In this problem, we would like to use the gradient descent to calculate the parameters $W$ for the parabola.

The loss function $$\backslash$mathcal$\{$L$\}($W$)$$ now contains two parts: A squared $L$\_2$$ norm and a $L$\_1$$ norm.

A coefficient $$\backslash$alpha$ is used to control the ratio of these two norms:

$$

$\backslash$begin$\{$aligned$\}$

$\backslash$mathcal$\{$L$\}($W$)$

& $=\backslash$sum$\_\{$i$=1\}^\{$n$\}$

$\backslash$Big$(\backslash$alpha$\backslash$big$(\backslash$mathbf$\{$x$\}\_$i$^$T W $-$ y$\_$i$\backslash$big$)^2+(1-\backslash$alpha$)|\backslash$mathbf$\{$x$\}\_$i$^$T W $-$ y$\_$i$|\backslash$Big$)\backslash \backslash$

& $=\backslash$alpha$\backslash$left$\backslash$lVert X W $-$ Y $\backslash$right$\backslash$rVert$\_2^2+(1-\backslash$alpha$)\backslash$left$\backslash$lVert X W $-$ Y $\backslash$right$\backslash$rVert$\_1\backslash \backslash$

onumber

$\backslash$end$\{$aligned$\}$

$$

Complete the following code to use the $**$gradient descent$**$ to find $W$^*$$ when $$\backslash$alpha$=0,\backslash$alpha$=0\mathrm{.}03,\backslash$alpha$=0\mathrm{.}05,\backslash$alpha$=0\mathrm{.}1$$$,$ and $$\backslash$alpha$=1$$$,$ espectively.

Write your code in the $`...`$ part.

$**$Hint$**$: You may refer to Q$3\mathrm{.}1$ for the gradient of $L$\_2$$ norm.

$**$Note:$**$ It may take $2$~$3$ mins to run the algorithm.