scirs2_series::gpu_acceleration::ndarray::compat

Crate ndarray_linalg

Expand description

The ndarray-linalg crate provides linear algebra functionalities for ArrayBase, the n-dimensional array data structure provided by ndarray.

ndarray-linalg leverages LAPACK’s routines using the bindings provided by blas-lapack-rs/lapack.

§Linear algebra methods

§Naming Convention

Each routine is usually exposed as a trait, implemented by the relevant types.

For each routine there might be multiple “variants”: different traits corresponding to the different ownership possibilities of the array you intend to work on.

For example, if you are interested in the QR decomposition of a square matrix, you can use:

QRSquare, if you hold an immutable reference (i.e. &self) to the matrix you want to decompose;
QRSquareInplace, if you hold a mutable reference (i.e. &mut self) to the matrix you want to decompose;
QRSquareInto, if you can pass the matrix you want to decompose by value (e.g. self).

Depending on the algorithm, each variant might require more or less copy operations of the underlying data.

Details are provided in the description of each routine.

§Utilities

Modules§

assert: Assertions for array
cholesky: Cholesky decomposition of Hermitian (or real symmetric) positive definite matrices
convert: utilities for convert array
diagonal: Vector as a Diagonal matrix
eig: Eigenvalue decomposition for non-symmetric square matrices
eigh: Eigendecomposition for Hermitian matrices.
error: Define Errors
generate: Generator functions for matrices
inner
krylov: Krylov subspace methods
layout: Convert ndarray into LAPACK-compatible matrix format
least_squares: Least Squares
lobpcg
norm: Norm of vectors
operator: Linear operator algebra
opnorm: Operator norm
qr: QR decomposition
solve: Solve systems of linear equations and invert matrices
solveh: Solve Hermitian (or real symmetric) linear problems and invert Hermitian (or real symmetric) matrices
svd: Singular-value decomposition (SVD)
svddc: Singular-value decomposition (SVD) by divide-and-conquer (?gesdd)
trace: Trace calculation
triangular: Methods for triangular matrices
tridiagonal: Vectors as a Tridiagonal matrix & Methods for tridiagonal matrices
types: Basic types and their methods for linear algebra

Macros§

assert_aclose
assert_close_l1
assert_close_l2
assert_close_max
assert_rclose

Structs§

BKFactorized: Represents the Bunch–Kaufman factorization of a Hermitian (or real symmetric) matrix as A = P * U * D * U^H * P^T.
CholeskyFactorized: Cholesky decomposition of Hermitian (or real symmetric) positive definite matrix
Diagonal: Vector as a Diagonal matrix
LUFactorized: Represents the LU factorization of a matrix A as A = P*L*U.
LUFactorizedTridiagonal: Represents the LU factorization of a tridiagonal matrix A as A = P*L*U.
LeastSquaresResult: Result of a LeastSquares computation
Tridiagonal: Represents a tridiagonal matrix as 3 one-dimensional vectors.
TruncatedEig: Truncated eigenproblem solver
TruncatedSvd: Truncated singular value decomposition

Enums§

Diag: Specify whether input triangular matrix is unit or not
JobSvd: Specifies how many singular vectors are computed
MatrixLayout
NormType
NormalizeAxis
Transpose
TruncatedOrder: Find largest or smallest eigenvalues
UPLO: Upper/Lower specification for seveal usages

