hTensor-0.6.0: Multidimensional arrays and simple tensor computations. Source code Contents Index

Numeric.LinearAlgebra.Tensor Stability experimental Maintainer Alberto Ruiz <[email protected]>

Contents The Tensor type Tensor creation utilities Index manipulation General array operations

Description

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

Synopsis

type Tensor t = NArray Variant t data Variant = Contra | Co listTensor :: Coord t => [Int] -> [t] -> Tensor t superindex :: Coord t => Name -> [Tensor t] -> Tensor t subindex :: Coord t => Name -> [Tensor t] -> Tensor t vector :: [Double] -> Tensor Double covector :: [Double] -> Tensor Double transf :: [[Double]] -> Tensor Double switch :: Tensor t -> Tensor t cov :: NArray i t -> Tensor t contrav :: NArray i t -> Tensor t forget :: NArray i t -> Array t module Numeric.LinearAlgebra.Array

The Tensor type

type Tensor t = NArray Variant t Source

data Variant Source

Constructors Contra Co Instances Eq Variant Show Variant Compat Variant Show (Idx Variant)

listTensor Source

:: 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 Source

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

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

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

vector :: [Double] -> Tensor Double Source

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

covector :: [Double] -> Tensor Double Source

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

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

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

Index manipulation

switch :: Tensor t -> Tensor t Source

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

cov :: NArray i t -> Tensor t Source

Make all dimensions covariant.

contrav :: NArray i t -> Tensor t Source

Make all dimensions contravariant.

forget :: NArray i t -> Array t Source

Remove the Variant nature of coordinates.

General array operations

module Numeric.LinearAlgebra.Array

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