Struct IMF 

pub struct IMF {
    pub data: Vec<f64>,
    pub frequency: Option<Vec<f64>>,
    pub amplitude: Option<Vec<f64>>,
}

Numerical tolerance for singularity detection in cubic spline interpolation

This threshold is used in the Thomas algorithm (tridiagonal matrix solver) to detect near-singular matrices that would cause numerical instability or division by zero.

Mathematical Rationale

The value 1e-12 is chosen based on:

• Machine epsilon for f64: ~2.22e-16 (smallest representable difference)
• Safety margin: 1e-12 is ~10^4 times larger than machine epsilon
• Numerical stability: Provides buffer against round-off error accumulation
• Practical experience: Standard threshold in numerical analysis libraries

When This Matters

Singularity occurs when:

• Input points have identical or nearly-identical x-coordinates
• Extreme spacing variations cause ill-conditioned interpolation
• Accumulated floating-point errors approach matrix degeneracy

Trade-offs

• Smaller values (e.g., 1e-15): Risk false positives from round-off errors
• Larger values (e.g., 1e-9): May reject valid but ill-conditioned problems
• Default value (1e-12): Balances robustness with numerical accuracy

Users can override the default if they need to handle extremely ill-conditioned data. Intrinsic Mode Function (IMF) - a single component from EMD

Fields

data: Vec<f64>

The IMF data

frequency: Option<Vec<f64>>

The instantaneous frequency (if computed)

amplitude: Option<Vec<f64>>

The instantaneous amplitude (if computed)

Implementations

impl IMF

pub fn new(data: Vec<f64>) -> Self

Create a new IMF from data

pub fn compute_instantaneous_attributes(&mut self) -> Result<()>

Compute instantaneous frequency and amplitude using Hilbert transform

This method computes the analytic signal via Hilbert transform to extract:

• Instantaneous amplitude (envelope)
• Instantaneous frequency (derivative of phase)

Trait Implementations

impl Clone for IMF

fn clone(&self) -> IMF

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl Debug for IMF

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.