Create a vector from a list of elements and explicit dimension. The input list is truncated if it is too long, so it may safely be used, for instance, with infinite lists.

>>> 5 |> [1..]
[1.0,2.0,3.0,4.0,5.0]
it :: (Enum a, Num a, Foreign.Storable.Storable a) => Vector a

vector :: [R] -> Vector R Source #

Create a real vector.

>>> vector [1..5]
[1.0,2.0,3.0,4.0,5.0]
it :: Vector R

range :: Int -> Vector I Source #

>>> range 5
[0,1,2,3,4]
it :: Vector I

idxs :: [Int] -> Vector I Source #

Create a vector of indexes, useful for matrix extraction using (??)

Matrix

The main data type of hmatrix is a 2D dense array defined on top of a storable vector. The internal representation is suitable for direct interface with standard numeric libraries.

(><) :: Storable a => Int -> Int -> [a] -> Matrix a Source #

Create a matrix from a list of elements

>>> (2><3) [2, 4, 7+2*iC,   -3, 11, 0]
(2><3)
 [       2.0 :+ 0.0,  4.0 :+ 0.0, 7.0 :+ 2.0
 , (-3.0) :+ (-0.0), 11.0 :+ 0.0, 0.0 :+ 0.0 ]

The input list is explicitly truncated, so that it can safely be used with lists that are too long (like infinite lists).

>>> (2><3)[1..]
(2><3)
 [ 1.0, 2.0, 3.0
 , 4.0, 5.0, 6.0 ]

This is the format produced by the instances of Show (Matrix a), which can also be used for input.

matrix Source #

Arguments

:: Int	number of columns
-> [R]	elements in row order
-> Matrix R

Create a real matrix.

>>> matrix 5 [1..15]
(3><5)
 [  1.0,  2.0,  3.0,  4.0,  5.0
 ,  6.0,  7.0,  8.0,  9.0, 10.0
 , 11.0, 12.0, 13.0, 14.0, 15.0 ]

tr :: Transposable m mt => m -> mt Source #

conjugate transpose

tr' :: Transposable m mt => m -> mt Source #

transpose

Dimensions

size :: Container c t => c t -> IndexOf c Source #

>>> size $ vector [1..10]
10
>>> size $ (2><5)[1..10::Double]
(2,5)

rows :: Matrix t -> Int Source #

cols :: Matrix t -> Int Source #

Conversion from/to lists

fromLists :: Element t => [[t]] -> Matrix t Source #

Creates a Matrix from a list of lists (considered as rows).

>>> fromLists [[1,2],[3,4],[5,6]]
(3><2)
 [ 1.0, 2.0
 , 3.0, 4.0
 , 5.0, 6.0 ]

toLists :: Element t => Matrix t -> [[t]] Source #

the inverse of fromLists

row :: [Double] -> Matrix Double Source #

create a single row real matrix from a list

>>> row [2,3,1,8]
(1><4)
 [ 2.0, 3.0, 1.0, 8.0 ]

col :: [Double] -> Matrix Double Source #

create a single column real matrix from a list

>>> col [7,-2,4]
(3><1)
 [  7.0
 , -2.0
 ,  4.0 ]

Conversions vector/matrix

flatten :: Element t => Matrix t -> Vector t Source #

Creates a vector by concatenation of rows. If the matrix is ColumnMajor, this operation requires a transpose.

>>> flatten (ident 3)
[1.0,0.0,0.0,0.0,1.0,0.0,0.0,0.0,1.0]
it :: (Num t, Element t) => Vector t

reshape :: Storable t => Int -> Vector t -> Matrix t Source #

Creates a matrix from a vector by grouping the elements in rows with the desired number of columns. (GNU-Octave groups by columns. To do it you can define reshapeF r = tr' . reshape r where r is the desired number of rows.)

>>> reshape 4 (fromList [1..12])
(3><4)
 [ 1.0,  2.0,  3.0,  4.0
 , 5.0,  6.0,  7.0,  8.0
 , 9.0, 10.0, 11.0, 12.0 ]

asRow :: Storable a => Vector a -> Matrix a Source #

creates a 1-row matrix from a vector

>>> asRow (fromList [1..5])
 (1><5)
  [ 1.0, 2.0, 3.0, 4.0, 5.0 ]

asColumn :: Storable a => Vector a -> Matrix a Source #

creates a 1-column matrix from a vector

>>> asColumn (fromList [1..5])
(5><1)
 [ 1.0
 , 2.0
 , 3.0
 , 4.0
 , 5.0 ]

fromRows :: Element t => [Vector t] -> Matrix t Source #

Create a matrix from a list of vectors. All vectors must have the same dimension, or dimension 1, which is are automatically expanded.

toRows :: Element t => Matrix t -> [Vector t] Source #

extracts the rows of a matrix as a list of vectors

fromColumns :: Element t => [Vector t] -> Matrix t Source #

Creates a matrix from a list of vectors, as columns

toColumns :: Element t => Matrix t -> [Vector t] Source #

Creates a list of vectors from the columns of a matrix

Indexing

atIndex :: Container c e => c e -> IndexOf c -> e Source #

generic indexing function

>>> vector [1,2,3] `atIndex` 1
2.0

>>> matrix 3 [0..8] `atIndex` (2,0)
6.0

class Indexable c t | c -> t, t -> c where Source #

Alternative indexing function.

>>> vector [1..10] ! 3
4.0

On a matrix it gets the k-th row as a vector:

>>> matrix 5 [1..15] ! 1
[6.0,7.0,8.0,9.0,10.0]
it :: Vector Double

>>> matrix 5 [1..15] ! 1 ! 3
9.0

Methods

(!) :: c -> Int -> t infixl 9 Source #

Instances

Instances details

Indexable (Vector Double) Double Source #
Instance details Defined in Internal.Util Methods (!) :: Vector Double -> Int -> Double Source #
Indexable (Vector Float) Float Source #
Instance details Defined in Internal.Util Methods (!) :: Vector Float -> Int -> Float Source #
Indexable (Vector Z) Z Source #
Instance details Defined in Internal.Util Methods (!) :: Vector Z -> Int -> Z Source #
Indexable (Vector I) I Source #
Instance details Defined in Internal.Util Methods (!) :: Vector I -> Int -> I Source #
Indexable (Vector (Complex Double)) (Complex Double) Source #
Instance details Defined in Internal.Util Methods (!) :: Vector (Complex Double) -> Int -> Complex Double Source #
Indexable (Vector (Complex Float)) (Complex Float) Source #
Instance details Defined in Internal.Util Methods (!) :: Vector (Complex Float) -> Int -> Complex Float Source #
Element t => Indexable (Matrix t) (Vector t) Source #
Instance details Defined in Internal.Util Methods (!) :: Matrix t -> Int -> Vector t Source #
(Storable t, Indexable (Vector t) t) => Indexable (Vector (Mod m t)) (Mod m t) Source #
Instance details Defined in Internal.Modular Methods (!) :: Vector (Mod m t) -> Int -> Mod m t Source #

Construction

scalar :: Container c e => e -> c e Source #

create a structure with a single element

>>> let v = fromList [1..3::Double]
>>> v / scalar (norm2 v)
fromList [0.2672612419124244,0.5345224838248488,0.8017837257372732]

class Konst e d c | d -> c, c -> d where Source #

Methods

konst :: e -> d -> c e Source #

>>> konst 7 3 :: Vector Float
fromList [7.0,7.0,7.0]

>>> konst i (3::Int,4::Int)
(3><4)
 [ 0.0 :+ 1.0, 0.0 :+ 1.0, 0.0 :+ 1.0, 0.0 :+ 1.0
 , 0.0 :+ 1.0, 0.0 :+ 1.0, 0.0 :+ 1.0, 0.0 :+ 1.0
 , 0.0 :+ 1.0, 0.0 :+ 1.0, 0.0 :+ 1.0, 0.0 :+ 1.0 ]

Instances

Instances details

Container Vector e => Konst e Int Vector Source #
Instance details Defined in Internal.Numeric Methods konst :: e -> Int -> Vector e Source #
(Num e, Container Vector e) => Konst e (Int, Int) Matrix Source #
Instance details Defined in Internal.Numeric Methods konst :: e -> (Int, Int) -> Matrix e Source #

class Build d f c e | d -> c, c -> d, f -> e, f -> d, f -> c, c e -> f, d e -> f where Source #

Methods

build :: d -> f -> c e Source #

>>> build 5 (**2) :: Vector Double
[0.0,1.0,4.0,9.0,16.0]
it :: Vector Double

Hilbert matrix of order N:

>>> let hilb n = build (n,n) (\i j -> 1/(i+j+1)) :: Matrix Double
>>> putStr . dispf 2 $ hilb 3
3x3
1.00  0.50  0.33
0.50  0.33  0.25
0.33  0.25  0.20

Instances

Instances details

Container Vector e => Build Int (e -> e) Vector e Source #
Instance details Defined in Internal.Container Methods build :: Int -> (e -> e) -> Vector e Source #
Container Matrix e => Build (Int, Int) (e -> e -> e) Matrix e Source #
Instance details Defined in Internal.Container Methods build :: (Int, Int) -> (e -> e -> e) -> Matrix e Source #

assoc Source #

Arguments

:: Container c e
=> IndexOf c	size
-> e	default value
-> [(IndexOf c, e)]	association list
-> c e	result

Create a structure from an association list

>>> assoc 5 0 [(3,7),(1,4)] :: Vector Double
fromList [0.0,4.0,0.0,7.0,0.0]

>>> assoc (2,3) 0 [((0,2),7),((1,0),2*i-3)] :: Matrix (Complex Double)
(2><3)
 [    0.0 :+ 0.0, 0.0 :+ 0.0, 7.0 :+ 0.0
 , (-3.0) :+ 2.0, 0.0 :+ 0.0, 0.0 :+ 0.0 ]

accum Source #

Arguments

:: Container c e
=> c e	initial structure
-> (e -> e -> e)	update function
-> [(IndexOf c, e)]	association list
-> c e	result

Modify a structure using an update function

>>> accum (ident 5) (+) [((1,1),5),((0,3),3)] :: Matrix Double
(5><5)
 [ 1.0, 0.0, 0.0, 3.0, 0.0
 , 0.0, 6.0, 0.0, 0.0, 0.0
 , 0.0, 0.0, 1.0, 0.0, 0.0
 , 0.0, 0.0, 0.0, 1.0, 0.0
 , 0.0, 0.0, 0.0, 0.0, 1.0 ]

computation of histogram:

>>> accum (konst 0 7) (+) (map (flip (,) 1) [4,5,4,1,5,2,5]) :: Vector Double
fromList [0.0,1.0,1.0,0.0,2.0,3.0,0.0]

linspace :: (Fractional e, Container Vector e) => Int -> (e, e) -> Vector e Source #

Creates a real vector containing a range of values:

>>> linspace 5 (-3,7::Double)
[-3.0,-0.5,2.0,4.5,7.0]
it :: Vector Double

>>> linspace 5 (8,3:+2) :: Vector (Complex Double)
[8.0 :+ 0.0,6.75 :+ 0.5,5.5 :+ 1.0,4.25 :+ 1.5,3.0 :+ 2.0]
it :: Vector (Complex Double)

Logarithmic spacing can be defined as follows:

logspace n (a,b) = 10 ** linspace n (a,b)

Diagonal

ident :: (Num a, Element a) => Int -> Matrix a Source #

creates the identity matrix of given dimension

diag :: (Num a, Element a) => Vector a -> Matrix a Source #

Creates a square matrix with a given diagonal.

diagl :: [Double] -> Matrix Double Source #

create a real diagonal matrix from a list

>>> diagl [1,2,3]
(3><3)
 [ 1.0, 0.0, 0.0
 , 0.0, 2.0, 0.0
 , 0.0, 0.0, 3.0 ]

diagRect :: Storable t => t -> Vector t -> Int -> Int -> Matrix t Source #

creates a rectangular diagonal matrix:

>>> diagRect 7 (fromList [10,20,30]) 4 5 :: Matrix Double
(4><5)
 [ 10.0,  7.0,  7.0, 7.0, 7.0
 ,  7.0, 20.0,  7.0, 7.0, 7.0
 ,  7.0,  7.0, 30.0, 7.0, 7.0
 ,  7.0,  7.0,  7.0, 7.0, 7.0 ]

takeDiag :: Element t => Matrix t -> Vector t Source #

extracts the diagonal from a rectangular matrix

Vector extraction

subVector Source #

Arguments

:: Storable t
=> Int	index of the starting element
-> Int	number of elements to extract
-> Vector t	source
-> Vector t	result

takes a number of consecutive elements from a Vector

>>> subVector 2 3 (fromList [1..10])
[3.0,4.0,5.0]
it :: (Enum t, Num t, Foreign.Storable.Storable t) => Vector t

takesV :: Storable t => [Int] -> Vector t -> [Vector t] Source #

Extract consecutive subvectors of the given sizes.

