lm(): LINPACK/LAPACK 中 QR 分解返回的 qraux 是什么 [英] lm(): What is qraux returned by QR decomposition in LINPACK / LAPACK

问题描述

rich.main3 是 R 中的线性模型.我了解列表中的其余元素，但我不明白 qraux 是什么.文档指出它是

rich.main3 is a linear model in R. I understand the rest of the elements of the list but I don't get what qraux is. The documentation states that it is

长度为 ncol(x) 的向量，其中包含关于 old{Q}" 的附加信息.

a vector of length ncol(x) which contains additional information on old{Q}".

这意味着什么附加信息?

str(rich.main3$qr)

qr   : num [1:164, 1:147] -12.8062 0.0781 0.0781 0.0781 0.0781 ...


..- attr(*, "dimnames")=List of 2
  .. ..$ : chr [1:164] "1" "2" "3" "4" ...
  .. ..$ : chr [1:147] "(Intercept)" "S2" "S3" "x1" ...
  ..- attr(*, "assign")= int [1:147] 0 1 1 2 3 4 5 6 7 8 ...
  ..- attr(*, "contrasts")=List of 3
  .. ..$ S    : chr "contr.treatment"
  .. ..$ ID   : chr "contr.treatment"
  .. ..$ Block: chr "contr.treatment"
 $ qraux: num [1:147] 1.08 1.06 1.16 1.21 1.27 ...
 $ pivot: int [1:147] 1 2 3 4 5 6 7 8 10 11 ...
 $ tol  : num 1e-07
 $ rank : int 21
 - attr(*, "class")= chr "qr"

推荐答案

想必你不知道 QR 分解是如何计算的.我在 LaTeX 中写了以下内容，可能会帮助您澄清这一点.当然，在编程站点上，我需要向您展示一些代码.最后给大家推荐一个玩具R函数计算家庭反射.

Presumably you don't know how QR factorization is computed. I wrote the following in LaTeX which might help you clarify this. Surely on a programming site I need to show you some code. In the end I offer you a toy R function computing Householder reflection.

住户反映矩阵

家庭转型

家庭 QR 分解(无旋转)

QR 和重新缩放的紧凑存储

LAPACK 辅助例程 正在执行 Householder 变换.我还写了下面的玩具R函数来演示:

The LAPACK auxiliary routine dlarfg is performing Householder transform. I have also written the following toy R function for demonstration:

dlarfg <- function (x) {
  beta <- -1 * sign(x[1]) * sqrt(as.numeric(crossprod(x)))
  v <- c(1, x[-1] / (x[1] - beta))
  tau <- 1 - x[1] / beta
  y <- c(beta, rep(0, length(x)-1L))
  packed_yv <- c(beta, v[-1])
  oo <- cbind(x, y, v, packed_yv)
  attr(oo, "tau") <- tau
  oo
  }

假设我们有一个输入向量

Suppose we have an input vector

set.seed(0); x <- rnorm(5)

我的函数给出:

dlarfg(x)
#              x         y           v   packed_yv
#[1,]  1.2629543 -2.293655  1.00000000 -2.29365466
#[2,] -0.3262334  0.000000 -0.09172596 -0.09172596
#[3,]  1.3297993  0.000000  0.37389527  0.37389527
#[4,]  1.2724293  0.000000  0.35776475  0.35776475
#[5,]  0.4146414  0.000000  0.11658336  0.11658336
#attr(,"tau")
#[1] 1.55063

这篇关于lm(): LINPACK/LAPACK 中 QR 分解返回的 qraux 是什么的文章就介绍到这了，希望我们推荐的答案对大家有所帮助，也希望大家多多支持IT屋！