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  • 求助：Error in solve.default(A) : system is computationally singular: reciprocal

大家好，我在使用rmgarch包中dccfit函数进行拟合DCC-GARCH模型时，程序报如下的错误：
Error in solve.default(A) :
system is computationally singular: reciprocal condition number = 1.99569e-16
我在网上查了一下，但是没有找到解决方法，麻烦哪位朋友帮我看一下？谢谢！

我的数据x的都是一些股票指数的对数收益率（所有变量无缺失值，且都通过平稳性检验）。

我的程序如下：

x.xts <- xts(x=x[ , 2:ncol(x)], order.by=x[ , 1])

uspec = ugarchspec(variance.model = list(model="fGARCH", submodel="GARCH"), mean.model = list(armaOrder=c(1, 0)),distribution.model = "std")

mspec = multispec(replicate(n=ncol(x)-1, uspec))

DCCspec = dccspec(mspec)
dccgarch.fit = dccfit(DCCspec, data=x.xts, solver=c("hybrid", "solnp"))
Error in solve.default(A) :
system is computationally singular: reciprocal condition number = 1.94649e-16

这种情况并不是一直出现，完全一样的程序，改变数据集的时候，程序就正常运行，但遇到上面的数据时，程序就报出类似的错误。

在网上找到一些网页，但我看不出什么具体的方法，供大家参考：
http://stackoverflow.com/questions/13521937/error-in-mlogit-error-in-solve-defaulth-gfixed-system-is-computationall

http://tolstoy.newcastle.edu.au/R/e5/help/08/09/1293.html

2 年 后

简单来说，方阵不满秩，例子：线性模型中解释变量存在完全共线性。跟数据质量没啥关系，当然把矩阵singular当成数据质量问题好像也没什么错。
如果你能找到是哪个矩阵求逆出的问题，提供两个我能脑补出来的方案：
1.用广义逆
2.手动给该矩阵加上影响不大的一个小扰动
题外话，出现这种错误其实还是数据的原因，仔细检查下数据的各种特征，毕竟改别人的package比改数据难很多了。

    holydudu
    刚测试了下solve函数，就只有出现全部是0的情况之下才会出现此类singular错误信息～?

    > matrix(runif(25), nc = 5) %>% solve.default
           [,1]        [,2]         [,3]       [,4]       [,5]
[1,]  0.9069072 -0.72940986 -2.013602193  0.6193949  1.6909356
[2,]  2.5310537  0.09066826 -2.397023376 -0.1885138  0.1726358
[3,]  1.9180058 -0.91873135 -0.193985265  0.1208054 -0.5724837
[4,]  0.5484761  0.27082491  0.003404529 -0.9784695  0.4331857
[5,] -5.0098767  1.41098122  3.990183295  1.5030079 -1.0398107
> matrix(runif(25), nc = 5) %>% solve
            [,1]         [,2]       [,3]       [,4]       [,5]
[1,] -2.54403041 -3.270732792  3.8787546  1.4360276  0.2553427
[2,] -0.06831753 -0.564190663 -0.1453375  0.2050192  1.6809986
[3,] -1.69945917  0.002586251  0.5663346  0.7378965  0.3933298
[4,]  1.10519682  0.722224859  0.1642177 -0.8689460 -0.1381785
[5,]  4.88303095  3.945996611 -5.8467706 -0.7501183 -1.7452565
> matrix(c(runif(24), Inf), nc = 5) %>% solve
     [,1] [,2] [,3] [,4] [,5]
[1,]  NaN  NaN  NaN  NaN  NaN
[2,]  NaN  NaN  NaN  NaN  NaN
[3,]  NaN  NaN  NaN  NaN  NaN
[4,]  NaN  NaN  NaN  NaN  NaN
[5,]  NaN  NaN  NaN  NaN  NaN
> matrix(c(runif(24), -Inf), nc = 5) %>% solve
     [,1] [,2] [,3] [,4] [,5]
[1,]  NaN  NaN  NaN  NaN  NaN
[2,]  NaN  NaN  NaN  NaN  NaN
[3,]  NaN  NaN  NaN  NaN  NaN
[4,]  NaN  NaN  NaN  NaN  NaN
[5,]  NaN  NaN  NaN  NaN  NaN
> matrix(c(runif(24), NA), nc = 5) %>% solve
     [,1] [,2] [,3] [,4] [,5]
[1,]   NA   NA   NA   NA   NA
[2,]   NA   NA   NA   NA   NA
[3,]   NA   NA   NA   NA   NA
[4,]   NA   NA   NA   NA   NA
[5,]   NA   NA   NA   NA   NA
> solve.default(matrix(rep(0, 25), nc = 5))
Error in solve.default(matrix(rep(0, 25), nc = 5)) : Lapack routine dgesv: system is exactly singular: U[1,1] = 0

