hmatrix-static-0.3: hmatrix with vector and matrix sizes encoded in types Source code Contents Index

Numeric.LinearAlgebra.Static.Algorithms Portability portable Stability experimental Maintainer Reiner Pope <reiner.pope@gmail.com>

Contents Type hints Multiplication Concatenating Solving / inverting Determinant / rank / condition number Eigensystems Factorisations SVD QR Cholesky Hessenberg Schur LU Matrix functions Nullspace Norms Misc

Description

Common operations.

Synopsis

matT :: Matrix s t -> a vecT :: Vector s t -> a doubleT :: a s Double -> x complexT :: a s (Complex Double) -> x class Mul a b where type MulResult a b :: * -> * (<>) :: Field t => a t -> b t -> MulResult a b t (<.>) :: Field t => Vector n t -> Vector n t -> t (<->) :: (JoinableV a b, Element t) => a t -> b t -> Matrix (JoinShapeV a b) t (<|>) :: (JoinableH a b, Element t) => a t -> b t -> Matrix (JoinShapeH a b) t (<\>) :: Field t => Matrix (m, n) t -> Vector m t -> Vector n t linearSolve :: Field t => Matrix (m, m) t -> Matrix (m, n) t -> Matrix (m, n) t inv :: Field t => Matrix (m, m) t -> Matrix (m, m) t pinv :: Field t => Matrix (m, n) t -> Matrix (n, m) t det :: Field t => Matrix (m, m) t -> t rank :: Field t => Matrix (m, n) t -> Int rcond :: Field t => Matrix (m, n) t -> Double eig :: Field t => Matrix (m, m) t -> (Vector m (Complex Double), Matrix (m, m) (Complex Double)) eigSH :: Field t => Matrix (m, m) t -> (Vector m Double, Matrix (m, m) t) svd :: Field t => Matrix (m, n) t -> (Matrix (m, m) t, Vector (Min m n) Double, Matrix (n, n) t) fullSVD :: Field t => Matrix mn t -> (Matrix (m, m) t, Matrix (m, n) Double, Matrix (n, n) t) economySVDU :: Field t => Matrix (m, n) t -> (Matrix (m, Unknown) t, Vector Unknown Double, Matrix (n, Unknown) t) qr :: Field t => Matrix (m, n) t -> (Matrix (m, m) t, Matrix (m, n) t) chol :: Field t => Matrix (m, m) t -> Matrix (m, m) t hess :: Field t => Matrix (m, m) t -> (Matrix (m, m) t, Matrix (m, m) t) schur :: Field t => Matrix (m, m) t -> (Matrix (m, m) t, Matrix (m, m) t) lu :: Field t => Matrix (m, n) t -> (Matrix (m, Min m n) t, Matrix (Min m n, n) t, Matrix (m, m) t, t) luPacked :: Field t => Matrix (m, n) t -> (Matrix (m, n) t, [Int]) luSolve :: Field t => (Matrix (m, n) t, [Int]) -> Matrix (m, p) t -> Matrix (n, p) t expm :: Field t => Matrix (m, m) t -> Matrix (m, m) t sqrtm :: Field t => Matrix (m, m) t -> Matrix (m, m) t matFunc :: Field t => (Complex Double -> Complex Double) -> Matrix (m, m) t -> Matrix (m, m) (Complex Double) nullspacePrec :: Field t => Double -> Matrix (m, n) t -> [Vector n t] nullVector :: Field t => Matrix (m, n) t -> Vector n t pnorm NormType (Infinity, PNorm1, PNorm2) ctrans :: Field t => Matrix (m, n) t -> Matrix (n, m) t eps :: Double i :: Complex Double outer :: Field t => Vector m t -> Vector n t -> Matrix (m, n) t kronecker :: Field t => Matrix (m, n) t -> Matrix (p, q) t -> Matrix (m :*: p, n :*: q) t

Type hints

matT :: Matrix s t -> a Source

vecT :: Vector s t -> a Source

doubleT :: a s Double -> x Source

complexT :: a s (Complex Double) -> x Source

Multiplication

class Mul a b where Source

Associated Types type MulResult a b :: * -> * Source Methods (<>) :: Field t => a t -> b t -> MulResult a b t Source Overloaded matrix-matrix, matrix-vector, or vector-matrix product. The instances have type equalities to improve the quality of type inference. Instances n ~ n' => Mul (Matrix ((,) m n)) (Vector n') n ~ n' => Mul (Matrix ((,) m n)) (Vector n') n ~ n' => Mul (Matrix ((,) m n)) (Matrix ((,) n' p)) m ~ m' => Mul (Vector m) (Matrix ((,) m' n)) m ~ m' => Mul (Vector m) (Matrix ((,) m' n))

(<.>) :: Field t => Vector n t -> Vector n t -> t Source

Dot product

Concatenating

(<->) :: (JoinableV a b, Element t) => a t -> b t -> Matrix (JoinShapeV a b) t Source

Overloaded matrix-matrix, matrix-vector, vector-matrix, or vector-vector vertical concatenation. The instances have type equalities to improve the quality of type inference.

(<|>) :: (JoinableH a b, Element t) => a t -> b t -> Matrix (JoinShapeH a b) t Source

Overloaded matrix-matrix, matrix-vector, vector-matrix, or vector-vector horizontal concatenation. The instances have type equalities to improve the quality of type inference.

Solving / inverting

(<\>) :: Field t => Matrix (m, n) t -> Vector m t -> Vector n t Source

Least squares solution of a linear equation.

linearSolve :: Field t => Matrix (m, m) t -> Matrix (m, n) t -> Matrix (m, n) t Source

inv :: Field t => Matrix (m, m) t -> Matrix (m, m) t Source

pinv :: Field t => Matrix (m, n) t -> Matrix (n, m) t Source

Determinant / rank / condition number

det :: Field t => Matrix (m, m) t -> t Source

rank :: Field t => Matrix (m, n) t -> Int Source

rcond :: Field t => Matrix (m, n) t -> Double Source

Eigensystems

eig :: Field t => Matrix (m, m) t -> (Vector m (Complex Double), Matrix (m, m) (Complex Double)) Source

eigSH :: Field t => Matrix (m, m) t -> (Vector m Double, Matrix (m, m) t) Source

Factorisations

SVD

svd :: Field t => Matrix (m, n) t -> (Matrix (m, m) t, Vector (Min m n) Double, Matrix (n, n) t) Source

fullSVD :: Field t => Matrix mn t -> (Matrix (m, m) t, Matrix (m, n) Double, Matrix (n, n) t) Source

economySVDU :: Field t => Matrix (m, n) t -> (Matrix (m, Unknown) t, Vector Unknown Double, Matrix (n, Unknown) t) Source

QR

qr :: Field t => Matrix (m, n) t -> (Matrix (m, m) t, Matrix (m, n) t) Source

Cholesky

chol :: Field t => Matrix (m, m) t -> Matrix (m, m) t Source

Hessenberg

hess :: Field t => Matrix (m, m) t -> (Matrix (m, m) t, Matrix (m, m) t) Source

Schur

schur :: Field t => Matrix (m, m) t -> (Matrix (m, m) t, Matrix (m, m) t) Source

LU

lu :: Field t => Matrix (m, n) t -> (Matrix (m, Min m n) t, Matrix (Min m n, n) t, Matrix (m, m) t, t) Source

luPacked :: Field t => Matrix (m, n) t -> (Matrix (m, n) t, [Int]) Source

luSolve :: Field t => (Matrix (m, n) t, [Int]) -> Matrix (m, p) t -> Matrix (n, p) t Source

Matrix functions

expm :: Field t => Matrix (m, m) t -> Matrix (m, m) t Source

sqrtm :: Field t => Matrix (m, m) t -> Matrix (m, m) t Source

matFunc :: Field t => (Complex Double -> Complex Double) -> Matrix (m, m) t -> Matrix (m, m) (Complex Double) Source

Nullspace

nullspacePrec :: Field t => Double -> Matrix (m, n) t -> [Vector n t] Source

nullVector :: Field t => Matrix (m, n) t -> Vector n t Source

Norms

pnorm

NormType (Infinity, PNorm1, PNorm2)

Misc

ctrans :: Field t => Matrix (m, n) t -> Matrix (n, m) t Source

eps :: Double Source

i :: Complex Double Source

outer :: Field t => Vector m t -> Vector n t -> Matrix (m, n) t Source

kronecker :: Field t => Matrix (m, n) t -> Matrix (p, q) t -> Matrix (m :*: p, n :*: q) t Source

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