Using your favorite programming language $($Matlab$,$ Python with numpy, etc$)$ you should

Implement a routine to produce a kxm sketching matrix F$,$ with Fm$\backslash$times nA$=$U$*\backslash$Sigma $*$V$^($T$)$m$>=$nUm$\backslash$times nn$\backslash$times ntr$^($j$)$j$=0,1,$dots$\{$:$($n$)/($t$))-1$t$=10$r$=(1$e$-10)^((1)/(($n$)/(10)-1))1$e$-10$n$\backslash$times n$=[50,500]$m$=[2,10]^(**)$nm$\backslash$times nAt$=10$r$=(1$e$-10)^((1)/(($n$)/(10)-1))1$e$-10$k$=[\mathrm{.}1,\mathrm{.}5]^(**)$nF$^(**)$An$,$mm$,$nk