# GRADED FUNCTION: TripletLossFn

def TripletLossFn$($v$1,$ v$2,$ margin$=0\mathrm{.}25)$:

$"""$Custom Loss function.

Args:

v$1($numpy$.$ndarray or Tensor$)$: Array with dimension $($batch$\_$size, model$\_$dimension$)$ associated to Q$1.$

v$2($numpy$.$ndarray or Tensor$)$: Array with dimension $($batch$\_$size, model$\_$dimension$)$ associated to Q$2.$

margin $($float$,$ optional$)$: Desired margin. Defaults to $0\mathrm{.}25.$

Returns:

triplet$\_$loss $($numpy$.$ndarray or Tensor$)$

$"""$

### START CODE HERE ###

# use $`$tf$.$linalg.matmul$`$ to take the dot product of the two batches.

# Don't forget to transpose the second argument using $`$transpose$\_$b$=$True$`$

scores $=$ None

# calculate new batch size and cast it as the same datatype as scores.

batch$\_$size $=$ tf$.$cast$($tf$.$shape$($v$1)[0],$ scores.dtype$)$

# use $`$tf$.$linalg.diag$\_$part$`$ to grab the cosine similarity of all positive examples

positive $=$ None

# subtract the diagonal from scores. You can do this by creating a diagonal matrix with the values

# of all positive examples using $`$tf$.$linalg.diag$`$

negative$\_$zero$\_$on$\_$duplicate $=$ None

# use $`$tf$.$math.reduce$\_$sum$`$ on $`$negative$\_$zero$\_$on$\_$duplicate$`$ for $`$axis$=1`$ and divide it by $`($batch$\_$size $-1)`$

mean$\_$negative $=$ None

# create a composition of two masks:

#$$the first mask to extract the diagonal elements,

# the second mask to extract elements in the negative$\_$zero$\_$on$\_$duplicate matrix that are larger than the elements in the diagonal

mask$\_$exclude$\_$positives $=$ tf$.$cast$(($None$)|($None$),$

scores.dtype$)$

# multiply $`$mask$\_$exclude$\_$positives$`$ with $2\mathrm{.}0$ and subtract it out of $`$negative$\_$zero$\_$on$\_$duplicate$`$

negative$\_$without$\_$positive $=$ None

# take the row by row $`$max$`$ of $`$negative$\_$without$\_$positive$`.$

# Hint: $`$tf$.$math.reduce$\_$max$($negative$\_$without$\_$positive, axis $=$ None$)`$

closest$\_$negative $=$ None

# compute $`$tf$.$maximum$`$ among $0\mathrm{.}0$ and $`$A$`$

# A $=$ subtract $`$positive$`$ from $`$margin$`$ and add $`$closest$\_$negative$`$

triplet$\_$loss$1=$ None

# compute $`$tf$.$maximum$`$ among $0\mathrm{.}0$ and $`$B$`$

# B $=$ subtract $`$positive$`$ from $`$margin$`$ and add $`$mean$\_$negative$`$

triplet$\_$loss$2=$ None

# add the two losses together and take the $`$tf$.$math.reduce$\_$sum$`$ of it

triplet$\_$loss $=$ None

### END CODE HERE ###

return triplet$\_$loss