tutorial_lud

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 tutorial_lud [2015/10/06 16:09]sanjay tutorial_lud [2017/04/19 13:26]waruna [Generating and Testing Alphabets] 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 Next revision Both sides next revision 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: 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>​*/ + $$+ ​U_{i,​j}=\begin{cases} 1=i\le j & A_{i,j}\\ 1=i\le j & A_{i,j}\\ 1 +$$ + /*<\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===== =====Writing Alphabets===== Line 143: Line 147: L = case L = case ​{i,​j|1==j} : (A / (i,​j->​j,​j)@U);​ ​{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; esac; ​ 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. 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. Given below is an example script for that does several things using the LUD program we wrote above. - + # read program and store the internal representation in variable prog # read program and store the internal representation in variable prog prog = ReadAlphabets("​./​LUD.ab"​);​ prog = ReadAlphabets("​./​LUD.ab"​);​