Problem $5.$ Write a function that accepts the name of an image file and an integer $s.$ Use

your function from Problem $3,$ to compute the best rank$-$s approximation of the image. Plot

the original image and the approximation in separate subplots. In the figure title, report the

difference in number of entries required to store the original image and the approximation $($use

plt$.$suptitle$()).$

Your function should be able to handle both grayscale and color images. Read the image

in and check its dimensions to see if it is color or not. Grayscale images can be approximated

directly since they are represented by $2-$dimensional arrays. For color images, let $R,G,$ and $B$

be the matrices for the red, green, and blue layers of the image, respectively. Calculate the low$-$

rank approximations $R_s,G_s,$ and $B_s$ separately, then put them together in a new $3-$dimensional

array of the same shape as the original image.

$($Hint: np$.$dstack$()$ may be useful for putting the color layers back together.$)$

Finally, it is possible for the low$-$rank approximations to have values slightly outside the

valid range of RGB values. Set any values outside of the interval $0,1$ to the closer of the two

boundary values.

$($Hint: fancy indexing or np$.$clip$()$ may be useful here.$)$

To check, compressing hubble$\_$gray.jpg with a rank $20$ approximation should appear

similar to Figure $6\mathrm{.}3b$ and save $1,161,478$ matrix entries.