old_contents: r"""
  Definition
  ----------
  
  This model fits the Guinier function
  
  .. math::
  
      I(q) = \text{scale} \cdot \exp{\left[ \frac{-Q^2 R_g^2 }{3} \right]}
              + \text{background}
  
  to the data directly without any need for linearisation (*cf*. the usual
  plot of $\ln I(q)$ vs $q^2$\ ). Note that you may have to restrict the data
  range to include small q only, where the Guinier approximation actually
  applies. See also the guinier_porod model.
  
  For 2D data the scattering intensity is calculated in the same way as 1D,
  where the $q$ vector is defined as
  
  .. math:: q = \sqrt{q_x^2 + q_y^2}
  
  Note that $R_g^2$ may be negative, which happens when a form factor $P(Q)$ is
  increasing with $Q$ rather than decreasing. This can occur for core/shell
  particles, hollow particles, or for composite particles with domains of
  different SLDs in a solvent with an SLD close to the average match point.
  (Alternatively, this might be regarded as there being an internal inter-domain
  "structure factor" within a single particle which gives rise to a peak in the
  scattering).
  
  To specify a negative value of $R_g^2$ in SasView, simply give $R_g$ a negative
  value ($R_g^2$ will be evaluated as $R_g |R_g|$). Note that the physical radius 
  of gyration, of the exterior of the particle, will still be large and positive. 
  It is only the apparent size from the small $Q$ data that will give a small or 
  negative value of $R_g^2$.
  
  References
  ----------
  
  A Guinier and G Fournet, *Small-Angle Scattering of X-Rays*,
  John Wiley & Sons, New York (1955)
  """
  
  import numpy as np
  from numpy import inf
  
  name = "guinier"
  title = ""
  description = """
   I(q) = scale.exp ( - rg^2 q^2 / 3.0 )
  
      List of default parameters:
      scale = scale
      rg = Radius of gyration
  """
  category = "shape-independent"
  
  #             ["name", "units", default, [lower, upper], "type","description"],
  parameters = [["rg", "Ang", 60.0, [-inf, inf], "", "Radius of Gyration"]]
  
  Iq = """
      double exponent = abs(rg)*rg*q*q/3.0;
      double value = exp(-exponent);
      return value;
  """
  
  def random():
      scale = 10**np.random.uniform(1, 4)
      # Note: compare.py has Rg cutoff of 1e-30 at q=1 for guinier, so use that
      # log_10 Ae^(-(q Rg)^2/3) = log_10(A) - (q Rg)^2/ (3 ln 10) > -30
      #   => log_10(A) > Rg^2/(3 ln 10) - 30
      q_max = 1.0
      rg_max = np.sqrt(90*np.log(10) + 3*np.log(scale))/q_max
      rg = 10**np.random.uniform(0, np.log10(rg_max))
      pars = dict(
          #background=0,
          scale=scale,
          rg=rg,
      )
      return pars
  
  # parameters for demo
  demo = dict(scale=1.0,  background=0.001, rg=60.0 )
  
  # parameters for unit tests
  tests = [[{'rg' : 31.5}, 0.005, 0.992756]]
  
new_contents: r"""
  Definition
  ----------
  
  This model fits the Guinier function
  
  .. math::
  
      I(q) = \text{scale} \cdot \exp{\left[ \frac{-Q^2 R_g^2 }{3} \right]}
              + \text{background}
  
  to the data directly without any need for linearisation (*cf*. the usual
  plot of $\ln I(q)$ vs $q^2$\ ). Note that you may have to restrict the data
  range to include small q only, where the Guinier approximation actually
  applies. See also the guinier_porod model.
  
  For 2D data the scattering intensity is calculated in the same way as 1D,
  where the $q$ vector is defined as
  
  .. math:: q = \sqrt{q_x^2 + q_y^2}
  
  Note that $R_g^2$ may be negative, which happens when a form factor $P(Q)$ is
  increasing with $Q$ rather than decreasing. This can occur for core/shell
  particles, hollow particles, or for composite particles with domains of
  different SLDs in a solvent with an SLD close to the average match point.
  (Alternatively, this might be regarded as there being an internal inter-domain
  "structure factor" within a single particle which gives rise to a peak in the
  scattering).
  
  To specify a negative value of $R_g^2$ in SasView, simply give $R_g$ a negative
  value ($R_g^2$ will be evaluated as $R_g |R_g|$). Note that the physical radius 
  of gyration, of the exterior of the particle, will still be large and positive. 
  It is only the apparent size from the small $Q$ data that will give a small or 
  negative value of $R_g^2$.
  
  References
  ----------
  
  A Guinier and G Fournet, *Small-Angle Scattering of X-Rays*,
  John Wiley & Sons, New York (1955)
  """
  
  import numpy as np
  from numpy import inf
  
  name = "guinier"
  title = ""
  description = """
   I(q) = scale.exp ( - rg^2 q^2 / 3.0 )
  
      List of default parameters:
      scale = scale
      rg = Radius of gyration
  """
  category = "shape-independent"
  
  #             ["name", "units", default, [lower, upper], "type","description"],
  parameters = [["rg", "Ang", 60.0, [-inf, inf], "", "Radius of Gyration"]]
  
  Iq = """
      double exponent = fabs(rg)*rg*q*q/3.0;
      double value = exp(-exponent);
      return value;
  """
  
  def random():
      scale = 10**np.random.uniform(1, 4)
      # Note: compare.py has Rg cutoff of 1e-30 at q=1 for guinier, so use that
      # log_10 Ae^(-(q Rg)^2/3) = log_10(A) - (q Rg)^2/ (3 ln 10) > -30
      #   => log_10(A) > Rg^2/(3 ln 10) - 30
      q_max = 1.0
      rg_max = np.sqrt(90*np.log(10) + 3*np.log(scale))/q_max
      rg = 10**np.random.uniform(0, np.log10(rg_max))
      pars = dict(
          #background=0,
          scale=scale,
          rg=rg,
      )
      return pars
  
  # parameters for demo
  demo = dict(scale=1.0,  background=0.001, rg=60.0 )
  
  # parameters for unit tests
  tests = [[{'rg' : 31.5}, 0.005, 0.992756]]
  
subject: use floating point routine fabs (breaks in openCL otherwise)