Packages

class Hilbert extends AnyRef

The Hilbert class provides operators to add, subtract, mutiply, divide and raise functions. Given two functions, 'f' and 'g', a new function is created. It also provides methods for computing dot/inner products, norms and distances for functions defined in Hilbert Space. On interval [a, b]

Lp-norm (f) = [ ∫f(t)p dt ]1/p

See also

implicit conversion 'functionS2S2Hilbert' in package.scala

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Instance Constructors

  1. new Hilbert(f: FunctionS2S)

    f

    the function to convert into a Hilbert function

Value Members

  1. final def !=(arg0: Any): Boolean
    Definition Classes
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  2. final def ##(): Int
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  3. def *(g: Double): (Double) ⇒ Double
  4. def *(g: FunctionS2S): (Double) ⇒ Double

    Multiply function 'f' by function 'g', returning a new function.

    Multiply function 'f' by function 'g', returning a new function.

    g

    the other function

  5. def +(g: Double): (Double) ⇒ Double
  6. def +(g: FunctionS2S): (Double) ⇒ Double

    Add function 'f' and function 'g', returning a new function.

    Add function 'f' and function 'g', returning a new function.

    g

    the other function

  7. def -(g: Double): (Double) ⇒ Double
  8. def -(g: FunctionS2S): (Double) ⇒ Double

    From function 'f' subtract function 'g', returning a new function.

    From function 'f' subtract function 'g', returning a new function.

    g

    the other function

  9. def /(g: Double): (Double) ⇒ Double
  10. def /(g: FunctionS2S): (Double) ⇒ Double

    Divide function 'f' by function 'g', returning a new function.

    Divide function 'f' by function 'g', returning a new function.

    g

    the other function

  11. final def ==(arg0: Any): Boolean
    Definition Classes
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  12. final def asInstanceOf[T0]: T0
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  13. def clone(): AnyRef
    Attributes
    protected[java.lang]
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    @throws( ... )
  14. def dist(g: FunctionS2S, a: Double = 0.0, b: Double = 1.0): Double

    Compute the distance in L2 space between function 'f' and function 'g'.

    Compute the distance in L2 space between function 'f' and function 'g'.

    g

    the other function

    a

    the start of the interval

    b

    the end of the interval

  15. def dist_p(g: FunctionS2S, p: Int, a: Double = 0.0, b: Double = 1.0): Double

    Compute the distance in Lp space between function 'f' and function 'g'.

    Compute the distance in Lp space between function 'f' and function 'g'.

    g

    the other function

    p

    the level, e.g., 1, 2, ...

    a

    the start of the interval

    b

    the end of the interval

  16. def dot(g: FunctionS2S, a: Double = 0.0, b: Double = 1.0): Double

    Compute the dot/inner product of functions 'f' and 'g'.

    Compute the dot/inner product of functions 'f' and 'g'.

    g

    the other function

    a

    the start of the interval

    b

    the end of the interval

  17. final def eq(arg0: AnyRef): Boolean
    Definition Classes
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  18. def equals(arg0: Any): Boolean
    Definition Classes
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  19. def finalize(): Unit
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    protected[java.lang]
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    @throws( classOf[java.lang.Throwable] )
  20. final def getClass(): Class[_]
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  21. def hashCode(): Int
    Definition Classes
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  22. final def isInstanceOf[T0]: Boolean
    Definition Classes
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  23. final def ne(arg0: AnyRef): Boolean
    Definition Classes
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  24. def norm(a: Double = 0.0, b: Double = 1.0): Double

    Compute the L2 norm of function 'f'.

    Compute the L2 norm of function 'f'.

    a

    the start of the interval

    b

    the end of the interval

  25. def normSq(a: Double = 0.0, b: Double = 1.0): Double

    Compute the L2 norm squared of function 'f', returning a new function.

    Compute the L2 norm squared of function 'f', returning a new function.

    a

    the start of the interval

    b

    the end of the interval

  26. def normSq_p(p: Int, a: Double = 0.0, b: Double = 1.0): Double

    Compute the Lp norm squared of function 'f'.

    Compute the Lp norm squared of function 'f'.

    p

    the level, e.g., 1, 2, ...

    a

    the start of the interval

    b

    the end of the interval

  27. def norm_p(p: Int, a: Double = 0.0, b: Double = 1.0): Double

    Compute the Lp norm of function 'f'.

    Compute the Lp norm of function 'f'.

    p

    the level, e.g., 1, 2, ...

    a

    the start of the interval

    b

    the end of the interval

  28. final def notify(): Unit
    Definition Classes
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  29. final def notifyAll(): Unit
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  30. final def synchronized[T0](arg0: ⇒ T0): T0
    Definition Classes
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  31. def toString(): String
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  32. def unary_-: (Double) ⇒ Double

    Negate the function 'f' (unary minus), returning a new function.

  33. final def wait(): Unit
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    @throws( ... )
  34. final def wait(arg0: Long, arg1: Int): Unit
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    @throws( ... )
  35. final def wait(arg0: Long): Unit
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    @throws( ... )
  36. def ~^(p: Double): (Double) ⇒ Double

    Raise function 'f' to the 'p'th power, returning a new function.

    Raise function 'f' to the 'p'th power, returning a new function.

    p

    the power/exponent

  37. def ~^(p: Int): (Double) ⇒ Double

    Raise function 'f' to the 'p'th power, returning a new function.

    Raise function 'f' to the 'p'th power, returning a new function.

    p

    the integer-valued power/exponent

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