Math.FFT.Base

Documentation

class (Storable a, RealFloat a) => FFTWReal a where

Our API is polymorphic over the real data type. FFTW, at least in principle, supports single precision Float, double precision Double and long double CLDouble (presumable?).

Methods

plan_guru_dft :: CInt -> Ptr IODim -> CInt -> Ptr IODim -> Ptr (Complex a) -> Ptr (Complex a) -> FFTWSign -> FFTWFlag -> IO Plan

plan_guru_dft_r2c :: CInt -> Ptr IODim -> CInt -> Ptr IODim -> Ptr a -> Ptr (Complex a) -> FFTWFlag -> IO Plan

plan_guru_dft_c2r :: CInt -> Ptr IODim -> CInt -> Ptr IODim -> Ptr (Complex a) -> Ptr a -> FFTWFlag -> IO Plan

plan_guru_r2r :: CInt -> Ptr IODim -> CInt -> Ptr IODim -> Ptr a -> Ptr a -> Ptr FFTWKind -> FFTWFlag -> IO Plan

Instances

FFTWReal Double

Using this instance requires linking with -lfftw3.

lock :: MVar ()

This lock must be taken during planning of any transform. The FFTW library is not thread-safe in the planning phase. Thankfully, the lock is not needed during the execute phase.

withLock :: IO a -> IO a

type Plan = Ptr FFTWPlan

A plan is an opaque foreign object.

type FFTWPlan = ()

newtype Flag

The Flag type is used to influence the kind of plans which are created. To specify multiple flags, use a bitwise .|..

Constructors

Flag

Fields

unFlag :: FFTWFlag

Instances

Eq Flag

Num Flag

Show Flag

Bits Flag

type FFTWFlag = CUInt

c_measure :: FFTWFlag

c_destroy_input :: FFTWFlag

c_unaligned :: FFTWFlag

c_conserve_memory :: FFTWFlag

c_exhaustive :: FFTWFlag

c_preserve_input :: FFTWFlag

Default flag. For most transforms, this is equivalent to setting measure and preserveInput. The exceptions are complex to real and half-complex to real transforms.

c_patient :: FFTWFlag

nullFlag :: Flag

c_estimate :: FFTWFlag

destroyInput :: Flag

Allows FFTW to overwrite the input array with arbitrary data; this can sometimes allow more efficient algorithms to be employed.

Setting this flag implies that two memory allocations will be done, one for work space, and one for the result. When estimate is not set, we will be doing two memory allocations anyway, so we set this flag as well (since we don't retain the work array anyway).

preserveInput :: Flag

preserveInput specifies that an out-of-place transform must not change its input array. This is ordinarily the default, except for complex to real transforms for which destroyInput is the default. In the latter cases, passing preserveInput will attempt to use algorithms that do not destroy the input, at the expense of worse performance; for multi-dimensional complex to real transforms, however, no input-preserving algorithms are implemented so the Haskell bindings will set destroyInput and do a transform with two memory allocations.

unaligned :: Flag

Instruct FFTW not to generate a plan which uses SIMD instructions, even if the memory you are planning with is aligned. This should only be needed if you are using the guru interface and want to reuse a plan with memory that may be unaligned (i.e. you constructed the CArray with unsafeForeignPtrToCArray).

conserveMemory :: Flag

The header claims that this flag is documented, but in reality, it is not. I don't know what it does and it is here only for completeness.

estimate :: Flag

estimate specifies that, instead of actual measurements of different algorithms, a simple heuristic is used to pick a (probably sub-optimal) plan quickly. With this flag, the input/output arrays are not overwritten during planning.

This is the only planner flag for which a single memory allocation is possible.

measure :: Flag

measure tells FFTW to find an optimized plan by actually computing several FFTs and measuring their execution time. Depending on your machine, this can take some time (often a few seconds). measure is the default planning option.

patient :: Flag

patient is like measure, but considers a wider range of algorithms and often produces a more optimal plan (especially for large transforms), but at the expense of several times longer planning time (especially for large transforms).

exhaustive :: Flag

exhaustive is like patient but considers an even wider range of algorithms, including many that we think are unlikely to be fast, to produce the most optimal plan but with a substantially increased planning time.

data Sign

Determine which direction of DFT to execute.

Constructors

DFTForward

DFTBackward

Instances

Eq Sign

Show Sign

type FFTWSign = CInt

c_forward :: FFTWSign

c_backward :: FFTWSign

unSign :: Sign -> FFTWSign

data Kind

Real to Real transform kinds.

