PfHP Programming exercises

\( \newcommand{\R}{\mathbb R} \newcommand{\Rm}{\mathbb R^m} \newcommand{\Rn}{\mathbb R^n} \newcommand{\Rnxn}{\mathbb R^{n \times n}} \newcommand{\Rmxn}{\mathbb R^{m \times n}} \newcommand{\C}{\mathbb C} \newcommand{\Cm}{\mathbb C^m} \newcommand{\Cmxm}{\mathbb C^{m \times m}} \newcommand{\Cnxn}{\mathbb C^{n \times n}} \newcommand{\Cmxn}{\mathbb C^{m \times n}} \newcommand{\Cn}{\mathbb C^n} \newcommand{\Null}{{\cal N}} \newcommand{\Col}{{\cal C}} \newcommand{\Rowspace}{{\cal R}} \newcommand{\Span}{{\cal Span}} \newcommand{\rank}{{\rm rank}} \newcommand{\FlaTwoByTwo}[4]{ \left( \begin{array}{c | c} #1 \amp #2 \\ \hline #3 \amp #4 \end{array} \right) } \newcommand{\FlaTwoByTwoSingleLine}[4]{ \left( \begin{array}{c c} #1 \amp #2 \\ #3 \amp #4 \end{array} \right) } \newcommand{\FlaTwoByTwoSingleLineNoPar}[4]{ \begin{array}{c c} #1 \amp #2 \\ #3 \amp #4 \end{array} } \newcommand{\FlaOneByTwo}[2]{ \left( \begin{array}{c | c} #1 \amp #2 \end{array} \right) } \newcommand{\FlaOneByTwoSingleLine}[2]{ \left( \begin{array}{c c} #1 \amp #2 \end{array} \right) } \newcommand{\FlaTwoByOne}[2]{ \left( \begin{array}{c} #1 \\ \hline #2 \end{array} \right) } \newcommand{\FlaTwoByOneSingleLine}[2]{ \left( \begin{array}{c} #1 \\ #2 \end{array} \right) } \newcommand{\FlaThreeByOneB}[3]{ \left( \begin{array}{c} #1 \\ \hline #2 \\ #3 \end{array} \right) } \newcommand{\FlaThreeByOneT}[3]{ \left( \begin{array}{c} #1 \\ #2 \\ \hline #3 \end{array} \right) } \newcommand{\FlaOneByThreeR}[3]{ \left( \begin{array}{c | c c} #1 \amp #2 \amp #3 \end{array} \right) } \newcommand{\FlaOneByThreeL}[3]{ \left( \begin{array}{c c | c} #1 \amp #2 \amp #3 \end{array} \right) } \newcommand{\FlaThreeByThreeBR}[9]{ \left( \begin{array}{c | c c} #1 \amp #2 \amp #3 \\ \hline #4 \amp #5 \amp #6 \\ #7 \amp #8 \amp #9 \end{array} \right) } \newcommand{\FlaThreeByThreeTL}[9]{ \left( \begin{array}{c c | c} #1 \amp #2 \amp #3 \\ #4 \amp #5 \amp #6 \\ \hline #7 \amp #8 \amp #9 \end{array} \right) } \newcommand{\diag}[1]{{\rm diag}( #1 )} \newcommand{\URt}{{\sc HQR}} \newcommand{\FlaAlgorithm}{ \begin{array}{|l|} \hline \routinename \\ \hline \partitionings \\ ~~~ \begin{array}{l} \partitionsizes \end{array} \\ {\bf \color{blue} {while}~} \guard \\ ~~~ \begin{array}{l} \repartitionings \end{array} \\ ~~~ \color{red} { \begin{array}{l} \hline \color{black} {\update} \\ \hline \end{array}} \\ ~~~ \begin{array}{l} \moveboundaries \end{array} \\ {\bf \color{blue} {endwhile}} \\ \hline \end{array} } \newcommand{\FlaAlgorithmWithInit}{ \begin{array}{|l|} \hline \routinename \\ \hline \initialize \\ \partitionings \\ ~~~ \begin{array}{l} \partitionsizes \end{array} \\ {\bf \color{blue} {while}~} \guard \\ ~~~ \begin{array}{l} \repartitionings \end{array} \\ ~~~ \color{red} { \begin{array}{l} \hline \color{black} {\update} \\ \hline \end{array}} \\ ~~~ \begin{array}{l} \moveboundaries \end{array} \\ {\bf \color{blue} {endwhile}} \\ \hline \end{array} } \newcommand{\FlaBlkAlgorithm}{ \begin{array}{|l|} \hline \routinename \\ \hline \partitionings \\ ~~~ \begin{array}{l} \partitionsizes \end{array} \\ {\bf \color{blue} {while}~} \guard \\ ~~~ {\bf choose~block~size~} \blocksize \\ ~~~ \begin{array}{l} \repartitionings \end{array} \\ ~~~ ~~~ \repartitionsizes \\ ~~~ \color{red} { \begin{array}{l} \hline \color{black} {\update} \\ \hline \end{array}} \\ ~~~ \begin{array}{l} \moveboundaries \end{array} \\ {\bf \color{blue} {endwhile}} \\ \hline \end{array} } \newcommand{\complexone}{ \begin{array}{|c|}\hline \!\pm\! \\ \hline \end{array}~ } \newcommand{\HQR}{{\rm HQR}} \newcommand{\QR}{{\rm QR}} \newcommand{\st}{{\rm \ s.t. }} \newcommand{\QRQ}{{\rm {\normalsize \bf Q}{\rm \tiny R}}} \newcommand{\QRR}{{\rm {\rm \tiny Q}{\bf \normalsize R}}} \newcommand{\deltaalpha}{\delta\!\alpha} \newcommand{\deltax}{\delta\!x} \newcommand{\deltay}{\delta\!y} \newcommand{\deltaz}{\delta\!z} \newcommand{\deltaw}{\delta\!w} \newcommand{\DeltaA}{\delta\!\!A} \newcommand{\meps}{\epsilon_{\rm mach}} \newcommand{\fl}[1]{{\rm fl( #1 )}} \newcommand{\becomes}{:=} \newcommand{\defrowvector}[2]{ \left(#1_0, #1_1, \ldots, #1_{#2-1}\right) } \newcommand{\tr}[1]{{#1}^T} \newcommand{\LUpiv}[1]{{\rm LU}(#1)} \newcommand{\maxi}{{\rm maxi}} \newcommand{\Chol}[1]{{\rm Chol}( #1 )} \newcommand{\lt}{<} \newcommand{\gt}{>} \newcommand{\amp}{&} \)

Unit 0.4.1 Programming exercises

For each week, we will explore high-performance programming through a number of programming exercises. To keep the course accessible to a wide audience, we limit the actual amount of coding so as to allow us to focus on the key issues. Typically, we will only program a few lines of code. In the remainder of this section, we discuss the setup that supports this.

Most of the material in the section is here for reference. It may be best to quickly scan it and then revisit it after you have completed the first programming homework in Unit 1.1.1.