Changeset e526a9d in sasmodels for doc/guide

Timestamp:

Feb 4, 2018 7:40:01 PM (7 years ago)

Author:

GitHub <noreply@…>

Branches:

master, core_shell_microgels, magnetic_model, ticket-1257-vesicle-product, ticket_1156, ticket_1265_superball, ticket_822_more_unit_tests

Children:

aadec17

Parents:

032646d (diff), 72e41a0 (diff)
Note: this is a merge changeset, the changes displayed below correspond to the merge itself.
Use the (diff) links above to see all the changes relative to each parent.

git-author:

Paul Butler <butlerpd@…> (02/04/18 19:40:01)

git-committer:

GitHub <noreply@…> (02/04/18 19:40:01)

Message:

Merge pull request #59 from SasView?/boltzmann

add BoltzmannDistribution? and UniformDistribution?

Since Paul K approved the code and the only issue found by R. Heenan and P. Butler has been resolved by sasview PR 141 we should be able to merge this now.

Location:

doc/guide

Files:

• pd/pd_boltzmann.jpg (added)
• pd/pd_uniform.jpg (added)
• pd/polydispersity.rst (modified) (4 diffs)
• orientation/orientation.rst (modified) (1 diff)

doc/guide/pd/polydispersity.rst

@@ -42 +42 @@
 calculations are generally more robust with more data points or more angles.
 
-The following five distribution functions are provided:
+The following distribution functions are provided:
 
 *  *Rectangular Distribution*
+*  *Uniform Distribution*
 *  *Gaussian Distribution*
 *  *Lognormal Distribution*
 *  *Schulz Distribution*
 *  *Array Distribution*
+*  *Boltzmann Distribution*
 
 These are all implemented as *number-average* distributions.
@@ -85 +87 @@
     Rectangular distribution.
 
+
+
+Uniform Distribution
+^^^^^^^^^^^^^^^^^^^^^^^^
+
+The Uniform Distribution is defined as
+
+    .. math::
+
+        f(x) = \frac{1}{\text{Norm}}
+        \begin{cases}
+          1 & \text{for } |x - \bar x| \leq \sigma \\
+          0 & \text{for } |x - \bar x| > \sigma
+        \end{cases}
+
+    where $\bar x$ is the mean of the distribution, $\sigma$ is the half-width, and
+    *Norm* is a normalization factor which is determined during the numerical
+    calculation.
+
+    Note that the polydispersity is given by
+
+    .. math:: \text{PD} = \sigma / \bar x
+
+    .. figure:: pd_uniform.jpg
+
+        Uniform distribution.
+
+The value $N_\sigma$ is ignored for this distribution.
+
 .. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ
 
@@ -183 +214 @@
 ^^^^^^^^^^^^^^^^^^
 
-This user-definable distribution should be given as as a simple ASCII text
+This user-definable distribution should be given as a simple ASCII text
 file where the array is defined by two columns of numbers: $x$ and $f(x)$.
 The $f(x)$ will be normalized to 1 during the computation.
@@ -202 +233 @@
 given for the model will have no affect, and will be ignored when computing
 the average.  This means that any parameter with an array distribution will
-not be fittable.
+not be fitable.
+
+.. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ
+
+Boltzmann Distribution
+^^^^^^^^^^^^^^^^^^^^^^
+
+The Boltzmann Distribution is defined as
+
+.. math::
+
+    f(x) = \frac{1}{\text{Norm}}
+           \exp\left(-\frac{ | x - \bar x | }{\sigma}\right)
+
+where $\bar x$ is the mean of the distribution and *Norm* is a normalization
+factor which is determined during the numerical calculation.
+The width is defined as
+
+.. math:: \sigma=\frac{k T}{E}
+
+which is the inverse Boltzmann factor,
+where $k$ is the Boltzmann constant, $T$ the temperature in Kelvin and $E$ a
+characteristic energy per particle.
+
+.. figure:: pd_boltzmann.jpg
+
+    Boltzmann distribution.
 
 .. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ

doc/guide/orientation/orientation.rst

@@ -52 +52 @@
 yaw angle $\theta$ about the $b$-axis and pitch angle $\phi$ about the
 $a$-axis.
+
+You can explore the view and jitter angles interactively using
+:func:`sasmodels.jitter.run`.  Enter the following into the python
+interpreter::
+
+    from sasmodels import jitter
+    jitter.run()
 
 More formally, starting with axes $a$-$b$-$c$ of the particle aligned