# How to change the tolerance of the QRPivoted method

Hi there

I’m using the LinearAlgebra package in Julia to use the QRPivoted method. The documentation is not very clear about the use of the tolerance. I want to use que qr pivoted function on a matrix A but I want to be able to change the tolerance.
To use the qr pivoted function, the documentation says to do the following:

qr(A, Val(false)) which actually works once you do it in Julia for any matrix A


However, the only mention of tolerance in the documentation is
qr(A::SparseMatrixCSC; tol=_default_tol(A), ordering=ORDERING_DEFAULT)

I don’t know how to use it in Julia because I have tried
qr(A, 10e-10, ordering = false) and
qr(A, 10e-10)

and nothing works. Can anyone help with that?
I would like to do something like
qr(A, Val(false), 10e-10) to make a QRPivoted matrix with a tolerance of the method of 10e-10.

It should work on any matrix A so feel free to use any one you want.

I would try qr(A, tol=10e-10).

1 Like

tol is keyword argument which is set by calling qr(A, tol=1e-10) as @goerch indicated. The clue for this in the documentation is the semicolon in

qr(A::SparseMatrixCSC; tol=_default_tol(A), ordering=ORDERING_DEFAULT)


For the function def f(x, y, z; a=default1, b=default2), the arguments x,y,z before the semicolon are required and specified by order. The arguments a and b come with default values and can be set in any order or left to default values, but you need to name them when calling, as in f(1,2,3, a="foo") or f(1,2,3, b="bar", a="foo").

Julia Doc: Keyword Arguments

By the way, 10e-10 is a literal for 10 \times 10^{-10} = 10^{-9}. If what you want is 10^{-10}, enter it as 1e-10. Just guessing here!

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No, I have tried that and it doesn’t work.

I have tried both F = qr(A; tol = 10e-10) and F = qr(A, Val(true); tol = 10e-10) and none of them work.

Here’s a minimal working example that works (julia-1.6.0)

julia> using LinearAlgebra, SparseArrays

julia> i = [1,1,2,2,3,3,4,4];

julia> j = [1,2,2,3,3,4,4,2];

julia> v = [1.0,2.0,-5.0,3.0,-1.0,2.0,-2.0,4.0];

julia> A = sparse(i,j,v)
4×4 SparseMatrixCSC{Float64, Int64} with 8 stored entries:
1.0   2.0    ⋅     ⋅
⋅   -5.0   3.0    ⋅
⋅     ⋅   -1.0   2.0
⋅    4.0    ⋅   -2.0

julia> F = qr(A, tol=1-08)
SuiteSparse.SPQR.QRSparse{Float64, Int64}
Q factor:
4×4 SuiteSparse.SPQR.QRSparseQ{Float64, Int64}:
1.0   0.0        0.0       0.0
0.0  -0.780869  -0.551142  0.294086
0.0   0.624695  -0.688927  0.367607
0.0   0.0        0.470767  0.882258
R factor:
4×4 SparseMatrixCSC{Float64, Int64} with 8 stored entries:
1.0  2.0        ⋅         ⋅
⋅   6.40312  -2.34261  -1.24939
⋅    ⋅       -2.12419   2.31939
⋅    ⋅         ⋅        1.0293
Row permutation:
4-element Vector{Int64}:
1
2
4
3
Column permutation:
4-element Vector{Int64}:
1
2
3
4
julia>

2 Likes