Changeset 785cbec in sasmodels for sasmodels/models/spherical_sld.py

Timestamp:

Aug 5, 2016 11:03:19 AM (8 years ago)

Author:

Paul Kienzle <pkienzle@…>

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:

c8de1bd

Parents:

e187b25

Message:

doc fixes

File:

• sasmodels/models/spherical_sld.py (modified) (10 diffs)

sasmodels/models/spherical_sld.py

@@ -46 +46 @@
 
 .. math::
-    f_\text{core} = 4 \pi \int_{0}^{r_\text{core}} \rho_\text{core}
+
+    f_\text{core} &= 4 \pi \int_{0}^{r_\text{core}} \rho_\text{core}
     \frac{\sin(qr)} {qr} r^2 dr =
     3 \rho_\text{core} V(r_\text{core})
@@ -52 +53 @@
     {qr_\text{core}^3} \Big]
 
-    f_{\text{inter}_i} = 4 \pi \int_{\Delta t_{ \text{inter}_i } }
+    f_{\text{inter}_i} &= 4 \pi \int_{\Delta t_{ \text{inter}_i } }
     \rho_{ \text{inter}_i } \frac{\sin(qr)} {qr} r^2 dr
 
-    f_{\text{shell}_i} = 4 \pi \int_{\Delta t_{ \text{inter}_i } }
+    f_{\text{shell}_i} &= 4 \pi \int_{\Delta t_{ \text{inter}_i } }
     \rho_{ \text{flat}_i } \frac{\sin(qr)} {qr} r^2 dr =
     3 \rho_{ \text{flat}_i } V ( r_{ \text{inter}_i } +
@@ -67 +68 @@
     \cos(qr_{\text{inter}_i}) } {qr_{\text{inter}_i}^3} \Big]
 
-    f_\text{solvent} = 4 \pi \int_{r_N}^{\infty} \rho_\text{solvent}
+    f_\text{solvent} &= 4 \pi \int_{r_N}^{\infty} \rho_\text{solvent}
     \frac{\sin(qr)} {qr} r^2 dr =
     3 \rho_\text{solvent} V(r_N)
@@ -80 +81 @@
 
 .. math::
-    \rho_{{inter}_i} (r) = \begin{cases}
+
+    \rho_{{inter}_i} (r) &= \begin{cases}
     B \exp\Big( \frac {\pm A(r - r_{\text{flat}_i})}
-    {\Delta t_{ \text{inter}_i }} \Big) +C  & \text{for} A \neq 0 \\
+    {\Delta t_{ \text{inter}_i }} \Big) +C  & \mbox{for } A \neq 0 \\
     B \Big( \frac {(r - r_{\text{flat}_i})}
-    {\Delta t_{ \text{inter}_i }} \Big) +C  & \text{for} A = 0 \\
+    {\Delta t_{ \text{inter}_i }} \Big) +C  & \mbox{for } A = 0 \\
     \end{cases}
 
@@ -90 +92 @@
 
 .. math::
-    \rho_{{inter}_i} (r) = \begin{cases}
+
+    \rho_{{inter}_i} (r) &= \begin{cases}
     \pm B \Big( \frac {(r - r_{\text{flat}_i} )} {\Delta t_{ \text{inter}_i }}
-    \Big) ^A  +C  & \text{for} A \neq 0 \\
-    \rho_{\text{flat}_{i+1}}  & \text{for} A = 0 \\
+    \Big) ^A  +C  & \mbox{for } A \neq 0 \\
+    \rho_{\text{flat}_{i+1}}  & \mbox{for } A = 0 \\
     \end{cases}
 
@@ -101 +104 @@
     \rho_{{inter}_i} (r) = \begin{cases}
     B \text{erf} \Big( \frac { A(r - r_{\text{flat}_i})}
-    {\sqrt{2} \Delta t_{ \text{inter}_i }} \Big) +C  & \text{for} A \neq 0 \\
+    {\sqrt{2} \Delta t_{ \text{inter}_i }} \Big) +C  & \mbox{for } A \neq 0 \\
     B \Big( \frac {(r - r_{\text{flat}_i} )} {\Delta t_{ \text{inter}_i }}
-    \Big)  +C  & \text{for} A = 0 \\
+    \Big)  +C  & \mbox{for } A = 0 \\
     \end{cases}
 
