"""
Class interface to the model calculator.
Calling a model is somewhat non-trivial since the functions called depend
on the data type. For 1D data the *Iq* kernel needs to be called, for
2D data the *Iqxy* kernel needs to be called, and for SESANS data the
*Iq* kernel needs to be called followed by a Hankel transform. Before
the kernel is called an appropriate *q* calculation vector needs to be
constructed. This is not the simple *q* vector where you have measured
the data since the resolution calculation will require values beyond the
range of the measured data. After the calculation the resolution calculator
must be called to return the predicted value for each measured data point.
:class:`DirectModel` is a callable object that takes *parameter=value*
keyword arguments and returns the appropriate theory values for the data.
:class:`DataMixin` does the real work of interpreting the data and calling
the model calculator. This is used by :class:`DirectModel`, which uses
direct parameter values and by :class:`.bumps_model.Experiment` which wraps
the parameter values in boxes so that the user can set fitting ranges, etc.
on the individual parameters and send the model to the Bumps optimizers.
"""
from __future__ import print_function, division
import numpy as np # type: ignore
# TODO: fix sesans module
from . import sesans # type: ignore
from . import weights
from . import resolution
from . import resolution2d
from .details import make_kernel_args, dispersion_mesh
from .product import RADIUS_MODE_ID
# pylint: disable=unused-import
try:
from typing import Optional, Dict, Tuple, List, Callable
from collections import OrderedDict
from .data import Data
from .kernel import Kernel, KernelModel
from .modelinfo import Parameter, ParameterSet, ModelInfo
except ImportError:
pass
# pylint: enable=unused-import
[docs]def call_kernel(calculator, pars, cutoff=0., mono=False):
# type: (Kernel, ParameterSet, float, bool) -> np.ndarray
"""
Call *kernel* returned from *model.make_kernel* with parameters *pars*.
*cutoff* is the limiting value for the product of dispersion weights used
to perform the multidimensional dispersion calculation more quickly at a
slight cost to accuracy. The default value of *cutoff=0* integrates over
the entire dispersion cube. Using *cutoff=1e-5* can be 50% faster, but
with an error of about 1%, which is usually less than the measurement
uncertainty.
*mono* is True if polydispersity should be set to none on all parameters.
"""
mesh = get_mesh(calculator.info, pars, dim=calculator.dim, mono=mono)
#print("in call_kernel: pars:", list(zip(*mesh))[0])
call_details, values, is_magnetic = make_kernel_args(calculator, mesh)
#print("in call_kernel: values:", values)
return calculator(call_details, values, cutoff, is_magnetic)
[docs]def call_Fq(calculator, pars, cutoff=0., mono=False):
# type: (Kernel, ParameterSet, float, bool) -> np.ndarray
"""
Like :func:`call_kernel`, but returning F, F^2, R_eff, V_shell, V_form/V_shell.
For solid objects V_shell is equal to V_form and the volume ratio is 1.
Use parameter *radius_effective_mode* to select the effective radius
calculation to use amongst the *radius_effective_modes* list given in the
model.
"""
R_eff_type = int(pars.pop(RADIUS_MODE_ID, 1.0))
mesh = get_mesh(calculator.info, pars, dim=calculator.dim, mono=mono)
#print("in call_Fq: pars", list(zip(*mesh))[0])
call_details, values, is_magnetic = make_kernel_args(calculator, mesh)
#print("in call_Fq: values:", values)
return calculator.Fq(call_details, values, cutoff, is_magnetic, R_eff_type)
[docs]def call_profile(model_info, pars=None):
# type: (ModelInfo, ParameterSet) -> Tuple[np.ndarray, np.ndarray, Tuple[str, str]]
"""
Returns the profile *x, y, (xlabel, ylabel)* representing the model.
"""
if pars is None:
pars = {}
args = {}
for p in model_info.parameters.kernel_parameters:
if p.length > 1:
value = np.array([pars.get(p.id+str(j), p.default)
for j in range(1, p.length+1)])
else:
value = pars.get(p.id, p.default)
args[p.id] = value
x, y = model_info.profile(**args)
return x, y, model_info.profile_axes
[docs]def get_mesh(model_info, values, dim='1d', mono=False):
# type: (ModelInfo, Dict[str, float], str, bool) -> List[Tuple[float, np.ndarray, np.ndarry]]
"""
Retrieve the dispersity mesh described by the parameter set.
Returns a list of *(value, dispersity, weights)* with one tuple for each
parameter in the model call parameters. Inactive parameters return the
default value with a weight of 1.0.
