R 中矩阵的逆

我想知道你推荐的计算矩阵逆的方法是什么？

我找到的方法似乎并不令人满意。例如,

> c=rbind(c(1, -1/4), c(-1/4, 1))
> c
[,1]  [,2]
[1,]  1.00 -0.25
[2,] -0.25  1.00
> inv(c)
Error: could not find function "inv"
> solve(c)
[,1]      [,2]
[1,] 1.0666667 0.2666667
[2,] 0.2666667 1.0666667
> solve(c)*c
[,1]        [,2]
[1,]  1.06666667 -0.06666667
[2,] -0.06666667  1.06666667
> qr.solve(c)*c
[,1]        [,2]
[1,]  1.06666667 -0.06666667
[2,] -0.06666667  1.06666667

谢谢！

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最佳答案

solve(c) does give the correct inverse. The issue with your code is that you are using the wrong operator for matrix multiplication. You should use solve(c) %*% c to invoke matrix multiplication in R.

R performs element by element multiplication when you invoke solve(c) * c.

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You can use the function ginv() (Moore-Penrose generalized inverse) in the MASS package

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Note that if you care about speed and do not need to worry about singularities, solve() should be preferred to ginv() because it is much faster, as you can check:

require(MASS)
mat <- matrix(rnorm(1e6),nrow=1e3,ncol=1e3)


t0 <- proc.time()
inv0 <- ginv(mat)
proc.time() - t0


t1 <- proc.time()
inv1 <- solve(mat)
proc.time() - t1

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Use solve(matrix) if the matrix is larger than 1820x1820. Using inv() from matlib or ginv() from MASS takes longer or will not solve at all because of RAM limits.