# Feasible solution for a probability distribution which must satisfy a system of linear equality and inequality constraints.

### 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 |

### 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 |