Changeset 6debc16 in sasview for src/sas

Timestamp:

Nov 28, 2017 9:21:33 AM (7 years ago)

Author:

GitHub <noreply@…>

Branches:

master, magnetic_scatt, release-4.2.2, ticket-1009, ticket-1094-headless, ticket-1242-2d-resolution, ticket-1243, ticket-1249, ticket885, unittest-saveload

Children:

45bfe3f1

Parents:

0fc5a03 (diff), 1b67f3e (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:

Steve K <smk78@…> (11/28/17 09:21:33)

git-committer:

GitHub <noreply@…> (11/28/17 09:21:33)

Message:

Merge pull request #125 from SasView?/docs

translate equation images back into latex for sas_calculator_help

Location:

src/sas/sasgui/perspectives/calculator/media

Files:

• dm_eq.png (deleted)
• gen_debye_eq.png (deleted)
• gen_i.png (deleted)
• gen_mag_pic.png (deleted)
• mqx.png (deleted)
• mqy.png (deleted)
• mxp.png (deleted)
• myp.png (deleted)
• mzp.png (deleted)
• sas_calculator_help.rst (modified) (7 diffs)
• sld1.png (deleted)
• sld2.png (deleted)

src/sas/sasgui/perspectives/calculator/media/sas_calculator_help.rst

@@ -26 +26 @@
 intensity from the particle is
 
-.. image:: gen_i.png
+.. math::
+
+    I(\vec Q) = \frac{1}{V}\left|
+        \sum_j^N v_j \beta_j \exp(i\vec Q \cdot \vec r_j)\right|^2
 
 Equation 1.
@@ -46 +49 @@
 atomic structure (such as taken from a PDB file) to get the right normalization.
 
-*NOTE! $\beta_j$ displayed in the GUI may be incorrect but this will not
+*NOTE!* $\beta_j$ *displayed in the GUI may be incorrect but this will not
 affect the scattering computation if the correction of the total volume V is made.*
 
@@ -56 +59 @@
 ^^^^^^^^^^^^^^^^^^^
 
-For magnetic scattering, only the magnetization component, $M_\perp$,
-perpendicular to the scattering vector $Q$ contributes to the magnetic
+For magnetic scattering, only the magnetization component, $\mathbf{M}_\perp$,
+perpendicular to the scattering vector $\vec Q$ contributes to the magnetic
 scattering length.
 
@@ -64 +67 @@
 The magnetic scattering length density is then
 
-.. image:: dm_eq.png
+.. math::
+
+    \beta_M = \frac{\gamma r_0}{2 \mu_B}\sigma \cdot \mathbf{M}_\perp
+        = D_M\sigma \cdot \mathbf{M}_\perp
 
 where the gyromagnetic ratio is $\gamma = -1.913$, $\mu_B$ is the Bohr
@@ -81 +87 @@
 .. image:: gen_mag_pic.png
 
-Now let us assume that the angles of the *Q* vector and the spin-axis (x')
-to the x-axis are $\phi$ and $\theta_\text{up}$ respectively (see above). Then,
+Now let us assume that the angles of the $\vec Q$ vector and the spin-axis ($x'$)
+to the $x$-axis are $\phi$ and $\theta_\text{up}$ respectively (see above). Then,
 depending upon the polarization (spin) state of neutrons, the scattering
 length densities, including the nuclear scattering length density ($\beta_N$)
@@ -89 +95 @@
 *  for non-spin-flips
 
-   .. image:: sld1.png
+.. math::
+    \beta_{\pm\pm} = \beta_N \mp D_M M_{\perp x'}
 
 *  for spin-flips
 
-   .. image:: sld2.png
+.. math::
+    \beta_{\pm\mp} = - D_M(M_{\perp y'} \pm i M_{\perp z'})
 
 where
 
-.. image:: mxp.png
+.. math::
 
-.. image:: myp.png
+    M_{\perp x'} &= M_{0q_x}\cos\theta_\text{up} + M_{0q_y}\sin\theta_\text{up} \\
+    M_{\perp y'} &= M_{0q_y}\cos\theta_\text{up} - M_{0q_x}\sin\theta_\text{up} \\
+    M_{\perp z'} &= M_{0z} \\
+    M_{0q_x} &= (M_{0x}\cos\phi - M_{0y}\sin\phi)\cos\phi \\
+    M_{0q_y} &= (M_{0y}\sin\phi - M_{0y}\cos\phi)\sin\phi
 
-.. image:: mzp.png
-
-.. image:: mqx.png
-
-.. image:: mqy.png
-
-Here the $M0_x$, $M0_y$ and $M0_z$ are the $x$, $y$ and $z$
-components of the magnetisation vector in the laboratory $xyz$ frame.
+Here the $M_{0x}$, $M_{0y}$ and $M_{0z}$ are
+the $x$, $y$ and $z$ components of the magnetisation vector in the
+laboratory $x$-$y$-$z$ frame.
 
 .. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ
@@ -148 +155 @@
 uses the Debye equation below providing a 1D output
 
-.. image:: gen_debye_eq.png
+.. math::
+
+    I(|\vec Q|) = \frac{1}{V}\sum_j^N v_j\beta_j \sum_k^N v_k \beta_k
+        \frac{\sin(|\vec Q||\vec r_j - \vec r_k|)}{|\vec Q||\vec r_j - \vec r_k|}
 
 where $v_j \beta_j \equiv b_j$ is the scattering