hTensor-0.8.0: Multidimensional arrays and simple tensor computations.

Portability portable provisional Alberto Ruiz

Numeric.LinearAlgebra.Array.Util

Description

Additional tools for manipulation of multidimensional arrays.

Synopsis

# Documentation

class (Num (Vector t), Field t, Normed Vector t, Show t) => Coord t Source

Types that can be elements of the multidimensional arrays.

Instances

 Coord Double Coord (Complex Double)

class (Eq a, Show (Idx a)) => Compat a whereSource

Class of compatible indices for contractions.

Methods

compat :: Idx a -> Idx a -> BoolSource

opos :: Idx a -> Idx aSource

Instances

 Compat None Compat Variant

data NArray i t Source

A multidimensional array with index type i and elements t.

Instances

 Coord t => Show (Array t) Coord t => Show (Tensor t) (Eq t, Coord t, Compat i) => Eq (NArray i t) (Coord t, Compat i, Fractional (NArray i t), Floating t, Floating (Vector t)) => Floating (NArray i t) (Coord t, Compat i, Num (NArray i t)) => Fractional (NArray i t) (Show (NArray i t), Coord t, Compat i) => Num (NArray i t)

data Idx i Source

Dimension descriptor.

Constructors

 Idx FieldsiType :: i iDim :: Int iName :: Name

Instances

 Eq i => Eq (Idx i) Eq i => Ord (Idx i) Show (Idx None) Show (Idx Variant)

type Name = StringSource

indices are denoted by strings, (frequently single-letter)

scalar :: Coord t => t -> NArray i tSource

Create a 0-dimensional structure.

order :: NArray i t -> IntSource

The number of dimensions of a multidimensional array.

names :: NArray i t -> [Name]Source

Index names.

size :: Name -> NArray i t -> IntSource

Dimension of given index.

sizes :: NArray i t -> [Int]Source

typeOf :: Compat i => Name -> NArray i t -> iSource

Type of given index.

dims :: NArray i t -> [Idx i]Source

Get detailed dimension information about the array.

coords :: NArray i t -> Vector tSource

Get the coordinates of an array as a flattened structure (in the order specified by `dims`).

renameExplicit :: (Compat i, Coord t) => [(Name, Name)] -> NArray i t -> NArray i tSource

Rename indices using an association list.

(!>) :: (Compat i, Coord t) => NArray i t -> [Char] -> NArray i tSource

Explicit renaming of single letter index names.

For instance, `t >@> "pi qj"` changes index "p" to "i" and "q" to "j".

renameO :: (Coord t, Compat i) => NArray i t -> [Name] -> NArray i tSource

Rename indices in alphabetical order. Equal indices of compatible type are contracted out.

(!) :: (Compat i, Coord t) => NArray i t -> [Char] -> NArray i tSource

Rename indices in alphabetical order (`renameO`) using single letter names.

Arguments

 :: Coord t => NArray i t -> Name index to expand -> [NArray i t]

Create a list of the substructures at the given level.

Arguments

 :: (Coord t, Compat i) => i index type -> Name -> [NArray i t] -> NArray i t

Create an array from a list of subarrays. (The inverse of `parts`.)

mapArray :: Coord b => (Vector a -> Vector b) -> NArray i a -> NArray i bSource

Apply a function (defined on hmatrix `Vector`s) to all elements of a structure. Use `mapArray (mapVector f)` for general functions.

Arguments

 :: (Coord a, Coord b, Compat i) => (Vector a -> Vector b -> Vector c) transformation -> NArray i a -> NArray i b -> NArray i c

Apply an element-by-element binary function to the coordinates of two arrays. The arguments are automatically made conformant.

(|*|) :: (Coord t, Compat i) => NArray i t -> NArray i t -> NArray i tSource

Tensor product with automatic contraction of repeated indices, following Einstein summation convention.

smartProduct :: (Coord t, Compat i, Num (NArray i t)) => [NArray i t] -> NArray i tSource

This is equivalent to the regular `product`, but in the order that minimizes the size of the intermediate factors.

outers :: (Coord a, Compat i) => [NArray i a] -> NArray i aSource

Outer product of a list of arrays along the common indices.

extract :: (Compat i, Coord t) => (Int -> NArray i t -> Bool) -> Name -> NArray i t -> NArray i tSource

Select some parts of an array, taking into account position and value.

onIndex :: (Coord a, Coord b, Compat i) => ([NArray i a] -> [NArray i b]) -> Name -> NArray i a -> NArray i bSource

Apply a list function to the parts of an array at a given index.

mapTat :: (Coord a, Coord b, Compat i) => (NArray i a -> NArray i b) -> [Name] -> NArray i a -> NArray i bSource

Map a function at the internal level selected by a set of indices

reorder :: Coord t => [Name] -> NArray i t -> NArray i tSource

Change the internal layout of coordinates. The array, considered as an abstract object, does not change.

