Fix eqns

scijs · Jul 25, 2015 · 358af21 · 358af21
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diff --git a/README.md b/README.md
@@ -5,7 +5,15 @@
 
 ## Introduction
 
-This module integrates a system of ordinary differential equations of the form <p align="center"><img alt="undefined" valign="middle" src="images/yt-ft-yt-fae25965d3.png" width="151.5" height="25"></p> <p align="center"><img alt="undefined" valign="middle" src="images/yt_0-y_0-42d14f447f.png" width="91.5" height="24"></p> where <img alt="undefined" valign="middle" src="images/y-adb83ba1d7.png" width="14.5" height="16.5"> is a vector of length <img alt="undefined" valign="middle" src="images/n-66e1b1ee17.png" width="16" height="13">. Given time step <img alt="undefined" valign="middle" src="images/delta-t-9813ae7971.png" width="28" height="18">, the Runge-Kutta 4 method integrates the ODE with update <p align="center"><img alt="undefined" valign="middle" src="images/y_n1-fracdelta-t6leftk_1-2k_2-2k_3-k_4right-58f49ef625.png" width="289" height="45"></p> <p align="center"><img alt="undefined" valign="middle" src="images/t_n1-t_n-delta-t-a6feda606a.png" width="135" height="22.5"></p> where <img alt="undefined" valign="middle" src="images/k_n-bcd1333065.png" width="25.5" height="21"> are given by <p align="center"><img alt="undefined" valign="middle" src="images/k_1-ft_n-y_n-9aa4e00ef0.png" width="130.5" height="24"></p> <p align="center"><img alt="undefined" valign="middle" src="images/k_2-ft_n-fracdelta-t2-y_n-fracdelta-t2-k_1-d1c9d16d54.png" width="255.5" height="45"></p> <p align="center"><img alt="undefined" valign="middle" src="images/k_3-ft_n-fracdelta-t2-y_n-fracdelta-t2-k_2-605f389527.png" width="255.5" height="45"></p> <p align="center"><img alt="undefined" valign="middle" src="images/k_4-ft_n-delta-t-y_n-delta-tk_3-8ee3750675.png" width="246" height="24"></p>
+This module integrates a system of ordinary differential equations of the form
+
+<p align="center"><img alt="&bsol;begin&lcub;eqnarray&midast;&rcub; y&apos;&lpar;t&rpar; &amp;&equals;&amp; f&lpar;t&comma; y&lpar;t&rpar;&rpar;&comma; &bsol;&bsol; y&lpar;t&lowbar;0&rpar; &amp;&equals;&amp; y&lowbar;0 &bsol;end&lcub;eqnarray&midast;&rcub;" valign="middle" src="docs/images/begineqnarray-yt-ft-yt-yt_0-y_0-endeqnarray-0298eae3db.png" width="187" height="61"></p>
+
+where <img alt="y" valign="middle" src="docs/images/y-720f311276.png" width="14.5" height="20"> is a vector of length <img alt="n" valign="middle" src="docs/images/n-9baedbc330.png" width="16" height="16">. Given time step <img alt="&bsol;Delta t" valign="middle" src="docs/images/delta-t-a20a5fe4f2.png" width="28" height="16">, the Runge-Kutta 4 method integrates the ODE with update
+
+<p align="center"><img alt="&bsol;begin&lcub;eqnarray&midast;&rcub; y&lowbar;&lcub;n&plus;1&rcub; &amp;&equals;&amp; &bsol;frac&lcub;&bsol;Delta t&rcub;&lcub;6&rcub;&bsol;left&lpar;k&lowbar;1 &plus; 2k&lowbar;2 &plus; 2k&lowbar;3 &plus; k&lowbar;4&bsol;right&rpar; &bsol;&bsol; t&lowbar;&lcub;n&plus;1&rcub; &amp;&equals;&amp; t&lowbar;n &plus; &bsol;Delta t &bsol;end&lcub;eqnarray&midast;&rcub;" valign="middle" src="docs/images/begineqnarray-y_n1-fracdelta-t6leftk_1-2k_2-2-41157480a7.png" width="321.5" height="71"></p>
+where <img alt="k&lowbar;n" valign="middle" src="docs/images/k_n-d413726dee.png" width="25.5" height="19"> are given by
+<p align="center"><img alt="&bsol;begin&lcub;eqnarray&midast;&rcub; k&lowbar;1 &amp;&equals;&amp; f&lpar;t&lowbar;n&comma; y&lowbar;n&rpar;&comma; &bsol;&bsol; k&lowbar;2 &amp;&equals;&amp; f&lpar;t&lowbar;n &plus; &bsol;frac&lcub;&bsol;Delta t&rcub;&lcub;2&rcub;&comma; y&lowbar;n &plus; &bsol;frac&lcub;&bsol;Delta t&rcub;&lcub;2&rcub; k&lowbar;1&rpar;&comma; &bsol;&bsol; k&lowbar;3 &amp;&equals;&amp; f&lpar;t&lowbar;n &plus; &bsol;frac&lcub;&bsol;Delta t&rcub;&lcub;2&rcub;&comma; y&lowbar;n &plus; &bsol;frac&lcub;&bsol;Delta t&rcub;&lcub;2&rcub; k&lowbar;2&rpar;&comma; &bsol;&bsol; k&lowbar;4 &amp;&equals;&amp; f&lpar;t&lowbar;n &plus; &bsol;Delta t&comma; y&lowbar;n &plus; &bsol;Delta tk&lowbar;3&rpar;&period;  &bsol;end&lcub;eqnarray&midast;&rcub;" valign="middle" src="docs/images/begineqnarray-k_1-ft_n-y_n-k_2-ft_n-fracdelta-35d808c6ef.png" width="288" height="156.5"></p>
 
