From 7e3b0a9cec7f8ef12292cecfe1829350daf428ee Mon Sep 17 00:00:00 2001
From: Jeremie Vandenplas <jeremie.vandenplas@gmail.com>
Date: Sat, 2 May 2026 20:50:49 +0200
Subject: [PATCH 1/8] Low-level interfaces for COO

---
 src/sparse/stdlib_sparse_spmv.fypp     | 12 ++++++++++++
 src/sparse/stdlib_sparse_spmv_coo.fypp | 19 ++++++++++++++++---
 2 files changed, 28 insertions(+), 3 deletions(-)

diff --git a/src/sparse/stdlib_sparse_spmv.fypp b/src/sparse/stdlib_sparse_spmv.fypp
index 5524ef7c0..1445a7dc7 100644
--- a/src/sparse/stdlib_sparse_spmv.fypp
+++ b/src/sparse/stdlib_sparse_spmv.fypp
@@ -32,6 +32,18 @@ module stdlib_sparse_spmv
             character(1), intent(in), optional :: op
         end subroutine
 
+        module subroutine spmv_coo_sub_${rank}$d_${s1}$(data, index, storage, nnz, vec_x,vec_y,alpha,beta,op)
+            ${t1}$, intent(in) :: data(:) 
+            integer(ilp), intent(in) :: index(:,:)
+            integer, intent(in) :: storage
+            integer(ilp), intent(in) :: nnz
+            ${t1}$, intent(in)    :: vec_x${ranksuffix(rank)}$
+            ${t1}$, intent(inout) :: vec_y${ranksuffix(rank)}$
+            ${t1}$, intent(in), optional :: alpha
+            ${t1}$, intent(in), optional :: beta
+            character(1), intent(in), optional :: op
+        end subroutine
+ 
         module subroutine spmv_csr_${rank}$d_${s1}$(matrix,vec_x,vec_y,alpha,beta,op)
             type(CSR_${s1}$_type), intent(in) :: matrix
             ${t1}$, intent(in)    :: vec_x${ranksuffix(rank)}$
diff --git a/src/sparse/stdlib_sparse_spmv_coo.fypp b/src/sparse/stdlib_sparse_spmv_coo.fypp
index 7aba6e9d8..0d009299b 100644
--- a/src/sparse/stdlib_sparse_spmv_coo.fypp
+++ b/src/sparse/stdlib_sparse_spmv_coo.fypp
@@ -20,6 +20,21 @@ contains
         ${t1}$, intent(in), optional :: alpha
         ${t1}$, intent(in), optional :: beta
         character(1), intent(in), optional :: op
+
+        call spmv_coo_sub_${rank}$d_${s1}$(matrix%data, matrix%index, matrix%storage, matrix%nnz, vec_x,vec_y,alpha,beta,op)
+
+    end subroutine
+
+    module subroutine spmv_coo_sub_${rank}$d_${s1}$(data, index, storage, nnz, vec_x,vec_y,alpha,beta,op)
+        ${t1}$, intent(in) :: data(:) 
+        integer(ilp), intent(in) :: index(:,:) !! Matrix coordinates index(2,nnz)
+        integer, intent(in) :: storage !! storage
+        integer(ilp), intent(in) :: nnz !! number of non-zero values
+        ${t1}$, intent(in)    :: vec_x${ranksuffix(rank)}$
+        ${t1}$, intent(inout) :: vec_y${ranksuffix(rank)}$
+        ${t1}$, intent(in), optional :: alpha
+        ${t1}$, intent(in), optional :: beta
+        character(1), intent(in), optional :: op
         ${t1}$ :: alpha_
         character(1) :: op_
         integer(ilp) :: col_index, k, row_index
@@ -33,7 +48,6 @@ contains
             vec_y = zero_${s1}$
         endif
 
-        associate( data => matrix%data, index => matrix%index, storage => matrix%storage, nnz => matrix%nnz )
         select case(op_)
         case(sparse_op_none)
             if(storage == sparse_full) then
@@ -92,10 +106,9 @@ contains
             end if
         #:endif
         end select
-        end associate
     end subroutine
 
     #:endfor
     #:endfor
 
-end submodule stdlib_sparse_spmv_coo
\ No newline at end of file
+end submodule stdlib_sparse_spmv_coo

