search a 2D matrix

def searchMatrix(self, matrix, target):
        if len(matrix) == 0 or len(matrix[0]) == 0:
            return False
        upp,bot,lef,rig,tar_row = 0,len(matrix)-1,0,len(matrix[0])-1,0
        #ascertain target row
        while upp < bot:
            if target > matrix[upp][rig] and target < matrix[bot][lef]:
                upp += 1
                bot -= 1
            elif target < matrix[upp][rig]:
                tar_row = upp
                break
            elif target > matrix[bot][lef]:
                tar_row = bot
                break
            elif target == matrix[upp][rig] or target == matrix[bot][lef]:
                return True
        if upp > bot:
            return False
        if upp == bot:
            tar_row = upp
        #apply binary search to ascertain target column
        while lef <= rig:
            middle = int((lef+rig)/2)
            if matrix[tar_row][middle] == target:
                return True
            elif matrix[tar_row][middle] > target:
                rig = middle - 1
            else:
                lef = middle + 1
        return False