Enum LogError 

#[non_exhaustive]
pub enum LogError {
    NotNearIdentity {
        distance: f64,
        threshold: f64,
    },
    Singularity {
        reason: String,
    },
    NumericalInstability {
        reason: String,
    },
}

Errors that can occur during Lie group logarithm computation

The logarithm map log: G → 𝔤 is only well-defined on a neighborhood of the identity. Elements far from the identity may not have a unique or well-defined logarithm.

Mathematical Background

For matrix Lie groups, the logarithm is the inverse of the exponential map. However, unlike exp: 𝔤 → G which is always defined, log: G → 𝔤 has a restricted domain:

• U(1): Log defined for all elements except exact multiples of e^{iπ}
• SU(2): Log defined for all elements except -I
• SU(3): Log defined in a neighborhood of the identity
• SO(3): Log defined for rotations with angle < π

Physical Interpretation

In lattice gauge theory, when computing curvature F = log(U_□) from the Wilson loop U_□:

• If U_□ ≈ I (small plaquette, weak field), log is well-defined
• If U_□ far from I (large plaquette, strong field), log may fail
• Solution: Use smaller lattice spacing or smearing techniques

Variants (Non-exhaustive)

Non-exhaustive enums could have additional variants added in future. Therefore, when matching against variants of non-exhaustive enums, an extra wildcard arm must be added to account for any future variants.

NotNearIdentity

Element is too far from identity for logarithm to be computed

The logarithm map is only guaranteed to exist in a neighborhood of the identity. This error indicates the element is outside that neighborhood.

Fields

distance: f64

Distance from identity

threshold: f64

Maximum allowed distance for this group

Singularity

Element is exactly at a singularity of the log map

For example:

• SU(2): element = -I (rotation by π with ambiguous axis)
• SO(3): rotation by exactly π (axis ambiguous)

Fields

reason: String

Description of the singularity

NumericalInstability

Numerical precision insufficient for accurate logarithm

When the element is very close to a singularity, numerical errors can dominate. This indicates the computation would be unreliable.

Fields

reason: String

Description of the instability

Trait Implementations

impl Clone for LogError

fn clone(&self) -> LogError

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for LogError

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

Formats the value using the given formatter.

impl Display for LogError

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

Formats the value using the given formatter.

impl Error for LogError

fn source(&self) -> Option<&(dyn Error + 'static)>

Returns the lower-level source of this error, if any.

fn description(&self) -> &str

👎Deprecated since 1.42.0:

use the Display impl or to_string()

fn cause(&self) -> Option<&dyn Error>

👎Deprecated since 1.33.0:

replaced by Error::source, which can support downcasting

fn provide<'a>(&'a self, request: &mut Request<'a>)

🔬This is a nightly-only experimental API. (error_generic_member_access)

Provides type-based access to context intended for error reports.

impl PartialEq for LogError

fn eq(&self, other: &LogError) -> bool

Tests for self and other values to be equal, and is used by ==.

fn ne(&self, other: &Rhs) -> bool

Tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.

impl StructuralPartialEq for LogError