From 51780555855940ade51bd5425d5f0f6d82d2c06a Mon Sep 17 00:00:00 2001
From: Jeremie Vandenplas <jeremie.vandenplas@gmail.com>
Date: Sat, 2 May 2026 20:54:44 +0200
Subject: [PATCH 2/8] COO: low-level interfaces

---
 src/sparse/stdlib_sparse_spmv.fypp | 37 ++++++++++++++++++++----------
 1 file changed, 25 insertions(+), 12 deletions(-)

diff --git a/src/sparse/stdlib_sparse_spmv.fypp b/src/sparse/stdlib_sparse_spmv.fypp
index 1445a7dc7..43b2522e2 100644
--- a/src/sparse/stdlib_sparse_spmv.fypp
+++ b/src/sparse/stdlib_sparse_spmv.fypp
@@ -16,6 +16,7 @@ module stdlib_sparse_spmv
     implicit none
     private
 
+
     !! Version experimental
     !!
     !! Apply the sparse matrix-vector product $$y = \alpha * op(M) * x + \beta * y $$
@@ -31,18 +32,6 @@ module stdlib_sparse_spmv
             ${t1}$, intent(in), optional :: beta
             character(1), intent(in), optional :: op
         end subroutine
-
-        module subroutine spmv_coo_sub_${rank}$d_${s1}$(data, index, storage, nnz, vec_x,vec_y,alpha,beta,op)
-            ${t1}$, intent(in) :: data(:) 
-            integer(ilp), intent(in) :: index(:,:)
-            integer, intent(in) :: storage
-            integer(ilp), intent(in) :: nnz
-            ${t1}$, intent(in)    :: vec_x${ranksuffix(rank)}$
-            ${t1}$, intent(inout) :: vec_y${ranksuffix(rank)}$
-            ${t1}$, intent(in), optional :: alpha
-            ${t1}$, intent(in), optional :: beta
-            character(1), intent(in), optional :: op
-        end subroutine
  
         module subroutine spmv_csr_${rank}$d_${s1}$(matrix,vec_x,vec_y,alpha,beta,op)
             type(CSR_${s1}$_type), intent(in) :: matrix
@@ -82,6 +71,30 @@ module stdlib_sparse_spmv
         end subroutine
         #:endfor
     end interface
+
+    !! Version experimental
+    !!
+    !! Apply the COO sparse matrix-vector product $$y = \alpha * op(M) * x + \beta * y $$
+    !! [Specifications](../page/specs/stdlib_sparse.html#spmv)
+    interface spmv_coo
+        #:for k1, t1, s1 in (KINDS_TYPES)
+        #:for rank in RANKS
+        module subroutine spmv_coo_sub_${rank}$d_${s1}$(data, index, storage, nnz, vec_x,vec_y,alpha,beta,op)
+            ${t1}$, intent(in) :: data(:)
+            integer(ilp), intent(in) :: index(:,:)
+            integer, intent(in) :: storage
+            integer(ilp), intent(in) :: nnz
+            ${t1}$, intent(in)    :: vec_x${ranksuffix(rank)}$
+            ${t1}$, intent(inout) :: vec_y${ranksuffix(rank)}$
+            ${t1}$, intent(in), optional :: alpha
+            ${t1}$, intent(in), optional :: beta
+            character(1), intent(in), optional :: op
+        end subroutine
+        #:endfor
+        #:endfor
+    end interface
+
     public :: spmv
+    public :: spmv_coo
 
 end module

From 71519b9950bff58557c430406e4014751def764e Mon Sep 17 00:00:00 2001
From: Jeremie Vandenplas <jeremie.vandenplas@gmail.com>
Date: Sat, 2 May 2026 21:09:14 +0200
Subject: [PATCH 3/8] COO: test for low-level spmv

---
 test/linalg/test_linalg_sparse.fypp | 15 ++++++++++++++-
 1 file changed, 14 insertions(+), 1 deletion(-)

diff --git a/test/linalg/test_linalg_sparse.fypp b/test/linalg/test_linalg_sparse.fypp
index 0ebe235b5..35b16eac3 100644
--- a/test/linalg/test_linalg_sparse.fypp
+++ b/test/linalg/test_linalg_sparse.fypp
@@ -63,15 +63,28 @@ contains
             call check(error, all(vec_y1 == real([6,11,15,15],kind=wp)) )
             if (allocated(error)) return
 