    就如 https://d.cosx.org/d/6181-6181/28 帖子所述，目前得阅读些参考文献，才能知道Copula原理和如何使用运用：

    • 略读过rmgarch作者的使用Rcpp编程（僕还不会高效率的C++）
    • 阅读过他的背景和部落格，不简单。博士生背景经验老道的量化交易兼某家公司的首席经济学家。

    兄台您真是爱说笑了，小巫见大巫。?
    这两天得嚼嚼以下文献才行... 之后还得学习高频率模型、投资建模、投资组合建模吖。一摞摞的科研，叹气～（身边每个人频频催僕赶快找工作，僕就连科研都尚未完成，如何踏入量化交易行业呢？）

      照您这么卖力学量化，相信不久后必然可以直播做量化了?，纯粹说笑，莫介意！

      set.seed(123)                 
aaa <- matrix(rnorm(20), 5, 4)
bbb <- cbind(aaa, aaa[, 4])   
solve(bbb)                    
#> Error in solve.default(bbb): system is computationally singular: reciprocal condition number = 2.55787e-18

      报的错误不同，也只是分母非常接近于0和分母等于0的区别，我猜。

        holydudu 多谢前辈教导，不过就不晓得为啥电脑程序也会出错呢？?

        > solve(matrix(rnorm(25), 5, 5))
            [,1]          [,2]       [,3]       [,4]       [,5]
[1,]  8.24446226  -8.799586412 -7.8797734 -8.4941483 10.2240770
[2,]  0.12945761   0.003591567 -0.2092521 -0.4213559  0.6124343
[3,]  9.97508114 -10.277994259 -8.7824676 -9.8373951 12.4311528
[4,]  8.35414720  -7.059080960 -7.5637485 -7.8476009  9.7568802
[5,] -0.02154905   0.210138922 -0.2691161  0.2612327  0.1006492
> ccc <- cbind(aaa[,1:2], aaa[,1:2], aaa[,1])
> solve(ccc)
Error in solve.default(ccc) : Lapack routine dgesv: system is exactly singular: U[4,4] = 0
> solve(matrix(rep(0, 25), 5,5))
Error in solve.default(matrix(rep(0, 25), 5, 5)) : Lapack routine dgesv: system is exactly singular: U[1,1] = 0
> solve(ccc)
Error in solve.default(ccc) : Lapack routine dgesv: system is exactly singular: U[4,4] = 0

        以下乃错误预测价格之一。

        • 2014-07-10 USDCNY.Lo 2.201就是数据错误吧？毕竟人民币都未曾涨至2.201的兑换率。
        • 预测价错误2015-07-28 USDCHF.Op 0.962 -1674.2440018，运行结果的T+1预测价竟然会是Loglikelihood-1674.2440018。

        比方说程序在计算时偶尔出错还有可能（例子：使用cluster或者for loop连续与并行计算，基本上还有可能出现内存地址储存错误，3.3 指针 （Pointers）），晚辈不明的是为啥僕尝试单一（没使用for loop和 cluster预测单日价格）运行代码也会出错？?

        Error data
.id	Cat	Date	        Type	        Price	Price.T1	Akaike	        Bayes	        Shibata	        Hannan.Quinn	diff	       se
USDCHF	pred1	2015-07-28	USDCHF.Op	0.962	-1674.2440018	-6.855036	-6.691600	-6.858992	-6.789348	1740.3783803	1
USDCHF	pred1	2015-01-15	USDCHF.Lo	0.733	1.0165024	-5.799861	-5.718143	-5.800879	-5.767017	1.3867699	1
USDCNY	pred1	2014-07-10	USDCNY.Lo	2.201	6.1863967	-2.713266	-2.631323	-2.714291	-2.680328	2.8107209	1
USDCNY	pred1	2014-07-14	USDCNY.Lo	6.196	1.2948723	-3.150394	-3.013822	-3.153188	-3.095496	0.2089852	1
USDJPY	pred1	2013-06-27	USDJPY.Op	98.468	78.3949808	4.713287	4.795004	4.712269	4.746131	0.7961468	1
USDJPY	pred1	2013-06-30	USDJPY.Op	99.411	78.3964420	4.735608	4.817551	4.734583	4.768547	0.7886093	1

        原文：binary.com 面试试题 I - GARCH模型中的ARIMA(p,d,q)参数最优化