From ebc61cd15278e270988341664856b873ba07c3a3 Mon Sep 17 00:00:00 2001
From: zoziha13 <1325686572@qq.com>
Date: Sun, 1 Aug 2021 21:52:58 +0800
Subject: [PATCH 1/5] Update eye function.

---
 doc/specs/stdlib_linalg.md       | 19 ++++++++++++----
 src/stdlib_linalg.fypp           | 37 ++++++++++++++++++++------------
 src/tests/Makefile.manual        |  1 +
 src/tests/linalg/Makefile.manual |  4 ++++
 src/tests/linalg/test_linalg.f90 |  7 ++++++
 5 files changed, 50 insertions(+), 18 deletions(-)
 create mode 100644 src/tests/linalg/Makefile.manual

diff --git a/doc/specs/stdlib_linalg.md b/doc/specs/stdlib_linalg.md
index cab16279c..b1a42e067 100644
--- a/doc/specs/stdlib_linalg.md
+++ b/doc/specs/stdlib_linalg.md
@@ -101,21 +101,29 @@ end program demo_diag5
 
 Experimental
 
+### Class
+
+Pure function.
+
 ### Description
 
-Construct the identity matrix
+Construct the identity matrix.
 
 ### Syntax
 
-`I = [[stdlib_linalg(module):eye(function)]](n)`
+`I = [[stdlib_linalg(module):eye(function)]](dim1 [, dim2])`
 
 ### Arguments
 
-`n`: Shall be a scalar of default type `integer`. 
+`dim1`: Shall be a scalar of default type `integer`.
+This is an `intent(in)` argument. 
+
+`dim2`: Shall be a scalar of default type `integer`.
+This is an `intent(in)` and `optional` argument. 
 
 ### Return value
 
-Returns the identity matrix, i.e. a square matrix with ones on the main diagonal and zeros elsewhere. The return value is of type `integer(int8)`.
+Returns the identity matrix, i.e. a square matrix with ones on the main diagonal and zeros elsewhere. The return value is of type `integer`.
 
