def grad$($beta$,$ b$,$ xTr$,$ yTr$,$ xTe, yTe, C$,$ kerneltype, kpar$=1)$:

$"""$

INPUT:

beta : n dimensional vector that stores the linear combination coefficient

xTr : nxd dimensional matrix $($training set, each row is an input vector$)$

yTr : n dimensional vector $($training label, each entry is a label$)$

b : scalar $($bias$)$

xTe : mxd dimensional matrix $($test set, each row is an input vector$)$

yTe : m dimensional vector $($test label, each entry is a label$)$

C : scalar $($constant that controls the tradeoff between l$2-$regularizer and hinge$-$loss$)$

kerneltype: either 'linear','polynomial',$\text{'}$rbf$\text{'}$

kpar : kernel parameter $($inverse kernel width gamma in case of RBF$,$ degree in case of polynomial$)$

OUTPUTS:

beta$\_$grad : n dimensional vector $($the gradient of the hinge loss with respect to the alphas$)$

bgrad : constant $($the gradient of he hinge loss with respect to the bias, b$)$

$"""$

n$,$ d $=$ xTr$.$shape

beta$\_$grad $=$ np$.$zeros$($n$)$

bgrad $=$ np$.$zeros$(1)$

# compute the kernel values between xTr and xTr

kernel$\_$train $=$ computeK$($kerneltype$,$ xTr$,$ xTr$,$ kpar$)$

# compute the kernel values between xTe and xTr

kernel$\_$test $=$ computeK$($kerneltype$,$ xTe, xTr$,$ kpar$)$

# # YOUR CODE HERE