Numeric.FFTW.RankN

Documentation

fourier :: (MultiCyclic sh, Real a) => Sign -> Array sh (Complex a) -> Array sh (Complex a)

>>> complexFloatList $ TrafoM.fourier TrafoM.Forward $ Array.fromList (Shape.Cyclic (5::Int), Shape.Cyclic (5::Int)) [0,0,0,0,0, 0,1,0,0,0, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0]
[1.00:+0.00,0.31:+(-0.95),(-0.81):+(-0.59),(-0.81):+0.59,0.31:+0.95,0.31:+(-0.95),(-0.81):+(-0.59),(-0.81):+0.59,0.31:+0.95,1.00:+0.00,(-0.81):+(-0.59),(-0.81):+0.59,0.31:+0.95,1.00:+0.00,0.31:+(-0.95),(-0.81):+0.59,0.31:+0.95,1.00:+0.00,0.31:+(-0.95),(-0.81):+(-0.59),0.31:+0.95,1.00:+0.00,0.31:+(-0.95),(-0.81):+(-0.59),(-0.81):+0.59]

QC.forAll genCyclicArray1 $ \xs sign -> approxComplex floatTol (array1 $ Trafo1.fourier sign xs) (TrafoM.fourier sign $ array1 xs)

QC.forAll genCyclicArray1 $ \xs sign -> approxComplex doubleTol (array1 $ Trafo1.fourier sign xs) (TrafoM.fourier sign $ array1 xs)

QC.forAll genCyclicArray2 $ \xs sign -> approxComplex floatTol (Trafo2.fourier sign xs) (TrafoM.fourier sign xs)

QC.forAll genCyclicArray2 $ \xs sign -> approxComplex doubleTol (Trafo2.fourier sign xs) (TrafoM.fourier sign xs)

QC.forAll genCyclicArray3 $ \xs sign -> approxComplex floatTol (array3 $ Trafo3.fourier sign xs) (TrafoM.fourier sign $ array3 xs)

QC.forAll genCyclicArray3 $ \xs sign -> approxComplex doubleTol (array3 $ Trafo3.fourier sign xs) (TrafoM.fourier sign $ array3 xs)

data Sign

Order is chosen such that the numeric sign is (-1) ^ fromEnum sign.

Constructors

Backward

Forward

Instances

Enum Sign

Defined in Numeric.FFTW.Private

Methods

succ :: Sign -> Sign

pred :: Sign -> Sign

toEnum :: Int -> Sign

fromEnum :: Sign -> Int

enumFrom :: Sign -> [Sign]

enumFromThen :: Sign -> Sign -> [Sign]

enumFromTo :: Sign -> Sign -> [Sign]

enumFromThenTo :: Sign -> Sign -> Sign -> [Sign]

Eq Sign

Defined in Numeric.FFTW.Private

Methods

(==) :: Sign -> Sign -> Bool

(/=) :: Sign -> Sign -> Bool

Ord Sign

Defined in Numeric.FFTW.Private

Methods

compare :: Sign -> Sign -> Ordering

(<) :: Sign -> Sign -> Bool

(<=) :: Sign -> Sign -> Bool

(>) :: Sign -> Sign -> Bool

(>=) :: Sign -> Sign -> Bool

max :: Sign -> Sign -> Sign

min :: Sign -> Sign -> Sign

Show Sign

Defined in Numeric.FFTW.Private

Methods

showsPrec :: Int -> Sign -> ShowS

show :: Sign -> String

showList :: [Sign] -> ShowS

Arbitrary Sign

Defined in Numeric.FFTW.Private

Methods

arbitrary :: Gen Sign

shrink :: Sign -> [Sign]

flipSign :: Sign -> Sign

fourierRC :: (MultiCyclic sh0, Integral n1, Real a) => Array (sh0, Cyclic n1) a -> Array (sh0, Half n1) (Complex a)

QC.forAll genCyclicArray1 $ \xs -> approxComplex floatTol (array1 $ Trafo1.fourierRC xs) (TrafoM.fourierRC $ array1 xs)

QC.forAll genCyclicArray1 $ \xs -> approxComplex doubleTol (array1 $ Trafo1.fourierRC xs) (TrafoM.fourierRC $ array1 xs)

