# [R] Solving sparse, singular systems of equations

Jeff Newmiller jdnewmil at dcn.davis.ca.us
Wed Apr 20 17:01:08 CEST 2016

```This is kind of like asking for a solution to x+1=x+1. Go back to linear algebra and look up Singular Value Decomposition, and decide if you really want to proceed.  See also ?svd and package irlba.
--
Sent from my phone. Please excuse my brevity.

On April 20, 2016 4:22:34 AM PDT, A A via R-help <r-help at r-project.org> wrote:
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>I have a situation in R where I would like to find any x (if one
>exists) that solves the linear system of equations Ax = b, where A is
>square, sparse, and singular, and b is a vector. Here is some code that
>mimics my issue with a relatively simple A and b, along with three
>other methods of solving this system that I found online, two of which
>give me an error and one of which succeeds on the simplified problem,
>but fails on my data set(attached). Is there a solver in R that I can
>use in order to get x without any errors given the structure of A?
>#CODE STARTS HEREA =
>as(matrix(c(1.5,-1.5,0,-1.5,2.5,-1,0,-1,1),nrow=3,ncol=3),"sparseMatrix")b
>= matrix(c(-30,40,-10),nrow=3,ncol=1)
>#solve for x, Error in LU.dgC(a) : cs_lu(A) failed: near-singular A (or
>out of memory)solve(A,b,sparse=TRUE,tol=.Machine\$double.eps)
>#one x that happens to solve Ax = bx =
>matrix(c(-10,10,0),nrow=3,ncol=1)A %*% x
>#Error in lsfit(A, b) : only 3 cases, but 4 variableslsfit(A,b)#solves
>the system, but fails belowsolve(qr(A, LAPACK=TRUE),b)#Error in
>qr.solve(A, b) : singular matrix 'a' in solveqr.solve(A,b)
>#matrices used in my actual problem (see attached files)A =
>#Error in as(x, "matrix")[i, , drop = drop] : subscript out of
>boundssolve(qr(A, LAPACK=TRUE),b)
>
>
>
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