Source code for qutip.utilities

# This file is part of QuTiP: Quantum Toolbox in Python.
#
#    Copyright (c) 2011 and later, Paul D. Nation and Robert J. Johansson.
#    All rights reserved.
#
#    Redistribution and use in source and binary forms, with or without
#    modification, are permitted provided that the following conditions are
#    met:
#
#    1. Redistributions of source code must retain the above copyright notice,
#       this list of conditions and the following disclaimer.
#
#    2. Redistributions in binary form must reproduce the above copyright
#       notice, this list of conditions and the following disclaimer in the
#       documentation and/or other materials provided with the distribution.
#
#    3. Neither the name of the QuTiP: Quantum Toolbox in Python nor the names
#       of its contributors may be used to endorse or promote products derived
#       from this software without specific prior written permission.
#
#    THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
#    "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
#    LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A
#    PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
#    HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
#    SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
#    LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
#    DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
#    THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
#    (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
#    OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
###############################################################################

"""
This module contains utility functions that are commonly needed in other
qutip modules.
"""

__all__ = ['n_thermal', 'linspace_with', 'clebsch', 'convert_unit',
           'view_methods']

import numpy as np

[docs]def n_thermal(w, w_th): """ Return the number of photons in thermal equilibrium for an harmonic oscillator mode with frequency 'w', at the temperature described by 'w_th' where :math:`\\omega_{\\rm th} = k_BT/\\hbar`. Parameters ---------- w : *float* or *array* Frequency of the oscillator. w_th : *float* The temperature in units of frequency (or the same units as `w`). Returns ------- n_avg : *float* or *array* Return the number of average photons in thermal equilibrium for a an oscillator with the given frequency and temperature. """ if type(w) is np.ndarray: return 1.0 / (np.exp(w / w_th) - 1.0) else: if (w_th > 0) and np.exp(w / w_th) != 1.0: return 1.0 / (np.exp(w / w_th) - 1.0) else: return 0.0
[docs]def linspace_with(start, stop, num=50, elems=[]): """ Return an array of numbers sampled over specified interval with additional elements added. Returns `num` spaced array with elements from `elems` inserted if not already included in set. Returned sample array is not evenly spaced if addtional elements are added. Parameters ---------- start : int The starting value of the sequence. stop : int The stoping values of the sequence. num : int, optional Number of samples to generate. elems : list/ndarray, optional Requested elements to include in array Returns ------- samples : ndadrray Original equally spaced sample array with additional elements added. """ elems = np.array(elems) lspace = np.linspace(start, stop, num) return np.union1d(lspace, elems)
[docs]def clebsch(j1, j2, j3, m1, m2, m3): """Calculates the Clebsch-Gordon coefficient for coupling (j1,m1) and (j2,m2) to give (j3,m3). Parameters ---------- j1 : float Total angular momentum 1. j2 : float Total angular momentum 2. j3 : float Total angular momentum 3. m1 : float z-component of angular momentum 1. m2 : float z-component of angular momentum 2. m3 : float z-component of angular momentum 3. Returns ------- cg_coeff : float Requested Clebsch-Gordan coefficient. """ from scipy.misc import factorial if m3 != m1 + m2: return 0 vmin = int(np.max([-j1 + j2 + m3, -j1 + m1, 0])) vmax = int(np.min([j2 + j3 + m1, j3 - j1 + j2, j3 + m3])) C = np.sqrt((2.0 * j3 + 1.0) * factorial(j3 + j1 - j2) * factorial(j3 - j1 + j2) * factorial(j1 + j2 - j3) * factorial(j3 + m3) * factorial(j3 - m3) / (factorial(j1 + j2 + j3 + 1) * factorial(j1 - m1) * factorial(j1 + m1) * factorial(j2 - m2) * factorial(j2 + m2))) S = 0 for v in range(vmin, vmax + 1): S += (-1.0) ** (v + j2 + m2) / factorial(v) * \ factorial(j2 + j3 + m1 - v) * factorial(j1 - m1 + v) / \ factorial(j3 - j1 + j2 - v) / factorial(j3 + m3 - v) / \ factorial(v + j1 - j2 - m3) C = C * S return C
