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LinearAlgebraWiki: Apdot/Algorithms/BlkVar2 (last edited 2007-05-24 21:56:37 by
MarthaGanser
)
![\resetsteps % Reset all the commands to create a blank worksheet
% Define the operation to be computed
\renewcommand{\routinename}{ \left[ \alpha \right] := \mbox{\sc Apdot\_blk}( \alpha, x, y ) }
% Step 3: Loop-guard
\renewcommand{\guard}{
m( x_B ) < m( x )
}
% Step 4: Define Initialize
\renewcommand{\partitionings}{
$
x \rightarrow
\FlaTwoByOne{x_{T}}
{x_{B}}
$
,
$
y \rightarrow
\FlaTwoByOne{y_{T}}
{y_{B}}
$
}
\renewcommand{\partitionsizes}{
$ x_{B} $ has $ 0 $ rows,
$ y_{B} $ has $ 0 $ rows
}
% Step 5a: Repartition the operands
\renewcommand{\blocksize}{b}
\renewcommand{\repartitionings}{
$
\FlaTwoByOne{ x_T }
{ x_B }
\rightarrow
\FlaThreeByOneT{x_0}
{x_1}
{x_2}
$
,
$
\FlaTwoByOne{ y_T }
{ y_B }
\rightarrow
\FlaThreeByOneT{y_0}
{y_1}
{y_2}
$
}
\renewcommand{\repartitionsizes}{
$ x_1 $ has $ b $ rows,
$ y_1 $ has $ b $ rows}
% Step 5b: Move the double lines
\renewcommand{\moveboundaries}{
$
\FlaTwoByOne{ x_T }
{ x_B }
\leftarrow
\FlaThreeByOneB{x_0}
{x_1}
{x_2}
$
,
$
\FlaTwoByOne{ y_T }
{ y_B }
\leftarrow
\FlaThreeByOneB{y_0}
{y_1}
{y_2}
$
}
% Step 8: Insert the updates required to change the
% state from that given in Step 6 to that given in Step 7
% Note: The below needs editing!!!
\renewcommand{\update}{
$
\begin{array}{l}
\alpha = x_1^T y_1 + \alpha
\end{array}
$
}
\footnotesize
\FlaAlgorithmNarrow % this command generates the algorithm](/wiki/LA.wiki/Apdot/Algorithms/BlkVar2?action=AttachFile&do=get&target=latex_6d82e46744eaeff0da32a00396cf362e2f066de7_p1.png "\resetsteps % Reset all the commands to create a blank worksheet
% Define the operation to be computed
\renewcommand{\routinename}{ \left[ \alpha \right] := \mbox{\sc Apdot\_blk}( \alpha, x, y ) }
% Step 3: Loop-guard
\renewcommand{\guard}{
m( x_B ) < m( x )
}
% Step 4: Define Initialize
\renewcommand{\partitionings}{
$
x \rightarrow
\FlaTwoByOne{x_{T}}
{x_{B}}
$
,
$
y \rightarrow
\FlaTwoByOne{y_{T}}
{y_{B}}
$
}
\renewcommand{\partitionsizes}{
$ x_{B} $ has $ 0 $ rows,
$ y_{B} $ has $ 0 $ rows
}
% Step 5a: Repartition the operands
\renewcommand{\blocksize}{b}
\renewcommand{\repartitionings}{
$
\FlaTwoByOne{ x_T }
{ x_B }
\rightarrow
\FlaThreeByOneT{x_0}
{x_1}
{x_2}
$
,
$
\FlaTwoByOne{ y_T }
{ y_B }
\rightarrow
\FlaThreeByOneT{y_0}
{y_1}
{y_2}
$
}
\renewcommand{\repartitionsizes}{
$ x_1 $ has $ b $ rows,
$ y_1 $ has $ b $ rows}
% Step 5b: Move the double lines
\renewcommand{\moveboundaries}{
$
\FlaTwoByOne{ x_T }
{ x_B }
\leftarrow
\FlaThreeByOneB{x_0}
{x_1}
{x_2}
$
,
$
\FlaTwoByOne{ y_T }
{ y_B }
\leftarrow
\FlaThreeByOneB{y_0}
{y_1}
{y_2}
$
}
% Step 8: Insert the updates required to change the
% state from that given in Step 6 to that given in Step 7
% Note: The below needs editing!!!
\renewcommand{\update}{
$
\begin{array}{l}
\alpha = x_1^T y_1 + \alpha
\end{array}
$
}
\footnotesize
\FlaAlgorithmNarrow % this command generates the algorithm")
