Numeric.LinearAlgebra.Devel

The library can be easily extended using the tools in this module.

FFI helpers

Sample usage, to upload a perspective matrix to a shader.

 glUniformMatrix4fv 0 1 (fromIntegral gl_TRUE) `appMatrix` perspective 0.01 100 (pi/2) (4/3)

app :: (a -> b) -> a -> b infixl 1

Only useful since it is left associated with a precedence of 1, unlike $, which is right associative. e.g.

someFunction
    `appMatrixLen` m
    `appVectorLen` v
    `app` other
    `app` arguments
    `app` go here

One could also write:

(someFunction 
    `appMatrixLen` m
    `appVectorLen` v) 
    other 
    arguments 
    (go here)

appVector :: Storable a => (Ptr a -> b) -> Vector a -> b infixl 1

appVectorLen :: Storable a => (CInt -> Ptr a -> b) -> Vector a -> b

appMatrix :: Element a => (Ptr a -> b) -> Matrix a -> b infixl 1

appMatrixLen :: Element a => (CInt -> CInt -> Ptr a -> b) -> Matrix a -> b

appMatrixRaw :: Storable a => (Ptr a -> b) -> Matrix a -> b infixl 1

appMatrixRawLen :: Element a => (CInt -> CInt -> Ptr a -> b) -> Matrix a -> b

unsafeMatrixToVector :: Matrix a -> Vector a

This will disregard the order of the matrix, and simply return it as-is. If the order of the matrix is RowMajor, this function is identical to flatten.

unsafeMatrixToForeignPtr :: Storable a => Matrix a -> (ForeignPtr a, Int)

FFI tools

Illustrative usage examples can be found in the examples/devel folder included in the package.

createVector :: Storable a => Int -> IO (Vector a)

createMatrix :: Storable a => MatrixOrder -> Int -> Int -> IO (Matrix a)

vec :: Storable t => Vector t -> (((CInt -> Ptr t -> t1) -> t1) -> IO b) -> IO b

mat :: Storable t => Matrix t -> (((CInt -> CInt -> Ptr t -> t1) -> t1) -> IO b) -> IO b

app1 :: f -> Adapt1 f t1

app2 :: f -> Adapt2 f t1 r1 t2

app3 :: f -> Adapt3 f t1 r1 t2 r2 t3

app4 :: f -> Adapt4 f t1 r1 t2 r2 t3 r3 t4

app5 :: f -> Adapt5 f t1 r1 t2 r2 t3 r3 t4 r4 t5

app6 :: f -> Adapt6 f t1 r1 t2 r2 t3 r3 t4 r4 t5 r5 t6

app7 :: f -> Adapt7 f t1 r1 t2 r2 t3 r3 t4 r4 t5 r5 t6 r6 t7

app8 :: f -> Adapt8 f t1 r1 t2 r2 t3 r3 t4 r4 t5 r5 t6 r6 t7 r7 t8

app9 :: f -> Adapt9 f t1 r1 t2 r2 t3 r3 t4 r4 t5 r5 t6 r6 t7 r7 t8 r8 t9

app10 :: f -> Adapt10 f t1 r1 t2 r2 t3 r3 t4 r4 t5 r5 t6 r6 t7 r7 t8 r8 t9 r9 t10

data MatrixOrder

Constructors

RowMajor

ColumnMajor

Instances

Eq MatrixOrder

Show MatrixOrder

orderOf :: Matrix t -> MatrixOrder

cmat :: Element t => Matrix t -> Matrix t

fmat :: Element t => Matrix t -> Matrix t

matrixFromVector :: Storable t => MatrixOrder -> Int -> Int -> Vector t -> Matrix t

unsafeFromForeignPtr

Arguments

:: Storable a

=> ForeignPtr a

pointer

-> Int

offset

-> Int

length

-> Vector a

O(1) Create a vector from a ForeignPtr with an offset and a length.

The data may not be modified through the ForeignPtr afterwards.