>>> takesV [3,4] (linspace 10 (1,10::Double))
[[1.0,2.0,3.0],[4.0,5.0,6.0,7.0]]
it :: [Vector Double]

vjoin :: Storable t => [Vector t] -> Vector t Source #

concatenate a list of vectors

>>> vjoin [fromList [1..5::Double], konst 1 3]
[1.0,2.0,3.0,4.0,5.0,1.0,1.0,1.0]
it :: Vector Double

Matrix extraction

data Extractor Source #

Specification of indexes for the operator ??.

Constructors

All
Range Int Int Int
Pos (Vector I)
PosCyc (Vector I)
Take Int
TakeLast Int
Drop Int
DropLast Int

Instances

Instances details

Show Extractor Source #
Instance details Defined in Internal.Element Methods showsPrec :: Int -> Extractor -> ShowS show :: Extractor -> String showList :: [Extractor] -> ShowS

(??) :: Element t => Matrix t -> (Extractor, Extractor) -> Matrix t infixl 9 Source #

General matrix slicing.

>>> m
(4><5)
 [  0,  1,  2,  3,  4
 ,  5,  6,  7,  8,  9
 , 10, 11, 12, 13, 14
 , 15, 16, 17, 18, 19 ]

>>> m ?? (Take 3, DropLast 2)
(3><3)
 [  0,  1,  2
 ,  5,  6,  7
 , 10, 11, 12 ]

>>> m ?? (Pos (idxs[2,1]), All)
(2><5)
 [ 10, 11, 12, 13, 14
 ,  5,  6,  7,  8,  9 ]

>>> m ?? (PosCyc (idxs[-7,80]), Range 4 (-2) 0)
(2><3)
 [ 9, 7, 5
 , 4, 2, 0 ]

(?) :: Element t => Matrix t -> [Int] -> Matrix t infixl 9 Source #

extract rows

>>> (20><4) [1..] ? [2,1,1]
(3><4)
 [ 9.0, 10.0, 11.0, 12.0
 , 5.0,  6.0,  7.0,  8.0
 , 5.0,  6.0,  7.0,  8.0 ]

(¿) :: Element t => Matrix t -> [Int] -> Matrix t infixl 9 Source #

extract columns

(unicode 0x00bf, inverted question mark, Alt-Gr ?)

>>> (3><4) [1..] ¿ [3,0]
(3><2)
 [  4.0, 1.0
 ,  8.0, 5.0
 , 12.0, 9.0 ]

fliprl :: Element t => Matrix t -> Matrix t Source #

Reverse columns

flipud :: Element t => Matrix t -> Matrix t Source #

Reverse rows

subMatrix Source #

Arguments

:: Element a
=> (Int, Int)	(r0,c0) starting position
-> (Int, Int)	(rt,ct) dimensions of submatrix
-> Matrix a	input matrix
-> Matrix a	result

reference to a rectangular slice of a matrix (no data copy)

takeRows :: Element t => Int -> Matrix t -> Matrix t Source #

dropRows :: Element t => Int -> Matrix t -> Matrix t Source #

takeColumns :: Element t => Int -> Matrix t -> Matrix t Source #

dropColumns :: Element t => Int -> Matrix t -> Matrix t Source #

remap :: Element t => Matrix I -> Matrix I -> Matrix t -> Matrix t Source #

Extract elements from positions given in matrices of rows and columns.

>>> r
(3><3)
 [ 1, 1, 1
 , 1, 2, 2
 , 1, 2, 3 ]
>>> c
(3><3)
 [ 0, 1, 5
 , 2, 2, 1
 , 4, 4, 1 ]
>>> m
(4><6)
 [  0,  1,  2,  3,  4,  5
 ,  6,  7,  8,  9, 10, 11
 , 12, 13, 14, 15, 16, 17
 , 18, 19, 20, 21, 22, 23 ]

>>> remap r c m
(3><3)
 [  6,  7, 11
 ,  8, 14, 13
 , 10, 16, 19 ]

The indexes are autoconformable.

>>> c'
(3><1)
 [ 1
 , 2
 , 4 ]
>>> remap r c' m
(3><3)
 [  7,  7,  7
 ,  8, 14, 14
 , 10, 16, 22 ]

Block matrix

fromBlocks :: Element t => [[Matrix t]] -> Matrix t Source #

Create a matrix from blocks given as a list of lists of matrices.

Single row-column components are automatically expanded to match the corresponding common row and column:

disp = putStr . dispf 2

>>> disp $ fromBlocks [[ident 5, 7, row[10,20]], [3, diagl[1,2,3], 0]]
8x10
1  0  0  0  0  7  7  7  10  20
0  1  0  0  0  7  7  7  10  20
0  0  1  0  0  7  7  7  10  20
0  0  0  1  0  7  7  7  10  20
0  0  0  0  1  7  7  7  10  20
3  3  3  3  3  1  0  0   0   0
3  3  3  3  3  0  2  0   0   0
3  3  3  3  3  0  0  3   0   0

(|||) :: Element t => Matrix t -> Matrix t -> Matrix t infixl 3 Source #

horizontal concatenation

>>> ident 3 ||| konst 7 (3,4)
(3><7)
 [ 1.0, 0.0, 0.0, 7.0, 7.0, 7.0, 7.0
 , 0.0, 1.0, 0.0, 7.0, 7.0, 7.0, 7.0
 , 0.0, 0.0, 1.0, 7.0, 7.0, 7.0, 7.0 ]

(===) :: Element t => Matrix t -> Matrix t -> Matrix t infixl 2 Source #

vertical concatenation

diagBlock :: (Element t, Num t) => [Matrix t] -> Matrix t Source #

create a block diagonal matrix

>>> disp 2 $ diagBlock [konst 1 (2,2), konst 2 (3,5), col [5,7]]
7x8
1  1  0  0  0  0  0  0
1  1  0  0  0  0  0  0
0  0  2  2  2  2  2  0
0  0  2  2  2  2  2  0
0  0  2  2  2  2  2  0
0  0  0  0  0  0  0  5
0  0  0  0  0  0  0  7

>>> diagBlock [(0><4)[], konst 2 (2,3)]  :: Matrix Double
(2><7)
 [ 0.0, 0.0, 0.0, 0.0, 2.0, 2.0, 2.0
 , 0.0, 0.0, 0.0, 0.0, 2.0, 2.0, 2.0 ]

repmat :: Element t => Matrix t -> Int -> Int -> Matrix t Source #

creates matrix by repetition of a matrix a given number of rows and columns

>>> repmat (ident 2) 2 3
(4><6)
 [ 1.0, 0.0, 1.0, 0.0, 1.0, 0.0
 , 0.0, 1.0, 0.0, 1.0, 0.0, 1.0
 , 1.0, 0.0, 1.0, 0.0, 1.0, 0.0
 , 0.0, 1.0, 0.0, 1.0, 0.0, 1.0 ]

toBlocks :: Element t => [Int] -> [Int] -> Matrix t -> [[Matrix t]] Source #

Partition a matrix into blocks with the given numbers of rows and columns. The remaining rows and columns are discarded.

toBlocksEvery :: Element t => Int -> Int -> Matrix t -> [[Matrix t]] Source #

Fully partition a matrix into blocks of the same size. If the dimensions are not a multiple of the given size the last blocks will be smaller.

Mapping functions

conj :: Container c e => c e -> c e Source #

complex conjugate

cmap :: (Element b, Container c e) => (e -> b) -> c e -> c b Source #

like fmap (cannot implement instance Functor because of Element class constraint)

cmod :: (Integral e, Container c e) => e -> c e -> c e Source #

mod for integer arrays

>>> cmod 3 (range 5)
fromList [0,1,2,0,1]

step :: (Ord e, Container c e) => c e -> c e Source #

A more efficient implementation of cmap (\x -> if x>0 then 1 else 0)

>>> step $ linspace 5 (-1,1::Double)
5 |> [0.0,0.0,0.0,1.0,1.0]

cond Source #

Arguments

:: (Ord e, Container c e, Container c x)
=> c e	a
-> c e	b
-> c x	l
-> c x	e
-> c x	g
-> c x	result

Element by element version of case compare a b of {LT -> l; EQ -> e; GT -> g}.

Arguments with any dimension = 1 are automatically expanded:

>>> cond ((1><4)[1..]) ((3><1)[1..]) 0 100 ((3><4)[1..]) :: Matrix Double
(3><4)
[ 100.0,   2.0,   3.0,  4.0
,   0.0, 100.0,   7.0,  8.0
,   0.0,   0.0, 100.0, 12.0 ]

>>> let chop x = cond (abs x) 1E-6 0 0 x

Find elements

find :: Container c e => (e -> Bool) -> c e -> [IndexOf c] Source #

Find index of elements which satisfy a predicate

>>> find (>0) (ident 3 :: Matrix Double)
[(0,0),(1,1),(2,2)]

maxIndex :: Container c e => c e -> IndexOf c Source #

index of maximum element

minIndex :: Container c e => c e -> IndexOf c Source #

index of minimum element

maxElement :: Container c e => c e -> e Source #

value of maximum element

minElement :: Container c e => c e -> e Source #

value of minimum element

sortVector :: (Ord t, Element t) => Vector t -> Vector t Source #

sortIndex :: (Ord t, Element t) => Vector t -> Vector I Source #

>>> m <- randn 4 10
>>> disp 2 m
4x10
-0.31   0.41   0.43  -0.19  -0.17  -0.23  -0.17  -1.04  -0.07  -1.24
 0.26   0.19   0.14   0.83  -1.54  -0.09   0.37  -0.63   0.71  -0.50
-0.11  -0.10  -1.29  -1.40  -1.04  -0.89  -0.68   0.35  -1.46   1.86
 1.04  -0.29   0.19  -0.75  -2.20  -0.01   1.06   0.11  -2.09  -1.58

>>> disp 2 $ m ?? (All, Pos $ sortIndex (m!1))
4x10
-0.17  -1.04  -1.24  -0.23   0.43   0.41  -0.31  -0.17  -0.07  -0.19
-1.54  -0.63  -0.50  -0.09   0.14   0.19   0.26   0.37   0.71   0.83
-1.04   0.35   1.86  -0.89  -1.29  -0.10  -0.11  -0.68  -1.46  -1.40
-2.20   0.11  -1.58  -0.01   0.19  -0.29   1.04   1.06  -2.09  -0.75

Sparse

type AssocMatrix = [((Int, Int), Double)] Source #

toDense :: AssocMatrix -> Matrix Double Source #

mkSparse :: AssocMatrix -> GMatrix Source #

mkDiagR :: Int -> Int -> Vector Double -> GMatrix Source #

mkDense :: Matrix Double -> GMatrix Source #

IO

disp :: Int -> Matrix Double -> IO () Source #

print a real matrix with given number of digits after the decimal point

>>> disp 5 $ ident 2 / 3
2x2
0.33333  0.00000
0.00000  0.33333

loadMatrix :: FilePath -> IO (Matrix Double) Source #

load a matrix from an ASCII file formatted as a 2D table.

loadMatrix' :: FilePath -> IO (Maybe (Matrix Double)) Source #

saveMatrix Source #

Arguments

:: FilePath
-> String	"printf" format (e.g. "%.2f", "%g", etc.)
-> Matrix Double
-> IO ()

save a matrix as a 2D ASCII table

latexFormat Source #

Arguments

:: String	type of braces: "matrix", "bmatrix", "pmatrix", etc.
-> String	Formatted matrix, with elements separated by spaces and newlines
-> String

Tool to display matrices with latex syntax.

