deprecate orthogonal decomposition keyword "thin" to "full" (#24279)

* Deprecate keyword argument "thin" in favor of "full" in svd methods.
* Deprecate keyword argument "thin" in favor of "full" in qr methods.
* Deprecate keyword argument "thin" in favor of "full" in lq methods.

NEWS.md

@@ -381,6 +381,10 @@ Deprecated or removed
   * The `cholfact`/`cholfact!` methods that accepted an `uplo` symbol have been deprecated
     in favor of using `Hermitian` (or `Symmetric`) views ([#22187], [#22188]).
 
+  * The `thin` keyword argument for orthogonal decomposition methods has
+    been deprecated in favor of `full`, which has the opposite meaning:
+    `thin == true` if and only if `full == false` ([#24279]).
+
   * `isposdef(A::AbstractMatrix, UL::Symbol)` and `isposdef!(A::AbstractMatrix, UL::Symbol)`
     have been deprecated in favor of `isposdef(Hermitian(A, UL))` and `isposdef!(Hermitian(A, UL))`
     respectively ([#22245]).

base/deprecated.jl

@@ -2034,6 +2034,11 @@ end
 @deprecate strwidth textwidth
 @deprecate charwidth textwidth
 
+# TODO: after 0.7, remove thin keyword argument and associated logic from...
+# (1) base/linalg/svd.jl
+# (2) base/linalg/qr.jl
+# (3) base/linalg/lq.jl
+
 @deprecate find(x::Number)            find(!iszero, x)
 @deprecate findnext(A, v, i::Integer) findnext(equalto(v), A, i)
 @deprecate findfirst(A, v)            findfirst(equalto(v), A)

base/linalg/bidiag.jl

@@ -182,11 +182,27 @@ similar(B::Bidiagonal, ::Type{T}, dims::Union{Dims{1},Dims{2}}) where {T} = spze
 
 #Singular values
 svdvals!(M::Bidiagonal{<:BlasReal}) = LAPACK.bdsdc!(M.uplo, 'N', M.dv, M.ev)[1]
-function svdfact!(M::Bidiagonal{<:BlasReal}; thin::Bool=true)
+function svdfact!(M::Bidiagonal{<:BlasReal}; full::Bool = false, thin::Union{Bool,Void} = nothing)
+    # DEPRECATION TODO: remove deprecated thin argument and associated logic after 0.7
+    if thin != nothing
+        Base.depwarn(string("the `thin` keyword argument in `svdfact!(A; thin = $(thin))` has ",
+            "been deprecated in favor of `full`, which has the opposite meaning, ",
+            "e.g. `svdfact!(A; full = $(!thin))`."), :svdfact!)
+        full::Bool = !thin
+    end
     d, e, U, Vt, Q, iQ = LAPACK.bdsdc!(M.uplo, 'I', M.dv, M.ev)
     SVD(U, d, Vt)
 end
-svdfact(M::Bidiagonal; thin::Bool=true) = svdfact!(copy(M),thin=thin)
+function svdfact(M::Bidiagonal; full::Bool = false, thin::Union{Bool,Void} = nothing)
+    # DEPRECATION TODO: remove deprecated thin argument and associated logic after 0.7
+    if thin != nothing
+        Base.depwarn(string("the `thin` keyword argument in `svdfact(A; thin = $(thin))` has ",
+            "been deprecated in favor of `full`, which has the opposite meaning, ",
+            "e.g. `svdfact(A; full = $(!thin))`."), :svdfact)
+        full::Bool = !thin
+    end
+    return svdfact!(copy(M), full = full)
+end
 
 ####################
 # Generic routines #

base/linalg/dense.jl

@@ -1263,7 +1263,7 @@ function pinv(A::StridedMatrix{T}, tol::Real) where T
             return B
         end
     end
-    SVD         = svdfact(A, thin=true)
+    SVD         = svdfact(A, full = false)
     Stype       = eltype(SVD.S)
     Sinv        = zeros(Stype, length(SVD.S))
     index       = SVD.S .> tol*maximum(SVD.S)
@@ -1305,7 +1305,7 @@ julia> nullspace(M)
 function nullspace(A::StridedMatrix{T}) where T
     m, n = size(A)
     (m == 0 || n == 0) && return eye(T, n)
-    SVD = svdfact(A, thin = false)
+    SVD = svdfact(A, full = true)
     indstart = sum(SVD.S .> max(m,n)*maximum(SVD.S)*eps(eltype(SVD.S))) + 1
     return SVD.Vt[indstart:end,:]'
 end

base/linalg/lq.jl

@@ -33,24 +33,31 @@ lqfact(A::StridedMatrix{<:BlasFloat})  = lqfact!(copy(A))
 lqfact(x::Number) = lqfact(fill(x,1,1))
 
