Modify these codes

def SGD$($self$,$ training$\_$data, $*,$ mini$\_$batch$\_$size, eta, lmbda$=0,$ test$\_$data$=[],$ max$\_$epochs$=100,$ patience$)$:

# Initialize variables for early stopping

best$\_$accuracy $=0$

epochs$\_$no$\_$improve $=0$

best$\_$epoch $=0$

should$\_$stop $=$ False

# Training loop

for epoch in range$($max$\_$epochs$)$:

np$.$random.shuffle$($training$\_$data$)$

for j in range$(0,$ len$($training$\_$data$),$ mini$\_$batch$\_$size$)$:

mini$\_$batch $=$ training$\_$data$[$j:j$+$mini$\_$batch$\_$size$]$

self.update$\_$mini$\_$batch$($mini$\_$batch, eta, lmbda$)$

# Calculate accuracy on training and test data

train$\_$accuracy $=$ self.evaluate$($training$\_$data$)[1]$

test$\_$accuracy $=$ self.evaluate$($test$\_$data$)[1]$

print$($f$"$Epoch $\{$epoch$\}$: Training Accuracy $\{$train$\_$accuracy$\},$ Test Accuracy $\{$test$\_$accuracy$\}")$

# Check for improvement in test accuracy

if test$\_$accuracy $>$ best$\_$accuracy:

best$\_$accuracy $=$ test$\_$accuracy

best$\_$epoch $=$ epoch

epochs$\_$no$\_$improve $=0$

else:

epochs$\_$no$\_$improve $+=1$

# If there is no improvement for 'patience' epochs, stop training

if epochs$\_$no$\_$improve $>=$ patience:

should$\_$stop $=$ True

break

print$($f$"$Early stopping at epoch $\{$best$\_$epoch$\}.$ Best Test Accuracy: $\{$best$\_$accuracy$\}")$

return best$\_$accuracy