source: sasmodels/sasmodels/models/flexible_cylinder.py @ 2573fa1

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Last change on this file since 2573fa1 was 2573fa1, checked in by Paul Kienzle <pkienzle@…>, 5 years ago

flexible_cylinder: restore previously disabled test

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1r"""
2This model provides the form factor, $P(q)$, for a flexible cylinder
3where the form factor is normalized by the volume of the cylinder.
4**Inter-cylinder interactions are NOT provided for.**
5
6.. math::
7
8    P(q) = \text{scale} \left<F^2\right>/V + \text{background}
9
10where the averaging $\left<\ldots\right>$ is applied only for the 1D
11calculation
12
13The 2D scattering intensity is the same as 1D, regardless of the orientation of
14the q vector which is defined as
15
16.. math::
17
18    q = \sqrt{q_x^2 + q_y^2}
19
20Definitions
21-----------
22
23.. figure:: img/flexible_cylinder_geometry.jpg
24
25
26The chain of contour length, $L$, (the total length) can be described as a
27chain of some number of locally stiff segments of length $l_p$, the persistence
28length (the length along the cylinder over which the flexible cylinder can be
29considered a rigid rod).
30The Kuhn length $(b = 2*l_p)$ is also used to describe the stiffness of a chain.
31
32The returned value is in units of $cm^{-1}$, on absolute scale.
33
34In the parameters, the sld and sld\_solvent represent the SLD of the cylinder
35and solvent respectively.
36
37Our model uses the form factor calculations implemented in a c-library provided
38by the NIST Center for Neutron Research (Kline, 2006).
39
40
41From the reference:
42
43    'Method 3 With Excluded Volume' is used.
44    The model is a parametrization of simulations of a discrete representation
45    of the worm-like chain model of Kratky and Porod applied in the
46    pseudocontinuous limit.
47    See equations (13,26-27) in the original reference for the details.
48
49References
50----------
51
52J S Pedersen and P Schurtenberger. *Scattering functions of semiflexible
53polymers with and without excluded volume effects.* Macromolecules,
5429 (1996) 7602-7612
55
56Correction of the formula can be found in
57
58W R Chen, P D Butler and L J Magid, *Incorporating Intermicellar Interactions
59in the Fitting of SANS Data from Cationic Wormlike Micelles.* Langmuir,
6022(15) 2006 6539-6548
61"""
62from numpy import inf
63
64name = "flexible_cylinder"
65title = "Flexible cylinder where the form factor is normalized by the volume" \
66        "of the cylinder."
67description = """Note : scale and contrast = (sld - sld_solvent) are both
68                multiplicative factors in the model and are perfectly
69                correlated. One or both of these parameters must be held fixed
70                during model fitting.
71              """
72
73category = "shape:cylinder"
74single = False  # double precision only!
75
76# pylint: disable=bad-whitespace, line-too-long
77#             ["name", "units", default, [lower, upper], "type", "description"],
78parameters = [
79    ["length",      "Ang",       1000.0, [0, inf],    "volume", "Length of the flexible cylinder"],
80    ["kuhn_length", "Ang",        100.0, [0, inf],    "volume", "Kuhn length of the flexible cylinder"],
81    ["radius",      "Ang",         20.0, [0, inf],    "volume", "Radius of the flexible cylinder"],
82    ["sld",         "1e-6/Ang^2",   1.0, [-inf, inf], "sld",    "Cylinder scattering length density"],
83    ["sld_solvent", "1e-6/Ang^2",   6.3, [-inf, inf], "sld",    "Solvent scattering length density"],
84    ]
85# pylint: enable=bad-whitespace, line-too-long
86source = ["lib/polevl.c", "lib/sas_J1.c", "lib/wrc_cyl.c", "flexible_cylinder.c"]
87
88def random():
89    import numpy as np
90    length = 10**np.random.uniform(2, 6)
91    radius = 10**np.random.uniform(1, 3)
92    kuhn_length = 10**np.random.uniform(-2, 0)*length
93    pars = dict(
94        length=length,
95        radius=radius,
96        kuhn_length=kuhn_length,
97    )
98    return pars
99
100tests = [
101    # Accuracy tests based on content in test/utest_other_models.py
102    [{'length':     1000.0,  # test T1
103      'kuhn_length': 100.0,
104      'radius':       20.0,
105      'sld':           1.0,
106      'sld_solvent':   6.3,
107      'background':    0.0001,
108     }, 0.001, 3509.2187],
109
110    # Additional tests with larger range of parameters
111    [{'length':    1000.0,  # test T2
112      'kuhn_length': 100.0,
113      'radius':       20.0,
114      'sld':           1.0,
115      'sld_solvent':   6.3,
116      'background':    0.0001,
117     }, 1.0, 0.000595345],
118    [{'length':        10.0,  # test T3
119      'kuhn_length': 800.0,
120      'radius':        2.0,
121      'sld':           6.0,
122      'sld_solvent':  12.3,
123      'background':    0.001,
124     }, 0.1, 1.55228],
125    [{'length':        100.0,  # test T4
126      'kuhn_length': 800.0,
127      'radius':       50.0,
128      'sld':           0.1,
129      'sld_solvent':   5.1,
130      'background':    0.0,
131     }, 1.0, 0.000938456]
132    ]
133
134# There are a few branches in the code that ought to have test values:
135#
136# For length > 4 * kuhn_length
137#        if length > 10 * kuhn_length then C is scaled by 3.06 (L/b)^(-0.44)
138#        q*kuhn_length <= 3.1  => Sexv_new
139#           dS/dQ < 0 has different behaviour from dS/dQ >= 0
140#  T2    q*kuhn_length > 3.1   => a_long
141#
142# For length <= 4 * kuhn_length
143#        q*kuhn_length <= max(1.9/Rg_short, 3.0)  => Sdebye((q*Rg)^2)
144#           q*Rg < 0.5 uses Pade approx, q*Rg > 1.0 uses math lib
145#  T3,T4 q*kuhn_length > max(1.9/Rg_short, 3.0)   => a_short
146#
147# Note that the transitions between branches may be abrupt.  You can see a
148# several percent change around length=10*kuhn_length and length=4*kuhn_length
149# using the following:
150#
151#    sascomp flexible_cylinder -calc=double -sets=10 length=10*kuhn_length,10.000001*kuhn_length
152#    sascomp flexible_cylinder -calc=double -sets=10 length=4*kuhn_length,4.000001*kuhn_length
153#
154# The transition between low q and high q around q*kuhn_length = 3 seems
155# to be good to 4 digits or better.  This was tested by computing the value
156# on each branches near the transition point and reporting the relative error
157# for kuhn lengths of 10, 100 and 1000 and a variety of length:kuhn_length
158# ratios.
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