Struct LogCondition 

pub struct LogCondition { /* private fields */ }

Conditioning information for logarithm computations.

The logarithm map on Lie groups becomes ill-conditioned near the cut locus (e.g., θ → π for SU(2), where the rotation axis becomes ambiguous). This structure provides quantitative information about the reliability of the computed logarithm.

Condition Number Interpretation

The condition number κ measures how sensitive the output is to input perturbations: |δ(log U)|/|log U| ≤ κ · |δU|/|U|

• κ ≈ 1: Well-conditioned, result is reliable
• κ ~ 10: Mildly ill-conditioned, expect ~1 digit loss of precision
• κ > 100: Severely ill-conditioned, result may be unreliable
• κ = ∞: At singularity (cut locus), axis is undefined

Example

let (log_u, cond) = g.log_with_condition()?;
if cond.is_well_conditioned() {
    // Safe to use log_u
} else if cond.is_usable() {
    // Use with caution, reduced precision
    eprintln!("Warning: log condition number = {:.1}", cond.condition_number());
} else {
    // Result unreliable
    return Err(...);
}

Implementations

impl LogCondition

pub fn from_angle(angle: f64) -> Self

Create a new LogCondition from the rotation angle.

For SU(2)/SO(3), the condition number is approximately 1/sin(θ/2) where θ is the rotation angle.

pub fn condition_number(&self) -> f64

Returns the condition number κ.

pub fn angle(&self) -> f64

Returns the rotation angle θ.

pub fn distance_to_cut_locus(&self) -> f64

Returns the distance from the cut locus.

pub fn quality(&self) -> LogQuality

Returns the quality assessment.

pub fn is_well_conditioned(&self) -> bool

Returns true if the result is well-conditioned (κ < 10).

pub fn is_usable(&self) -> bool

Returns true if the result is usable (κ < 100).

pub fn is_singular(&self) -> bool

Returns true if the result is at or near a singularity.

Trait Implementations

impl Clone for LogCondition

fn clone(&self) -> LogCondition

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for LogCondition

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

Formats the value using the given formatter.