Changeset 513efc5 in sasmodels for sasmodels/models/polymer_excl_volume.py

Timestamp:

Jan 20, 2016 4:50:50 AM (8 years ago)

Author:

piotr

Branches:

master, core_shell_microgels, costrafo411, magnetic_model, release_v0.94, release_v0.95, ticket-1257-vesicle-product, ticket_1156, ticket_1265_superball, ticket_822_more_unit_tests

Children:

7ed702f

Parents:

30b4ddf

Message:

Code review issues from PK addressed.

Added Taylor expansion utility function.

File:

• sasmodels/models/polymer_excl_volume.py (modified) (6 diffs)

sasmodels/models/polymer_excl_volume.py

@@ -1 +1 @@
 r"""
-This model describes the scattering from polymer chains subject to excluded volume effects
-and has been used as a template for describing mass fractals.
+This model describes the scattering from polymer chains subject to excluded
+volume effects and has been used as a template for describing mass fractals.
 
 Definition
 ----------
 
-The form factor was originally presented in the following integral form (Benoit, 1957)
+The form factor was originally presented in the following integral form
+(Benoit, 1957)
 
 .. math::
@@ -16 +17 @@
 $a$ is the statistical segment length of the polymer chain,
 and $n$ is the degree of polymerization.
-This integral was later put into an almost analytical form as follows (Hammouda, 1993)
+This integral was later put into an almost analytical form as follows
+(Hammouda, 1993)
 
 .. math::
@@ -43 +45 @@
 Note that this model applies only in the mass fractal range (ie, $5/3<=m<=3$ )
 and **does not apply** to surface fractals ( $3<m<=4$ ).
-It also does not reproduce the rigid rod limit (m=1) because it assumes chain flexibility
-from the outset. It may cover a portion of the semi-flexible chain range ( $1<m<5/3$ ).
+It also does not reproduce the rigid rod limit (m=1) because it assumes chain
+flexibility from the outset. It may cover a portion of the semi-flexible chain
+range ( $1<m<5/3$ ).
 
-A low-Q expansion yields the Guinier form and a high-Q expansion yields the Porod form
-which is given by
+A low-Q expansion yields the Guinier form and a high-Q expansion yields the
+Porod form which is given by
 
 .. math::
 
-    P(Q\rightarrow \infty) = \frac{1}{\nu U^{1/2\nu}}\Gamma\left(\frac{1}{2\nu}\right) -
-    \frac{1}{\nu U^{1/\nu}}\Gamma\left(\frac{1}{\nu}\right)
+    P(Q\rightarrow \infty) = \frac{1}{\nu U^{1/2\nu}}\Gamma\left(
+    \frac{1}{2\nu}\right) - \frac{1}{\nu U^{1/\nu}}\Gamma\left(
+    \frac{1}{\nu}\right)
 
 Here $\Gamma(x) = \gamma(x,\infty)$ is the gamma function.
@@ -102 +106 @@
 name = "polymer_excl_volume"
 title = "Polymer Excluded Volume model"
-description = """Compute the scattering intensity from polymers with excluded volume effects.
+description = """Compute the scattering intensity from polymers with excluded
+                volume effects.
                 rg:         radius of gyration
                 porod_exp:  Porod exponent
@@ -127 +132 @@
 
     intensity = ((1.0/(nu*power(u, o2nu))) * (gamma(o2nu)*gammainc(o2nu, u) -
-                 1.0/power(u, o2nu) * gamma(porod_exp)*gammainc(porod_exp, u)))*(q > 0) + \
-                 1.0*(q <= 0)
+                  1.0/power(u, o2nu) * gamma(porod_exp) *
+                  gammainc(porod_exp, u))) * (q > 0) + 1.0*(q <= 0)
 
     return intensity
@@ -156 +161 @@
          [{'rg': 2.2, 'porod_exp': 22.0, 'background': 100.0}, 5.0, 100.0],
 
-         [{'rg': 1.1, 'porod_exp': 1, 'background': 10.0, 'scale': 1.25}, 20000., 10.0000712097]
+         [{'rg': 1.1, 'porod_exp': 1, 'background': 10.0, 'scale': 1.25},
+         20000., 10.0000712097]
          ]