From a1f55bc9f717ad66bd8f75c9439052c73ea431d2 Mon Sep 17 00:00:00 2001 From: "Ryan C. Cooper" Date: Mon, 27 Feb 2017 11:55:30 -0500 Subject: [PATCH] updated lecture 11 notes --- lecture_09/mass_springs.png | Bin 0 -> 5031 bytes lecture_11/lecture_11.aux | 28 ++-- lecture_11/lecture_11.log | 117 ++++++++------- lecture_11/lecture_11.out | 12 +- lecture_11/lecture_11.pdf | Bin 154124 -> 191934 bytes lecture_11/lecture_11.tex | 136 +++++++++++++---- .../lecture_11_files/lecture_11_8_0.pdf | Bin 0 -> 8728 bytes .../lecture_11_files/lecture_11_8_0.svg | 139 ++++++++++++++++++ lecture_11/octave-workspace | Bin 0 -> 153 bytes 9 files changed, 338 insertions(+), 94 deletions(-) create mode 100644 lecture_09/mass_springs.png create mode 100644 lecture_11/lecture_11_files/lecture_11_8_0.pdf create mode 100644 lecture_11/lecture_11_files/lecture_11_8_0.svg diff --git a/lecture_09/mass_springs.png b/lecture_09/mass_springs.png new file mode 100644 index 0000000000000000000000000000000000000000..d0dc65cb340f830eb2b8dd7145ef38908fb8419a GIT binary patch literal 5031 zcmZ{GWmwc-(Do0P5D}Gb=?+1?KSHiutRuJrmB^U0)}>9q8AU2Y{zlL4l9ir8trafMFnETyu*ENH7B?hDgwN zMiI~zqoF|sFm2(W1|Jg=gXCRs0O9>-j0Aw~q$T(#bGDcn>96ovxk zr{2a_d!5he?{2}x^gt^CM_C7te*y#-B;c(Bak>$>-bd-o05TEb0$vg>ZX=j{lIPJ;7yWL4>>?VA6II81@egPZ;BC-)(9x*mGLa4N9dRDv_36+KK`3;H zCxOj;vq=!K{B)7KJ$`05Wuf0Uo{uE5pf(%sZsjkxRX5g(xFP6-O?M1#{e!(uh1YSQ6=A#)j4d*5afG zYN=?0?>67>J7j)@P_kAg^A9d<*dK9t&|o4LG&@vtS)S?ka%Yk|X#nhr4Z(WK4y6nE zG5SmT{O#zD&807V<1HLW2V)m+9f^Az6C3L@Gc_5NmW%YKs-YRCx7 z2sT2`7}T586TODNCR%&w&g$-ZNPehyXmB{cCQJ$;BqrpHw2xGbgp*FQbI?#LrLK0Z z2zfovq!y>v*Se>l{QIkxb()~IaCpXX5@`}gl0p(DsVOO)EtD^&_=^Xey>ZCM&N$x4 z5>1Y7(G$}1L(dhfpec(t(O5Jb9bGJqRxR!vsI$qoPO?53MhwfO_YLk0Tnzmhc$(PG zEX~=U(wMY9NHLs~>cd8RlW!A$lX;V!0-7qHdN1`+>Q)8$%Q(j> z$56+-owm%R%yg3uldL)Yw+&LNvKH3~7pRNEuo9KJuP(7Ju{2NzsQ9SNsMx4G|L3%7 zgD``lDJAD1F;!{x%es>Q23S9g)1uU1D_5YxsU$1k&*+^u1v0g-V)A8d<=4OVzGm%j z+Qr%l1JXK5k?)b8ZcIUTeBKNR{(HXYJZE?Db7UdLb;?D|smAu{D+@dD*H<3?62;l3 zl-@*s(aw}q{9w~e;|F}>CO5B&?NY6OI*K-`ctS@qOGJ~Wc%~Akh^G|knxP@1x^xBA z4bEuiBCMwL%U1hV+g67fG4VvdsLQFPiCouZht6%Q-*tVf6|BFu*NpZgHrQ6lw_)pl zyN&xK$1tNlOMR0zjl(Yu+bY9%k<&urc;dOH(erJsm`lo2GA44!c^a zoz4BXT~7Yh7ju(Mi%TomUjbd0nD`Ryu<`K@Tua7flVwAs3i2EYx_NjTdsBVG2-*V; z-OI&u#Iwaa!HdKXC1}Fs$Ct)WCm>RKsMs8`K%7bpy^kei4Z{l+4d<`&GiJ2*Lc_kTXSz_5WSr#b*BXuJZ8A9WyE8=!6A9jWPaJ3XZTM26NIvGwunxS6K