Numeric.FFTW.Rank3

Documentation

fourier :: (Integral n0, Integral n1, Integral n2, Real a) => Sign -> Array (Cyclic n0, Cyclic n1, Cyclic n2) (Complex a) -> Array (Cyclic n0, Cyclic n1, Cyclic n2) (Complex a)

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

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

QC.forAll genCyclicArray3 $ \xs sign -> approxComplex floatTol (Trafo3.fourier sign (Array.map Complex.conjugate xs)) (Array.map Complex.conjugate (Trafo3.fourier (flipSign sign) xs))

QC.forAll genCyclicArray3 $ \xs sign -> approxComplex doubleTol (Trafo3.fourier sign (Array.map Complex.conjugate xs)) (Array.map Complex.conjugate (Trafo3.fourier (flipSign sign) xs))

QC.forAll genCyclicArray3 $ \xys sign -> let (xs,ys) = split xys in approxComplex floatTol (Trafo3.fourier sign $ Array.zipWith (+) xs ys) (Array.zipWith (+) (Trafo3.fourier sign xs) (Trafo3.fourier sign ys))

QC.forAll genCyclicArray3 $ \xys sign -> let (xs,ys) = split xys in approxComplex doubleTol (Trafo3.fourier sign $ Array.zipWith (+) xs ys) (Array.zipWith (+) (Trafo3.fourier sign xs) (Trafo3.fourier sign ys))

QC.forAll genCyclicArray3 $ \xys sign -> let (xs,ys) = split xys in Complex.magnitude (scalarProduct (adjust xs) ys - scalarProduct (Trafo3.fourier sign xs) (Trafo3.fourier sign ys)) <= floatTol * normInf Complex.magnitude (adjust xs) * normInf Complex.magnitude ys

QC.forAll genCyclicArray3 $ \xys sign -> let (xs,ys) = split xys in Complex.magnitude (scalarProduct (adjust xs) ys - scalarProduct (Trafo3.fourier sign xs) (Trafo3.fourier sign ys)) <= doubleTol * normInf Complex.magnitude (adjust xs) * normInf Complex.magnitude ys

\sign -> QC.forAll genCyclicArray3 $ immutable (Trafo3.fourier sign) . arrayComplexFloat

\sign -> QC.forAll genCyclicArray3 $ immutable (Trafo3.fourier sign) . arrayComplexDouble

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 :: (Integral n0, Integral n1, Integral n2, Real a) => Array (Cyclic n0, Cyclic n1, Cyclic n2) a -> Array (Cyclic n0, Cyclic n1, Half n2) (Complex a)

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

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

QC.forAll genCyclicArray3 $ immutable Trafo3.fourierRC . arrayFloat

QC.forAll genCyclicArray3 $ immutable Trafo3.fourierRC . arrayDouble

fourierCR :: (Integral n0, Integral n1, Integral n2, Real a) => Array (Cyclic n0, Cyclic n1, Half n2) (Complex a) -> Array (Cyclic n0, Cyclic n1, Cyclic n2) a

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

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