The components Submodule

pyhdc.components exposes the individual building blocks that underpin every encoding. Most users never need this module: the encoding classes assemble the right components automatically. It is useful when:

You are writing a custom encoding subclass
You want to apply a specific operation (e.g., remap_to_unit) without a full encoding context
You are debugging or testing individual operations in isolation

Submodule layout

pyhdc.components
├── binding          : all binding functions
├── bundling         : all bundling functions
├── similarity       : all similarity functions + remap_to_unit
├── elements         : element generator functions (how random values are drawn)
├── thinning         : thinning functions (post-process sparse binary vectors)
├── unary            : permutation and per-vector unary functions (inverse, negative, normalize)
├── basis            : family-aware basis builders (codebooks for data encoders)
├── quantization     : sign and tanh quantization of raw element values
└── input_formatting : internal normalisation utilities

The EncodingSpec wiring

When you define a custom encoding by subclassing Encoding and implementing _get_encoding_spec(), you return an EncodingSpec that names the component functions to use:

from pyhdc.encodings.base import Encoding, EncodingSpec
from pyhdc.components.binding   import ElementMultiplication
from pyhdc.components.bundling  import ElementAdditionCut
from pyhdc.components.similarity import CosineSimilarity
from pyhdc.components.elements  import UniformBipolar
from pyhdc.components.thinning  import NoThin
import numpy as np

class MyEncoding(Encoding):
    def _get_encoding_spec(self) -> EncodingSpec:
        return EncodingSpec(
            dtype=np.float32,
            element_generator=UniformBipolar,
            similarity_fn=CosineSimilarity,
            bundling_fn=ElementAdditionCut,
            thinning_fn=NoThin,
            binding_fn=ElementMultiplication,
            unbinding_fn=ElementMultiplication,   # self-inverse
            generator_output_type="floats",
        )

elements submodule

Element generators control how individual hypervector values are drawn.

Function	Description
`UniformBipolar`	Uniform random from {-1, +1} (Bernoulli p=0.5 then x2-1)
`UniformAngles`	Uniform random in [-π, π)
`NormalReal`	Normal distribution N(0, 1)
`BernoulliBinary`	Bernoulli(p=0.5) -> {0, 1}
`BernoulliBipolar`	Bernoulli(p=0.5) -> {-1, +1}
`BernoulliSparse`	k-sparse binary: exactly k elements are 1, rest are 0
`SparseSegmented`	Per-segment sparse binary: k ones placed uniformly within each segment

thinning submodule

Thinning operations post-process a bundled binary hypervector to reduce density.

Function	Description
`NoThin`	No-op; returns the input unchanged. Used by encodings that do not thin.

unary submodule

Added in 2.1.0. The pyhdc.components.unary module holds the permutation function and the per-vector unary functions. Each takes raw array data, operates dimension-first (axis 0 is the hypervector dimension D), and works on both numpy and torch backends. An EncodingSpec wires these into the permute_fn, inverse_fn, negative_fn, and normalize_fn fields, leaving permute_fn at None selects the shared CyclicShift.

Function	Description
`CyclicShift`	Cyclic-shift permutation along axis 0. Broadcasts over trailing batch axes. The default `permute` for every encoding.
`IdentityInverse`	Returns the input unchanged, the binding inverse for self-inverse schemes (MAP bipolar multiply, BSC XOR).
`ReverseInverse`	Exact involution inverse of circular convolution (HRR). Keeps index 0 and reverses the remaining coordinates along axis 0.
`PhaseNegate`	FHRR binding inverse, negates the phase modulo 2π.
`Negate`	Additive (bundling) inverse, element-wise negation `-data`.
`L2Normalize`	Normalizes each hypervector to unit L2 length along axis 0.
`WrapPhase`	Normalizes FHRR phases to the canonical range [-π, π).
`SignNormalize`	Normalizes MAP hypervectors back to bipolar {-1, 0, +1} by sign.

basis submodule

Added in 2.2.0. The pyhdc.components.basis package holds the family-aware builders that produce a codebook for a given encoding. Each builder has the signature fn(encoding, count, dimension=None) and returns a (D, count) array in the encoding’s value domain and backend. These builders back the codebook data encoders (Level, Thermometer, Circular, etc.), see Data Encoders.

Function	Description
`empty`	`count` all-zero hypervectors as a `(D, count)` array.
`identity`	`count` copies of the binding-identity element `e` (where `bind(x, e) == x`).
`random`	`count` independent random hypervectors as a `(D, count)` codebook.
`level`	A linear level codebook: adjacent columns correlated, ends near-orthogonal.
`circular`	A ring level codebook: similarity wraps, so level 0 ~ level L-1.
`thermometer`	A deterministic cumulative (unary) codebook. Discrete families only.

Two scalar helpers sit alongside the builders:

family_endpoints(encoding) : the (low, high) element endpoints for the encoding’s value domain.
binding_identity(encoding, dimension=None) : the binding-identity element e as a (D,) array.

quantization submodule

Added in 2.2.0. The pyhdc.components.quantization module maps continuous element values to a bipolar form. Both functions take a raw array, operate dimension-first (axis 0 is the hypervector dimension D), and work on the numpy and torch backends.

Function	Description
`hard_quantize(data)`	Maps each value to `{-1, 0, +1}` by sign.
`soft_quantize(data, temperature=1.0)`	Smooth bipolar surrogate `tanh(data / temperature)` in `(-1, 1)`.

bundling helpers

Added in 2.2.0. The pyhdc.components.bundling module now has composable helpers that reduce a stacked set without a family-specific threshold or thinning step. For family-aware bundling, use Encoding.bundle.

Function	Description
`randsel(data, p=None)`	Random-selection bundling: copy each coordinate from one randomly chosen input column. `p` is an optional length-`N` weight vector (default uniform, normalized internally).
`multirandsel(data, count, p=None)`	`count` independent `randsel` draws as a `(D, count)` array.
`multiset(data, axis=-1)`	Additive multiset: sum a stacked `(D, N)` set into a single `(D,)` vector over `axis`.
`multibundle(data, axis=-1)`	Alias of `multiset` under its conventional HDC name.

binding helper

Added in 2.2.0. The pyhdc.components.binding module gains a product-reduce helper. For non-multiplicative binders, use Encoding.bind.

Function	Description
`multibind(data, axis=-1)`	Multiplicative bind of a stacked `(D, N)` set into a single `(D,)` vector (product over `axis`).

similarity submodule

The similarity module exports the four metric functions and the remap utility:

CosineSimilarity(*hvs) : cosine similarity
HammingDistance(*hvs) : normalised Hamming, output in [-1, 1]
Overlap(*hvs) : normalised overlap, output in [-1, 1]
AngleDistance(*hvs) : angle-based distance, output in [-1, 1]
remap_to_unit(sim) : maps [-1, 1] -> [0, 1]

Each function accepts one or two arguments in the same calling conventions as the Encoding.similarity() method. Each metric also takes a mode of "pairwise" or "cross" and a keyword-only axis, see Similarity Metrics.

input_formatting submodule

Internal utilities used by encoding methods to normalise inputs. These are considered private API and may change between releases:

_extract_data(hv) : extract the raw array from a Hypervector or pass through if already an array
_normalize_inputs(*hvs) : validate and normalise a sequence of inputs
_detect_batch_structure(*hvs) : determine whether inputs are single (D,) vectors or (D, N) batches and which column-wise calling convention applies