""" Star HF-iterations, preparing variables and density matrix """

        """ Coefficients for setting up density matrix, assuming only one along the diagonals """
	C = np.eye(spOrbitals) # HF coefficients
        DensityMatrix = np.zeros([spOrbitals,spOrbitals])
        for gamma in range(spOrbitals):
            for delta in range(spOrbitals):
                sum = 0.0
                for i in range(Nparticles):
                    sum += C[gamma][i]*C[delta][i]
                DensityMatrix[gamma][delta] = Decimal(sum)
        maxHFiter = 100
        epsilon =  1.0e-10 
        difference = 1.0
	hf_count = 0
	oldenergies = np.zeros(spOrbitals)
	newenergies = np.zeros(spOrbitals)
	while hf_count < maxHFiter and difference > epsilon:
		print "############### Iteration %i ###############" % hf_count
   	        HFmatrix = np.zeros([spOrbitals,spOrbitals])		
		for alpha in range(spOrbitals):
			for beta in range(spOrbitals):
                            """  If tests for three-dimensional systems, including isospin conservation """
                            if l[alpha] != l[beta] and j[alpha] != j[beta] and mj[alpha] != mj[beta] and tz[alpha] != tz[beta]: continue
                            """  Setting up the Fock matrix using the density matrix and antisymmetrized NN interaction in m-scheme """
     		            sumFockTerm = 0.0
                            for gamma in range(spOrbitals):
                                for delta in range(spOrbitals):
                                    if (mj[alpha]+mj[gamma]) != (mj[beta]+mj[delta]) and (tz[alpha]+tz[gamma]) != (tz[beta]+tz[delta]): continue
                                    sumFockTerm += DensityMatrix[gamma][delta]*nninteraction[alpha][gamma][beta][delta]
                            HFmatrix[alpha][beta] = Decimal(sumFockTerm)
                            """  Adding the one-body term, here plain harmonic oscillator """
                            if beta == alpha:   HFmatrix[alpha][alpha] += singleparticleH[alpha]
		spenergies, C = np.linalg.eigh(HFmatrix)
                """ Setting up new density matrix in m-scheme """
                DensityMatrix = np.zeros([spOrbitals,spOrbitals])
                for gamma in range(spOrbitals):
                    for delta in range(spOrbitals):
                        sum = 0.0
                        for i in range(Nparticles):
                            sum += C[gamma][i]*C[delta][i]
                        DensityMatrix[gamma][delta] = Decimal(sum)
		newenergies = spenergies
                """ Brute force computation of difference between previous and new sp HF energies """
                sum =0.0
                for i in range(spOrbitals):
                    sum += (abs(newenergies[i]-oldenergies[i]))/spOrbitals
                difference = sum
                oldenergies = newenergies
                print "Single-particle energies, ordering may have changed "
                for i in range(spOrbitals):
                    print('{0:4d}  {1:.4f}'.format(i, Decimal(oldenergies[i])))
		hf_count += 1