Problem $1(20$ marks$)$: Reading, plotting, and analysing data from a file.

Read in the contents of the file 'rev$26\_27.$dat' into a RecArray. This is a data file containing results from a spacecraft called Cassini: the magnetometer measurements from two orbits around Saturn in $2007.$ The columns are day$-$of$-$year since $2004,$ and three field components in spherical polar coordinates $\backslash (\backslash$left$($B$\_\{$r$\},$ B$\_\{\backslash$theta$\},$ B$\_\{\backslash$varphi$\}\backslash$right$)\backslash ).$ Make the following plot:

$-$ Plot $\backslash ($ B$\_\{$r$\}\backslash )$ versus day of year since $2004$ with cyan dots.

$-$ Limit the time $($date$)$ axis to between $935$ to $955$ days, and the $\backslash ($ y $\backslash )$ axis to between $-3\mathrm{.}5$ to $6\mathrm{.}5$

$-$ Label the axes appropriately and add a title and a legend.

$-$ Add a dotted green horizontal line at $\backslash ($ B$\_\{$r$\}=0\backslash ).$

$-$ Plot a quadratic regression $($line of best fit with a polynomial of second order$)$ in blue, and print the coefficients of the fit.

$-$ Introduce an array of days from $935$ to $955($e$.$g$.,\backslash (935,936,\backslash$ldots $954\backslash )).$ For each of the days, calculate the daily mean of $\backslash ($ B$\_\{$r$\}\backslash )$ and also its daily maximum. Call these arrays Brmean and Brmax, respectively. Use array slicing and Boolean True$/$False to select the data for this.

$-$ Plot Brmean and Brmax versus day of the year on the same panel as the data above with red crosses and a blue dosh$-$dat line, respectively, labelling the data appropriately.

$-$ Calculate the mean of Brmax and print it to the third significant digit using the format method.