inv — Compute the inverse of a square matrix with MATLAB-compatible pivoting and GPU fallbacks.

X = inv(A) returns the matrix inverse of a square, full-rank matrix A. The result satisfies A * X = eye(size(A)) within round-off. Scalars behave like 1 ./ A, matching MATLAB semantics.

How inv works

• Inputs must be 2-D matrices (trailing singleton dimensions are accepted). Non-square matrices raise the MATLAB error "inv: input must be a square matrix."
• Singular or rank-deficient matrices raise "inv: matrix is singular to working precision."
• Logical and integer inputs are promoted to double precision before inversion.
• Complex inputs are handled in full complex arithmetic.
• Empty matrices return an empty matrix with the same dimensions (e.g., inv([]) yields []).

How RunMat runs inv on the GPU

When a GPU acceleration provider is active, RunMat forwards the operation to its inv hook. If the provider does not implement a native kernel, RunMat gathers the data to the host, uses the shared CPU implementation, and attempts to re-upload the result so downstream GPU work keeps its residency. The shipping WGPU backend currently follows this gather/compute/upload pattern.

GPU memory and residency

You typically do not need to move data manually. If A already resides on the GPU and the provider implements inv, the computation stays on the device. Providers without a native kernel (including the current WGPU backend) download A, compute the inverse on the host, and re-upload the result, so subsequent GPU code continues to operate on device-resident data. gpuArray remains available for compatibility and for explicitly seeding GPU residency.

Examples

Inverting a 2x2 matrix for solving linear systems

A = [4 -2; 1 3];
X = inv(A)

Expected output:

X =
    0.3    0.2
   -0.1    0.4

Checking that inv(A) produces the identity matrix

A = [2 1 0; 0 1 -1; 0 0 3];
X = inv(A);
product = A * X

Expected output:

product =
    1.0000         0         0
         0    1.0000         0
         0         0    1.0000

Inverting a diagonal matrix with symbolic structure

D = diag([2, 5, 10]);
X = inv(D)

Expected output:

X =
    0.5000         0         0
         0    0.2000         0
         0         0    0.1000

Computing the inverse of a complex matrix

A = [1+2i  0; 3i  4-1i];
X = inv(A)

Expected output:

X =
   0.2105 - 0.1053i  -0.0158 - 0.1579i
  -0.1579 - 0.1184i   0.0526 + 0.2632i

Using inv on a GPU-resident matrix

G = gpuArray([3 1; 0 2]);
invG = inv(G);       % stays on the GPU when the provider implements inv
result = gather(invG)

Expected output:

result =
    0.3333   -0.1667
         0    0.5000

Handling singular matrices gracefully

A = [1 2; 2 4];
X = inv(A)

Expected output:

Error using inv
inv: matrix is singular to working precision.

FAQ

Related Linalg functions

Open-source implementation

Unlike proprietary runtimes, every RunMat function is open-source. Read exactly how inv works, line by line, in Rust.

• View inv.rs on GitHub
• Learn how the runtime works
• Found a bug? Open an issue with a minimal reproduction.

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