs - np.intersect1d(bra,ket).shape[0] == 1:
+				H_mat[row,col] += -0.5*g
+	return(H_mat)
+
+
+def stateMatrix(n_pairs,n_basis):
+	L = []
+	states = range(1,n_basis+1)
+	for perm in it.permutations(states,n_pairs):
+		L.append(perm)
+	L = np.array(L)
+	L.sort(axis=1)
+	L = unique_rows(L)
+	return(L)
+
+
+
+g = 0.5
+
+H = hamiltonian(4,8,1,g)
+print("Hamiltonian calculated")
+
+A = H
+x = np.zeros(A.shape[0])
+x[0] = 1
+
+def f(t,x):
+	return(-(x.T@x)*A@x + (x.T@A@x)*x)
+
+
+
+r = ode(f)
+r.set_initial_value(x,0) #langsos algorithm
+
+t1=10
+dt=0.1
+start = time.time()
+while r.successful() and r.t < t1:
+	r.integrate(r.t+dt)
+end = time.time()
+
+
+
+print("RNN eig: ",r.y.T@A@r.y/(r.y.T@r.y))
+print("calculation time with RNN: ", end - start)
+
+
+start = time.time()
+eigvals, eigvecs = np.linalg.eig(H)
+end = time.time()
+print("numpy eig: ",np.sort(eigvals))
+print("calculation time with numpy eig: ", end - start)