<s>[INST] This problem is from the LeetCode (https://leetcode.com/problems/range-sum-query-2d-immutable/)
Given a 2D matrix matrix, find the sum of the elements inside the rectangle defined by its upper left corner (row1, col1) and lower right corner (row2, col2).


Example:

Given matrix = [
  [3, 0, 1, 4, 2],
  [5, 6, 3, 2, 1],
  [1, 2, 0, 1, 5],
  [4, 1, 0, 1, 7],
  [1, 0, 3, 0, 5]
]

sumRegion(2, 1, 4, 3) -> 8
sumRegion(1, 1, 2, 2) -> 11
sumRegion(1, 2, 2, 4) -> 12
 

Note:
You may assume that the matrix does not change.
There are many calls to sumRegion function.
You may assume row1 ≤ row2 and col1 ≤ col2.

You can perform the operation of any matrix operation.

Use Python (python 2.7.x or python 3.x)

Here is my answer with 2D array to store the cumulative sum of all elements. Here is my code:
```python
class NumMatrix(object):

    def __init__(self, matrix):

        self.matrix = matrix
        if len(matrix) == 0:
            self.dp = [[0]]
        else:
            m, n = len(matrix), len(matrix[0])
            self.dp = [[0]*(n+1) for _ in range(m+1)]
            for i in range(1, m+1):
                for j in range(1, n+1):
                    self.dp[i][j] = matrix[i-1][j-1]+self.dp[i-1][j]+self.dp[i][j-1]-self.dp[i-1][j-1]

    def sumRegion(self, row1, col1, row2, col2):
        """
        :type row1: int
        :type col1: int
        :type row2: int
        :type col2: int
        :rtype: int
        """
        return self.dp[row2+1][col2+1] - self.dp[row2+1][col1] - self.dp[row1][col2+1] + self.dp[row1][col1]
```
There are several things I want to improve

1.  I want to add some comments to explain what this does and what each line does.
2.  I want to add some error detection code to make sure the row and column numbers are valid
3.  I have a minor gripe about the naming of the variables, could you suggest some alternatives?[/INST]