Support complex filters in Convolve1D adjoints

[antonsoo]

Convolve1D reverses the filter for its adjoint but does not conjugate it. This extends the operator to complex filters: the forward result is already correct, and the added conjugation supplies the corresponding Hermitian adjoint for short and long filters. Complex-filter use was previously unsupported.

Conjugate the reversed filter before the existing contiguous copy, preserving the CuPy stride handling from #797. Extend the existing dot-test, dtype and inversion cases to complex64/complex128 with h + 1j*h, add the conjugation to the adjoint equations, and repeat the plotted example with a complex filter.

For example, this adjoint error is about 42.85 on dev and near machine precision with the fix:

import numpy as np
from scipy.linalg import convolution_matrix
from pylops.signalprocessing import Convolve1D

h = np.array([1 + .5j, -.2 + .3j, .1 - .1j])
y = np.arange(12) + 1j * np.arange(12)[::-1]
op = Convolve1D(12, h=h, offset=1, dtype="complex128")
matrix = convolution_matrix(h, 12, "same")
print(np.linalg.norm(op.H @ y - matrix.conj().T @ y))

Validation:

• All 24 added complex cases in the existing one-dimensional test fail before and pass after, covering both precisions, compact/extended filters, offsets and direct/FFT methods. Independent matrix checks also cover overlap-add, multidimensional filters and broadcasting. The complete convolution suite passes on CPU and CuPy: 382 cases each.
• Recorded speech and guitar deconvolution/calibration agree with independent dense damped least squares in all 48 complex-filter cases per backend. Maximum relative inverse error drops from 6.62 to 9.60e-7 on CPU and 1.80e-6 on an RTX 5070. All forward outputs and 48 real-filter controls per backend remain byte-identical.
• Project lint/hooks, wheel build, documentation build and the convolution example pass. Mypy diagnostics are unchanged from dev. A broader integration run encountered a randomized float32 ChirpRadon dot-test tolerance failure; a 500-seed comparison gives identical results on unmodified dev and the patched tree, including two failing seeds.

The recorded-audio workload is a constructed numerical validation. It does not establish an existing production PyLops use case or demand for complex filters.

AI disclosure: Codex was used to investigate the failure, implement the change, write and run the independent checks, and prepare the documentation and PR text.

[codacy-production]

Up to standards ✅

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[mrava87]

Thanks @antonsoo for this. I would say this is more of an enhancement than a bug per se, as we never really support complex valued filters (no tests or examples with it) mostly because I am not aware of any real application that would benefit from it - although, of course we also don't have any guardrail in place to check for the dtype and raise an error otherwise.

Looks like the fix is very minor though, so I am going to have a closer look soon and let you know if I have any comment before merging 😄

[antonsoo]

Classifying this as a small support enhancement makes sense. The speech/guitar inverse was a constructed numerical validation; I don't have an existing production PyLops use case for complex filters to point to. I've updated the title and description to make that scope clear. The implementation and real-filter controls are unchanged.

[mrava87]

@antonsoo thanks for the contribution. I think adding support for complex-valued filters in Convolved1D is a good enhancement, however quite a few things don't follow the standards in the rest of the library... left comments for you to adjust before I can merge 😄

[antonsoo]

Updated the tests to extend test_Convolve1D_1d with h + 1j*h, both complex precisions, and the existing dot/dtype/inversion checks. The example now repeats the plotted inverse with / and real/imaginary panels; it contains no assertions. I also removed the changelog entry.

For the time-domain equation I kept t+tau using the equivalent correlation form h(tau)^* y(t+tau); this preserves the conjugate adjoint of the forward convolution.

Rebased on current dev. CPU checks, lint, the example and documentation build pass. The recorded CPU/GPU inverses still agree with independent dense references, with all real-filter controls unchanged.