projection_C {sharpPen}

Projection operator for rectangle or nonnegative space

Description

Compute the projection operator for rectangle or nonnegative space. For example, we construct

\lambda P_{C}(x/\lambda) = projection_C(\lambda,C,x)

, where C can be rectangle or nonnegative space.

Usage

projection_C(
lambda,family=c("rectangle","nonnegative"),
input,bound=c(-1,1))

Arguments

lambda

parameter \lambda in the above equation

family

type of C, can be rectangle or nonnegative space

input

input x in the above equation

bound

lower bound and upper bound for rectangle

Details

Take x as input, \lambda as parameter. Calculate \lambda P_{C}(x/\lambda) for a given C family

Value

projection

\lambda P_{C}(x/\lambda)

Author(s)

D.Wang and W.J.Braun

Examples

set.seed(1234567)
family <- "nonnegative"
temp_p1<-runif(10,-1,1)
projection_C(0.5,family=family,temp_p1)