.. product.rst: ####### Product ####### .. code-block:: cpp Product // Product reduction operation. Description =========== Reduces the tensor, eliminating the specified reduction axes by taking the product. Inputs ------ +-----------------+-------------------------+--------------------------------+ | Name | Element Type | Shape | +=================+=========================+================================+ | arg | Any | Any | +-----------------+-------------------------+--------------------------------+ Attributes ---------- +--------------------+----------------------------------------------------------------+ | Name | Description | +====================+================================================================+ | reduction_axes | The axis positions (0-based) on which to calculate the product | +--------------------+----------------------------------------------------------------+ Outputs ------- +-----------------+-------------------------+---------------------------------------------------+ | Name | Element Type | Shape | +=================+=========================+===================================================+ | output | Same as arg | Same as arg, with reduction_axes removed. | +-----------------+-------------------------+---------------------------------------------------+ Mathematical Definition ======================= .. math:: \mathit{product}\left(\{0\}, \left[ \begin{array}{ccc} 1 & 2 \\ 3 & 4 \\ 5 & 6 \end{array} \right]\right) &= \left[ (1 * 3 * 5), (2 * 4 * 6) \right] = \left[ 15, 48 \right]&\text{ dimension 0 (rows) is eliminated} \\ \mathit{product}\left(\{1\}, \left[ \begin{array}{ccc} 1 & 2 \\ 3 & 4 \\ 5 & 6 \end{array} \right]\right) &= \left[ (1 * 2), (3 * 4), (5 * 6) \right] = \left[ 2, 12, 30 \right]&\text{ dimension 1 (columns) is eliminated}\\ \mathit{product}\left(\{0,1\}, \left[ \begin{array}{ccc} 1 & 2 \\ 3 & 4 \\ 5 & 6 \end{array} \right]\right) &= (1 * 2) * (3 * 4) * (5 * 6) = 720&\text{ both dimensions (rows and columns) are eliminated} C++ Interface ============= .. doxygenclass:: ngraph::op::Product :project: ngraph :members: