solveCrossprod求 X'X的逆, ( X' == t(X), 即X的行列变换矩阵 )-白红宇

很多时候，我们需要计算形如X’X的逆(即X' %*% X)。这很容易实现，例如：

> x=matrix(rnorm(9),ncol=3,nrow=3)

> x

[,1] [,2] [,3]

[1,] -0.1806586 -0.76340512 0.002652331

[2,] -1.8018584 0.04467943 1.416332187

[3,] 1.2785359 -1.31653513 0.180653002

> solve(crossprod(x))

[,1] [,2] [,3]

[1,] 1.2181837 0.9664576 1.470940

[2,] 0.9664576 1.2010110 1.204599

[3,] 1.4709402 1.2045986 2.269921

R中的strucchange包中的函数solveCrossprod()也可完成：

> install.packages("strucchange")

> library("strucchange")

参数

> args(solveCrossprod)

function (X, method = c("qr", "chol", "solve"))

NULL

> solveCrossprod(x,method=”qr”)

[,1] [,2] [,3]

[1,] 1.2181837 0.9664576 1.470940

[2,] 0.9664576 1.2010110 1.204599

[3,] 1.4709402 1.2045986 2.269921

> solveCrossprod(x,method=”chol”)

[,1] [,2] [,3]

[1,] 1.2181837 0.9664576 1.470940

[2,] 0.9664576 1.2010110 1.204599

[3,] 1.4709402 1.2045986 2.269921

> solveCrossprod(x,method=”solve”)

[,1] [,2] [,3]

[1,] 1.2181837 0.9664576 1.470940

[2,] 0.9664576 1.2010110 1.204599

[3,] 1.4709402 1.2045986 2.269921

[参考]

1. > help("solveCrossprod")

solveCrossprod           package:strucchange           R DocumentationInversion of X'XDescription:     Computes the inverse of the cross-product of a matrix X.Usage:     solveCrossprod(X, method = c("qr", "chol", "solve"))     Arguments:       X: a matrix, typically a regressor matrix.  method: a string indicating whether the QR decomposition, the          Cholesky decomposition or ‘solve’ should be used.Details:     Using the Cholesky decomposition of X'X (as computed by     ‘crossprod(X)’) is computationally faster and preferred to     ‘solve(crossprod(X))’. Using the QR decomposition of X is slower     but should be more accurate.Value:     a matrix containing the inverse of ‘crossprod(X)’.Examples:     X <- cbind(1, rnorm(100))     solveCrossprod(X)     solve(crossprod(X))