log — Natural logarithm of scalars, vectors, matrices, or N-D tensors.

Y = log(X) computes the natural logarithm of every element in X, extending MATLAB semantics to real, logical, character, and complex inputs. Negative real values are promoted to complex results so that log(-1) yields 0 + iπ.

How log works in RunMat

• log(X) applies the operation element-wise with MATLAB broadcasting rules.
• Logical values convert to doubles (true → 1.0, false → 0.0) before the logarithm is taken.
• Character arrays are interpreted as their numeric code points and return dense double tensors.
• Negative real values produce complex results: log([-1 1]) returns [0 + iπ, 0].
• Complex inputs follow MATLAB's definition: log(a + bi) = log(|a + bi|) + i·atan2(b, a).
• log(0) returns -Inf, matching MATLAB's handling of the logarithm singularity at zero.

How log runs on the GPU

RunMat Accelerate keeps tensors on the GPU when the active provider implements unary_log *and* reduce_min. The runtime queries the device-side minimum to confirm that all values are non-negative, so positive datasets stay resident and can participate in fused elementwise kernels. When complex outputs are required or the provider cannot supply these hooks, RunMat gathers the tensor to the host, computes the exact MATLAB-compatible result (including complex promotion), updates residency metadata, and returns the host-resident value.

GPU memory and residency

You typically do **not** need to call gpuArray yourself. The auto-offload planner tracks residency and keeps tensors on the GPU when profitable. When your expression produces complex results (e.g., negative inputs to log), RunMat will gather the data automatically and still return exactly the MATLAB-compatible output. You can force explicit residency with gpuArray and gather if you want to mirror MathWorks MATLAB workflows.

Examples

Natural log of a positive scalar

y = log(exp(3))

Expected output:

y = 3

Understanding log of zero

value = log(0)

Expected output:

value = -Inf

Taking the logarithm of negative values

data = [-1 -2 -4];
result = log(data)

Expected output:

result = [0.0000 + 3.1416i, 0.6931 + 3.1416i, 1.3863 + 3.1416i]

Applying log to complex numbers

z = [1+2i, -1+pi*i];
w = log(z)

Expected output:

w = [0.8047 + 1.1071i, 1.1447 + 1.2626i]

Element-wise log on a matrix living on the GPU

G = gpuArray([1 2; 4 8]);
out = log(G);
result = gather(out)

Expected output:

result = [0.0000 0.6931; 1.3863 2.0794]

Logging character codes from a string

C = 'ABC';
values = log(C)

Expected output:

values = [4.1744 4.1897 4.2047]

FAQ

When should I use the log function?

Use log whenever you need the natural logarithm of your data—for example, to linearize exponential growth, compute likelihoods, or transform multiplicative relationships into additive ones.

What happens if the input contains zeros?

log(0) returns negative infinity (-Inf). Entire tensors follow the same rule element-wise.

How are negative real numbers handled?

Negative values automatically promote to complex results: log(-x) returns log(x) + iπ. This matches MATLAB behaviour and avoids losing information compared with returning NaN.

What about tiny floating-point noise producing small negative numbers?

Values that are numerically negative (e.g., -1e-15) are treated just like other negatives and promote to complex outputs. Use abs or max to clip values if you require a purely real result.

Does the GPU implementation support complex outputs?

Providers currently operate on real buffers. When complex results are required, RunMat gathers data to the host to compute the exact result and keeps residency metadata consistent.

Does log accept complex inputs directly?

Yes. Complex scalars and tensors follow the MATLAB definition using magnitude and phase (log(|z|) + i·angle(z)).

Related functions to explore

These functions work well alongside log. Each page has runnable examples you can try in the browser.

exp, expm1, abs, angle, gpuArray, gather, conj, double, factorial, gamma, hypot, imag, ldivide, log10, log1p, log2, minus, plus, pow2, power, rdivide, real, sign, single, sqrt, times

Open-source implementation

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

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

About RunMat

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• Simulations that took hours now take minutes. RunMat automatically optimizes your math for GPU execution on Apple, Nvidia, and AMD hardware. No code changes needed.
• Start running code in seconds. Open the browser sandbox or download a single binary. No license server, no IT ticket, no setup.
• A full development environment. GPU-accelerated 2D and 3D plotting, automatic versioning on every save, and a browser IDE you can share with a link.

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