cumprod_op

→TensorImplPtr

int cumprod_op(const int & a, int axis)

source edit

Python wrappers

pylucid.ops.cumprodfunction

Inclusive cumulative product along a single axis, $y_k = \prod_{j \le k} x_j$ .

The output has the same shape and dtype as the input. Backward reuses the reverse-cumsum primitive against the saved cumprod output and divides by the saved input: $dx = \mathrm{reverse}(\mathrm{cumsum}(\mathrm{reverse}(dy \cdot y))) / x$ .

Math

y_k = \prod_{j \le k} x_j, \qquad \frac{\partial \mathcal{L}}{\partial x_i} = \sum_{j \ge i} \frac{\partial \mathcal{L}}{\partial y_j} \cdot \frac{y_j}{x_i}.

Parameters

aTensorImplPtr

Input tensor of any non-scalar shape and real dtype.

axisint

Axis along which to accumulate (negative wraps).

Returns

TensorImplPtr

Output tensor of the same shape and dtype as a.

Notes

Backward is undefined where $x_i = 0$ because the formula divides by $x$ . Forward saves both $x$ and $y$ on the backward node.