 ## Install
 
@@ -45,8 +53,8 @@ integrator.steps(n)
 **Arguments:**
 - `y0`: an array or typed array containing initial conditions. This vector is updated in-place with each integrator step.
 - `deriv`: a function that calculates the derivative. Format is `function( dydt, y, t )`. Inputs are current state `y` and current time `t`, output is calcualted derivative `dydt`.
-- `t0`: initial time <img alt="undefined" valign="middle" src="images/t-3f19307093.png" width="11.5" height="16.5">.
-- `dt`: time step <img alt="undefined" valign="middle" src="images/delta-t-9813ae7971.png" width="28" height="18">.
+- `t0`: initial time <img alt="t" valign="middle" src="docs/images/t-fc93da6f4d.png" width="11.5" height="16">.
+- `dt`: time step <img alt="&bsol;Delta t" valign="middle" src="docs/images/delta-t-a20a5fe4f2.png" width="28" height="16">.
 
 **Returns**:
 Initialized integrator object.
@@ -56,12 +64,12 @@ Initialized integrator object.
 - `y`: current state. Initialized as a shallow copy of input `y0`.
 - `deriv`: function that calcualtes derivative. Initialized from input. May be changed.
 - `t`: current time, incremented by `dt` with each time step.
-- `dt`: time step <img alt="undefined" valign="middle" src="images/delta-t-9813ae7971.png" width="28" height="18">. Initialized from input `dt`. May be changed.
+- `dt`: time step <img alt="&bsol;Delta t" valign="middle" src="docs/images/delta-t-a20a5fe4f2.png" width="28" height="16">. Initialized from input `dt`. May be changed.
 
 **Methods:**
 - `.step()`: takes a single step of the RK-4 integrator and stores the result in-place in the `y` property.
 - `.steps( n )`: takes `n` steps of the RK-4 integrator, storing the result in-place in the `y` property.
 
 ## Credits
 
-(c) 2015 Ricky Reusser. MIT License
+(c) 2015 Ricky Reusser. MIT License
diff --git a/README.mdtex b/README.mdtex
@@ -5,7 +5,15 @@
 
