Nothing

```
#### computes the limits of the norm of Pz = P(y - mu)
#### used for non-sampling selective inference when mu is specified
#### selective constarints such that Ay <= b
#### y is a VECTOR
find.norm.limits <-
function(U, y, mu, A, b){
# precompute
b.tilde = b - mu*apply(A, 1, sum)
z = y - mu
Pz = U%*%(t(U)%*%z)
APz = A%*%Pz
delta = A%*%z - APz
v = Pz/sqrt(sum(Pz^2))
Av = A%*%v
## limits for each of the replications of y
# positive and negtaive indices
which.pos = which (Av > 0)
which.neg = which (Av < 0)
values = (b.tilde - delta)/Av
# compute the limits
options(warn=-1)
lower = max(values[which.neg])
upper = min(values[which.pos])
options(warn=0)
c(lower, upper)
}
```

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