Trait linxal::prelude::LinxalMatrix [−] [src]

pub trait LinxalMatrix<F: LinxalScalar> {
    fn eigenvalues(&self) -> Result<Array<F::Complex, Ix1>, EigenError>;
    fn eigenvalues_vectors(
        &self, 
        compute_left: bool, 
        compute_right: bool
    ) -> Result<Solution<F, F::Complex>, EigenError>;
    fn symmetric_eigenvalues(
        &self, 
        uplo: Symmetric
    ) -> Result<Array<F::RealPart, Ix1>, EigenError>;
    fn symmetric_eigenvalues_vectors(
        &self, 
        uplo: Symmetric
    ) -> Result<Solution<F, F::RealPart>, EigenError>;
    fn solve_linear<D1: Data<Elem = F>>(
        &self, 
        b: &ArrayBase<D1, Ix1>
    ) -> Result<Array<F, Ix1>, SolveError>;
    fn solve_symmetric_linear<D1: Data<Elem = F>>(
        &self, 
        b: &ArrayBase<D1, Ix1>, 
        uplo: Symmetric
    ) -> Result<Array<F, Ix1>, SolveError>;
    fn solve_multi_linear<D1: Data<Elem = F>>(
        &self, 
        b: &ArrayBase<D1, Ix2>
    ) -> Result<Array<F, Ix2>, SolveError>;
    fn solve_symmetric_multi_linear<D1: Data<Elem = F>>(
        &self, 
        b: &ArrayBase<D1, Ix2>, 
        uplo: Symmetric
    ) -> Result<Array<F, Ix2>, SolveError>;
    fn least_squares<D1, PT>(
        &self, 
        b: &ArrayBase<D1, Ix1>, 
        problem_type: PT
    ) -> Result<LeastSquaresSolution<F, Ix1>, LeastSquaresError>
    where
        D1: Data<Elem = F>,
        PT: Into<Option<LeastSquaresType>>;
    fn multi_least_squares<D1, PT>(
        &self, 
        b: &ArrayBase<D1, Ix2>, 
        problem_type: PT
    ) -> Result<LeastSquaresSolution<F, Ix2>, LeastSquaresError>
    where
        D1: Data<Elem = F>,
        PT: Into<Option<LeastSquaresType>>;
    fn qr(&self) -> Result<QRFactors<F>, QRError>;
    fn lu(&self) -> Result<LUFactors<F>, LUError>;
    fn cholesky(&self, uplo: Symmetric) -> Result<Array<F, Ix2>, CholeskyError>;
    fn svd_full(&self) -> Result<SVDSolution<F>, SVDError>;
    fn svd_econ(&self) -> Result<SVDSolution<F>, SVDError>;
    fn singular_values(&self) -> Result<Array<F::RealPart, Ix1>, SVDError>;
    fn inverse(&self) -> Result<Array<F, Ix2>, Error>;
    fn conj(&self) -> Array<F, Ix2>;
    fn conj_t(&self) -> Array<F, Ix2>;
    fn is_square(&self) -> bool;
    fn is_identity<T: Into<Option<F::RealPart>>>(&self, tolerance: T) -> bool;
    fn is_diagonal<T: Into<Option<F::RealPart>>>(&self, tolerance: T) -> bool;
    fn is_symmetric<T: Into<Option<F::RealPart>>>(&self, tolerance: T) -> bool;
    fn is_unitary<T: Into<Option<F::RealPart>>>(&self, tolerance: T) -> bool;
    fn is_triangular<T: Into<Option<F::RealPart>>>(
        &self, 
        uplo: Symmetric, 
        tolerance: T
    ) -> bool;
}

All-encompassing matrix trait, supporting all of the linear algebra operations defined for any LinxalScalar.

Required Methods

Compute the eigenvalues of a matrix.

Compute the eigenvalues and eigenvectors of a matrix.

Compute the eigenvalues of a symmetric matrix.

Compute the eigenvalues and eigenvectors of a symmetric matrix.

Solve a single system of linear equations.

Solve a single system of linear equations with a symmetrix coefficient matrix.

Solve a system of linear equations with multiple RHS vectors.

Solve a system of linear equations with a symmetrix coefficient matrix for multiple RHS vectors.

Each column of b is a RHS vector to be solved for.

Compute the least squares solution for a single RHS.

Compute the least squares solution for a multiple RHS.

Return the QR factorization of the matrix.

See QR::compute.

Return the LU factorization of the matrix.

See LU::compute

Return the cholesky factorization of the matrix, via the upper- or lower-triangular matrix defining it.

Return the full singular value decomposition of the matrix.

The SVDSolution contains full size matrices u (m x m) and vt (n x n).

Return the economic singular value decomposition of the matrix.

The SVDSolution contains sufficient matrices u (m x p) and vt (p x n), where p is the minimum of m and n.

Return the full singular value decomposition of the matrix.

The SVDSolution contains full size matrices u (m x m) and vt (n x n).

Return the inverse of the matrix, if it has one.

Return the conjugate of the matrix.

Return the cojugate transpose of the matrix.

Returns true iff the matrix is square.

Returns true iff the matrix is the identity matrix, within an optional tolerance.

Returns true iff the matrix is diagnoal, within a certain tolerance.

Returns true iff the matrix is symmetric (or Hermitian, in the complex case), within an optional tolerance.

Returns true iff the matrix is unitary, within an optional tolerance.

Returns true iff the matrix is triangular or trapezoidal, with size specified by uplo.

Implementors