Module linalg 

Linear algebra operations for sparse matrices

This module provides linear algebra operations for sparse matrices, including solvers, eigenvalue computations, and matrix functions.

Modules

lanczos

Lanczos algorithm for sparse matrix eigenvalue computation

power_iteration

Power iteration method for sparse matrix eigenvalue computation

Structs

AMGOptions

Options for the AMG preconditioner

AMGPreconditioner

AMG preconditioner implementation

ArpackOptions

BiCGOptions

Options for BiCG solver

BiCGSTABOptions

Options for BiCGSTAB solver

CGOptions

Options for conjugate gradient solver

CholeskyResult

Cholesky decomposition result

ConvolutionOperator

Convolution operator for matrix-free convolution operations

DiagonalOperator

Diagonal operator: D * x where D is a diagonal matrix

EigenResult

Result of an eigenvalue computation

EnhancedDiagonalOperator

Enhanced diagonal operator with SIMD and parallel acceleration

EnhancedDifferenceOperator

Enhanced difference operator with parallel acceleration

EnhancedOperatorOptions

Configuration for enhanced operators

EnhancedScaledOperator

Enhanced scaled operator with parallel acceleration

EnhancedSumOperator

Enhanced sum operator with parallel acceleration

FiniteDifferenceOperator

Finite difference operator for computing derivatives

GCROTOptions

Options for the GCROT solver

GCROTResult

Result from GCROT solver

GMRESOptions

Options for GMRES solver

IC0Preconditioner

Incomplete Cholesky factorization preconditioner (IC(0))

ICOptions

Options for incomplete Cholesky decomposition

ILU0Preconditioner

Incomplete LU factorization with zero fill-in (ILU(0))

ILUOptions

Options for incomplete LU decomposition

IdentityOperator

Identity operator: I * x = x

IterationResult

Result of an iterative solver

JacobiPreconditioner

Jacobi (diagonal) preconditioner

LDLTResult

LDLT decomposition result for symmetric indefinite matrices

LGMRESOptions

Options for the LGMRES solver

LGMRESResult

Result of the LGMRES solver

LSMROptions

Options for the LSMR solver

LSMRResult

Result from LSMR solver

LSQROptions

Options for the LSQR solver

LSQRResult

Result from LSQR solver

LUOptions

Options for LU decomposition

LUResult

LU decomposition result

LanczosOptions

Configuration options for the Lanczos algorithm

MINRESOptions

Options for MINRES solver

MINRESResult

Result of MINRES solver

PivotedCholeskyResult

Pivoted Cholesky decomposition result

PowerIterationOptions

Configuration options for the power iteration method

QMROptions

Options for QMR solver

QMRResult

Result of QMR solver

QRResult

QR decomposition result

SSORPreconditioner

Symmetric Successive Over-Relaxation (SSOR) preconditioner

SVDOptions

Options for SVD computation

SVDResult

Result of SVD computation

ScaledIdentityOperator

Scaled identity operator: (alpha * I) * x = alpha * x

SpaiOptions

Options for the SPAI preconditioner

SpaiPreconditioner

Sparse Approximate Inverse (SPAI) preconditioner

TFQMROptions

Options for the TFQMR solver

TFQMRResult

Result from TFQMR solver

Enums

BoundaryCondition

ConvolutionMode

CycleType

Cycle types for AMG

EigenvalueMethod

EigenvalueMode

InterpolationType

Interpolation methods for AMG

PivotingStrategy

Pivoting strategy for LU decomposition

SmootherType

Smoother types for AMG

Traits

AsLinearOperator

Convert a sparse matrix to a linear operator

IterativeSolver

Trait for iterative solvers

LinearOperator

Trait for representing a linear operator

Functions

add

Matrix addition

bicg

Biconjugate Gradient solver

bicgstab

BiConjugate Gradient Stabilized method

cg

Conjugate gradient solver for symmetric positive definite systems

cgs

Conjugate Gradient Squared solver (CGS)

cholesky_decomposition

Compute sparse Cholesky decomposition

condest

Estimate the condition number of a sparse matrix

condest_enhanced

Enhanced condition number estimation for sparse arrays

convolution_operator

Create a convolution operator

diag_matrix

Create a diagonal matrix

eigs

Find eigenvalues and eigenvectors of a general (non-symmetric) sparse matrix

eigsh

Find eigenvalues and eigenvectors of a symmetric matrix using the Lanczos algorithm

eigsh_generalized

Solve the generalized symmetric eigenvalue problem Ax = λBx

eigsh_generalized_enhanced

Enhanced generalized eigenvalue solver with additional features

eigsh_shift_invert

Find eigenvalues near a target value using shift-and-invert mode

eigsh_shift_invert_enhanced

Enhanced symmetric eigenvalue solver with additional features

enhanced_add

Create an enhanced sum operator

enhanced_diagonal

Create utility functions for enhanced operators Create an enhanced diagonal operator

enhanced_scale

Create an enhanced scaled operator

enhanced_subtract

Create an enhanced difference operator

expm

Compute the matrix exponential using scaling and squaring with Padé approximation

expm_multiply

Compute the action of the matrix exponential on a vector: y = exp(t*A) * v

eye

Create an identity matrix

finite_difference_operator

Create a finite difference operator

gcrot

Generalized Conjugate Residual with Orthogonalization and Truncation method

gmres

Generalized Minimal Residual Method

incomplete_cholesky

Compute incomplete Cholesky decomposition (IC)

incomplete_lu

Compute incomplete LU decomposition (ILU)

inv

Matrix inverse

lanczos

Computes the extreme eigenvalues and corresponding eigenvectors of a symmetric matrix using the Lanczos algorithm.

ldlt_decomposition

Compute LDLT decomposition for symmetric indefinite matrices

lgmres

Solve A*x = b using the LGMRES method

lsmr

LSMR algorithm for sparse least squares problems

lsqr

LSQR algorithm for sparse least squares problems

lu_decomposition

Compute sparse LU decomposition with partial pivoting (backward compatibility)

lu_decomposition_with_options

Compute sparse LU decomposition with enhanced pivoting strategies

matmul

Matrix multiplication

matrix_power

Matrix power

minres

MINRES solver for symmetric indefinite systems

multiply

Element-wise multiplication (Hadamard product)

norm

Compute matrix norm

onenormest

Estimate the 1-norm of a sparse matrix using a randomized algorithm

onenormest_enhanced

Enhanced 1-norm estimation for sparse arrays

pivoted_cholesky_decomposition

Compute pivoted Cholesky decomposition

power_iteration

Computes the largest eigenvalue and corresponding eigenvector of a symmetric matrix using the power iteration method.

qmr

QMR (Quasi-Minimal Residual) solver for non-symmetric systems

qr_decomposition

Compute sparse QR decomposition using Givens rotations

sparse_direct_solve

Solve a sparse linear system using direct methods

sparse_lstsq

Solve a least squares problem

spsolve

Solve a sparse linear system Ax = b

svd_truncated

Compute truncated SVD using a specific method and parameters

svds

Compute the truncated SVD of a sparse matrix

tfqmr

Transpose-Free Quasi-Minimal Residual method

twonormest

Estimate the 2-norm (spectral norm) of a sparse matrix using power iteration

twonormest_enhanced

Enhanced 2-norm estimation for sparse arrays using power iteration

Type Aliases

BiCGSTABResult

Result from BiCGSTAB solver

CGSOptions

Options for CGS solver

CGSResult