"""
parameters = model_info.parameters
if mono:
active = lambda name: False
elif dim == '1d':
active = lambda name: name in parameters.pd_1d
elif dim == '2d':
active = lambda name: name in parameters.pd_2d
else:
active = lambda name: True
#print("in get_mesh: pars:",[p.id for p in parameters.call_parameters])
mesh = [_get_par_weights(p, values, active(p.name))
for p in parameters.call_parameters]
return mesh
def _get_par_weights(parameter, values, active=True):
# type: (Parameter, Dict[str, float], bool) -> Tuple[float, np.ndarray, np.ndarray]
"""
Generate the distribution for parameter *name* given the parameter values
in *pars*.
Uses "name", "name_pd", "name_pd_type", "name_pd_n", "name_pd_sigma"
from the *pars* dictionary for parameter value and parameter dispersion.
"""
value = float(values.get(parameter.name, parameter.default))
npts = values.get(parameter.name+'_pd_n', 0)
width = values.get(parameter.name+'_pd', 0.0)
relative = parameter.relative_pd
if npts == 0 or width == 0.0 or not active:
# Note: orientation parameters have the viewing angle as the parameter
# value and the jitter in the distribution, so be sure to set the
# empty pd for orientation parameters to 0.
pd = [value if relative or not parameter.polydisperse else 0.0], [1.0]
else:
limits = parameter.limits
disperser = values.get(parameter.name+'_pd_type', 'gaussian')
nsigma = values.get(parameter.name+'_pd_nsigma', 3.0)
pd = weights.get_weights(disperser, npts, width, nsigma,
value, limits, relative)
return value, pd[0], pd[1]
def _vol_pars(model_info, values):
# type: (ModelInfo, ParameterSet) -> Tuple[np.ndarray, np.ndarray]
vol_pars = [_get_par_weights(p, values)
for p in model_info.parameters.call_parameters
if p.type == 'volume']
#import pylab; pylab.plot(vol_pars[0][0],vol_pars[0][1]); pylab.show()
dispersity, weight = dispersion_mesh(model_info, vol_pars)
return dispersity, weight
def _make_sesans_transform(data):
from sas.sascalc.data_util.nxsunit import Converter
# Pre-compute the Hankel matrix (H)
SElength = Converter(data._xunit)(data.x, "A")
theta_max = Converter("radians")(data.sample.zacceptance)[0]
q_max = 2 * np.pi / np.max(data.source.wavelength) * np.sin(theta_max)
zaccept = Converter("1/A")(q_max, "1/" + data.source.wavelength_unit),
Rmax = 10000000
hankel = sesans.SesansTransform(data.x, SElength,
data.source.wavelength,
zaccept, Rmax)
return hankel
[docs]class DataMixin(object):
"""
DataMixin captures the common aspects of evaluating a SAS model for a
particular data set, including calculating Iq and evaluating the
resolution function. It is used in particular by :class:`DirectModel`,
which evaluates a SAS model parameters as key word arguments to the
calculator method, and by :class:`.bumps_model.Experiment`, which wraps the
model and data for use with the Bumps fitting engine. It is not
currently used by :class:`.sasview_model.SasviewModel` since this will
require a number of changes to SasView before we can do it.
*_interpret_data* initializes the data structures necessary
to manage the calculations. This sets attributes in the child class
such as *data_type* and *resolution*.
*_calc_theory* evaluates the model at the given control values.
*_set_data* sets the intensity data in the data object,
possibly with random noise added. This is useful for simulating a
dataset with the results from *_calc_theory*.
