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

Linear Supertypes
AnyRef, Any
Ordering
  1. Alphabetic
  2. By Inheritance
Inherited
  1. Hilbert
  2. AnyRef
  3. Any
  1. Hide All
  2. Show All
Visibility
  1. Public
  2. All

Instance Constructors

  1. new Hilbert(f: FunctionS2S)

    f

    the function to convert into a Hilbert function

Value Members

  1. def *(g: Double): (Double) ⇒ Double
  2. 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

  3. def +(g: Double): (Double) ⇒ Double
  4. 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

  5. def -(g: Double): (Double) ⇒ Double
  6. 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

  7. def /(g: Double): (Double) ⇒ Double
  8. 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

  9. 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

  10. 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

  11. 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

  12. 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

  13. 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

  14. 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

  15. 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

  16. def unary_-: (Double) ⇒ Double

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

  17. 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

  18. 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