sqrt — Compute principal square roots element-wise with MATLAB-compatible real and complex behavior.

Y = sqrt(X) computes the principal square root of each element in X, preserving single precision for documented single inputs and promoting negative real values to the corresponding complex floating class.

Syntax

Y = sqrt(X)

Inputs

Returns

Errors

How sqrt works

• sqrt(X) applies the operation element-wise with MATLAB broadcasting rules.
• Typed integer values are a RunMat-only extension. They enter double square-root arithmetic only when every authoritative value is exactly representable, so wide integers that would round are rejected.
• RunMat currently converts logical values to doubles (true → 1.0, false → 0.0) before the square root is taken.
• RunMat currently interprets character arrays as numeric code points and returns dense double tensors.
• Negative real inputs yield purely imaginary outputs: sqrt([-1 4]) returns [0 + 1i, 2].
• Complex inputs follow MATLAB's definition and stay on the principal branch of the complex square root, ensuring continuity across the negative real axis.
• Zeros (including -0) remain zero in the output; infinities and NaNs propagate according to IEEE arithmetic.

Does RunMat run sqrt on the GPU?

RunMat Accelerate keeps tensors on the GPU when the active provider implements both unary_sqrt and reduce_min, allowing the runtime to prove that every element is non-negative before launching the kernel. When the dataset contains negative values (and therefore requires complex promotion) or when either hook is missing, RunMat gathers the data to the host, computes the MATLAB-compatible result, and updates residency metadata so subsequent operations see the correct value.

GPU memory and residency

You typically do not need to call gpuArray manually. The acceleration planner and fusion engine keep tensors on the GPU when profitable. If your data contains negative values, RunMat automatically gathers the tensor, produces the complex result on the host, and keeps residency metadata in sync. You can still use gpuArray/gather to mirror MathWorks MATLAB workflows.

Examples

Taking the square root of a positive scalar

y = sqrt(9)

Expected output:

y = 3

Square roots of a matrix

A = [1 4 9; 16 25 36];
R = sqrt(A)

Expected output:

R = [1 2 3; 4 5 6]

Square roots of negative inputs produce complex results

values = [-1 -4 9];
roots = sqrt(values)

Expected output:

roots = [0.0000 + 1.0000i, 0.0000 + 2.0000i, 3.0000 + 0.0000i]

Element-wise square root on GPU data

G = gpuArray([0 1; 4 9]);
out = sqrt(G);
result = gather(out)

Expected output:

result = [0 1; 2 3]

Square root of complex numbers

z = [3 + 4i, -1 + 2i];
w = sqrt(z)

Expected output:

w = [2 + 1i, 0.7862 + 1.2720i]

Square root of character codes

C = 'AB';
numericRoots = sqrt(C)

Expected output:

numericRoots = [8.0623 8.2462]

Using sqrt with coding agents

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

FAQ

Related Math functions

Open-source implementation

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

• View the source for sqrt 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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