# ----------------------------------------------------------------------------- # Functions for unit conversions # _e = 1.602176565e-19 # C _kB = 1.3806488e-23 # J/K _h = 6.62606957e-34 # Js _unit_factor_tbl = { # "unit": "factor that convert argument from unit 'unit' to Joule" "J": 1.0, "eV": _e, "meV": 1.0e-3 * _e, "GHz": 1.0e9 * _h, "mK": 1.0e-3 * _kB, }
[docs]def convert_unit(value, orig="meV", to="GHz"): """ Convert an energy from unit `orig` to unit `to`. Parameters ---------- value : float / array The energy in the old unit. orig : string The name of the original unit ("J", "eV", "meV", "GHz", "mK") to : string The name of the new unit ("J", "eV", "meV", "GHz", "mK") Returns ------- value_new_unit : float / array The energy in the new unit. """ if orig not in _unit_factor_tbl: raise TypeError("Unsupported unit %s" % orig) if to not in _unit_factor_tbl: raise TypeError("Unsupported unit %s" % to) return value * (_unit_factor_tbl[orig] / _unit_factor_tbl[to])
def convert_GHz_to_meV(w): """ Convert an energy from unit GHz to unit meV. Parameters ---------- w : float / array The energy in the old unit. Returns ------- w_new_unit : float / array The energy in the new unit. """ # 1 GHz = 4.1357e-6 eV = 4.1357e-3 meV w_meV = w * 4.1357e-3 return w_meV def convert_meV_to_GHz(w): """ Convert an energy from unit meV to unit GHz. Parameters ---------- w : float / array The energy in the old unit. Returns ------- w_new_unit : float / array The energy in the new unit. """ # 1 meV = 1.0/4.1357e-3 GHz w_GHz = w / 4.1357e-3 return w_GHz def convert_J_to_meV(w): """ Convert an energy from unit J to unit meV. Parameters ---------- w : float / array The energy in the old unit. Returns ------- w_new_unit : float / array The energy in the new unit. """ # 1 eV = 1.602e-19 J w_meV = 1000.0 * w / _e return w_meV def convert_meV_to_J(w): """ Convert an energy from unit meV to unit J. Parameters ---------- w : float / array The energy in the old unit. Returns ------- w_new_unit : float / array The energy in the new unit. """ # 1 eV = 1.602e-19 J w_J = 0.001 * w * _e return w_J def convert_meV_to_mK(w): """ Convert an energy from unit meV to unit mK. Parameters ---------- w : float / array The energy in the old unit. Returns ------- w_new_unit : float / array The energy in the new unit. """ # 1 mK = 0.0000861740 meV w_mK = w / 0.0000861740 return w_mK def convert_mK_to_meV(w): """ Convert an energy from unit mK to unit meV. Parameters ---------- w : float / array The energy in the old unit. Returns ------- w_new_unit : float / array The energy in the new unit. """ # 1 mK = 0.0000861740 meV w_meV = w * 0.0000861740 return w_meV def convert_GHz_to_mK(w): """ Convert an energy from unit GHz to unit mK. Parameters ---------- w : float / array The energy in the old unit. Returns ------- w_new_unit : float / array The energy in the new unit. """ # h v [Hz] = kB T [K] # h 1e9 v [GHz] = kB 1e-3 T [mK] # T [mK] = 1e12 * (h/kB) * v [GHz] w_mK = w * 1.0e12 * (_h / _kB) return w_mK def convert_mK_to_GHz(w): """ Convert an energy from unit mK to unit GHz. Parameters ---------- w : float / array The energy in the old unit. Returns ------- w_new_unit : float / array The energy in the new unit. """ w_GHz = w * 1.0e-12 * (_kB / _h) return w_GHz def view_methods(Q): """ View the methods and corresponding doc strings for a Qobj class. Parameters ---------- Q : Qobj Input Quantum object. """ meth = dir(Q) qobj_props = ['data', 'dims', 'isherm', 'shape', 'type'] pub_meth = [x for x in meth if x.find('_') and x not in qobj_props] ml = max([len(x) for x in pub_meth]) nl = len(Q.__class__.__name__ + 'Class Methods:') print(Q.__class__.__name__ + ' Class Methods:') print('-' * nl) for ii in range(len(pub_meth)): m = getattr(Q, pub_meth[ii]) meth_str = m.__doc__ ind = meth_str.find('\n') pub_len = len(pub_meth[ii] + ': ') print(pub_meth[ii] + ':' + ' ' * (ml+3-pub_len) + meth_str[:ind]) def _version2int(version_string): str_list = version_string.split( "-dev")[0].split("rc")[0].split("a")[0].split("b")[0].split( "post")[0].split('.') return sum([int(d if len(d) > 0 else 0) * (100 ** (3 - n)) for n, d in enumerate(str_list[:3])]) def _blas_info(): config = np.__config__ blas_info = config.blas_opt_info _has_lib_key = 'libraries' in blas_info.keys() blas = None if hasattr(config,'mkl_info') or \ (_has_lib_key and any('mkl' in lib for lib in blas_info['libraries'])): blas = 'INTEL MKL' elif hasattr(config,'openblas_info') or \ (_has_lib_key and any('openblas' in lib for lib in blas_info['libraries'])): blas = 'OPENBLAS' elif 'extra_link_args' in blas_info.keys() and ('-Wl,Accelerate' in blas_info['extra_link_args']): blas = 'Accelerate' else: blas = 'Generic' return blas