 """
-    lq(A; [thin=true]) -> L, Q
+    lq(A; full = false) -> L, Q
 
-Perform an LQ factorization of `A` such that `A = L*Q`. The default is to compute
-a "thin" factorization. The LQ factorization is the QR factorization of `A.'`.
-`L` is not extendedwith zeros if the explicit, square form of `Q`
-is requested via `thin = false`.
+Perform an LQ factorization of `A` such that `A = L*Q`. The default (`full = false`)
+computes a factorization with possibly-rectangular `L` and `Q`, commonly the "thin"
+factorization. The LQ factorization is the QR factorization of `A.'`. If the explicit,
+full/square form of `Q` is requested via `full = true`, `L` is not extended with zeros.
 
 !!! note
     While in QR factorization the "thin" factorization is so named due to yielding
-    either a square or "tall"/"thin" factor `Q`, in LQ factorization the "thin"
-    factorization somewhat confusingly produces either a square or "short"/"wide"
-    factor `Q`. "Thin" factorizations more broadly are also (more descriptively)
-    referred to as "truncated" or "reduced" factorizatons.
+    either a square or "tall"/"thin" rectangular factor `Q`, in LQ factorization the
+    "thin" factorization somewhat confusingly produces either a square or "short"/"wide"
+    rectangular factor `Q`. "Thin" factorizations more broadly are also
+    referred to as "reduced" factorizatons.
 """
-function lq(A::Union{Number,AbstractMatrix}; thin::Bool = true)
+function lq(A::Union{Number,AbstractMatrix}; full::Bool = false, thin::Union{Bool,Void} = nothing)
+    # DEPRECATION TODO: remove deprecated thin argument and associated logic after 0.7
+    if thin != nothing
+        Base.depwarn(string("the `thin` keyword argument in `lq(A; thin = $(thin))` has ",
+            "been deprecated in favor of `full`, which has the opposite meaning, ",
+            "e.g. `lq(A; full = $(!thin))`."), :lq)
+        full::Bool = !thin
+    end
     F = lqfact(A)
     L, Q = F[:L], F[:Q]
-    return L, thin ? Array(Q) : A_mul_B!(Q, eye(eltype(Q), size(Q.factors, 2)))
+    return L, !full ? Array(Q) : A_mul_B!(Q, eye(eltype(Q), size(Q.factors, 2)))
 end
 
 copy(A::LQ) = LQ(copy(A.factors), copy(A.τ))

base/linalg/qr.jl

@@ -265,7 +265,7 @@ The following functions are available for the `QR` objects: [`inv`](@ref), [`siz
 and [`\\`](@ref). When `A` is rectangular, `\\` will return a least squares
 solution and if the solution is not unique, the one with smallest norm is returned.
 
-Multiplication with respect to either thin or full `Q` is allowed, i.e. both `F[:Q]*F[:R]`
+Multiplication with respect to either full/square or non-full/square `Q` is allowed, i.e. both `F[:Q]*F[:R]`
 and `F[:Q]*A` are supported. A `Q` matrix can be converted into a regular matrix with
 [`Matrix`](@ref).
 
@@ -305,24 +305,33 @@ end
 qrfact(x::Number) = qrfact(fill(x,1,1))
 
 """
-    qr(A, pivot=Val(false); thin::Bool=true) -> Q, R, [p]
+    qr(A, pivot=Val(false); full::Bool = false) -> Q, R, [p]
 
