Change QR/LQ decompositions to use positive = true by default (#170)

* Systematically set `positive = true`

* update changelog

---------

Co-authored-by: Lukas Devos <ldevos98@gmail.com>

Author: leburgel

docs/src/changelog.md

@@ -30,6 +30,8 @@ When releasing a new version, move the "Unreleased" changes to a new version sec
 
 ### Fixed
 
+- QR and LQ decompositions were supposed to default to `positive = true` ([#170](https://github.com/QuantumKitHub/MatrixAlgebraKit.jl/pull/170)).
+
 ## [0.6.4](https://github.com/QuantumKitHub/MatrixAlgebraKit.jl/compare/v0.6.3...v0.6.4) - 2026-01-29
 
 ### Added

ext/MatrixAlgebraKitGenericLinearAlgebraExt.jl

@@ -78,7 +78,7 @@ function MatrixAlgebraKit.qr_null!(A::AbstractMatrix, N, alg::GLA_HouseholderQR)
     return _gla_householder_qr_null!(A, N; alg.kwargs...)
 end
 
-function _gla_householder_qr!(A::AbstractMatrix, Q, R; positive = false, blocksize = 1, pivoted = false)
+function _gla_householder_qr!(A::AbstractMatrix, Q, R; positive = true, blocksize = 1, pivoted = false)
     pivoted && throw(ArgumentError("Only pivoted = false implemented for GLA_HouseholderQR."))
     (blocksize == 1) || throw(ArgumentError("Only blocksize = 1 implemented for GLA_HouseholderQR."))
 
@@ -117,7 +117,7 @@ end
 
 function _gla_householder_qr_null!(
         A::AbstractMatrix, N::AbstractMatrix;
-        positive = false, blocksize = 1, pivoted = false
+        positive = true, blocksize = 1, pivoted = false
     )
     pivoted && throw(ArgumentError("Only pivoted = false implemented for GLA_HouseholderQR."))
     (blocksize == 1) || throw(ArgumentError("Only blocksize = 1 implemented for GLA_HouseholderQR."))

src/implementations/lq.jl

@@ -145,7 +145,7 @@ end
 # ------------
 function _lapack_lq!(
         A::AbstractMatrix, L::AbstractMatrix, Q::AbstractMatrix;
-        positive = false, pivoted = false,
+        positive = true, pivoted = false,
         blocksize = ((pivoted || A === Q) ? 1 : YALAPACK.default_qr_blocksize(A))
     )
     m, n = size(A)
@@ -203,7 +203,7 @@ end
 
 function _lapack_lq_null!(
         A::AbstractMatrix, Nᴴ::AbstractMatrix;
-        positive = false, pivoted = false, blocksize = YALAPACK.default_qr_blocksize(A)
+        positive = true, pivoted = false, blocksize = YALAPACK.default_qr_blocksize(A)
     )
     m, n = size(A)
     minmn = min(m, n)
@@ -253,7 +253,7 @@ end
 # Diagonal logic
 # --------------
 function _diagonal_lq!(
-        A::AbstractMatrix, L::AbstractMatrix, Q::AbstractMatrix; positive::Bool = false
+        A::AbstractMatrix, L::AbstractMatrix, Q::AbstractMatrix; positive::Bool = true
     )
     # note: Ad and Qd might share memory here so order of operations is important
     Ad = diagview(A)
@@ -269,7 +269,7 @@ function _diagonal_lq!(
     return L, Q
 end
 
-_diagonal_lq_null!(A::AbstractMatrix, N; positive::Bool = false) = N
+_diagonal_lq_null!(A::AbstractMatrix, N; positive::Bool = true) = N
 
 # Native logic
 # -------------

src/implementations/qr.jl

@@ -129,7 +129,7 @@ end
 # ------------
 function _lapack_qr!(
         A::AbstractMatrix, Q::AbstractMatrix, R::AbstractMatrix;
-        positive = false, pivoted = false,
+        positive = true, pivoted = false,
         blocksize = ((pivoted || A === Q) ? 1 : YALAPACK.default_qr_blocksize(A))
     )
     m, n = size(A)
@@ -195,7 +195,7 @@ end
 
 function _lapack_qr_null!(
         A::AbstractMatrix, N::AbstractMatrix;
-        positive = false, pivoted = false, blocksize = YALAPACK.default_qr_blocksize(A)
+        positive = true, pivoted = false, blocksize = YALAPACK.default_qr_blocksize(A)
     )
     m, n = size(A)
     minmn = min(m, n)
@@ -215,7 +215,7 @@ end
 # Diagonal logic
 # --------------
 function _diagonal_qr!(
-        A::AbstractMatrix, Q::AbstractMatrix, R::AbstractMatrix; positive::Bool = false
+        A::AbstractMatrix, Q::AbstractMatrix, R::AbstractMatrix; positive::Bool = true
     )
     # note: Ad and Qd might share memory here so order of operations is important
     Ad = diagview(A)
@@ -231,7 +231,7 @@ function _diagonal_qr!(
     return Q, R
 end
 
