Math.Linear.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

squared 2-norm

L1 norm

Euclidean norm

Lp norm (p > 0)

infinity-norm

normalize w.r.t. p-norm (p finite)

Lp inner product (p > 0)

reciprocal

scale

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 (e.g. of which we can take the union and the intersection)

class Set f

IntMap implementation

Sparse Vector

data SpVector a

instances for SpVector

Create new sparse vector

fromListDenseSV

findWithDefault0IM

Outer vector product

Sparse Matrix

data SpMatrix a

Instances for SpMatrix

multiply matrix by a scalar

Frobenius norm (sqrt of trace of M^T M)

MATRIX METADATA

type Rows

type Cols

type IxRow

type IxCol

predicates

Non-zero elements in a row

bandwidth bounds (min, max)

SPARSE MATRIX BUILDERS

fromListDenseSM

Diagonal matrix

Identity matrix

Create Super- or sub- diagonal matrix

SUB-MATRICES

extractSubmatrixSM

Extract jth column

Extract ith row

MATRIX STACKING

MATRIX ELEMENT LOOKUP

MISC SpMatrix OPERATIONS

countSubdiagonalNZSM

extractDiagonalDSM

subdiagIndicesSM

sparsify : remove 0s (!!!)

ROUNDING operations (!!!)

ALGEBRAIC PRIMITIVE OPERATIONS

Matrix transpose

matrix action on a vector

Matrix-matrix product

Matrix-matrix product, sparsified (prunes all elements `x` for which `abs x <= eps`)

matMatSparsified

Predicates

Condition number

conditionNumberSM

Householder transformation

Givens rotation matrix

firstNonZeroColumn

QR decomposition

Eigenvalue algorithms

All eigenvalues using QR algorithm

One eigenvalue and corresponding eigenvector, using Rayleigh iteration

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

SVD

LINEAR SOLVERS : solve A x = b

CGS

data CGS

BiCSSTAB

LINEAR SOLVERS INTERFACE

data LinSolveMethod

PRETTY PRINTING

toDenseListClip

Pretty printer typeclass

class PrintDense a

normDiffConverged

type LB

type UB