 Compute the (pivoted) QR factorization of `A` such that either `A = Q*R` or `A[:,p] = Q*R`.
 Also see [`qrfact`](@ref).
-The default is to compute a thin factorization. Note that `R` is not
-extended with zeros when the full `Q` is requested.
+The default is to compute a "thin" factorization. Note that `R` is not
+extended with zeros when a full/square orthogonal factor `Q` is requested (via `full = true`).
 """
-qr(A::Union{Number, AbstractMatrix}, pivot::Union{Val{false}, Val{true}}=Val(false); thin::Bool=true) =
-    _qr(A, pivot, thin=thin)
-function _qr(A::Union{Number, AbstractMatrix}, ::Val{false}; thin::Bool=true)
+function qr(A::Union{Number,AbstractMatrix}, pivot::Union{Val{false},Val{true}} = Val(false);
+            full::Bool = false, thin::Union{Bool,Void} = nothing)
+    # DEPRECATION TODO: remove deprecated thin argument and associated logic after 0.7
+    if thin != nothing
+        Base.depwarn(string("the `thin` keyword argument in `qr(A, pivot; thin = $(thin))` has ",
+            "been deprecated in favor of `full`, which has the opposite meaning, ",
+            "e.g. `qr(A, pivot; full = $(!thin))`."), :qr)
+        full::Bool = !thin
+    end
+    return _qr(A, pivot, full = full)
+end
+function _qr(A::Union{Number,AbstractMatrix}, ::Val{false}; full::Bool = false)
     F = qrfact(A, Val(false))
     Q, R = getq(F), F[:R]::Matrix{eltype(F)}
-    return (thin ? Array(Q) : A_mul_B!(Q, eye(eltype(Q), size(Q.factors, 1)))), R
+    return (!full ? Array(Q) : A_mul_B!(Q, eye(eltype(Q), size(Q.factors, 1)))), R
 end
-function _qr(A::Union{Number, AbstractMatrix}, ::Val{true}; thin::Bool=true)
+function _qr(A::Union{Number, AbstractMatrix}, ::Val{true}; full::Bool = false)
     F = qrfact(A, Val(true))
     Q, R, p = getq(F), F[:R]::Matrix{eltype(F)}, F[:p]::Vector{BlasInt}
-    return (thin ? Array(Q) : A_mul_B!(Q, eye(eltype(Q), size(Q.factors, 1)))), R, p
+    return (!full ? Array(Q) : A_mul_B!(Q, eye(eltype(Q), size(Q.factors, 1)))), R, p
 end
 
 """

base/linalg/svd.jl

@@ -11,23 +11,30 @@ end
 SVD(U::AbstractArray{T}, S::Vector{Tr}, Vt::AbstractArray{T}) where {T,Tr} = SVD{T,Tr,typeof(U)}(U, S, Vt)
 
 """
-    svdfact!(A, thin::Bool=true) -> SVD
+    svdfact!(A; full::Bool = false) -> SVD
 
 `svdfact!` is the same as [`svdfact`](@ref), but saves space by
 overwriting the input `A`, instead of creating a copy.
 """
-function svdfact!(A::StridedMatrix{T}; thin::Bool=true) where T<:BlasFloat
+function svdfact!(A::StridedMatrix{T}; full::Bool = false, thin::Union{Bool,Void} = nothing) where T<:BlasFloat
+    # DEPRECATION TODO: remove deprecated thin argument and associated logic after 0.7
+    if thin != nothing
+        Base.depwarn(string("the `thin` keyword argument in `svdfact!(A; thin = $(thin))` has ",
+            "been deprecated in favor of `full`, which has the opposite meaning, ",
+            "e.g. `svdfact!(A; full = $(!thin))`."), :svdfact!)
+        full::Bool = !thin
+    end
     m,n = size(A)
     if m == 0 || n == 0
-        u,s,vt = (eye(T, m, thin ? n : m), real(zeros(T,0)), eye(T,n,n))
+        u,s,vt = (eye(T, m, full ? m : n), real(zeros(T,0)), eye(T,n,n))
     else
-        u,s,vt = LAPACK.gesdd!(thin ? 'S' : 'A', A)
+        u,s,vt = LAPACK.gesdd!(full ? 'A' : 'S', A)
     end
     SVD(u,s,vt)
 end
 
 """
-    svdfact(A; thin::Bool=true) -> SVD
+    svdfact(A; full::Bool = false) -> SVD
 
 Compute the singular value decomposition (SVD) of `A` and return an `SVD` object.
 
@@ -36,9 +43,9 @@ Compute the singular value decomposition (SVD) of `A` and return an `SVD` object
 The algorithm produces `Vt` and hence `Vt` is more efficient to extract than `V`.
 The singular values in `S` are sorted in descending order.
 
-If `thin=true` (default), a thin SVD is returned. For a ``M \\times N`` matrix
-`A`, `U` is ``M \\times M`` for a full SVD (`thin=false`) and
-``M \\times \\min(M, N)`` for a thin SVD.
+If `full = false` (default), a "thin" SVD is returned. For a
+``M \\times N`` matrix `A`, `U` is ``M \\times M`` for a "full" SVD (`full = true`) and
+``M \\times \\min(M, N)`` for a "thin" SVD.
 
