Struct SvdRec 

pub struct SvdRec<T> {
    pub d: usize,
    pub u: Array2<T>,
    pub s: Array1<T>,
    pub vt: Array2<T>,
    pub total_squared_norm: T,
    pub diagnostics: Diagnostics<T>,
}

A singular value decomposition.

Orientation

A ≈ u · diag(s) · vt, matching the numpy.linalg.svd / scipy convention:

• u is m × d — left singular vectors are columns
• s is d, descending
• vt is d × n — right singular vectors are rows

In 1.x this was inconsistent: the Lanczos path returned u transposed (d × m) while the randomized path returned it as m × d, so SvdRec::recompose only worked for square inputs. Both paths now follow the convention above.

Fields

d: usize

Number of singular triplets returned.

u: Array2<T>

Left singular vectors, m × d.

s: Array1<T>

Singular values, length d, descending.

vt: Array2<T>

Transposed right singular vectors, d × n.

total_squared_norm: T

‖A‖²_F of what was decomposed — the centered matrix if the solver was centering.

Recorded because a truncated result can’t recover it: Σᵢ sᵢ² over the returned d values is only the part that was kept, not the tail it’s measured against.

diagnostics: Diagnostics<T>

Implementations

impl<T: SvdFloat> SvdRec<T>

pub fn recompose(&self) -> Array2<T>

Rebuild the dense approximation u · diag(s) · vt.

Allocates an m × n dense matrix — only reasonable for small inputs or for checking reconstruction error in tests.

pub fn converged(&self) -> bool

Whether an iterative method reached its tolerance.

Always true for the randomized methods — they do a fixed amount of work and have no convergence test. For IRLBA it’s real: false means the restart budget ran out. IRLBA refuses to return such a result by default, so this only matters if you called allow_unconverged.

pub fn max_residual(&self) -> Option<T>

Largest ‖A·vᵢ − σᵢ·uᵢ‖ over the returned triplets, for algorithms that track it. Judge it against s[0]: 1e-9 · σ_max is excellent, 0.1 · σ_max is unusable.

pub fn scores(&self) -> Array2<T>

PCA scores, u · diag(s), shaped m × d — the embedding you’d cluster or plot.

pub fn explained_variance(&self) -> Array1<T>

sᵢ² / (m − 1), matching sklearn’s explained_variance_. Only a variance in the statistical sense if the decomposition was centered.

pub fn explained_variance_ratio(&self) -> Array1<T>

Fraction of the total squared norm each component captures. Sums to at most 1, and to zero (not NaN) for an all-zero input.

pub fn total_variance(&self) -> T

‖A‖²_F / (m − 1) — the same scale as explained_variance.

pub fn nrows(&self) -> usize

Number of rows of the original matrix.

pub fn ncols(&self) -> usize

Number of columns of the original matrix.

pub fn truncate(&mut self, k: usize)

Truncate to the leading k triplets in place.

Trait Implementations

impl<T: Clone> Clone for SvdRec<T>

fn clone(&self) -> SvdRec<T>

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl<T: Debug> Debug for SvdRec<T>

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

Formats the value using the given formatter.

impl<T: PartialEq> PartialEq for SvdRec<T>

fn eq(&self, other: &SvdRec<T>) -> bool

Equality operator ==.

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

Inequality operator !=.

impl<T: PartialEq> StructuralPartialEq for SvdRec<T>