Module functions 

Auto-generated module

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Functions

arnoldi

Arnoldi iteration: build an orthonormal Krylov basis for A.

backward_substitution

Backward substitution: solve U x = b where U is upper triangular (CSR).

banded_matrix

Build a CSR matrix from a banded stencil.

bicgstab_solve

Biconjugate Gradient Stabilised (BICGStab) solver for non-symmetric systems A x = b.

cg_solve

Conjugate Gradient solver for symmetric positive-definite systems A x = b.

col_scale

Column-scale a CSR matrix: A D_c where D_c = diag(scales).

coo_to_csr

Convert COO (coordinate format) triplets directly to CSR.

diagonal_preconditioner

Build a diagonal (Jacobi) preconditioner: returns 1 / a_ii for each i.

equilibration_scales

Two-sided equilibration scaling: compute row/col scale vectors so that the scaled matrix has unit diagonal (i.e., sqrt(|A_ii|) scaling).

forward_substitution

Forward substitution: solve L x = b where L is lower triangular (CSR).

gauss_seidel_solve

Gauss-Seidel iterative solver for A x = b.

identity_csr

Return the n×n identity matrix in CSR format.

jacobi_scale

Diagonal (Jacobi) scaling: return D^{-1} A where D = diag(A).

jacobi_solve

Jacobi iterative solver.

lanczos

Lanczos iteration: build a tridiagonal approximation of a symmetric matrix A.

laplacian_1d

1-D finite-difference Laplacian on n interior nodes.

laplacian_2d

2-D finite-difference Laplacian on an nx × ny grid (5-point stencil).

lower_triangular

Extract the lower triangular part of a sparse matrix (including diagonal).

minres_solve

Minimum Residual (MINRES) method for symmetric (possibly indefinite) systems A x = b.

multi_rhs_cg

Solve A X = B for multiple right-hand sides simultaneously using CG.

pcg_solve

Preconditioned Conjugate Gradient solver.

ritz_values

Compute Ritz values from a Lanczos tridiagonal matrix via QR iteration.

row_scale

Row-scale a CSR matrix: D_r A where D_r = diag(scales).

saddle_point_solve

Solve the saddle-point system: [ A B^T ] [ x ] [ f ] [ B 0 ] [ p ] = [ g ]

sor_solve

Successive Over-Relaxation (SOR) solver. Use omega = 1 for Gauss-Seidel.

sparse_eig_power

Compute the dominant eigenvalue and eigenvector of a sparse matrix using the power method.

sparse_eig_smallest

Compute the smallest eigenvalue of a sparse SPD matrix using inverse iteration (shift-and-invert with the ILU preconditioner).

spectral_radius_estimate

Estimate the spectral radius (largest singular value approximation) via the power method applied to A^T A.

spgemm

Sparse-sparse matrix multiply: C = A * B.