deconv — Compute one-dimensional deconvolution in MATLAB and RunMat.
deconv(b, a) performs one-dimensional polynomial long division and returns quotient q plus remainder r. Coefficients use MATLAB/RunMat polynomial ordering (highest-order term first), with support for real and complex inputs.
Syntax
Q = deconv(numerator, denominator)
[Q, R] = deconv(numerator, denominator)Inputs
| Name | Type | Required | Default | Description |
|---|---|---|---|---|
numerator | Any | Yes | — | Numerator coefficients. |
denominator | Any | Yes | — | Denominator coefficients. |
Returns
| Name | Type | Description |
|---|---|---|
Q | NumericArray | Quotient polynomial coefficients. |
R | NumericArray | Remainder polynomial coefficients. |
Returned values from deconv depend on how many outputs the caller requests.
Errors
| Identifier | When | Message |
|---|---|---|
RunMat:deconv:InvalidInput | Numerator/denominator input value is not supported for polynomial conversion. | deconv: unsupported input type |
RunMat:deconv:VectorRequired | Input is not scalar/row/column vector. | deconv: inputs must be scalars, row vectors, or column vectors |
RunMat:deconv:DenominatorInvalid | Denominator is empty or contains only exact zero coefficients. | deconv: denominator is invalid |
RunMat:deconv:GatherFailed | GPU input cannot be gathered for host fallback normalization. | deconv: failed to gather GPU input |
RunMat:deconv:BuildComplexOutput | Complex output tensor allocation fails. | deconv: failed to build complex tensor |
RunMat:deconv:BuildOutput | Real output tensor allocation fails. | deconv: failed to build tensor |
RunMat:deconv:TooManyOutputs | More than two outputs are requested. | deconv: too many output arguments |
How deconv works
- Inputs must be scalars, row vectors, or column vectors. Multi-dimensional tensors are rejected.
- Only exact zero coefficients are treated as leading zeros. The remainder retains the numerator's full length and orientation so
conv(a, q) + rreconstructs the numerator with ordinary aligned polynomial addition. - When
length(b) < length(a), the quotient is zero and the remainder equalsb. - MATLAB documents single and double coefficients. RunMat extension mode additionally accepts logical coefficients and integer coefficients that are exactly representable as double; inexact wide integers are rejected.
- Single and complex-single coefficients preserve single output precision when every coefficient input is floating-point. Any logical or typed-integer coefficient selects double output precision, independent of whether inputs are host values or resident gpuArrays; complex coefficients preserve complex output storage.
- Empty denominators and all-zero denominators raise MATLAB-compatible errors.
- This implementation currently covers classic vector polynomial division. The newer shape, least-squares Method, and RegularizationFactor forms remain an explicit compatibility gap.
Does RunMat run deconv on the GPU?
When either input is resident, RunMat gathers it through its registered owner and performs polynomial division on the CPU. Two resident inputs must already share an owner and device. Results return to that owner/device only when it can physically supply the computed precision, and restored handles are accepted only when their owner, device, shape, storage, and precision match the computed result.
Examples
Recovering a factor from a polynomial product
p = conv([1 2], [1 -3 2]); % Multiply two polynomials
[q, r] = deconv(p, [1 2]) % Divide by the first factorExpected output:
q = [1 -3 2];
r = [0 0 0 0]Obtaining a non-zero remainder
[q, r] = deconv([1 4 7], [1 2])Expected output:
q = [1 2];
r = [0 0 3]Dividing by a longer sequence
[q, r] = deconv([3 5], [1 0 2])Expected output:
q = 0;
r = [3 5]Handling leading zeros explicitly
b = [0 0 1 2];
a = [0 1 1];
[q, r] = deconv(b, a)Expected output:
q = [1];
r = [0 0 0 1]Complex polynomial division
b = [1+2i 3-4i 2];
a = [1-i 2+i];
[q, r] = deconv(b, a)Expected output:
q = [-0.5+1.5i 6-0.5i];
r = [-10.5-5i]GPU inputs with automatic host fallback
b = gpuArray([1 3 3 1]);
a = gpuArray([1 1]);
[q, r] = deconv(b, a); % Quotient stays on the GPU when possible
r = gather(r); % Explicitly gather the remainder if needed on the hostUsing deconv with coding agents
Open a RunMat example with live inputs, then ask the agent to explain how deconv changes the result.
Run a small deconv example, explain the result, then change one input and compare the output.
FAQ
What happens if the denominator is empty or entirely zero?⌄
An error is raised. MATLAB requires a non-empty, non-zero denominator polynomial.
Can I pass logical or integer vectors?⌄
They are RunMat-only extensions, not MATLAB-compatible input forms. Extension mode accepts logical coefficients and exactly-double-representable integer coefficients; strict compatibility mode rejects them before data access. If either coefficient input is logical or typed integer, quotient and remainder use double precision on both host and resident execution paths.
Why does the remainder contain leading zeros?⌄
The remainder has the numerator's full length. This preserves the documented coefficient identity and makes reconstruction with conv(a, q) + r unambiguous.
Does deconv support column vectors?⌄
Absolutely. The orientation of the numerator (b) determines the orientation of both the quotient and remainder.
How should I reconstruct the original polynomial?⌄
conv(a, q) + r (using MATLAB’s polynomial addition rules, which pad shorter vectors on the left) recreates the original numerator.
Are FFT-based deconvolutions supported?⌄
deconv implements exact polynomial long division. For FFT-based signal deconvolution, combine fft, elementwise division, and ifft manually.
What about numerical stability?⌄
deconv mirrors MATLAB’s long-division semantics. For ill-conditioned problems, consider scaling the coefficients or using higher precision (e.g., symbolic toolboxes) just as you would in MATLAB.
Can I request both outputs in one statement?⌄
Yes. [q, r] = deconv(b, a) returns both quotient and remainder; requesting only one output returns the quotient.
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Open-source implementation
Unlike proprietary runtimes, every RunMat function is open-source. Read exactly how deconv is executed, line by line, in Rust.
- View the source for deconv in Rust on GitHub
- Learn how the RunMat runtime works
- Found a bug? Open an issue with a minimal reproduction.
About RunMat
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