Accumulate¶

This example implements and tests a generic accumulation operator which applies and accumulates a lambda function across a specified axis of the input tensor. This generic accumulation operator is used to define the cumsum and cumprod functions, which are equivalent to those defined for numpy.

accumulate(x, inner_fcn=None, axis=None)¶

Define the operator function.

Parameters:	x – The input tensor inner_fcn – a lambda function to be applied for accumulation axis – The axis across which accumulation will be applied
Returns:	The accumulated result

cumsum(x, axis=0)[source]¶

Define the cumsum operator by defining the inner_fcn to be addition

\[y_{n_0,n_1,n_2,n_3} = \sum_{n_2=0}^{n_2} x_{n_0,n_1,n_2,n_3}\]

where \(n_2\) is the index over which to perform the addition.

Parameters:	x – the input tensor axis – the accumulation axis
Returns:	the cumulative sum across the accumulation axis
Examples:

>>> import numpy
>>> from opveclib import evaluate
>>> from opveclib.examples import cumsum
>>> a = numpy.arange(1, 6)
>>> evaluate(cumsum(a))
array([ 1,  3,  6, 10, 15])
>>> b = numpy.arange(1,16).reshape(3,5)
>>> evaluate(cumsum(b, axis=0))
array([[ 1,  2,  3,  4,  5],
       [ 7,  9, 11, 13, 15],
       [18, 21, 24, 27, 30]])

cumprod(x, axis=0)[source]¶

Define the cumprod operator by defining the inner_fcn to be multiplication

\[y_{n_0,n_1,n_2,n_3} = \prod_{n_2=0}^{n_2} x_{n_0,n_1,n_2,n_3}\]

where \(n_2\) is the index over which to perform the multipilication.

Parameters:	x – the input tensor axis – the accumulation axis
Returns:	the cumulative product across the accumulation axis
Examples:

>>> import numpy
>>> from opveclib import evaluate
>>> from opveclib.examples import cumprod
>>> a = numpy.arange(1, 6)
>>> evaluate(cumprod(a))
array([  1,   2,   6,  24, 120])
>>> b = numpy.arange(1,16).reshape(3,5)
>>> evaluate(cumprod(b, axis=0))
array([[  1,   2,   3,   4,   5],
       [  6,  14,  24,  36,  50],
       [ 66, 168, 312, 504, 750]])