Module linalg

Expand description

Linear algebra operations for sparse matrices

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

Structs§

BiCGOptions: Options for BiCG solver
BiCGSTABOptions: Options for BiCGSTAB solver
CGOptions: Options for conjugate gradient solver
DiagonalOperator: Diagonal operator: D * x where D is a diagonal matrix
GMRESOptions: Options for GMRES solver
IC0Preconditioner: Incomplete Cholesky factorization preconditioner (IC(0))
ILU0Preconditioner: Incomplete LU factorization with zero fill-in (ILU(0))
IdentityOperator: Identity operator: I * x = x
IterationResult: Result of an iterative solver
JacobiPreconditioner: Jacobi (diagonal) preconditioner
LGMRESOptions: Options for the LGMRES solver
LGMRESResult: Result of the LGMRES solver
MINRESOptions: Options for MINRES solver
MINRESResult: Result of MINRES solver
QMROptions: Options for QMR solver
QMRResult: Result of QMR solver
SSORPreconditioner: Symmetric Successive Over-Relaxation (SSOR) preconditioner
ScaledIdentityOperator: Scaled identity operator: (alpha * I) * x = alpha * x
SpaiOptions: Options for the SPAI preconditioner
SpaiPreconditioner: Sparse Approximate Inverse (SPAI) preconditioner

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)
diag_matrix: Create a diagonal matrix
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
gmres: Generalized Minimal Residual Method
inv: Matrix inverse
lgmres: Solve A*x = b using the LGMRES method
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
qmr: QMR (Quasi-Minimal Residual) solver for non-symmetric systems
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