+            ! High-level API
             call spmv( COO, vec_x, vec_y2 )
             call check(error, all(vec_y1 == vec_y2) )
             if (allocated(error)) return
 
+            ! Low-level API
+            call spmv_coo( COO%data ,COO%index, COO%storage, COO%nnz, vec_x, vec_y2 )
+            call check(error, all(vec_y1 == vec_y2), 'COO - low level API: wrong output' )
+            if (allocated(error)) return
+
             ! Test in-place transpose
             vec_y1 = 1._wp
+            ! High-level API
             call spmv( COO, vec_y1, vec_x, op=sparse_op_transpose )
             call check(error, all(vec_x == real([17,15,4,14,-3],kind=wp)) )
             if (allocated(error)) return
+
+            ! Low-level API
+            call spmv_coo( COO%data ,COO%index, COO%storage, COO%nnz, vec_y1, vec_x, op=sparse_op_transpose )
+            call check(error, all(vec_x == real([17,15,4,14,-3],kind=wp)), 'COO - transpose - low level API: wrong output' )
+            if (allocated(error)) return
+ 
         end block
         #:endfor
     end subroutine
@@ -715,4 +728,4 @@ program tester
         write(error_unit, '(i0, 1x, a)') stat, "test(s) failed!"
         error stop
     end if
-end program
\ No newline at end of file
+end program

From 0ccedc844c0bac4f13a4c169759783cccb2078d2 Mon Sep 17 00:00:00 2001
From: Jeremie Vandenplas <jeremie.vandenplas@gmail.com>
Date: Sat, 2 May 2026 21:23:28 +0200
Subject: [PATCH 4/8] cleaning

---
 src/sparse/stdlib_sparse_spmv.fypp | 3 +--
 1 file changed, 1 insertion(+), 2 deletions(-)

diff --git a/src/sparse/stdlib_sparse_spmv.fypp b/src/sparse/stdlib_sparse_spmv.fypp
index 43b2522e2..aeb5113a6 100644
--- a/src/sparse/stdlib_sparse_spmv.fypp
+++ b/src/sparse/stdlib_sparse_spmv.fypp
@@ -16,7 +16,6 @@ module stdlib_sparse_spmv
     implicit none
     private
 
-
     !! Version experimental
     !!
     !! Apply the sparse matrix-vector product $$y = \alpha * op(M) * x + \beta * y $$
@@ -32,7 +31,7 @@ module stdlib_sparse_spmv
             ${t1}$, intent(in), optional :: beta
             character(1), intent(in), optional :: op
         end subroutine
- 
+
         module subroutine spmv_csr_${rank}$d_${s1}$(matrix,vec_x,vec_y,alpha,beta,op)
             type(CSR_${s1}$_type), intent(in) :: matrix
             ${t1}$, intent(in)    :: vec_x${ranksuffix(rank)}$

From 2be029fb84291761d1bbee54a2d023ec4f33d43b Mon Sep 17 00:00:00 2001
From: Jeremie Vandenplas <jeremie.vandenplas@gmail.com>
Date: Mon, 4 May 2026 19:38:08 +0200
Subject: [PATCH 5/8] CRS: low-level API

---
 src/sparse/stdlib_sparse_spmv.fypp     | 28 +++++++++++++++++++++++++-
 src/sparse/stdlib_sparse_spmv_coo.fypp |  9 +++++----
 src/sparse/stdlib_sparse_spmv_csr.fypp | 27 +++++++++++++++++++------
 test/linalg/test_linalg_sparse.fypp    | 22 ++++++++++++++++----
 4 files changed, 71 insertions(+), 15 deletions(-)

diff --git a/src/sparse/stdlib_sparse_spmv.fypp b/src/sparse/stdlib_sparse_spmv.fypp
index aeb5113a6..cea11dd0c 100644
--- a/src/sparse/stdlib_sparse_spmv.fypp
+++ b/src/sparse/stdlib_sparse_spmv.fypp
@@ -78,7 +78,7 @@ module stdlib_sparse_spmv
     interface spmv_coo
         #:for k1, t1, s1 in (KINDS_TYPES)
         #:for rank in RANKS
-        module subroutine spmv_coo_sub_${rank}$d_${s1}$(data, index, storage, nnz, vec_x,vec_y,alpha,beta,op)
+        module subroutine spmv_coo_sub_${rank}$d_${s1}$(data, index, nnz, storage, vec_x,vec_y,alpha,beta,op)
             ${t1}$, intent(in) :: data(:)
             integer(ilp), intent(in) :: index(:,:)
             integer, intent(in) :: storage
@@ -93,7 +93,33 @@ module stdlib_sparse_spmv
         #:endfor
     end interface
 
