tutorial_lud

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 tutorial_lud [2018/06/19 15:41]sanjay tutorial_lud [2018/06/19 15:45]sanjay Both sides previous revision Previous revision 2018/06/19 15:45 sanjay 2018/06/19 15:45 sanjay 2018/06/19 15:41 sanjay 2018/06/19 15:40 sanjay 2017/04/19 14:09 external edit2017/04/19 13:26 waruna [Generating and Testing Alphabets] 2016/12/12 10:12 waruna Changed the latex notation to support new dokuwiki2015/10/06 16:12 sanjay [Step 3 : Equations] 2015/10/06 16:10 sanjay 2015/10/06 16:09 sanjay 2015/03/06 09:34 guillaume 2015/03/06 09:33 guillaume old revision restored (2015/03/02 12:09)2015/03/06 09:32 guillaume input/output/local keywords used2015/03/02 12:09 guillaume Modifying the latex code delete it => old version restored + temp note added2015/03/02 12:05 guillaume old revision restored (2014/05/30 11:49)2015/02/27 08:36 guillaume Corrected condition of second domain of L in equation + alpha program2014/05/30 11:49 external edit Next revision Previous revision 2018/06/19 15:45 sanjay 2018/06/19 15:45 sanjay 2018/06/19 15:41 sanjay 2018/06/19 15:40 sanjay 2017/04/19 14:09 external edit2017/04/19 13:26 waruna [Generating and Testing Alphabets] 2016/12/12 10:12 waruna Changed the latex notation to support new dokuwiki2015/10/06 16:12 sanjay [Step 3 : Equations] 2015/10/06 16:10 sanjay 2015/10/06 16:09 sanjay 2015/03/06 09:34 guillaume 2015/03/06 09:33 guillaume old revision restored (2015/03/02 12:09)2015/03/06 09:32 guillaume input/output/local keywords used2015/03/02 12:09 guillaume Modifying the latex code delete it => old version restored + temp note added2015/03/02 12:05 guillaume old revision restored (2014/05/30 11:49)2015/02/27 08:36 guillaume Corrected condition of second domain of L in equation + alpha program2014/05/30 11:49 external edit Line 1: Line 1: - In this tutorial, we write an Alphabets (or Alpha, for now the two are synonymous) program, starting from a mathematical equation for LU decomposition. ​ Then we will generate code to execute the alphabets ​program, and test the generated code for correctness. + In this tutorial, we write an Alphabets (or Alpha, for now the two are synonymous) program, starting from a mathematical equation for LU decomposition. ​ Then we will generate code to execute the alpha program, and test the generated code for correctness. The equation for LU Decomposition,​ derived from first principles using simple algebra in {{:​foundations.pdf|Foundations}} (pg.3), is as follows: The equation for LU Decomposition,​ derived from first principles using simple algebra in {{:​foundations.pdf|Foundations}} (pg.3), is as follows: Line 20: Line 20: [Temp note due to : 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===== + =====Writing ​Alpha===== ====Step 1 : Affine System and Parameters ==== ====Step 1 : Affine System and Parameters ==== - Let's start from an empty alphabets ​file, with LUD as the name of the system, and a positive integer N as its parameter. + Let's start from an empty alpha file, with LUD as the name of the system, and a positive integer N as its parameter. - A system (Affine System) takes its name from system of affine recurrence equations, and represents a block of computation. An Alphabets ​program may contain multiple systems. + A system (Affine System) takes its name from system of affine recurrence equations, and represents a block of computation. An Alpha program may contain multiple systems. **Caveat:​** ​ Remember the phrase, "​It'​s not a bug, it's a feature"? ​ Well, in a tutorial, a feature is called a "​learning opportunity."​ **Caveat:​** ​ Remember the phrase, "​It'​s not a bug, it's a feature"? ​ Well, in a tutorial, a feature is called a "​learning opportunity."​