 ### Example
 
@@ -124,7 +132,10 @@ program demo_eye1
     use stdlib_linalg, only: eye
     implicit none
     real :: a(3,3)
+    real :: b(3,4)
     A = eye(3)
+    A = eye(3,3)
+    B = eye(3,4)
 end program demo_eye1
 ```
 
diff --git a/src/stdlib_linalg.fypp b/src/stdlib_linalg.fypp
index 5e0388c0b..ed4fd6fe8 100644
--- a/src/stdlib_linalg.fypp
+++ b/src/stdlib_linalg.fypp
@@ -82,20 +82,28 @@ module stdlib_linalg
 
 contains
 
-    function eye(n) result(res)
-      !! version: experimental
-      !!
-      !! Constructs the identity matrix
-      !! ([Specification](../page/specs/stdlib_linalg.html#description_1))
-      integer, intent(in) :: n
-      integer(int8) :: res(n, n)
-      integer :: i
-      res = 0
-      do i = 1, n
-         res(i, i) = 1
-      end do
-    end function eye
+    !> Version: experimental
+    !>
+    !> Constructs the identity matrix.
+    !> ([Specification](../page/specs/stdlib_linalg.html#eye-construct-the-identity-matrix))
+    pure function eye(dim1, dim2) result(result)
+
+        integer, intent(in) :: dim1
+        integer, intent(in), optional :: dim2
+        integer, allocatable :: result(:, :)
+
+        integer :: dim2_
+        integer :: i
 
+        dim2_ = merge(dim2, dim1, present(dim2))
+        allocate(result(dim1, dim2_))
+        
+        result = 0
+        do i = 1, min(dim1, dim2_)
+            result(i, i) = 1
+        end do
+
+    end function eye
 
     #:for k1, t1 in RCI_KINDS_TYPES
       function trace_${t1[0]}$${k1}$(A) result(res)
@@ -108,4 +116,5 @@ contains
         end do
       end function trace_${t1[0]}$${k1}$
     #:endfor
-end module
+
+end module stdlib_linalg
diff --git a/src/tests/Makefile.manual b/src/tests/Makefile.manual
index 7ab184016..c29170e24 100644
--- a/src/tests/Makefile.manual
+++ b/src/tests/Makefile.manual
@@ -11,3 +11,4 @@ all test clean:
 	$(MAKE) -f Makefile.manual --directory=stats $@
 	$(MAKE) -f Makefile.manual --directory=string $@
 	$(MAKE) -f Makefile.manual --directory=math $@
+	$(MAKE) -f Makefile.manual --directory=linalg $@
diff --git a/src/tests/linalg/Makefile.manual b/src/tests/linalg/Makefile.manual
new file mode 100644
index 000000000..a95f600c7
--- /dev/null
+++ b/src/tests/linalg/Makefile.manual
@@ -0,0 +1,4 @@
+PROGS_SRC = test_linalg.f90
+
+
+include ../Makefile.manual.test.mk
diff --git a/src/tests/linalg/test_linalg.f90 b/src/tests/linalg/test_linalg.f90
index cc8d0db68..599dbd35a 100644
--- a/src/tests/linalg/test_linalg.f90
+++ b/src/tests/linalg/test_linalg.f90
@@ -81,6 +81,13 @@ subroutine test_eye
     integer :: i
     write(*,*) "test_eye"
 
+    call check(all(eye(3,3) == diag([(1,i=1,3)])), &
+               msg="all(eye(3,3) == diag([(1,i=1,3)])) failed.",warn=warn)
+    
+    rye = eye(3,4)
+    call check(sum(rye(:,1:3) - diag([(1.0_sp,i=1,3)])) < sptol, &
+               msg="sum(rye(:,1:3) - diag([(1.0_sp,i=1,3)])) < sptol", warn=warn)
+
     call check(all(eye(5) == diag([(1,i=1,5)])), &
           msg="all(eye(5) == diag([(1,i=1,5)] failed.",warn=warn)
     

From 8745725a6e9df846d961e7f5aa37cfd0a23e845e Mon Sep 17 00:00:00 2001
From: zoziha13 <1325686572@qq.com>
Date: Tue, 3 Aug 2021 16:59:46 +0800
Subject: [PATCH 2/5] Improve `eye` function help docs.

---
 doc/specs/stdlib_linalg.md | 32 +++++++++++++++++++++++++++-----
 1 file changed, 27 insertions(+), 5 deletions(-)

diff --git a/doc/specs/stdlib_linalg.md b/doc/specs/stdlib_linalg.md
index b1a42e067..800defc3c 100644
--- a/doc/specs/stdlib_linalg.md
+++ b/doc/specs/stdlib_linalg.md
@@ -121,9 +121,26 @@ This is an `intent(in)` argument.
 `dim2`: Shall be a scalar of default type `integer`.
 This is an `intent(in)` and `optional` argument. 
 
+#### Note
+
+Because of `huge(integer :: i) = 2147483647`, the dimensional maximum length of array created by the `eye` function is `2147483647`. 
+
 ### Return value
 
-Returns the identity matrix, i.e. a square matrix with ones on the main diagonal and zeros elsewhere. The return value is of type `integer`.
+Return the identity matrix, i.e. a square matrix with ones on the main diagonal and zeros elsewhere. The return value is of type `integer`.
+
+#### Warning
+
+If the array that receives the return value of the `eye` function is of `real/complex` type, conversion from `integer` type to `real/complex` type will occur.  
+
+Just as `Fortran` is a strongly typed statically compiled language, be careful with the following statements:
+```fortran
+real :: A(:,:)
+!> Be careful
+A = eye(2,2)/2     !! A == 0.0
+!> Recommend
+A = eye(2,2)/2.0   !! A == diag([0.5, 0.5])
+```
 
 ### Example
 
@@ -131,11 +148,16 @@ Returns the identity matrix, i.e. a square matrix with ones on the main diagonal
 program demo_eye1
     use stdlib_linalg, only: eye
     implicit none
+    integer :: i(2,2)
     real :: a(3,3)
-    real :: b(3,4)
-    A = eye(3)
-    A = eye(3,3)
-    B = eye(3,4)
+    real :: b(2,3)  !! Matrix is non-square.
+    complex :: c(2,2)
+    I = eye(2)              !! [1,0; 0,1]
+    A = eye(3)              !! [1.0,0.0,0.0; 0.0,1.0,0.0; 0.0,0.0,1.0]
+    A = eye(3,3)            !! [1.0,0.0,0.0; 0.0,1.0,0.0; 0.0,0.0,1.0]
+    B = eye(2,3)            !! [1.0,0.0,0.0; 0.0,1.0,0.0]
+    C = eye(2,2)            !! [(1.0,0.0),(0.0,0.0); (0.0,0.0),(1.0,0.0)]
+    C = (1.0,1.0)*eye(2,2)  !! [(1.0,1.0),(0.0,0.0); (0.0,0.0),(1.0,1.0)]
 end program demo_eye1
 ```
 