+    !! Version experimental
+    !!
+    !! Apply the CRS sparse matrix-vector product $$y = \alpha * op(M) * x + \beta * y $$
+    !! [Specifications](../page/specs/stdlib_sparse.html#spmv)
+    interface spmv_csr
+        #:for k1, t1, s1 in (KINDS_TYPES)
+        #:for rank in RANKS
+        module subroutine spmv_csr_sub_${rank}$d_${s1}$(data,col,rowptr,nnz,nrows,ncols,storage,vec_x,vec_y,alpha,beta,op)
+            ${t1}$, intent(in) :: data(:)
+            integer(ilp), intent(in) :: col(:) !! matrix column pointer
+            integer(ilp), intent(in) :: rowptr(:)  !! matrix row pointer
+            integer(ilp), intent(in) :: nnz !! number of non-zero values
+            integer(ilp), intent(in) :: nrows
+            integer(ilp), intent(in) :: ncols
+            integer, intent(in) :: storage !! storage
+            ${t1}$, intent(in)    :: vec_x${ranksuffix(rank)}$
+            ${t1}$, intent(inout) :: vec_y${ranksuffix(rank)}$
+            ${t1}$, intent(in), optional :: alpha
+            ${t1}$, intent(in), optional :: beta
+            character(1), intent(in), optional :: op
+        end subroutine
+        #:endfor
+        #:endfor
+    end interface
+
     public :: spmv
     public :: spmv_coo
+    public :: spmv_csr
 
 end module
diff --git a/src/sparse/stdlib_sparse_spmv_coo.fypp b/src/sparse/stdlib_sparse_spmv_coo.fypp
index 0d009299b..a7a362b08 100644
--- a/src/sparse/stdlib_sparse_spmv_coo.fypp
+++ b/src/sparse/stdlib_sparse_spmv_coo.fypp
@@ -21,15 +21,16 @@ contains
         ${t1}$, intent(in), optional :: beta
         character(1), intent(in), optional :: op
 
-        call spmv_coo_sub_${rank}$d_${s1}$(matrix%data, matrix%index, matrix%storage, matrix%nnz, vec_x,vec_y,alpha,beta,op)
+        call spmv_coo_sub_${rank}$d_${s1}$(matrix%data, matrix%index, matrix%nnz, matrix%storage, &
+            vec_x,vec_y,alpha,beta,op)
 
     end subroutine
 
-    module subroutine spmv_coo_sub_${rank}$d_${s1}$(data, index, storage, nnz, vec_x,vec_y,alpha,beta,op)
-        ${t1}$, intent(in) :: data(:) 
+    module subroutine spmv_coo_sub_${rank}$d_${s1}$(data,index,nnz,storage,vec_x,vec_y,alpha,beta,op)
+        ${t1}$, intent(in) :: data(:)
         integer(ilp), intent(in) :: index(:,:) !! Matrix coordinates index(2,nnz)
-        integer, intent(in) :: storage !! storage
         integer(ilp), intent(in) :: nnz !! number of non-zero values
+        integer, intent(in) :: storage !! storage
         ${t1}$, intent(in)    :: vec_x${ranksuffix(rank)}$
         ${t1}$, intent(inout) :: vec_y${ranksuffix(rank)}$
         ${t1}$, intent(in), optional :: alpha
diff --git a/src/sparse/stdlib_sparse_spmv_csr.fypp b/src/sparse/stdlib_sparse_spmv_csr.fypp
index 929449969..f1e4bee22 100644
--- a/src/sparse/stdlib_sparse_spmv_csr.fypp
+++ b/src/sparse/stdlib_sparse_spmv_csr.fypp
@@ -20,6 +20,25 @@ contains
         ${t1}$, intent(in), optional :: alpha
         ${t1}$, intent(in), optional :: beta
         character(1), intent(in), optional :: op
+
+        call spmv_csr_sub_${rank}$d_${s1}$(matrix%data, matrix%col, matrix%rowptr, matrix%nnz, matrix%nrows, matrix%ncols, matrix%storage, &
+            vec_x,vec_y,alpha,beta,op)
+
+    end subroutine
+
+    module subroutine spmv_csr_sub_${rank}$d_${s1}$(data,col,rowptr,nnz,nrows,ncols,storage,vec_x,vec_y,alpha,beta,op)
+        ${t1}$, intent(in) :: data(:)
+        integer(ilp), intent(in) :: col(:) !! matrix column pointer
+        integer(ilp), intent(in) :: rowptr(:)  !! matrix row pointer
+        integer(ilp), intent(in) :: nnz !! number of non-zero values
+        integer(ilp), intent(in) :: nrows
+        integer(ilp), intent(in) :: ncols
+        integer, intent(in) :: storage !! storage
+        ${t1}$, intent(in)    :: vec_x${ranksuffix(rank)}$
+        ${t1}$, intent(inout) :: vec_y${ranksuffix(rank)}$
+        ${t1}$, intent(in), optional :: alpha
+        ${t1}$, intent(in), optional :: beta
+        character(1), intent(in), optional :: op
         ${t1}$ :: alpha_
         character(1) :: op_
         integer(ilp) :: i, j
@@ -37,9 +56,6 @@ contains
         else 
             vec_y = zero_${s1}$
         endif
-
-        associate( data => matrix%data, col => matrix%col, rowptr => matrix%rowptr, &
-            & nnz => matrix%nnz, nrows => matrix%nrows, ncols => matrix%ncols, storage => matrix%storage )
     