Constructors

R2HC

HC2R

DHT

REDFT00

REDFT10

REDFT01

REDFT11

RODFT00

RODFT01

RODFT10

RODFT11

Instances

Eq Kind

Show Kind

unKind :: Kind -> FFTWKind

type FFTWKind = CInt

c_r2hc :: FFTWKind

c_hc2r :: FFTWKind

c_dht :: FFTWKind

c_redft00 :: FFTWKind

c_redft10 :: FFTWKind

c_redft01 :: FFTWKind

c_redft11 :: FFTWKind

c_rodft00 :: FFTWKind

Corresponds to the fftw_iodim structure. It completely describes the layout of each dimension, before and after the transform.

data IODim

Constructors

IODim

Fields

nIODim :: Int

Logical size of dimension

isIODim :: Int

Stride along dimension in input array

osIODim :: Int

Stride along dimension in output array

Instances

Eq IODim

Data IODim

Show IODim

Typeable IODim

Storable IODim

c_rodft10 :: FFTWKind

c_rodft01 :: FFTWKind

c_rodft11 :: FFTWKind

type TSpec = ([IODim], [IODim])

Tuple of transform dimensions and non-transform dimensions of the array.

data DFT

Types of transforms. Used to control dftShape.

Constructors

CC

RC

CR

CRO

RR

Instances

Eq DFT

Show DFT

check :: Plan -> IO ()

Verify that a plan is valid. Thows an exception if not.

execute :: Plan -> IO ()

Confirm that the plan is valid, then execute the transform.

unsafeNormalize :: (Ix i, Shapable i, Fractional e, Storable e) => [Int] -> CArray i e -> CArray i e

In-place normalization outside of IO. You must be able to prove that no reference to the original can be retained.

dftG :: (FFTWReal r, Ix i, Shapable i) => Sign -> Flag -> [Int] -> CArray i (Complex r) -> CArray i (Complex r)

Normalized general complex DFT

dftCRG :: (FFTWReal r, Ix i, Shapable i) => Flag -> [Int] -> CArray i (Complex r) -> CArray i r

Normalized general complex to real DFT where the last transformed dimension is logically even.

dftCROG :: (FFTWReal r, Ix i, Shapable i) => Flag -> [Int] -> CArray i (Complex r) -> CArray i r

Normalized general complex to real DFT where the last transformed dimension is logicall odd.

dftN :: (FFTWReal r, Ix i, Shapable i) => [Int] -> CArray i (Complex r) -> CArray i (Complex r)

Multi-dimensional forward DFT.

idftN :: (FFTWReal r, Ix i, Shapable i) => [Int] -> CArray i (Complex r) -> CArray i (Complex r)

Multi-dimensional inverse DFT.

dftRCN :: (FFTWReal r, Ix i, Shapable i) => [Int] -> CArray i r -> CArray i (Complex r)

Multi-dimensional forward DFT of real data.

dftCRN :: (FFTWReal r, Ix i, Shapable i) => [Int] -> CArray i (Complex r) -> CArray i r

Multi-dimensional inverse DFT of Hermitian-symmetric data (where only the non-negative frequencies are given).

dftCRON :: (FFTWReal r, Ix i, Shapable i) => [Int] -> CArray i (Complex r) -> CArray i r

Multi-dimensional inverse DFT of Hermitian-symmetric data (where only the non-negative frequencies are given) and the last transformed dimension is logically odd.

fzr :: b -> [a] -> [(a, b)]

drr :: (FFTWReal r, Ix i, Shapable i) => Kind -> [Int] -> CArray i r -> CArray i r

dftRRN :: (FFTWReal r, Ix i, Shapable i) => [(Int, Kind)] -> CArray i r -> CArray i r

Multi-dimensional real to real transform. The result is not normalized.

dftRHN :: (FFTWReal r, Ix i, Shapable i) => [Int] -> CArray i r -> CArray i r

Multi-dimensional real to half-complex transform. The result is not normalized.

dftHRN :: (FFTWReal r, Ix i, Shapable i) => [Int] -> CArray i r -> CArray i r

Multi-dimensional half-complex to real transform. The result is not normalized.

dhtN :: (FFTWReal r, Ix i, Shapable i) => [Int] -> CArray i r -> CArray i r

Multi-dimensional Discrete Hartley Transform. The result is not normalized.

