Numeric.LinearAlgebra.Sparse

Additive ring

class Additive f

Vector space

class VectorSpace f

Hilbert space (inner product)

class Hilbert f

Normed vector space

class Normed f

Norms and related results

FiniteDim : finite-dimensional objects

class FiniteDim f

HasData : accessing inner data (do not export)

class HasData f a

Sparse : sparse datastructures

class Sparse f a

Set : things that behave as sets

class Set f

Sparse Vector

data SpVector a

Creation

fromListDenseSV

Element insertion

fromList

toList

Lookup

Sub-vectors

Outer vector product

Sparse Matrix

data SpMatrix a

Creation

Diagonal matrix

Identity matrix

Super- or sub- diagonal matrix

Element insertion

fromList

fromListDenseSM

toList

Lookup

type Rows

type Cols

type IxRow

type IxCol

Predicates

Matrix data and metadata

Non-zero elements in a row

Bandwidth bounds (min, max)

Sub-matrices

extractSubmatrixSM

Extract j'th column

Extract i'th row

Matrix stacking

Misc. SpMatrix operations

countSubdiagonalNZSM

extractDiagonalDSM

subdiagIndicesSM

Sparsify : remove almost-0 elements (i.e. if |x| < eps)

Value rounding

Primitive algebra operations

Matrix transpose

Multiply matrix by a scalar

Frobenius norm

Matrix action on a vector

Matrix-matrix product

Matrix-matrix product, sparsified

matMatSparsified

Sparsified matrix products of two matrices

Matrix condition number

conditionNumberSM

Householder transformation

Givens rotation matrix

firstNonZeroColumn

QR decomposition

Eigenvalue algorithms

All eigenvalues (QR algorithm)

One eigenvalue and eigenvector (Rayleigh iteration)

Householder vector (G & VL Alg. 5.1.1, function `house`)

SVD

Iterative linear solvers

CGS

data CGS

BiCSSTAB

Linear solver interface

data LinSolveMethod

Control primitives for bounded iteration with convergence check

normDiffConverged

Rounding operations

Random matrices and vectors

Pretty printing

toDenseListClip

Pretty printer typeclass

class PrintDense a

Misc. utilities

Bounds checking

type LB

type UB