Core API

Public transform functions, plan management, and spectral utilities.

Arbitrary-precision FFT for mpmath.

mpmath_fft.build_plan(N)

Build a FFT plan for transform of size N.

Plans are cached by (N, mp.mp.dps) so twiddle factors are recomputed when mpmath precision changes.

The cache holds at most _MAX_PLAN_CACHE_SIZE entries (default 128). When the cache is full, the oldest entry is evicted (FIFO).

Thread-safe: uses double-checked locking to protect the plan cache.

Parameters

Nint

Transform size.

Returns

plantuple of ndarray

Plan arrays (type, N, p1, p2, c1, c2, tw_data, tw_start).

mpmath_fft.clear_plan_cache()

Clear the plan cache.

All cached plans are discarded. Subsequent calls to build_plan() will reconstruct plans at the current mpmath precision.

Thread-safe: acquires the plan cache lock.

mpmath_fft.fft(x, axis=-1)

Discrete Fourier Transform via Cooley-Tukey / radix-2 / Bluestein decomposition. Operates on numpy object arrays of mpmath mpc values.

Parameters

xndarray[dtype=object]

Input array of mpc values.

axisint

Axis along which to compute the FFT (default -1).

Returns

yndarray[dtype=object]

Transformed array.

Examples

>>> import mpmath as mp
>>> import numpy as np
>>> mp.mp.dps = 15
>>> x = np.array([mp.mpc(1, 0), mp.mpc(2, 0)], dtype=object)
>>> y = fft(x)
>>> [complex(v) for v in y.flat]
[(3+0j), (-1+0j)]

mpmath_fft.fftfreq(n, d=1.0)

Frequency bins for an n-point FFT.

Returns frequencies f_k = k / (n*d) for k = 0..n-1, wrapped so that f_k = (k-n) / (n*d) for k > n/2 (negative frequencies).

Parameters

nint

Number of sample points.

dfloat or mpmath scalar, optional

Sample spacing (default 1.0). Inverse of sampling rate.

Returns

fndarray[dtype=object]

Array of mp.mpf values of length n.

Examples

>>> import mpmath as mp
>>> mp.mp.dps = 15
>>> f = fftfreq(4, d=1.0)
>>> [float(v) for v in f.flat]
[0.0, 0.25, -0.5, -0.25]

mpmath_fft.fftshift(x, axes=None)

Shift zero-frequency component to center of spectrum.

Swaps half-spaces for each specified axis. Operates on object arrays (copies the input).

Parameters

xndarray[dtype=object]

Input array.

axesint or tuple of int, optional

Axes to shift. Default: all axes.

Returns

yndarray[dtype=object]

Shifted array.

Examples

>>> import mpmath as mp
>>> import numpy as np
>>> x = np.array([mp.mpc(0), mp.mpc(1), mp.mpc(2), mp.mpc(3)], dtype=object)
>>> y = fftshift(x)
>>> [complex(v) for v in y.flat]
[(2+0j), (3+0j), 0j, (1+0j)]

mpmath_fft.hfft(x, n=None, axis=-1)

Hermitian FFT.

Computes the inverse FFT of a Hermitian-symmetric half-spectrum. Equivalent to n_used * irfft(conj(x), n=n, axis=axis).

Parameters

xndarray[dtype=object] of mp.mpc

Half-spectrum input.

nint, optional

Output length. Default: 2 * (x.shape[axis] - 1).

axisint

Transform axis (default -1).

Returns

yndarray[dtype=object] of mp.mpf

Real-valued output.

mpmath_fft.ifft(x, axis=-1)

Inverse FFT: ifft(x) = conj(fft(conj(x))) / N.

Parameters

xndarray[dtype=object]

Input array of mpc values.

axisint

Axis along which to compute the iFFT (default -1).

Returns

yndarray[dtype=object]

Inverse transformed array.

Examples

>>> import mpmath as mp
>>> import numpy as np
>>> mp.mp.dps = 15
>>> x = np.array([mp.mpc(1, 0), mp.mpc(2, 0)], dtype=object)
>>> y = fft(x)
>>> z = ifft(y)
>>> [complex(v) for v in z.flat]
[(1+0j), (2+0j)]

mpmath_fft.ifftshift(x, axes=None)

Inverse of fftshift.

Undoes the shift so that zero frequency returns to index 0.

Parameters

xndarray[dtype=object]

Input array.

axesint or tuple of int, optional

Axes to unshift. Default: all axes.

Returns

yndarray[dtype=object]

Unshifted array.

mpmath_fft.ihfft(x, n=None, axis=-1)

Inverse Hermitian FFT.

Computes the forward FFT of a real signal and returns the non-redundant half-spectrum, with 1/n scaling. Equivalent to conj(rfft(x, n=n, axis=axis)) / n_used.

Parameters

xndarray[dtype=object] of mp.mpf

Real-valued input.

nint, optional

Transform length. Default: x.shape[axis].

axisint

Transform axis (default -1).

Returns

yndarray[dtype=object] of mp.mpc

Half-spectrum output.

mpmath_fft.irfft(x, n=None, axis=-1)

Complex-to-real inverse FFT.

Reconstructs the full Hermitian-symmetric spectrum from the non-redundant half, computes the inverse DFT, and returns the real part.

Parameters

xndarray[dtype=object] of mp.mpc

Half-spectrum, shape = (…, M, …) where M = n_orig//2 + 1.

nint, optional

Output length along transform axis. Default: 2 * (x.shape[axis] - 1).

axisint

Transform axis (default -1).

Returns

yndarray[dtype=object] of mp.mpf

Real-valued inverse transform.

mpmath_fft.rfft(x, n=None, axis=-1)

Real-to-complex FFT.

Computes the forward DFT of real-valued input and returns only the non-redundant half of the spectrum (indices 0..n//2).

Parameters

xndarray[dtype=object] of mp.mpf

Real-valued input array.

nint, optional

Transform length. If n > x.shape[axis], zero-pad. If n < x.shape[axis], truncate. Default: x.shape[axis].

axisint

Transform axis (default -1).

Returns

yndarray[dtype=object] of mp.mpc

Half-spectrum, shape = (…, n//2 + 1, …).

mpmath_fft.rfftfreq(n, d=1.0)

Frequency bins for an n-point real FFT.

Returns the non-negative frequencies f_k = k / (n*d) for k = 0..n//2.

Parameters

nint

Number of sample points.

dfloat or mpmath scalar, optional

Sample spacing (default 1.0).

Returns

fndarray[dtype=object] of mp.mpf

Frequencies, shape (n//2 + 1,).