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torch.heaviside

function heaviside(input: unknown, values: unknown, options: unknown): Tensor

Computes the Heaviside step function element-wise.

Returns 1 where input > 0, 0 where input < 0, and values at input == 0. Essential for:

Discontinuous functions and indicator variables
Conditional logic in differentiable models (gate mechanisms)
Unit step responses in control theory
Activation threshold functions
On-off switches and binary conditions

\begin{aligned} H(x, v) = \begin{cases} 0 & \text{if } x < 0 \\ v & \text{if } x = 0 \\ 1 & \text{if } x > 0 \end{cases} \end{aligned}

Zero handling: Parameter v controls behavior at exactly x = 0
Discontinuous: Has jump discontinuity at x = 0
ReLU relation: ReLU(x) = x * Heaviside(x)

Non-differentiable: Not differentiable at x = 0

Parameters

inputunknown: The input tensor
valuesunknown: The value to use at input == 0 (can be scalar or tensor)
optionsunknown: Optional settings including out parameter

Returns

Tensor– A new tensor with Heaviside(x) values

Examples

// Basic usage - step function with custom zero value
const x = torch.tensor([-1, 0, 1]);
torch.heaviside(x, torch.tensor([0.5]));  // [0, 0.5, 1]

// Standard Heaviside: zero value is 0
const x = torch.tensor([-5, -1, 0, 1, 5]);
torch.heaviside(x, torch.tensor([0]));  // [0, 0, 0, 1, 1]

// Indicator: mask elements above threshold
const signal = torch.tensor([1.5, -0.5, 2.3]);
torch.heaviside(signal, torch.tensor([0]));  // [1, 0, 1]

See Also

PyTorch torch.heaviside()
relu - Related: ReLU(x) = x * Heaviside(x)
where - Conditional selection