From c2f0abf9f35157887b850b7135d179336b83b2b9 Mon Sep 17 00:00:00 2001
From: zoziha13 <1325686572@qq.com>
Date: Thu, 5 Aug 2021 11:33:38 +0800
Subject: [PATCH 3/5] Update `eye` func: 1. `merge` -> `optval` inside.

---
 src/Makefile.manual    | 3 ++-
 src/stdlib_linalg.fypp | 3 ++-
 2 files changed, 4 insertions(+), 2 deletions(-)

diff --git a/src/Makefile.manual b/src/Makefile.manual
index a12f81255..ecfc92c7a 100644
--- a/src/Makefile.manual
+++ b/src/Makefile.manual
@@ -149,7 +149,8 @@ stdlib_string_type.o: stdlib_ascii.o \
 stdlib_strings.o: stdlib_ascii.o \
     stdlib_string_type.o \
 	stdlib_optval.o
-stdlib_math.o: stdlib_kinds.o
+stdlib_math.o: stdlib_kinds.o \
+    stdlib_optval.o
 stdlib_math_linspace.o: \
 	stdlib_math.o
 stdlib_math_logspace.o: \
diff --git a/src/stdlib_linalg.fypp b/src/stdlib_linalg.fypp
index ed4fd6fe8..4a687fb0d 100644
--- a/src/stdlib_linalg.fypp
+++ b/src/stdlib_linalg.fypp
@@ -5,6 +5,7 @@ module stdlib_linalg
   !! ([Specification](../page/specs/stdlib_linalg.html))
   use stdlib_kinds, only: sp, dp, qp, &
     int8, int16, int32, int64
+  use stdlib_optval, only: optval
   implicit none
   private
 
@@ -95,7 +96,7 @@ contains
         integer :: dim2_
         integer :: i
 
-        dim2_ = merge(dim2, dim1, present(dim2))
+        dim2_ = optval(dim2, dim1)
         allocate(result(dim1, dim2_))
         
         result = 0

From c20f69f059126d17d8d731f024d83ef3c2392d42 Mon Sep 17 00:00:00 2001
From: zoziha13 <1325686572@qq.com>
Date: Fri, 6 Aug 2021 13:12:29 +0800
Subject: [PATCH 4/5] Improve `eye` func test and doc.

---
 doc/specs/stdlib_linalg.md       | 10 ++--------
 src/tests/linalg/test_linalg.f90 |  8 ++++----
 2 files changed, 6 insertions(+), 12 deletions(-)

diff --git a/doc/specs/stdlib_linalg.md b/doc/specs/stdlib_linalg.md
index 800defc3c..2fc45dfb2 100644
--- a/doc/specs/stdlib_linalg.md
+++ b/doc/specs/stdlib_linalg.md
@@ -121,19 +121,13 @@ This is an `intent(in)` argument.
 `dim2`: Shall be a scalar of default type `integer`.
 This is an `intent(in)` and `optional` argument. 
 
-#### Note
-
-Because of `huge(integer :: i) = 2147483647`, the dimensional maximum length of array created by the `eye` function is `2147483647`. 
-
 ### Return value
 
-Return the identity matrix, i.e. a square matrix with ones on the main diagonal and zeros elsewhere. The return value is of type `integer`.
+Return the identity matrix, i.e. a matrix with ones on the main diagonal and zeros elsewhere. The return value is of type `integer`.
 