             if( storage == sparse_full .and. op_==sparse_op_none ) then
                 do i = 1, nrows
@@ -114,10 +130,9 @@ contains
                 end do
             #:endif
             end if
-        end associate
     end subroutine
-    
+
     #:endfor
     #:endfor
 
-end submodule stdlib_sparse_spmv_csr
\ No newline at end of file
+end submodule stdlib_sparse_spmv_csr
diff --git a/test/linalg/test_linalg_sparse.fypp b/test/linalg/test_linalg_sparse.fypp
index 35b16eac3..fe191d0e6 100644
--- a/test/linalg/test_linalg_sparse.fypp
+++ b/test/linalg/test_linalg_sparse.fypp
@@ -69,7 +69,7 @@ contains
             if (allocated(error)) return
 
             ! Low-level API
-            call spmv_coo( COO%data ,COO%index, COO%storage, COO%nnz, vec_x, vec_y2 )
+            call spmv_coo( COO%data ,COO%index, COO%nnz, COO%storage, vec_x, vec_y2 )
             call check(error, all(vec_y1 == vec_y2), 'COO - low level API: wrong output' )
             if (allocated(error)) return
 
@@ -81,7 +81,7 @@ contains
             if (allocated(error)) return
 
             ! Low-level API
-            call spmv_coo( COO%data ,COO%index, COO%storage, COO%nnz, vec_y1, vec_x, op=sparse_op_transpose )
+            call spmv_coo( COO%data ,COO%index, COO%nnz, COO%storage, vec_y1, vec_x, op=sparse_op_transpose )
             call check(error, all(vec_x == real([17,15,4,14,-3],kind=wp)), 'COO - transpose - low level API: wrong output' )
             if (allocated(error)) return
  
@@ -134,15 +134,29 @@ contains
             
             allocate( vec_x(5) , source = 1._wp )
             allocate( vec_y(4) , source = 0._wp )
+            ! High-level API
             call spmv( CSR, vec_x, vec_y )
             
-            call check(error, all(vec_y == real([6,11,15,15],kind=wp)) )
+            call check(error, all(vec_y == real([6,11,15,15],kind=wp)), 'CSR - high-level API - wrong output' )
+            if (allocated(error)) return
+
+            ! Low-level API
+            call spmv_csr( CSR%data, CSR%col, CSR%rowptr, CSR%nnz, CSR%nrows, CSR%ncols, CSR%storage, &
+                vec_x, vec_y )
+            
+            call check(error, all(vec_y == real([6,11,15,15],kind=wp)), 'CSR - low-level API - wrong output' )
             if (allocated(error)) return
 
