linear-1.3: Linear Algebra

Portability portable provisional Edward Kmett Trustworthy

Linear.Vector

Description

Operations on free vector spaces.

Synopsis

# Documentation

class Functor f => Additive f whereSource

A vector is an additive group with additional structure.

Methods

zero :: Num a => f aSource

The zero vector

(^+^) :: Num a => f a -> f a -> f aSource

Compute the sum of two vectors

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

(^-^) :: Num a => f a -> f a -> f aSource

Compute the difference between two vectors

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

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

Linearly interpolate between two vectors.

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

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 cSource

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 [] Additive Complex Additive ZipList Additive Maybe Additive IntMap Additive Identity Additive Vector Additive V0 Additive V1 Additive V2 Additive V3 Additive V4 Additive Plucker Additive Quaternion Additive ((->) b) Ord k => Additive (Map k) (Eq k, Hashable k) => Additive (HashMap k) Additive f => Additive (Point f) Dim k n => Additive (V k n)

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

Compute the negation of a vector

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

(^*) :: (Functor f, Num a) => f a -> a -> f aSource

Compute the right scalar product

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

(*^) :: (Functor f, Num a) => a -> f a -> f aSource

Compute the left scalar product

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

(^/) :: (Functor f, Fractional a) => f a -> a -> f aSource

Compute division by a scalar on the right.

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

Sum over multiple vectors

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

basis :: (Applicative 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, Enum a, Num a) => t a -> [t a]Source

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

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

Produce a diagonal matrix from a vector.

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

Outer (tensor) product of two vectors