Question

我需要解决一个线性方程组：

aQ + bP = c
dQ + eP = f

其中：

a ~ N(100;10)
b ~ N(-1;0.1)
c ~ N(10;1)
d ~ N(10;0.1)
e ~ N(100;10)
f ~ N(10;0.1)

到目前为止，我写过：

a <- rnorm(100, mean=100, sd=10)
b <- rnorm(100, mean=-1, sd=0.1)
c <- rnorm(100, mean=10, sd=1)
d <- rnorm(100, mean=10, sd=0.1)
e <- rnorm(100, mean=100, sd=10)
f <- rnorm(100, mean=10, sd=0.1)

P <- vector()
Q <- vector()

for (i in 1:100) {
    coefs <- matrix(c(a[i],d[i],b[i],e[i]),2,2)
    ys <- array(c(c,f),2)
    solve(coefs[i], ys[i])
}

问题是for循环只给我一个P和Q的解决方案我希望for循环计算100组值做a，b，c，d，e和f并存储关于向量Q和P的数据。

Answer 1

您可以尝试使用apply()

# data  
df = data.frame(a,b,c,d,e,f)

# apply function
out = t(apply(df, 1, 
      function(x){ 
      coefs = matrix( c(x['a'], x['d'], x['b'], x['e']), 2, 2); 
      ys = array(c(x['c'],x['f']),2); 
      out = solve(coefs, ys); 
      names(out) = c('P','Q');
      out}))

或者使用sapply()

out = t(sapply(seq(100), function(i){
       coefs = matrix(c(a[i], d[i], b[i] ,e[i]),2,2); ys = array(c(c[i],f[i]),2);
       out = solve(coefs, ys); names(out) = c('P','Q'); 
       out}))

如果您想使用for循环，可以执行以下操作

# declare matrix to store the output
out = matrix(ncol=2, nrow=100) 

# populate declared matrix using for loop
for(i in 1:100){  
    coefs = matrix(c(a[i],d[i],b[i],e[i]),2,2)
    ys = array(c(c[i],f[i]),2)
    out[i,] = as.vector(solve(coefs, ys))
    colnames(out) = c('P','Q')
    out}

