final edits on detspeed

parent a39cf176
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 ... ... @@ -23998,18 +23998,18 @@ octave:6> gplot z \begin{ans}{1} \begin{exparts} \partsitem Under Octave, \texttt{rank(rand(5))} finds the rank of a $\nbyn{5}$ matrix whose entries are (uniformily rank of a $\nbyn{5}$ matrix whose entries are (uniformly distributed) in the interval $[0..1)$. This loop which runs the test $5000$ times \begin{computercode} \begin{lstlisting} octave:1> for i=1:5000 > if rank(rand(5))<5 printf("That's one."); endif > endfor \end{computercode} \end{lstlisting} produces (after a few seconds) returns the prompt, with no output. The Octave script \begin{computercode} \begin{lstlisting} function elapsed_time = detspeed (size) a=rand(size); tic(); ... ... @@ -24018,9 +24018,9 @@ function elapsed_time = detspeed (size) endfor elapsed_time=toc(); endfunction \end{computercode} \end{lstlisting} lead to this session (obviously, your times will vary). \begin{computercode} \begin{lstlisting} octave:1> detspeed(5) ans = 0.019505 octave:2> detspeed(15) ... ... @@ -24029,7 +24029,7 @@ octave:3> detspeed(25) ans = 0.0097431 octave:4> detspeed(35) ans = 0.017398 \end{computercode} \end{lstlisting} \partsitem Here is the data (rounded a bit), and the graph. \begin{center} \begin{tabular}{r|ccccccccc} ... ... @@ -24060,8 +24060,7 @@ ans = 0.017398 \end{ans} \begin{ans}{2} The number of operations depends on exactly how the operations are carried out. The number of operations depends on exactly how we do the operations. \begin{exparts} \partsitem The determinant is $-11$. To row reduce takes a single row combination ... ... @@ -24086,20 +24085,6 @@ ans = 0.017398 \end{ans} \begin{ans}{4} This is a simple one. \begin{computercode} DO 5 ROW=1, N PIVINV=1.0/A(ROW,ROW) DO 10 I=ROW+1, N DO 20 J=I, N A(I,J)=A(I,J)-PIVINV*A(ROW,J) 20 CONTINUE 10 CONTINUE 5 CONTINUE \end{computercode} \end{ans} \begin{ans}{5} Yes, because the $J$ is in the innermost loop. \end{ans}
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 ... ... @@ -300,7 +300,8 @@ keywordstyle=\color{blue}\bfseries, showstringspaces=false, xleftmargin=.7em, } } \lstdefinestyle{inline}{basicstyle=\ttfamily\small} % In mechanics of matrix manipulation; ... ...
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