 # Examples
 ```jldoctest
@@ -59,22 +66,47 @@ julia> F[:U] * Diagonal(F[:S]) * F[:Vt]
  0.0  2.0  0.0  0.0  0.0
 ```
 """
-function svdfact(A::StridedVecOrMat{T}; thin::Bool = true) where T
+function svdfact(A::StridedVecOrMat{T}; full::Bool = false, thin::Union{Bool,Void} = nothing) where T
+    # DEPRECATION TODO: remove deprecated thin argument and associated logic after 0.7
+    if thin != nothing
+        Base.depwarn(string("the `thin` keyword argument in `svdfact(A; thin = $(thin))` has ",
+            "been deprecated in favor of `full`, which has the opposite meaning, ",
+            "e.g. `svdfact(A; full = $(!thin))`."), :svdfact)
+        full::Bool = !thin
+    end
     S = promote_type(Float32, typeof(one(T)/norm(one(T))))
-    svdfact!(copy_oftype(A, S), thin = thin)
+    svdfact!(copy_oftype(A, S), full = full)
+end
+function svdfact(x::Number; full::Bool = false, thin::Union{Bool,Void} = nothing)
+    # DEPRECATION TODO: remove deprecated thin argument and associated logic after 0.7
+    if thin != nothing
+        Base.depwarn(string("the `thin` keyword argument in `svdfact(A; thin = $(thin))` has ",
+            "been deprecated in favor of `full`, which has the opposite meaning, ",
+            "e.g. `svdfact(A; full = $(!thin))`."), :svdfact)
+        full::Bool = !thin
+    end
+    return SVD(x == 0 ? fill(one(x), 1, 1) : fill(x/abs(x), 1, 1), [abs(x)], fill(one(x), 1, 1))
+end
+function svdfact(x::Integer; full::Bool = false, thin::Union{Bool,Void} = nothing)
+    # DEPRECATION TODO: remove deprecated thin argument and associated logic after 0.7
+    if thin != nothing
+        Base.depwarn(string("the `thin` keyword argument in `svdfact(A; thin = $(thin))` has ",
+            "been deprecated in favor of `full`, which has the opposite meaning, ",
+            "e.g. `svdfact(A; full = $(!thin))`."), :svdfact)
+        full::Bool = !thin
+    end
+    return svdfact(float(x), full = full)
 end
-svdfact(x::Number; thin::Bool=true) = SVD(x == 0 ? fill(one(x), 1, 1) : fill(x/abs(x), 1, 1), [abs(x)], fill(one(x), 1, 1))
-svdfact(x::Integer; thin::Bool=true) = svdfact(float(x), thin=thin)
 
 """
-    svd(A; thin::Bool=true) -> U, S, V
+    svd(A; full::Bool = false) -> U, S, V
 
 Computes the SVD of `A`, returning `U`, vector `S`, and `V` such that
 `A == U * Diagonal(S) * V'`. The singular values in `S` are sorted in descending order.
 
-If `thin = true` (default), a thin SVD is returned. For a ``M \\times N`` matrix
-`A`, `U` is ``M \\times M`` for a full SVD (`thin=false`) and
-``M \\times \\min(M, N)`` for a thin SVD.
+If `full = false` (default), a "thin" SVD is returned. For a ``M \\times N`` matrix
+`A`, `U` is ``M \\times M`` for a "full" SVD (`full = true`) and
+``M \\times \\min(M, N)`` for a "thin" SVD.
 
 `svd` is a wrapper around [`svdfact`](@ref), extracting all parts
 of the `SVD` factorization to a tuple. Direct use of `svdfact` is therefore more
@@ -99,11 +131,27 @@ julia> U * Diagonal(S) * V'
  0.0  2.0  0.0  0.0  0.0
 ```
 """
-function svd(A::AbstractArray; thin::Bool=true)
-    F = svdfact(A, thin=thin)
+function svd(A::AbstractArray; full::Bool = false, thin::Union{Bool,Void} = nothing)
+    # DEPRECATION TODO: remove deprecated thin argument and associated logic after 0.7
+    if thin != nothing
+        Base.depwarn(string("the `thin` keyword argument in `svd(A; thin = $(thin))` has ",
+            "been deprecated in favor of `full`, which has the opposite meaning, ",
+            "e.g `svd(A; full = $(!thin))`."), :svd)
+        full::Bool = !thin
+    end
+    F = svdfact(A, full = full)
     F.U, F.S, F.Vt'
 end
-svd(x::Number; thin::Bool=true) = first.(svd(fill(x, 1, 1)))
+function svd(x::Number; full::Bool = false, thin::Union{Bool,Void} = nothing)
+    # DEPRECATION TODO: remove deprecated thin argument and associated logic after 0.7
+    if thin != nothing
+        Base.depwarn(string("the `thin` keyword argument in `svd(A; thin = $(thin))` has ",
+            "been deprecated in favor of `full`, which has the opposite meaning, ",
+            "e.g. `svd(A; full = $(!thin))`."), :svd)
+        full::Bool = !thin
+    end
+    return first.(svd(fill(x, 1, 1)))
+end
 
 function getindex(F::SVD, d::Symbol)
     if d == :U