Support qr for quasimatrices (#247)

* Support qr for quasimatrices

* Update Project.toml

Author: dlfivefifty

Project.toml

@@ -1,7 +1,7 @@
 name = "ClassicalOrthogonalPolynomials"
 uuid = "b30e2e7b-c4ee-47da-9d5f-2c5c27239acd"
 authors = ["Sheehan Olver <[email protected]>"]
-version = "0.15.4"
+version = "0.15.5"
 
 
 [deps]
@@ -49,7 +49,7 @@ HypergeometricFunctions = "0.3.4"
 InfiniteArrays = " 0.15"
 InfiniteLinearAlgebra = "0.10.1"
 IntervalSets = "0.7"
-LazyArrays = "2.7"
+LazyArrays = "2.8"
 LazyBandedMatrices = "0.11"
 MutableArithmetics = "1"
 QuasiArrays = "0.12"

src/normalized.jl

@@ -303,3 +303,9 @@ diff_layout(::MappedOPLayouts, A, order::Int; dims...) = diff_layout(MappedBasis
 diff_layout(::MappedOPLayouts, A, order...; dims...) = diff_layout(MappedBasisLayout(), A, order...; dims...)
 
 diff_layout(::AbstractNormalizedOPLayout, A, order...; dims...) = diff_layout(ApplyLayout{typeof(*)}(), A, order...; dims...)
+
+function qr(A::AbstractQuasiMatrix)
+    P = normalized(basis(A))
+    Q,R = qr(P \ A)
+    P * Q[:, axes(A,2)], R # TODO: ContinuumFactorization
+end

test/test_roots.jl

@@ -1,4 +1,4 @@
-using ClassicalOrthogonalPolynomials, Random, Test
+using ClassicalOrthogonalPolynomials, QuasiArrays, Random, Test
 using ClassicalOrthogonalPolynomials: sample
 
 Random.seed!(5)
@@ -24,6 +24,13 @@ end
     @test (Legendre() \ A)[1:5,1] ≈ [1; zeros(4)] # test transform bug
     @test (P \ A)[1:5,1] ≈ [sqrt(2); zeros(4)]
     Q,R = qr(P \ A)
+    @test (P * (Q*R))[0.1,:] ≈ A[0.1,:]
+    @test (A*inv(R))[0.1,:] ≈ QuasiArrays.ApplyQuasiArray(*, P, Q)[0.1,1:6] 
+
+    Q,R = qr(A)
+    @test Q[0.1,:]'R ≈ A[0.1,:]'
+
+    # sum(expand(Q[:,k] .^2) for k=axes(Q,2))
 end
 
 @testset "minimum/maximum/extrema (#242)" begin