dct1N :: (FFTWReal r, Ix i, Shapable i) => [Int] -> CArray i r -> CArray i r

Multi-dimensional Type 1 discrete cosine transform.

dct2N :: (FFTWReal r, Ix i, Shapable i) => [Int] -> CArray i r -> CArray i r

Multi-dimensional Type 2 discrete cosine transform. This is commonly known as the DCT.

dct3N :: (FFTWReal r, Ix i, Shapable i) => [Int] -> CArray i r -> CArray i r

Multi-dimensional Type 3 discrete cosine transform. This is commonly known as the inverse DCT. The result is not normalized.

dct4N :: (FFTWReal r, Ix i, Shapable i) => [Int] -> CArray i r -> CArray i r

Multi-dimensional Type 4 discrete cosine transform.

dst1N :: (FFTWReal r, Ix i, Shapable i) => [Int] -> CArray i r -> CArray i r

Multi-dimensional Type 1 discrete sine transform.

dst2N :: (FFTWReal r, Ix i, Shapable i) => [Int] -> CArray i r -> CArray i r

Multi-dimensional Type 2 discrete sine transform.

dst3N :: (FFTWReal r, Ix i, Shapable i) => [Int] -> CArray i r -> CArray i r

Multi-dimensional Type 3 discrete sine transform.

dst4N :: (FFTWReal r, Ix i, Shapable i) => [Int] -> CArray i r -> CArray i r

Multi-dimensional Type 4 discrete sine transform.

dft :: (FFTWReal r, Ix i, Shapable i) => CArray i (Complex r) -> CArray i (Complex r)

1-dimensional complex DFT.

idft :: (FFTWReal r, Ix i, Shapable i) => CArray i (Complex r) -> CArray i (Complex r)

1-dimensional complex inverse DFT. Inverse of dft.

dftRC :: (FFTWReal r, Ix i, Shapable i) => CArray i r -> CArray i (Complex r)

1-dimensional real to complex DFT.

dftCR :: (FFTWReal r, Ix i, Shapable i) => CArray i (Complex r) -> CArray i r

1-dimensional complex to real DFT with logically even dimension. Inverse of dftRC.

dftCRO :: (FFTWReal r, Ix i, Shapable i) => CArray i (Complex r) -> CArray i r

1-dimensional complex to real DFT with logically odd dimension. Inverse of dftRC.

dftRH :: (FFTWReal r, Ix i, Shapable i) => CArray i r -> CArray i r

1-dimensional real to half-complex DFT.

dftHR :: (FFTWReal r, Ix i, Shapable i) => CArray i r -> CArray i r

1-dimensional half-complex to real DFT. Inverse of dftRH after normalization.

dht :: (FFTWReal r, Ix i, Shapable i) => CArray i r -> CArray i r

1-dimensional Discrete Hartley Transform. Self-inverse after normalization.

dct1 :: (FFTWReal r, Ix i, Shapable i) => CArray i r -> CArray i r

1-dimensional Type 1 discrete cosine transform.

dct2 :: (FFTWReal r, Ix i, Shapable i) => CArray i r -> CArray i r

1-dimensional Type 2 discrete cosine transform. This is commonly known as the DCT.

dct3 :: (FFTWReal r, Ix i, Shapable i) => CArray i r -> CArray i r

1-dimensional Type 3 discrete cosine transform. This is commonly known as the inverse DCT.

dct4 :: (FFTWReal r, Ix i, Shapable i) => CArray i r -> CArray i r

1-dimensional Type 4 discrete cosine transform.

dst1 :: (FFTWReal r, Ix i, Shapable i) => CArray i r -> CArray i r

1-dimensional Type 1 discrete sine transform.

dst2 :: (FFTWReal r, Ix i, Shapable i) => CArray i r -> CArray i r

1-dimensional Type 2 discrete sine transform.

dst3 :: (FFTWReal r, Ix i, Shapable i) => CArray i r -> CArray i r

1-dimensional Type 3 discrete sine transform.

dst4 :: (FFTWReal r, Ix i, Shapable i) => CArray i r -> CArray i r

1-dimensional Type 4 discrete sine transform.

has :: Flag -> Flag -> Bool

transformCArray :: (Ix i, Storable a, Storable b) => Flag -> CArray i a -> (i, i) -> (FFTWFlag -> Ptr a -> Ptr b -> IO Plan) -> CArray i b

