# feasible: Feasible solution for a probability distribution which must... In polyapost: Simulating from the Polya Posterior

## Description

This function finds a feasible solution, p=(p1,...,pn), in the n-dimensional simplex of probability distributions which must satisfy A1p = b1, A2p <= b2 and A3p >= b3. All the components of the bi's must be nonnegative In addition each probability in the solution must be at least as big as `eps`, a small positive number.

## Usage

 `1` ```feasible(A1,A2,A3,b1,b2,b3,eps) ```

## Arguments

 `A1` The matrix for the equality constraints.This must always contain the constraint that the sum of the pi's is one. `A2` The matrix for the <= inequality constraints. This must always contain the constraints -pi <= 0, i.e. that the pi's must be nonnegative. `A3` The matrix for the >= inequality constraints. If there are no such constraints A3 must be set equal to NULL. `b1` The rhs vector for A1, each component must be nonnegative. `b2` The rhs vector for A2, each component must be nonnegative. `b3` The rhs vector for A3, each component must be nonnegative. If A3 is NULL then b3 must be NULL. `eps` A small positive number. Each member of the solution must be at least as large as `eps`. Care must be taken not to choose a value of `eps` which is too large.

## Value

The function returns a vector. If the components of the vector are positive then the feasible solution is the vector returned, otherwise there is no feasible solution.

## Examples

 ```1 2 3 4 5 6 7 8``` ```A1<-rbind(rep(1,7),1:7) b1<-c(1,4) A2<-rbind(c(1,1,1,1,0,0,0),c(.2,.4,.6,.8,1,1.2,1.4)) b2<-c(1,2) A3<-rbind(c(1,3,5,7,9,10,11),c(1,1,1,0,0,0,1)) b3<-c(5,.5) eps<-1/100 feasible(A1,A2,A3,b1,b2,b3,eps) ```

polyapost documentation built on June 20, 2017, 9:06 a.m.