>>> latexFormat "bmatrix" (dispf 2 $ ident 2)
"\\begin{bmatrix}\n1  &  0\n\\\\\n0  &  1\n\\end{bmatrix}"

dispf :: Int -> Matrix Double -> String Source #

Show a matrix with a given number of decimal places.

>>> dispf 2 (1/3 + ident 3)
"3x3\n1.33  0.33  0.33\n0.33  1.33  0.33\n0.33  0.33  1.33\n"

>>> putStr . dispf 2 $ (3><4)[1,1.5..]
3x4
1.00  1.50  2.00  2.50
3.00  3.50  4.00  4.50
5.00  5.50  6.00  6.50

>>> putStr . unlines . tail . lines . dispf 2 . asRow $ linspace 10 (0,1)
0.00  0.11  0.22  0.33  0.44  0.56  0.67  0.78  0.89  1.00

disps :: Int -> Matrix Double -> String Source #

Show a matrix with "autoscaling" and a given number of decimal places.

>>> putStr . disps 2 $ 120 * (3><4) [1..]
3x4  E3
 0.12  0.24  0.36  0.48
 0.60  0.72  0.84  0.96
 1.08  1.20  1.32  1.44

dispcf :: Int -> Matrix (Complex Double) -> String Source #

Pretty print a complex matrix with at most n decimal digits.

format :: Element t => String -> (t -> String) -> Matrix t -> String Source #

Creates a string from a matrix given a separator and a function to show each entry. Using this function the user can easily define any desired display function:

import Text.Printf(printf)

disp = putStr . format "  " (printf "%.2f")

dispDots :: Int -> Matrix Double -> IO () Source #

dispBlanks :: Int -> Matrix Double -> IO () Source #

dispShort :: Int -> Int -> Int -> Matrix Double -> IO () Source #

Element conversion

class Convert t where Source #

Methods

real :: Complexable c => c (RealOf t) -> c t Source #

complex :: Complexable c => c t -> c (ComplexOf t) Source #

single :: Complexable c => c t -> c (SingleOf t) Source #

double :: Complexable c => c t -> c (DoubleOf t) Source #

toComplex :: (Complexable c, RealElement t) => (c t, c t) -> c (Complex t) Source #

fromComplex :: (Complexable c, RealElement t) => c (Complex t) -> (c t, c t) Source #

Instances

Instances details

Convert Double Source #
Instance details Defined in Internal.Numeric Methods real :: Complexable c => c (RealOf Double) -> c Double Source # complex :: Complexable c => c Double -> c (ComplexOf Double) Source # single :: Complexable c => c Double -> c (SingleOf Double) Source # double :: Complexable c => c Double -> c (DoubleOf Double) Source # toComplex :: (Complexable c, RealElement Double) => (c Double, c Double) -> c (Complex Double) Source # fromComplex :: (Complexable c, RealElement Double) => c (Complex Double) -> (c Double, c Double) Source #
Convert Float Source #
Instance details Defined in Internal.Numeric Methods real :: Complexable c => c (RealOf Float) -> c Float Source # complex :: Complexable c => c Float -> c (ComplexOf Float) Source # single :: Complexable c => c Float -> c (SingleOf Float) Source # double :: Complexable c => c Float -> c (DoubleOf Float) Source # toComplex :: (Complexable c, RealElement Float) => (c Float, c Float) -> c (Complex Float) Source # fromComplex :: (Complexable c, RealElement Float) => c (Complex Float) -> (c Float, c Float) Source #
Convert (Complex Double) Source #
Instance details Defined in Internal.Numeric Methods real :: Complexable c => c (RealOf (Complex Double)) -> c (Complex Double) Source # complex :: Complexable c => c (Complex Double) -> c (ComplexOf (Complex Double)) Source # single :: Complexable c => c (Complex Double) -> c (SingleOf (Complex Double)) Source # double :: Complexable c => c (Complex Double) -> c (DoubleOf (Complex Double)) Source # toComplex :: (Complexable c, RealElement (Complex Double)) => (c (Complex Double), c (Complex Double)) -> c (Complex (Complex Double)) Source # fromComplex :: (Complexable c, RealElement (Complex Double)) => c (Complex (Complex Double)) -> (c (Complex Double), c (Complex Double)) Source #
Convert (Complex Float) Source #
Instance details Defined in Internal.Numeric Methods real :: Complexable c => c (RealOf (Complex Float)) -> c (Complex Float) Source # complex :: Complexable c => c (Complex Float) -> c (ComplexOf (Complex Float)) Source # single :: Complexable c => c (Complex Float) -> c (SingleOf (Complex Float)) Source # double :: Complexable c => c (Complex Float) -> c (DoubleOf (Complex Float)) Source # toComplex :: (Complexable c, RealElement (Complex Float)) => (c (Complex Float), c (Complex Float)) -> c (Complex (Complex Float)) Source # fromComplex :: (Complexable c, RealElement (Complex Float)) => c (Complex (Complex Float)) -> (c (Complex Float), c (Complex Float)) Source #

roundVector :: Vector Double -> Vector Double Source #

fromInt :: Container c e => c I -> c e Source #

>>> fromInt ((2><2) [0..3]) :: Matrix (Complex Double)
(2><2)
[ 0.0 :+ 0.0, 1.0 :+ 0.0
, 2.0 :+ 0.0, 3.0 :+ 0.0 ]

toInt :: Container c e => c e -> c I Source #

fromZ :: Container c e => c Z -> c e Source #

toZ :: Container c e => c e -> c Z Source #

Misc

arctan2 :: (Fractional e, Container c e) => c e -> c e -> c e Source #

separable :: Element t => (Vector t -> Vector t) -> Matrix t -> Matrix t Source #

matrix computation implemented as separated vector operations by rows and columns.

fromArray2D :: Storable e => Array (Int, Int) e -> Matrix e Source #

data Mod (n :: Nat) t Source #

Wrapper with a phantom integer for statically checked modular arithmetic.

