# STEP $2$ Define a vector source by combining two consecutive pixels

# and calculate the probabilities of these vector symbols

# ADD YOUR CODE HERE

# notes:

# since each pixel has $8$ intensity levels, there will be $8$x$8=64$ symbols in the vector source.

# the symbols for the vector source could be represented as $"$aa$,$ ab$,$ ac$,...,$ hf$,$ fg$,$ hh$."$

# there are a total of $512*512/2=131,072$ sample vectors in the input image to calculate the histogram

# calculate the histogram of the vector symbols

# obtain the pdf by normalizing the histogram

# plot the pdf of this vector source# STEP $3.$b Calculate the entropy of the vector source per input source symbol

# ADD YOUR CODE HERE

# note:

# divide the vector entropy value by $2$ to find the entropy per input source symbol

# print the value of the entropy of the vector source per input source symbol

def my$\_$Entropy$($pdf$)$:

assert pdf$.$ndim $==1$

size $=$ pdf$.$size

entropy $=0\mathrm{.}0$

for i in range$($size$)$:

val $=$ pdf$[$i$]$

if val:

entropy $+=-$ val $*$ math.log$2($val$)$

return entropy

entropy$\_$vector $=$ my$\_$Entropy$($pdf$)$

entropy$\_$per$\_$symbol $=$ entropy$\_$vector $/2$

print$($f$"$Entropy of the vector source per input source symbol: $\{$entropy$\_$per$\_$symbol$\}")$