From 99d11d81a5efa5f0b90d9bd1ac99877b072ca04c Mon Sep 17 00:00:00 2001
From: WalterMadelim <143272683+WalterMadelim@users.noreply.github.com>
Date: Sat, 10 May 2025 15:50:26 +0800
Subject: [PATCH 1/4] Update the docstring of ldiv!

The existing two examples in docstring reads well respectively, but not in conjunction: In the above example it mutates Y, whereas in the lower example it mutates X. Hope that after revising it looks more clean and intelligible.
---
 src/LinearAlgebra.jl | 20 ++++++++------------
 1 file changed, 8 insertions(+), 12 deletions(-)

diff --git a/src/LinearAlgebra.jl b/src/LinearAlgebra.jl
index 7be8c25a..44740a8c 100644
--- a/src/LinearAlgebra.jl
+++ b/src/LinearAlgebra.jl
@@ -392,15 +392,13 @@ control over the factorization of `A`.
 
 # Examples
 ```jldoctest
-julia> A = [1 2.2 4; 3.1 0.2 3; 4 1 2];
+julia> A, B = [1 2.2 4; 3.1 0.2 3; 4 1 2], [1, 2.5, 3];
 
-julia> X = [1; 2.5; 3];
+julia> Y = copy(B);
 
-julia> Y = zero(X);
+julia> ldiv!(Y, qr(A), B); # also try qr!(A) for the 2nd arg
 
-julia> ldiv!(Y, qr(A), X);
-
-julia> Y ≈ A\\X
+julia> Y ≈ A \ B
 true
 ```
 """
@@ -424,15 +422,13 @@ control over the factorization of `A`.
 
 # Examples
 ```jldoctest
-julia> A = [1 2.2 4; 3.1 0.2 3; 4 1 2];
-
-julia> X = [1; 2.5; 3];
+julia> A, B = [1 2.2 4; 3.1 0.2 3; 4 1 2], [1, 2.5, 3];
 
-julia> Y = copy(X);
+julia> B0 = copy(B);
 
-julia> ldiv!(qr(A), X);
+julia> ldiv!(lu(A), B); # also try lu!(A) for the 1st arg
 
-julia> X ≈ A\\Y
+julia> B ≈ A \ B0
 true
 ```
 """

From 97ee7d233d253d04abb8b0cfe368175f5a3cfe33 Mon Sep 17 00:00:00 2001
From: WalterMadelim <143272683+WalterMadelim@users.noreply.github.com>
Date: Sat, 10 May 2025 16:02:40 +0800
Subject: [PATCH 2/4] Update the docstring of ldiv!

---
 src/LinearAlgebra.jl | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/src/LinearAlgebra.jl b/src/LinearAlgebra.jl
index 44740a8c..441ab85f 100644
--- a/src/LinearAlgebra.jl
+++ b/src/LinearAlgebra.jl
@@ -398,7 +398,7 @@ julia> Y = copy(B);
 
 julia> ldiv!(Y, qr(A), B); # also try qr!(A) for the 2nd arg
 
-julia> Y ≈ A \ B
+julia> Y ≈ A \\ B
 true
 ```
 """
@@ -428,7 +428,7 @@ julia> B0 = copy(B);
 
 julia> ldiv!(lu(A), B); # also try lu!(A) for the 1st arg
 
-julia> B ≈ A \ B0
+julia> B ≈ A \\ B0
 true
 ```
 """

From d947bcdc37df973ea0061ce24f022ad42d843c6d Mon Sep 17 00:00:00 2001
From: WalterMadelim <143272683+WalterMadelim@users.noreply.github.com>
Date: Sat, 10 May 2025 18:55:05 +0800
Subject: [PATCH 3/4] Update docstring for ldiv!

---
 src/LinearAlgebra.jl | 12 ++++++++----
 1 file changed, 8 insertions(+), 4 deletions(-)

diff --git a/src/LinearAlgebra.jl b/src/LinearAlgebra.jl
index 441ab85f..4001f277 100644
--- a/src/LinearAlgebra.jl
+++ b/src/LinearAlgebra.jl
@@ -392,11 +392,13 @@ control over the factorization of `A`.
 
 # Examples
 ```jldoctest
-julia> A, B = [1 2.2 4; 3.1 0.2 3; 4 1 2], [1, 2.5, 3];
+julia> A = [1 2.2 4; 3.1 0.2 3; 4 1 2];
+
+julia> B = [1, 2.5, 3];
 
 julia> Y = copy(B);
 
-julia> ldiv!(Y, qr(A), B); # also try qr!(A) for the 2nd arg
+julia> ldiv!(Y, qr(A), B); # you may also try qr!(A) to further reduce allocation
 
 julia> Y ≈ A \\ B
 true
@@ -422,11 +424,13 @@ control over the factorization of `A`.
 
 # Examples
 ```jldoctest
-julia> A, B = [1 2.2 4; 3.1 0.2 3; 4 1 2], [1, 2.5, 3];
+julia> A = [1 2.2 4; 3.1 0.2 3; 4 1 2];
+
+julia> B = [1, 2.5, 3];
 
 julia> B0 = copy(B);
 
-julia> ldiv!(lu(A), B); # also try lu!(A) for the 1st arg
+julia> ldiv!(lu(A), B); # you may also try lu!(A) to further reduce allocation
 
 julia> B ≈ A \\ B0
 true

From 0df47a53c7f02887d075b3fdd30bd8e8f42905ad Mon Sep 17 00:00:00 2001
From: WalterMadelim <143272683+WalterMadelim@users.noreply.github.com>
Date: Sat, 10 May 2025 19:26:07 +0800
Subject: [PATCH 4/4] use similar

---
 src/LinearAlgebra.jl | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/src/LinearAlgebra.jl b/src/LinearAlgebra.jl
index 4001f277..bfeaa7e3 100644
--- a/src/LinearAlgebra.jl
+++ b/src/LinearAlgebra.jl
@@ -396,7 +396,7 @@ julia> A = [1 2.2 4; 3.1 0.2 3; 4 1 2];
 
 julia> B = [1, 2.5, 3];
 
-julia> Y = copy(B);
+julia> Y = similar(B); # use similar since there is no need to read from it
 
 julia> ldiv!(Y, qr(A), B); # you may also try qr!(A) to further reduce allocation
 
@@ -428,7 +428,7 @@ julia> A = [1 2.2 4; 3.1 0.2 3; 4 1 2];
 
 julia> B = [1, 2.5, 3];
 
-julia> B0 = copy(B);
+julia> B0 = copy(B); # a backup copy to facilitate testing
 
 julia> ldiv!(lu(A), B); # you may also try lu!(A) to further reduce allocation