\resetsteps % Reset all the commands to create a blank worksheet % Define the operation to be computed \renewcommand{\operation}{ (b := x) \wedge (Lx = b) } \renewcommand{\routinename}{ b \becomes \mbox{\sc trsv\_var2}(L, b) } \renewcommand{\routinecost}{ n^2 } % Step 3: Loop-guard \renewcommand{\guard}{ m( b_{T} ) < m( b ) } % Step 4: Initialize \renewcommand{\partitionings}{ $ L \rightarrow \FlaTwoByTwo{L_{TL}}{ 0 } {L_{BL}}{L_{BR}} $ , $ b \rightarrow \FlaTwoByOne{b_{T}} {b_{B}} $ } \renewcommand{\partitionsizes}{ $ L_{TL} $ is $ 0 \times 0 $ and $ b_{T} $ has $ 0 $ elements } % Step 5a: Repartition the operands \renewcommand{\repartitionings}{ $ \FlaTwoByTwo{L_{TL}}{ 0 } {L_{BL}}{L_{BR}} \rightarrow \FlaThreeByThreeBR{L_{00}}{ 0 }{ 0 } {\tr{l}_{10}}{\lambda_{11}}{ 0 } {L_{20}}{l_{21}}{L_{22}} $, $ \FlaTwoByOne{ b_T } { b_B } \rightarrow \FlaThreeByOneB{b_0} {\beta_1} {b_2} $ } \renewcommand{\repartitionsizes}{ $ \lambda_{11} $ and $ \beta_1 $ are scalars} % Step 5b: Move the double lines \renewcommand{\moveboundaries}{ $ \FlaTwoByTwo{L_{TL}}{ 0 } {L_{BL}}{L_{BR}} \leftarrow \FlaThreeByThreeTL{L_{00}}{ 0 }{ 0 } {\tr{l}_{10}}{\lambda_{11}}{ 0 } {L_{20}}{l_{21}}{L_{22}} $, $ \FlaTwoByOne{ b_T } { b_B } \leftarrow \FlaThreeByOneT{b_0} {\beta_1} {b_2} $ } \renewcommand{\update}{ $ \begin{array}{l} \beta_1 \becomes \beta_1 / \lambda_{11} \\ b_2 \becomes b_2 - \beta_1 l_{21} ~~~~~~~(\saxpy) \end{array} $ } \FlaAlgorithm % this command generates the algorithm

LinearAlgebraWiki: Algorithms/Trsv/UnbVar2 (last edited 2007-01-10 13:48:03 by RobertVanDeGeijn)