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) -------------- next part -------------- An embedded and charset-unspecified text was scrubbed... Name: A.txt URL: <https://stat.ethz.ch/pipermail/r-help/attachments/20160420/d5cf4593/attachment-0002.txt> -------------- next part -------------- An embedded and charset-unspecified text was scrubbed... Name: b.txt URL: <https://stat.ethz.ch/pipermail/r-help/attachments/20160420/d5cf4593/attachment-0003.txt>
This is not a solution but your lsfit attempt #Error in lsfit(A, b) : only 3 cases, but 4 variables lsfit(A,b) gave that error because lsfit adds a column of 1 to its first argument unless you use intercept=FALSE. Then it will give you an answer (but I think it converts your sparse matrix into a dense one before doing any linear algebra). Bill Dunlap TIBCO Software wdunlap tibco.com On Wed, Apr 20, 2016 at 4:22 AM, 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) > > > ______________________________________________ > R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide > http://www.R-project.org/posting-guide.html > and provide commented, minimal, self-contained, reproducible code. >[[alternative HTML version deleted]]
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$double.eps) >#one x that happens to solve Ax = bx >matrix(c(-10,10,0),nrow=3,ncol=1)A %*% x >#Error in lsfit(A, b) : only 3 cases, but 4 variableslsfit(A,b)#solves >the system, but fails belowsolve(qr(A, LAPACK=TRUE),b)#Error in >qr.solve(A, b) : singular matrix 'a' in solveqr.solve(A,b) >#matrices used in my actual problem (see attached files)A >readMM("A.txt")b = readMM("b.txt") >#Error in as(x, "matrix")[i, , drop = drop] : subscript out of >boundssolve(qr(A, LAPACK=TRUE),b) > > > >------------------------------------------------------------------------ > >______________________________________________ >R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see >https://stat.ethz.ch/mailman/listinfo/r-help >PLEASE do read the posting guide >http://www.R-project.org/posting-guide.html >and provide commented, minimal, self-contained, reproducible code.[[alternative HTML version deleted]]
> On 20 Apr 2016, at 13:22, A A via R-help <r-help at r-project.org> wrote: > > > > > I have a situation in R where I would like to find any x (if one exists) that solves the linear system of equations Ax = b, where A is square, sparse, and singular, and b is a vector. Here is some code that mimics my issue with a relatively simple A and b, along with three other methods of solving this system that I found online, two of which give me an error and one of which succeeds on the simplified problem, but fails on my data set(attached). Is there a solver in R that I can use in order to get x without any errors given the structure of A? Thanks for your time. > #CODE STARTS HEREA = as(matrix(c(1.5,-1.5,0,-1.5,2.5,-1,0,-1,1),nrow=3,ncol=3),"sparseMatrix")b = matrix(c(-30,40,-10),nrow=3,ncol=1) > #solve for x, Error in LU.dgC(a) : cs_lu(A) failed: near-singular A (or out of memory)solve(A,b,sparse=TRUE,tol=.Machine$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)Your code is a mess. A singular square system of linear equations has an infinity of solutions if a solution exists at all. How that works you can find here: https://en.wikipedia.org/wiki/System_of_linear_equations in the section "Matrix solutions". For your simple example you can do it like this: library(MASS) Ag <- ginv(A) # pseudoinverse xb <- Ag %*% b # minimum norm solution Aw <- diag(nrow=nrow(Ag)) - Ag %*% A # see the Wikipedia page w <- runif(3) z <- xb + Aw %*% w A %*% z - b N <- Null(t(A)) # null space of A; see the help for Null in package MASS A %*% N A %*% (xb + 2 * N) - b For sparse systems you will have to approach this differently; I have no experience with that. Berend
Thanks for the advice. I fixed the function and ran it on my systems just to see if it would work; for the first set of A and b, I got a valid solution, but for the second set, I got the error "Error in complete.cases(x, y, wt) : not all arguments have the same length".? On Wednesday, April 20, 2016 10:59 AM, William Dunlap <wdunlap at tibco.com> wrote: This is not a solution but your lsfit attempt? ?#Error in lsfit(A, b) : only 3 cases, but 4 variables? ?lsfit(A,b)gave that error because lsfit adds a column of 1 toits first argument unless you use intercept=FALSE.Then it will give you an answer (but I think it convertsyour sparse matrix into a dense one before doingany linear algebra). Bill Dunlap TIBCO Software wdunlap tibco.com On Wed, Apr 20, 2016 at 4:22 AM, 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) ? ? ______________________________________________ R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code. [[alternative HTML version deleted]]
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) R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code. [[alternative HTML version deleted]]
Thanks for the help. Sorry, I am not sure why it looks like that in the mailing list - it looks much more neat on my end (see attached file). On Wednesday, April 20, 2016 2:01 PM, Berend Hasselman <bhh at xs4all.nl> wrote:> On 20 Apr 2016, at 13:22, 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)Your code is a mess. A singular square system of linear equations has an infinity of solutions if a solution exists at all. How that works you can find here: https://en.wikipedia.org/wiki/System_of_linear_equations in the section "Matrix solutions". For your simple example you can do it like this: library(MASS) Ag <- ginv(A)??? # pseudoinverse xb <- Ag %*% b # minimum norm solution Aw <- diag(nrow=nrow(Ag)) - Ag %*% A? # see the Wikipedia page w <- runif(3) z <- xb + Aw %*% w A %*% z - b N <- Null(t(A))??? # null space of A;? see the help for Null in package MASS A %*% N A %*% (xb + 2 * N) - b For sparse systems you will have to approach this differently; I have no experience with that. Berend