Fix QR based fitting

Avoid erroring out for low rank design matrices when dropcollinear=false.
Avoid unnecessary triangular solves. Avoid indexing in the Q.
Avoid slicing R matrix in a way that triggers a minimum norm solution.
Remove unnecessary temporaries.

Project.toml

@@ -36,9 +36,10 @@ julia = "1.6"
 CSV = "336ed68f-0bac-5ca0-87d4-7b16caf5d00b"
 CategoricalArrays = "324d7699-5711-5eae-9e2f-1d82baa6b597"
 DataFrames = "a93c6f00-e57d-5684-b7b6-d8193f3e46c0"
+Downloads = "f43a241f-c20a-4ad4-852c-f6b1247861c6"
 RDatasets = "ce6b1742-4840-55fa-b093-852dadbb1d8b"
 StableRNGs = "860ef19b-820b-49d6-a774-d7a799459cd3"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 
 [targets]
-test = ["CategoricalArrays", "CSV", "DataFrames", "RDatasets", "StableRNGs", "Test"]
+test = ["CategoricalArrays", "CSV", "DataFrames", "Downloads", "RDatasets", "StableRNGs", "Test"]

src/linpred.jl

@@ -63,23 +63,19 @@ function delbeta! end
 
 function delbeta!(p::DensePredQR{T,<:QRCompactWY}, r::Vector{T}) where T<:BlasReal
     rnk = rank(p.qr.R)
-    rnk == length(p.delbeta) || throw(RankDeficientException(rnk))
-    p.delbeta = p.qr\r
-    mul!(p.scratchm1, Diagonal(ones(size(r))), p.X)
+    p.delbeta = p.qr \ r
     return p
 end
 
 function delbeta!(p::DensePredQR{T,<:QRCompactWY}, r::Vector{T}, wt::Vector{T}) where T<:BlasReal
     rnk = rank(p.qr.R)
-    rnk == length(p.delbeta) || throw(RankDeficientException(rnk))
     X = p.X
     W = Diagonal(wt)
     sqrtW = Diagonal(sqrt.(wt))
     mul!(p.scratchm1, sqrtW, X)
-    mul!(p.delbeta, X'W, r)
-    qnr = qr(p.scratchm1)
-    Rinv = inv(qnr.R)
-    p.delbeta = Rinv * Rinv' * p.delbeta
+    ỹ = sqrtW * r
+    p.qr = qr!(p.scratchm1)
+    p.delbeta = p.qr \ ỹ
     return p
 end
 
@@ -88,44 +84,32 @@ function delbeta!(p::DensePredQR{T,<:QRPivoted}, r::Vector{T}) where T<:BlasReal
     if rnk == length(p.delbeta)
         p.delbeta = p.qr\r
     else
-        R = @view p.qr.R[:, 1:rnk]
-        Q = @view p.qr.Q[:, 1:size(R, 1)]
+        R = UpperTriangular(view(parent(p.qr.R), 1:rnk, 1:rnk))
         piv = p.qr.p
-        p.delbeta = zeros(size(p.delbeta))
-        p.delbeta[1:rnk] = R \ Q'r
+        fill!(p.delbeta, 0)
+        p.delbeta[1:rnk] = R \ view(p.qr.Q'r, 1:rnk)
         invpermute!(p.delbeta, piv)
     end
-    mul!(p.scratchm1, Diagonal(ones(size(r))), p.X)
     return p
 end
 
 function delbeta!(p::DensePredQR{T,<:QRPivoted}, r::Vector{T}, wt::Vector{T}) where T<:BlasReal
-    rnk = rank(p.qr.R)
     X = p.X
     W = Diagonal(wt)
     sqrtW = Diagonal(sqrt.(wt))
-    delbeta = p.delbeta
-    scratchm2 = similar(X, T)
     mul!(p.scratchm1, sqrtW, X)
-    mul!(scratchm2, W, X)
-    mul!(delbeta, transpose(scratchm2), r)
-
-    if rnk == length(p.delbeta)
-        qnr = qr(p.scratchm1)
-        Rinv = inv(qnr.R)
-        p.delbeta = Rinv * Rinv' * delbeta
-    else
-        qnr = pivoted_qr!(copy(p.scratchm1))
-        R = @view qnr.R[1:rnk, 1:rnk]
-        Rinv = inv(R)
-        piv = qnr.p
-        permute!(delbeta, piv)
-        for k=(rnk+1):length(delbeta)
-            delbeta[k] = -zero(T)
-        end
-        p.delbeta[1:rnk] = Rinv * Rinv' * view(delbeta, 1:rnk)
-        invpermute!(delbeta, piv)
+    r̃ = sqrtW * r
+
+    p.qr = pivoted_qr!(copy(p.scratchm1))
+    rnk = rank(p.qr.R) # FIXME! Don't use svd for this
+    R = UpperTriangular(view(parent(p.qr.R), 1:rnk, 1:rnk))
+    permute!(p.delbeta, p.qr.p)
+    for k = (rnk + 1):length(p.delbeta)
+        p.delbeta[k] = -zero(T)
     end
+    p.delbeta[1:rnk] = R \ (p.qr.Q'*r̃)[1:rnk]
+    invpermute!(p.delbeta, p.qr.p)
+
     return p
 end
 