Instances

Instances details

KnownNat m => Container Vector (Mod m Z) Source #
Instance details Defined in Internal.Modular Methods conj' :: Vector (Mod m Z) -> Vector (Mod m Z) size' :: Vector (Mod m Z) -> IndexOf Vector scalar' :: Mod m Z -> Vector (Mod m Z) scale' :: Mod m Z -> Vector (Mod m Z) -> Vector (Mod m Z) addConstant :: Mod m Z -> Vector (Mod m Z) -> Vector (Mod m Z) add' :: Vector (Mod m Z) -> Vector (Mod m Z) -> Vector (Mod m Z) sub :: Vector (Mod m Z) -> Vector (Mod m Z) -> Vector (Mod m Z) mul :: Vector (Mod m Z) -> Vector (Mod m Z) -> Vector (Mod m Z) equal :: Vector (Mod m Z) -> Vector (Mod m Z) -> Bool cmap' :: Element b => (Mod m Z -> b) -> Vector (Mod m Z) -> Vector b konst' :: Mod m Z -> IndexOf Vector -> Vector (Mod m Z) build' :: IndexOf Vector -> ArgOf Vector (Mod m Z) -> Vector (Mod m Z) atIndex' :: Vector (Mod m Z) -> IndexOf Vector -> Mod m Z minIndex' :: Vector (Mod m Z) -> IndexOf Vector maxIndex' :: Vector (Mod m Z) -> IndexOf Vector minElement' :: Vector (Mod m Z) -> Mod m Z maxElement' :: Vector (Mod m Z) -> Mod m Z sumElements' :: Vector (Mod m Z) -> Mod m Z prodElements' :: Vector (Mod m Z) -> Mod m Z step' :: Vector (Mod m Z) -> Vector (Mod m Z) ccompare' :: Vector (Mod m Z) -> Vector (Mod m Z) -> Vector I cselect' :: Vector I -> Vector (Mod m Z) -> Vector (Mod m Z) -> Vector (Mod m Z) -> Vector (Mod m Z) find' :: (Mod m Z -> Bool) -> Vector (Mod m Z) -> [IndexOf Vector] assoc' :: IndexOf Vector -> Mod m Z -> [(IndexOf Vector, Mod m Z)] -> Vector (Mod m Z) accum' :: Vector (Mod m Z) -> (Mod m Z -> Mod m Z -> Mod m Z) -> [(IndexOf Vector, Mod m Z)] -> Vector (Mod m Z) scaleRecip :: Mod m Z -> Vector (Mod m Z) -> Vector (Mod m Z) divide :: Vector (Mod m Z) -> Vector (Mod m Z) -> Vector (Mod m Z) arctan2' :: Vector (Mod m Z) -> Vector (Mod m Z) -> Vector (Mod m Z) cmod' :: Mod m Z -> Vector (Mod m Z) -> Vector (Mod m Z) fromInt' :: Vector I -> Vector (Mod m Z) toInt' :: Vector (Mod m Z) -> Vector I fromZ' :: Vector Z -> Vector (Mod m Z) toZ' :: Vector (Mod m Z) -> Vector Z
KnownNat m => Container Vector (Mod m I) Source #
Instance details Defined in Internal.Modular Methods conj' :: Vector (Mod m I) -> Vector (Mod m I) size' :: Vector (Mod m I) -> IndexOf Vector scalar' :: Mod m I -> Vector (Mod m I) scale' :: Mod m I -> Vector (Mod m I) -> Vector (Mod m I) addConstant :: Mod m I -> Vector (Mod m I) -> Vector (Mod m I) add' :: Vector (Mod m I) -> Vector (Mod m I) -> Vector (Mod m I) sub :: Vector (Mod m I) -> Vector (Mod m I) -> Vector (Mod m I) mul :: Vector (Mod m I) -> Vector (Mod m I) -> Vector (Mod m I) equal :: Vector (Mod m I) -> Vector (Mod m I) -> Bool cmap' :: Element b => (Mod m I -> b) -> Vector (Mod m I) -> Vector b konst' :: Mod m I -> IndexOf Vector -> Vector (Mod m I) build' :: IndexOf Vector -> ArgOf Vector (Mod m I) -> Vector (Mod m I) atIndex' :: Vector (Mod m I) -> IndexOf Vector -> Mod m I minIndex' :: Vector (Mod m I) -> IndexOf Vector maxIndex' :: Vector (Mod m I) -> IndexOf Vector minElement' :: Vector (Mod m I) -> Mod m I maxElement' :: Vector (Mod m I) -> Mod m I sumElements' :: Vector (Mod m I) -> Mod m I prodElements' :: Vector (Mod m I) -> Mod m I step' :: Vector (Mod m I) -> Vector (Mod m I) ccompare' :: Vector (Mod m I) -> Vector (Mod m I) -> Vector I cselect' :: Vector I -> Vector (Mod m I) -> Vector (Mod m I) -> Vector (Mod m I) -> Vector (Mod m I) find' :: (Mod m I -> Bool) -> Vector (Mod m I) -> [IndexOf Vector] assoc' :: IndexOf Vector -> Mod m I -> [(IndexOf Vector, Mod m I)] -> Vector (Mod m I) accum' :: Vector (Mod m I) -> (Mod m I -> Mod m I -> Mod m I) -> [(IndexOf Vector, Mod m I)] -> Vector (Mod m I) scaleRecip :: Mod m I -> Vector (Mod m I) -> Vector (Mod m I) divide :: Vector (Mod m I) -> Vector (Mod m I) -> Vector (Mod m I) arctan2' :: Vector (Mod m I) -> Vector (Mod m I) -> Vector (Mod m I) cmod' :: Mod m I -> Vector (Mod m I) -> Vector (Mod m I) fromInt' :: Vector I -> Vector (Mod m I) toInt' :: Vector (Mod m I) -> Vector I fromZ' :: Vector Z -> Vector (Mod m I) toZ' :: Vector (Mod m I) -> Vector Z
KnownNat m => Num (Vector (Mod m Z)) Source #
Instance details Defined in Internal.Modular Methods (+) :: Vector (Mod m Z) -> Vector (Mod m Z) -> Vector (Mod m Z) (-) :: Vector (Mod m Z) -> Vector (Mod m Z) -> Vector (Mod m Z) (*) :: Vector (Mod m Z) -> Vector (Mod m Z) -> Vector (Mod m Z) negate :: Vector (Mod m Z) -> Vector (Mod m Z) abs :: Vector (Mod m Z) -> Vector (Mod m Z) signum :: Vector (Mod m Z) -> Vector (Mod m Z) fromInteger :: Integer -> Vector (Mod m Z)
KnownNat m => Num (Vector (Mod m I)) Source #
Instance details Defined in Internal.Modular Methods (+) :: Vector (Mod m I) -> Vector (Mod m I) -> Vector (Mod m I) (-) :: Vector (Mod m I) -> Vector (Mod m I) -> Vector (Mod m I) (*) :: Vector (Mod m I) -> Vector (Mod m I) -> Vector (Mod m I) negate :: Vector (Mod m I) -> Vector (Mod m I) abs :: Vector (Mod m I) -> Vector (Mod m I) signum :: Vector (Mod m I) -> Vector (Mod m I) fromInteger :: Integer -> Vector (Mod m I)
KnownNat m => Testable (Matrix (Mod m I)) Source #
Instance details Defined in Internal.Modular Methods checkT :: Matrix (Mod m I) -> (Bool, IO ()) Source # ioCheckT :: Matrix (Mod m I) -> IO (Bool, IO ()) Source #
KnownNat m => Normed (Vector (Mod m Z)) Source #
Instance details Defined in Internal.Modular Methods norm_0 :: Vector (Mod m Z) -> R Source # norm_1 :: Vector (Mod m Z) -> R Source # norm_2 :: Vector (Mod m Z) -> R Source # norm_Inf :: Vector (Mod m Z) -> R Source #
KnownNat m => Normed (Vector (Mod m I)) Source #
Instance details Defined in Internal.Modular Methods norm_0 :: Vector (Mod m I) -> R Source # norm_1 :: Vector (Mod m I) -> R Source # norm_2 :: Vector (Mod m I) -> R Source # norm_Inf :: Vector (Mod m I) -> R Source #
(Storable t, Indexable (Vector t) t) => Indexable (Vector (Mod m t)) (Mod m t) Source #
Instance details Defined in Internal.Modular Methods (!) :: Vector (Mod m t) -> Int -> Mod m t Source #
(Integral t, Enum t, KnownNat m) => Enum (Mod m t) Source #
Instance details Defined in Internal.Modular Methods succ :: Mod m t -> Mod m t pred :: Mod m t -> Mod m t toEnum :: Int -> Mod m t fromEnum :: Mod m t -> Int enumFrom :: Mod m t -> [Mod m t] enumFromThen :: Mod m t -> Mod m t -> [Mod m t] enumFromTo :: Mod m t -> Mod m t -> [Mod m t] enumFromThenTo :: Mod m t -> Mod m t -> Mod m t -> [Mod m t]
(Eq t, KnownNat m) => Eq (Mod m t) Source #
Instance details Defined in Internal.Modular Methods (==) :: Mod m t -> Mod m t -> Bool (/=) :: Mod m t -> Mod m t -> Bool
(Show (Mod m t), Num (Mod m t), Eq t, KnownNat m) => Fractional (Mod m t) Source #	this instance is only valid for prime m
Instance details Defined in Internal.Modular Methods (/) :: Mod m t -> Mod m t -> Mod m t recip :: Mod m t -> Mod m t fromRational :: Rational -> Mod m t
(Integral t, KnownNat m, Num (Mod m t)) => Integral (Mod m t) Source #
Instance details Defined in Internal.Modular Methods quot :: Mod m t -> Mod m t -> Mod m t rem :: Mod m t -> Mod m t -> Mod m t div :: Mod m t -> Mod m t -> Mod m t mod :: Mod m t -> Mod m t -> Mod m t quotRem :: Mod m t -> Mod m t -> (Mod m t, Mod m t) divMod :: Mod m t -> Mod m t -> (Mod m t, Mod m t) toInteger :: Mod m t -> Integer
(Integral t, KnownNat n) => Num (Mod n t) Source #
Instance details Defined in Internal.Modular Methods (+) :: Mod n t -> Mod n t -> Mod n t (-) :: Mod n t -> Mod n t -> Mod n t (*) :: Mod n t -> Mod n t -> Mod n t negate :: Mod n t -> Mod n t abs :: Mod n t -> Mod n t signum :: Mod n t -> Mod n t fromInteger :: Integer -> Mod n t
(Ord t, KnownNat m) => Ord (Mod m t) Source #
Instance details Defined in Internal.Modular Methods compare :: Mod m t -> Mod m t -> Ordering (<) :: Mod m t -> Mod m t -> Bool (<=) :: Mod m t -> Mod m t -> Bool (>) :: Mod m t -> Mod m t -> Bool (>=) :: Mod m t -> Mod m t -> Bool max :: Mod m t -> Mod m t -> Mod m t min :: Mod m t -> Mod m t -> Mod m t
(Integral t, Real t, KnownNat m, Integral (Mod m t)) => Real (Mod m t) Source #
Instance details Defined in Internal.Modular Methods toRational :: Mod m t -> Rational
Show t => Show (Mod n t) Source #
Instance details Defined in Internal.Modular Methods showsPrec :: Int -> Mod n t -> ShowS show :: Mod n t -> String showList :: [Mod n t] -> ShowS
Storable t => Storable (Mod n t) Source #
Instance details Defined in Internal.Modular Methods sizeOf :: Mod n t -> Int alignment :: Mod n t -> Int peekElemOff :: Ptr (Mod n t) -> Int -> IO (Mod n t) pokeElemOff :: Ptr (Mod n t) -> Int -> Mod n t -> IO () peekByteOff :: Ptr b -> Int -> IO (Mod n t) pokeByteOff :: Ptr b -> Int -> Mod n t -> IO () peek :: Ptr (Mod n t) -> IO (Mod n t) poke :: Ptr (Mod n t) -> Mod n t -> IO ()
NFData t => NFData (Mod n t) Source #
Instance details Defined in Internal.Modular Methods rnf :: Mod n t -> ()
KnownNat m => Element (Mod m Z) Source #
Instance details Defined in Internal.Modular Methods constantD :: Mod m Z -> Int -> Vector (Mod m Z) extractR :: MatrixOrder -> Matrix (Mod m Z) -> CInt -> Vector CInt -> CInt -> Vector CInt -> IO (Matrix (Mod m Z)) setRect :: Int -> Int -> Matrix (Mod m Z) -> Matrix (Mod m Z) -> IO () sortI :: Vector (Mod m Z) -> Vector CInt sortV :: Vector (Mod m Z) -> Vector (Mod m Z) compareV :: Vector (Mod m Z) -> Vector (Mod m Z) -> Vector CInt selectV :: Vector CInt -> Vector (Mod m Z) -> Vector (Mod m Z) -> Vector (Mod m Z) -> Vector (Mod m Z) remapM :: Matrix CInt -> Matrix CInt -> Matrix (Mod m Z) -> Matrix (Mod m Z) rowOp :: Int -> Mod m Z -> Int -> Int -> Int -> Int -> Matrix (Mod m Z) -> IO () gemm :: Vector (Mod m Z) -> Matrix (Mod m Z) -> Matrix (Mod m Z) -> Matrix (Mod m Z) -> IO () reorderV :: Vector CInt -> Vector CInt -> Vector (Mod m Z) -> Vector (Mod m Z)
KnownNat m => Element (Mod m I) Source #
Instance details Defined in Internal.Modular Methods constantD :: Mod m I -> Int -> Vector (Mod m I) extractR :: MatrixOrder -> Matrix (Mod m I) -> CInt -> Vector CInt -> CInt -> Vector CInt -> IO (Matrix (Mod m I)) setRect :: Int -> Int -> Matrix (Mod m I) -> Matrix (Mod m I) -> IO () sortI :: Vector (Mod m I) -> Vector CInt sortV :: Vector (Mod m I) -> Vector (Mod m I) compareV :: Vector (Mod m I) -> Vector (Mod m I) -> Vector CInt selectV :: Vector CInt -> Vector (Mod m I) -> Vector (Mod m I) -> Vector (Mod m I) -> Vector (Mod m I) remapM :: Matrix CInt -> Matrix CInt -> Matrix (Mod m I) -> Matrix (Mod m I) rowOp :: Int -> Mod m I -> Int -> Int -> Int -> Int -> Matrix (Mod m I) -> IO () gemm :: Vector (Mod m I) -> Matrix (Mod m I) -> Matrix (Mod m I) -> Matrix (Mod m I) -> IO () reorderV :: Vector CInt -> Vector CInt -> Vector (Mod m I) -> Vector (Mod m I)
KnownNat m => Product (Mod m Z) Source #
Instance details Defined in Internal.Modular Methods multiply :: Matrix (Mod m Z) -> Matrix (Mod m Z) -> Matrix (Mod m Z) absSum :: Vector (Mod m Z) -> RealOf (Mod m Z) norm1 :: Vector (Mod m Z) -> RealOf (Mod m Z) norm2 :: Vector (Mod m Z) -> RealOf (Mod m Z) normInf :: Vector (Mod m Z) -> RealOf (Mod m Z)
KnownNat m => Product (Mod m I) Source #
Instance details Defined in Internal.Modular Methods multiply :: Matrix (Mod m I) -> Matrix (Mod m I) -> Matrix (Mod m I) absSum :: Vector (Mod m I) -> RealOf (Mod m I) norm1 :: Vector (Mod m I) -> RealOf (Mod m I) norm2 :: Vector (Mod m I) -> RealOf (Mod m I) normInf :: Vector (Mod m I) -> RealOf (Mod m I)
KnownNat m => Numeric (Mod m Z) Source #
Instance details Defined in Internal.Modular
KnownNat m => Numeric (Mod m I) Source #
Instance details Defined in Internal.Modular
type RealOf (Mod n Z) Source #
Instance details Defined in Internal.Modular type RealOf (Mod n Z) = Z
type RealOf (Mod n I) Source #
Instance details Defined in Internal.Modular type RealOf (Mod n I) = I

