Using perl's reduce to compute dot-product - perl

Question

Suppose I have the following two equal-sized arrays in my perl program:
my #arr1 = 1..5;
my #arr2 = 6..10;
I'm trying to get their dot-product using the reduce function defined in the List::Util core module but the following is not working for me:
my $dot_prod = reduce { $arr1[$a] * $arr2[$a] + $arr1[$b] * $arr2[$b] }0..$#arr1;
I get 50 as my output instead of the expected 130.

Answer 1

The documentation describes the behavior of reduce as follows:
The first call will be with $a and $b set to the first two elements of
the list, subsequent calls will be done by setting $a to the result of
the previous call and $b to the next element in the list.
Thus, in this case, on the first iteration reduce will set $a = 0 and $b = 1, and hence, execute
$arr1[0] * $arr2[0] + $arr1[1] * $arr2[1]
This temporary result happens to be 20.
Now, for the second iteration, $a is set to the result of the previous iteratrion and so $a = 20 and $b = 2. Thus, the following will be executed
$arr1[20] * $arr2[20] + $arr1[2] * $arr2[2]
which is not what we want.
A possible workaround:
prepend an initial 0 to the list provided as input to reduce as follows:
my $dot_prod = reduce { $a + $arr1[$b] * $arr2[$b] } 0, 0..$#arr1;
This gives us the desired result since on the first iteration $a = $b = 0 and we'll compute
0 + $arr[0] * $arr[0]
whose result will be 6.
Then in the second iteration, we'll have $a = 6 $b = 1 and so we'll compute
6 + $arr1[1] * $arr2[1]
etc.

Answer 2

Honestly,
my $dot_prod = reduce { $a + $arr1[$b] * $arr2[$b] } 0, 0..$#arr1;
isn't the most readable. There is this:
my $dot_prod = sum map { $arr1[$_]*$arr2[$_] } 0..$#arr1;
But that doesn't use reduce. Well, we could simply implement sum in terms of reduce instead of using List::Util's, and perhaps even inline it:
my $dot_prod = reduce { $a+$b } map { $arr1[$_]*$arr2[$_] } 0..$#arr1;

Answer 3

Here are the previously posted solutions in a runnable program:
my #arr1 = 1..3;
my #arr2 = 6..8;
use List::Util qw(reduce sum) ;
my $dot_prod0 = reduce { $a + $arr1[$b] * $arr2[$b] } 0,0..$#arr1; #reduce
print "Dot product0 = ".$dot_prod0."\n";
my $dot_prod1 = sum map { $arr1[$_]*$arr2[$_] } 0..$#arr1; #sum map
print "Dot product1 = ".$dot_prod1."\n";
my $dot_prod2 = reduce { $a+$b } map { $arr1[$_]*$arr2[$_] } 0..$#arr1; #reduce map
print "Dot product2 = ".$dot_prod2."\n";