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torch.Tensor.Tensor.reciprocal

Tensor.reciprocal(): Tensor<S, D, Dev>

Reciprocal (element-wise inverse).

Computes 1/x for each element. Undefined at x=0 which produces inf/-inf. Used in division operations and normalization techniques.

Use Cases:

  • Computing inverse/reciprocal relationships
  • Probabilistic model computations
  • Impedance and resistance calculations
  • Harmonic mean and rate calculations
  • Normalization by sum/mean
reciprocal(x)=1xGradient: ∂(1/x)∂x=−1x2\begin{aligned} \text{reciprocal}(x) = \frac{1}{x} \\ \text{Gradient: } \frac{\partial (1/x)}{\partial x} = -\frac{1}{x^2} \end{aligned}reciprocal(x)=x1​Gradient: ∂x∂(1/x)​=−x21​​
  • Singularity: reciprocal(0) = inf (undefined mathematically)
  • Inverse: reciprocal(reciprocal(x)) = x
  • Gradient magnitude: Gradient becomes large for small x
  • Division by zero: x=0 produces Infinity or NaN
  • Numerical instability: For very small x, gradient becomes very large

Returns

Tensor<S, D, Dev>– New tensor with reciprocal applied element-wise

Examples

// Basic reciprocal
const x = torch.tensor([1, 2, 4, 0.5]);
const result = x.reciprocal();  // [1, 0.5, 0.25, 2]

// Invert probabilities for odds ratio
const probs = torch.tensor([0.1, 0.5, 0.9]);
const odds = probs.reciprocal().sub(1).reciprocal();  // odds from probs

// Harmonic mean (1/mean(1/x))
const values = torch.tensor([2, 4, 6, 8]);
const harmonic_mean = values.reciprocal().mean().reciprocal();

// Normalization by value magnitude
const scales = torch.tensor([0.5, 2, 4]);
const normalized = torch.randn(10, 3).mul(scales.reciprocal());

See Also

  • PyTorch tensor.reciprocal()
  • reciprocal_ - In-place version
  • rsqrt - Reciprocal square root (1/sqrt(x))
  • div - Element-wise division
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