Packages

  • package root

    High level Smile operators in Scala.

    High level Smile operators in Scala.

    Definition Classes
    root
  • package smile
    Definition Classes
    root
  • package wavelet

    A wavelet is a wave-like oscillation with an amplitude that starts out at zero, increases, and then decreases back to zero.

    A wavelet is a wave-like oscillation with an amplitude that starts out at zero, increases, and then decreases back to zero. Like the fast Fourier transform (FFT), the discrete wavelet transform (DWT) is a fast, linear operation that operates on a data vector whose length is an integer power of 2, transforming it into a numerically different vector of the same length. The wavelet transform is invertible and in fact orthogonal. Both FFT and DWT can be viewed as a rotation in function space.

    Definition Classes
    smile
  • Operators
t

smile.wavelet

Operators

trait Operators extends AnyRef

Discrete wavelet transform (DWT).

Linear Supertypes
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  1. final def !=(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  2. final def ##(): Int
    Definition Classes
    AnyRef → Any
  3. def +(other: String): String
    Implicit
    This member is added by an implicit conversion from Operators to any2stringadd[Operators] performed by method any2stringadd in scala.Predef.
    Definition Classes
    any2stringadd
  4. def ->[B](y: B): (Operators, B)
    Implicit
    This member is added by an implicit conversion from Operators to ArrowAssoc[Operators] performed by method ArrowAssoc in scala.Predef.
    Definition Classes
    ArrowAssoc
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    @inline()
  5. final def ==(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  6. final def asInstanceOf[T0]: T0
    Definition Classes
    Any
  7. def clone(): AnyRef
    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  8. def dwt(t: Array[Double], filter: String): Unit

    Discrete wavelet transform.

    Discrete wavelet transform.

    t

    the time series array. The size should be a power of 2. For time series of size no power of 2, 0 padding can be applied.

    filter

    wavelet filter.

  9. def ensuring(cond: (Operators) ⇒ Boolean, msg: ⇒ Any): Operators
    Implicit
    This member is added by an implicit conversion from Operators to Ensuring[Operators] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  10. def ensuring(cond: (Operators) ⇒ Boolean): Operators
    Implicit
    This member is added by an implicit conversion from Operators to Ensuring[Operators] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  11. def ensuring(cond: Boolean, msg: ⇒ Any): Operators
    Implicit
    This member is added by an implicit conversion from Operators to Ensuring[Operators] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  12. def ensuring(cond: Boolean): Operators
    Implicit
    This member is added by an implicit conversion from Operators to Ensuring[Operators] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  13. final def eq(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  14. def equals(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  15. def finalize(): Unit
    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( classOf[java.lang.Throwable] )
  16. def formatted(fmtstr: String): String
    Implicit
    This member is added by an implicit conversion from Operators to StringFormat[Operators] performed by method StringFormat in scala.Predef.
    Definition Classes
    StringFormat
    Annotations
    @inline()
  17. final def getClass(): Class[_]
    Definition Classes
    AnyRef → Any
  18. def hashCode(): Int
    Definition Classes
    AnyRef → Any
  19. def idwt(wt: Array[Double], filter: String): Unit

    Inverse discrete wavelet transform.

    Inverse discrete wavelet transform.

    wt

    the wavelet coefficients. The size should be a power of 2. For time series of size no power of 2, 0 padding can be applied.

    filter

    wavelet filter.

  20. final def isInstanceOf[T0]: Boolean
    Definition Classes
    Any
  21. final def ne(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  22. final def notify(): Unit
    Definition Classes
    AnyRef
  23. final def notifyAll(): Unit
    Definition Classes
    AnyRef
  24. final def synchronized[T0](arg0: ⇒ T0): T0
    Definition Classes
    AnyRef
  25. def toString(): String
    Definition Classes
    AnyRef → Any
  26. final def wait(): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  27. final def wait(arg0: Long, arg1: Int): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  28. final def wait(arg0: Long): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  29. def wavelet(filter: String): Wavelet

    Returns the wavelet filter.

    Returns the wavelet filter. The filter name is derived from one of four classes of wavelet transform filters: Daubechies, Least Asymetric, Best Localized and Coiflet. The prefixes for filters of these classes are d, la, bl and c, respectively. Following the prefix, the filter name consists of an integer indicating length. Supported lengths are as follows:

    Daubechies 4,6,8,10,12,14,16,18,20.

    Least Asymetric 8,10,12,14,16,18,20.

    Best Localized 14,18,20.

    Coiflet 6,12,18,24,30.

    Additionally "haar" is supported for Haar wavelet.

    Besides, "d4", the simplest and most localized wavelet, uses a different centering method from other Daubechies wavelet.

    filter

    filter name

  30. def wsdenoise(t: Array[Double], filter: String, soft: Boolean = false): Unit

    The wavelet shrinkage is a signal denoising technique based on the idea of thresholding the wavelet coefficients.

    The wavelet shrinkage is a signal denoising technique based on the idea of thresholding the wavelet coefficients. Wavelet coefficients having small absolute value are considered to encode mostly noise and very fine details of the signal. In contrast, the important information is encoded by the coefficients having large absolute value. Removing the small absolute value coefficients and then reconstructing the signal should produce signal with lesser amount of noise. The wavelet shrinkage approach can be summarized as follows:

    • Apply the wavelet transform to the signal.
    • Estimate a threshold value.
    • The so-called hard thresholding method zeros the coefficients that are smaller than the threshold and leaves the other ones unchanged. In contrast, the soft thresholding scales the remaining coefficients in order to form a continuous distribution of the coefficients centered on zero.
    • Reconstruct the signal (apply the inverse wavelet transform).

    The biggest challenge in the wavelet shrinkage approach is finding an appropriate threshold value. In this method, we use the universal threshold T = σ sqrt(2*log(N)), where N is the length of time series and σ is the estimate of standard deviation of the noise by the so-called scaled median absolute deviation (MAD) computed from the high-pass wavelet coefficients of the first level of the transform.

    t

    the time series array. The size should be a power of 2. For time series of size no power of 2, 0 padding can be applied.

    filter

    the wavelet filter to transform the time series.

    soft

    true if apply soft thresholding.

  31. def [B](y: B): (Operators, B)
    Implicit
    This member is added by an implicit conversion from Operators to ArrowAssoc[Operators] performed by method ArrowAssoc in scala.Predef.
    Definition Classes
    ArrowAssoc

Inherited from AnyRef

Inherited from Any

Inherited by implicit conversion any2stringadd from Operators to any2stringadd[Operators]

Inherited by implicit conversion StringFormat from Operators to StringFormat[Operators]

Inherited by implicit conversion Ensuring from Operators to Ensuring[Operators]

Inherited by implicit conversion ArrowAssoc from Operators to ArrowAssoc[Operators]

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