comparing three diagonal array and find which two are most similar

Question

I have three diagonal arrays A,B,C all are double of size 508X508. All the values above the principal diagonal are non-zero, and every other cell holds zero.

Data in both A and B are collected from sensor in Day-1 and then Day-2. Meanwhile, the optimal data are stored in C.

My question is how to find which of the arrays A,B is more similar to C ???

What is the best statistical method to achieve that, if possible maybe a C# code snap ?

Answer 1

I think Corak pointed you to the right way. Just select a distance measure, compute the total sum of distances for each matrix.

Try something like this

    public double ComputeArrayDistance(double[,] firstArray, double[,] secondArray)
    {
        // some quick and dirty guardClauses to prevent hedaches 
        if (firstArray.GetLength(0) != firstArray.GetLength(1)) throw new ArgumentException("the first array is not squared ..");
        if (secondArray.GetLength(0) != secondArray.GetLength(1)) throw new ArgumentException("the second array is not squared ..");
        if (firstArray.GetLength(0) != secondArray.GetLength(0)) throw new ArgumentException("the size of two array don't match");

        double totalDistance = 0; 

        // if the array(matrix) is lower triangular
        for(int i = 0; i < firstArray.GetLength(0); i++)
        {
            for(int j = 0; j <= i; j++ )
            {
                totalDistance += this.GetDistance(firstArray[i, j], secondArray[i, j]);
            }
        }

        return totalDistance;
    }

    private double GetDistance(double elemOne, double elemTwo)
    {
        // an acceptable measure should be the square of the difference  
        return Math.Pow((elemOne - elemTwo), 2);
    }