 ## Introduction
 
-This module integrates a system of ordinary differential equations of the form $$ y'(t) &=& f(t, y(t)),$$ $$y(t_0) = y_0$$ where $y$ is a vector of length $n$. Given time step $\Delta t$, the Runge-Kutta 4 method integrates the ODE with update $$y_{n+1} = \frac{\Delta t}{6}\left(k_1 + 2k_2 + 2k_3 + k_4\right)$$ $$t_{n+1} = t_n + \Delta t$$ where $k_n$ are given by $$k_1 = f(t_n, y_n),$$ $$k_2 = f(t_n + \frac{\Delta t}{2}, y_n + \frac{\Delta t}{2} k_1),$$ $$k_3 = f(t_n + \frac{\Delta t}{2}, y_n + \frac{\Delta t}{2} k_2),$$ $$k_4 = f(t_n + \Delta t, y_n + \Delta tk_3).$$
+This module integrates a system of ordinary differential equations of the form
+
+$$[plain=true] \begin{eqnarray*} y'(t) &=& f(t, y(t)), \\ y(t_0) &=& y_0 \end{eqnarray*} $$
+
+where $y$ is a vector of length $n$. Given time step $\Delta t$, the Runge-Kutta 4 method integrates the ODE with update
+
+$$[plain=true] \begin{eqnarray*} y_{n+1} &=& \frac{\Delta t}{6}\left(k_1 + 2k_2 + 2k_3 + k_4\right) \\ t_{n+1} &=& t_n + \Delta t \end{eqnarray*}$$
+where $k_n$ are given by
+$$[plain=true] \begin{eqnarray*} k_1 &=& f(t_n, y_n), \\ k_2 &=& f(t_n + \frac{\Delta t}{2}, y_n + \frac{\Delta t}{2} k_1), \\ k_3 &=& f(t_n + \frac{\Delta t}{2}, y_n + \frac{\Delta t}{2} k_2), \\ k_4 &=& f(t_n + \Delta t, y_n + \Delta tk_3).  \end{eqnarray*}$$
 
 ## Install
 

diff --git a/docs/images/begineqnarray-k_1-ft_n-y_n-k_2-ft_n-fracdelta-35d808c6ef.png b/docs/images/begineqnarray-k_1-ft_n-y_n-k_2-ft_n-fracdelta-35d808c6ef.png
diff --git a/docs/images/begineqnarray-y_n1-fracdelta-t6leftk_1-2k_2-2-41157480a7.png b/docs/images/begineqnarray-y_n1-fracdelta-t6leftk_1-2k_2-2-41157480a7.png
diff --git a/docs/images/begineqnarray-yt-ft-yt-yt_0-y_0-endeqnarray-0298eae3db.png b/docs/images/begineqnarray-yt-ft-yt-yt_0-y_0-endeqnarray-0298eae3db.png
diff --git a/docs/images/delta-t-a20a5fe4f2.png b/docs/images/delta-t-a20a5fe4f2.png
diff --git a/docs/images/k_n-d413726dee.png b/docs/images/k_n-d413726dee.png
diff --git a/docs/images/n-9baedbc330.png b/docs/images/n-9baedbc330.png
diff --git a/docs/images/t-fc93da6f4d.png b/docs/images/t-fc93da6f4d.png
diff --git a/docs/images/y-720f311276.png b/docs/images/y-720f311276.png
diff --git a/gulpfile.js b/gulpfile.js
@@ -12,23 +12,23 @@ gulp.task('mdtex',function() {
 
   var transform = mdEqs({
     defaults: {
-      display: { margin: '1pt' },
-      inline:  { margin: '1pt' }
+      display: { margin: '1pt 1pt 1pt -10pt' },
+      inline:  { margin: '1pt 1pt 1pt -5pt' }
     }
   })
 
   return gulp.src('*.mdtex')
     .pipe(transform)
     .pipe(texFilter)
-    //.pipe(tap(function(file) { console.log(file.contents.toString()) }))
+    .pipe(tap(function(file) { console.log(file.contents.toString()) }))
     .pipe(latex())
     .pipe(pdftocairo({format: 'png'}))
-    .pipe(gulp.dest('images'))
+    .pipe(gulp.dest('docs/images'))
     .pipe(tap(function(file) {
       transform.completeSync(file,function() {
         var img = '<img alt="'+this.alt+'" valign="middle" src="'+this.path+
                   '" width="'+this.width/2+'" height="'+this.height/2+'">'
-        return this.display ? '<p align="center">'+img+'</p>' : img
+        return this.inline ? img : '<p align="center">'+img+'</p>'
       })
     }))
     .pipe(texFilter.restore()).pipe(mdFilter)

