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plUniform

A plUniform on $\Omega$ is a kernel where the compute function is defined as follows:

$$Compute(\omega) = Uniform(\omega)$$ (3.12)

$$Uniform(\omega) = Card(\Omega)$$ (3.13)

Example 8   Here we define a plUniform on $\Omega _o=\{[0,15]\}$.

図 3.8: A discrete uniform kernel on $\Omega _o=\{[0,15]\}$.

The construction of the kernel is given by

  plUniform Px(X);

The output of the plUniform example is the following:

X = {x} with x in [0,1,...,15]
P(x) =  1/16

Generating 5 random values
draw # 0 = { x=13 }
draw # 1 = { x=6 }
draw # 2 = { x=12 }
draw # 3 = { x=12 }
draw # 4 = { x=14 }

Generating 5 best values
best # 0 = { x=3 }
best # 1 = { x=5 }
best # 2 = { x=12 }
best # 3 = { x=4 }
best # 4 = { x=8 }

Examples of compute
compute({ x=0 } )= 0.0625
compute({ x=7 } )= 0.0625
compute({ x=3 } )= 0.0625
compute({ x=4 } )= 0.0625
compute({ x=15 } )= 0.0625