data Vector a Source #

Storable-based vectors

Instances

Instances details

NFData1 Vector	Since: vector-0.12.1.0
Instance details Defined in Data.Vector.Storable Methods liftRnf :: (a -> ()) -> Vector a -> ()
Complexable Vector Source #
Instance details Defined in Internal.Conversion Methods toComplex' :: RealElement e => (Vector e, Vector e) -> Vector (Complex e) fromComplex' :: RealElement e => Vector (Complex e) -> (Vector e, Vector e) comp' :: RealElement e => Vector e -> Vector (Complex e) single' :: Precision a b => Vector b -> Vector a double' :: Precision a b => Vector a -> Vector b
LSDiv Vector Source #
Instance details Defined in Internal.Container Methods linSolve :: Field t => Matrix t -> Vector t -> Vector t
Storable a => Vector Vector a
Instance details Defined in Data.Vector.Storable Methods basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) a -> m (Vector a) Source # basicUnsafeThaw :: PrimMonad m => Vector a -> m (Mutable Vector (PrimState m) a) Source # basicLength :: Vector a -> Int Source # basicUnsafeSlice :: Int -> Int -> Vector a -> Vector a Source # basicUnsafeIndexM :: Monad m => Vector a -> Int -> m a Source # basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) a -> Vector a -> m () Source # elemseq :: Vector a -> a -> b -> b Source #
Container Vector t => Linear t Vector Source #
Instance details Defined in Internal.Numeric Methods scale :: t -> Vector t -> Vector t Source #
Container Vector Double Source #
Instance details Defined in Internal.Numeric Methods conj' :: Vector Double -> Vector Double size' :: Vector Double -> IndexOf Vector scalar' :: Double -> Vector Double scale' :: Double -> Vector Double -> Vector Double addConstant :: Double -> Vector Double -> Vector Double add' :: Vector Double -> Vector Double -> Vector Double sub :: Vector Double -> Vector Double -> Vector Double mul :: Vector Double -> Vector Double -> Vector Double equal :: Vector Double -> Vector Double -> Bool cmap' :: Element b => (Double -> b) -> Vector Double -> Vector b konst' :: Double -> IndexOf Vector -> Vector Double build' :: IndexOf Vector -> ArgOf Vector Double -> Vector Double atIndex' :: Vector Double -> IndexOf Vector -> Double minIndex' :: Vector Double -> IndexOf Vector maxIndex' :: Vector Double -> IndexOf Vector minElement' :: Vector Double -> Double maxElement' :: Vector Double -> Double sumElements' :: Vector Double -> Double prodElements' :: Vector Double -> Double step' :: Vector Double -> Vector Double ccompare' :: Vector Double -> Vector Double -> Vector I cselect' :: Vector I -> Vector Double -> Vector Double -> Vector Double -> Vector Double find' :: (Double -> Bool) -> Vector Double -> [IndexOf Vector] assoc' :: IndexOf Vector -> Double -> [(IndexOf Vector, Double)] -> Vector Double accum' :: Vector Double -> (Double -> Double -> Double) -> [(IndexOf Vector, Double)] -> Vector Double scaleRecip :: Double -> Vector Double -> Vector Double divide :: Vector Double -> Vector Double -> Vector Double arctan2' :: Vector Double -> Vector Double -> Vector Double cmod' :: Double -> Vector Double -> Vector Double fromInt' :: Vector I -> Vector Double toInt' :: Vector Double -> Vector I fromZ' :: Vector Z -> Vector Double toZ' :: Vector Double -> Vector Z
Container Vector Float Source #
Instance details Defined in Internal.Numeric Methods conj' :: Vector Float -> Vector Float size' :: Vector Float -> IndexOf Vector scalar' :: Float -> Vector Float scale' :: Float -> Vector Float -> Vector Float addConstant :: Float -> Vector Float -> Vector Float add' :: Vector Float -> Vector Float -> Vector Float sub :: Vector Float -> Vector Float -> Vector Float mul :: Vector Float -> Vector Float -> Vector Float equal :: Vector Float -> Vector Float -> Bool cmap' :: Element b => (Float -> b) -> Vector Float -> Vector b konst' :: Float -> IndexOf Vector -> Vector Float build' :: IndexOf Vector -> ArgOf Vector Float -> Vector Float atIndex' :: Vector Float -> IndexOf Vector -> Float minIndex' :: Vector Float -> IndexOf Vector maxIndex' :: Vector Float -> IndexOf Vector minElement' :: Vector Float -> Float maxElement' :: Vector Float -> Float sumElements' :: Vector Float -> Float prodElements' :: Vector Float -> Float step' :: Vector Float -> Vector Float ccompare' :: Vector Float -> Vector Float -> Vector I cselect' :: Vector I -> Vector Float -> Vector Float -> Vector Float -> Vector Float find' :: (Float -> Bool) -> Vector Float -> [IndexOf Vector] assoc' :: IndexOf Vector -> Float -> [(IndexOf Vector, Float)] -> Vector Float accum' :: Vector Float -> (Float -> Float -> Float) -> [(IndexOf Vector, Float)] -> Vector Float scaleRecip :: Float -> Vector Float -> Vector Float divide :: Vector Float -> Vector Float -> Vector Float arctan2' :: Vector Float -> Vector Float -> Vector Float cmod' :: Float -> Vector Float -> Vector Float fromInt' :: Vector I -> Vector Float toInt' :: Vector Float -> Vector I fromZ' :: Vector Z -> Vector Float toZ' :: Vector Float -> Vector Z
Container Vector Z Source #
Instance details Defined in Internal.Numeric Methods conj' :: Vector Z -> Vector Z size' :: Vector Z -> IndexOf Vector scalar' :: Z -> Vector Z scale' :: Z -> Vector Z -> Vector Z addConstant :: Z -> Vector Z -> Vector Z add' :: Vector Z -> Vector Z -> Vector Z sub :: Vector Z -> Vector Z -> Vector Z mul :: Vector Z -> Vector Z -> Vector Z equal :: Vector Z -> Vector Z -> Bool cmap' :: Element b => (Z -> b) -> Vector Z -> Vector b konst' :: Z -> IndexOf Vector -> Vector Z build' :: IndexOf Vector -> ArgOf Vector Z -> Vector Z atIndex' :: Vector Z -> IndexOf Vector -> Z minIndex' :: Vector Z -> IndexOf Vector maxIndex' :: Vector Z -> IndexOf Vector minElement' :: Vector Z -> Z maxElement' :: Vector Z -> Z sumElements' :: Vector Z -> Z prodElements' :: Vector Z -> Z step' :: Vector Z -> Vector Z ccompare' :: Vector Z -> Vector Z -> Vector I cselect' :: Vector I -> Vector Z -> Vector Z -> Vector Z -> Vector Z find' :: (Z -> Bool) -> Vector Z -> [IndexOf Vector] assoc' :: IndexOf Vector -> Z -> [(IndexOf Vector, Z)] -> Vector Z accum' :: Vector Z -> (Z -> Z -> Z) -> [(IndexOf Vector, Z)] -> Vector Z scaleRecip :: Z -> Vector Z -> Vector Z divide :: Vector Z -> Vector Z -> Vector Z arctan2' :: Vector Z -> Vector Z -> Vector Z cmod' :: Z -> Vector Z -> Vector Z fromInt' :: Vector I -> Vector Z toInt' :: Vector Z -> Vector I fromZ' :: Vector Z -> Vector Z toZ' :: Vector Z -> Vector Z
Container Vector I Source #
Instance details Defined in Internal.Numeric Methods conj' :: Vector I -> Vector I size' :: Vector I -> IndexOf Vector scalar' :: I -> Vector I scale' :: I -> Vector I -> Vector I addConstant :: I -> Vector I -> Vector I add' :: Vector I -> Vector I -> Vector I sub :: Vector I -> Vector I -> Vector I mul :: Vector I -> Vector I -> Vector I equal :: Vector I -> Vector I -> Bool cmap' :: Element b => (I -> b) -> Vector I -> Vector b konst' :: I -> IndexOf Vector -> Vector I build' :: IndexOf Vector -> ArgOf Vector I -> Vector I atIndex' :: Vector I -> IndexOf Vector -> I minIndex' :: Vector I -> IndexOf Vector maxIndex' :: Vector I -> IndexOf Vector minElement' :: Vector I -> I maxElement' :: Vector I -> I sumElements' :: Vector I -> I prodElements' :: Vector I -> I step' :: Vector I -> Vector I ccompare' :: Vector I -> Vector I -> Vector I cselect' :: Vector I -> Vector I -> Vector I -> Vector I -> Vector I find' :: (I -> Bool) -> Vector I -> [IndexOf Vector] assoc' :: IndexOf Vector -> I -> [(IndexOf Vector, I)] -> Vector I accum' :: Vector I -> (I -> I -> I) -> [(IndexOf Vector, I)] -> Vector I scaleRecip :: I -> Vector I -> Vector I divide :: Vector I -> Vector I -> Vector I arctan2' :: Vector I -> Vector I -> Vector I cmod' :: I -> Vector I -> Vector I fromInt' :: Vector I -> Vector I toInt' :: Vector I -> Vector I fromZ' :: Vector Z -> Vector I toZ' :: Vector I -> Vector Z
Container Vector e => Konst e Int Vector Source #
Instance details Defined in Internal.Numeric Methods konst :: e -> Int -> Vector e Source #
Container Vector (Complex Double) Source #
Instance details Defined in Internal.Numeric Methods conj' :: Vector (Complex Double) -> Vector (Complex Double) size' :: Vector (Complex Double) -> IndexOf Vector scalar' :: Complex Double -> Vector (Complex Double) scale' :: Complex Double -> Vector (Complex Double) -> Vector (Complex Double) addConstant :: Complex Double -> Vector (Complex Double) -> Vector (Complex Double) add' :: Vector (Complex Double) -> Vector (Complex Double) -> Vector (Complex Double) sub :: Vector (Complex Double) -> Vector (Complex Double) -> Vector (Complex Double) mul :: Vector (Complex Double) -> Vector (Complex Double) -> Vector (Complex Double) equal :: Vector (Complex Double) -> Vector (Complex Double) -> Bool cmap' :: Element b => (Complex Double -> b) -> Vector (Complex Double) -> Vector b konst' :: Complex Double -> IndexOf Vector -> Vector (Complex Double) build' :: IndexOf Vector -> ArgOf Vector (Complex Double) -> Vector (Complex Double) atIndex' :: Vector (Complex Double) -> IndexOf Vector -> Complex Double minIndex' :: Vector (Complex Double) -> IndexOf Vector maxIndex' :: Vector (Complex Double) -> IndexOf Vector minElement' :: Vector (Complex Double) -> Complex Double maxElement' :: Vector (Complex Double) -> Complex Double sumElements' :: Vector (Complex Double) -> Complex Double prodElements' :: Vector (Complex Double) -> Complex Double step' :: Vector (Complex Double) -> Vector (Complex Double) ccompare' :: Vector (Complex Double) -> Vector (Complex Double) -> Vector I cselect' :: Vector I -> Vector (Complex Double) -> Vector (Complex Double) -> Vector (Complex Double) -> Vector (Complex Double) find' :: (Complex Double -> Bool) -> Vector (Complex Double) -> [IndexOf Vector] assoc' :: IndexOf Vector -> Complex Double -> [(IndexOf Vector, Complex Double)] -> Vector (Complex Double) accum' :: Vector (Complex Double) -> (Complex Double -> Complex Double -> Complex Double) -> [(IndexOf Vector, Complex Double)] -> Vector (Complex Double) scaleRecip :: Complex Double -> Vector (Complex Double) -> Vector (Complex Double) divide :: Vector (Complex Double) -> Vector (Complex Double) -> Vector (Complex Double) arctan2' :: Vector (Complex Double) -> Vector (Complex Double) -> Vector (Complex Double) cmod' :: Complex Double -> Vector (Complex Double) -> Vector (Complex Double) fromInt' :: Vector I -> Vector (Complex Double) toInt' :: Vector (Complex Double) -> Vector I fromZ' :: Vector Z -> Vector (Complex Double) toZ' :: Vector (Complex Double) -> Vector Z
Container Vector (Complex Float) Source #
