One-Hot to Integer Conversion

A one-hot vector is a binary vector in which exactly one element is 1 and all others are 0. The position of the 1 encodes an integer value. For example, [0, 0, 1, 0] represents the integer 2.

The global function qbpp.onehot_to_int() decodes one-hot encoded rows in an integer array and returns an array of integers indicating the positions of the 1s.

Basic Usage (2D Array)

For a 2D array of size $n \times m$, onehot_to_int() decodes each row and returns a 1D array of $n$ integers, each in the range $[0, m-1]$. If a row is not a valid one-hot vector (i.e., it does not contain exactly one 1), the function returns $-1$ for that row.

import pyqbpp as qbpp

n, m = 5, 5
x = qbpp.var("x", n, m)

# One-hot constraint: each row has exactly one 1
onehot = qbpp.sum(qbpp.vector_sum(x) == 1)
# All-different constraint: each column has exactly one 1
alldiff = qbpp.sum(qbpp.vector_sum(x, 0) == 1)

f = onehot + alldiff
f.simplify_as_binary()

solver = qbpp.EasySolver(f)
sol = solver.search({"target_energy": 0})

print("x =", sol(x))

result = qbpp.onehot_to_int(sol(x))
print("onehot_to_int =", result)

This program defines a $5 \times 5$ permutation matrix and decodes it into a permutation:

x = {{0,0,0,1,0},{1,0,0,0,0},{0,0,1,0,0},{0,1,0,0,0},{0,0,0,0,1}}
onehot_to_int = {3,0,2,1,4}

Specifying the Axis

By default, onehot_to_int() decodes along the last axis (axis=-1). You can specify any axis using onehot_to_int(arr, axis). Negative indices are also supported: axis -1 refers to the last axis, -2 to the second-to-last, and so on.

For a 2D array of size $n \times m$:

• onehot_to_int(arr) or onehot_to_int(arr, 1): decodes each row, returns $n$ integers in $[0, m-1]$.
• onehot_to_int(arr, 0): decodes each column, returns $m$ integers in $[0, n-1]$.

row_result = qbpp.onehot_to_int(sol(x))     # {3,0,2,1,4}
col_result = qbpp.onehot_to_int(sol(x), 0)  # {1,3,2,0,4}

When x is a permutation matrix, onehot_to_int(sol(x)) gives the permutation $\sigma$, and onehot_to_int(sol(x), 0) gives its inverse $\sigma^{-1}$.

1D Input

For a 1D array of size $m$, onehot_to_int() returns a single-element array containing the position of the 1, or $-1$ if the input is not a valid one-hot vector.

v = qbpp.var("v", 4)
# ... solve so that v = {0, 0, 1, 0} ...
idx = qbpp.onehot_to_int(sol(v))  # {2}

Higher-Dimensional Arrays

For arrays with dimension $d \geq 3$, onehot_to_int() decodes along the specified axis and returns an array with dimension $d - 1$. For example, for a $2 \times 3 \times 4$ array:

• onehot_to_int(arr) or onehot_to_int(arr, 2): decode along axis 2 (last), result shape $2 \times 3$.
• onehot_to_int(arr, 1): decode along axis 1, result shape $2 \times 4$.
• onehot_to_int(arr, 0): decode along axis 0, result shape $3 \times 4$.

Summary

Input Shape	Axis	Output Shape	Value Range
$(m)$	—	$(1)$	$[0, m-1]$ or $-1$
$(d_0 \times \cdots \times d_{n-1})$	$k$	all dims except $d_k$	$[0, d_k-1]$ or $-1$

Comparison with C++ QUBO++

C++ QUBO++	PyQBPP
qbpp::onehot_to_int(sol(x))	qbpp.onehot_to_int(sol(x))
qbpp::onehot_to_int(sol(x), k)	qbpp.onehot_to_int(sol(x), k)