content: """
  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
  