pub fn normal_(
shape: &[usize],
mean: f32,
std: f32,
generator: Option<u64>,
) -> Result<Tensor>Expand description
Generate tensor with values drawn from normal distribution
§Mathematical Background
The normal (Gaussian) distribution N(μ, σ²) has probability density function:
f(x) = (1/(σ√(2π))) × exp(-½((x-μ)/σ)²)
```text
Properties:
- **Mean**: μ
- **Variance**: σ²
- **Standard deviation**: σ
- **Support**: (-∞, ∞)
- **68-95-99.7 rule**: ~68% within μ±σ, ~95% within μ±2σ, ~99.7% within μ±3σ
## Box-Muller Transformation
Converts uniform random variables to normal:
```text
U₁, U₂ ~ Uniform(0,1)
Z₀ = √(-2 ln U₁) × cos(2π U₂)
Z₁ = √(-2 ln U₁) × sin(2π U₂)
Z₀, Z₁ ~ N(0,1)
X = μ + σZ ~ N(μ, σ²)
```text
## Parameters
* `shape` - Shape of the tensor
* `mean` - Mean of the normal distribution
* `std` - Standard deviation of the normal distribution
* `generator` - Optional random number generator seed
## Returns
* Tensor filled with normally distributed values N(mean, std²)