Try to transform a CArray with only one memory allocation (for the result). If we can find a way to prove that FFTW already has a sufficiently good plan for this transform size and the input will not be overwritten, then we could call have a version of this that does not require estimate. Since this is not currently the case, we require estimate to be set. Note that we do not check for the preserveInput flag here. This is because the default is to preserve input for all but the C->R and HC->R transforms. Therefore, this function must not be called for those transforms, unless preserveInput is set.

transformCArray' :: (Ix i, Storable a, Storable b) => Flag -> CArray i a -> (i, i) -> (FFTWFlag -> Ptr a -> Ptr b -> IO Plan) -> CArray i b

Transform a CArray with two memory allocations. This is entirely safe with all transforms, but it must allocate a temporary array to do the planning in.

dftShape :: (Ix i, Shapable i, Storable e) => DFT -> [Int] -> CArray i e -> ((i, i), TSpec)

All the logic for determining shape of resulting array, and how to do the transform.

withTSpec :: TSpec -> (CInt -> Ptr IODim -> CInt -> Ptr IODim -> IO a) -> IO a

A simple helper.

adjust :: (a -> a) -> Int -> [a] -> [a]

A generally useful list utility

dftGU :: (FFTWReal r, Ix i, Shapable i) => Sign -> Flag -> [Int] -> CArray i (Complex r) -> CArray i (Complex r)

Complex to Complex DFT, un-normalized.

dftRCG :: (FFTWReal r, Ix i, Shapable i) => Flag -> [Int] -> CArray i r -> CArray i (Complex r)

Real to Complex DFT.

dftCRG_ :: (FFTWReal r, Ix i, Shapable i) => Bool -> Flag -> [Int] -> CArray i (Complex r) -> CArray i r

Complex to Real DFT. The first argument determines whether the last transformed dimension is logically odd or even. True implies the dimension is odd.

dftCRGU :: (FFTWReal r, Ix i, Shapable i) => Flag -> [Int] -> CArray i (Complex r) -> CArray i r

Complex to Real DFT where last transformed dimension is logically even.

dftCROGU :: (FFTWReal r, Ix i, Shapable i) => Flag -> [Int] -> CArray i (Complex r) -> CArray i r

Complex to Real DFT where last transformed dimension is logically odd.

dftRRG :: (FFTWReal r, Ix i, Shapable i) => Flag -> [(Int, Kind)] -> CArray i r -> CArray i r

Real to Real transforms.

exportWisdomString :: IO String

Queries the FFTW cache. The String can be written to a file so the wisdom can be reused on a subsequent run.

importWisdomString :: String -> IO Bool

Add wisdom to the FFTW cache. Returns True if it is successful.

importWisdomSystem :: IO Bool

Tries to import wisdom from a global source, typically etcfftw/wisdom. Returns True if it was successful.

c_plan_guru_dft :: CInt -> Ptr IODim -> CInt -> Ptr IODim -> Ptr (Complex Double) -> Ptr (Complex Double) -> FFTWSign -> FFTWFlag -> IO Plan

Plan a complex to complex transform using the guru interface.

c_plan_guru_dft_r2c :: CInt -> Ptr IODim -> CInt -> Ptr IODim -> Ptr Double -> Ptr (Complex Double) -> FFTWFlag -> IO Plan

Plan a real to complex transform using the guru interface.

c_plan_guru_dft_c2r :: CInt -> Ptr IODim -> CInt -> Ptr IODim -> Ptr (Complex Double) -> Ptr Double -> FFTWFlag -> IO Plan

Plan a complex to real transform using the guru interface.

c_plan_guru_r2r :: CInt -> Ptr IODim -> CInt -> Ptr IODim -> Ptr Double -> Ptr Double -> Ptr FFTWKind -> FFTWFlag -> IO Plan

Plan a real to real transform using the guru interface.

c_execute :: Plan -> IO ()

Simple plan execution

c_execute_dft :: Plan -> Ptr (Complex Double) -> Ptr (Complex Double) -> IO ()

c_execute_dft_r2c :: Plan -> Ptr Double -> Ptr (Complex Double) -> IO ()

c_execute_dft_c2r :: Plan -> Ptr (Complex Double) -> Ptr Double -> IO ()

c_execute_r2r :: Plan -> Ptr Double -> Ptr Double -> IO ()

c_export_wisdom_string :: IO CString

c_import_wisdom_string :: CString -> IO CInt

c_import_wisdom_system :: IO CInt

c_free :: Ptr a -> IO ()

Frees memory allocated by fftw_malloc. Currently, we only need this to free the wisdom string.