zC#Bi>*`Am+OgSbv3n7M`70KDke&;XjBJApE+2L^$cNNLMz)x(NSgmV%*<9|zyCBxI zXmdHpkiwuYjpP>O<9c>hC+uzKTA;Xk(miM{&^i|di8@n;w^n;i-=Z#=SHlZrD^Fnu z=LYoV{-wQj=mu*{ilOh8Y7t{4(rlKl^o*ltE{^6|wWMW0ouha_7dO|A#Er7fZ}g6_+IJ#<4rHo5zCmMNF-~S-$&ZC&xQmyHYec zedcP@B{k>!XD+X_?Z^M%oe~AK8?@)h?cVyY6(04?X(pu)3Fr$@Sy*6_-r1}=Ui`#3 zxleOkik--|KJ~bM)#-XWK^#x_$wg|p4cx`h;xT+N)iDj{S!tV|zuTM@Bh`M8{ zAC^+#BVnKSKP>NJT-`h0d5`|tB$-cidQ8u_;JFA-G+Y+ zQ-5gu;1~WXOl6m2chG5Z>bnEI$STGZF82l2`c?irxnlGRd^i?9qTRmUX?ouHw|(T2 zj8O~xm;a2f?JVQS-J$+0d89NsPco0712^!4#gH+FfMLMTo4L!;_4zZ6p`oEbK%g+8 zO{a9f{%&_-f~)C40l=3708k+SaB+8p+6I8Pf&j2%1prbR06^uI{aIJ$E^zO)rYZ!u z4UZq`yz>a%)QmmvQ0@PT%AgbY&LBXjLzM|u@6kOG2dqTbWbe{g)FBEm?>TIaTxMpDgW2`4|R+$jz(ws>rM3I4qMpwii6LuVdSh z#{6B7vHJ}RRKddJ3cSi0Z5bZ7We#|#%z970Gc7$aDm}8-388e0f2%n3>!EiM3|xxe zx)bO-Yt0JlIIaxb`(`yQk)taHs@BgnKG)O6=?};ASDF3WCH)D@fI*FO(G?7BRo=`x z;K|r-W_4g?^|~%URGt+JuMqRBOf=ApK9gL@F~5$#sl}%IPFiXVEw|H`kBL0)n76sl2F@!^ue8skEstu&{xz~1-o)09eP5ZrS}nupoky)Q`p0S_ zM*`2s+;8-e1L9-!;Ca7p*Yncjs|;G1Ib!PQl8m9Ha&W@IZ}1CC7oeX!*-TVES?>@X zH^IZOvELChc^DamWqCjfo{9Z@EmBbyS&nMuUisY?Oe6FJildE}e?1^gn`R4E=B=0> zfQ%UFW9)|Uax1S|?(II6=yX7BOn&~8vVe<<{6OYzXZX1`Ur+n%2CQn2z}eg0Xrgxn z<0v=tr2YebZXDyA7Eq%|a*J>3y9u$A_jo^FO8ed}Y}36XvtlH+HY?4t-;@g1{1KH_ z6tDHrKTlhB+J?ikm>|OYN0M&C(j^=^Yrfv|nm?sg?)mWU-#R74+B9Tj5Eb@vzJ-kq z(na>TdDh(SJ!gZL1`lX|@X-&iZA5B5mc@~8xW&-R#Yt-ew{~(uha_#op|? 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--- a/lecture_11/lecture_11.tex +++ b/lecture_11/lecture_11.tex @@ -277,13 +277,68 @@ \begin{Verbatim}[commandchars=\\\{\}] -{\color{incolor}In [{\color{incolor}18}]:} \PY{c}{\PYZpc{}plot \PYZhy{}\PYZhy{}format svg} +{\color{incolor}In [{\color{incolor}1}]:} \PY{c}{\PYZpc{}plot \PYZhy{}\PYZhy{}format svg} \end{Verbatim} \begin{Verbatim}[commandchars=\\\{\}] -{\color{incolor}In [{\color{incolor}19}]:} \PY{n}{setdefaults} +{\color{incolor}In [{\color{incolor}2}]:} \PY{n}{setdefaults} \end{Verbatim} + \subsection{My question from last +class}\label{my-question-from-last-class} + +\(A=\left[ \begin{array}{ccc} 10 & 2 & 1 \\ 0 & 1 & 1 \\ 0 & 0 & 10\end{array} \right]\) + +\begin{figure}[htbp] +\centering +\includegraphics{det_A.png} +\caption{responses to determinant of A} +\end{figure} + +\subsection{Your questions from last +class}\label{your-questions-from-last-class} + +\begin{enumerate} +\def\labelenumi{\arabic{enumi}.