"""
def _interpret_data(self, data, model):
# type: (Data, KernelModel) -> None
# pylint: disable=attribute-defined-outside-init
self._data = data
self._model = model
# interpret data
if hasattr(data, 'isSesans') and data.isSesans:
self.data_type = 'sesans'
elif hasattr(data, 'qx_data'):
self.data_type = 'Iqxy'
elif getattr(data, 'oriented', False):
self.data_type = 'Iq-oriented'
else:
self.data_type = 'Iq'
if self.data_type == 'sesans':
res = _make_sesans_transform(data)
index = slice(None, None)
if data.y is not None:
Iq, dIq = data.y, data.dy
else:
Iq, dIq = None, None
elif self.data_type == 'Iqxy':
#if not model.info.parameters.has_2d:
# raise ValueError("not 2D without orientation or magnetic parameters")
q = np.sqrt(data.qx_data**2 + data.qy_data**2)
qmin = getattr(data, 'qmin', 1e-16)
qmax = getattr(data, 'qmax', np.inf)
accuracy = getattr(data, 'accuracy', 'Low')
index = (data.mask == 0) & (q >= qmin) & (q <= qmax)
if data.data is not None:
index &= ~np.isnan(data.data)
Iq = data.data[index]
dIq = data.err_data[index]
else:
Iq, dIq = None, None
res = resolution2d.Pinhole2D(data=data, index=index,
nsigma=3.0, accuracy=accuracy)
elif self.data_type == 'Iq':
index = (data.x >= data.qmin) & (data.x <= data.qmax)
mask = getattr(data, 'mask', None)
if mask is not None:
index &= (mask == 0)
if data.y is not None:
index &= ~np.isnan(data.y)
Iq = data.y[index]
dIq = data.dy[index]
else:
Iq, dIq = None, None
if getattr(data, 'dx', None) is not None:
q, dq = data.x[index], data.dx[index]
if (dq > 0).any():
res = resolution.Pinhole1D(q, dq)
else:
res = resolution.Perfect1D(q)
elif (getattr(data, 'dxl', None) is not None
and getattr(data, 'dxw', None) is not None):
res = resolution.Slit1D(data.x[index],
qx_width=data.dxl[index],
qy_width=data.dxw[index])
else:
res = resolution.Perfect1D(data.x[index])
elif self.data_type == 'Iq-oriented':
index = (data.x >= data.qmin) & (data.x <= data.qmax)
if data.y is not None:
index &= ~np.isnan(data.y)
Iq = data.y[index]
dIq = data.dy[index]
else:
Iq, dIq = None, None
if (getattr(data, 'dxl', None) is None
or getattr(data, 'dxw', None) is None):
raise ValueError("oriented sample with 1D data needs slit resolution")
res = resolution2d.Slit2D(data.x[index],
qx_width=data.dxw[index],
qy_width=data.dxl[index])
else:
raise ValueError("Unknown data type") # never gets here
# Remember function inputs so we can delay loading the function and
# so we can save/restore state
self._kernel = None
self.Iq, self.dIq, self.index = Iq, dIq, index
self.resolution = res
self.results = None # type: Optional[Callable[[], OrderedDict]]
def _set_data(self, Iq, noise=None):
# type: (np.ndarray, Optional[float]) -> None
# pylint: disable=attribute-defined-outside-init
if noise is not None:
self.dIq = Iq*noise*0.01
dy = self.dIq
y = Iq + np.random.randn(*dy.shape) * dy
self.Iq = y
if self.data_type in ('Iq', 'Iq-oriented'):
if self._data.y is None:
self._data.y = np.empty(len(self._data.x), 'd')
if self._data.dy is None:
self._data.dy = np.empty(len(self._data.x), 'd')
self._data.dy[self.index] = dy
self._data.y[self.index] = y
elif self.data_type == 'Iqxy':
if self._data.data is None:
self._data.data = np.empty_like(self._data.qx_data, 'd')
if self._data.err_data is None:
self._data.err_data = np.empty_like(self._data.qx_data, 'd')
self._data.data[self.index] = y
self._data.err_data[self.index] = dy
elif self.data_type == 'sesans':
if self._data.y is None:
self._data.y = np.empty(len(self._data.x), 'd')
self._data.y[self.index] = y
else:
raise ValueError("Unknown model")
def _calc_theory(self, pars, cutoff=0.0):
# type: (ParameterSet, float) -> np.ndarray
if self._kernel is None:
# TODO: change interfaces so that resolution returns kernel inputs
# Maybe have resolution always return a tuple, or maybe have
# make_kernel accept either an ndarray or a pair of ndarrays.
kernel_inputs = self.resolution.q_calc
if isinstance(kernel_inputs, np.ndarray):
kernel_inputs = (kernel_inputs,)
self._kernel = self._model.make_kernel(kernel_inputs)
# Need to pull background out of resolution for multiple scattering
default_background = self._model.info.parameters.common_parameters[1].default
background = pars.get('background', default_background)
pars = pars.copy()
pars['background'] = 0.
Iq_calc = call_kernel(self._kernel, pars, cutoff=cutoff)
self.results = getattr(self._kernel, 'results', None)
# Storing the calculated Iq values so that they can be plotted.
# Only applies to oriented USANS data for now.
# TODO: extend plotting of calculate Iq to other measurement types
# TODO: refactor so we don't store the result in the model
self.Iq_calc = Iq_calc
result = self.resolution.apply(Iq_calc)
if hasattr(self.resolution, 'nx'):
self.Iq_calc = (
self.resolution.qx_calc, self.resolution.qy_calc,
np.reshape(Iq_calc, (self.resolution.ny, self.resolution.nx))
)
return result + background
[docs]class DirectModel(DataMixin):
"""
Create a calculator object for a model.