QC.forAll genCyclicArray2 $ \xs -> approxComplex floatTol (Trafo2.fourierRC xs) (TrafoM.fourierRC xs)

QC.forAll genCyclicArray2 $ \xs -> approxComplex doubleTol (Trafo2.fourierRC xs) (TrafoM.fourierRC xs)

QC.forAll genCyclicArray3 $ \xs -> approxComplex floatTol (array3 $ Trafo3.fourierRC xs) (TrafoM.fourierRC $ array3 xs)

QC.forAll genCyclicArray3 $ \xs -> approxComplex doubleTol (array3 $ Trafo3.fourierRC xs) (TrafoM.fourierRC $ array3 xs)

QC.forAll genCyclicArray1 $ immutable TrafoM.fourierRC . array1 . arrayFloat

QC.forAll genCyclicArray1 $ immutable TrafoM.fourierRC . array1 . arrayDouble

QC.forAll genCyclicArray2 $ immutable TrafoM.fourierRC . arrayFloat

QC.forAll genCyclicArray2 $ immutable TrafoM.fourierRC . arrayDouble

QC.forAll genCyclicArray3 $ immutable TrafoM.fourierRC . array3 . arrayFloat

QC.forAll genCyclicArray3 $ immutable TrafoM.fourierRC . array3 . arrayDouble

fourierCR :: (MultiCyclic sh0, Integral n1, Real a) => Array (sh0, Half n1) (Complex a) -> Array (sh0, Cyclic n1) a

>>> floatList $ Trafo1.fourierCR $ Array.fromList (Spectrum.Half (3::Int)) [1,0 ]
[1.00,1.00,1.00]
>>> floatList $ TrafoM.fourierCR $ Array.fromList ((), Spectrum.Half (3::Int)) [1,0]
[1.00,1.00,1.00]

>>> floatList $ Trafo2.fourierCR $ Array.fromList (Shape.Cyclic (3::Int), Spectrum.Half (1::Int)) [1,0,0]
[1.00,1.00,1.00]
>>> floatList $ TrafoM.fourierCR $ Array.fromList (Shape.Cyclic (3::Int), Spectrum.Half (1::Int)) [1,0,0]
[1.00,1.00,1.00]

QC.forAll (fmap Trafo1.fourierRC genCyclicArray1) $ \xs -> approxReal floatTol (array1 $ Trafo1.fourierCR xs) (TrafoM.fourierCR $ array1 xs)

QC.forAll (fmap Trafo1.fourierRC genCyclicArray1) $ \xs -> approxReal doubleTol (array1 $ Trafo1.fourierCR xs) (TrafoM.fourierCR $ array1 xs)

QC.forAll (fmap Trafo2.fourierRC genCyclicArray2) $ \xs -> approxReal floatTol (Trafo2.fourierCR xs) (TrafoM.fourierCR xs)

QC.forAll (fmap Trafo2.fourierRC genCyclicArray2) $ \xs -> approxReal doubleTol (Trafo2.fourierCR xs) (TrafoM.fourierCR xs)

QC.forAll (fmap Trafo3.fourierRC genCyclicArray3) $ \xs -> approxReal floatTol (array3 $ Trafo3.fourierCR xs) (TrafoM.fourierCR $ array3 xs)

QC.forAll (fmap Trafo3.fourierRC genCyclicArray3) $ \xs -> approxReal doubleTol (array3 $ Trafo3.fourierCR xs) (TrafoM.fourierCR $ array3 xs)

QC.forAll (fmap Trafo1.fourierRC genCyclicArray1) $ immutable TrafoM.fourierCR . array1 . arrayComplexFloat

QC.forAll (fmap Trafo1.fourierRC genCyclicArray1) $ immutable TrafoM.fourierCR . array1 . arrayComplexDouble

QC.forAll (fmap Trafo2.fourierRC genCyclicArray2) $ immutable TrafoM.fourierCR . arrayComplexFloat

QC.forAll (fmap Trafo2.fourierRC genCyclicArray2) $ immutable TrafoM.fourierCR . arrayComplexDouble

QC.forAll (fmap Trafo3.fourierRC genCyclicArray3) $ immutable TrafoM.fourierCR . array3 . arrayComplexFloat

QC.forAll (fmap Trafo3.fourierRC genCyclicArray3) $ immutable TrafoM.fourierCR . array3 . arrayComplexDouble