-_diagonal_qr_null!(A::AbstractMatrix, N; positive::Bool = false) = N
+_diagonal_qr_null!(A::AbstractMatrix, N; positive::Bool = true) = N
 
 # GPU logic
 # --------------
@@ -269,7 +269,7 @@ function _gpu_unmqr!(
 end
 
 function _gpu_qr!(
-        A::AbstractMatrix, Q::AbstractMatrix, R::AbstractMatrix; positive = false, blocksize = 1, pivoted = false
+        A::AbstractMatrix, Q::AbstractMatrix, R::AbstractMatrix; positive = true, blocksize = 1, pivoted = false
     )
     blocksize > 1 &&
         throw(ArgumentError("CUSOLVER/ROCSOLVER does not provide a blocked implementation for a QR decomposition"))
@@ -310,7 +310,7 @@ function _gpu_qr!(
 end
 
 function _gpu_qr_null!(
-        A::AbstractMatrix, N::AbstractMatrix; positive = false, blocksize = 1, pivoted = false
+        A::AbstractMatrix, N::AbstractMatrix; positive = true, blocksize = 1, pivoted = false
     )
     blocksize > 1 &&
         throw(ArgumentError("CUSOLVER/ROCSOLVER does not provide a blocked implementation for a QR decomposition"))

src/interface/decompositions.jl

@@ -28,34 +28,34 @@ by construction.
 @algdef Native_HouseholderLQ
 
 """
-    LAPACK_HouseholderQR(; blocksize, positive = false, pivoted = false)
+    LAPACK_HouseholderQR(; blocksize, positive = true, pivoted = false)
 
 Algorithm type to denote the standard LAPACK algorithm for computing the QR decomposition of
 a matrix using Householder reflectors. The specific LAPACK function can be controlled using
 the keyword arugments, i.e.  `?geqrt` will be chosen if `blocksize > 1`. With
 `blocksize == 1`, `?geqrf` will be chosen if `pivoted == false` and `?geqp3` will be chosen
-if `pivoted == true`. The keyword `positive = true` can be used to ensure that the diagonal
+if `pivoted == true`. The keyword `positive = true` is used to ensure that the diagonal
 elements of `R` are non-negative.
 """
 @algdef LAPACK_HouseholderQR
 
 """
-    LAPACK_HouseholderLQ(; blocksize, positive = false)
+    LAPACK_HouseholderLQ(; blocksize, positive = true)
 
 Algorithm type to denote the standard LAPACK algorithm for computing the LQ decomposition of
 a matrix using Householder reflectors. The specific LAPACK function can be controlled using
 the keyword arugments, i.e. `?gelqt` will be chosen if `blocksize > 1` or `?gelqf` will be
-chosen if `blocksize == 1`. The keyword `positive = true` can be used to ensure that the diagonal
-elements of `L` are non-negative.
+chosen if `blocksize == 1`. The keyword `positive = true` is used to ensure that the
+diagonal elements of `L` are non-negative.
 """
 @algdef LAPACK_HouseholderLQ
 
 """
-    GLA_HouseholderQR(; positive = false)
+    GLA_HouseholderQR(; positive = true)
 
 Algorithm type to denote the GenericLinearAlgebra.jl implementation for computing the QR decomposition
 of a matrix using Householder reflectors. Currently, only `blocksize = 1` and `pivoted == false`
-are supported. The keyword `positive = true` can be used to ensure that the diagonal elements
+are supported. The keyword `positive = true` is used to ensure that the diagonal elements
 of `R` are non-negative.
 """
 @algdef GLA_HouseholderQR
@@ -230,7 +230,7 @@ end
 # CUSOLVER ALGORITHMS
 # =========================
 """
-    CUSOLVER_HouseholderQR(; positive = false)
+    CUSOLVER_HouseholderQR(; positive = true)
 
 Algorithm type to denote the standard CUSOLVER algorithm for computing the QR decomposition of
 a matrix using Householder reflectors. The keyword `positive = true` can be used to ensure that
@@ -318,10 +318,10 @@ const CUSOLVER_SVDAlgorithm = Union{
 # ROCSOLVER ALGORITHMS
 # =========================
 """
-    ROCSOLVER_HouseholderQR(; positive = false)
+    ROCSOLVER_HouseholderQR(; positive = true)
 
 Algorithm type to denote the standard ROCSOLVER algorithm for computing the QR decomposition of
-a matrix using Householder reflectors. The keyword `positive=true` can be used to ensure that
+a matrix using Householder reflectors. The keyword `positive = true` is used to ensure that
 the diagonal elements of `R` are non-negative.
 """
 @algdef ROCSOLVER_HouseholderQR