(~>) :: Coord t => NArray i t -> String -> NArray i tSource

`reorder` (transpose) dimensions of the array (with single letter names).

Operations are defined by named indices, so the transposed array is operationally equivalent to the original one.

Arguments

 :: (Coord t, Compat i) => (t -> String) format function (eg. printf "5.2f") -> NArray i t -> String

Show a multidimensional array as a nested 2D table.

Arguments

 :: Compat i => Int number of of decimal places -> NArray i Double -> String

Show the array as a nested table with a "%.nf" format. If all entries are approximate integers the array is shown without the .00.. digits.

Arguments

 :: Compat i => Int number of of decimal places -> NArray i Double -> String

Show the array as a nested table with autoscaled entries.

dummyAt :: Coord t => Int -> NArray i t -> NArray i tSource

Insert a dummy index of dimension 1 at a given level (for formatting purposes).

noIdx :: Compat i => NArray i t -> NArray i tSource

Rename indices so that they are not shown in formatted output.

conformable :: Compat i => [[Idx i]] -> Maybe [Idx i]Source

Obtains most general structure of a list of dimension specifications

sameStructure :: Eq i => NArray i t1 -> NArray i t2 -> BoolSource

Check if two arrays have the same structure.

makeConformant :: (Coord t, Compat i) => [NArray i t] -> [NArray i t]Source

Converts a list of arrays to a common structure.

basisOf :: Coord t => NArray i t -> [NArray i t]Source

Obtain a canonical base for the array.

atT :: (Compat i, Coord t) => NArray i t -> [Int] -> NArray i tSource

takeDiagT :: (Compat i, Coord t) => NArray i t -> [t]Source

diagT :: [Double] -> Int -> Array DoubleSource

Multidimensional diagonal of given order.

mkFun :: [Int] -> ([Int] -> Double) -> Array DoubleSource

Define an array using a function.

mkAssoc :: [Int] -> [([Int], Double)] -> Array DoubleSource

Define an array using an association list.

setType :: (Compat i, Coord t) => Name -> i -> NArray i t -> NArray i tSource

Change type of index.

Arguments

 :: (Compat i, Coord t) => Name index of the parts to extract -> NArray i t input array -> Name index to renameRaw -> String prefix for the new names -> [NArray i t] list or results

Extract the `parts` of an array, and renameRaw one of the remaining indices with succesive integers.

asScalar :: Coord t => NArray i t -> tSource

Extract the scalar element corresponding to a 0-dimensional array.

asVector :: Coord t => NArray i t -> Vector tSource

Extract the `Vector` corresponding to a one-dimensional array.

asMatrix :: Coord t => NArray i t -> Matrix tSource

Extract the `Matrix` corresponding to a two-dimensional array, in the rows,cols order.

applyAsMatrix :: (Coord t, Compat i) => (Matrix t -> Matrix t) -> NArray i t -> NArray i tSource

fibers :: Coord t => Name -> NArray i t -> Matrix tSource

Obtain a matrix whose columns are the fibers of the array in the given dimension. The column order depends on the selected index (see `matrixator`).

Arguments

 :: Coord t => NArray i t input array -> [Name] row dimensions -> [Name] column dimensions -> Matrix t result

Reshapes an array as a matrix with the desired dimensions as flattened rows and flattened columns.

Arguments

 :: Coord t => NArray i t input array -> [Name] row dimensions -> (Matrix t, [Name]) (result, column dimensions)

Reshapes an array as a matrix with the desired dimensions as flattened rows and flattened columns. We do not force the order of the columns.

analyzeProduct :: (Coord t, Compat i) => NArray i t -> NArray i t -> Maybe (NArray i t, Int)Source

fromVector :: (Coord t, Compat i) => i -> Vector t -> NArray i tSource

Create a 1st order array from a `Vector`.

fromMatrix :: (Compat i, Coord t) => i -> i -> Matrix t -> NArray i tSource

Create a 2nd order array from a `Matrix`.