// a function to calculate the convolution of two vectors
// or to multiply the two algebraic expressions.

/*
**

idea :
------
vec1 = [2,3,4]
vec2 = [1,2,3]

multiply vec2 by vec1[0] = 2    4   6
multiply vec2 by vec1[1] = -    3   6   9
multiply vec2 by vec1[2] = -    -   4   8   12
-----------------------------------------------
add the above three      = 2    7   14  17  12

the - above shows the displacement after each vector multiplication by element of another vector

**
*/

function conv(vec1, vec2){
    var disp = 0; // displacement given after each vector multiplication by element of another vector
    var convVec = [];
    // for first multiplication
    for (j = 0; j < vec2.length ; j++){
        convVec.push(vec1[0] * vec2[j]);
    }
    disp = disp + 1;
    for (i = 1; i < vec1.length ; i++){
        for (j = 0; j < vec2.length ; j++){
            if ((disp + j) !== convVec.length){
                convVec[disp + j] = convVec[disp + j] + (vec1[i] * vec2[j])
            }
            else{
                convVec.push(vec1[i] * vec2[j]);
            }
        }
        disp = disp + 1;
    }
    return convVec;
}

/*
**

Usage:
------
vecA = [2,3,2,1]
vecB = [4,1,2,3]
ans = conv(vecA, vecB);

**
*/