pxdct 0.3.3

Fast DCT/DST types I–VIII

pxdct — Fast DCT/DST for Python

Rust-backed DCT and DST types I–VIII with SIMD, exposed to Python via maturin and PyO3.

scipy.fft covers DCT types I–IV only. pxdct adds types V–VIII for both cosine and sine families, MDCT/IMDCT, pre-planned reusable executors, a 2-D executor for image processing, and three normalization modes including orthonormal scaling.

Install

pip install pxdct

Build from source (requires a Rust toolchain):

pip install maturin
maturin develop --release  # installs into the current venv

Quick start

import numpy as np
import pxdct

x = np.random.randn(256)

# one-shot
y = pxdct.dct(x, type=2)                   # DCT-II, unscaled
y = pxdct.dct(x, type=4)                   # DCT-IV
y = pxdct.dst(x, type=7)                   # DST-VII
y = pxdct.dct(x, type=2, scaling='ortho')  # orthonormal DCT-II

# reusable plan
plan = pxdct.plan('dct2', 256)
out  = np.empty(256)

for frame in audio_frames:
    plan.execute_into(frame, out)

# in-place variant
plan.execute(out)   # overwrites out

# ortho-normalised round-trip (no manual rescaling needed)
fwd = pxdct.plan('dct2', 256, scaling='ortho')
inv = pxdct.plan('dct3', 256, scaling='ortho')
y      = fwd(x)
x_back = inv(y)     # ≈ x

# MDCT / IMDCT (length must be even; scaling is ignored)
mdct_plan  = pxdct.plan('mdct',  256)
imdct_plan = pxdct.plan('imdct', 256)
coeffs = mdct_plan(x)
x_back = imdct_plan(coeffs)

# 2-D
p2 = pxdct.plan2d('dct2', 512)              # 512×512, same kind on both axes
p2 = pxdct.plan2d('dct2', 640, height=480)  # rectangular

img_flat = image.ravel().astype('float64')   # row-major, length = width × height
p2.execute(img_flat)

# 2-D ortho round-trip with DCT-IV (self-inverse under ortho)
p = pxdct.plan2d('dct4', 8, scaling='ortho') 
p.execute(block)   # forward
p.execute(block)   # inverse — recovers original

API reference

pxdct.dct(x, type=2, *, kind=None, dtype='f64', scaling='none') → ndarray

pxdct.dst(x, type=2, *, kind=None, dtype='f64', scaling='none') → ndarray

One-shot transforms. type selects DCT/DST type 1–8. kind overrides type with an explicit string such as "dct4", "dst7", "mdct", or "imdct". scaling controls normalization (see Scaling below).

pxdct.plan(kind, length, dtype='f64', scaling='none') → DctPlan

Factory for DctPlan.

pxdct.plan2d(kind_width, width, kind_height=None, height=None, dtype='f64', scaling='none') → DctPlan2D

Factory for DctPlan2D. kind_height and height default to kind_width and width (square, same kind on both axes). scaling is applied to both axes.

class DctPlan

Method / attribute	Description
execute(data)	In-place transform on a 1-D numpy array
execute_into(input[, output])	Out-of-place; input is not modified; allocates output if omitted
plan(input[, output])	Alias for execute_into via __call__
.length	Transform size
.kind	Kind string, e.g. "dct2"
.dtype	"f32" or "f64"
.scaling	Normalization mode: "none", "scale", or "ortho"

class DctPlan2D

Method / attribute	Description
execute(data)	In-place transform on a flat row-major array of length width × height. Output is in transposed H×W order — see layout note below.
.width, .height, .dtype	Read-only attributes

Layout contract: For performance, DctPlan2D omits the final transpose. Input is W×H row-major; output is H×W row-major (transposed). To restore W×H order: arr.reshape(width, height).T. For a round-trip, build the inverse plan with axes swapped: plan2d(inv_kind, height, width).

Supported transforms

Kind	Full name	Inverse of
dct1	DCT type I	itself (up to scaling)
type2	DCT type II (the "standard" DCT)	dct3
dct3	DCT type III (inverse DCT)	type2
type4	DCT type IV	itself
dct5–dct8	DCT types V–VIII	see literature
dst1–dst8	DST types I–VIII	see literature
mdct	Modified DCT	imdct
imdct	Inverse MDCT	mdct

Scaling

Three normalization modes are available via the scaling parameter:

scaling	Effect
"none"	Unscaled output
"scale"	Multiply every output element by sqrt(2 / N)
"ortho"	Per-type orthonormal scaling — a forward/inverse pair round-trips to the identity

scaling is ignored for "mdct" and "imdct".

Unscaled round-trip (default)

y         = pxdct.dct(x, type=2)   # DCT-II
recovered = pxdct.dct(y, type=3)   # DCT-III
recovered *= 2.0 / len(x)          # manual rescaling required

Ortho round-trip (no manual rescaling)

fwd = pxdct.plan('dct2', len(x), scaling='ortho')
inv = pxdct.plan('dct3', len(x), scaling='ortho')
y         = fwd(x)
recovered = inv(y)   # ≈ x, no rescaling needed

2-D ortho note

The 2-D executor applies the 1-D transform independently along rows and columns. For a clean 2-D ortho round-trip without manual rescaling, use DCT-IV, which is self-inverse under ortho scaling on every axis:

p = pxdct.plan2d('dct4', 8, scaling='ortho')
p.execute(block)   # forward
p.execute(block)   # inverse — recovers original exactly

A DCT-II/III ortho pair also works in 2-D, but requires the inverse plan to apply DCT-III on both axes independently (not a single combined plan object).

Precision

dtype	Description
"f64"	float64 — default
"f32"	float32 — ~2× faster on SIMD hardware