Dear R-users,
May I seek some suggestions from you. I have a long programme written in R
with several 'for' loops inside. I just want to get them out by any elegant
way (if there is!) to reduce the computational time of the main programme.
For instance, is there any smart way for the following programme that will
lessen time?

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dose<-seq(0,10,.5)
alpha1<--4
beta1<-0.5
alpha2<--6
beta2<--.7

psi1<-function(alpha1,beta1,alpha2,beta2,d){
z1<-exp(alpha1+beta1*d)
z2<-exp(alpha2+beta2*d)
z1/((1+z1)*(1+z2))
                                                                      }
psi2<-function(alpha2,beta2,d) {
z2<-exp(alpha2+beta2*d)
z2/(1+z2)
                                                 }
psi1.hat=c()
psi2.hat=c()
for (i in 1:length(dose)){     # just want to avoid this 'for' loop
d<-dose[i]
psi1.hat[i]<-psi1(alpha1,beta1,alpha2,beta2,d)
psi2.hat[i]<-psi2(alpha2,beta2,d)
                                     }

print(psi1.hat)
print(psi2.hat)

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Many  thanks for your kind attention.

Regards,
Jamil.

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