If your offset is 0 it is more efficient to use unsafeFromForeignPtr0.

unsafeToForeignPtr :: Storable a => Vector a -> (ForeignPtr a, Int, Int)

O(1) Yield the underlying ForeignPtr together with the offset to the data and its length. The data may not be modified through the ForeignPtr.

check :: String -> IO CInt -> IO ()

check the error code

(//) :: x -> (x -> y) -> y infixl 0

postfix function application (flip ($))

at' :: Storable a => Vector a -> Int -> a

access to Vector elements without range checking

atM' :: Storable a => Matrix a -> Int -> Int -> a

fi :: Int -> CInt

specialized fromIntegral

ST

In-place manipulation inside the ST monad. See examples/inplace.hs in the distribution.

Mutable Vectors

data STVector s t

newVector :: Storable t => t -> Int -> ST s (STVector s t)

thawVector :: Storable t => Vector t -> ST s (STVector s t)

freezeVector :: Storable t => STVector s1 t -> ST s2 (Vector t)

runSTVector :: Storable t => (forall s. ST s (STVector s t)) -> Vector t

readVector :: Storable t => STVector s t -> Int -> ST s t

writeVector :: Storable t => STVector s t -> Int -> t -> ST s ()

modifyVector :: Storable t => STVector s t -> Int -> (t -> t) -> ST s ()

liftSTVector :: Storable t => (Vector t -> a) -> STVector s1 t -> ST s2 a

Mutable Matrices

data STMatrix s t

newMatrix :: Storable t => t -> Int -> Int -> ST s (STMatrix s t)

thawMatrix :: Storable t => Matrix t -> ST s (STMatrix s t)

freezeMatrix :: Storable t => STMatrix s1 t -> ST s2 (Matrix t)

runSTMatrix :: Storable t => (forall s. ST s (STMatrix s t)) -> Matrix t

readMatrix :: Storable t => STMatrix s t -> Int -> Int -> ST s t

writeMatrix :: Storable t => STMatrix s t -> Int -> Int -> t -> ST s ()

modifyMatrix :: Storable t => STMatrix s t -> Int -> Int -> (t -> t) -> ST s ()

liftSTMatrix :: Storable t => (Matrix t -> a) -> STMatrix s1 t -> ST s2 a

Unsafe functions

newUndefinedVector :: Storable t => Int -> ST s (STVector s t)

unsafeReadVector :: Storable t => STVector s t -> Int -> ST s t

unsafeWriteVector :: Storable t => STVector s t -> Int -> t -> ST s ()

unsafeThawVector :: Storable t => Vector t -> ST s (STVector s t)

unsafeFreezeVector :: Storable t => STVector s1 t -> ST s2 (Vector t)

newUndefinedMatrix :: Storable t => MatrixOrder -> Int -> Int -> ST s (STMatrix s t)

unsafeReadMatrix :: Storable t => STMatrix s t -> Int -> Int -> ST s t

unsafeWriteMatrix :: Storable t => STMatrix s t -> Int -> Int -> t -> ST s ()

unsafeThawMatrix :: Storable t => Matrix t -> ST s (STMatrix s t)

unsafeFreezeMatrix :: Storable t => STMatrix s1 t -> ST s2 (Matrix t)

Special maps and zips

mapVectorWithIndex :: (Storable a, Storable b) => (Int -> a -> b) -> Vector a -> Vector b

zipVector :: (Storable a, Storable b, Storable (a, b)) => Vector a -> Vector b -> Vector (a, b)

zip for Vectors

zipVectorWith :: (Storable a, Storable b, Storable c) => (a -> b -> c) -> Vector a -> Vector b -> Vector c

zipWith for Vectors

unzipVector :: (Storable a, Storable b, Storable (a, b)) => Vector (a, b) -> (Vector a, Vector b)

unzip for Vectors

unzipVectorWith :: (Storable (a, b), Storable c, Storable d) => ((a, b) -> (c, d)) -> Vector (a, b) -> (Vector c, Vector d)

unzipWith for Vectors

mapVectorM :: (Storable a, Storable b, Monad m) => (a -> m b) -> Vector a -> m (Vector b)

