Cumulative sum product with numpy

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Let's suppose I have 2 2D numpy arrays V and W:

V = [[v11 , v12 , v13] [v21 , v22 , v23]]

W = [[w11 , w12 , v13] [w21 , w22 , w23]]

I want to do a cumulative sum product of the arrays using numpy and without a loop in order to have the following :

[[v11 * w11 , (v11 * w11 + w12) * v12 , ((v11 * w11 + w12) * v12 + w13) * v13]

[v21 * w21 , (v21 * w21 + w32) * v22 , ((v21 * w21 + w22) * v22 + w23) * v23]]

Any idea? Thanks for all the help

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