Data.Matrix.Static.LinearAlgebra

Documentation

class Arithmetic (mat1 :: MatrixKind) (mat2 :: MatrixKind) where

Methods

(@@) :: (Numeric a, SingI n, SingI m, If (mat1 == mat2) mat1 Matrix ~ mat3) => mat1 n p Vector a -> mat2 p m Vector a -> mat3 n m Vector a infixr 8

Matrix multiplication

(%+%) :: (Numeric a, SingI n, SingI m, If (mat1 == mat2) mat1 Matrix ~ mat3) => mat1 n m Vector a -> mat2 n m Vector a -> mat3 n m Vector a infixr 8

(%-%) :: (Numeric a, SingI n, SingI m, If (mat1 == mat2) mat1 Matrix ~ mat3) => mat1 n m Vector a -> mat2 n m Vector a -> mat3 n m Vector a infixr 8

(%*%) :: (Numeric a, SingI n, SingI m, If (mat1 == mat2) mat1 SparseMatrix ~ mat3) => mat1 n m Vector a -> mat2 n m Vector a -> mat3 n m Vector a infixr 8

Instances

Arithmetic Matrix Matrix

Defined in Data.Matrix.Static.LinearAlgebra

Methods

(@@) :: (Numeric a, SingI n, SingI m, If (Matrix == Matrix) Matrix Matrix ~ mat3) => Matrix n p Vector a -> Matrix p m Vector a -> mat3 n m Vector a

(%+%) :: (Numeric a, SingI n, SingI m, If (Matrix == Matrix) Matrix Matrix ~ mat3) => Matrix n m Vector a -> Matrix n m Vector a -> mat3 n m Vector a

(%-%) :: (Numeric a, SingI n, SingI m, If (Matrix == Matrix) Matrix Matrix ~ mat3) => Matrix n m Vector a -> Matrix n m Vector a -> mat3 n m Vector a

(%*%) :: (Numeric a, SingI n, SingI m, If (Matrix == Matrix) Matrix SparseMatrix ~ mat3) => Matrix n m Vector a -> Matrix n m Vector a -> mat3 n m Vector a

Arithmetic Matrix SparseMatrix

Defined in Data.Matrix.Static.LinearAlgebra

Methods

(@@) :: (Numeric a, SingI n, SingI m, If (Matrix == SparseMatrix) Matrix Matrix ~ mat3) => Matrix n p Vector a -> SparseMatrix p m Vector a -> mat3 n m Vector a

(%+%) :: (Numeric a, SingI n, SingI m, If (Matrix == SparseMatrix) Matrix Matrix ~ mat3) => Matrix n m Vector a -> SparseMatrix n m Vector a -> mat3 n m Vector a

(%-%) :: (Numeric a, SingI n, SingI m, If (Matrix == SparseMatrix) Matrix Matrix ~ mat3) => Matrix n m Vector a -> SparseMatrix n m Vector a -> mat3 n m Vector a

(%*%) :: (Numeric a, SingI n, SingI m, If (Matrix == SparseMatrix) Matrix SparseMatrix ~ mat3) => Matrix n m Vector a -> SparseMatrix n m Vector a -> mat3 n m Vector a

Arithmetic SparseMatrix Matrix

Defined in Data.Matrix.Static.LinearAlgebra

Methods

(@@) :: (Numeric a, SingI n, SingI m, If (SparseMatrix == Matrix) SparseMatrix Matrix ~ mat3) => SparseMatrix n p Vector a -> Matrix p m Vector a -> mat3 n m Vector a

(%+%) :: (Numeric a, SingI n, SingI m, If (SparseMatrix == Matrix) SparseMatrix Matrix ~ mat3) => SparseMatrix n m Vector a -> Matrix n m Vector a -> mat3 n m Vector a

(%-%) :: (Numeric a, SingI n, SingI m, If (SparseMatrix == Matrix) SparseMatrix Matrix ~ mat3) => SparseMatrix n m Vector a -> Matrix n m Vector a -> mat3 n m Vector a

(%*%) :: (Numeric a, SingI n, SingI m, If (SparseMatrix == Matrix) SparseMatrix SparseMatrix ~ mat3) => SparseMatrix n m Vector a -> Matrix n m Vector a -> mat3 n m Vector a

Arithmetic SparseMatrix SparseMatrix

Defined in Data.Matrix.Static.LinearAlgebra

Methods

(@@) :: (Numeric a, SingI n, SingI m, If (SparseMatrix == SparseMatrix) SparseMatrix Matrix ~ mat3) => SparseMatrix n p Vector a -> SparseMatrix p m Vector a -> mat3 n m Vector a

(%+%) :: (Numeric a, SingI n, SingI m, If (SparseMatrix == SparseMatrix) SparseMatrix Matrix ~ mat3) => SparseMatrix n m Vector a -> SparseMatrix n m Vector a -> mat3 n m Vector a

(%-%) :: (Numeric a, SingI n, SingI m, If (SparseMatrix == SparseMatrix) SparseMatrix Matrix ~ mat3) => SparseMatrix n m Vector a -> SparseMatrix n m Vector a -> mat3 n m Vector a

(%*%) :: (Numeric a, SingI n, SingI m, If (SparseMatrix == SparseMatrix) SparseMatrix SparseMatrix ~ mat3) => SparseMatrix n m Vector a -> SparseMatrix n m Vector a -> mat3 n m Vector a

class Factorization mat where

Methods

inverse :: (SingI n, Numeric a) => mat n n Vector a -> mat n n Vector a

Matrix inverse

eigs :: (SingI k, SingI n, (k <= (n - 2)) ~ True) => Sing k -> mat n n Vector Double -> (Matrix k 1 (Complex Double), Matrix n k (Complex Double))

Eigenvalues (not ordered) and eigenvectors (as columns) of a general square matrix.

cholesky :: (Numeric a, SingI n) => mat n n Vector a -> mat n n Vector a

Cholesky decomposition

Instances

Factorization Matrix

Defined in Data.Matrix.Static.LinearAlgebra

Methods

inverse :: (SingI n, Numeric a) => Matrix n n Vector a -> Matrix n n Vector a

eigs :: (SingI k, SingI n, (k <= (n - 2)) ~ True) => Sing k -> Matrix n n Vector Double -> (Matrix0 k 1 (Complex Double), Matrix0 n k (Complex Double))

cholesky :: (Numeric a, SingI n) => Matrix n n Vector a -> Matrix n n Vector a

Factorization SparseMatrix

Defined in Data.Matrix.Static.LinearAlgebra

Methods

inverse :: (SingI n, Numeric a) => SparseMatrix n n Vector a -> SparseMatrix n n Vector a

eigs :: (SingI k, SingI n, (k <= (n - 2)) ~ True) => Sing k -> SparseMatrix n n Vector Double -> (Matrix k 1 (Complex Double), Matrix n k (Complex Double))

cholesky :: (Numeric a, SingI n) => SparseMatrix n n Vector a -> SparseMatrix n n Vector a

module Data.Matrix.Static.LinearAlgebra.Types