} +\item + Need more linear algebra review + + -We will keep doing Linear Algebra, try the practice problems in + 'linear\_algebra' +\item + How do I do HW3? + + -demo today +\item + For hw4 is the spring constant (K) suppose to be given? + + -yes, its 30 N/m +\item + Deapool or Joker? +\end{enumerate} + +\subsection{Midterm preference}\label{midterm-preference} + +\begin{figure}[htbp] +\centering +\includegraphics{midterm_date.png} +\caption{responses to midterm date} +\end{figure} + +\subsubsection{Midterm Questions}\label{midterm-questions} + +\begin{enumerate} +\def\labelenumi{\arabic{enumi}.} +\item + Notes allowed + + -no +\item + Will there be a review/study sheet + + -yes +\end{enumerate} + \section{LU Decomposition}\label{lu-decomposition} \subsubsection{efficient storage of matrices for @@ -366,6 +421,25 @@ y = 1 + \end{Verbatim} + + \begin{Verbatim}[commandchars=\\\{\}] +{\color{incolor}In [{\color{incolor}5}]:} \PY{c}{\PYZpc{} what is the determinant of L, U and A?} + + \PY{n+nb}{det}\PY{p}{(}\PY{n}{A}\PY{p}{)} + \PY{n+nb}{det}\PY{p}{(}\PY{n}{L}\PY{p}{)} + \PY{n+nb}{det}\PY{p}{(}\PY{n}{U}\PY{p}{)} + \PY{n+nb}{det}\PY{p}{(}\PY{n}{L}\PY{p}{)}\PY{o}{*}\PY{n+nb}{det}\PY{p}{(}\PY{n}{U}\PY{p}{)} + \PY{n+nb}{det}\PY{p}{(}\PY{n}{L}\PY{o}{*}\PY{n}{U}\PY{p}{)} +\end{Verbatim} + + \begin{Verbatim}[commandchars=\\\{\}] +ans = 5.0000 +ans = 1 +ans = 5 +ans = 5 +ans = 5.0000 + \end{Verbatim} \subsection{Pivoting for LU @@ -467,24 +541,24 @@ mailing list. \end{Verbatim} \begin{Verbatim}[commandchars=\\\{\}] -{\color{incolor}In [{\color{incolor}22}]:} \PY{c}{\PYZpc{} time LU solution vs backslash} - \PY{n}{t\PYZus{}lu}\PY{p}{=}\PY{n+nb}{zeros}\PY{p}{(}\PY{l+m+mi}{100}\PY{p}{,}\PY{l+m+mi}{1}\PY{p}{)}\PY{p}{;} - \PY{n}{t\PYZus{}bs}\PY{p}{=}\PY{n+nb}{zeros}\PY{p}{(}\PY{l+m+mi}{100}\PY{p}{,}\PY{l+m+mi}{1}\PY{p}{)}\PY{p}{;} - \PY{k}{for} \PY{n}{N}\PY{p}{=}\PY{l+m+mi}{1}\PY{p}{:}\PY{l+m+mi}{100} - \PY{n}{A}\PY{p}{=}\PY{n+nb}{rand}\PY{p}{(}\PY{n}{N}\PY{p}{,}\PY{n}{N}\PY{p}{)}\PY{p}{;} - \PY{n}{y}\PY{p}{=}\PY{n+nb}{rand}\PY{p}{(}\PY{n}{N}\PY{p}{,}\PY{l+m+mi}{1}\PY{p}{)}\PY{p}{;} - \PY{p}{[}\PY{n}{L}\PY{p}{,}