hTensor-0.6.0: Multidimensional arrays and simple tensor computations.Source codeContentsIndex
Numeric.LinearAlgebra.Array.Util
Portabilityportable
Stabilityprovisional
MaintainerAlberto Ruiz <[email protected]>
Description
Additional tools for manipulation of multidimensional arrays.
Synopsis
class (Num (Vector t), Field t, Storable t) => Coord t
class (Eq a, Show (Idx a)) => Compat a where
compat :: Idx a -> Idx a -> Bool
opos :: Idx a -> Idx a
data NArray i t
data Idx i = Idx {
iType :: i
iDim :: Int
iName :: Name
}
type Name = String
scalar :: Coord t => t -> NArray i t
order :: NArray i t -> Int
names :: NArray i t -> [Name]
size :: Name -> NArray i t -> Int
sizes :: NArray i t -> [Int]
typeOf :: Compat i => Name -> NArray i t -> i
dims :: NArray i t -> [Idx i]
coords :: NArray i t -> Vector t
renameExplicit :: (Compat i, Coord t) => [(Name, Name)] -> NArray i t -> NArray i t
(!>) :: (Compat i, Coord t) => NArray i t -> [Char] -> NArray i t
renameO :: (Coord t, Compat i) => NArray i t -> [Name] -> NArray i t
(!) :: (Compat i, Coord t) => NArray i t -> [Char] -> NArray i t
parts :: Coord t => NArray i t -> Name -> [NArray i t]
newIndex :: (Coord t, Compat i) => i -> Name -> [NArray i t] -> NArray i t
mapArray :: Coord b => (Vector a -> Vector b) -> NArray i a -> NArray i b
zipArray :: (Coord a, Coord b, Compat i) => (Vector a -> Vector b -> Vector c) -> NArray i a -> NArray i b -> NArray i c
(|*|) :: (Coord t, Compat i) => NArray i t -> NArray i t -> NArray i t
smartProduct :: (Coord t, Compat i, Num (NArray i t)) => [NArray i t] -> NArray i t
outers :: (Coord a, Compat i) => [NArray i a] -> NArray i a
extract :: (Compat i, Coord t) => (Int -> NArray i t -> Bool) -> Name -> NArray i t -> NArray i t
onIndex :: (Coord a, Coord b, Compat i) => ([NArray i a] -> [NArray i b]) -> Name -> NArray i a -> NArray i b
mapTat :: (Coord a, Coord b, Compat i) => (NArray i a -> NArray i b) -> [Name] -> NArray i a -> NArray i b
reorder :: Coord t => [Name] -> NArray i t -> NArray i t
(~>) :: Coord t => NArray i t -> String -> NArray i t
formatArray :: (Coord t, Compat i) => (t -> String) -> NArray i t -> String
formatFixed :: Compat i => Int -> NArray i Double -> String
formatScaled :: Compat i => Int -> NArray i Double -> String
dummyAt :: Coord t => Int -> NArray i t -> NArray i t
noIdx :: Compat i => NArray i t -> NArray i t
conformable :: Compat i => [[Idx i]] -> Maybe [Idx i]
sameStructure :: Eq i => NArray i t1 -> NArray i t2 -> Bool
makeConformant :: (Coord t, Compat i) => [NArray i t] -> [NArray i t]
basisOf :: Coord t => NArray i t -> [NArray i t]
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
mkFun :: [Int] -> ([Int] -> Double) -> Array Double
mkAssoc :: [Int] -> [([Int], Double)] -> Array Double
setType :: (Compat i, Coord t) => Name -> i -> NArray i t -> NArray i t
renameParts :: (Compat i, Coord t) => Name -> NArray i t -> Name -> String -> [NArray i t]
asScalar :: Coord t => NArray i t -> t
asVector :: Coord t => NArray i t -> Vector t
asMatrix :: Coord t => NArray i t -> Matrix t
applyAsMatrix :: (Coord t, Compat i) => (Matrix t -> Matrix t) -> NArray i t -> NArray i t
fibers :: Coord t => Name -> NArray i t -> Matrix t
matrixator :: Coord t => NArray i t -> [Name] -> [Name] -> Matrix t
matrixatorFree :: Coord t => NArray i t -> [Name] -> (Matrix t, [Name])
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
fromMatrix :: (Compat i, Coord t) => i -> i -> Matrix t -> NArray i t
class Element e => Container c e where
toComplex :: (c e, c e) -> c (Complex e)
fromComplex :: c (Complex e) -> (c e, c e)
comp :: c e -> c (Complex e)
conj :: c (Complex e) -> c (Complex e)
real :: c Double -> c e
complex :: c e -> c (Complex Double)
Documentation
class (Num (Vector t), Field t, Storable t) => Coord t Source
Types that can be elements of the multidimensional arrays.
show/hide Instances
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
show/hide Instances
data NArray i t Source
A multidimensional array with index type i and elements t.
show/hide Instances
(Coord t, Coord (Complex t), Compat i, Container Vector t) => Container (NArray i) t
(Coord t, Compat i) => Eq (NArray i t)
(Coord t, Compat i, Fractional (NArray i 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
iType :: i
iDim :: Int
iName :: Name
show/hide 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.
partsSource
:: Coord t
=> NArray i t
-> Nameindex to expand
-> [NArray i t]
Create a list of the substructures at the given level.
newIndexSource
:: (Coord t, Compat i)
=> iindex 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 Vectors) to all elements of a structure. Use mapArray (mapVector f) for general functions.
zipArraySource
:: (Coord a, Coord b, Compat i)
=> Vector a -> Vector b -> Vector ctransformation
-> 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.

formatArraySource
:: (Coord t, Compat i)
=> t -> Stringformat function (eg. printf "5.2f")
-> NArray i t
-> String
Show a multidimensional array as a nested 2D table.
formatFixedSource
:: Compat i
=> Intnumber 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.
formatScaledSource
:: Compat i
=> Intnumber 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.
renamePartsSource
:: (Compat i, Coord t)
=> Nameindex of the parts to extract
-> NArray i tinput array
-> Nameindex to renameRaw
-> Stringprefix 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).
matrixatorSource
:: Coord t
=> NArray i tinput array
-> [Name]row dimensions
-> [Name]column dimensions
-> Matrix tresult
Reshapes an array as a matrix with the desired dimensions as flattened rows and flattened columns.
matrixatorFreeSource
:: Coord t
=> NArray i tinput 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.
class Element e => Container c e whereSource
conversion utilities
Methods
toComplex :: (c e, c e) -> c (Complex e)Source
fromComplex :: c (Complex e) -> (c e, c e)Source
comp :: c e -> c (Complex e)Source
conj :: c (Complex e) -> c (Complex e)Source
real :: c Double -> c eSource
complex :: c e -> c (Complex Double)Source
show/hide Instances
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