计算R中稀疏矩阵的特征向量(Computing eigenvectors of a sparse matrix in R)

 我试图计算R中大的稀疏矩阵的m第一特征向量。使用eigen()是不现实的，因为大意味着N> 10 6 。 
 
 到目前为止，我发现我应该使用igraph包中的ARPACK，它可以处理稀疏矩阵。 但是我不能让它在一个非常简单的（3x3）矩阵上工作： 
 
library(Matrix)
library(igraph)

TestDiag <- Diagonal(3, 3:1)
TestMatrix <- t(sparseMatrix(i = c(1, 1, 2, 2, 3), j = c(1, 2, 1, 2, 3), x = c(3/5, 4/5, -4/5, 3/5, 1)))
TestMultipliedMatrix <- t(TestMatrix) %*% TestDiag %*% TestMatrix
 
 然后使用arpack()函数帮助示例中给出的代码来提取2个第一个特征向量： 
 
func <- function(x, extra=NULL) { as.vector(TestMultipliedMatrix %*% x) } 
arpack(func, options=list(n = 3, nev = 2, ncv = 3, sym=TRUE, which="LM", maxiter=200), complex = FALSE)
 
 我收到一条错误消息： 
 
Error in arpack(func, options = list(n = 3, nev = 2, ncv = 3, sym = TRUE,  :
  At arpack.c:1156 : ARPACK error, NCV must be greater than NEV and less than or equal to N
 
 我不明白这个错误，因为这里ncv（3）大于nev（2），并且等于N（3）。 
 
 我是否犯了一些愚蠢的错误，或者有更好的方法来计算R中稀疏矩阵的特征向量？ 
 
 
 更新 
 
 此错误显然是由于arpack()函数中的大写/小写NCV和NEV的错误。 
 
 任何解决这个bug的建议（我试着看一下包代码，但这对我来说太复杂了）或者以其他方式计算特征向量是值得欢迎的。 

I am trying to compute the m first eigenvectors of a large sparse matrix in R. Using eigen() is not realistic because large means N > 106 here.
 
So far I figured out that I should use ARPACK from the igraph package, which can deal with sparse matrices. However I can't get it to work on a very simple (3x3) matrix:
 
library(Matrix)
library(igraph)

TestDiag <- Diagonal(3, 3:1)
TestMatrix <- t(sparseMatrix(i = c(1, 1, 2, 2, 3), j = c(1, 2, 1, 2, 3), x = c(3/5, 4/5, -4/5, 3/5, 1)))
TestMultipliedMatrix <- t(TestMatrix) %*% TestDiag %*% TestMatrix
 
And then using the code given in example of the help of the arpack() function to extract the 2 first eigenvectors :
 
func <- function(x, extra=NULL) { as.vector(TestMultipliedMatrix %*% x) } 
arpack(func, options=list(n = 3, nev = 2, ncv = 3, sym=TRUE, which="LM", maxiter=200), complex = FALSE)
 
I get an error message:
 
Error in arpack(func, options = list(n = 3, nev = 2, ncv = 3, sym = TRUE,  :
  At arpack.c:1156 : ARPACK error, NCV must be greater than NEV and less than or equal to N
 
I don't understand this error, as ncv (3) is greater than nev (2) here, and equal to N (3).
 
Am I making some stupid mistake or is there a better way to compute eigenvectors of a sparse matrix in R?
 
 
Update
 
This error is apparently due to a bug in the arpack() function with uppercase / lowercase NCV and NEV. 
 
Any suggestions to solve the bug (I tried to have a look at the package code but it is far too complex for me to understand) or compute the eigenvectors in an other way are welcome.

原文：https://stackoverflow.com/questions/16966748