@@ -279,27 +263,25 @@ end
 LinearAlgebra.cholesky(p::SparsePredChol{T}) where {T} = copy(p.chol)
 LinearAlgebra.cholesky!(p::SparsePredChol{T}) where {T} = p.chol
 
-function invqr(x::DensePredQR{T,<: QRCompactWY}) where T
-    Q,R = qr(x.scratchm1)
-    Rinv = inv(R)
+function invqr(p::DensePredQR{T,<: QRCompactWY}) where T
+    Rinv = inv(p.qr.R)
     Rinv*Rinv'
 end
 
-function invqr(x::DensePredQR{T,<: QRPivoted}) where T
-    Q,R,pv = pivoted_qr!(copy(x.scratchm1))
-    rnk = rank(R)
-    p = length(x.delbeta)
-    if rnk == p
-        Rinv = inv(R)
+function invqr(p::DensePredQR{T,<: QRPivoted}) where T
+    rnk = rank(p.qr.R)
+    k = length(p.delbeta)
+    if rnk == k
+        Rinv = inv(p.qr.R)
         xinv = Rinv*Rinv'
-        ipiv = invperm(pv)
+        ipiv = invperm(p.qr.p)
         return xinv[ipiv, ipiv]
     else
-        Rsub = R[1:rnk, 1:rnk]
+        Rsub = UpperTriangular(view(p.qr.R, 1:rnk, 1:rnk))
         RsubInv = inv(Rsub)
-        xinv = fill(convert(T, NaN), (p,p))
+        xinv = fill(convert(T, NaN), (k, k))
         xinv[1:rnk, 1:rnk] = RsubInv*RsubInv'
-        ipiv = invperm(pv)
+        ipiv = invperm(p.qr.p)
         return xinv[ipiv, ipiv]
     end
 end

test/runtests.jl

@@ -177,8 +177,8 @@ end
         @test isa(m2p_dep_pos.pp.chol, CholeskyPivoted)
         @test isa(m2p_dep_pos_kw.pp.chol, CholeskyPivoted)
     elseif dmethod == :qr
-        @test_throws RankDeficientException m2 = fit(LinearModel, Xmissingcell, ymissingcell;
-                                                        method = dmethod, dropcollinear=false)
+        @test fit(LinearModel, Xmissingcell, ymissingcell;
+            method = dmethod, dropcollinear=false) isa LinearModel
         @test isapprox(coef(m2p), [0.9772643585228962, 11.889730016918342, 3.027347397503282,
                                    3.9661379199401177, 5.079410103608539, 6.194461814118862,
                                   -2.9863884084219015, 7.930328728005132, 8.87999491860477,
@@ -2055,3 +2055,20 @@ end
     # values. It doesn't care about links, offsets, etc. as long as the model matrix,
     # vcov matrix and stderrors are well defined.
 end
+
+@testset "NIST - Filip. Issue 558" begin
+    fn = Downloads.download("https://www.itl.nist.gov/div898/strd/lls/data/LINKS/DATA/Filip.dat")
+    filip_estimates_df = CSV.read(fn, DataFrame; skipto = 31, limit = 11, header = ["parameter", "estimate", "se"], delim = " ", ignorerepeated = true)
+    filip_data_df = CSV.read(fn, DataFrame; skipto = 61, header = ["y", "x"], delim = " ", ignorerepeated = true)
+    X = [filip_data_df.x[i]^j for i in 1:length(filip_data_df.x), j in 0:10]
+
+    # No weights
+    f1 = lm(X, filip_data_df.y, dropcollinear = false, method = :qr)
+    @test coef(f1) ≈ filip_estimates_df.estimate rtol = 1e-8
+    @test stderror(f1) ≈ filip_estimates_df.se rtol = 1e-7
+
+    # Weights
+    f2 = lm(X, filip_data_df.y, dropcollinear = false, method = :qr, wts = ones(length(filip_data_df.y)))
+    @test coef(f2) ≈ filip_estimates_df.estimate rtol = 1e-8
+    @test stderror(f2) ≈ filip_estimates_df.se rtol = 1e-7
+end