added project folder

project/testing.ipynb

@@ -0,0 +1,83 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "id": "57a2b335-a7f3-4ace-a2d8-52219c4febc5",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "include(\"thinQR.jl\")\n",
+    "using .thinQR"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "id": "426735f0-859a-4f7d-83cf-f52f464a2737",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "3-element Vector{Float64}:\n",
+       "  2.8498844747360086\n",
+       " -2.404529848146403\n",
+       " -0.3104749426792832"
+      ]
+     },
+     "execution_count": 2,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "A = [1. 2; 3 4; 5 6]\n",
+    "A = qrhous!(A)\n",
+    "A * [1., 2, 3]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "id": "afd34800-7b9a-4006-9849-071fa197d962",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "3-element Vector{Float64}:\n",
+       "  2.8498844747360064\n",
+       " -2.404529848146404\n",
+       " -0.31047494267928366"
+      ]
+     },
+     "execution_count": 3,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "using LinearAlgebra: qr!\n",
+    "A = [1. 2.; 3. 4.; 5. 6.]\n",
+    "(Q, R) = qr!(A)\n",
+    "Q * [1., 2, 3]"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Julia 1.9.3",
+   "language": "julia",
+   "name": "julia-1.9"
+  },
+  "language_info": {
+   "file_extension": ".jl",
+   "mimetype": "application/julia",
+   "name": "julia",
+   "version": "1.9.3"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}

project/thinQR.jl

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+module thinQR
+
+import Base: size, show, getproperty, getfield, propertynames, *
+using LinearAlgebra: norm, I, triu, diagm
+
+export QRthin, qrhous!, qyhous
+
+mutable struct QRthin{T <: Real}
+    A::AbstractVecOrMat{T}
+    d::AbstractArray{T}
+    AQ::Union{Nothing, AbstractVecOrMat{T}}
+    AR::Union{Nothing, AbstractVecOrMat{T}}
+
+    QRthin(A, d, AQ=nothing, AR=nothing) = new{eltype(A)}(A, d, AQ, AR)
+end
+
+function qrhous!(A::AbstractMatrix{T})::QRthin{T} where T
+    m, n = size(A)
+
+    d = zeros(n)
+    for j ∈ 1:n
+        s = norm(A[j:m, j])
+        # iszero(s) && throw(ArgumentError("The matrix A is singular"))
+        d[j]= copysign(s, -A[j,j])
+        fak = sqrt(s * (s + abs(A[j,j])))
+        A[j,j] -= d[j]
+        A[j:m, j] ./= fak
+
+        if j < n
+            A[j:m, j+1:n] -= A[j:m, j] * (A[j:m, j]' * A[j:m, j+1:n])
+        end
+    end
+
+    return QRthin(A, d)
+end
+
+function qyhous(A::QRthin{T}, y::AbstractArray{T}) where T
+    m, n = size(A.A)
+    z = deepcopy(y)
+    for j ∈ n:-1:1
+        z[j:m] = z[j:m] - A.A[j:m, j] * (A.A[j:m, j]' * z[j:m])
+    end
+    return z
+end
+
+function calculateQ(A::QRthin{T}) where T
+    if A.AQ != nothing
+        return A.AQ
+    end
+    m, n = size(A.A)
+    A.AQ = zeros(m, 0)
+    id = Matrix{eltype(A.A)}(I, m, n)
+    for i ∈ eachcol(id)
+        A.AQ = [A.AQ qyhous(A, i)]
+    end
+    return A.AQ
+end
+
+function calculateR(A::QRthin{T}) where T
+    if A.AR != nothing
+        return A.AR
+    end
+    m, n = size(A.A)
+    A.AR = triu(A.A[1:n, :], 1) + diagm(A.d)
+    return A.AR
+end
+
+function Base.show(io::IO, mime::MIME{Symbol("text/plain")}, A::QRthin{T}) where T
+    summary(io, A); println(io)
+    print(io, "Q factor: ")
+    show(io, mime, A.Q)
+    print(io, "\nR factor: ")
+    show(io, mime, A.R)
+end
+
+function Base.getproperty(A::QRthin{T}, d::Symbol) where T
+    if d === :R
+        return calculateR(A)
+    elseif d === :Q
+        return calculateQ(A)
+    else
+        getfield(A, d)
+    end
+end
+
+Base.propertynames(A::QRthin, private::Bool=false) = (:R, :Q, (private ? fieldnames(typeof(A)) : ())...)
+
+Base.size(A::QRthin) = size(getfield(A, :A))
+
+function *(A::QRthin{T}, b::AbstractVector{T}) where {T}
+    return qyhous(A, b)
+end
+
+end # module