Instance details Defined in Internal.Numeric Methods conj' :: Vector (Complex Float) -> Vector (Complex Float) size' :: Vector (Complex Float) -> IndexOf Vector scalar' :: Complex Float -> Vector (Complex Float) scale' :: Complex Float -> Vector (Complex Float) -> Vector (Complex Float) addConstant :: Complex Float -> Vector (Complex Float) -> Vector (Complex Float) add' :: Vector (Complex Float) -> Vector (Complex Float) -> Vector (Complex Float) sub :: Vector (Complex Float) -> Vector (Complex Float) -> Vector (Complex Float) mul :: Vector (Complex Float) -> Vector (Complex Float) -> Vector (Complex Float) equal :: Vector (Complex Float) -> Vector (Complex Float) -> Bool cmap' :: Element b => (Complex Float -> b) -> Vector (Complex Float) -> Vector b konst' :: Complex Float -> IndexOf Vector -> Vector (Complex Float) build' :: IndexOf Vector -> ArgOf Vector (Complex Float) -> Vector (Complex Float) atIndex' :: Vector (Complex Float) -> IndexOf Vector -> Complex Float minIndex' :: Vector (Complex Float) -> IndexOf Vector maxIndex' :: Vector (Complex Float) -> IndexOf Vector minElement' :: Vector (Complex Float) -> Complex Float maxElement' :: Vector (Complex Float) -> Complex Float sumElements' :: Vector (Complex Float) -> Complex Float prodElements' :: Vector (Complex Float) -> Complex Float step' :: Vector (Complex Float) -> Vector (Complex Float) ccompare' :: Vector (Complex Float) -> Vector (Complex Float) -> Vector I cselect' :: Vector I -> Vector (Complex Float) -> Vector (Complex Float) -> Vector (Complex Float) -> Vector (Complex Float) find' :: (Complex Float -> Bool) -> Vector (Complex Float) -> [IndexOf Vector] assoc' :: IndexOf Vector -> Complex Float -> [(IndexOf Vector, Complex Float)] -> Vector (Complex Float) accum' :: Vector (Complex Float) -> (Complex Float -> Complex Float -> Complex Float) -> [(IndexOf Vector, Complex Float)] -> Vector (Complex Float) scaleRecip :: Complex Float -> Vector (Complex Float) -> Vector (Complex Float) divide :: Vector (Complex Float) -> Vector (Complex Float) -> Vector (Complex Float) arctan2' :: Vector (Complex Float) -> Vector (Complex Float) -> Vector (Complex Float) cmod' :: Complex Float -> Vector (Complex Float) -> Vector (Complex Float) fromInt' :: Vector I -> Vector (Complex Float) toInt' :: Vector (Complex Float) -> Vector I fromZ' :: Vector Z -> Vector (Complex Float) toZ' :: Vector (Complex Float) -> Vector Z
KnownNat n => Sized ℂ (C n) Vector Source #
Instance details Defined in Internal.Static Methods konst :: ℂ -> C n Source # unwrap :: C n -> Vector ℂ Source # fromList :: [ℂ] -> C n Source # extract :: C n -> Vector ℂ Source # create :: Vector ℂ -> Maybe (C n) Source # size :: C n -> IndexOf Vector Source #
KnownNat n => Sized ℝ (R n) Vector Source #
Instance details Defined in Internal.Static Methods konst :: ℝ -> R n Source # unwrap :: R n -> Vector ℝ Source # fromList :: [ℝ] -> R n Source # extract :: R n -> Vector ℝ Source # create :: Vector ℝ -> Maybe (R n) Source # size :: R n -> IndexOf Vector Source #
KnownNat m => Container Vector (Mod m Z) Source #
Instance details Defined in Internal.Modular Methods conj' :: Vector (Mod m Z) -> Vector (Mod m Z) size' :: Vector (Mod m Z) -> IndexOf Vector scalar' :: Mod m Z -> Vector (Mod m Z) scale' :: Mod m Z -> Vector (Mod m Z) -> Vector (Mod m Z) addConstant :: Mod m Z -> Vector (Mod m Z) -> Vector (Mod m Z) add' :: Vector (Mod m Z) -> Vector (Mod m Z) -> Vector (Mod m Z) sub :: Vector (Mod m Z) -> Vector (Mod m Z) -> Vector (Mod m Z) mul :: Vector (Mod m Z) -> Vector (Mod m Z) -> Vector (Mod m Z) equal :: Vector (Mod m Z) -> Vector (Mod m Z) -> Bool cmap' :: Element b => (Mod m Z -> b) -> Vector (Mod m Z) -> Vector b konst' :: Mod m Z -> IndexOf Vector -> Vector (Mod m Z) build' :: IndexOf Vector -> ArgOf Vector (Mod m Z) -> Vector (Mod m Z) atIndex' :: Vector (Mod m Z) -> IndexOf Vector -> Mod m Z minIndex' :: Vector (Mod m Z) -> IndexOf Vector maxIndex' :: Vector (Mod m Z) -> IndexOf Vector minElement' :: Vector (Mod m Z) -> Mod m Z maxElement' :: Vector (Mod m Z) -> Mod m Z sumElements' :: Vector (Mod m Z) -> Mod m Z prodElements' :: Vector (Mod m Z) -> Mod m Z step' :: Vector (Mod m Z) -> Vector (Mod m Z) ccompare' :: Vector (Mod m Z) -> Vector (Mod m Z) -> Vector I cselect' :: Vector I -> Vector (Mod m Z) -> Vector (Mod m Z) -> Vector (Mod m Z) -> Vector (Mod m Z) find' :: (Mod m Z -> Bool) -> Vector (Mod m Z) -> [IndexOf Vector] assoc' :: IndexOf Vector -> Mod m Z -> [(IndexOf Vector, Mod m Z)] -> Vector (Mod m Z) accum' :: Vector (Mod m Z) -> (Mod m Z -> Mod m Z -> Mod m Z) -> [(IndexOf Vector, Mod m Z)] -> Vector (Mod m Z) scaleRecip :: Mod m Z -> Vector (Mod m Z) -> Vector (Mod m Z) divide :: Vector (Mod m Z) -> Vector (Mod m Z) -> Vector (Mod m Z) arctan2' :: Vector (Mod m Z) -> Vector (Mod m Z) -> Vector (Mod m Z) cmod' :: Mod m Z -> Vector (Mod m Z) -> Vector (Mod m Z) fromInt' :: Vector I -> Vector (Mod m Z) toInt' :: Vector (Mod m Z) -> Vector I fromZ' :: Vector Z -> Vector (Mod m Z) toZ' :: Vector (Mod m Z) -> Vector Z
KnownNat m => Container Vector (Mod m I) Source #
Instance details Defined in Internal.Modular Methods conj' :: Vector (Mod m I) -> Vector (Mod m I) size' :: Vector (Mod m I) -> IndexOf Vector scalar' :: Mod m I -> Vector (Mod m I) scale' :: Mod m I -> Vector (Mod m I) -> Vector (Mod m I) addConstant :: Mod m I -> Vector (Mod m I) -> Vector (Mod m I) add' :: Vector (Mod m I) -> Vector (Mod m I) -> Vector (Mod m I) sub :: Vector (Mod m I) -> Vector (Mod m I) -> Vector (Mod m I) mul :: Vector (Mod m I) -> Vector (Mod m I) -> Vector (Mod m I) equal :: Vector (Mod m I) -> Vector (Mod m I) -> Bool cmap' :: Element b => (Mod m I -> b) -> Vector (Mod m I) -> Vector b konst' :: Mod m I -> IndexOf Vector -> Vector (Mod m I) build' :: IndexOf Vector -> ArgOf Vector (Mod m I) -> Vector (Mod m I) atIndex' :: Vector (Mod m I) -> IndexOf Vector -> Mod m I minIndex' :: Vector (Mod m I) -> IndexOf Vector maxIndex' :: Vector (Mod m I) -> IndexOf Vector minElement' :: Vector (Mod m I) -> Mod m I maxElement' :: Vector (Mod m I) -> Mod m I sumElements' :: Vector (Mod m I) -> Mod m I prodElements' :: Vector (Mod m I) -> Mod m I step' :: Vector (Mod m I) -> Vector (Mod m I) ccompare' :: Vector (Mod m I) -> Vector (Mod m I) -> Vector I cselect' :: Vector I -> Vector (Mod m I) -> Vector (Mod m I) -> Vector (Mod m I) -> Vector (Mod m I) find' :: (Mod m I -> Bool) -> Vector (Mod m I) -> [IndexOf Vector] assoc' :: IndexOf Vector -> Mod m I -> [(IndexOf Vector, Mod m I)] -> Vector (Mod m I) accum' :: Vector (Mod m I) -> (Mod m I -> Mod m I -> Mod m I) -> [(IndexOf Vector, Mod m I)] -> Vector (Mod m I) scaleRecip :: Mod m I -> Vector (Mod m I) -> Vector (Mod m I) divide :: Vector (Mod m I) -> Vector (Mod m I) -> Vector (Mod m I) arctan2' :: Vector (Mod m I) -> Vector (Mod m I) -> Vector (Mod m I) cmod' :: Mod m I -> Vector (Mod m I) -> Vector (Mod m I) fromInt' :: Vector I -> Vector (Mod m I) toInt' :: Vector (Mod m I) -> Vector I fromZ' :: Vector Z -> Vector (Mod m I) toZ' :: Vector (Mod m I) -> Vector Z
Container Vector e => Build Int (e -> e) Vector e Source #
Instance details Defined in Internal.Container Methods build :: Int -> (e -> e) -> Vector e Source #
Storable a => IsList (Vector a)
Instance details Defined in Data.Vector.Storable Associated Types type Item (Vector a) Methods fromList :: [Item (Vector a)] -> Vector a fromListN :: Int -> [Item (Vector a)] -> Vector a toList :: Vector a -> [Item (Vector a)]
(Storable a, Eq a) => Eq (Vector a)
Instance details Defined in Data.Vector.Storable Methods (==) :: Vector a -> Vector a -> Bool (/=) :: Vector a -> Vector a -> Bool
Floating (Vector Double)
Instance details Defined in Numeric.Vector Methods pi :: Vector Double exp :: Vector Double -> Vector Double log :: Vector Double -> Vector Double sqrt :: Vector Double -> Vector Double (**) :: Vector Double -> Vector Double -> Vector Double logBase :: Vector Double -> Vector Double -> Vector Double sin :: Vector Double -> Vector Double cos :: Vector Double -> Vector Double tan :: Vector Double -> Vector Double asin :: Vector Double -> Vector Double acos :: Vector Double -> Vector Double atan :: Vector Double -> Vector Double sinh :: Vector Double -> Vector Double cosh :: Vector Double -> Vector Double tanh :: Vector Double -> Vector Double asinh :: Vector Double -> Vector Double acosh :: Vector Double -> Vector Double atanh :: Vector Double -> Vector Double log1p :: Vector Double -> Vector Double expm1 :: Vector Double -> Vector Double log1pexp :: Vector Double -> Vector Double log1mexp :: Vector Double -> Vector Double
Floating (Vector Float)
Instance details Defined in Numeric.Vector Methods pi :: Vector Float exp :: Vector Float -> Vector Float log :: Vector Float -> Vector Float sqrt :: Vector Float -> Vector Float (**) :: Vector Float -> Vector Float -> Vector Float logBase :: Vector Float -> Vector Float -> Vector Float sin :: Vector Float -> Vector Float cos :: Vector Float -> Vector Float tan :: Vector Float -> Vector Float asin :: Vector Float -> Vector Float acos :: Vector Float -> Vector Float atan :: Vector Float -> Vector Float sinh :: Vector Float -> Vector Float cosh :: Vector Float -> Vector Float tanh :: Vector Float -> Vector Float asinh :: Vector Float -> Vector Float acosh :: Vector Float -> Vector Float atanh :: Vector Float -> Vector Float log1p :: Vector Float -> Vector Float expm1 :: Vector Float -> Vector Float log1pexp :: Vector Float -> Vector Float log1mexp :: Vector Float -> Vector Float
Floating (Vector (Complex Double))
Instance details Defined in Numeric.Vector Methods pi :: Vector (Complex Double) exp :: Vector (Complex Double) -> Vector (Complex Double) log :: Vector (Complex Double) -> Vector (Complex Double) sqrt :: Vector (Complex Double) -> Vector (Complex Double) (**) :: Vector (Complex Double) -> Vector (Complex Double) -> Vector (Complex Double) logBase :: Vector (Complex Double) -> Vector (Complex Double) -> Vector (Complex Double) sin :: Vector (Complex Double) -> Vector (Complex Double) cos :: Vector (Complex Double) -> Vector (Complex Double) tan :: Vector (Complex Double) -> Vector (Complex Double) asin :: Vector (Complex Double) -> Vector (Complex Double) acos :: Vector (Complex Double) -> Vector (Complex Double) atan :: Vector (Complex Double) -> Vector (Complex Double) sinh :: Vector (Complex Double) -> Vector (Complex Double) cosh :: Vector (Complex Double) -> Vector (Complex Double) tanh :: Vector (Complex Double) -> Vector (Complex Double) asinh :: Vector (Complex Double) -> Vector (Complex Double) acosh :: Vector (Complex Double) -> Vector (Complex Double) atanh :: Vector (Complex Double) -> Vector (Complex Double) log1p :: Vector (Complex Double) -> Vector (Complex Double) expm1 :: Vector (Complex Double) -> Vector (Complex Double) log1pexp :: Vector (Complex Double) -> Vector (Complex Double) log1mexp :: Vector (Complex Double) -> Vector (Complex Double)
Floating (Vector (Complex Float))