 #### Warning
 
-If the array that receives the return value of the `eye` function is of `real/complex` type, conversion from `integer` type to `real/complex` type will occur.  
-
-Just as `Fortran` is a strongly typed statically compiled language, be careful with the following statements:
+Since the result of `eye` is of `integer` type, one should be careful about using it in arithmetic expressions. For example:
 ```fortran
 real :: A(:,:)
 !> Be careful
diff --git a/src/tests/linalg/test_linalg.f90 b/src/tests/linalg/test_linalg.f90
index 599dbd35a..7583f0585 100644
--- a/src/tests/linalg/test_linalg.f90
+++ b/src/tests/linalg/test_linalg.f90
@@ -85,15 +85,15 @@ subroutine test_eye
                msg="all(eye(3,3) == diag([(1,i=1,3)])) failed.",warn=warn)
     
     rye = eye(3,4)
-    call check(sum(rye(:,1:3) - diag([(1.0_sp,i=1,3)])) < sptol, &
-               msg="sum(rye(:,1:3) - diag([(1.0_sp,i=1,3)])) < sptol", warn=warn)
+    call check(sum(abs(rye(:,1:3) - diag([(1.0_sp,i=1,3)]))) < sptol, &
+          msg="sum(abs(rye(:,1:3) - diag([(1.0_sp,i=1,3)]))) < sptol failed", warn=warn)
 
     call check(all(eye(5) == diag([(1,i=1,5)])), &
           msg="all(eye(5) == diag([(1,i=1,5)] failed.",warn=warn)
     
     rye = eye(6)
-    call check(sum(rye - diag([(1.0_sp,i=1,6)])) < sptol, &
-          msg="sum(rye - diag([(1.0_sp,i=1,6)])) < sptol failed.",warn=warn)
+    call check(sum(abs(rye - diag([(1.0_sp,i=1,6)]))) < sptol, &
+          msg="sum(abs(rye - diag([(1.0_sp,i=1,6)]))) < sptol failed.",warn=warn)
 
     cye = eye(7)
     call check(abs(trace(cye) - cmplx(7.0_sp,0.0_sp,kind=sp)) < sptol, &

From c326353f0410b14aec100f6ba6a8586bd274193e Mon Sep 17 00:00:00 2001
From: zoziha13 <1325686572@qq.com>
Date: Sun, 22 Aug 2021 00:43:39 +0800
Subject: [PATCH 5/5] Update `eye` func: `integer(int8)`

---
 doc/specs/stdlib_linalg.md | 5 +++--
 src/stdlib_linalg.fypp     | 6 +++---
 2 files changed, 6 insertions(+), 5 deletions(-)

diff --git a/doc/specs/stdlib_linalg.md b/doc/specs/stdlib_linalg.md
index 2fc45dfb2..7ca3b9198 100644
--- a/doc/specs/stdlib_linalg.md
+++ b/doc/specs/stdlib_linalg.md
@@ -123,11 +123,12 @@ This is an `intent(in)` and `optional` argument.
 
 ### Return value
 
-Return the identity matrix, i.e. a matrix with ones on the main diagonal and zeros elsewhere. The return value is of type `integer`.
+Return the identity matrix, i.e. a matrix with ones on the main diagonal and zeros elsewhere. The return value is of type `integer(int8)`.
+The use of `int8` was suggested to save storage.
 
 #### Warning
 
-Since the result of `eye` is of `integer` type, one should be careful about using it in arithmetic expressions. For example:
+Since the result of `eye` is of `integer(int8)` type, one should be careful about using it in arithmetic expressions. For example:
 ```fortran
 real :: A(:,:)
 !> Be careful
diff --git a/src/stdlib_linalg.fypp b/src/stdlib_linalg.fypp
index 4a687fb0d..3faaeb9af 100644
--- a/src/stdlib_linalg.fypp
+++ b/src/stdlib_linalg.fypp
@@ -91,7 +91,7 @@ contains
 
         integer, intent(in) :: dim1
         integer, intent(in), optional :: dim2
-        integer, allocatable :: result(:, :)
+        integer(int8), allocatable :: result(:, :)
 
         integer :: dim2_
         integer :: i
@@ -99,9 +99,9 @@ contains
         dim2_ = optval(dim2, dim1)
         allocate(result(dim1, dim2_))
         
-        result = 0
+        result = 0_int8
         do i = 1, min(dim1, dim2_)
-            result(i, i) = 1
+            result(i, i) = 1_int8
         end do
 
     end function eye