spam solve(spam)
spam solve()所属R语言包：spam
Linear Equation Solving for Sparse Matrices
稀疏矩阵的线性方程组求解
译者：生物统计家园网 机器人LoveR
描述----------Description----------
backsolve and forwardsolve solve a system of linear equations where the coefficient matrix is upper or lower triangular. <br> solve solves a linear system or computes the inverse of a matrix if the right-hand-side is missing.
backsolve和forwardsolve求解线性方程组的系统，其中系数矩阵是上或下三角。参考solve解决线性系统或者如果右手侧缺少计算逆矩阵。
用法----------Usage----------
# solve(a, b, ...)
# solve.spam(a, b, ...)
## S3 method for class 'spam'
solve(a, b, ...)
# backsolve(r, x, ...)
backsolve.spam(r, x, ...)
# forwardsolve(l, x, ...)
forwardsolve.spam(l, x, ...)
chol2inv(x,...)
参数----------Arguments----------
参数：a
symmetric positive definite matrix of class spam or a Cholesky factor as the result of a chol call.
对称正定矩阵类spam或Cholesky因子的chol调用的结果。
参数：l,r
object of class spam or spam.chol.method returned by the function chol.
类的对象spam或spam.chol.方法返回的功能chol。
参数：x,b
vector or regular matrix of right-hand-side(s) of a system of linear equations.
矢量或右手侧（s）的线性方程系统的正则矩阵。
参数：...
further arguments passed to or from other methods, see "Details" below.
进一步的参数传递给其他方法，请参见下面的“详细信息”。
Details
详细信息----------Details----------
We can solve A %*% x = b by first computing the Cholesky decomposition A = t(R)%*%R), then solving t(R)%*%y = b for y, and finally solving R%*%x = y for x. solve combines chol, a Cholesky decomposition of a symmetric positive definite sparse matrix, with forwardsolve and then backsolve.<br>
我们可以解决A %*% x = b通过先计算Cholesky分解A = t(R)%*%R)，然后解决t(R)%*%y = by，并最终解决R%*%x = yx。 solve结合与cholforwardsolve的对称正定稀疏矩阵，Cholesky分解，然后backsolve。<BR>
In case a is from a chol, then solve is an efficient way to calculate backsolve(a, forwardsolve( t(a), b)).
a是从chol，那么solve是一种有效的方式来计算backsolve(a, forwardsolve( t(a), b))。
However, for a.spam and a.mat from a chol call wit a sparse and ordinary matrix, note that forwardsolve( a.mat, b, transpose=T, upper.tri=T) is equivalent to forwardsolve( t(a.mat), b) and backsolve(a.spam, forwardsolve(a.spam, b, transpose=T, upper.tri=T)) yields the desired result. But backsolve(a.spam,forwardsolve(t(a.spam), resid)) is wrong because t(a.spam) is a spam and not a spam.chol.NgPeyton object.
然而，a.spam和a.mat从chol调用机智的稀疏和普通的矩阵，请注意，forwardsolve( a.mat, b, transpose=T, upper.tri=T)等于forwardsolve( t(a.mat), b)和backsolve(a.spam, forwardsolve(a.spam, b, transpose=T, upper.tri=T))的，产生所需的结果。但backsolve(a.spam,forwardsolve(t(a.spam), resid))是错误的，因为t(a.spam)是spam，而不是一个spam.chol.NgPeyton对象。
forwardsolve and backsolve solve a system of linear equations where the coefficient matrix is lower (forwardsolve) or upper (backsolve) triangular. Usually, the triangular matrix is result from a chol call and it is not required to transpose it for forwardsolve. Note that arguments of the default methods k, upper.tri and transpose do not have any effects here.
forwardsolve和backsolve解决的线性方程系统的系数矩阵是低级（forwardsolve）或上部（backsolve）三角。一般，三角矩阵是从chol呼叫的结果，它不要求它移调forwardsolve。请注意参数的默认方法k，upper.tri和transpose：“没有任何影响。
Notice that it is more efficient to solve successively the linear equations (both triangular solves) than to implement these in the Fortran code.
注意，它是更有效的解决连续的线性方程组（两个三角形解决了），而不是实施这些Fortran代码。
If the right-hand-side in solve is missing it will compute the inverse of a matrix. For details about the specific Cholsesky decomposition, see chol.
如果右手侧solve缺少它会计算一个矩阵的逆。有关的具体Cholsesky分解的详细信息，请参阅chol。
Recall that the Cholesky factors are from ordered matrices.
回想一下，从有序矩阵的Cholesky因素。
chol2inv(x) is a faster way to solve(x).
chol2inv(x)是一个更快的方法solve(x)。
注意----------Note----------
There is intentionally no <acronym>S3</acronym> distinction between the classes
是故意不<acronym> S3 </首字母缩写类之间的区别
（作者）----------Author(s)----------
Reinhard Furrer, based on Ng and Peyton (1993) Fortran routines
参考文献----------References----------
参见----------See Also----------
det, chol and ordering.
det，chol和ordering。
实例----------Examples----------
# Generate multivariate form a covariance inverse:[生成多变量的协方差逆：]
# (usefull for GRMF)[（有用为GRMF）]
set.seed(13)
n <- 25 # dimension[尺寸]
N <- 1000 # sample size[样本量]
Sigmainv <- .25^abs(outer(1:n,1:n,"-"))
Sigmainv <- as.spam( Sigmainv, eps=1e-4)
Sigma <- solve( Sigmainv) # for verification [为验证]
iidsample <- array(rnorm(N*n),c(n,N))
mvsample <- backsolve( chol(Sigmainv), iidsample)
norm( var(t(mvsample)) - Sigma)
# compare with:[对比：]
mvsample <- backsolve( chol(as.matrix( Sigmainv)), iidsample, n)
#### ,n as patch [＃＃＃，n为补丁]
norm( var(t(mvsample)) - Sigma)
# 'solve' step by step:[“解决”一步一步：]
b <- rnorm( n)
R <- chol(Sigmainv)
norm( backsolve( R, forwardsolve( R, b))-
solve( Sigmainv, b) )
norm( backsolve( R, forwardsolve( R, diag(n)))- Sigma )
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注：
注1：为了方便大家学习，本文档为生物统计家园网机器人LoveR翻译而成，仅供个人R语言学习参考使用，生物统计家园保留版权。
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发表于 2012-9-30 12:23:52