*data* is 1D SAS, 2D SAS or SESANS data
*model* is a model calculator return from :func:`.core.load_model`
*cutoff* is the polydispersity weight cutoff.
"""
def __init__(self, data, model, cutoff=1e-5):
# type: (Data, KernelModel, float) -> None
self.model = model
self.cutoff = cutoff
# Note: _interpret_data defines the model attributes
self._interpret_data(data, model)
def __call__(self, **pars):
# type: (**float) -> np.ndarray
return self._calc_theory(pars, cutoff=self.cutoff)
[docs] def simulate_data(self, noise=None, **pars):
# type: (Optional[float], **float) -> None
"""
Generate simulated data for the model.
"""
Iq = self.__call__(**pars)
self._set_data(Iq, noise=noise)
[docs] def profile(self, **pars):
# type: (**float) -> None
"""
Generate a plottable profile.
"""
return call_profile(self.model.info, pars)
[docs]def test_reparameterize():
# type: () -> None
"""Check simple reparameterized models will load and build"""
from numpy import inf, pi
from numpy.linalg import norm
from .data import empty_data1D
from .core import load_model_info, build_model, reparameterize
parameters = [
["volume", "Ang^3", 1e5, [0, inf], "volume", "ellipsoid volume"],
["eccentricity", "", 1, [0, inf], "volume", "polar:equatorial radius"],
]
translation = """
Re = cbrt(volume/eccentricity/M_4PI_3)
radius_polar = eccentricity*Re
radius_equatorial = Re # python style comments allowed
"""
info = reparameterize('ellipsoid', parameters, translation)
# Check translated parameters
actual = [p.name for p in info.parameters.kernel_parameters]
target = ["sld", "sld_solvent", "volume", "eccentricity", "theta", "phi"]
assert target == actual, "%s != %s"%(target, actual)
data = empty_data1D([0.01, 0.1])
Rp, Re = 30, 50
base_model = build_model(load_model_info('ellipsoid'), dtype='d')
base_calculator = DirectModel(data, base_model)
base_Iq = base_calculator(radius_polar=Rp, radius_equatorial=Re)
derived_model = build_model(info, dtype='d')
derived_calculator = DirectModel(data, derived_model)
derived_Iq = derived_calculator(volume=4*pi/3*Rp*Re**2, eccentricity=Rp/Re)
assert norm((base_Iq - derived_Iq)/base_Iq) < 1e-13
# Again using insert_after.
insert_after = {
'': 'eccentricity',
'radius_equatorial': 'volume',
}
info = reparameterize('ellipsoid', parameters, translation,
insert_after=insert_after)
# Check translated parameters
actual = [p.name for p in info.parameters.kernel_parameters]
target = ["eccentricity", "sld", "sld_solvent", "volume", "theta", "phi"]
assert target == actual, "%s != %s"%(target, actual)
# Check calculation.
derived_model = build_model(info, dtype='d')
derived_calculator = DirectModel(data, derived_model)
derived_Iq = derived_calculator(volume=4*pi/3*Rp*Re**2, eccentricity=Rp/Re)
assert norm((base_Iq - derived_Iq)/base_Iq) < 1e-13
[docs]def main():
# type: () -> None
"""
Program to evaluate a particular model at a set of q values.
"""
import sys
from .data import empty_data1D, empty_data2D
from .core import load_model_info, build_model
if len(sys.argv) < 3:
print("usage: python -m sasmodels.direct_model modelname (q|qx,qy) par=val ...")
sys.exit(1)
model_name = sys.argv[1]
call = sys.argv[2].upper()
try:
values = [float(v) for v in call.split(',')]
except ValueError:
values = []
if len(values) == 1:
q, = values
data = empty_data1D([q])
elif len(values) == 2:
qx, qy = values
data = empty_data2D([qx], [qy])
else:
print("use q or qx,qy")
sys.exit(1)
model_info = load_model_info(model_name)
model = build_model(model_info)
calculator = DirectModel(data, model)
pars = dict((k, (float(v) if not k.endswith("_pd_type") else v))
for pair in sys.argv[3:]
for k, v in [pair.split('=')])
Iq = calculator(**pars)
print(Iq[0])
if __name__ == "__main__":
main()