source: sasmodels/sasmodels/product.py @ 19e8a2b

"""
Product model
-------------

The product model multiplies the structure factor by the form factor,
modulated by the effective radius of the form.  The resulting model
has a attributes of both the model description (with parameters, etc.)
and the module evaluator (with call, release, etc.).

To use it, first load form factor P and structure factor S, then create
*make_product_info(P, S)*.
"""
from __future__ import print_function, division

from collections import OrderedDict

from copy import copy
import numpy as np  # type: ignore

from .modelinfo import ParameterTable, ModelInfo, Parameter, parse_parameter
from .kernel import KernelModel, Kernel
from .details import make_details, dispersion_mesh

# pylint: disable=unused-import
try:
    from typing import Tuple, Callable, Union
except ImportError:
    pass
else:
    from .modelinfo import ParameterSet
# pylint: enable=unused-import

# TODO: make estimates available to constraints
#ESTIMATED_PARAMETERS = [
#    ["est_radius_effective", "A", 0.0, [0, np.inf], "", "Estimated effective radius"],
#    ["est_volume_ratio", "", 1.0, [0, np.inf], "", "Estimated volume ratio"],
#]

RADIUS_ID = "radius_effective"
VOLFRAC_ID = "volfraction"
def make_extra_pars(p_info):
    pars = []
    if p_info.have_Fq:
        par = parse_parameter(
                "structure_factor_mode",
                "",
                0,
                [["P*S","P*(1+beta*(S-1))"]],
                "",
                "Structure factor calculation")
        pars.append(par)
    if p_info.effective_radius_type is not None:
        par = parse_parameter(
                "radius_effective_mode",
                "",
                0,
                [["unconstrained"] + p_info.effective_radius_type],
                "",
                "Effective radius calculation")
        pars.append(par)
    return pars

# TODO: core_shell_sphere model has suppressed the volume ratio calculation
# revert it after making VR and ER available at run time as constraints.
def make_product_info(p_info, s_info):
    # type: (ModelInfo, ModelInfo) -> ModelInfo
    """
    Create info block for product model.
    """
    # Make sure effective radius is the first parameter and
    # make sure volume fraction is the second parameter of the
    # structure factor calculator.  Structure factors should not
    # have any magnetic parameters
    if not len(s_info.parameters.kernel_parameters) >= 2:
        raise TypeError("S needs {} and {} as its first parameters".format(RADIUS_ID, VOLFRAC_ID))
    if not s_info.parameters.kernel_parameters[0].id == RADIUS_ID:
        raise TypeError("S needs {} as first parameter".format(RADIUS_ID))
    if not s_info.parameters.kernel_parameters[1].id == VOLFRAC_ID:
        raise TypeError("S needs {} as second parameter".format(VOLFRAC_ID))
    if not s_info.parameters.magnetism_index == []:
        raise TypeError("S should not have SLD parameters")
    p_id, p_name, p_pars = p_info.id, p_info.name, p_info.parameters
    s_id, s_name, s_pars = s_info.id, s_info.name, s_info.parameters

    # Create list of parameters for the combined model.  If there
    # are any names in P that overlap with those in S, modify the name in S
    # to distinguish it.
    p_set = set(p.id for p in p_pars.kernel_parameters)
    s_list = [(_tag_parameter(par) if par.id in p_set else par)
              for par in s_pars.kernel_parameters]
    # Check if still a collision after renaming.  This could happen if for
    # example S has volfrac and P has both volfrac and volfrac_S.
    if any(p.id in p_set for p in s_list):
        raise TypeError("name collision: P has P.name and P.name_S while S has S.name")

    # make sure effective radius is not a polydisperse parameter in product
    s_list[0] = copy(s_list[0])
    s_list[0].polydisperse = False

    translate_name = dict((old.id, new.id) for old, new
                          in zip(s_pars.kernel_parameters, s_list))
    combined_pars = p_pars.kernel_parameters + s_list + make_extra_pars(p_info)
    parameters = ParameterTable(combined_pars)
    parameters.max_pd = p_pars.max_pd + s_pars.max_pd
    def random():
        combined_pars = p_info.random()
        s_names = set(par.id for par in s_pars.kernel_parameters)
        combined_pars.update((translate_name[k], v)
                             for k, v in s_info.random().items()
                             if k in s_names)
        return combined_pars

    model_info = ModelInfo()
    model_info.id = '@'.join((p_id, s_id))
    model_info.name = '@'.join((p_name, s_name))
    model_info.filename = None
    model_info.title = 'Product of %s and %s'%(p_name, s_name)
    model_info.description = model_info.title
    model_info.docs = model_info.title
    model_info.category = "custom"
    model_info.parameters = parameters
    model_info.random = random
    #model_info.single = p_info.single and s_info.single
    model_info.structure_factor = False
    model_info.variant_info = None
    #model_info.tests = []
    #model_info.source = []
    # Iq, Iqxy, form_volume, ER, VR and sesans
    # Remember the component info blocks so we can build the model
    model_info.composition = ('product', [p_info, s_info])
    model_info.control = p_info.control
    model_info.hidden = p_info.hidden
    if getattr(p_info, 'profile', None) is not None:
        profile_pars = set(p.id for p in p_info.parameters.kernel_parameters)
        def profile(**kwargs):
            # extract the profile args
            kwargs = dict((k, v) for k, v in kwargs.items() if k in profile_pars)
            return p_info.profile(**kwargs)
    else:
        profile = None
    model_info.profile = profile
    model_info.profile_axes = p_info.profile_axes