@@ -114 +117 @@
 
 .. math::
-    f_{\text{inter}_i} = 4 \pi \int_{\Delta t_{ \text{inter}_i } }
+
+    f_{\text{inter}_i} &= 4 \pi \int_{\Delta t_{ \text{inter}_i } }
     \rho_{ \text{inter}_i } \frac{\sin(qr)} {qr} r^2 dr =
-    4 \pi \sum_{j=0}^{npts_{\text{inter}_i} -1 }
+    4 \pi \sum_{j=1}^{n_\text{steps}}
     \int_{r_j}^{r_{j+1}} \rho_{ \text{inter}_i } (r_j)
-    \frac{\sin(qr)} {qr} r^2 dr \approx
-
-    4 \pi \sum_{j=0}^{npts_{\text{inter}_i} -1 } \Big[
+    \frac{\sin(qr)} {qr} r^2 dr
+
+    &\approx 4 \pi \sum_{j=1}^{n_\text{steps}} \Big[
     3 ( \rho_{ \text{inter}_i } ( r_{j+1} ) - \rho_{ \text{inter}_i }
-    ( r_{j} ) V ( r_{ \text{subshell}_j } )
+    ( r_{j} ) V (r_j)
     \Big[ \frac {r_j^2 \beta_\text{out}^2 \sin(\beta_\text{out})
     - (\beta_\text{out}^2-2) \cos(\beta_\text{out}) }
     {\beta_\text{out}^4 } \Big]
 
-    - 3 ( \rho_{ \text{inter}_i } ( r_{j+1} ) - \rho_{ \text{inter}_i }
-    ( r_{j} ) V ( r_{ \text{subshell}_j-1 } )
+    &{} - 3 ( \rho_{ \text{inter}_i } ( r_{j+1} ) - \rho_{ \text{inter}_i }
+    ( r_{j} ) V ( r_{j-1} )
     \Big[ \frac {r_{j-1}^2 \sin(\beta_\text{in})
     - (\beta_\text{in}^2-2) \cos(\beta_\text{in}) }
     {\beta_\text{in}^4 } \Big]
 
-    + 3 \rho_{ \text{inter}_i } ( r_{j+1} )  V ( r_j )
+    &{} + 3 \rho_{ \text{inter}_i } ( r_{j+1} )  V ( r_j )
     \Big[ \frac {\sin(\beta_\text{out}) - \cos(\beta_\text{out}) }
     {\beta_\text{out}^4 } \Big]
-
     - 3 \rho_{ \text{inter}_i } ( r_{j} )  V ( r_j )
     \Big[ \frac {\sin(\beta_\text{in}) - \cos(\beta_\text{in}) }
@@ -145 +148 @@
 
 .. math::
-    V(a) = \frac {4\pi}{3}a^3
-
-    a_\text{in} ~ \frac{r_j}{r_{j+1} -r_j} \text{, } a_\text{out}
-    ~ \frac{r_{j+1}}{r_{j+1} -r_j}
-
-    \beta_\text{in} = qr_j \text{, } \beta_\text{out} = qr_{j+1}
+    :nowrap:
+
+    \begin{align*}
+    V(a) &= \frac {4\pi}{3}a^3 && \\
+    a_\text{in} &\sim \frac{r_j}{r_{j+1} -r_j} \text{, } &a_\text{out}
+    &\sim \frac{r_{j+1}}{r_{j+1} -r_j} \\
+    \beta_\text{in} &= qr_j \text{, } &\beta_\text{out} &= qr_{j+1}
+    \end{align*}
 
 
@@ -160 +165 @@
 .. math::
 
-    P(q) = \frac{[f]^2} {V_\text{particle}} \text{where} V_\text{particle}
+    P(q) = \frac{[f]^2} {V_\text{particle}} \mbox{ where } V_\text{particle}
     = V(r_{\text{shell}_N})
 
@@ -172 +177 @@
 .. note::
 
-    The outer most radius is used as the effective radius for S(Q)
+    The outer most radius is used as the effective radius for $S(Q)$
     when $P(Q) * S(Q)$ is applied.