             ! Test in-place transpose
             vec_y = 1._wp
+            ! High-level API
             call spmv( CSR, vec_y, vec_x, op=sparse_op_transpose )
-            call check(error, all(vec_x == real([17,15,4,14,-3],kind=wp)) )
+            call check(error, all(vec_x == real([17,15,4,14,-3],kind=wp)), 'CSR transpose - high-level API - wrong output' )
+            if (allocated(error)) return
+
+            call spmv_csr( CSR%data, CSR%col, CSR%rowptr, CSR%nnz, CSR%nrows, CSR%ncols, CSR%storage, &
+                vec_y, vec_x, op=sparse_op_transpose )
+            call check(error, all(vec_x == real([17,15,4,14,-3],kind=wp)), 'CSR transpose - low-level API - wrong output' )
             if (allocated(error)) return
         end block
         #:endfor

From f0b85fa5080cb1fae5b63ad4279890d50e19cbd0 Mon Sep 17 00:00:00 2001
From: Jeremie Vandenplas <jeremie.vandenplas@gmail.com>
Date: Mon, 4 May 2026 19:53:26 +0200
Subject: [PATCH 6/8] CSC: low-level API

---
 src/sparse/stdlib_sparse_spmv.fypp     | 28 +++++++++++++++++++++++++-
 src/sparse/stdlib_sparse_spmv_csc.fypp | 25 ++++++++++++++++++-----
 test/linalg/test_linalg_sparse.fypp    | 15 ++++++++++++++
 3 files changed, 62 insertions(+), 6 deletions(-)

diff --git a/src/sparse/stdlib_sparse_spmv.fypp b/src/sparse/stdlib_sparse_spmv.fypp
index cea11dd0c..a68b47028 100644
--- a/src/sparse/stdlib_sparse_spmv.fypp
+++ b/src/sparse/stdlib_sparse_spmv.fypp
@@ -95,7 +95,32 @@ module stdlib_sparse_spmv
 
     !! Version experimental
     !!
-    !! Apply the CRS sparse matrix-vector product $$y = \alpha * op(M) * x + \beta * y $$
+    !! Apply the CSC sparse matrix-vector product $$y = \alpha * op(M) * x + \beta * y $$
+    !! [Specifications](../page/specs/stdlib_sparse.html#spmv)
+    interface spmv_csc
+        #:for k1, t1, s1 in (KINDS_TYPES)
+        #:for rank in RANKS
+        module subroutine spmv_csc_sub_${rank}$d_${s1}$(data,colptr,row,nnz,nrows,ncols,storage,vec_x,vec_y,alpha,beta,op)
+            ${t1}$, intent(in) :: data(:)
+            integer(ilp), intent(in) :: colptr(:) !! matrix column pointer
+            integer(ilp), intent(in) :: row(:)  !! matrix row pointer
+            integer(ilp), intent(in) :: nnz !! number of non-zero values
+            integer(ilp), intent(in) :: nrows
+            integer(ilp), intent(in) :: ncols
+            integer, intent(in) :: storage !! storage
+            ${t1}$, intent(in)    :: vec_x${ranksuffix(rank)}$
+            ${t1}$, intent(inout) :: vec_y${ranksuffix(rank)}$
+            ${t1}$, intent(in), optional :: alpha
+            ${t1}$, intent(in), optional :: beta
+            character(1), intent(in), optional :: op
+        end subroutine
+        #:endfor
+        #:endfor
+    end interface
+
+    !! Version experimental
+    !!
+    !! Apply the CSR sparse matrix-vector product $$y = \alpha * op(M) * x + \beta * y $$
     !! [Specifications](../page/specs/stdlib_sparse.html#spmv)
     interface spmv_csr
         #:for k1, t1, s1 in (KINDS_TYPES)
@@ -120,6 +145,7 @@ module stdlib_sparse_spmv
 
     public :: spmv
     public :: spmv_coo
+    public :: spmv_csc
     public :: spmv_csr
 
