linear-1.20.4: Linear Algebra

Linear.Vector

Description

Operations on free vector spaces.

Synopsis

# Documentation

class Functor f => Additive f where Source

Minimal complete definition

Nothing

Methods

zero :: Num a => f a Source

The zero vector

(^+^) :: Num a => f a -> f a -> f a infixl 6 Source

Compute the sum of two vectors

````>>> ````V2 1 2 ^+^ V2 3 4
```V2 4 6
```

(^-^) :: Num a => f a -> f a -> f a infixl 6 Source

Compute the difference between two vectors

````>>> ````V2 4 5 ^-^ V2 3 1
```V2 1 4
```

lerp :: Num a => a -> f a -> f a -> f a Source

Linearly interpolate between two vectors.

liftU2 :: (a -> a -> a) -> f a -> f a -> f a Source

Apply a function to merge the 'non-zero' components of two vectors, unioning the rest of the values.

• For a dense vector this is equivalent to `liftA2`.
• For a sparse vector this is equivalent to `unionWith`.

liftI2 :: (a -> b -> c) -> f a -> f b -> f c Source

Apply a function to the components of two vectors.

• For a dense vector this is equivalent to `liftA2`.
• For a sparse vector this is equivalent to `intersectionWith`.

Instances

 Additive [] Source Source Source Source Source Source Source Source Source Source Source Source Source Source Additive ((->) b) Source Ord k => Additive (Map k) Source (Eq k, Hashable k) => Additive (HashMap k) Source Additive f => Additive (Point f) Source Dim k n => Additive (V k n) Source

newtype E t Source

Basis element

Constructors

 E Fieldsel :: forall x. Lens' (t x) x

Instances

 (Num r, TrivialConjugate r) => Coalgebra r (E Quaternion) Source Num r => Coalgebra r (E Complex) Source Num r => Coalgebra r (E V4) Source Num r => Coalgebra r (E V3) Source Num r => Coalgebra r (E V2) Source Num r => Coalgebra r (E V1) Source Num r => Coalgebra r (E V0) Source (Num r, TrivialConjugate r) => Algebra r (E Quaternion) Source Num r => Algebra r (E Complex) Source Num r => Algebra r (E V1) Source Num r => Algebra r (E V0) Source

negated :: (Functor f, Num a) => f a -> f a Source

Compute the negation of a vector

````>>> ````negated (V2 2 4)
```V2 (-2) (-4)
```

(^*) :: (Functor f, Num a) => f a -> a -> f a infixl 7 Source

Compute the right scalar product

````>>> ````V2 3 4 ^* 2
```V2 6 8
```

(*^) :: (Functor f, Num a) => a -> f a -> f a infixl 7 Source

Compute the left scalar product

````>>> ````2 *^ V2 3 4
```V2 6 8
```

(^/) :: (Functor f, Fractional a) => f a -> a -> f a infixl 7 Source

Compute division by a scalar on the right.

sumV :: (Foldable f, Additive v, Num a) => f (v a) -> v a Source

Sum over multiple vectors

````>>> ````sumV [V2 1 1, V2 3 4]
```V2 4 5
```

basis :: (Additive t, Traversable t, Num a) => [t a] Source

Produce a default basis for a vector space. If the dimensionality of the vector space is not statically known, see `basisFor`.

basisFor :: (Traversable t, Num a) => t b -> [t a] Source

Produce a default basis for a vector space from which the argument is drawn.

scaled :: (Traversable t, Num a) => t a -> t (t a) Source

Produce a diagonal (scale) matrix from a vector.

````>>> ````scaled (V2 2 3)
```V2 (V2 2 0) (V2 0 3)
```

outer :: (Functor f, Functor g, Num a) => f a -> g a -> f (g a) Source

Outer (tensor) product of two vectors

unit :: (Additive t, Num a) => ASetter' (t a) a -> t a Source

Create a unit vector.

````>>> ````unit _x :: V2 Int
```V2 1 0
```