Hilbert

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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new Hilbert(f: FunctionS2S)
f
the function to convert into a Hilbert function

Value Members

final def !=(arg0: Any): Boolean

Definition Classes
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final def ##(): Int

Definition Classes
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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[java.lang]
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@native() @throws( ... )
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: Any): Boolean

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def finalize(): Unit

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protected[java.lang]
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@throws( classOf[java.lang.Throwable] )
final def getClass(): Class[_]

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@native()
def hashCode(): Int

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@native()
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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@native()
final def notifyAll(): Unit

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@native()
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(): Unit

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final def wait(arg0: Long, arg1: Int): Unit

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@throws( ... )
final def wait(arg0: Long): Unit

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@native() @throws( ... )
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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Hilbert

class Hilbert extends AnyRef

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Hilbert 

class Hilbert extends AnyRef

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Hilbert