bbq.txt

a = [2,3,4,5]

b = [9,7,8,6]

i0
  j0
  sum = 0
    k0 sum += a[i+] * b[k+j]
              a[0+0] * b[0+0]
              2 * 9 = 18
    k1 sum += a[i+k] * b[k+j] 
              a[0+1] * b[1+0]
              3 * 7 = 21
    sum = 39
  j1
    k0 sum += a[i+k] * b[k+j]
              a[0+0] * b[0+1]
              2 * 7 = 
    k1 sum += a[i+k] * b[k+j]
i1
  j0
    k0 sum += a[i+k] * b[k+j]
    k1 sum += a[i+k] * b[k+j]
  j1
    k0 sum += a[i+k] * b[k+j]
    k1 sum += a[i+k] * b[k+j]
   
            // matMult(counter, matA, matB, shapeA, shapeB) {
            //     var matC = [],
            //         sum = 0

        //     if ((shapeA[1] == shapeB[0]) && shapeA[1] > 0) {
        //         for (let i = 0; i < shapeA[0]; i++) {
        //             for (let j = 0; j < shapeB[1]; j++) {
        //                 sum = 0
        //                 for (let k = 0; k < shapeB[0]; k++) {
        //                     let aIndex = this.getIndex(i, k, shapeA[1]),
        //                         bIndex = this.getIndex(k, j, shapeB[1])
        //                     sum += matA[aIndex] * matB[bIndex]
        //                 }
        //                 matC[counter.add().value()] = sum
        //             }
        //         }
        //     }
        //     counter.change(-1)
        //     return [matC, [shapeA[0], shapeB[1]]]
        // }


                // In the first case above, the dot product is the sum of the multiplication of the corresponding pairs of the two vectors.
        // e.g [3,5,2] . [9,3,2] = [3*9] + [5*3] + [2*2] = 27 + 15 + 4  = 46.

        // While for the second case above, the dot product will correspond to the multiplication of two vector magnitudes x the cosine of the angle between them.

        // Eg. using the above vectors:

        // mag([3,5,2]) = sqrt([3**2+5**2+2**2]) = approx. 6.1644.
        // mag([9,3,2]) = sqrt([9**2+3**2+2**2]) = approx. 9.6953.

        // The angle between the two vectors is defined as the dot product of the two vectors (46),
        // divided by the multiplication of their magnitudes (6.1644 * 9.6953) = 59.7657,
        // that is 46/59.7657 which is 0.7696,
        // which is then plugged into the inverse cosine function to yield the angle in radians,
        // which will give us approx. 0.6925 rad or approx. 39.6773 deg, we will use radians because the standard JS trig. functions use radian units.

        // Therefore the dot product using the second method would be 6.1644 * 9.6953 * 0.6925 which is approx. 41.3877.

        // The above result is off from the original 46 by -4.6123 units due to rounding errors (4 d.p was used, the higher the d.p the higher the accuracy ...slightly though),
        // and also due to hardware limitations resulting from division in computers being non-perfect as denary decimals,
        // have to be converted to binary decimals using floating point arithmetic, refer to the wikipedia page on IEEE754 floating numbers for more on this.

        // Use vectors if you know the components e.g [x,y] values for 2d vectors, [x,y,z] values for 3d vectors and so on.
        // Use magnitudes and an angle if you know the magnitudes of the vectors and the angle between the two vectors.