code: # MIT License
  # 
  # Copyright (c) 2019 Edward D. Lee, Bryan C. Daniels
  # 
  # Permission is hereby granted, free of charge, to any person obtaining a copy
  # of this software and associated documentation files (the "Software"), to deal
  # in the Software without restriction, including without limitation the rights
  # to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
  # copies of the Software, and to permit persons to whom the Software is
  # furnished to do so, subject to the following conditions:
  # 
  # The above copyright notice and this permission notice shall be included in all
  # copies or substantial portions of the Software.
  # 
  # THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
  # IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
  # FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
  # AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
  # LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
  # OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
  # SOFTWARE.
  
  # Equations for 2-spin Ising model.
  
  # Written on 2019/09/19.
  from numpy import zeros, exp, array, prod, isnan
  from ..enumerate import fast_logsumexp
  
  def calc_observables(params):
      """
      Give all parameters concatenated into one array from lowest to highest order.
      Returns all correlations.
      """
      Cout = zeros((3))
      H = params[0:2]
      J = params[2:3]
      energyTerms = array([            +H[0]+H[1]+J[0], +H[0]-H[1]-J[0], -H[0]+H[1]-J[0], -H[0]-H[1]+J[0],])
      logZ = fast_logsumexp(energyTerms)[0]
      num = fast_logsumexp(energyTerms, [ 1, 1,-1,-1])
      Cout[0] = exp( num[0] - logZ ) * num[1]
      num = fast_logsumexp(energyTerms, [ 1,-1, 1,-1])
      Cout[1] = exp( num[0] - logZ ) * num[1]
      num = fast_logsumexp(energyTerms, [ 1,-1,-1, 1])
      Cout[2] = exp( num[0] - logZ ) * num[1]
      Cout[isnan(Cout)] = 0.
      return(Cout)
  
  def p(params):
      """
      Give all parameters concatenated into one array from lowest to highest order.
      Returns probabilities of all configurations.
      """
      Cout = zeros((3))
      H = params[0:2]
      J = params[2:3]
      H = params[0:2]
      J = params[2:3]
      Pout = zeros((4))
      energyTerms = array([            +H[0]+H[1]+J[0], +H[0]-H[1]-J[0], -H[0]+H[1]-J[0], -H[0]-H[1]+J[0],])
      logZ = fast_logsumexp(energyTerms)[0]
      Pout[0] = exp( +H[0]+H[1]+J[0] - logZ )
      Pout[1] = exp( +H[0]-H[1]-J[0] - logZ )
      Pout[2] = exp( -H[0]+H[1]-J[0] - logZ )
      Pout[3] = exp( -H[0]-H[1]+J[0] - logZ )
  
      Pout = Pout[::-1]
      return(Pout)
  
apis: numpy.array numpy.exp numpy.zeros numpy.isnan