cond — Compute matrix condition numbers in MATLAB and RunMat.
k = cond(A) returns the condition number of matrix A, measuring sensitivity of linear-system solutions to perturbations. By default, it computes the 2-norm condition number from singular-value extrema, following MATLAB semantics.
Syntax
c = cond(A)
c = cond(A, p)Inputs
| Name | Type | Required | Default | Description |
|---|---|---|---|---|
A | Any | Yes | — | Input matrix. |
p | Any | No | — | Norm selector (1, 2, inf, or "fro"). |
Returns
| Name | Type | Description |
|---|---|---|
c | NumericScalar | Condition number estimate of A. |
Errors
| Identifier | When | Message |
|---|---|---|
RunMat:cond:InvalidArgument | Norm selector argument is malformed or unsupported. | cond: invalid argument |
RunMat:cond:InvalidInput | Input shape/type cannot be processed for condition-number evaluation. | cond: invalid input |
RunMat:cond:Internal | Runtime fails while computing cond or executing fallback/upload paths. | cond: internal runtime failure |
How cond works
cond(A)andcond(A, 2)use the singular values ofA, so rectangular matrices are supported.cond(A, 1),cond(A, Inf), andcond(A, 'fro')require a square, invertible matrix and use the definitionnorm(A, p) * norm(inv(A), p)with MATLAB's norm semantics.- Scalars behave like 1x1 matrices. Non-zero scalars have condition number
1, whilecond(0) = Inf. - Empty matrices return
0, matching MATLAB's convention. - Singular or rank-deficient matrices return
Inf. - Any NaN or infinite matrix element returns
NaN, matching the current MATLAB nonfinite-input convention. - Single-precision host input returns a native single scalar; double input returns double. Resident output retains the owning provider's selected precision, including integer gather-fallback results re-uploaded through that provider.
- Complex inputs are handled in full complex arithmetic.
- The documented matrix domain is single or double. Typed-integer and logical matrices are independent RunMat-only extensions; integer matrices must be exactly representable as binary64 before crossing the floating linear-algebra boundary.
- Typed-integer norm selectors are a separate RunMat-only structural extension. They are decoded exactly and accept only 1 or 2 without entering matrix arithmetic.
Does RunMat run cond on the GPU?
When the input already lives on a GPU, RunMat first looks for an acceleration provider that exposes the custom cond hook registered below. Current providers gather the matrix to host memory, reuse the shared CPU implementation, and then re-upload the scalar so downstream GPU computations preserve residency. This mirrors MATLAB semantics while keeping the user-facing API uniform.
GPU memory and residency
G = gpuArray([]); % Empty 0x0 matrix on the GPU
k = cond(G); % Returns 0 and keeps residency when possible
result = gather(k);Expected output:
result = 0Examples
Condition number of the identity matrix
A = eye(3);
k = cond(A)Expected output:
k = 1Diagnosing an ill-conditioned diagonal matrix
D = diag([1, 1e-8]);
k = cond(D)Expected output:
k = 1.0e+8Condition number of a rectangular matrix (2-norm)
A = [1 0; 0 1; 1 1];
k = cond(A, 2)Expected output:
k = 1.7321Using a different norm specification
A = [4 -1; 2 3];
k1 = cond(A, 1)
kInf = cond(A, Inf)Expected output:
k1 = 2.1429
kInf = 2.1429Complex-valued matrices
A = [1+2i 0; 3i 4-1i];
k = cond(A)Expected output:
k = 3.0327Empty inputs and GPU residency
G = gpuArray([]); % Empty 0x0 matrix on the GPU
k = cond(G); % Returns 0 and keeps residency when possible
result = gather(k)Expected output:
result = 0Using cond with coding agents
Open a RunMat example with live inputs, then ask the agent to explain how cond changes the result.
Run a small cond example, explain the result, then change one input and compare the output.
FAQ
What does a large condition number mean?⌄
Large condition numbers (>> 1) indicate that small perturbations in the input can produce large changes in the solution of a linear system involving A. Values close to 1 indicate a well- conditioned matrix.
Why does cond return Inf for singular matrices?⌄
Singular matrices have at least one zero singular value (or an undefined inverse), so the condition number is mathematically infinite. RunMat mirrors MATLAB and returns Inf in these cases.
Does cond support rectangular matrices?⌄
Yes for the default 2-norm: cond(A) uses singular values and accepts any two-dimensional matrix. Norms 1, Inf, and 'fro' require a square, invertible matrix because they are defined using the matrix inverse.
How does cond handle empty matrices?⌄
All norm choices return 0 for empty matrices (0x0), matching MATLAB's behaviour.
Will calling cond move my data off the GPU?⌄
Only when the owning provider lacks a dedicated implementation. RunMat then gathers, computes on the host, and uploads the scalar through that same provider; an upload failure is reported rather than silently changing residency.
Related Linalg functions
Structure
bandwidth · isdiag · ishermitian · issymmetric · istril · istriu · symrcm
Ops
cross · ctranspose · dot · mldivide · mpower · mrdivide · mtimes · pagemtimes · pagetranspose · trace · transpose
Open-source implementation
Unlike proprietary runtimes, every RunMat function is open-source. Read exactly how cond is executed, line by line, in Rust.
- View the source for cond in Rust on GitHub
- Learn how the RunMat runtime works
- Found a bug? Open an issue with a minimal reproduction.
About RunMat
RunMat is an open-source runtime that executes MATLAB-syntax code blazing on any GPU. It is licensed under the Apache 2.0 license.
- RunMat automatically optimizes your math for GPU execution on Apple, Nvidia, and AMD hardware. No code changes needed. Simulations that took hours now take minutes.
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