monadic map over Vectors the monad m must be strict

mapVectorM_ :: (Storable a, Monad m) => (a -> m ()) -> Vector a -> m ()

monadic map over Vectors

mapVectorWithIndexM :: (Storable a, Storable b, Monad m) => (Int -> a -> m b) -> Vector a -> m (Vector b)

monadic map over Vectors with the zero-indexed index passed to the mapping function the monad m must be strict

mapVectorWithIndexM_ :: (Storable a, Monad m) => (Int -> a -> m ()) -> Vector a -> m ()

monadic map over Vectors with the zero-indexed index passed to the mapping function

foldLoop :: (Int -> t -> t) -> t -> Int -> t

foldVector :: Storable a => (a -> b -> b) -> b -> Vector a -> b

foldVectorG :: Storable t1 => (Int -> (Int -> t1) -> t -> t) -> t -> Vector t1 -> t

foldVectorWithIndex :: Storable a => (Int -> a -> b -> b) -> b -> Vector a -> b

mapMatrixWithIndex :: (Element a, Storable b) => ((Int, Int) -> a -> b) -> Matrix a -> Matrix b

>>> mapMatrixWithIndex (\(i,j) v -> 100*v + 10*fromIntegral i + fromIntegral j) (ident 3:: Matrix Double)
(3><3)
 [ 100.0,   1.0,   2.0
 ,  10.0, 111.0,  12.0
 ,  20.0,  21.0, 122.0 ]

mapMatrixWithIndexM :: (Element a, Storable b, Monad m) => ((Int, Int) -> a -> m b) -> Matrix a -> m (Matrix b)

>>> mapMatrixWithIndexM (\(i,j) v -> Just $ 100*v + 10*fromIntegral i + fromIntegral j) (ident 3:: Matrix Double)
Just (3><3)
 [ 100.0,   1.0,   2.0
 ,  10.0, 111.0,  12.0
 ,  20.0,  21.0, 122.0 ]

mapMatrixWithIndexM_ :: (Element a, Num a, Monad m) => ((Int, Int) -> a -> m ()) -> Matrix a -> m ()

>>> mapMatrixWithIndexM_ (\(i,j) v -> printf "m[%d,%d] = %.f\n" i j v :: IO()) ((2><3)[1 :: Double ..])
m[0,0] = 1
m[0,1] = 2
m[0,2] = 3
m[1,0] = 4
m[1,1] = 5
m[1,2] = 6

liftMatrix :: (Storable a, Storable b) => (Vector a -> Vector b) -> Matrix a -> Matrix b

application of a vector function on the flattened matrix elements

liftMatrix2 :: (Element t, Element a, Element b) => (Vector a -> Vector b -> Vector t) -> Matrix a -> Matrix b -> Matrix t

application of a vector function on the flattened matrices elements

liftMatrix2Auto :: (Element t, Element a, Element b) => (Vector a -> Vector b -> Vector t) -> Matrix a -> Matrix b -> Matrix t

A version of liftMatrix2 which automatically adapt matrices with a single row or column to match the dimensions of the other matrix.

Sparse representation

data CSR

Constructors

CSR

Fields

csrVals :: Vector Double

csrCols :: Vector CInt

csrRows :: Vector CInt

csrNRows :: Int

csrNCols :: Int

Instances

Show CSR

fromCSR :: CSR -> GMatrix

mkCSR :: AssocMatrix -> CSR

data GMatrix

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}

Constructors

SparseR

Fields

gmCSR :: CSR

nRows :: Int

nCols :: Int

SparseC

Fields

gmCSC :: CSC

nRows :: Int

nCols :: Int

Diag

Fields

diagVals :: Vector Double

nRows :: Int

nCols :: Int

Dense

Fields

gmDense :: Matrix Double

nRows :: Int

nCols :: Int

Instances

Show GMatrix

Testable GMatrix

Transposable GMatrix GMatrix

Misc

toByteString :: Storable t => Vector t -> ByteString

fromByteString :: Storable t => ByteString -> Vector t