Sum of sub-matrices (dynamic programming method)

sumSubDynamic.js

function dynamicSumSubmatrices(mat){
    // n and m represent dimensions of the matrix
    let n = mat.length;
    let m = mat[0].length;
  
    // declaring a (n*m) matrix
    let sumMat = [...new Array(n)].map(row => [...new Array(m)]);
  
    // part 1
    sumMat[0][0] = mat[0][0];
  
    // part 2
    for(let i = 1; i < m; i++) sumMat[0][i] = mat[0][i] + sumMat[0][i-1];
  
    // part 3
    for(let i = 1; i < n; i++) sumMat[i][0] = mat[i][0] + sumMat[i-1][0]; 
  
    // part 4
    for(let i = 1; i < n; i++){
        for(let j = 1; j < m; j++)
            sumMat[i][j] = mat[i][j] + sumMat[i-1][j] + sumMat[i][j-1] - sumMat[i-1][j-1];
    }
  
    return sumMat;
}