[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:
>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?
>Thanks for your time.
>= 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 =
>readMM("A.txt")b = readMM("b.txt")
>#Error in as(x, "matrix")[i, , drop = drop] : subscript out of
>boundssolve(qr(A, LAPACK=TRUE),b)
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>and provide commented, minimal, self-contained, reproducible code.

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