Numeric.LinearAlgebra.Tensor

Tensor computations. Indices can only be contracted if they are of different Variant type.

The Tensor type

type Tensor t = NArray Variant t

data Variant

Constructors

Contra

Co

Instances

Eq Variant

Methods

(==) :: Variant -> Variant -> Bool

(/=) :: Variant -> Variant -> Bool

Show Variant

Methods

showsPrec :: Int -> Variant -> ShowS

show :: Variant -> String

showList :: [Variant] -> ShowS

Compat Variant

Methods

compat :: Idx Variant -> Idx Variant -> Bool

opos :: Idx Variant -> Idx Variant

Show (Idx Variant)

Methods

showsPrec :: Int -> Idx Variant -> ShowS

show :: Idx Variant -> String

showList :: [Idx Variant] -> ShowS

Coord t => Show (Tensor t)

Methods

showsPrec :: Int -> Tensor t -> ShowS

show :: Tensor t -> String

showList :: [Tensor t] -> ShowS

listTensor

Arguments

:: Coord t

=> [Int]

dimensions

-> [t]

coordinates

-> Tensor t

Creates a tensor from a list of dimensions and a list of coordinates. A positive dimension means that the index is assumed to be contravariant (vector-like), and a negative dimension means that the index is assumed to be covariant (like a linear function, or covector). Contractions can only be performed between indices of different type.

Tensor creation utilities

superindex :: Coord t => Name -> [Tensor t] -> Tensor t

Create an Tensor from a list of parts with a contravariant index (superindex = newIndex Contra).

subindex :: Coord t => Name -> [Tensor t] -> Tensor t

Create an Tensor from a list of parts with a covariant index (subindex = newIndex Co).

vector :: [Double] -> Tensor Double

Create a contravariant 1st order tensor from a list of coordinates.

covector :: [Double] -> Tensor Double

Create a covariant 1st order tensor from a list of coordinates.

transf :: [[Double]] -> Tensor Double

Create a 1-contravariant, 1-covariant 2nd order from list of lists of coordinates.

Index manipulation

switch :: Tensor t -> Tensor t

Change the Variant nature of all dimensions to the opposite ones.

cov :: NArray i t -> Tensor t

Make all dimensions covariant.

contrav :: NArray i t -> Tensor t

Make all dimensions contravariant.

forget :: NArray i t -> Array t

Remove the Variant nature of coordinates.

General array operations

module Numeric.LinearAlgebra.Array