tutorial_lud

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tutorial_lud [2015/10/06 16:12] sanjay [Step 3 : Equations] |
tutorial_lud [2017/04/19 13:26] waruna [Generating and Testing Alphabets] |
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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<i\le j & A_{i,j}-\sum_{k=1}^{i-1}L_{i,k}U_{k,j} | 1<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} | L_{i,j}=\begin{cases} | ||

1 = i\le j & \frac{A_{i,j}}{U_{j,j}}\\ | 1 = i\le j & \frac{A_{i,j}}{U_{j,j}}\\ | ||

1< i\le j & \frac{1}{U_{j,j}}(A_{i,j}-\sum_{k=1}^{j-1}L_{i,k}U_{k,j}) | 1< 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 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"] | ||

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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. | ||

- | <sxh cs; gutter:false> | + | <sxh cs; gutter:true> |

# 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"); |

tutorial_lud.txt · Last modified: 2017/04/19 14:09 (external edit)