#!/usr/bin/env python

"""
Calculates the Coupled-Cluster energy- and amplitude equations
See 'An Introduction to Coupled Cluster Theory' by
T. Daniel Crawford and Henry F. Schaefer III.
http://www.ccc.uga.edu/lec_top/cc/html/review.html
"""

from sympy.physics.secondquant import (AntiSymmetricTensor, wicks,
        F, Fd, NO, evaluate_deltas, substitute_dummies, Commutator,
        simplify_index_permutations, PermutationOperator)
from sympy import (
    symbols, expand, pprint, Rational, latex, Dummy
)

pretty_dummies_dict = {
    'above': 'cdefgh',
    'below': 'klmno',
    'general': 'pqrstu'
}


def get_CC_operators():
    """
    Returns a tuple (T1,T2) of unique operators.
    """
    i = symbols('i', below_fermi=True, cls=Dummy)
    a = symbols('a', above_fermi=True, cls=Dummy)
    t_ai = AntiSymmetricTensor('t', (a,), (i,))
    ai = NO(Fd(a)*F(i))
    i, j = symbols('i,j', below_fermi=True, cls=Dummy)
    a, b = symbols('a,b', above_fermi=True, cls=Dummy)
    t_abij = AntiSymmetricTensor('t', (a, b), (i, j))
    abji = NO(Fd(a)*Fd(b)*F(j)*F(i))

    T1 = t_ai*ai
    T2 = Rational(1, 4)*t_abij*abji
    return (T1, T2)


def main():
    print
    print "Calculates the Coupled-Cluster energy- and amplitude equations"
    print "See 'An Introduction to Coupled Cluster Theory' by"
    print "T. Daniel Crawford and Henry F. Schaefer III"
    print "http://www.ccc.uga.edu/lec_top/cc/html/review.html"
    print

    # setup hamiltonian
    p, q, r, s = symbols('p,q,r,s', cls=Dummy)
    f = AntiSymmetricTensor('f', (p,), (q,))
    pr = NO((Fd(p)*F(q)))
    v = AntiSymmetricTensor('v', (p, q), (r, s))
    pqsr = NO(Fd(p)*Fd(q)*F(s)*F(r))

    H = f*pr + Rational(1, 4)*v*pqsr
    print "Using the hamiltonian:", latex(H)

    print "Calculating 4 nested commutators"
    C = Commutator

    T1, T2 = get_CC_operators()
    T = T1 + T2
    print "commutator 1..."
    comm1 = wicks(C(H, T))
    comm1 = evaluate_deltas(comm1)
    comm1 = substitute_dummies(comm1)

    T1, T2 = get_CC_operators()
    T = T1 + T2
    print "commutator 2..."
    comm2 = wicks(C(comm1, T))
    comm2 = evaluate_deltas(comm2)
    comm2 = substitute_dummies(comm2)

    T1, T2 = get_CC_operators()
    T = T1 + T2
    print "commutator 3..."
    comm3 = wicks(C(comm2, T))
    comm3 = evaluate_deltas(comm3)
    comm3 = substitute_dummies(comm3)

    T1, T2 = get_CC_operators()
    T = T1 + T2
    print "commutator 4..."
    comm4 = wicks(C(comm3, T))
    comm4 = evaluate_deltas(comm4)
    comm4 = substitute_dummies(comm4)

    print "construct Hausdoff expansion..."
    eq = H + comm1 + comm2/2 + comm3/6 + comm4/24
    eq = eq.expand()
    eq = evaluate_deltas(eq)
    eq = substitute_dummies(eq, new_indices=True,
            pretty_indices=pretty_dummies_dict)
    print "*********************"
    print

    print "extracting CC equations from full Hbar"
    i, j, k, l = symbols('i,j,k,l', below_fermi=True)
    a, b, c, d = symbols('a,b,c,d', above_fermi=True)
    print
    print "CC Energy:"
    print latex(wicks(eq, simplify_dummies=True,
        keep_only_fully_contracted=True))
    print
    print "CC T1:"
    eqT1 = wicks(NO(Fd(i)*F(a))*eq, simplify_kronecker_deltas=True, keep_only_fully_contracted=True)
    eqT1 = substitute_dummies(eqT1)
    print latex(eqT1)
    print
    print "CC T2:"
    eqT2 = wicks(NO(Fd(i)*Fd(j)*F(b)*F(a))*eq, simplify_dummies=True, keep_only_fully_contracted=True, simplify_kronecker_deltas=True)
    P = PermutationOperator
    eqT2 = simplify_index_permutations(eqT2, [P(a, b), P(i, j)])
    print latex(eqT2)

if __name__ == "__main__":
    main()