Instance details Defined in Numeric.Vector Methods pi :: Vector (Complex Float) exp :: Vector (Complex Float) -> Vector (Complex Float) log :: Vector (Complex Float) -> Vector (Complex Float) sqrt :: Vector (Complex Float) -> Vector (Complex Float) (**) :: Vector (Complex Float) -> Vector (Complex Float) -> Vector (Complex Float) logBase :: Vector (Complex Float) -> Vector (Complex Float) -> Vector (Complex Float) sin :: Vector (Complex Float) -> Vector (Complex Float) cos :: Vector (Complex Float) -> Vector (Complex Float) tan :: Vector (Complex Float) -> Vector (Complex Float) asin :: Vector (Complex Float) -> Vector (Complex Float) acos :: Vector (Complex Float) -> Vector (Complex Float) atan :: Vector (Complex Float) -> Vector (Complex Float) sinh :: Vector (Complex Float) -> Vector (Complex Float) cosh :: Vector (Complex Float) -> Vector (Complex Float) tanh :: Vector (Complex Float) -> Vector (Complex Float) asinh :: Vector (Complex Float) -> Vector (Complex Float) acosh :: Vector (Complex Float) -> Vector (Complex Float) atanh :: Vector (Complex Float) -> Vector (Complex Float) log1p :: Vector (Complex Float) -> Vector (Complex Float) expm1 :: Vector (Complex Float) -> Vector (Complex Float) log1pexp :: Vector (Complex Float) -> Vector (Complex Float) log1mexp :: Vector (Complex Float) -> Vector (Complex Float)
(Container Vector a, Num (Vector a), Fractional a) => Fractional (Vector a)
Instance details Defined in Numeric.Vector Methods (/) :: Vector a -> Vector a -> Vector a recip :: Vector a -> Vector a fromRational :: Rational -> Vector a
(Data a, Storable a) => Data (Vector a)
Instance details Defined in Data.Vector.Storable Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Vector a -> c (Vector a) gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Vector a) toConstr :: Vector a -> Constr dataTypeOf :: Vector a -> DataType dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Vector a)) dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Vector a)) gmapT :: (forall b. Data b => b -> b) -> Vector a -> Vector a gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Vector a -> r gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Vector a -> r gmapQ :: (forall d. Data d => d -> u) -> Vector a -> [u] gmapQi :: Int -> (forall d. Data d => d -> u) -> Vector a -> u gmapM :: Monad m => (forall d. Data d => d -> m d) -> Vector a -> m (Vector a) gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Vector a -> m (Vector a) gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Vector a -> m (Vector a)
Num (Vector Double)
Instance details Defined in Numeric.Vector Methods (+) :: Vector Double -> Vector Double -> Vector Double (-) :: Vector Double -> Vector Double -> Vector Double (*) :: Vector Double -> Vector Double -> Vector Double negate :: Vector Double -> Vector Double abs :: Vector Double -> Vector Double signum :: Vector Double -> Vector Double fromInteger :: Integer -> Vector Double
Num (Vector Float)
Instance details Defined in Numeric.Vector Methods (+) :: Vector Float -> Vector Float -> Vector Float (-) :: Vector Float -> Vector Float -> Vector Float (*) :: Vector Float -> Vector Float -> Vector Float negate :: Vector Float -> Vector Float abs :: Vector Float -> Vector Float signum :: Vector Float -> Vector Float fromInteger :: Integer -> Vector Float
Num (Vector (Complex Double))
Instance details Defined in Numeric.Vector Methods (+) :: Vector (Complex Double) -> Vector (Complex Double) -> Vector (Complex Double) (-) :: Vector (Complex Double) -> Vector (Complex Double) -> Vector (Complex Double) (*) :: Vector (Complex Double) -> Vector (Complex Double) -> Vector (Complex Double) negate :: Vector (Complex Double) -> Vector (Complex Double) abs :: Vector (Complex Double) -> Vector (Complex Double) signum :: Vector (Complex Double) -> Vector (Complex Double) fromInteger :: Integer -> Vector (Complex Double)
Num (Vector (Complex Float))
Instance details Defined in Numeric.Vector Methods (+) :: Vector (Complex Float) -> Vector (Complex Float) -> Vector (Complex Float) (-) :: Vector (Complex Float) -> Vector (Complex Float) -> Vector (Complex Float) (*) :: Vector (Complex Float) -> Vector (Complex Float) -> Vector (Complex Float) negate :: Vector (Complex Float) -> Vector (Complex Float) abs :: Vector (Complex Float) -> Vector (Complex Float) signum :: Vector (Complex Float) -> Vector (Complex Float) fromInteger :: Integer -> Vector (Complex Float)
Num (Vector Z)
Instance details Defined in Numeric.Vector Methods (+) :: Vector Z -> Vector Z -> Vector Z (-) :: Vector Z -> Vector Z -> Vector Z (*) :: Vector Z -> Vector Z -> Vector Z negate :: Vector Z -> Vector Z abs :: Vector Z -> Vector Z signum :: Vector Z -> Vector Z fromInteger :: Integer -> Vector Z
Num (Vector I)
Instance details Defined in Numeric.Vector Methods (+) :: Vector I -> Vector I -> Vector I (-) :: Vector I -> Vector I -> Vector I (*) :: Vector I -> Vector I -> Vector I negate :: Vector I -> Vector I abs :: Vector I -> Vector I signum :: Vector I -> Vector I fromInteger :: Integer -> Vector I
KnownNat m => Num (Vector (Mod m Z))
Instance details Defined in Internal.Modular Methods (+) :: Vector (Mod m Z) -> Vector (Mod m Z) -> Vector (Mod m Z) (-) :: Vector (Mod m Z) -> Vector (Mod m Z) -> Vector (Mod m Z) (*) :: Vector (Mod m Z) -> Vector (Mod m Z) -> Vector (Mod m Z) negate :: Vector (Mod m Z) -> Vector (Mod m Z) abs :: Vector (Mod m Z) -> Vector (Mod m Z) signum :: Vector (Mod m Z) -> Vector (Mod m Z) fromInteger :: Integer -> Vector (Mod m Z)
KnownNat m => Num (Vector (Mod m I))
Instance details Defined in Internal.Modular Methods (+) :: Vector (Mod m I) -> Vector (Mod m I) -> Vector (Mod m I) (-) :: Vector (Mod m I) -> Vector (Mod m I) -> Vector (Mod m I) (*) :: Vector (Mod m I) -> Vector (Mod m I) -> Vector (Mod m I) negate :: Vector (Mod m I) -> Vector (Mod m I) abs :: Vector (Mod m I) -> Vector (Mod m I) signum :: Vector (Mod m I) -> Vector (Mod m I) fromInteger :: Integer -> Vector (Mod m I)
(Storable a, Ord a) => Ord (Vector a)
Instance details Defined in Data.Vector.Storable Methods compare :: Vector a -> Vector a -> Ordering (<) :: Vector a -> Vector a -> Bool (<=) :: Vector a -> Vector a -> Bool (>) :: Vector a -> Vector a -> Bool (>=) :: Vector a -> Vector a -> Bool max :: Vector a -> Vector a -> Vector a min :: Vector a -> Vector a -> Vector a
(Read a, Storable a) => Read (Vector a)
Instance details Defined in Data.Vector.Storable Methods readsPrec :: Int -> ReadS (Vector a) readList :: ReadS [Vector a] readPrec :: ReadPrec (Vector a) readListPrec :: ReadPrec [Vector a]
(Show a, Storable a) => Show (Vector a)
Instance details Defined in Data.Vector.Storable Methods showsPrec :: Int -> Vector a -> ShowS show :: Vector a -> String showList :: [Vector a] -> ShowS
Storable a => Semigroup (Vector a)
Instance details Defined in Data.Vector.Storable Methods (<>) :: Vector a -> Vector a -> Vector a sconcat :: NonEmpty (Vector a) -> Vector a stimes :: Integral b => b -> Vector a -> Vector a
Storable a => Monoid (Vector a)
Instance details Defined in Data.Vector.Storable Methods mempty :: Vector a mappend :: Vector a -> Vector a -> Vector a mconcat :: [Vector a] -> Vector a
NFData (Vector a)
Instance details Defined in Data.Vector.Storable Methods rnf :: Vector a -> ()
(Binary a, Storable a) => Binary (Vector a)
Instance details Defined in Internal.Vector Methods put :: Vector a -> Put get :: Get (Vector a) putList :: [Vector a] -> Put
Storable t => TransArray (Vector t) Source #
Instance details Defined in Internal.Devel Associated Types type Trans (Vector t) b Source # type TransRaw (Vector t) b Source # Methods apply :: Vector t -> (b -> IO r) -> Trans (Vector t) b -> IO r Source # applyRaw :: Vector t -> (b -> IO r) -> TransRaw (Vector t) b -> IO r Source #
Container Vector t => Additive (Vector t) Source #
Instance details Defined in Internal.Numeric Methods add :: Vector t -> Vector t -> Vector t Source #
Normed (Vector Float) Source #
Instance details Defined in Internal.Util Methods norm_0 :: Vector Float -> R Source # norm_1 :: Vector Float -> R Source # norm_2 :: Vector Float -> R Source # norm_Inf :: Vector Float -> R Source #
Normed (Vector (Complex Float)) Source #
Instance details Defined in Internal.Util Methods norm_0 :: Vector (Complex Float) -> R Source # norm_1 :: Vector (Complex Float) -> R Source # norm_2 :: Vector (Complex Float) -> R Source # norm_Inf :: Vector (Complex Float) -> R Source #
Normed (Vector C) Source #
Instance details Defined in Internal.Util Methods norm_0 :: Vector C -> R Source # norm_1 :: Vector C -> R Source # norm_2 :: Vector C -> R Source # norm_Inf :: Vector C -> R Source #
Normed (Vector R) Source #
Instance details Defined in Internal.Util Methods norm_0 :: Vector R -> R Source # norm_1 :: Vector R -> R Source # norm_2 :: Vector R -> R Source # norm_Inf :: Vector R -> R Source #
Normed (Vector Z) Source #
Instance details Defined in Internal.Util Methods norm_0 :: Vector Z -> R Source # norm_1 :: Vector Z -> R Source # norm_2 :: Vector Z -> R Source # norm_Inf :: Vector Z -> R Source #
Normed (Vector I) Source #
Instance details Defined in Internal.Util Methods norm_0 :: Vector I -> R Source # norm_1 :: Vector I -> R Source # norm_2 :: Vector I -> R Source # norm_Inf :: Vector I -> R Source #
KnownNat m => Normed (Vector (Mod m Z)) Source #
Instance details Defined in Internal.Modular Methods norm_0 :: Vector (Mod m Z) -> R Source # norm_1 :: Vector (Mod m Z) -> R Source # norm_2 :: Vector (Mod m Z) -> R Source # norm_Inf :: Vector (Mod m Z) -> R Source #
KnownNat m => Normed (Vector (Mod m I)) Source #
Instance details Defined in Internal.Modular Methods norm_0 :: Vector (Mod m I) -> R Source # norm_1 :: Vector (Mod m I) -> R Source # norm_2 :: Vector (Mod m I) -> R Source # norm_Inf :: Vector (Mod m I) -> R Source #
Indexable (Vector Double) Double Source #
Instance details Defined in Internal.Util Methods (!) :: Vector Double -> Int -> Double Source #
Indexable (Vector Float) Float Source #
Instance details Defined in Internal.Util Methods (!) :: Vector Float -> Int -> Float Source #
Indexable (Vector Z) Z Source #
Instance details Defined in Internal.Util Methods (!) :: Vector Z -> Int -> Z Source #
Indexable (Vector I) I Source #
Instance details Defined in Internal.Util Methods (!) :: Vector I -> Int -> I Source #
Indexable (Vector (Complex Double)) (Complex Double) Source #
Instance details Defined in Internal.Util Methods (!) :: Vector (Complex Double) -> Int -> Complex Double Source #
Indexable (Vector (Complex Float)) (Complex Float) Source #
Instance details Defined in Internal.Util Methods (!) :: Vector (Complex Float) -> Int -> Complex Float Source #
Element t => Indexable (Matrix t) (Vector t) Source #
Instance details Defined in Internal.Util Methods (!) :: Matrix t -> Int -> Vector t Source #
(Storable t, Indexable (Vector t) t) => Indexable (Vector (Mod m t)) (Mod m t) Source #
Instance details Defined in Internal.Modular Methods (!) :: Vector (Mod m t) -> Int -> Mod m t Source #
type Mutable Vector
Instance details Defined in Data.Vector.Storable type Mutable Vector = MVector
type IndexOf Vector Source #
Instance details Defined in Internal.Numeric type IndexOf Vector = Int
type Item (Vector a)
Instance details Defined in Data.Vector.Storable type Item (Vector a) = a
type Trans (Vector t) b Source #
Instance details Defined in Internal.Devel type Trans (Vector t) b = CInt -> Ptr t -> b
type TransRaw (Vector t) b Source #
Instance details Defined in Internal.Devel type TransRaw (Vector t) b = CInt -> Ptr t -> b

