Struct SvdvalsResidual 

pub struct SvdvalsResidual {
    u: Mat<Complex>,
    v: Mat<Complex>,
    values: Vec<f64>,
}

What svdvals saves for its derivatives: the thin singular vectors and the singular values.

Fields

u: Mat<Complex>

v: Mat<Complex>

values: Vec<f64>

Implementations

impl SvdvalsResidual

pub fn state_size(m: usize, n: usize) -> Result<usize>

Byte count for the native saved state of an m × n operator.

impl SvdvalsResidual

pub fn values(&self) -> &[f64]

The singular values, in descending order, which the pullback reads.

pub fn shape(&self) -> (usize, usize)

The shape of the input operator.

pub fn pushforward(&self, operator: &DMatrix<Complex>) -> Result<Vec<f64>>

Singular-value tangents Re(uᴴ dA v) for simple positive singular values.

The ordered individual singular values have no linear derivative at repeated or zero values. Unlike the pullback of a smooth spectral sum, a pushforward returns each individual derivative and therefore rejects these cases. Values within 64 ε of the largest value’s scale are numerically unresolved and are treated as zero, including roundoff from rank-deficient matrices.

pub fn pullback(&self, cotangent: &[f64]) -> Result<DMatrix<Complex>>

Equal weights are supported at repeated positive values; numerically zero values require numerically zero weights because the singular value itself is not smooth there. Both tests use relative tolerance 64 ε.

Trait Implementations

impl Debug for SvdvalsResidual

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

Formats the value using the given formatter.

impl SavedState for SvdvalsResidual

fn save_state(&self) -> Result<Vec<u8>>

Copy the saved numerical state into its fixed byte layout.

fn from_state(bytes: &[u8]) -> Result<Self>

Restore numerical state from bytes produced by this extension.