Trait TracedTensorLinalgExt 

pub trait TracedTensorLinalgExt {
    // Required methods
    fn svd(&self) -> Result<(TracedTensor, TracedTensor, TracedTensor)>;
    fn svd_with_options(
        &self,
        options: SvdOptions,
    ) -> Result<(TracedTensor, TracedTensor, TracedTensor)>;
    fn svd_full(&self) -> Result<(TracedTensor, TracedTensor, TracedTensor)>;
    fn qr(&self) -> Result<(TracedTensor, TracedTensor)>;
    fn qr_with_options(
        &self,
        options: QrOptions,
    ) -> Result<(TracedTensor, TracedTensor)>;
    fn eigh(&self) -> Result<(TracedTensor, TracedTensor)>;
    fn eigh_with_options(
        &self,
        options: EighOptions,
    ) -> Result<(TracedTensor, TracedTensor)>;
    fn cholesky(&self) -> Result<TracedTensor>;
    fn lu(
        &self,
    ) -> Result<(TracedTensor, TracedTensor, TracedTensor, TracedTensor)>;
    fn full_piv_lu(
        &self,
    ) -> Result<(TracedTensor, TracedTensor, TracedTensor, TracedTensor, TracedTensor)>;
    fn eig(&self) -> Result<(TracedTensor, TracedTensor)>;
    fn solve(&self, b: &TracedTensor) -> Result<TracedTensor>;
    fn lstsq(&self, b: &TracedTensor) -> Result<TracedTensor>;
    fn full_piv_lu_solve(&self, b: &TracedTensor) -> Result<TracedTensor>;
    fn triangular_solve(
        &self,
        b: &TracedTensor,
        left_side: bool,
        lower: bool,
        transpose_a: bool,
        unit_diagonal: bool,
    ) -> Result<TracedTensor>;
    fn slogdet(&self) -> Result<(TracedTensor, TracedTensor)>;
    fn det(&self) -> Result<TracedTensor>;
    fn inv(&self) -> Result<TracedTensor>;
    fn eigvalsh(&self) -> Result<TracedTensor>;
    fn eigvals(&self) -> Result<TracedTensor>;
    fn pinv(&self) -> Result<TracedTensor>;
    fn pinv_with_rtol(&self, rtol: f64) -> Result<TracedTensor>;
    fn norm(
        &self,
        ord: Option<f64>,
        dim: Option<&[usize]>,
        keepdim: bool,
    ) -> Result<TracedTensor>;
}

Linear algebra extension methods for [TracedTensor].

Required Methods

fn svd(&self) -> Result<(TracedTensor, TracedTensor, TracedTensor)>

Build a traced SVD operation with default options.

Errors

Returns Error::Extension with ErrorKind::Unsupported for an unsupported dtype, or Error::Validation for invalid graph metadata.

Deferred errors

Backend numerical failures and concrete shape mismatches can be reported as Error::Extension or Error::Validation during compile or execution when symbolic inputs are bound.

fn svd_with_options( &self, options: SvdOptions, ) -> Result<(TracedTensor, TracedTensor, TracedTensor)>

Build a traced SVD operation with explicit derivative and gauge options.

Errors

Returns Error::Validation::InvalidArgument for a non-finite or non-positive derivative epsilon, or Error::Extension for unsupported dtype and graph registration failures.

Deferred errors

Solver convergence and symbolic shape checks may be reported during compile or execution.

fn svd_full(&self) -> Result<(TracedTensor, TracedTensor, TracedTensor)>

Build a traced full-matrices SVD operation returning square U (m x m) and Vh (n x n), whose trailing n - rank rows span the input’s right nullspace.

Errors

Returns Error::Validation when the input is not a batched matrix (rank >= 2), or Error::Extension for graph registration failures.

Deferred errors

The active backend returns Error::Extension with ErrorKind::Unsupported at execution if it does not implement full-matrices SVD (only the CPU faer provider does in this slice; the LAPACK provider and GPU backends are unsupported). Automatic differentiation is intentionally unsupported for the full variant (see the linalg AD support manifest) and surfaces a typed AD error rather than a silent thin-SVD fallback.

fn qr(&self) -> Result<(TracedTensor, TracedTensor)>

Build a traced QR operation.

Errors

Returns Error::Extension with ErrorKind::Unsupported for an unsupported dtype or Error::Validation for invalid graph metadata.

Deferred errors

Concrete shape validation and backend QR failures may be reported at compile or execution time for symbolic inputs.

fn qr_with_options( &self, options: QrOptions, ) -> Result<(TracedTensor, TracedTensor)>

Build a traced QR operation with explicit gauge options.

