How to multiply each element of N vectors to each other N^N times

Question

The problem is I have to multiply each element of N vectors to each other. As for example, If there are two vectors name X,Y. Each has three elements. Such as X={X1,x2,x3} and Y={y1,y2,y3} . So the multiplication is following

M1={X1*Y1}, M2={X1*Y2}, M3={X1*Y3}, M4={X2*Y1}, M5={X2*Y2}, M6={X2*Y3}, M7={X3*Y1}, M8={X3*Y2}, M9={X4*Y3}

I can easily do it using two 'for' loops. But the problem is the number of vector is variable. It can be X,Y,Z or X,Y or W,X,Y,Z. So how can I multiply them? Is there any mathematical name of this operation.

One of my idea is consider the vectors as one matrix.

what kind of result do you have in mind for 3 vectors? Can you give an example (with only 2 numbers per vector to keep it short)? Also, can you guarantee that all vectors have the same dimensions (numbers in them)? — Erwin Moller
– Erwin Moller, Commented Jul 8, 2015 at 12:00
vectors wil contain integer or decimal.Nope i cannot guarantee that all vectors have the same dimensions. :( — newCommer
– newCommer, Commented Jul 8, 2015 at 12:05

Pratik Soni · Accepted Answer · 2015-07-08 13:43:04Z

Here is the solution for your problem. Syntax may be different or depends on programming language you are using. It will initially store the first element and then perform multiplication of upcoming arrays. So each and every element of arrays are being multiplied one by one.

<?php function multiplyVector($a=array(),$b) { $count_a = count($a); $count_b = count($b); if($count_a) { for($i=0;$i<$count_a;$i++) { for($j=0;$j<$count_b;$j++) { $result[] = $a[$i] * $b[$j]; } } } else { $result = $b; } return $result; } $X = [ 1, 2, 3 ]; $Y = [ 7, 8, 9, 10 ]; $Z = [ 10, 20, 50]; // add multiple array to $main $main = [ $X, $Y, $Z ]; $result = array(); foreach($main as $m) { $result = multiplyVector($result,$m); } echo "<pre>";print_r($result);die;

And the result is here.

Array ( [0] => 70 [1] => 140 [2] => 350 [3] => 80 [4] => 160 [5] => 400 [6] => 90 [7] => 180 [8] => 450 [9] => 100 [10] => 200 [11] => 500 [12] => 140 [13] => 280 [14] => 700 [15] => 160 [16] => 320 [17] => 800 [18] => 180 [19] => 360 [20] => 900 [21] => 200 [22] => 400 [23] => 1000 [24] => 210 [25] => 420 [26] => 1050 [27] => 240 [28] => 480 [29] => 1200 [30] => 270 [31] => 540 [32] => 1350 [33] => 300 [34] => 600 [35] => 1500 )

thanks for the syntax. But my problem is the number of arrays are not fixed. It can be two or more. If there are more array i add more loops. So the code changes. I want to have a fixed function which can compute the multiplication
Do you mean something like this? $A = [ 1, 2, 3 ]; $B = [ 7, 8, 9, 10 ]; $C = [ 1, 2, 8 ]; ........ $Z = [ 1, 5, 8 ];
if $Z comes in picture then will it be like this ? M1={X1*Y1*Z1},
then it will be like following code M1={X1*Y1*Z1}, M2={X1*Y1*Z2}, M3={X1*Y1*Z3}, M4={X1*Y2*Z1}, M5={X1*Y2*Z2}, M6={X1*Y2*Z3}, M7={X1*Y3*Z1}, M8={X1*Y3*Z2}, M8={X1*Y3*Z3}, M10={X2*Y1*Z1}, M11={X2*Y1*Z2}, M12={X2*Y1*Z3},

Petr · Accepted Answer · 2015-07-08 12:19:12Z

You can use recursion to iterate over all possible combinations of elements of vectors, that's a standard approach when you need to generate some combinatoric objects. Something like this (don't remember php syntax well, so it's just php-like pseudocode):

// $X is the array of vectors, that is the first vector is // $X[0][0], $X[0][1], $X[0][2], ... // the second is $X[1][0], $X[1][1], $X[1][2], ... // and so on function rec($X, $i, $prod, $res) // $i is the number of vector from where we currently choose // $prod is current product // $res is the list of all found products if ($i>length($X)) append($res, $prod) return for ($j=0; $j<length($X[$i]); $j++) // choose element $j from vector $i rec($X, $i+1, $prod*$X[$i][$j], $res) ... $res=array(); rec($X, 0, 1, $res);

Viswanath Polaki · Accepted Answer · 2015-07-08 12:55:52Z

If you are implementing in php then you can use foreach loop instead of for loop shown as below: If you have two vectors with unknown number of values then use this.

$x = array(1, 2, 3, 4, 5, 6, 7, 8, 9, 10); $y = array(1, 2, 3, 4, 5, 6, 7, 8, 9, 10); foreach ($x as $key => $value) { foreach ($y as $k => $v) { echo $value * $v . " "; } }

Note: $x can hold any number of values and so as $y.

If you dont know how many vectors or arrays you need to multiply try like below:

function multiply_arrays() { $args = func_get_args(); $number_of_args = count($args); for ($i = 0; $i < ($number_of_args - 1); $i++) { if (is_array($multiplied_array)) { $multiplied_array = multiply_two_arrays($multiplied_array, $args[$i]); } else { $multiplied_array = multiply_two_arrays($args[$i], $args[$i + 1]); } } return $multiplied_array; } function multiply_two_arrays($x, $y) { $multi_array = array(); foreach ($x as $key => $value) { foreach ($y as $k => $v) { $multi_array[] = $value * $v; } } return $multi_array; } $x = array(1, 2, 3); $y = array(1, 2, 3); $z = array(1, 2, 3); $a = array(1, 2, 3, 4, 5, 6, 7, 8, 9, 10); $b = array(1, 2, 3, 4, 5, 6, 7, 8, 9, 10); $c = array(1, 2, 3, 4, 5, 6, 7, 8, 9, 10); echo "<pre>"; print_r(multiply_arrays($x, $a, $b, $c)); echo "</pre>";

Thanks

This will work, but the number of arrays is predetermined. You'd want something that takes in a random number of params. A combination of func_num_args and some recursivness should do the trick.
if you have two vectors or arrays in php terms then foreach will loop through all the values in that vector or array. we dont need to worry about the number of elements or values in that vector
@Andrew I think my new edit of the answer will solve single dimensions array multiplications problem, if you are unaware of number of vectors or arrays you want to multiply

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