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--- tutorial_lud [2015/10/06 16:09]
sanjay
+++ tutorial_lud [2017/04/19 13:26]
waruna [Generating and Testing Alphabets]
@@ Line 2: / Line 2: @@
 The equation for LU Decomposition, derived from first principles using simple algebra in {{:foundations.pdf|Foundations}} (pg.3), is as follows:
-<latex>
-    $U_{i,j}=\begin{cases}
+/*<latex>*/
+$$
+    U_{i,j}=\begin{cases}
 =i\le j & A_{i,j}\\
 <i\le j & A_{i,j}-\sum_{k=1}^{i-1}L_{i,k}U_{k,j}
-\end{cases}
+\end{cases}\\
 L_{i,j}=\begin{cases}
-=j<i & \frac{A_{i,j}}{U_{j,j}}\\
+= i\le j & \frac{A_{i,j}}{U_{j,j}}\\
-<j<i & \frac{1}{U_{j,j}}(A_{i,j}-\sum_{k=1}^{j-1}L_{i,k}U_{k,j})
+< i\le j & \frac{1}{U_{j,j}}(A_{i,j}-\sum_{k=1}^{j-1}L_{i,k}U_{k,j})
-\end{cases}$
+\end{cases}
-</latex>
+$$
+/*<\latex>*/
-[Temp note: in the last case of L, the condition is "1 < j <= i"]
+[Temp note due to : in the last case of L, the condition is "1 < j <= i"]
 =====Writing Alphabets=====
@@ Line 143: / Line 147: @@
 L = case
    {i,j|1==j} : (A / (i,j->j,j)@U);
-   {i,j|1<i} : (A - reduce(+, (i,j,k->i,j), (i,j,k->i,k)@L*(i,j,k->k,j)@U))/(i,j->i,i)@U;
+   {i,j|1<i} : (A - reduce(+, (i,j,k->i,j), (i,j,k->i,k)@L*(i,j,k->k,j)@U))/(i,j->j,j)@U;
 esac;
 </sxh>
@@ Line 169: / Line 173: @@
 Analyses, transformations, and code generation of Alphabets programs are performed using the AlphaZ system. The normal interface for using AlphaZ is the scripting interface called compiler scripts.
 Given below is an example script for that does several things using the LUD program we wrote above.
-<sxh cs; gutter:false>
+<sxh cs; gutter:true>
 # read program and store the internal representation in variable prog
 prog = ReadAlphabets("./LUD.ab");

AlphaZ

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