R：矩阵双重求和和矢量归一化

Question

我有这个公式，我想在R。

中实现

这是双循环方式：

munew = 0
mu_normalizer = 0

for (j in 1:dim(x)[2] ) {
  for (i in 1:dim(x)[1] ) {
    munew = munew + (x[i,j]/(sigma_2[j] *omega_2[i]))
    }}
for (j in 1:dim(x)[2] ) {
  for (i in 1:dim(x)[1] ) {
    mu_normalizer = mu_normalizer + (1/(sigma_2[j] *omega_2[i]))
    }}

munew = munew/mu_normalizer

其中sigma_2和omega_2分别为sigma ^ 2和omega ^ 2.

我在R中实现这个的最快方法是什么？

Answer 1

或许outer（或其%o%）有帮助：

x = matrix(sample(1:3, 20, T), 5)
sigma_2 = runif(4)
omega_2 = runif(5)
munew = 0
mu_normalizer = 0

for (j in 1:dim(x)[2] ) {
  for (i in 1:dim(x)[1] ) {
    munew = munew + (x[i,j]/(sigma_2[j] *omega_2[i]))
    }}
munew
#[1] 445.5648
sum(x / (omega_2 %o% sigma_2))
#[1] 445.5648

for (j in 1:dim(x)[2] ) {
  for (i in 1:dim(x)[1] ) {
    mu_normalizer = mu_normalizer + (1/(sigma_2[j] *omega_2[i]))
    }}
mu_normalizer
#[1] 201.6099
sum(1 / (omega_2 %o% sigma_2))
#[1] 201.6099

munew/mu_normalizer
#[1] 2.210034
sum(x / (omega_2 %o% sigma_2)) / sum(1 / (omega_2 %o% sigma_2)) #this is the actual answer
#[1] 2.210034