polycirc.permutation

Basic permutations and maps which do not rely on operations

polycirc.permutation.identity(n: int)

identity(n) : n → n is the circuit which returns its inputs unchanged

polycirc.permutation.twist(m: int, n: int)

twist(a, b) : a + b → b + a swaps the first a inputs with the remaining b inputs.

polycirc.permutation.interleave(n: int)

interleave(n) : n + n → 2n is the circuit taking two n-dimensional inputs and interleaving their values.

>>> from polycirc.ast import diagram_to_function
>>> f = diagram_to_function(interleave(2))
>>> f(1, 2, 1, 2)
[1, 1, 2, 2]

polycirc.permutation.cointerleave(n: int)

cointerleave(n) : 2n → n is the inverse of interleave(n)

>>> from polycirc.ast import diagram_to_function
>>> f = diagram_to_function(cointerleave(2))
>>> f(1, 1, 2, 2)
[1, 2, 1, 2]

polycirc.permutation.block_interleave(num_blocks: int, block_size: int)

block_interleave(num_blocks, block_size) is like interleave, each n-dimensional input vector is thought of having elements of size m.

>>> from polycirc.ast import diagram_to_function
>>> f = diagram_to_function(interleave(2))
>>> g = diagram_to_function(block_interleave(num_blocks=2, block_size=1))
>>> f(1, 1, 2, 2) == g(1, 1, 2, 2)
True

polycirc.permutation.transpose(n: int, m: int)

Given an n×m-dimensional input thought of as a 2D array, transpose it to get a m×n-dimensional output