data Matrix t Source #

Matrix representation suitable for BLAS/LAPACK computations.

Instances

Instances details

Complexable Matrix Source #
Instance details Defined in Internal.Conversion Methods toComplex' :: RealElement e => (Matrix e, Matrix e) -> Matrix (Complex e) fromComplex' :: RealElement e => Matrix (Complex e) -> (Matrix e, Matrix e) comp' :: RealElement e => Matrix e -> Matrix (Complex e) single' :: Precision a b => Matrix b -> Matrix a double' :: Precision a b => Matrix a -> Matrix b
LSDiv Matrix Source #
Instance details Defined in Internal.Container Methods linSolve :: Field t => Matrix t -> Matrix t -> Matrix t
Container Matrix t => Linear t Matrix Source #
Instance details Defined in Internal.Numeric Methods scale :: t -> Matrix t -> Matrix t Source #
(Num a, Element a, Container Vector a) => Container Matrix a Source #
Instance details Defined in Internal.Numeric Methods conj' :: Matrix a -> Matrix a size' :: Matrix a -> IndexOf Matrix scalar' :: a -> Matrix a scale' :: a -> Matrix a -> Matrix a addConstant :: a -> Matrix a -> Matrix a add' :: Matrix a -> Matrix a -> Matrix a sub :: Matrix a -> Matrix a -> Matrix a mul :: Matrix a -> Matrix a -> Matrix a equal :: Matrix a -> Matrix a -> Bool cmap' :: Element b => (a -> b) -> Matrix a -> Matrix b konst' :: a -> IndexOf Matrix -> Matrix a build' :: IndexOf Matrix -> ArgOf Matrix a -> Matrix a atIndex' :: Matrix a -> IndexOf Matrix -> a minIndex' :: Matrix a -> IndexOf Matrix maxIndex' :: Matrix a -> IndexOf Matrix minElement' :: Matrix a -> a maxElement' :: Matrix a -> a sumElements' :: Matrix a -> a prodElements' :: Matrix a -> a step' :: Matrix a -> Matrix a ccompare' :: Matrix a -> Matrix a -> Matrix I cselect' :: Matrix I -> Matrix a -> Matrix a -> Matrix a -> Matrix a find' :: (a -> Bool) -> Matrix a -> [IndexOf Matrix] assoc' :: IndexOf Matrix -> a -> [(IndexOf Matrix, a)] -> Matrix a accum' :: Matrix a -> (a -> a -> a) -> [(IndexOf Matrix, a)] -> Matrix a scaleRecip :: a -> Matrix a -> Matrix a divide :: Matrix a -> Matrix a -> Matrix a arctan2' :: Matrix a -> Matrix a -> Matrix a cmod' :: a -> Matrix a -> Matrix a fromInt' :: Matrix I -> Matrix a toInt' :: Matrix a -> Matrix I fromZ' :: Matrix Z -> Matrix a toZ' :: Matrix a -> Matrix Z
(Num e, Container Vector e) => Konst e (Int, Int) Matrix Source #
Instance details Defined in Internal.Numeric Methods konst :: e -> (Int, Int) -> Matrix e Source #
(KnownNat m, KnownNat n) => Sized ℂ (M m n) Matrix Source #
Instance details Defined in Internal.Static Methods konst :: ℂ -> M m n Source # unwrap :: M m n -> Matrix ℂ Source # fromList :: [ℂ] -> M m n Source # extract :: M m n -> Matrix ℂ Source # create :: Matrix ℂ -> Maybe (M m n) Source # size :: M m n -> IndexOf Matrix Source #
(KnownNat m, KnownNat n) => Sized ℝ (L m n) Matrix Source #
Instance details Defined in Internal.Static Methods konst :: ℝ -> L m n Source # unwrap :: L m n -> Matrix ℝ Source # fromList :: [ℝ] -> L m n Source # extract :: L m n -> Matrix ℝ Source # create :: Matrix ℝ -> Maybe (L m n) Source # size :: L m n -> IndexOf Matrix Source #
Container Matrix a => Eq (Matrix a)
Instance details Defined in Numeric.Matrix Methods (==) :: Matrix a -> Matrix a -> Bool (/=) :: Matrix a -> Matrix a -> Bool
(Floating a, Container Vector a, Floating (Vector a), Fractional (Matrix a)) => Floating (Matrix a)
Instance details Defined in Numeric.Matrix Methods pi :: Matrix a exp :: Matrix a -> Matrix a log :: Matrix a -> Matrix a sqrt :: Matrix a -> Matrix a (**) :: Matrix a -> Matrix a -> Matrix a logBase :: Matrix a -> Matrix a -> Matrix a sin :: Matrix a -> Matrix a cos :: Matrix a -> Matrix a tan :: Matrix a -> Matrix a asin :: Matrix a -> Matrix a acos :: Matrix a -> Matrix a atan :: Matrix a -> Matrix a sinh :: Matrix a -> Matrix a cosh :: Matrix a -> Matrix a tanh :: Matrix a -> Matrix a asinh :: Matrix a -> Matrix a acosh :: Matrix a -> Matrix a atanh :: Matrix a -> Matrix a log1p :: Matrix a -> Matrix a expm1 :: Matrix a -> Matrix a log1pexp :: Matrix a -> Matrix a log1mexp :: Matrix a -> Matrix a
(Container Vector a, Fractional a, Fractional (Vector a), Num (Matrix a)) => Fractional (Matrix a)
Instance details Defined in Numeric.Matrix Methods (/) :: Matrix a -> Matrix a -> Matrix a recip :: Matrix a -> Matrix a fromRational :: Rational -> Matrix a
(Container Matrix a, Num a, Num (Vector a)) => Num (Matrix a)
Instance details Defined in Numeric.Matrix Methods (+) :: Matrix a -> Matrix a -> Matrix a (-) :: Matrix a -> Matrix a -> Matrix a (*) :: Matrix a -> Matrix a -> Matrix a negate :: Matrix a -> Matrix a abs :: Matrix a -> Matrix a signum :: Matrix a -> Matrix a fromInteger :: Integer -> Matrix a
(Element a, Read a) => Read (Matrix a)
Instance details Defined in Internal.Element Methods readsPrec :: Int -> ReadS (Matrix a) readList :: ReadS [Matrix a] readPrec :: ReadPrec (Matrix a) readListPrec :: ReadPrec [Matrix a]
(Show a, Element a) => Show (Matrix a)
Instance details Defined in Internal.Element Methods showsPrec :: Int -> Matrix a -> ShowS show :: Matrix a -> String showList :: [Matrix a] -> ShowS
(Container Vector t, Eq t, Num (Vector t), Product t) => Semigroup (Matrix t)
Instance details Defined in Numeric.Matrix Methods (<>) :: Matrix t -> Matrix t -> Matrix t sconcat :: NonEmpty (Matrix t) -> Matrix t stimes :: Integral b => b -> Matrix t -> Matrix t
(Container Vector t, Eq t, Num (Vector t), Product t) => Monoid (Matrix t)
Instance details Defined in Numeric.Matrix Methods mempty :: Matrix t mappend :: Matrix t -> Matrix t -> Matrix t mconcat :: [Matrix t] -> Matrix t
(Storable t, NFData t) => NFData (Matrix t) Source #
Instance details Defined in Internal.Matrix Methods rnf :: Matrix t -> ()
(Binary (Vector a), Element a) => Binary (Matrix a)
Instance details Defined in Internal.Element Methods put :: Matrix a -> Put get :: Get (Matrix a) putList :: [Matrix a] -> Put
Storable t => TransArray (Matrix t) Source #
Instance details Defined in Internal.Matrix Associated Types type Trans (Matrix t) b Source # type TransRaw (Matrix t) b Source # Methods apply :: Matrix t -> (b -> IO r) -> Trans (Matrix t) b -> IO r Source # applyRaw :: Matrix t -> (b -> IO r) -> TransRaw (Matrix t) b -> IO r Source #
Testable (Matrix I) Source #
Instance details Defined in Internal.Util Methods checkT :: Matrix I -> (Bool, IO ()) Source # ioCheckT :: Matrix I -> IO (Bool, IO ()) Source #
KnownNat m => Testable (Matrix (Mod m I)) Source #
Instance details Defined in Internal.Modular Methods checkT :: Matrix (Mod m I) -> (Bool, IO ()) Source # ioCheckT :: Matrix (Mod m I) -> IO (Bool, IO ()) Source #
Container Matrix t => Additive (Matrix t) Source #
Instance details Defined in Internal.Numeric Methods add :: Matrix t -> Matrix t -> Matrix t Source #
Normed (Matrix C) Source #
Instance details Defined in Internal.Util Methods norm_0 :: Matrix C -> R Source # norm_1 :: Matrix C -> R Source # norm_2 :: Matrix C -> R Source # norm_Inf :: Matrix C -> R Source #
Normed (Matrix R) Source #
Instance details Defined in Internal.Util Methods norm_0 :: Matrix R -> R Source # norm_1 :: Matrix R -> R Source # norm_2 :: Matrix R -> R Source # norm_Inf :: Matrix R -> R Source #
(CTrans t, Container Vector t) => Transposable (Matrix t) (Matrix t) Source #
Instance details Defined in Internal.Numeric Methods tr :: Matrix t -> Matrix t Source # tr' :: Matrix t -> Matrix t Source #
Element t => Indexable (Matrix t) (Vector t) Source #
Instance details Defined in Internal.Util Methods (!) :: Matrix t -> Int -> Vector t Source #
Container Matrix e => Build (Int, Int) (e -> e -> e) Matrix e Source #
Instance details Defined in Internal.Container Methods build :: (Int, Int) -> (e -> e -> e) -> Matrix e Source #
type IndexOf Matrix Source #
Instance details Defined in Internal.Numeric type IndexOf Matrix = (Int, Int)
type Trans (Matrix t) b Source #
Instance details Defined in Internal.Matrix type Trans (Matrix t) b = CInt -> CInt -> CInt -> CInt -> Ptr t -> b
type TransRaw (Matrix t) b Source #
Instance details Defined in Internal.Matrix type TransRaw (Matrix t) b = CInt -> CInt -> Ptr t -> b

data GMatrix Source #

General matrix with specialized internal representations for dense, sparse, diagonal, banded, and constant elements.

>>> let m = mkSparse [((0,999),1.0),((1,1999),2.0)]
>>> m
SparseR {gmCSR = CSR {csrVals = fromList [1.0,2.0],
                      csrCols = fromList [1000,2000],
                      csrRows = fromList [1,2,3],
                      csrNRows = 2,
                      csrNCols = 2000},
                      nRows = 2,
                      nCols = 2000}

>>> let m = mkDense (mat 2 [1..4])
>>> m
Dense {gmDense = (2><2)
 [ 1.0, 2.0
 , 3.0, 4.0 ], nRows = 2, nCols = 2}

Instances

Instances details

Show GMatrix Source #
Instance details Defined in Internal.Sparse Methods showsPrec :: Int -> GMatrix -> ShowS show :: GMatrix -> String showList :: [GMatrix] -> ShowS
Testable GMatrix Source #
Instance details Defined in Internal.CG Methods checkT :: GMatrix -> (Bool, IO ()) Source # ioCheckT :: GMatrix -> IO (Bool, IO ()) Source #
Transposable GMatrix GMatrix Source #
Instance details Defined in Internal.Sparse Methods tr :: GMatrix -> GMatrix Source # tr' :: GMatrix -> GMatrix Source #

nRows :: GMatrix -> Int Source #

nCols :: GMatrix -> Int Source #