Flatten numpy array but also keep index of value positions?

Question

I have several 2D numpy arrays (matrix) and for each one I would like to convert it to vector containing the values of the array and a vector containing each row/column index.

Answer 1

Update November 2020 (tested on pandas v1.1.3 and numpy v1.19):

This should be a no-brainer by using np.meshgrid and .reshape(-1).

x = np.array([[3, 1, 4],
              [1, 5, 9]])

x_coor, y_coor = np.meshgrid(range(x.shape[1]), range(x.shape[0]))    
df = pd.DataFrame({"V": x.reshape(-1), "x": x_coor.reshape(-1), "y": y_coor.reshape(-1)})

For 2-dimensional cases, you don't even need a meshgrid. Just np.tile the range of the column axis and np.repeat for the row axis.

df = pd.DataFrame({
    "V": x.reshape(-1),
    "x": np.tile(np.arange(x.shape[1]), x.shape[0]),
    "y": np.repeat(np.arange(x.shape[0]), x.shape[1])
})

The sample data is trimmed to shape=(2, 3) to better reflect the axes location.

Result

print(df)

   V  x  y
0  3  0  0
1  1  1  0
2  4  2  0
3  1  0  1
4  5  1  1
5  9  2  1