Errors

Returns Error::Extension with ErrorKind::Unsupported for an unsupported dtype, or Error::Validation for invalid graph metadata.

Deferred errors

Symbolic shape checks and backend QR failures can be deferred to compile or execution.

fn eigh(&self) -> Result<(TracedTensor, TracedTensor)>

Build a traced Hermitian eigendecomposition operation.

Errors

Returns Error::Extension with ErrorKind::Unsupported for an unsupported dtype or Error::Validation for invalid graph metadata.

Deferred errors

Concrete square-shape validation and solver failures may be reported at compile or execution time.

fn eigh_with_options( &self, options: EighOptions, ) -> Result<(TracedTensor, TracedTensor)>

Build a traced Hermitian eigendecomposition with explicit options.

Errors

Returns Error::Validation::InvalidArgument for an invalid derivative epsilon, or Error::Extension for unsupported dtype and registration failures.

Deferred errors

Symbolic square-shape checks and numerical eigensolver failures may be reported during compile or execution.

fn cholesky(&self) -> Result<TracedTensor>

Build a traced Cholesky factorization operation.

Errors

Returns Error::Extension with ErrorKind::Unsupported for an unsupported dtype or Error::Validation for invalid graph metadata.

Deferred errors

Non-square or non-positive-definite concrete inputs can produce validation or numerical extension errors during compile or execution.

fn lu(&self) -> Result<(TracedTensor, TracedTensor, TracedTensor, TracedTensor)>

Build a traced LU factorization operation.

Errors

Returns Error::Extension with ErrorKind::Unsupported for an unsupported dtype or Error::Validation for invalid graph metadata.

Deferred errors

Concrete shape checks and backend factorization failures may be reported during compile or execution.

fn full_piv_lu( &self, ) -> Result<(TracedTensor, TracedTensor, TracedTensor, TracedTensor, TracedTensor)>

Build a traced complete-pivot LU factorization operation.

Errors

Returns Error::Extension with ErrorKind::Unsupported for an unsupported dtype or Error::Validation for invalid graph metadata.

Deferred errors

Concrete square-shape checks and backend factorization failures may be reported during compile or execution.

fn eig(&self) -> Result<(TracedTensor, TracedTensor)>

Build a traced general eigendecomposition operation.

Errors

Returns Error::Extension with ErrorKind::Unsupported for an unsupported dtype or Error::Validation for invalid graph metadata.

Deferred errors

Concrete shape validation and numerical eigensolver failures may be reported during compile or execution.

fn solve(&self, b: &TracedTensor) -> Result<TracedTensor>

Build a traced linear solve operation.

Errors

Returns Error::Validation for incompatible coefficient/rhs metadata and Error::Extension for unsupported dtype or registration failures.

Deferred errors

Singular systems and concrete shape mismatches are reported as numerical or validation errors during compile or execution.

fn lstsq(&self, b: &TracedTensor) -> Result<TracedTensor>

Build a traced least-squares solve argmin_x ||A x - b||_2 for a tall or square, full-column-rank A, via the thin QR factorization.

Errors

Returns Error::Validation for an invalid rank (A or b not a batched matrix, rank < 2), a symbolic shape, a wide/underdetermined A (rows < cols), or an unsupported dtype (not floating-point or complex).

Deferred errors

Backend QR and triangular-solve failures and concrete shape mismatches are reported during compile or execution. Rank-deficient A is not detected: R is singular and the result is ill-defined, so callers must ensure full column rank.

fn full_piv_lu_solve(&self, b: &TracedTensor) -> Result<TracedTensor>

Build a traced complete-pivot LU solve operation.

Errors

Returns Error::Validation for incompatible coefficient/rhs metadata and Error::Extension for unsupported dtype or registration failures.

Deferred errors

Singular systems and concrete shape mismatches may be reported during compile or execution.

fn triangular_solve( &self, b: &TracedTensor, left_side: bool, lower: bool, transpose_a: bool, unit_diagonal: bool, ) -> Result<TracedTensor>

Build a traced triangular solve operation.

Errors

Returns Error::Validation for incompatible coefficient/rhs shapes or invalid solve flags, and Error::Extension for unsupported dtype.

Deferred errors

Singular or zero-diagonal systems can fail numerically during compile or execution after symbolic inputs are bound.

fn slogdet(&self) -> Result<(TracedTensor, TracedTensor)>

Build a traced sign/log-determinant operation.

