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Improve PyAPI wmp docstrings; support E arrays
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Sterling Harper
parent
85d26be07a
commit
1bc72660de
1 changed files with 132 additions and 8 deletions
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@ -38,7 +38,7 @@ FIT_A = 1 # Absorption
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FIT_F = 2 # Fission
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def faddeeva(z):
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def _faddeeva(z):
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"""Evaluate the complex Faddeeva function.
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Technically, the value we want is given by the equation:
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@ -54,6 +54,16 @@ def faddeeva(z):
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For imag(z) > 0, w_int(z) = w_fun(z)
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For imag(z) < 0, w_int(z) = -conjg(w_fun(conjg(z)))
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Parameters
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----------
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z : Complex
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Argument to the Faddeeva function.
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Returns
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-------
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Complex
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I/Pi * Integrate[Exp[-t^2]/(z-t), {t, -Infinity, Infinity}]
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"""
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if np.angle(z) > 0:
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return wofz(z)
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@ -61,8 +71,28 @@ def faddeeva(z):
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return -np.conj(wofz(z))
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def broaden_wmp_polynomials(En, dopp, n):
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sqrtE = sqrt(En)
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def _broaden_wmp_polynomials(En, dopp, n):
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"""Evaluate Doppler-broadened windowed multipole curvefit.
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The curvefit is a polynomial of the form
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a/En + b/sqrt(En) + c + d sqrt(En) ...
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Parameters
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----------
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En : Real
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Energy to evaluate at.
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dopp : Real
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sqrt(atomic weight ratio / kT) in units of eV.
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n : Integral
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Number of components to the polynomial.
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Returns
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-------
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np.ndarray
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The value of each Doppler-broadened curvefit polynomial term.
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"""
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sqrtE = np.sqrt(En)
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beta = sqrtE * dopp
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half_inv_dopp2 = 0.5 / dopp**2
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quarter_inv_dopp4 = half_inv_dopp2**2
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@ -81,7 +111,7 @@ def broaden_wmp_polynomials(En, dopp, n):
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factors = np.zeros(n)
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factors[0] = erfbeta / En
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factors[0] = erfBeta / En
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factors[1] = 1.0 / sqrtE
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factors[2] = (factors[0] * (half_inv_dopp2 + En)
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+ exp_m_beta2 / (beta * np.sqrt(np.pi)))
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@ -100,6 +130,62 @@ def broaden_wmp_polynomials(En, dopp, n):
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class WindowedMultipole(EqualityMixin):
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"""Resonant cross sections represented in the windowed multipole format.
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Attributes
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----------
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num_l : Integral
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Number of possible l quantum states for this nuclide.
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fit_order : Integral
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Order of the windowed curvefit.
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fissionable : bool
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Whether or not the target nuclide has fission data.
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formalism : str
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The R-matrix formalism used to reconstruct resonances. Either 'MLBW'
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for multi-level Breit Wigner or 'RM' for Reich-Moore.
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spacing : Real
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The width of each window in sqrt(E)-space. For example, the frst window
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will end at (sqrt(start_E) + spacing)**2 and the second window at
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(sqrt(start_E) + 2*spacing)**2.
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sqrtAWR : Real
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Square root of the atomic weight ratio of the target nuclide.
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start_E : Real
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Lowest energy in eV the library is valid for.
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end_E : Real
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Highest energy in eV the library is valid for.
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data : np.ndarray
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A 2D array of complex poles and residues. data[i, 0] gives the energy
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at which pole i is located. data[i, 1:] gives the residues associated
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with the i-th pole. There are 3 residues for Reich-Moore data, one each
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for the total, absorption, and fission channels. Multi-level
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Breit Wigner data has an additional residue for the competitive channel.
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pseudo_k0RS : np.ndarray
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A 1D array of Real values. There is one value for each valid l
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quantum number. The values are equal to
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sqrt(2 m / hbar) * AWR / (AWR + 1) * r
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where m is the neutron mass, AWR is the atomic weight ratio, and r
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is the l-dependent scattering radius.
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l_value : np.ndarray
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A 1D array of Integral values equal to the l quantum number for each
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pole + 1.
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w_start : np.ndarray
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A 1D array of Integral values. w_start[i] - 1 is the index of the first
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pole in window i.
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w_end : np.ndarray
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A 1D array of Integral values. w_end[i] - 1 is the index of the last
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pole in window i.
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broaden_poly : np.ndarray
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A 1D array of boolean values indicating whether or not the polynomial
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curvefit in that window should be Doppler broadened.
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curvefit : np.ndarray
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A 3D array of Real curvefit polynomial coefficients. curvefit[i, 0, :]
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gives coefficients for the total cross section in window i.
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curvefit[i, 1, :] gives absorption coefficients and curvefit[i, 2, :]
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gives fission coefficients. The polynomial terms are increasing powers
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of sqrt(E) starting with 1/E e.g:
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a/E + b/sqrt(E) + c + d sqrt(E) + ...
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"""
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def __init__(self):
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self.num_l = None
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self.fit_order = None
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@ -382,7 +468,24 @@ class WindowedMultipole(EqualityMixin):
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return out
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def evaluate(self, E, T):
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def _evaluate(self, E, T):
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"""Return total, absorption, and fission XS at a single energy and temp.
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Parameters
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----------
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E : Real
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Energy of the incident neutron in eV.
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T : Real
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Temperature of the target in K.
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Returns
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-------
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3-tuple of Real
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Total, absorption, and fission microscopic cross sections at the
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given energy and temperature.
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"""
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# ======================================================================
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# Bookkeeping
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@ -427,8 +530,8 @@ class WindowedMultipole(EqualityMixin):
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if sqrtkT != 0 and self.broaden_poly[i_window]:
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# Broaden the curvefit.
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broadened_polynomials = broaden_wmp_polynomials(E, dopp,
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self.fit_order + 1)
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broadened_polynomials = _broaden_wmp_polynomials(E, dopp,
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self.fit_order + 1)
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for i_poly in range(self.fit_order+1):
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sigT += (self.curvefit[i_window, i_poly, FIT_T]
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* broadened_polynomials[i_poly])
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@ -471,7 +574,7 @@ class WindowedMultipole(EqualityMixin):
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# At temperature, use Faddeeva function-based form.
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for i_pole in range(startw, endw):
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Z = (sqrtE - self.data[i_pole, MP_EA]) * dopp
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w_val = faddeeva(Z) * dopp * invE * np.sqrt(np.pi)
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w_val = _faddeeva(Z) * dopp * invE * np.sqrt(np.pi)
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if self.formalism == 'MLBW':
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sigT += ((self.data[i_pole, MLBW_RT] *
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sigT_factor[self.l_value[i_pole]-1] +
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@ -488,3 +591,24 @@ class WindowedMultipole(EqualityMixin):
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' formalism')
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return sigT, sigA, sigF
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def __call__(self, E, T):
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"""Return total, absorption, and fission XS at given energy and temp.
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Parameters
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----------
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E : Real or Iterable of Real
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Energy of the incident neutron in eV.
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T : Real
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Temperature of the target in K.
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Returns
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-------
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3-tuple of Real or 3-tuple of numpy.ndarray
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Total, absorption, and fission microscopic cross sections at the
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given energy and temperature.
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"""
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fun = np.vectorize(lambda x: self._evaluate(x, T))
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return fun(E)
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