[R] Solving sparse, singular systems of equations

A A awawaed at yahoo.com
Wed Apr 20 20:50:34 CEST 2016

Thanks for the response. Yes, in that situation a solution of x = 1 would be just as good as x = 1000 or any other value of x for me (but in my problem the matrix has nonzero rank, so I can't just randomly choose a vector and have it be a solution). If it helps, what I'm interested in is the R equivalent of 
x = A\b
in MATLAB, for these particular kinds of A matrices. I looked into irlba, and it seems to be able to calculate some of the singular values/vectors for the large dataset without taking too much time. I'll look more into seeing how I can solve the system with it. 

    On Wednesday, April 20, 2016 11:01 AM, Jeff Newmiller <jdnewmil at dcn.davis.ca.us> wrote:

 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.
#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 = 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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