Function standardize_simd 

pub fn standardize_simd<F>(x: &ArrayView1<'_, F>) -> Array1<F>
where
    F: Float + SimdUnifiedOps,

Standardize a 1D array to zero mean and unit variance (SIMD-accelerated).

Computes (x - μ) / σ where μ is the mean and σ is the sample standard deviation. The resulting array will have mean ≈ 0 and standard deviation ≈ 1.

Arguments

• x - Input 1D array to standardize

Returns

Array1<F> with the same length as input, standardized to zero mean and unit variance. Returns zero array if input has <= 1 element or zero standard deviation.

Performance

• SIMD: Automatically used for large arrays (1000+ elements)
• Scalar: Used for small arrays or when SIMD unavailable
• Speedup: 2-4x for large f32 arrays on AVX2 systems

Mathematical Definition

standardize(x) = (x - μ) / σ
where:
  μ = (1/n) Σ xᵢ         (sample mean)
  σ = sqrt((1/(n-1)) Σ (xᵢ - μ)²)  (sample std, ddof=1)

Examples

use scirs2_core::ndarray::array;
use scirs2_core::ndarray_ext::preprocessing::standardize_simd;

let x = array![2.0, 4.0, 4.0, 4.0, 5.0, 5.0, 7.0, 9.0];
let result = standardize_simd(&x.view());

// Verify mean ≈ 0
let mean: f64 = result.iter().sum::<f64>() / result.len() as f64;
assert!(mean.abs() < 1e-10);

// Verify std ≈ 1 (sample std with ddof=1)
let variance: f64 = result.iter()
    .map(|&x| x * x)
    .sum::<f64>() / (result.len() - 1) as f64;
let std = variance.sqrt();
assert!((std - 1.0).abs() < 1e-10);

Edge Cases

• Empty array: Returns empty array
• Single element: Returns zero array (std undefined for n=1)
• Constant array: Returns zero array (std = 0)
• NaN values: Returns zero array

Applications

• Machine Learning: Feature preprocessing for models assuming normally distributed features
• Statistical Analysis: Z-score computation for outlier detection
• Time Series: Detrending and variance normalization
• Data Science: Preparing features for PCA, clustering, regression
• Neural Networks: Input normalization for faster convergence

Implementation Notes

Uses sample standard deviation (ddof=1, Bessel’s correction) rather than population standard deviation (ddof=0). This is consistent with NumPy, SciPy, and pandas default behavior.