Math.ExpPairs.Matrix3

Provides types and functions for matrices and vectors of order 3. Can be used instead of Data.Matrix to reduce overhead and simplify code.

Documentation

data Matrix3 t

Matrix of order 3. Instances of Num, Fractional and Monoid are defined in terms of the multiplicative group of matrices, not the additive one. E. g.,

toList 1 == [1,0,0,0,1,0,0,0,1]
toList 1 /= [1,1,1,1,1,1,1,1,1]

Constructors

Matrix3

Fields

a11 :: t

a12 :: t

a13 :: t

a21 :: t

a22 :: t

a23 :: t

a31 :: t

a32 :: t

a33 :: t

Instances

Functor Matrix3

Eq t => Eq (Matrix3 t)

Fractional t => Fractional (Matrix3 t)

Num t => Num (Matrix3 t)

Show t => Show (Matrix3 t)

Num t => Monoid (Matrix3 t)

data Vector3 t

Three-component vector.

Constructors

Vector3

Fields

a1 :: t

a2 :: t

a3 :: t

Instances

Eq t => Eq (Vector3 t)

Show t => Show (Vector3 t)

fromList :: [t] -> Matrix3 t

Convert a list of 9 elements into Matrix3.

toList :: Matrix3 t -> [t]

Convert Matrix3 into a list of 9 elements.

det :: Num t => Matrix3 t -> t

Computes the determinant of a matrix.

multCol :: Num t => Matrix3 t -> Vector3 t -> Vector3 t

Multiplicate a matrix by a vector (considered as a column).

normalize :: Integral t => Matrix3 t -> Matrix3 t

Divide all elements of the matrix by their greatest common divisor. This is useful for matrices of projective transformations to reduce the magnitude of computations.

prettyMatrix :: Show t => Matrix3 t -> String

Print a matrix, separating rows with new lines and elements with spaces.