Traits§

AllocatedArray
AllocatedArrayMut
AsDiagonal
Cholesky: Cholesky decomposition of Hermitian (or real symmetric) positive definite matrix reference
CholeskyInplace: Cholesky decomposition of Hermitian (or real symmetric) positive definite mutable reference of matrix
CholeskyInto: Cholesky decomposition of Hermitian (or real symmetric) positive definite matrix
Determinant: An interface for calculating determinants of matrix refs.
DeterminantC: Determinant of Hermitian (or real symmetric) positive definite matrix ref
DeterminantCInto: Determinant of Hermitian (or real symmetric) positive definite matrix
DeterminantH: An interface for calculating determinants of Hermitian (or real symmetric) matrix refs.
DeterminantHInto: An interface for calculating determinants of Hermitian (or real symmetric) matrices.
DeterminantInto: An interface for calculating determinants of matrices.
DeterminantTridiagonal: An interface for calculating determinants of tridiagonal matrix refs.
Eig: Eigenvalue decomposition of general matrix reference
EigVals: Calculate eigenvalues without eigenvectors
EigValsh: Calculate eigenvalues without eigenvectors
EigValshInplace: Calculate eigenvalues without eigenvectors
EigValshInto: Calculate eigenvalues without eigenvectors
Eigh: Eigenvalue decomposition of Hermite matrix reference
EighInplace: Eigenvalue decomposition of mutable reference of Hermite matrix
EighInto: Eigenvalue decomposition of Hermite matrix
ExtractTridiagonal: An interface for making a Tridiagonal struct.
Factorize: An interface for computing LU factorizations of matrix refs.
FactorizeC: Cholesky decomposition of Hermitian (or real symmetric) positive definite matrix reference
FactorizeCInto: Cholesky decomposition of Hermitian (or real symmetric) positive definite matrix
FactorizeH: An interface for computing the Bunch–Kaufman factorization of Hermitian (or real symmetric) matrix refs.
FactorizeHInto: An interface for computing the Bunch–Kaufman factorization of Hermitian (or real symmetric) matrices.
FactorizeInto: An interface for computing LU factorizations of matrices.
FactorizeTridiagonal: An interface for computing LU factorizations of tridiagonal matrix refs.
FactorizeTridiagonalInto: An interface for computing LU factorizations of tridiagonal matrices.
InnerProduct: Inner Product
IntoDiagonal
IntoTriangular
Inverse: An interface for inverting matrix refs.
InverseC: Inverse of Hermitian (or real symmetric) positive definite matrix ref
InverseCInto: Inverse of Hermitian (or real symmetric) positive definite matrix
InverseH: An interface for inverting Hermitian (or real symmetric) matrix refs.
InverseHInto: An interface for inverting Hermitian (or real symmetric) matrices.
InverseInto: An interface for inverting matrices.
Lapack: Trait for primitive types which implements LAPACK subroutines
LeastSquaresSvd: Solve least squares for immutable references
LeastSquaresSvdInPlace: Solve least squares for mutable references, overwriting the input fields in the process
LeastSquaresSvdInto: Solve least squares for owned matrices
LinearOperator: Abstracted linear operator as an action to vector (ArrayBase<S, Ix1>) and matrix (ArrayBase<S, Ix2)
Norm: Define norm as a metric linear space (not as a matrix)
OperationNorm: Operator norm using *lange LAPACK routines
QR: QR decomposition for matrix reference
QRInto: QR decomposition
QRSquare: QR decomposition for square matrix reference
QRSquareInplace: QR decomposition for mutable reference of square matrix
QRSquareInto: QR decomposition for square matrix
ReciprocalConditionNum: An interface for estimating the reciprocal condition number of matrix refs.
ReciprocalConditionNumInto: An interface for estimating the reciprocal condition number of matrices.
ReciprocalConditionNumTridiagonal: An interface for estimating the reciprocal condition number of tridiagonal matrix refs.
ReciprocalConditionNumTridiagonalInto: An interface for estimating the reciprocal condition number of tridiagonal matrices.
SVD: singular-value decomposition of matrix reference
SVDDC: Singular-value decomposition of matrix (copying) by divide-and-conquer
SVDDCInplace: Singular-value decomposition of matrix reference by divide-and-conquer
SVDDCInto: Singular-value decomposition of matrix by divide-and-conquer
SVDInplace: singular-value decomposition for mutable reference of matrix
SVDInto: singular-value decomposition
Scalar
Solve: An interface for solving systems of linear equations.
SolveC: Solve systems of linear equations with Hermitian (or real symmetric) positive definite coefficient matrices
SolveH: An interface for solving systems of Hermitian (or real symmetric) linear equations.
SolveTriangular: solve a triangular system with upper triangular matrix
SolveTriangularInplace: solve a triangular system with upper triangular matrix
SolveTriangularInto: solve a triangular system with upper triangular matrix
SolveTridiagonal
SolveTridiagonalInplace
SymmetricSqrt: Calculate symmetric square-root matrix using eigh
SymmetricSqrtInto: Calculate symmetric square-root matrix using eigh
Trace

Functions§

aclose: check two values are close in terms of the absolute tolerance
close_l1: check two arrays are close in L1 norm
close_l2: check two arrays are close in L2 norm
close_max: check two arrays are close in maximum norm
conjugate: Hermite conjugate matrix
flatten
from_diag: construct matrix from diag
generalize
hstack: stack vectors into matrix horizontally
into_col
into_matrix
into_row
normalize: normalize in L2 norm
random: Generate random array with given shape
random_hermite: Random Hermite matrix
random_hermite_using: Random Hermite matrix with given RNG
random_hpd: Random Hermite Positive-definite matrix
random_hpd_using: Random Hermite Positive-definite matrix with given RNG
random_regular: Generate random regular matrix
random_regular_using: Generate random regular matrix with given RNG
random_unitary: Generate random unitary matrix using QR decomposition
random_unitary_using: Generate random unitary matrix using QR decomposition with given RNG
random_using: Generate random array with given RNG
rclose: check two values are close in terms of the relative tolerance
replicate
transpose_data
vstack: stack vectors into matrix vertically

Type Aliases§

Pivot
c32: Alias for a Complex<f32>
c64: Alias for a Complex<f64>