R语言:kappa()函数中文帮助文档(中英文对照)

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kappa(base)
kappa()所属R语言包：base

                                        Compute or Estimate the Condition Number of a Matrix
                                         计算或估计矩阵的条件数

                                         译者：生物统计家园网 机器人LoveR

描述----------Description----------

The condition number of a regular (square) matrix is the product of the norm of the matrix and the norm of its inverse (or pseudo-inverse), and hence depends on the kind of matrix-norm.
定期（平方米）矩阵的条件数是矩阵和其逆（或伪逆），规范的标准的产品，因此对矩阵范数的一种依赖。

kappa() computes by default (an estimate of) the 2-norm condition number of a matrix or of the R matrix of a QR decomposition, perhaps of a linear fit.  The 2-norm condition number can be shown to be the ratio of the largest to the smallest non-zero singular value of the matrix.
kappa()计算（估计）默认情况下，2  - 范数的条件数矩阵或R分解矩阵QR线性拟合，或许。 2规范的条件数可以被证明是最大的比例最小的非零矩阵的奇异值。

rcond() computes an approximation of the reciprocal condition number, see the details.
rcond()近似计算互惠的条件数，看到的细节。


用法----------Usage----------


kappa(z, ...)
## Default S3 method:[默认方法]
kappa(z, exact = FALSE,
      norm = NULL, method = c("qr", "direct"), ...)
## S3 method for class 'lm'
kappa(z, ...)
## S3 method for class 'qr'
kappa(z, ...)

kappa.tri(z, exact = FALSE, LINPACK = TRUE, norm=NULL, ...)

rcond(x, norm = c("O","I","1"), triangular = FALSE, ...)



参数----------Arguments----------

参数：z,x
A matrix or a the result of qr or a fit from a class inheriting from "lm".
矩阵或一个qr或从一个类继承从"lm"适合的结果。


参数：exact
logical.  Should the result be exact?
逻辑。应的结果准确吗？


参数：norm
character string, specifying the matrix norm with respect to which the condition number is to be computed, see also norm.  For rcond, the default is "O", meaning the One- or 1-norm.  The (currently only) other possible value is "I" for the infinity norm.
字符串，指定矩阵范数，条件数计算，也看到norm。 rcond，默认是"O"，这意味着一个或1规范。 （目前唯一）其他可能的值是"I"无穷规范。


参数：method
character string, specifying the method to be used; "qr" is default for back-compatibility, mainly.
字符串，指定要使用的方法; "qr"是默认情况下，主要向后兼容性。


参数：triangular
logical.  If true, the matrix used is just the lower triangular part of z.
逻辑。如果情况属实，使用矩阵只是较低z三角的一部分。


参数：LINPACK
logical.  If true and z is not complex, the Linpack routine dtrco() is called; otherwise the relevant Lapack routine is.
逻辑。如果真正和z并不复杂的Linpack例行dtrco()被称为否则有关LAPACK例程。


参数：...
further arguments passed to or from other methods; for kappa.*(), notably LINPACK when norm is not "2".
进一步的参数传递或其他方法;kappa.*()，尤其是LINPACK时norm不"2"。


Details

详情----------Details----------

For kappa(), if exact = FALSE (the default) the 2-norm condition number is estimated by a cheap approximation. Following S, by default, this uses the LINPACK routine dtrco(). However, in R (or S) the exact calculation (via svd) is also likely to be quick enough.
kappa()如果exact = FALSE（默认）2  - 范数的条件数是一种廉价的近似估计。后续的s，默认情况下，使用的LINPACK例行dtrco()。然而，在R（或S）的精确计算（通过svd）也可能是速度不够快。

Note that the 1- and Inf-norm condition numbers are much faster to calculate, and rcond() computes these reciprocal condition numbers, also for complex matrices, using standard Lapack routines.
注意：1  - 和INF-范数的条件数，更快的计算，和rcond()这些互惠条件数计算，也为复杂的矩阵，使用标准的LAPACK例程。

kappa and rcond are different interfaces to partly identical functionality.
kappa和rcond不同的接口部分相同的功能。

kappa.tri is an internal function called by kappa.qr.
kappa.tri是kappa.qr称为内部功能。


值----------Value----------

The condition number, kappa, or an approximation if exact = FALSE.
条件数，kappa如果exact = FALSE或近似。


作者（S）----------Author(s)----------



The design was inspired by (but differs considerably from)
the S function of the same name described in Chambers (1992).




参考文献----------References----------

Linear models. Chapter 4 of Statistical Models in S eds J. M. Chambers and T. J. Hastie, Wadsworth & Brooks/Cole.

参见----------See Also----------

norm; svd for the singular value decomposition and qr for the QR one.
norm;svd奇异值分解和qrQR独。


举例----------Examples----------


kappa(x1 <- cbind(1,1:10))# 15.71[15.71]
kappa(x1, exact = TRUE)        # 13.68[13.68]
kappa(x2 <- cbind(x1,2:11))# high! [x2 is singular!][高！ [X2是单数！]

hilbert <- function(n) { i <- 1:n; 1 / outer(i - 1, i, "+") }
sv9 <- svd(h9 <- hilbert(9))$ d
kappa(h9)# pretty high![相当高！]
kappa(h9, exact = TRUE) == max(sv9) / min(sv9)
kappa(h9, exact = TRUE) / kappa(h9) # .677 (i.e., rel.error = 32%)[0.677（即rel.error = 32％）]

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