diff --git a/images/begineqnarray-yt-ft-yt-yt_0-y_0-endeqnarray-0d72e38d4c.png b/images/begineqnarray-yt-ft-yt-yt_0-y_0-endeqnarray-0d72e38d4c.png
diff --git a/images/begineqnarray-yt-ft-yt-yt_0-y_0-endeqnarray-870096dfab.png b/images/begineqnarray-yt-ft-yt-yt_0-y_0-endeqnarray-870096dfab.png
diff --git a/images/delta-t-9813ae7971.png b/images/delta-t-9813ae7971.png
diff --git a/images/k_1-ft_n-y_n-9aa4e00ef0.png b/images/k_1-ft_n-y_n-9aa4e00ef0.png
diff --git a/images/k_2-ft_n-fracdelta-t2-y_n-fracdelta-t2-k_1-d1c9d16d54.png b/images/k_2-ft_n-fracdelta-t2-y_n-fracdelta-t2-k_1-d1c9d16d54.png
diff --git a/images/k_3-ft_n-fracdelta-t2-y_n-fracdelta-t2-k_2-605f389527.png b/images/k_3-ft_n-fracdelta-t2-y_n-fracdelta-t2-k_2-605f389527.png
diff --git a/images/k_4-ft_n-delta-t-y_n-delta-tk_3-8ee3750675.png b/images/k_4-ft_n-delta-t-y_n-delta-tk_3-8ee3750675.png
diff --git a/images/k_n-bcd1333065.png b/images/k_n-bcd1333065.png
diff --git a/images/n-66e1b1ee17.png b/images/n-66e1b1ee17.png
diff --git a/images/t-3f19307093.png b/images/t-3f19307093.png
diff --git a/images/t_n1-t_n-delta-t-a6feda606a.png b/images/t_n1-t_n-delta-t-a6feda606a.png
diff --git a/images/y-adb83ba1d7.png b/images/y-adb83ba1d7.png
diff --git a/images/y_n1-fracdelta-t6leftk_1-2k_2-2k_3-k_4right-58f49ef625.png b/images/y_n1-fracdelta-t6leftk_1-2k_2-2k_3-k_4right-58f49ef625.png
diff --git a/images/y_n1-y_n-delta-t-fleft-t_n-fracdelta-t2-y_n-f-0a92f940fc.png b/images/y_n1-y_n-delta-t-fleft-t_n-fracdelta-t2-y_n-f-0a92f940fc.png
diff --git a/images/y_n1-y_n-ft_n-y_n-a622b96922.png b/images/y_n1-y_n-ft_n-y_n-a622b96922.png
diff --git a/images/y_n1-y_n-ft_n-y_n-delta-t-7e1ddc48e6.png b/images/y_n1-y_n-ft_n-y_n-delta-t-7e1ddc48e6.png
diff --git a/images/yt-ft-yt-4304a0aa5e.png b/images/yt-ft-yt-4304a0aa5e.png
diff --git a/images/yt-ft-yt-fae25965d3.png b/images/yt-ft-yt-fae25965d3.png
diff --git a/images/yt-ft-yt-yt_0-y_0-309707f928.png b/images/yt-ft-yt-yt_0-y_0-309707f928.png
diff --git a/images/yt-ft-yt-yt_0-y_0-f7515619c6.png b/images/yt-ft-yt-yt_0-y_0-f7515619c6.png
diff --git a/images/yt_0-y_0-42d14f447f.png b/images/yt_0-y_0-42d14f447f.png
diff --git a/images/yt_0-y_0-d7b398c658.png b/images/yt_0-y_0-d7b398c658.png
diff --git a/package.json b/package.json
@@ -25,7 +25,7 @@
     "chai": "^3.0.0",
     "gulp-filter": "^2.0.2",
     "gulp-latex": "^1.0.1",
-    "gulp-markdown-equations": "^1.2.0",
+    "gulp-markdown-equations": "^1.2.3",
     "gulp-pdftocairo": "^0.2.0",
     "gulp-tap": "^0.1.3",
     "mocha": "^2.2.5"