Answer 2

为了提供另一种可能的方法，您可以使用mapply()有效地并行迭代每个系数和RHS向量：

set.seed(1);
a <- rnorm(100,100,10);
b <- rnorm(100,-1,0.1);
c <- rnorm(100,10,1);
d <- rnorm(100,10,0.1);
e <- rnorm(100,100,10);
f <- rnorm(100,10,0.1);
mapply(function(a,b,c,d,e,f) solve(matrix(c(a,d,b,e),2),matrix(c(c,f),2)),a,b,c,d,e,f);
##            [,1]       [,2]       [,3]      [,4]       [,5]       [,6]       [,7]       [,8]       [,9]      [,10]      [,11]      [,12]      [,13]      [,14]      [,15]      [,16]      [,17]      [,18]      [,19]      [,20]      [,21]      [,22]      [,23]     [,24]      [,25]      [,26]      [,27]      [,28]      [,29]      [,30]     [,31]      [,32]      [,33]      [,34]      [,35]      [,36]      [,37]      [,38]      [,39]      [,40]      [,41]      [,42]      [,43]     [,44]      [,45]      [,46]      [,47]      [,48]      [,49]     [,50]      [,51]      [,52]      [,53]     [,54]      [,55]      [,56]      [,57]     [,58]      [,59]      [,60]      [,61]      [,62]      [,63]      [,64]      [,65]     [,66]      [,67]      [,68]      [,69]      [,70]      [,71]     [,72]      [,73]      [,74]      [,75]     [,76]      [,77]      [,78]      [,79]      [,80]      [,81]      [,82]      [,83]      [,84]      [,85]      [,86]      [,87]      [,88]     [,89]     [,90]     [,91]      [,92]      [,93]      [,94]      [,95]      [,96]      [,97]      [,98]      [,99]     [,100]
## [1,] 0.11195915 0.11550647 0.12751804 0.0841975 0.07569079 0.13696420 0.10252485 0.09894877 0.09515799 0.10922284 0.08629273 0.10113763 0.10308528 0.11216529 0.09963416 0.11659483 0.09791256 0.08081292 0.09926686 0.09472402 0.07648024 0.09355051 0.09391840 0.1219382 0.08409615 0.11939194 0.09931966 0.09958410 0.10817085 0.09947289 0.0803567 0.07280706 0.09108175 0.10730635 0.11623282 0.10439468 0.11082056 0.08964156 0.10089985 0.09365293 0.10998488 0.11389442 0.09656601 0.0872372 0.12093390 0.08759978 0.09202209 0.09137391 0.10043375 0.1025373 0.09823991 0.11186173 0.09698966 0.1112308 0.09463053 0.09386283 0.07966344 0.1193879 0.09922995 0.09776010 0.08903184 0.09724774 0.09156914 0.10903049 0.12760021 0.1014739 0.11805636 0.07770935 0.09601201 0.07510938 0.09370570 0.1130247 0.08705415 0.14043486 0.11704624 0.1091617 0.08154497 0.10810454 0.08690775 0.11685334 0.11133037 0.09817079 0.10215157 0.11097263 0.08957527 0.08781713 0.08506901 0.11398943 0.1017468 0.1080845 0.1026900 0.09321191 0.09276108 0.08089681 0.10226763 0.09705664 0.12423443 0.11736748 0.11432446 0.10282015
## [2,] 0.08016778 0.07420647 0.09132015 0.0953508 0.09734921 0.09111316 0.09172938 0.09253545 0.08018053 0.09452145 0.09233637 0.08349215 0.07979583 0.09634328 0.09443451 0.08404651 0.08153545 0.09468065 0.10482579 0.07829014 0.08002979 0.09773864 0.09023393 0.1070831 0.08657002 0.07433625 0.10757136 0.09891601 0.09612082 0.09671603 0.1139721 0.08951823 0.10746614 0.08889339 0.08501627 0.09050828 0.08181816 0.09255519 0.09681833 0.08489033 0.09251537 0.07567294 0.09099927 0.0841442 0.08769969 0.13057528 0.10425570 0.09546615 0.08564604 0.1174630 0.08258592 0.09420732 0.09640516 0.1048073 0.10757819 0.08931113 0.08544322 0.1124914 0.09978848 0.08516907 0.09438840 0.07408315 0.08145526 0.08357922 0.08661255 0.0884171 0.09454044 0.08658720 0.07824592 0.08435285 0.09760972 0.1068059 0.09319386 0.08188822 0.07865432 0.1037524 0.08916170 0.08914854 0.07982980 0.08718701 0.09064425 0.10193109 0.09645453 0.09396509 0.07402690 0.07399806 0.09308106 0.09940533 0.1126132 0.0841854 0.1002329 0.07365820 0.10095744 0.08985023 0.06348183 0.10252098 0.08397957 0.09875275 0.08654524 0.09736881

或者如果您希望将结果作为列表获取，可以将SIMPLIFY=F传递给mapply()，或者只使用Map()，默认情况下不会简化：

Map(function(a,b,c,d,e,f) solve(matrix(c(a,d,b,e),2),matrix(c(c,f),2)),a,b,c,d,e,f);
## [[1]]
##            [,1]
## [1,] 0.11195915
## [2,] 0.08016778
##
## [[2]]
##            [,1]
## [1,] 0.11550647
## [2,] 0.07420647
##
## ... (snip) ...
##
## [[99]]
##            [,1]
## [1,] 0.11432446
## [2,] 0.08654524
##
## [[100]]
##            [,1]
## [1,] 0.10282015
## [2,] 0.09736881

用R编程求解一组线性方程组

2 个答案: