Numeric.EMD

Empirical Mode Decomposition (Hilbert-Huang Transform) in pure Haskell.

Main interface is emd, with defaultEO. A tracing version that outputs a log to stdout is also available, as emdTrace. This can be used to help track down a specific IMF that might be taking more time than desired.

This package uses "sized vectors" as its main interface, to ensure:

1. The resulting EMD contains IMFs that are all the same length as the input vector
2. We provide a vector of size of at least one.

There are many functions to convert unsized vectors to sized vectors in Data.Vector.Sized and associated modules, including toSized (for when you know the size at compile-time) and withSized (for when you don't).

However, for convenience, Numeric.EMD.Unsized is provided with an unsafe unsized interface.

EMD (Hilbert-Huang Transform)

emd :: (Vector v a, KnownNat n, Fractional a, Ord a) => EMDOpts a -> Vector v (n + 1) a -> EMD v (n + 1) a

EMD decomposition (Hilbert-Huang Transform) of a given time series with a given sifting stop condition.

Takes a sized vector to ensure that:

1. The resulting EMD contains IMFs that are all the same length as the input vector
2. We provide a vector of size of at least one.

emdTrace :: (Vector v a, KnownNat n, Fractional a, Ord a, MonadIO m) => EMDOpts a -> Vector v (n + 1) a -> m (EMD v (n + 1) a)

emd, but tracing results to stdout as IMFs are found. Useful for debugging to see how long each step is taking.

emd' :: (Vector v a, KnownNat n, Fractional a, Ord a, Applicative m) => (SiftResult v (n + 1) a -> m r) -> EMDOpts a -> Vector v (n + 1) a -> m (EMD v (n + 1) a)

emd with a callback for each found IMF.

data EMD v n a

An EMD v n a is a Hilbert-Huang transform of a time series with n items of type a stored in a vector v.

Constructors

EMD

Fields

• emdIMFs :: ![Vector v n a]
• emdResidual :: !(Vector v n a)

Instances

Show (v a) => Show (EMD v n a)

Defined in Numeric.EMD

Methods

showsPrec :: Int -> EMD v n a -> ShowS

show :: EMD v n a -> String

showList :: [EMD v n a] -> ShowS

data EMDOpts a

Options for EMD composition.

Constructors

EO

Fields

• eoSiftCondition :: SiftCondition a

  stop condition for sifting

• eoSplineEnd :: SplineEnd

  end conditions for envelope splines

• eoClampEnvelope :: Bool

  if True, use time series endpoints as part of min and max envelopes

Instances

Eq a => Eq (EMDOpts a)

Defined in Numeric.EMD

Methods

(==) :: EMDOpts a -> EMDOpts a -> Bool

(/=) :: EMDOpts a -> EMDOpts a -> Bool

Ord a => Ord (EMDOpts a)

Defined in Numeric.EMD

Methods

compare :: EMDOpts a -> EMDOpts a -> Ordering

(<) :: EMDOpts a -> EMDOpts a -> Bool

(<=) :: EMDOpts a -> EMDOpts a -> Bool

(>) :: EMDOpts a -> EMDOpts a -> Bool

(>=) :: EMDOpts a -> EMDOpts a -> Bool

max :: EMDOpts a -> EMDOpts a -> EMDOpts a

min :: EMDOpts a -> EMDOpts a -> EMDOpts a

Show a => Show (EMDOpts a)

Defined in Numeric.EMD

Methods

showsPrec :: Int -> EMDOpts a -> ShowS

show :: EMDOpts a -> String

showList :: [EMDOpts a] -> ShowS

defaultEO :: Fractional a => EMDOpts a

Default EMDOpts

data SiftCondition a

Stop conditions for sifting process

Constructors

SCStdDev a

Stop using standard SD method

SCTimes Int

Stop after a fixed number of iterations

SCOr (SiftCondition a) (SiftCondition a)

one or the other

SCAnd (SiftCondition a) (SiftCondition a)

both conditions met

Instances

Eq a => Eq (SiftCondition a)

Defined in Numeric.EMD

Methods

(==) :: SiftCondition a -> SiftCondition a -> Bool

(/=) :: SiftCondition a -> SiftCondition a -> Bool

Ord a => Ord (SiftCondition a)

Defined in Numeric.EMD

Methods

compare :: SiftCondition a -> SiftCondition a -> Ordering

(<) :: SiftCondition a -> SiftCondition a -> Bool

(<=) :: SiftCondition a -> SiftCondition a -> Bool

(>) :: SiftCondition a -> SiftCondition a -> Bool

(>=) :: SiftCondition a -> SiftCondition a -> Bool

max :: SiftCondition a -> SiftCondition a -> SiftCondition a

min :: SiftCondition a -> SiftCondition a -> SiftCondition a

Show a => Show (SiftCondition a)

Defined in Numeric.EMD

Methods

showsPrec :: Int -> SiftCondition a -> ShowS

show :: SiftCondition a -> String

showList :: [SiftCondition a] -> ShowS

defaultSC :: Fractional a => SiftCondition a

Default SiftCondition

data SplineEnd

End condition for spline

Constructors

SENotAKnot

SENatural

Instances

Eq SplineEnd

Defined in Numeric.EMD.Internal.Spline

Methods

(==) :: SplineEnd -> SplineEnd -> Bool

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

Ord SplineEnd

Defined in Numeric.EMD.Internal.Spline

Methods

compare :: SplineEnd -> SplineEnd -> Ordering

(<) :: SplineEnd -> SplineEnd -> Bool

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

(>) :: SplineEnd -> SplineEnd -> Bool

(>=) :: SplineEnd -> SplineEnd -> Bool

max :: SplineEnd -> SplineEnd -> SplineEnd

min :: SplineEnd -> SplineEnd -> SplineEnd

Show SplineEnd

Defined in Numeric.EMD.Internal.Spline

Methods

showsPrec :: Int -> SplineEnd -> ShowS

show :: SplineEnd -> String

showList :: [SplineEnd] -> ShowS

Internal

sift :: (Vector v a, KnownNat n, Fractional a, Ord a) => EMDOpts a -> Vector v (n + 1) a -> SiftResult v (n + 1) a

Iterated sifting process, used to produce either an IMF or a residual.

data SiftResult v n a

The result of a sifting operation. Each sift either yields a residual, or a new IMF.

Constructors

SRResidual !(Vector v n a)

SRIMF !(Vector v n a) !Int

number of iterations

envelopes :: (Vector v a, KnownNat n, Fractional a, Ord a) => SplineEnd -> Bool -> Vector v (n + 1) a -> Maybe (Vector v (n + 1) a, Vector v (n + 1) a)

Returns cubic splines of local minimums and maximums. Returns Nothing if there are not enough local minimum or maximums to create the splines.