Sparse Matrices
Sparse matrix creation, manipulation, and iterative solvers.
amd
Approximate Minimum Degree ordering.
amd(A: NDArray) → r
bicg
BiCG solver for general nonsymmetric systems.
bicg(A: NDArray, b: NDArray) → r
bicgstab
BiCGSTAB solver for general nonsymmetric systems.
bicgstab(A: NDArray, b: NDArray) → r
cgs
CGS solver for general nonsymmetric systems.
cgs(A: NDArray, b: NDArray) → r
colamd
Column Approximate Minimum Degree ordering.
colamd(A: NDArray) → r
eigs
Compute k largest eigenvalues.
eigs(A: NDArray, k: Int64) → r
etree
Elimination tree of a sparse matrix.
etree(A: NDArray) → r
find
Find nonzero elements. Returns [i, j, v] triplets.
find(S: NDArray) → r
full
Convert sparse to dense matrix.
full(S: NDArray) → r
gmres
GMRES solver for general nonsymmetric systems.
gmres(A: NDArray, b: NDArray) → r
ichol
Incomplete Cholesky factorization.
ichol(A: NDArray) → r
ilu
Incomplete LU factorization.
ilu(A: NDArray) → r
issparse
Test if matrix is sparse.
issparse(S: NDArray) → r
lsqr
LSQR solver for least-squares problems.
lsqr(A: NDArray, b: NDArray) → r
minres
MINRES solver for symmetric indefinite systems.
minres(A: NDArray, b: NDArray) → r
nnz
Count nonzero elements.
nnz(S: NDArray) → r
nonzeros
Extract nonzero values as column vector.
nonzeros(S: NDArray) → r
nzmax
Allocated storage size (equals nnz).
nzmax(S: NDArray) → r
pcg
PCG solver for symmetric positive definite systems.
pcg(A: NDArray, b: NDArray) → r
spadd
Sparse addition: C = A + B.
spadd(A: NDArray, B: NDArray) → r
spalloc
Pre-allocate an empty sparse matrix.
spalloc(m: Int64, n: Int64, nz: Int64) → r
sparse
Convert a dense matrix to sparse CSR format.
sparse(A: NDArray) → r
spchol
Sparse Cholesky factorization (A must be SPD).
spchol(A: NDArray) → r
spconvert
Convert [i, j, v] row data to sparse (1-based indices).
spconvert(D: NDArray) → r
spdiags
Build sparse matrix from diagonals.
spdiags(B: NDArray, d: NDArray, m: Int64, n: Int64) → r
speye
Create a sparse identity matrix.
speye(n: Int64) → r
splu
Sparse LU factorization with partial pivoting.
splu(A: NDArray) → r
spmm
Sparse matrix multiply: C = A * B.
spmm(A: NDArray, B: NDArray) → r
spones
Replace all nonzero values with 1.
spones(S: NDArray) → r
spparms
Compatibility stub.
spparms() → r
sprand
Random sparse matrix with uniform [0,1) values.
sprand(m: Int64, n: Int64, d: Float64) → r
sprandn
Random sparse matrix with standard normal values.
sprandn(m: Int64, n: Int64, d: Float64) → r
sprandsym
Random symmetric sparse matrix.
sprandsym(n: Int64, d: Float64) → r
sprank
Compute structural rank.
sprank(A: NDArray) → r
spsolve
Sparse solve: x = A\b
spsolve(A: NDArray, b: NDArray) → r
sptrans
Sparse matrix transpose.
sptrans(A: NDArray) → r
spy
Sparsity pattern visualization (returns boolean matrix).
spy(S: NDArray) → r
svds
Compute k largest singular values.
svds(A: NDArray, k: Int64) → r
symrcm
Symmetric Reverse Cuthill-McKee ordering.
symrcm(A: NDArray) → r
tfqmr
TFQMR solver (transpose-free quasi-minimal residual).
tfqmr(A: NDArray, b: NDArray) → r