Numeric.Matrix

Documentation

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

Methods

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

Transpose Mat

Instances

MatrixTranspose (t :: Type) (xn :: XNat) (xm :: XNat)

Defined in Numeric.Matrix

Methods

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

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

Defined in Numeric.Matrix

Methods

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

class SquareMatrix t (n :: Nat) where

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

Instances

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

Defined in Numeric.Matrix

Methods

eye :: Matrix t n n

diag :: Scalar t -> Matrix t n n

trace :: Matrix t n n -> Scalar t

class MatrixDeterminant t (n :: Nat) where

Methods

det :: Matrix t n n -> Scalar t

Determinant of Mat

Instances

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

Defined in Numeric.Matrix

Methods

det :: Matrix t n n -> Scalar t

class MatrixInverse t (n :: Nat) where

Methods

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

Matrix inverse

Instances

(KnownDim n, Ord t, Fractional t, PrimBytes t, PrimArray t (Matrix t n n), PrimArray t (Vector t n), PrimBytes (Vector t n), PrimBytes (Matrix t n n)) => MatrixInverse (t :: Type) n

Defined in Numeric.Matrix

Methods

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

class MatrixLU t (n :: Nat) where

Methods

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

Compute LU factorization with Partial Pivoting

Instances

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

Defined in Numeric.Matrix

Methods

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

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 t n n), Eq t) => Eq (LUFact t n)

Defined in Numeric.Matrix.Class

Methods

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

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

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

Defined in Numeric.Matrix.Class

Methods

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

show :: LUFact t n -> String

showList :: [LUFact t n] -> ShowS

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

Alias for DataFrames of rank 2

class HomTransform4 t where

Operations on 4x4 transformation matrices and vectors in homogeneous coordinates. All angles are specified in radians.

Methods

translate4 :: Vector t 4 -> Matrix t 4 4

Create a translation matrix from a vector. The 4th coordinate is ignored.

translate3 :: Vector t 3 -> Matrix t 4 4

Create a translation matrix from a vector.

rotateX :: t -> Matrix t 4 4

Rotation matrix for a rotation around the X axis, angle is given in radians.

rotateY :: t -> Matrix t 4 4

Rotation matrix for a rotation around the Y axis, angle is given in radians.

rotateZ :: t -> Matrix t 4 4

Rotation matrix for a rotation around the Z axis, angle is given in radians.

rotate :: Vector t 3 -> t -> Matrix t 4 4

Rotation matrix for a rotation around an arbitrary normalized vector

rotateEuler

Arguments

:: t

pitch (axis X'')

-> t

yaw (axis Y')

-> t

roll (axis Z)

-> Matrix t 4 4

Rotation matrix from the Euler angles roll (axis Z), yaw (axis Y'), and pitch (axis X''). This order is known as Tait-Bryan angles (Z-Y'-X'' intrinsic rotations), or nautical angles, or Cardan angles.

rotateEuler pitch yaw roll == rotateX pitch %* rotateY yaw %* rotateZ roll

https://en.wikipedia.org/wiki/Euler_angles#Conventions_2

lookAt

Arguments

:: Vector t 3

The up direction, not necessary unit length or perpendicular to the view vector

-> Vector t 3

The viewers position

-> Vector t 3

The point to look at

-> Matrix t 4 4

Create a transform matrix using up direction, camera position and a point to look at. Just the same as GluLookAt.

perspective

Arguments

:: t

Near plane clipping distance (always positive)

-> t

Far plane clipping distance (always positive)

-> t

Field of view of the y axis, in radians

-> t

Aspect ratio, i.e. screen's width/height

-> Matrix t 4 4

A perspective symmetric projection matrix. Right-handed coordinate system. (x - right, y - top) http://en.wikibooks.org/wiki/GLSL_Programming/Vertex_Transformations

orthogonal

Arguments

:: t

Near plane clipping distance

-> t

Far plane clipping distance

-> t

width

-> t

height

-> Matrix t 4 4

An orthogonal symmetric projection matrix. Right-handed coordinate system. (x - right, y - top) http://en.wikibooks.org/wiki/GLSL_Programming/Vertex_Transformations

toHomPoint :: Vector t 3 -> Vector t 4

Add one more dimension and set it to 1.

toHomVector :: Vector t 3 -> Vector t 4

Add one more dimension and set it to 0.

fromHom :: Vector t 4 -> Vector t 3

Transform a homogenous vector or point into a normal 3D vector. If the last coordinate is not zero, divide the rest by it.

Instances

HomTransform4 Double

Defined in Numeric.Matrix.Mat44d

Methods

translate4 :: Vector Double 4 -> Matrix Double 4 4

translate3 :: Vector Double 3 -> Matrix Double 4 4

rotateX :: Double -> Matrix Double 4 4

rotateY :: Double -> Matrix Double 4 4

rotateZ :: Double -> Matrix Double 4 4

rotate :: Vector Double 3 -> Double -> Matrix Double 4 4

rotateEuler :: Double -> Double -> Double -> Matrix Double 4 4

lookAt :: Vector Double 3 -> Vector Double 3 -> Vector Double 3 -> Matrix Double 4 4

perspective :: Double -> Double -> Double -> Double -> Matrix Double 4 4

orthogonal :: Double -> Double -> Double -> Double -> Matrix Double 4 4

toHomPoint :: Vector Double 3 -> Vector Double 4

toHomVector :: Vector Double 3 -> Vector Double 4

fromHom :: Vector Double 4 -> Vector Double 3

HomTransform4 Float

Defined in Numeric.Matrix.Mat44f

Methods

translate4 :: Vector Float 4 -> Matrix Float 4 4

translate3 :: Vector Float 3 -> Matrix Float 4 4

rotateX :: Float -> Matrix Float 4 4

rotateY :: Float -> Matrix Float 4 4

rotateZ :: Float -> Matrix Float 4 4

rotate :: Vector Float 3 -> Float -> Matrix Float 4 4

rotateEuler :: Float -> Float -> Float -> Matrix Float 4 4

lookAt :: Vector Float 3 -> Vector Float 3 -> Vector Float 3 -> Matrix Float 4 4

perspective :: Float -> Float -> Float -> Float -> Matrix Float 4 4

orthogonal :: Float -> Float -> Float -> Float -> Matrix Float 4 4

toHomPoint :: Vector Float 3 -> Vector Float 4

toHomVector :: Vector Float 3 -> Vector Float 4

fromHom :: Vector Float 4 -> Vector Float 3

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

Methods

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

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

Methods

det :: Matrix t n n -> Scalar t

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

Methods

eye :: Matrix t n n

diag :: Scalar t -> Matrix t n n

trace :: Matrix t n n -> Scalar t

MatrixTranspose (t :: Type) (xn :: XNat) (xm :: XNat)

Methods

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

(KnownDim n, Ord t, Fractional t, PrimBytes t, PrimArray t (Matrix t n n), PrimArray t (Vector t n), PrimBytes (Vector t n), PrimBytes (Matrix t n n)) => MatrixInverse (t :: Type) n

Methods

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

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

Methods

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