Errors

Returns Error::Validation for invalid matrix metadata or Error::Extension for unsupported dtype and registration failures.

Deferred errors

Concrete singularity and shape failures can be reported during compile or execution.

fn det(&self) -> Result<TracedTensor>

Build a traced determinant operation.

Errors

Returns Error::Validation for invalid matrix metadata or Error::Extension for unsupported dtype.

Deferred errors

Concrete singularity and shape failures may be reported during compile or execution.

fn inv(&self) -> Result<TracedTensor>

Build a traced matrix-inverse operation.

Errors

Returns Error::Validation for incompatible rank/shape metadata or Error::Extension for unsupported dtype.

Deferred errors

Singular matrices produce a numerical error during compile or execution.

fn eigvalsh(&self) -> Result<TracedTensor>

Build a traced Hermitian eigenvalue-only operation.

Errors

Returns Error::Validation for non-square metadata or Error::Extension for unsupported dtype.

Deferred errors

Concrete square-shape and solver failures may be reported during compile or execution.

fn eigvals(&self) -> Result<TracedTensor>

Build a traced general eigenvalue-only operation.

Errors

Returns Error::Validation for invalid matrix metadata or Error::Extension for unsupported dtype.

Deferred errors

Concrete shape and eigensolver failures may be reported during compile or execution.

fn pinv(&self) -> Result<TracedTensor>

Build a traced pseudoinverse operation with the default tolerance.

Errors

Returns Error::Validation for invalid rank/shape metadata or Error::Extension for unsupported dtype.

Deferred errors

SVD convergence and concrete shape failures may be reported during compile or execution.

fn pinv_with_rtol(&self, rtol: f64) -> Result<TracedTensor>

Build a traced pseudoinverse with an explicit relative tolerance.

Errors

Returns Error::Validation::InvalidArgument when rtol is non-finite or negative, or Error::Extension for unsupported dtype.

Deferred errors

SVD convergence and concrete shape failures may be reported during compile or execution.

fn norm( &self, ord: Option<f64>, dim: Option<&[usize]>, keepdim: bool, ) -> Result<TracedTensor>

Build a traced vector/matrix norm operation.

Errors

Returns Error::Validation for an invalid norm order or axis and Error::Extension for unsupported dtype.

Deferred errors

Symbolic axis and shape checks may be reported during compile or execution.

Implementations on Foreign Types

impl TracedTensorLinalgExt for TracedTensor

fn svd(&self) -> Result<(TracedTensor, TracedTensor, TracedTensor)>

fn svd_with_options( &self, options: SvdOptions, ) -> Result<(TracedTensor, TracedTensor, TracedTensor)>

fn svd_full(&self) -> Result<(TracedTensor, TracedTensor, TracedTensor)>

fn qr(&self) -> Result<(TracedTensor, TracedTensor)>

fn qr_with_options( &self, options: QrOptions, ) -> Result<(TracedTensor, TracedTensor)>

fn eigh(&self) -> Result<(TracedTensor, TracedTensor)>

fn eigh_with_options( &self, options: EighOptions, ) -> Result<(TracedTensor, TracedTensor)>

fn cholesky(&self) -> Result<TracedTensor>

fn lu(&self) -> Result<(TracedTensor, TracedTensor, TracedTensor, TracedTensor)>

fn full_piv_lu( &self, ) -> Result<(TracedTensor, TracedTensor, TracedTensor, TracedTensor, TracedTensor)>

fn eig(&self) -> Result<(TracedTensor, TracedTensor)>

fn solve(&self, b: &TracedTensor) -> Result<TracedTensor>

fn lstsq(&self, b: &TracedTensor) -> Result<TracedTensor>

fn full_piv_lu_solve(&self, b: &TracedTensor) -> Result<TracedTensor>

fn triangular_solve( &self, b: &TracedTensor, left_side: bool, lower: bool, transpose_a: bool, unit_diagonal: bool, ) -> Result<TracedTensor>

fn slogdet(&self) -> Result<(TracedTensor, TracedTensor)>

fn det(&self) -> Result<TracedTensor>

fn inv(&self) -> Result<TracedTensor>

fn eigvalsh(&self) -> Result<TracedTensor>

fn eigvals(&self) -> Result<TracedTensor>

fn pinv(&self) -> Result<TracedTensor>

fn pinv_with_rtol(&self, rtol: f64) -> Result<TracedTensor>

fn norm( &self, ord: Option<f64>, dim: Option<&[usize]>, keepdim: bool, ) -> Result<TracedTensor>

Implementors