\PY{n}{U}\PY{p}{,}\PY{n}{P}\PY{p}{]}\PY{p}{=}\PY{n+nb}{lu}\PY{p}{(}\PY{n}{A}\PY{p}{)}\PY{p}{;} - - \PY{n+nb}{tic}\PY{p}{;} \PY{n}{d}\PY{p}{=}\PY{n}{L}\PY{o}{\PYZbs{}}\PY{n}{y}\PY{p}{;} \PY{n}{x}\PY{p}{=}\PY{n}{U}\PY{o}{\PYZbs{}}\PY{n}{d}\PY{p}{;} \PY{n}{t\PYZus{}lu}\PY{p}{(}\PY{n}{N}\PY{p}{)}\PY{p}{=}\PY{n+nb}{toc}\PY{p}{;} - - \PY{n+nb}{tic}\PY{p}{;} \PY{n}{x}\PY{p}{=}\PY{n}{A}\PY{o}{\PYZbs{}}\PY{n}{y}\PY{p}{;} \PY{n}{t\PYZus{}bs}\PY{p}{(}\PY{n}{N}\PY{p}{)}\PY{p}{=}\PY{n+nb}{toc}\PY{p}{;} - \PY{k}{end} - \PY{n+nb}{plot}\PY{p}{(}\PY{p}{[}\PY{l+m+mi}{1}\PY{p}{:}\PY{l+m+mi}{100}\PY{p}{]}\PY{p}{,}\PY{n}{t\PYZus{}lu}\PY{p}{,}\PY{p}{[}\PY{l+m+mi}{1}\PY{p}{:}\PY{l+m+mi}{100}\PY{p}{]}\PY{p}{,}\PY{n}{t\PYZus{}bs}\PY{p}{)} - \PY{n+nb}{legend}\PY{p}{(}\PY{l+s}{\PYZsq{}}\PY{l+s}{LU decomp\PYZsq{}}\PY{p}{,}\PY{l+s}{\PYZsq{}}\PY{l+s}{Octave \PYZbs{}\PYZbs{}\PYZsq{}}\PY{p}{)} +{\color{incolor}In [{\color{incolor}9}]:} \PY{c}{\PYZpc{} time LU solution vs backslash} + \PY{n}{t\PYZus{}lu}\PY{p}{=}\PY{n+nb}{zeros}\PY{p}{(}\PY{l+m+mi}{100}\PY{p}{,}\PY{l+m+mi}{1}\PY{p}{)}\PY{p}{;} + \PY{n}{t\PYZus{}bs}\PY{p}{=}\PY{n+nb}{zeros}\PY{p}{(}\PY{l+m+mi}{100}\PY{p}{,}\PY{l+m+mi}{1}\PY{p}{)}\PY{p}{;} + \PY{k}{for} \PY{n}{N}\PY{p}{=}\PY{l+m+mi}{1}\PY{p}{:}\PY{l+m+mi}{100} + \PY{n}{A}\PY{p}{=}\PY{n+nb}{rand}\PY{p}{(}\PY{n}{N}\PY{p}{,}\PY{n}{N}\PY{p}{)}\PY{p}{;} + \PY{n}{y}\PY{p}{=}\PY{n+nb}{rand}\PY{p}{(}\PY{n}{N}\PY{p}{,}\PY{l+m+mi}{1}\PY{p}{)}\PY{p}{;} + \PY{p}{[}\PY{n}{L}\PY{p}{,}\PY{n}{U}\PY{p}{,}\PY{n}{P}\PY{p}{]}\PY{p}{=}\PY{n+nb}{lu}\PY{p}{(}\PY{n}{A}\PY{p}{)}\PY{p}{;} + + \PY{n+nb}{tic}\PY{p}{;} \PY{n}{d}\PY{p}{=}\PY{n+nb}{inv}\PY{p}{(}\PY{n}{L}\PY{p}{)}\PY{o}{*}\PY{n}{y}\PY{p}{;} \PY{n}{x}\PY{p}{=}\PY{n+nb}{inv}\PY{p}{(}\PY{n}{U}\PY{p}{)}\PY{o}{*}\PY{n}{d}\PY{p}{;} \PY{n}{t\PYZus{}lu}\PY{p}{(}\PY{n}{N}\PY{p}{)}\PY{p}{=}\PY{n+nb}{toc}\PY{p}{;} + + \PY{n+nb}{tic}\PY{p}{;} \PY{n}{x}\PY{p}{=}\PY{n+nb}{inv}\PY{p}{(}\PY{n}{A}\PY{p}{)}\PY{o}{*}\PY{n}{y}\PY{p}{;} \PY{n}{t\PYZus{}bs}\PY{p}{(}\PY{n}{N}\PY{p}{)}\PY{p}{=}\PY{n+nb}{toc}\PY{p}{;} + \PY{k}{end} + \PY{n+nb}{plot}\PY{p}{(}\PY{p}{[}\PY{l+m+mi}{1}\PY{p}{:}\PY{l+m+mi}{100}\PY{p}{]}\PY{p}{,}\PY{n}{t\PYZus{}lu}\PY{p}{,}\PY{p}{[}\PY{l+m+mi}{1}\PY{p}{:}\PY{l+m+mi}{100}\PY{p}{]}\PY{p}{,}\PY{n}{t\PYZus{}bs}\PY{p}{)} + \PY{n+nb}{legend}\PY{p}{(}\PY{l+s}{\PYZsq{}}\PY{l+s}{LU