R solve system is exactly singular

Question

I am solving simple optimization problem  The data set has 26 columns and over 3000 rows  The source code looks like   Means    lt - colMeans Returns  Sigma    lt - cov Returns  invSigma1  lt - solve Sigma    And everything works perfect- but then I want to do the same for shorter period  only 261 rows  and the solve function writes the following error   solve Sigma  Error in solve default Sigma       Lapack routine dgesv  system is exactly singular    Its weird because when I do the same with some random numbers   Returns lt -matrix runif 6786 -1 1   nrow 261  Means    lt - colMeans Returns  Sigma    lt - cov Returns  invSigma  lt - solve Sigma    no error occurs at all  Could someone explain me where could be the problem and how to treat it  Thank you very much  Alex

User · Answer

Lapack is a Linear Algebra package which is used by R (actually it's used everywhere) underneath solve(), dgesv spits this kind of error when the matrix you passed as a parameter is singular.

As an addendum: dgesv performs LU decomposition, which, when using your matrix, forces a division by 0, since this is ill-defined, it throws this error. This only happens when matrix is singular or when it's singular on your machine (due to approximation you can have a really small number be considered 0)

I'd suggest you check its determinant if the matrix you're using contains mostly integers and is not big. If it's big, then take a look at this link.

User · Answer

I guess your code uses somewhere in the second case a singular matrix  i e  not invertible   and the solve function needs to invert it  This has nothing to do with the size but with the fact that some of your vectors are  probably  colinear

User · Answer

Using solve with a single parameter is a request to invert a matrix   The error message is telling you that your matrix is singular and cannot be inverted

[r] R solve:system is exactly singular

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