    # TODO: delegate random to p_info, s_info
    #model_info.random = lambda: {}

    ## Show the parameter table
    #from .compare import get_pars, parlist
    #print("==== %s ====="%model_info.name)
    #values = get_pars(model_info)
    #print(parlist(model_info, values, is2d=True))
    return model_info

def _tag_parameter(par):
    """
    Tag the parameter name with _S to indicate that the parameter comes from
    the structure factor parameter set.  This is only necessary if the
    form factor model includes a parameter of the same name as a parameter
    in the structure factor.
    """
    par = copy(par)
    # Protect against a vector parameter in S by appending the vector length
    # to the renamed parameter.  Note: haven't tested this since no existing
    # structure factor models contain vector parameters.
    vector_length = par.name[len(par.id):]
    par.id = par.id + "_S"
    par.name = par.id + vector_length
    return par

def _intermediates(P, S, effective_radius):
    # type: (np.ndarray, np.ndarray, float) -> OrderedDict[str, np.ndarray]
    """
    Returns intermediate results for standard product (P(Q)*S(Q))
    """
    return OrderedDict((
        ("P(Q)", P),
        ("S(Q)", S),
        ("effective_radius", effective_radius),
    ))

def _intermediates_beta(F1,              # type: np.ndarray
                        F2,              # type: np.ndarray
                        S,               # type: np.ndarray
                        scale,           # type: np.ndarray
                        bg,              # type: np.ndarray
                        effective_radius # type: float
                        ):
    # type: (...) -> OrderedDict[str, Union[np.ndarray, float]]
    """
    Returns intermediate results for beta approximation-enabled product. The result may be an array or a float.
    """
    # TODO: 1. include calculated Q vector
    # TODO: 2. consider implications if there are intermediate results in P(Q)
    return OrderedDict((
        ("P(Q)", scale*F2),
        ("S(Q)", S),
        ("beta(Q)", F1**2 / F2),
        ("S_eff(Q)", 1 + (F1**2 / F2)*(S-1)),
        ("effective_radius", effective_radius),
        # ("I(Q)", scale*(F2 + (F1**2)*(S-1)) + bg),
    ))

class ProductModel(KernelModel):
    def __init__(self, model_info, P, S):
        # type: (ModelInfo, KernelModel, KernelModel) -> None
        #: Combined info plock for the product model
        self.info = model_info
        #: Form factor modelling individual particles.
        self.P = P
        #: Structure factor modelling interaction between particles.
        self.S = S

        #: Model precision. This is not really relevant, since it is the
        #: individual P and S models that control the effective dtype,
        #: converting the q-vectors to the correct type when the kernels
        #: for each are created. Ideally this should be set to the more
        #: precise type to avoid loss of precision, but precision in q is
        #: not critical (single is good enough for our purposes), so it just
        #: uses the precision of the form factor.
        self.dtype = P.dtype  # type: np.dtype

    def make_kernel(self, q_vectors):
        # type: (List[np.ndarray]) -> Kernel
        # Note: may be sending the q_vectors to the GPU twice even though they
        # are only needed once.  It would mess up modularity quite a bit to
        # handle this optimally, especially since there are many cases where
        # separate q vectors are needed (e.g., form in python and structure
        # in opencl; or both in opencl, but one in single precision and the
        # other in double precision).

        p_kernel = self.P.make_kernel(q_vectors)
        s_kernel = self.S.make_kernel(q_vectors)
        return ProductKernel(self.info, p_kernel, s_kernel)

    def release(self):
        # type: (None) -> None
        """
        Free resources associated with the model.
        """
        self.P.release()
        self.S.release()


class ProductKernel(Kernel):
    def __init__(self, model_info, p_kernel, s_kernel):
        # type: (ModelInfo, Kernel, Kernel) -> None
        self.info = model_info
        self.p_kernel = p_kernel
        self.s_kernel = s_kernel
        self.dtype = p_kernel.dtype
        self.results = []  # type: List[np.ndarray]

    def __call__(self, call_details, values, cutoff, magnetic):
        # type: (CallDetails, np.ndarray, float, bool) -> np.ndarray
        p_info, s_info = self.info.composition[1]

        # if there are magnetic parameters, they will only be on the
        # form factor P, not the structure factor S.
        nmagnetic = len(self.info.parameters.magnetism_index)
        if nmagnetic:
            spin_index = self.info.parameters.npars + 2
            magnetism = values[spin_index: spin_index+3+3*nmagnetic]
        else:
            magnetism = []
        nvalues = self.info.parameters.nvalues
        nweights = call_details.num_weights
        weights = values[nvalues:nvalues + 2*nweights]

        # Construct the calling parameters for P.
        p_npars = p_info.parameters.npars
        p_length = call_details.length[:p_npars]
        p_offset = call_details.offset[:p_npars]
        p_details = make_details(p_info, p_length, p_offset, nweights)

        # Set p scale to the volume fraction in s, which is the first of the
        # 'S' parameters in the parameter list, or 2+np in 0-origin.
        volfrac = values[2+p_npars]
        p_values = [[volfrac, 0.0], values[2:2+p_npars], magnetism, weights]
        spacer = (32 - sum(len(v) for v in p_values)%32)%32
        p_values.append([0.]*spacer)
        p_values = np.hstack(p_values).astype(self.p_kernel.dtype)

        # Construct the calling parameters for S.
        s_npars = s_info.parameters.npars
        s_length = call_details.length[p_npars:p_npars+s_npars]
        s_offset = call_details.offset[p_npars:p_npars+s_npars]
        s_length = np.hstack((1, s_length))
        s_offset = np.hstack((nweights, s_offset))
        s_details = make_details(s_info, s_length, s_offset, nweights+1)
        s_values = [
            # scale=1, background=0,
            [1., 0.],
            values[2+p_npars:2+p_npars+s_npars],
            weights,
        ]
        spacer = (32 - sum(len(v) for v in s_values)%32)%32
        s_values.append([0.]*spacer)
        s_values = np.hstack(s_values).astype(self.s_kernel.dtype)

        # beta mode is the first parameter after the structure factor pars
        extra_offset = 2+p_npars+s_npars
        if p_info.have_Fq:
            beta_mode = values[extra_offset]
            extra_offset += 1
        else:
            beta_mode = 0
        if p_info.effective_radius_type is not None:
            effective_radius_type = int(values[extra_offset])
            extra_offset += 1
        else:
            effective_radius_type = 0

        # Call the kernels
        scale, background = values[0], values[1]
        if beta_mode:
            F1, F2, volume_avg, effective_radius = self.p_kernel.beta(
                p_details, p_values, cutoff, magnetic, effective_radius_type)
            if effective_radius_type > 0:
                # Plug R_eff from p into S model (initial value and pd value)
                s_values[2] = s_values[2+s_npars+s_offset[0]] = effective_radius
            s_result = self.s_kernel.Iq(s_details, s_values, cutoff, False)
            combined_scale = scale*volfrac/volume_avg

            self.results = lambda: _intermediates_beta(F1, F2, s_result, volfrac/volume_avg, background, effective_radius)
            final_result = combined_scale*(F2 + (F1**2)*(s_result - 1)) + background

        else:
            p_result, effective_radius = self.p_kernel.Pq_Reff(
                p_details, p_values, cutoff, magnetic, effective_radius_type)
            if effective_radius_type > 0:
                # Plug R_eff from p into S model (initial value and pd value)
                s_values[2] = s_values[2+s_npars+s_offset[0]] = effective_radius
            s_result = self.s_kernel.Iq(s_details, s_values, cutoff, False)
            # remember the parts for plotting later
            self.results = lambda: _intermediates(p_result, s_result, effective_radius)
            final_result = scale*(p_result*s_result) + background

        #call_details.show(values)
        #print("values", values)
        #p_details.show(p_values)
        #print("=>", p_result)
        #s_details.show(s_values)
        #print("=>", s_result)
        #import pylab as plt
        #plt.subplot(211); plt.loglog(self.p_kernel.q_input.q, p_result, '-')
        #plt.subplot(212); plt.loglog(self.s_kernel.q_input.q, s_result, '-')
        #plt.figure()
        return final_result

    def release(self):
        # type: () -> None
        self.p_kernel.release()
        self.s_kernel.release()


def calc_er_vr(model_info, call_details, values):
    # type: (ModelInfo, ParameterSet) -> Tuple[float, float]

    if model_info.ER is None and model_info.VR is None:
        return 1.0, 1.0

    nvalues = model_info.parameters.nvalues
    value = values[nvalues:nvalues + call_details.num_weights]
    weight = values[nvalues + call_details.num_weights: nvalues + 2*call_details.num_weights]
    npars = model_info.parameters.npars
    # Note: changed from pairs ([v], [w]) to triples (p, [v], [w]), but the
    # dispersion mesh code doesn't actually care about the nominal parameter
    # value, p, so set it to None.
    pairs = [(None, value[offset:offset+length], weight[offset:offset+length])
             for p, offset, length
             in zip(model_info.parameters.call_parameters[2:2+npars],
                    call_details.offset,
                    call_details.length)
             if p.type == 'volume']
    value, weight = dispersion_mesh(model_info, pairs)

    if model_info.ER is not None:
        individual_radii = model_info.ER(*value)
        radius_effective = np.sum(weight*individual_radii) / np.sum(weight)
    else:
        radius_effective = 1.0

    if model_info.VR is not None:
        whole, part = model_info.VR(*value)
        volume_ratio = np.sum(weight*part)/np.sum(weight*whole)
    else:
        volume_ratio = 1.0

    return radius_effective, volume_ratio