Cell maps and cell operators

cnine takes advantage of the parallelism afforded by GPUs via cell maps and cell operators. A cell operator is an operation such as tensor addition, matrix multiplication, etc., that can be applied to a single cell in a tensor array or a pair of cells in two different tensor arrays, yielding a single cell as a result. A cell operator typically defines two different implementations of the same operation: one for the case when the operands are on the host, and one for the case when they are on the GPU.

A cell map is a C++ template class that determines in what pattern a given cell operator is applied to a combination of tensor arrays. For example, the cell map can be cellwise, capturing an outer product, inner product or determined by a cell mask object corresponding to a graph of interactions.

The power of the cell map/operator formalism lies in the fact that any cell operator can be combined with any cell map. Moreover, when applied on the GPU, cnine will perform the individual cell operations in parallel at the thread block level, meaning that each cell operation will be mapped to a separate streaming multiprocessor. Thus, according to the general architectural restrictions of NVIDIA GPU’s, the cell operation itself can utilize up to 1024 GPU threads, which can efficiently share data with each other via the multiprocessors shared memory.

The use of cell maps and cell operators from Python is limited by the fact that on the C++ side they are implemented via templates. It is not feasible to compile all possible template instantiations into the Python cnine module. Rather, for any new combination of cell operator/ cell map, the Python binding code in cnine_py.cpp has to be updated manually and the module must be recompiled.

Here we demonstrate the cell map functionality via a single cell operator, RtensorA_add_plus_cop.

Cellwise Cmap

>>> A=rtensor_arr.zero([2,2],[3,3])
>>> B=rtensor_arr.ones([2,2],[3,3])
>>> C=rtensor_arr.zero([2,2],[3,3])
>>> cellwise_add_plus(C,A,B)
>>> print(C)
Cell (0,0)
[ 1 1 1 ]
[ 1 1 1 ]
[ 1 1 1 ]


Cell (0,1)
[ 1 1 1 ]
[ 1 1 1 ]
[ 1 1 1 ]


Cell (1,0)
[ 1 1 1 ]
[ 1 1 1 ]
[ 1 1 1 ]


Cell (1,1)
[ 1 1 1 ]
[ 1 1 1 ]
[ 1 1 1 ]

Inner Cmap

>>> A=rtensor_arr.zero([2],[3,3])
>>> B=rtensor_arr.ones([2],[3,3])
>>> C=rtensor_arr.zero([1,1],[3,3])
>>> inner_add_plus(C,A,B)
>>> print(C)
Cell (0,0)
[ 2 2 2 ]
[ 2 2 2 ]
[ 2 2 2 ]

Outer Cmap

>>> A=rtensor_arr.zero([2],[3,3])
>>> B=rtensor_arr.ones([2],[3,3])
>>> C=rtensor_arr.zero([2,2],[3,3])
>>> outer_add_plus(C,A,B)
>>> print(C)
Cell (0,0)
[ 1 1 1 ]
[ 1 1 1 ]
[ 1 1 1 ]


Cell (0,1)
[ 1 1 1 ]
[ 1 1 1 ]
[ 1 1 1 ]


Cell (1,0)
[ 1 1 1 ]
[ 1 1 1 ]
[ 1 1 1 ]


Cell (1,1)
[ 1 1 1 ]
[ 1 1 1 ]
[ 1 1 1 ]

Mprod cmap

>>> A=rtensor_arr.ones([2,2],[3,3])
>>> B=rtensor_arr.ones([2],[3,3])
>>> C=rtensor_arr.zero([2],[3,3])
>>> mprod_add_plus(C,A,B)
>>> print(C)
Cell (0)
[ 4 4 4 ]
[ 4 4 4 ]
[ 4 4 4 ]


Cell (1)
[ 4 4 4 ]
[ 4 4 4 ]
[ 4 4 4 ]