Numeric.Matrix

Documentation

class MatrixTranspose t (n :: k) (m :: k) where

Minimal complete definition

transpose

Methods

transpose :: Matrix t n m -> Matrix t m n

Transpose Mat

class SquareMatrix t (n :: Nat) where

Minimal complete definition

eye, diag, trace

Methods

eye :: Matrix t n n

Mat with 1 on diagonal and 0 elsewhere

diag :: Scalar t -> Matrix t n n

Put the same value on the Mat diagonal, 0 otherwise

trace :: Matrix t n n -> Scalar t

Sum of diagonal elements

class MatrixDeterminant t (n :: Nat) where

Minimal complete definition

det

Methods

det :: Matrix t n n -> Scalar t

Determinant of Mat

class MatrixInverse t (n :: Nat) where

Minimal complete definition

inverse

Methods

inverse :: Matrix t n n -> Matrix t n n

Matrix inverse

class MatrixLU t (n :: Nat) where

Minimal complete definition

lu

Methods

lu :: Matrix t n n -> LUFact t n

Compute LU factorization with Partial Pivoting

data LUFact t n

Result of LU factorization with Partial Pivoting PA = LU .

Constructors

LUFact

Fields

• luLower :: Matrix t n n

  Lower triangular matrix L. All elements on the diagonal of L equal 1.

• luUpper :: Matrix t n n

  Upper triangular matrix U

• luPerm :: Matrix t n n

  Row permutation matrix P

• luPermSign :: Scalar t

  Sign of permutation luPermSign == det . luPerm

Instances

(Eq (Matrix * k t n n), Eq t) => Eq (LUFact k t n)

Methods

(==) :: LUFact k t n -> LUFact k t n -> Bool

(/=) :: LUFact k t n -> LUFact k t n -> Bool

(Show (Matrix * k t n n), Show t) => Show (LUFact k t n)

Methods

showsPrec :: Int -> LUFact k t n -> ShowS

show :: LUFact k t n -> String

showList :: [LUFact k t n] -> ShowS

type Matrix (t :: l) (n :: k) (m :: k) = DataFrame t '[n, m]

Alias for DataFrames of rank 2

type Mat22f = Matrix Float 2 2

type Mat23f = Matrix Float 2 3

type Mat24f = Matrix Float 2 4

type Mat32f = Matrix Float 3 2

type Mat33f = Matrix Float 3 3

type Mat34f = Matrix Float 3 4

type Mat42f = Matrix Float 4 2

type Mat43f = Matrix Float 4 3

type Mat44f = Matrix Float 4 4

type Mat22d = Matrix Double 2 2

type Mat23d = Matrix Double 2 3

type Mat24d = Matrix Double 2 4

type Mat32d = Matrix Double 3 2

type Mat33d = Matrix Double 3 3

type Mat34d = Matrix Double 3 4

type Mat42d = Matrix Double 4 2

type Mat43d = Matrix Double 4 3

type Mat44d = Matrix Double 4 4

mat22 :: (PrimBytes (Vector (t :: Type) 2), PrimBytes (Matrix t 2 2)) => Vector t 2 -> Vector t 2 -> Matrix t 2 2

Compose a 2x2D matrix

mat33 :: (PrimBytes (t :: Type), PrimBytes (Vector t 3), PrimBytes (Matrix t 3 3)) => Vector t 3 -> Vector t 3 -> Vector t 3 -> Matrix t 3 3

Compose a 3x3D matrix

mat44 :: forall (t :: Type). (PrimBytes t, PrimBytes (Vector t (4 :: Nat)), PrimBytes (Matrix t (4 :: Nat) (4 :: Nat))) => Vector t (4 :: Nat) -> Vector t (4 :: Nat) -> Vector t (4 :: Nat) -> Vector t (4 :: Nat) -> Matrix t (4 :: Nat) (4 :: Nat)

Compose a 4x4D matrix

(%*) :: (ConcatList as bs (as ++ bs), Contraction t as bs asbs, KnownDim m, PrimArray t (DataFrame t (as +: m)), PrimArray t (DataFrame t (m :+ bs)), PrimArray t (DataFrame t (as ++ bs))) => DataFrame t (as +: m) -> DataFrame t (m :+ bs) -> DataFrame t (as ++ bs) infixl 7

Tensor contraction. In particular: 1. matrix-matrix product 2. matrix-vector or vector-matrix product 3. dot product of two vectors.

pivotMat :: forall (t :: Type) (n :: k). (KnownDim n, PrimArray t (Matrix t n n), Ord t, Num t) => Matrix t n n -> (Matrix t n n, Matrix t n n, Scalar t)

Permute rows that the largest magnitude elements in columns are on diagonals.

Invariants of result matrix: * forall j >= i: |M[i,i]| >= M[j,i] * if M[i,i] == 0 then forall j >= i: |M[i+1,i+1]| >= M[j,i+1]

luSolve :: forall (t :: Type) (n :: Nat). (KnownDim n, Ord t, Fractional t, PrimBytes t, PrimArray t (Matrix t n n), PrimArray t (Vector t n)) => LUFact t n -> Vector t n -> Vector t n

Solve Ax = b problem given LU decomposition of A.

Orphan instances

(KnownDim Nat n, Ord t, Fractional t, PrimBytes t, PrimArray t (Matrix * Nat t n n)) => MatrixLU t n

Methods

lu :: Matrix * Nat t n n -> LUFact Nat t n

(KnownDim Nat n, Ord t, Fractional t, PrimBytes t, PrimArray t (Matrix * Nat t n n)) => MatrixDeterminant t n

Methods

det :: Matrix * Nat t n n -> Scalar t

(KnownDim Nat n, PrimArray t (Matrix * Nat t n n), Num t) => SquareMatrix t n

Methods

eye :: Matrix * Nat t n n

diag :: Scalar t -> Matrix * Nat t n n

trace :: Matrix * Nat t n n -> Scalar t

MatrixTranspose Type XNat t xn xm

Methods

transpose :: Matrix t xn xm n m -> Matrix t xn xm m n

(KnownDim Nat n, Ord t, Fractional t, PrimBytes t, PrimArray t (Matrix * Nat t n n), PrimArray t (Vector * Nat t n), PrimBytes (Vector * Nat t n), PrimBytes (Matrix * Nat t n n)) => MatrixInverse * t n

Methods

inverse :: Matrix t Nat n n n -> Matrix t Nat n n n

(KnownDim Nat n, KnownDim Nat m, PrimArray t (Matrix * Nat t n m), PrimArray t (Matrix * Nat t m n)) => MatrixTranspose * Nat t n m

Methods

transpose :: Matrix t n m n m -> Matrix t n m m n