Support tolerance in banded adaptive qr (#121)

* Support tolerance in banded adaptive qr

* Update Project.toml

* add tolerance test

* v0.6.13

Author: dlfivefifty

Project.toml

@@ -1,6 +1,6 @@
 name = "InfiniteLinearAlgebra"
 uuid = "cde9dba0-b1de-11e9-2c62-0bab9446c55c"
-version = "0.6.12"
+version = "0.6.13"
 
 [deps]
 ArrayLayouts = "4c555306-a7a7-4459-81d9-ec55ddd5c99a"
@@ -18,7 +18,7 @@ SemiseparableMatrices = "f8ebbe35-cbfb-4060-bf7f-b10e4670cf57"
 
 [compat]
 Aqua = "0.5"
-ArrayLayouts = "0.8.11"
+ArrayLayouts = "0.8.16"
 BandedMatrices = "0.17"
 BlockArrays = "0.16.14"
 BlockBandedMatrices = "0.11.5"

src/infqr.jl

@@ -205,11 +205,9 @@ end
 
 _norm(x::Number) = abs(x)
 
-function materialize!(M::MatLmulVec{<:AdjQRPackedQLayout{<:AdaptiveLayout},<:PaddedLayout})
+function materialize!(M::MatLmulVec{<:AdjQRPackedQLayout{<:AdaptiveLayout},<:PaddedLayout}; tolerance=floatmin(real(eltype(M))))
     adjA,B = M.A,M.B
-    T = eltype(M)
     COLGROWTH = 1000 # rate to grow columns
-    tol = floatmin(real(T))
 
     require_one_based_indexing(B)
     A = adjA.parent
@@ -235,7 +233,7 @@ function materialize!(M::MatLmulVec{<:AdjQRPackedQLayout{<:AdaptiveLayout},<:Pad
             kr = j:cs_max
             resizedata!(B, min(cs_max,mB))
             Bdata = paddeddata(B)
-            if (j > sB && maximum(_norm,view(Bdata,j:last(colsupport(A.factors,j)))) ≤ tol)
+            if (j > sB && maximum(_norm,view(Bdata,j:last(colsupport(A.factors,j)))) ≤ tolerance)
                 break
             end
             partialqr!(A.factors.data, min(cs_max,nA))
@@ -244,7 +242,7 @@ function materialize!(M::MatLmulVec{<:AdjQRPackedQLayout{<:AdaptiveLayout},<:Pad
             jr = last(jr)+1:min(last(jr)+COLGROWTH,nA)
         end
     end
-    resizedata_chop!(B, tol)
+    resizedata_chop!(B, tolerance)
 end
 
 function resizedata!(B::PseudoBlockVector, M::Block{1})
@@ -341,8 +339,7 @@ end
 
 
 
-ldiv!(dest::AbstractVector, F::QR{<:Any,<:AdaptiveQRFactors}, b::AbstractVector) =
-    ldiv!(F, copyto!(dest, b))
+ldiv!(dest::AbstractVector, F::QR{<:Any,<:AdaptiveQRFactors}, b::AbstractVector; kwds...) = ldiv!(F, copyto!(dest, b); kwds...)
 ldiv!(F::QR{<:Any,<:AdaptiveQRFactors}, b::AbstractVector; kwds...) = ldiv!(F.R, lmul!(F.Q',b; kwds...))
 ldiv!(F::QR{<:Any,<:AdaptiveQRFactors}, b::LayoutVector; kwds...) = ldiv!(F.R, lmul!(F.Q',b; kwds...))
 \(F::QR{<:Any,<:AdaptiveQRFactors}, B::AbstractVector; kwds...) = ldiv!(F.R, *(F.Q', B; kwds...))

test/test_infqr.jl

@@ -303,4 +303,10 @@ import SemiseparableMatrices: AlmostBandedLayout, VcatAlmostBandedLayout
         @test (Q*R)[1:10,1:10] ≈ A[1:10,1:10]
         @test (R*Q)[1:10,1:10] ≈ LazyBandedMatrices.SymTridiagonal((R*Q)[1:10,1:10])
     end
+
+    @testset "tolerance" begin
+        A = BandedMatrix(1 => Ones(∞), 0 => Fill(-2,∞), -1 => Ones(∞))
+        u = \(A, [1; zeros(∞)]; tolerance=1E-8)
+        @test A*u ≈ [1; zeros(∞)]
+    end
 end