decomp\PYZsq{}}\PY{p}{,}\PY{l+s}{\PYZsq{}}\PY{l+s}{Octave \PYZbs{}\PYZbs{}\PYZsq{}}\PY{p}{)} \end{Verbatim} \begin{center} - \adjustimage{max size={0.9\linewidth}{0.9\paperheight}}{lecture_11_files/lecture_11_6_0.pdf} + \adjustimage{max size={0.9\linewidth}{0.9\paperheight}}{lecture_11_files/lecture_11_8_0.pdf} \end{center} { \hspace*{\fill} \\} @@ -494,7 +568,7 @@ positions of the masses? \begin{figure}[htbp] \centering -\includegraphics{mass_springs.png} +\includegraphics{../lecture_09/mass_springs.png} \caption{Springs-masses} \end{figure} @@ -514,7 +588,7 @@ in matrix form: \(\left[ \begin{array}{cccc} 2k & -k & 0 & 0 \\ -k & 2k & -k & 0 \\ 0 & -k & 2k & -k \\ 0 & 0 & -k & k \end{array} \right] \left[ \begin{array}{c} x_{1} \\ x_{2} \\ x_{3} \\ x_{4} \end{array} \right]= \left[ \begin{array}{c} m_{1}g \\ m_{2}g \\ m_{3}g \\ m_{4}g \end{array} \right]\) \begin{Verbatim}[commandchars=\\\{\}] -{\color{incolor}In [{\color{incolor}24}]:} \PY{n}{k}\PY{p}{=}\PY{l+m+mi}{10}\PY{p}{;} \PY{c}{\PYZpc{} N/m} +{\color{incolor}In [{\color{incolor}10}]:} \PY{n}{k}\PY{p}{=}\PY{l+m+mi}{10}\PY{p}{;} \PY{c}{\PYZpc{} N/m} \PY{n}{m1}\PY{p}{=}\PY{l+m+mi}{1}\PY{p}{;} \PY{c}{\PYZpc{} kg} \PY{n}{m2}\PY{p}{=}\PY{l+m+mi}{2}\PY{p}{;} \PY{n}{m3}\PY{p}{=}\PY{l+m+mi}{3}\PY{p}{;} @@ -565,7 +639,7 @@ equations: so for K \begin{Verbatim}[commandchars=\\\{\}] -{\color{incolor}In [{\color{incolor}25}]:} \PY{n}{K} +{\color{incolor}In [{\color{incolor}11}]:} \PY{n}{K} \end{Verbatim} \begin{Verbatim}[commandchars=\\\{\}] @@ -580,7 +654,7 @@ K = \end{Verbatim} \begin{Verbatim}[commandchars=\\\{\}] -{\color{incolor}In [{\color{incolor}26}]:} \PY{n}{u11}\PY{p}{=}\PY{n+nb}{sqrt}\PY{p}{(}\PY{n}{K}\PY{p}{(}\PY{l+m+mi}{1}\PY{p}{,}\PY{l+m+mi}{1}\PY{p}{)}\PY{p}{)} +{\color{incolor}In [{\color{incolor}12}]:} \PY{n}{u11}\PY{p}{=}\PY{n+nb}{sqrt}\PY{p}{(}\PY{n}{K}\PY{p}{(}\PY{l+m+mi}{1}\PY{p}{,}\PY{l+m+mi}{1}\PY{p}{)}\PY{p}{)} \PY{n}{u12}\PY{p}{=}\PY{p}{(}\PY{n}{K}\PY{p}{(}\PY{l+m+mi}{1}\PY{p}{,}\PY{l+m+mi}{2}\PY{p}{)}\PY{p}{)}\PY{o}{/}\PY{n}{u11} \PY{n}{u13}\PY{p}{=}\PY{p}{(}\PY{n}{K}\PY{p}{(}\PY{l+m+mi}{1}\PY{p}{,}\PY{l+m+mi}{3}\PY{p}{)}\PY{p}{)}\PY{o}{/}\PY{n}{u11} \PY{n}{u14}\PY{p}{=}\PY{p}{(}\PY{n}{K}\PY{p}{(}\PY{l+m+mi}{1}\PY{p}{,}\PY{l+m+mi}{4}\PY{p}{)}\PY{p}{)}\PY{o}{/}\PY{n}{u11} @@ -615,22 +689,22 @@ U = \end{Verbatim} \begin{Verbatim}[commandchars=\\\{\}] -{\color{incolor}In [{\color{incolor}27}]:} \PY{n}{U}\PY{o}{\PYZsq{}}\PY{o}{*}\PY{n}{U} +{\color{incolor}In [{\color{incolor}17}]:} \PY{p}{(}\PY{n}{U}\PY{o}{\PYZsq{}}\PY{o}{*}\PY{n}{U}\PY{p}{)}\PY{o}{\PYZsq{}}\PY{o}{==}\PY{n}{U}\PY{o}{\PYZsq{}}\PY{o}{*}\PY{n}{U} \end{Verbatim} \begin{Verbatim}[commandchars=\\\{\}] ans = - 20.00000 -10.00000 0.00000 0.00000 - -10.00000 20.00000 -10.00000 0.00000 - 0.00000 -10.00000 20.00000 -10.00000 - 0.00000 0.00000 -10.00000 10.00000 + 1 1 1 1 + 1 1 1 1 + 1 1 1 1 + 1 1 1 1 \end{Verbatim} \begin{Verbatim}[commandchars=\\\{\}] -{\color{incolor}In [{\color{incolor}37}]:} \PY{c}{\PYZpc{} time solution for Cholesky vs backslash} +{\color{incolor}In [{\color{incolor}18}]:} \PY{c}{\PYZpc{} time solution for Cholesky vs backslash} \PY{n}{t\PYZus{}chol}\PY{p}{=}\PY{n+nb}{zeros}\PY{p}{(}\PY{l+m+mi}{1000}\PY{p}{,}\PY{l+m+mi}{1}\PY{p}{)}\PY{p}{;} \PY{n}{t\PYZus{}bs}\PY{p}{=}\PY{n+nb}{zeros}\PY{p}{(}\PY{l+m+mi}{1000}\PY{p}{,}\PY{l+m+mi}{1}\PY{p}{)}\PY{p}{;} \PY{k}{for} \PY{n}{i}\PY{p}{=}\PY{l+m+mi}{1}\PY{p}{:}\PY{l+m+mi}{1000} @@ -643,11 +717,15 @@ ans = \end{Verbatim} \begin{Verbatim}[commandchars=\\\{\}] -average time spent for Cholesky factored solution = 1.623154e-05+/-1.166726e-05 -average time spent for backslash solution = 1.675844e-05+/-1.187234e-05 +average time spent for Cholesky factored solution = 1.465964e-05+/-9.806001e-06 +average time spent for backslash solution = 1.555967e-05+/-1.048561e-05 \end{Verbatim} + \begin{Verbatim}[commandchars=\\\{\}] +{\color{incolor}In [{\color{incolor} }]:} +\end{Verbatim} + % Add a bibliography block to the postdoc diff --git a/lecture_11/lecture_11_files/lecture_11_8_0.pdf b/lecture_11/lecture_11_files/lecture_11_8_0.pdf new file mode 100644 index 0000000000000000000000000000000000000000..7f562c690445bbd18c791024c270af8abf6cd77a GIT binary patch literal 8728 zcma)i1z1#D_r4N>AR$QCpwcx1%+N@ebeHtdFvK7w!XP0rAdR$0cS{JOq$nklA}K8? z!qER2y!zey-T(JIzjLPcyVpKzueJ7>wV!t#7EL(?9uTh}0ZaX6#R-7`00@9tITDDA z1Nc;-u6A&HfFK&uCIA2cdIYX! zMbgm2vs{@aQWkI+Ltjs3Y?-EpIHy=)%vRX5T6xtRHu9d7GcRzag 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