Safe Haskell	None
Language	Haskell98

Numeric.FFTW.Batch

Synopsis

fourier :: (C loop, MultiCyclic sh, Real a) => Sign -> Array (loop, sh) (Complex a) -> Array (loop, sh) (Complex a)
data Sign
- = Backward
- | Forward
flipSign :: Sign -> Sign
fourierRC :: (C loop, MultiCyclic sh0, Integral n1, Real a) => Array (loop, sh0, Cyclic n1) a -> Array (loop, sh0, Half n1) (Complex a)
fourierCR :: (C loop, MultiCyclic sh0, Integral n1, Real a) => Array (loop, sh0, Half n1) (Complex a) -> Array (loop, sh0, Cyclic n1) a

Documentation

fourier :: (C loop, MultiCyclic sh, Real a) => Sign -> Array (loop, sh) (Complex a) -> Array (loop, sh) (Complex a) Source #

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

QC.forAll genCyclicArray2 $ \xs sign -> allApproxComplex floatTol (Array.toRowArray $ Batch.fourier sign xs) (fmap (Trafo1.fourier sign) $ Array.toRowArray xs)

QC.forAll genCyclicArray2 $ \xs sign -> allApproxComplex doubleTol (Array.toRowArray $ Batch.fourier sign xs) (fmap (Trafo1.fourier sign) $ Array.toRowArray xs)

QC.forAll (fmap array2s genCyclicArray3) $ \xs sign -> allApproxComplex floatTol (Array.toRowArray $ Batch.fourier sign xs) (fmap (Trafo2.fourier sign) $ Array.toRowArray xs)

QC.forAll (fmap array2s genCyclicArray3) $ \xs sign -> allApproxComplex doubleTol (Array.toRowArray $ Batch.fourier sign xs) (fmap (Trafo2.fourier sign) $ Array.toRowArray xs)

\sign -> QC.forAll genCyclicArray2 $ immutable (Batch.fourier sign) . arrayComplexFloat

\sign -> QC.forAll genCyclicArray2 $ immutable (Batch.fourier sign) . arrayComplexDouble

\sign -> QC.forAll genCyclicArray3 $ immutable (Batch.fourier sign) . array2s . arrayComplexFloat

\sign -> QC.forAll genCyclicArray3 $ immutable (Batch.fourier sign) . array2s . arrayComplexDouble

data Sign Source #

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

Constructors

Backward
Forward

Instances

Enum Sign Source #
Instance details 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 Source #
Instance details Defined in Numeric.FFTW.Private Methods (==) :: Sign -> Sign -> Bool # (/=) :: Sign -> Sign -> Bool #
Ord Sign Source #
Instance details 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 Source #
Instance details Defined in Numeric.FFTW.Private Methods showsPrec :: Int -> Sign -> ShowS # show :: Sign -> String # showList :: [Sign] -> ShowS #
Arbitrary Sign Source #
Instance details Defined in Numeric.FFTW.Private Methods arbitrary :: Gen Sign # shrink :: Sign -> [Sign] #

flipSign :: Sign -> Sign Source #

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

QC.forAll genCyclicArray2 $ \xs -> allApproxComplex floatTol (Array.toRowArray $ unarray1s $ Batch.fourierRC $ array1s xs) (fmap Trafo1.fourierRC $ Array.toRowArray xs)

QC.forAll genCyclicArray2 $ \xs -> allApproxComplex doubleTol (Array.toRowArray $ unarray1s $ Batch.fourierRC $ array1s xs) (fmap Trafo1.fourierRC $ Array.toRowArray xs)

QC.forAll genCyclicArray3 $ \xs -> allApproxComplex floatTol (Array.toRowArray $ array2s $ Batch.fourierRC xs) (fmap Trafo2.fourierRC $ Array.toRowArray $ array2s xs)

QC.forAll genCyclicArray3 $ \xs -> allApproxComplex doubleTol (Array.toRowArray $ array2s $ Batch.fourierRC xs) (fmap Trafo2.fourierRC $ Array.toRowArray $ array2s xs)

QC.forAll genCyclicArray2 $ immutable Batch.fourierRC . array1s . arrayFloat

QC.forAll genCyclicArray2 $ immutable Batch.fourierRC . array1s . arrayDouble

QC.forAll genCyclicArray3 $ immutable Batch.fourierRC . arrayFloat

QC.forAll genCyclicArray3 $ immutable Batch.fourierRC . arrayDouble

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

>>> floatList $ Batch.fourierCR $ Array.fromList (Shape.ZeroBased (2::Int), (), Spectrum.Half (3::Int)) [1,0, 0,-1]
[1.00,1.00,1.00,-2.00,1.00,1.00]

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

QC.forAll (fmap Trafo2.fourierRC genCyclicArray2) $ \xs -> allApproxReal floatTol (Array.toRowArray $ unarray1s $ Batch.fourierCR $ array1s xs) (fmap Trafo1.fourierCR $ Array.toRowArray xs)

QC.forAll (fmap Trafo2.fourierRC genCyclicArray2) $ \xs -> allApproxReal doubleTol (Array.toRowArray $ unarray1s $ Batch.fourierCR $ array1s xs) (fmap Trafo1.fourierCR $ Array.toRowArray xs)

QC.forAll (fmap Trafo3.fourierRC genCyclicArray3) $ \xs -> allApproxReal floatTol (Array.toRowArray $ array2s $ Batch.fourierCR xs) (fmap Trafo2.fourierCR $ Array.toRowArray $ array2s xs)

QC.forAll (fmap Trafo3.fourierRC genCyclicArray3) $ \xs -> allApproxReal doubleTol (Array.toRowArray $ array2s $ Batch.fourierCR xs) (fmap Trafo2.fourierCR $ Array.toRowArray $ array2s xs)

QC.forAll (fmap Trafo2.fourierRC genCyclicArray2) $ immutable Batch.fourierCR . array1s . arrayComplexFloat

QC.forAll (fmap Trafo2.fourierRC genCyclicArray2) $ immutable Batch.fourierCR . array1s . arrayComplexDouble

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

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