求解 R 函数的输入值

Question

在我附加的 R 函数中，我想知道如何解决 mdes（假设它是未知的）如果其他一切都已知，这是当前输入值之一？

如果其他一切都已知，是否也可以求解 mdes 和 power（均为当前输入值）？

foo <- function(A = 200, As = 15, B = 100,Bs = 10,iccmax = 0.15,mdes = .25,SD = 1.2,power = 80)
{
  tail <- 2
  alpha <- 5
  inv_d <- function(mdes) {
    c(mean_dif = 1, Vmax = 2/mdes^2)
  }
  SDr <- 1/SD
  pars <- inv_d(mdes)
  mean_dif <- pars[[1]]
  Vmax <- pars[[2]]
  zbeta <- qnorm((power/100))
  zalpha <- qnorm(1-(alpha/(100*tail)))
  maxvarmean_difhat <- (mean_dif / (zbeta + zalpha))**2
  ntreat <- sqrt((A/As)*((1-iccmax)/iccmax))
  ncont <- sqrt((B/Bs)*((1-iccmax)/iccmax))
  costpertreatcluster <- A + (As*ntreat)
  costperconcluster <- B + (Bs*ncont)
  gtreat <- (sqrt(A*iccmax) + sqrt(As*(1-iccmax)))**2
  gcon <- (sqrt(B*iccmax) + sqrt(Bs*(1-iccmax)))**2
  pratio <- sqrt(gtreat/gcon)
  budgetratio <- 99999
  budgetratio <- ifelse( ((pratio <= SD) & (pratio >= SDr)), pratio**2, ifelse((pratio > SD), pratio*SD, pratio*SDr))
  fraction <- budgetratio/(1 + budgetratio)
  mmvnumer <- 99999
  mmvnumer <- ifelse( ((pratio <= SD) & (pratio >= SDr)),
                      gcon*Vmax*(1+(pratio**2)),
                      ifelse((pratio > SD),
                             gcon*Vmax*(((pratio*SD)+1)**2/((SD**2)+1)),
                             gcon*Vmax*(((pratio*SDr)+1)**2/((SDr**2) + 1))) )
  budget <- mmvnumer/maxvarmean_difhat
  treatbudget <- fraction*budget
  conbudget <- (1-fraction)*budget
  ktreat <- treatbudget/costpertreatcluster
  kcont <- conbudget/costperconcluster
  ktreatrup <- ceiling(ktreat)
  kcontrup <- ceiling(kcont)
  ktreatplus <- ifelse(pmin(ktreatrup,kcontrup) < 8, ktreatrup + 3, ktreatrup + 2)
  kcontplus <- ifelse(pmin(ktreatrup,kcontrup) < 8, kcontrup + 3, kcontrup + 2)
  budgetplus <- (ktreatplus*costpertreatcluster) + (kcontplus*costperconcluster)
  
  return(c(ncont = ncont, kcont = kcontplus,
    ntreat = ntreat, ktreat = ktreatplus, budget = budgetplus))
}
#--------------------------------------------------------------------------------
# EXAMPLE OF USE:
foo()

       ncont        kcont       ntreat       ktreat       budget 
    7.527727    73.000000     8.692270    62.000000 33279.051347

Answer 1

定义一个单变量函数为

p0 = foo()
fn1 = function(x) sum((foo(mdes=x) - p0)^2)

并找到一个应该为 0 的最小值，它对应于您的 mdes = 0.25 输入！

optimize(fn1, c(0.0, 1.0))
## $minimum
## [1] 0.2497695
## $objective
## [1] 0

对于两个变量，这更困难，因为函数有很多局部最小值并且 ill-defined 在某些区域之外。申请 optim() 您将需要 well-chosen 个起点。

求解 R 函数的输入值

Solving for an input value of an R function

optimization

r

function

algebra

mathematical-optimization