 end module
diff --git a/src/sparse/stdlib_sparse_spmv_csc.fypp b/src/sparse/stdlib_sparse_spmv_csc.fypp
index 83b4ed41d..95a173c10 100644
--- a/src/sparse/stdlib_sparse_spmv_csc.fypp
+++ b/src/sparse/stdlib_sparse_spmv_csc.fypp
@@ -20,6 +20,25 @@ contains
         ${t1}$, intent(in), optional :: alpha
         ${t1}$, intent(in), optional :: beta
         character(1), intent(in), optional :: op
+
+        call spmv_csc_sub_${rank}$d_${s1}$(matrix%data,matrix%colptr,matrix%row,matrix%nnz,matrix%nrows,matrix%ncols,matrix%storage, &
+            vec_x,vec_y,alpha,beta,op)
+
+    end subroutine
+    
+    module subroutine spmv_csc_sub_${rank}$d_${s1}$(data,colptr,row,nnz,nrows,ncols,storage,vec_x,vec_y,alpha,beta,op)
+        ${t1}$, intent(in) :: data(:)
+        integer(ilp), intent(in) :: colptr(:) !! matrix column pointer
+        integer(ilp), intent(in) :: row(:)  !! matrix row pointer
+        integer(ilp), intent(in) :: nnz !! number of non-zero values
+        integer(ilp), intent(in) :: nrows
+        integer(ilp), intent(in) :: ncols
+        integer, intent(in) :: storage !! storage
+        ${t1}$, intent(in)    :: vec_x${ranksuffix(rank)}$
+        ${t1}$, intent(inout) :: vec_y${ranksuffix(rank)}$
+        ${t1}$, intent(in), optional :: alpha
+        ${t1}$, intent(in), optional :: beta
+        character(1), intent(in), optional :: op
         ${t1}$ :: alpha_
         character(1) :: op_
         integer(ilp) :: i, j
@@ -38,8 +57,6 @@ contains
             vec_y = zero_${s1}$
         endif
 
-        associate( data => matrix%data, colptr => matrix%colptr, row => matrix%row, &
-            & nnz => matrix%nnz, nrows => matrix%nrows, ncols => matrix%ncols, storage => matrix%storage )
             if( storage == sparse_full .and. op_==sparse_op_none ) then
                 do concurrent(j=1:ncols)
                     aux = alpha_ * vec_x(${rksfx2(rank-1)}$j)
@@ -110,10 +127,8 @@ contains
                 end do
             #:endif
             end if
-        end associate
     end subroutine
-    
     #:endfor
     #:endfor
 
-end submodule stdlib_sparse_spmv_csc
\ No newline at end of file
+end submodule stdlib_sparse_spmv_csc
diff --git a/test/linalg/test_linalg_sparse.fypp b/test/linalg/test_linalg_sparse.fypp
index fe191d0e6..b0e907c69 100644
--- a/test/linalg/test_linalg_sparse.fypp
+++ b/test/linalg/test_linalg_sparse.fypp
@@ -179,16 +179,31 @@ contains
             
             allocate( vec_x(5) , source = 1._wp )
             allocate( vec_y(4) , source = 0._wp )
+            !High-level API
             call spmv( CSC, vec_x, vec_y )
             
             call check(error, all(vec_y == real([6,11,15,15],kind=wp)) )
             if (allocated(error)) return
 
+            !High-level API
+            call spmv_csc( CSC%data, CSC%colptr, CSC%row, CSC%nnz, CSC%nrows, CSC%ncols, CSC%storage, vec_x, vec_y )
+            
+            call check(error, all(vec_y == real([6,11,15,15],kind=wp)) )
+            if (allocated(error)) return
+
             ! Test in-place transpose
             vec_y = 1._wp
+            !High-level API
             call spmv( CSC, vec_y, vec_x, op=sparse_op_transpose )
             call check(error, all(vec_x == real([17,15,4,14,-3],kind=wp)) )
             if (allocated(error)) return
+
+            !Low-level API
+            call spmv_csc( CSC%data, CSC%colptr, CSC%row, CSC%nnz, CSC%nrows, CSC%ncols, CSC%storage, vec_y, vec_x, &
+                op=sparse_op_transpose )
+            call check(error, all(vec_x == real([17,15,4,14,-3],kind=wp)) )
+            if (allocated(error)) return
+
         end block
         #:endfor
     end subroutine

From e4c796abde211d6833b86167575296fabae1d3ab Mon Sep 17 00:00:00 2001
From: Jeremie Vandenplas <jeremie.vandenplas@gmail.com>
Date: Mon, 4 May 2026 20:38:45 +0200
Subject: [PATCH 7/8] ELL: low-level API

