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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- Hilbert
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Instance Constructors
- new Hilbert(f: FunctionS2S)
- f
the function to convert into a Hilbert function
Value Members
- final def !=(arg0: Any): Boolean
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- final def ##: Int
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- def *(g: Double): (Double) => Double
- 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
- def +(g: Double): (Double) => Double
- 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
- def -(g: Double): (Double) => Double
- 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
- def /(g: Double): (Double) => Double
- 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
- final def ==(arg0: Any): Boolean
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- final def asInstanceOf[T0]: T0
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- def clone(): AnyRef
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- protected[lang]
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- @throws(classOf[java.lang.CloneNotSupportedException]) @native() @HotSpotIntrinsicCandidate()
- 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
- 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
- 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
- final def eq(arg0: AnyRef): Boolean
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- def equals(arg0: AnyRef): Boolean
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- final def getClass(): Class[_ <: AnyRef]
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- def hashCode(): Int
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- final def isInstanceOf[T0]: Boolean
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- final def ne(arg0: AnyRef): Boolean
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- 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
- 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
- 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
- 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
- final def notify(): Unit
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- final def notifyAll(): Unit
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- final def synchronized[T0](arg0: => T0): T0
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- def toString(): String
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- def unary_-: (Double) => Double
Negate the function 'f' (unary minus), returning a new function.
- final def wait(arg0: Long, arg1: Int): Unit
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- @throws(classOf[java.lang.InterruptedException])
- final def wait(arg0: Long): Unit
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- final def wait(): Unit
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- 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
- 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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- def finalize(): Unit
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- Deprecated