R code

fpkm2tpm = function(fpkm){
  exp(log(fpkm) - log(sum(fpkm)) + log(1e6))
}
tpm = apply(expMatrix, 2, fpkm2tpm)

If the expression matrix has NA value

fpkm2tpm <- function(fpkm){
  tpm <- exp(log(fpkm) - log(sum(fpkm,na.rm=T)) + log(1e6))
  tpm[which(is.na(tpm))] <- 0
  return(tpm)
}

TPMi=( FPKMi / sum(FPKMj ) * 10^6