Numeric.LinearAlgebra.Array.Util

Additional tools for manipulation of multidimensional arrays.

Documentation

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

Types that can be elements of the multidimensional arrays.

Instances

Coord Double

Coord (Complex Double)

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

Class of compatible indices for contractions.

Methods

compat :: Idx a -> Idx a -> Bool

opos :: Idx a -> Idx a

Instances

Compat None

Compat Variant

data NArray i t

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

Dimension descriptor.

Constructors

Idx

Fields

iType :: i

iDim :: Int

iName :: Name

Instances

Eq i => Eq (Idx i)

Eq i => Ord (Idx i)

Show (Idx None)

Show (Idx Variant)

type Name = String

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

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

Create a 0-dimensional structure.

order :: NArray i t -> Int

The number of dimensions of a multidimensional array.

names :: NArray i t -> [Name]

Index names.

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

Dimension of given index.

sizes :: NArray i t -> [Int]

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

Type of given index.

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

Get detailed dimension information about the array.

coords :: NArray i t -> Vector t

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 t

Rename indices using an association list.

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

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 t

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

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

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

parts

Arguments

:: Coord t

=> NArray i t

-> Name

index to expand

-> [NArray i t]

Create a list of the substructures at the given level.

newIndex

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 b

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

zipArray

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 t

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 t

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 a

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 t

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 b

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 b

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

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

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

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

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.

formatArray

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.

formatFixed

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.

formatScaled

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 t

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

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

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

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

Obtains most general structure of a list of dimension specifications

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

Check if two arrays have the same structure.

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

Converts a list of arrays to a common structure.

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

Obtain a canonical base for the array.

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

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

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

Multidimensional diagonal of given order.

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

Define an array using a function.

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

Define an array using an association list.

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

Change type of index.

renameParts

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.

resetCoords :: Coord t => NArray i t -> Vector t -> NArray i t

change the whole set of coordinates.

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

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

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

Extract the Vector corresponding to a one-dimensional array.

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

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 t

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

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).

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.

matrixatorFree

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)

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

Create a 1st order array from a Vector.

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

Create a 2nd order array from a Matrix.