Numeric.Matrix

Documentation

class MatrixCalculus t n m where

Minimal complete definition

transpose

Methods

transpose :: (MatrixCalculus t m n, PrimBytes (Matrix t m n)) => Matrix t n m -> Matrix t m n

Transpose Mat

class SquareMatrixCalculus t n where

Minimal complete definition

eye, diag, det, 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

det :: Matrix t n n -> Scalar t

Determinant of Mat

trace :: Matrix t n n -> Scalar t

Sum of diagonal elements

class MatrixInverse t n where

Minimal complete definition

inverse

Methods

inverse :: DataFrame t '[n, n] -> DataFrame t '[n, n]

Matrix inverse

class HomTransform4 t where

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

Minimal complete definition

translate4, translate3, rotateX, rotateY, rotateZ, rotate, rotateEuler, lookAt, perspective, orthogonal, toHomPoint, toHomVector, fromHom

Methods

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

Create a translation matrix from a vector

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 :: t -> t -> t -> Matrix t 4 4

Rotation matrix from the Euler angles yaw pitch and roll

lookAt :: Vector t 3 -> Vector t 3 -> Vector t 3 -> 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 :: t -> t -> t -> t -> 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 :: t -> t -> t -> t -> 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.

type Matrix t n m = 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 2), PrimBytes (Matrix t 2 2)) => Vector t 2 -> Vector t 2 -> Matrix t 2 2

Compose a 2x2D matrix

mat33 :: (PrimBytes t, 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. (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, PrimBytes (DataFrame t (as +: m)), PrimBytes (DataFrame t (m :+ bs)), PrimBytes (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.