"""
This module includes a collection of testing functions for the QuTiP scattering
module. Tests are approximate with low resolution to minimize runtime.
"""

# Author:  Ben Bartlett
# Contact: benbartlett@stanford.edu

import numpy as np
from qutip import create, destroy, basis
from qutip.solver.scattering import *


class TestScattering:
    """
    A test class for the QuTiP quantum optical scattering module. These tests
    only use the two-level system for comparison, since larger systems can
    take a long time to run.
    """

    def testScatteringProbability(self):
        """
        Asserts that pi pulse in TLS has P0 ~ 0 and P0+P1+P2 ~ 1
        """
        w0 = 1.0 * 2 * np.pi
        gamma = 1.0
        sm = np.sqrt(gamma) * destroy(2)
        pulseArea = np.pi
        pulseLength = 0.2 / gamma
        RabiFreq = pulseArea / (2 * pulseLength)
        psi0 = basis(2, 0)
        tlist = np.geomspace(gamma, 10 * gamma, 40) - gamma
        # Define TLS Hamiltonian
        H0S = w0 * create(2) * destroy(2)
        H1S1 = lambda t, args: \
            RabiFreq * 1j * np.exp(-1j * w0 * t) * (t < pulseLength)
        H1S2 = lambda t, args: \
            RabiFreq * -1j * np.exp(1j * w0 * t) * (t < pulseLength)
        Htls = [H0S, [sm.dag(), H1S1], [sm, H1S2]]
        # Run the test
        P0 = scattering_probability(Htls, psi0, 0, [sm], tlist)
        P1 = scattering_probability(Htls, psi0, 1, [sm], tlist)
        P2 = scattering_probability(Htls, psi0, 2, [sm], tlist)
        assert P0 < 1e-3
        assert np.abs(P0 + P1 + P2 - 1) < 1e-3

    def testScatteringAmplitude(self):
        """
        Asserts that a 2pi pulse in TLS has ~0 amplitude after pulse
        """
        w0 = 1.0 * 2 * np.pi
        gamma = 1.0
        sm = np.sqrt(gamma) * destroy(2)
        pulseArea = 2 * np.pi
        pulseLength = 0.2 / gamma
        RabiFreq = pulseArea / (2 * pulseLength)
        psi0 = basis(2, 0)
        T = 50
        tlist = np.linspace(0, 1 / gamma, T)
        # Define TLS Hamiltonian
        H0S = w0 * create(2) * destroy(2)
        H1S1 = lambda t, args: \
            RabiFreq * 1j * np.exp(-1j * w0 * t) * (t < pulseLength)
        H1S2 = lambda t, args: \
            RabiFreq * -1j * np.exp(1j * w0 * t) * (t < pulseLength)
        Htls = [H0S, [sm.dag(), H1S1], [sm, H1S2]]
        # Run the test
        state = temporal_scattered_state(Htls, psi0, 1, [sm], tlist)
        basisVec = temporal_basis_vector([[40]], T)
        assert np.abs(basisVec.dag() @ state) < 1e-3

    def testWaveguideSplit(self):
        """
        Checks that a trivial splitting of a waveguide collapse operator like
        [sm] -> [sm/sqrt2, sm/sqrt2] doesn't affect the normalization or result
        """
        gamma = 1.0
        sm = np.sqrt(gamma) * destroy(2)
        pulseArea = np.pi
        pulseLength = 0.2 / gamma
        RabiFreq = pulseArea / (2 * pulseLength)
        psi0 = basis(2, 0)
        tlist = np.geomspace(gamma, 10 * gamma, 40) - gamma
        # Define TLS Hamiltonian with rotating frame transformation
        Htls = [[sm.dag() + sm, lambda t, args: RabiFreq * (t < pulseLength)]]
        # Run the test
        c_ops = [sm]
        c_ops_split = [sm / np.sqrt(2), sm / np.sqrt(2)]
        P1 = scattering_probability(Htls, psi0, 1, c_ops, tlist)
        P1_split = scattering_probability(Htls, psi0, 1, c_ops_split, tlist)
        assert np.abs(P1/P1_split - 1) < 1e-7