tril — Extract lower-triangular portions of matrices with optional diagonal offsets.

tril(A) keeps elements on and below a selected diagonal and sets elements above that diagonal to zero. Optional k selects the diagonal boundary using MATLAB-compatible semantics.

Syntax

B = tril(A)
B = tril(A, k)

Inputs

Returns

Errors

How tril works

• Works on numeric, logical, and complex arrays.
• Operates on the first two dimensions; trailing dimensions are handled as independent pages.
• Accepts scalar, vector, matrix, or paged inputs of any size, including empty dimensions.
• Logical inputs remain logical, and complex values keep their real/imaginary components.
• Scalars are treated as 1×1 matrices and honour negative offsets (k < 0 yields zero).
• gpuArray inputs stay on the device when the provider exposes a native tril hook; otherwise RunMat performs a gather → compute → upload cycle.

Does RunMat run tril on the GPU?

If the active acceleration provider implements the custom tril hook the entire operation runs on the GPU.

When the hook is missing, RunMat gathers the data once, computes the result on the host, uploads the lower triangular tensor back to the device, and returns a gpuArray handle so residency is preserved for downstream kernels.

Falling back to the host never changes numerical results; it only affects where the computation is carried out.

GPU memory and residency

G = gpuArray(rand(5));
L = tril(G, -2);
isa(L, 'gpuArray')

Expected output:

ans =
  logical
   1

Examples

Extracting the lower triangular part of a matrix

A = [1 2 3; 4 5 6; 7 8 9];
L = tril(A)

Expected output:

L =
     1     0     0
     4     5     0
     7     8     9

Keeping one super-diagonal above the main diagonal

A = magic(4);
L = tril(A, 1)

Expected output:

L =
    16     2     0     0
     5    11    10     0
     9     7     6    12
     4    14    15     1

Dropping the main diagonal with a negative offset

A = [1 2 3; 4 5 6; 7 8 9];
strict = tril(A, -1)

Expected output:

strict =
     0     0     0
     4     0     0
     7     8     0

Applying tril to every page of a 3-D array

T = reshape(1:18, [3 3 2]);
L = tril(T)

Expected output:

L(:, :, 1) =
     1     0     0
     4     5     0
     7     8     9

L(:, :, 2) =
    10     0     0
    13    14     0
    16    17    18

Preserving gpuArray residency with tril

G = gpuArray(rand(5));
L = tril(G, -2);
isa(L, 'gpuArray')

Expected output:

ans =
  logical
   1

Using tril with coding agents

Open a RunMat example with live inputs, then ask the agent to explain how tril changes the result.

FAQ

Related Array functions

Open-source implementation

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

• View the source for tril 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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