PLEASE WRITE THE GRADIENT FUNCTION AND THE GRADIENT DESCENT FUNCTION. Do not use loops for the gradient function; use vectorized gradient descent. I have included the date $($tiny$\_$training.csv$),$ the other functions, the pytest, and the equations from the notes! Everything you need is here. # you can use a for loop to iterate through gradient descent def gradient$\_$descent$($df$,$ emb$\_$user, emb$\_$movie, iterations$=100,$ learning$\_$rate$=0\mathrm{.}01,$ df$\_$val$=$None$)$: $"$II$"$ Computes gradient descent with momentum $(0\mathrm{.}9)$ for a number of iterations. Prints training cost and validation cost $($if df$\_$val is not None$)$ every $50$ iterations. Returns: emb$\_$user: the trained user embedding emb$\_$movie: the trained movie embedding IIII Y$=$d f $2$ m a t r i x$($d f$,$ emb$\_$user.shape$[0],$ emb$\_$movie.shape $[0])$ ### BEGIN SOLUTION ### END SOLUTION return emb$\_$user, emb$\_$movie$[7]$: emb$\_$movie $[7]$: array$([[0\mathrm{.}66095748,0\mathrm{.}84977739,0\mathrm{.}34908569,0\mathrm{.}61299313,1\mathrm{.}07153635],[1\mathrm{.}07555171,0\mathrm{.}15070237,0\mathrm{.}24869145,0\mathrm{.}06176064,0\mathrm{.}52897181],[0\mathrm{.}03585145,0\mathrm{.}54819987,0\mathrm{.}77897286,0\mathrm{.}33418474,0\mathrm{.}81150588],[0\mathrm{.}70903538,0\mathrm{.}02877826,0\mathrm{.}67062491,0\mathrm{.}31110294,0\mathrm{.}49812144]])[8]$: emb$\_$user $[8]$ : array$([[0\mathrm{.}66095748,0\mathrm{.}84977739,0\mathrm{.}34908569,0\mathrm{.}61299313,1\mathrm{.}07153635],[1\mathrm{.}07555171,0\mathrm{.}15070237,0\mathrm{.}24869145,0\mathrm{.}06176064,0\mathrm{.}52897181],[0\mathrm{.}03585145,0\mathrm{.}54819987,0\mathrm{.}77897286,0\mathrm{.}33418474,0\mathrm{.}81150588],[0\mathrm{.}70903538,0\mathrm{.}02877826,0\mathrm{.}67062491,0\mathrm{.}31110294,0\mathrm{.}49812144],[0\mathrm{.}3402301,0\mathrm{.}8317655,0\mathrm{.}52854446,0\mathrm{.}18824129,0\mathrm{.}65357882],[0\mathrm{.}93637772,0\mathrm{.}36763624,0\mathrm{.}26634946,0\mathrm{.}46556551,1\mathrm{.}12366038],[1\mathrm{.}17119451,0\mathrm{.}80686041,1\mathrm{.}08340093,1\mathrm{.}01490105,0\mathrm{.}45359285]])[]$ :$[1$ userId, movieId, rating; $211,1,4$; $311,23,5$; $42,23,5$; $52,4,3$; $631,1,4$; $731,23,4$; $84,1,5$; $94,3,2$; $1052,1,1$; $1152,3,4$; $1261,3,5$; $137,23,1$; $147,3,3$; $15][$ E$/$ u$=-2/$N$\backslash$Delta v; $$ E$/$ v$=-2/$N$\backslash$Delta $^$ u $]$