---
 src/sparse/stdlib_sparse_spmv.fypp     | 26 ++++++++++++++++++++++++++
 src/sparse/stdlib_sparse_spmv_ell.fypp | 26 +++++++++++++++++++++-----
 test/linalg/test_linalg_sparse.fypp    | 15 +++++++++++++++
 3 files changed, 62 insertions(+), 5 deletions(-)

diff --git a/src/sparse/stdlib_sparse_spmv.fypp b/src/sparse/stdlib_sparse_spmv.fypp
index a68b47028..f7a36e9cb 100644
--- a/src/sparse/stdlib_sparse_spmv.fypp
+++ b/src/sparse/stdlib_sparse_spmv.fypp
@@ -143,9 +143,35 @@ module stdlib_sparse_spmv
         #:endfor
     end interface
 
+    !! Version experimental
+    !!
+    !! Apply the ELL sparse matrix-vector product $$y = \alpha * op(M) * x + \beta * y $$
+    !! [Specifications](../page/specs/stdlib_sparse.html#spmv)
+    interface spmv_ell
+        #:for k1, t1, s1 in (KINDS_TYPES)
+        #:for rank in RANKS
+        module subroutine spmv_ell_sub_${rank}$d_${s1}$(data,index,mnz_p_row,nnz,nrows,ncols,storage,vec_x,vec_y,alpha,beta,op)
+            ${t1}$, intent(in) :: data(:,:)
+            integer(ilp), intent(in) :: index(:,:)
+            integer(ilp), intent(in) :: mnz_p_row
+            integer(ilp), intent(in) :: nnz
+            integer(ilp), intent(in) :: nrows
+            integer(ilp), intent(in) :: ncols
+            integer, intent(in) :: storage
+            ${t1}$, intent(in)    :: vec_x${ranksuffix(rank)}$
+            ${t1}$, intent(inout) :: vec_y${ranksuffix(rank)}$
+            ${t1}$, intent(in), optional :: alpha
+            ${t1}$, intent(in), optional :: beta
+            character(1), intent(in), optional :: op
+        end subroutine
+        #:endfor
+        #:endfor
+    end interface
+
     public :: spmv
     public :: spmv_coo
     public :: spmv_csc
     public :: spmv_csr
+    public :: spmv_ell
 
 end module
diff --git a/src/sparse/stdlib_sparse_spmv_ell.fypp b/src/sparse/stdlib_sparse_spmv_ell.fypp
index 243d1cbd4..68e8b32d6 100644
--- a/src/sparse/stdlib_sparse_spmv_ell.fypp
+++ b/src/sparse/stdlib_sparse_spmv_ell.fypp
@@ -20,6 +20,25 @@ contains
         ${t1}$, intent(in), optional :: alpha
         ${t1}$, intent(in), optional :: beta
         character(1), intent(in), optional :: op
+
+        call spmv_ell_sub_${rank}$d_${s1}$(matrix%data,matrix%index,matrix%K, &
+            matrix%nnz,matrix%nrows,matrix%ncols,matrix%storage, &
+            vec_x,vec_y,alpha,beta,op)
+    end subroutine
+    
+    module subroutine spmv_ell_sub_${rank}$d_${s1}$(data,index,mnz_p_row,nnz,nrows,ncols,storage,vec_x,vec_y,alpha,beta,op)
+        ${t1}$, intent(in) :: data(:,:)
+        integer(ilp), intent(in) :: index(:,:)
+        integer, intent(in) :: mnz_p_row
+        integer(ilp), intent(in) :: nnz
+        integer(ilp), intent(in) :: nrows
+        integer(ilp), intent(in) :: ncols
+        integer, intent(in) :: storage
+        ${t1}$, intent(in)    :: vec_x${ranksuffix(rank)}$
+        ${t1}$, intent(inout) :: vec_y${ranksuffix(rank)}$
+        ${t1}$, intent(in), optional :: alpha
+        ${t1}$, intent(in), optional :: beta
+        character(1), intent(in), optional :: op
         ${t1}$ :: alpha_
         character(1) :: op_
         integer(ilp) :: i, j, k
@@ -32,8 +51,6 @@ contains
         else 
             vec_y = zero_${s1}$
         endif
-        associate( data => matrix%data, index => matrix%index, MNZ_P_ROW => matrix%K, &
-            & nnz => matrix%nnz, nrows => matrix%nrows, ncols => matrix%ncols, storage => matrix%storage )
             if( storage == sparse_full .and. op_==sparse_op_none ) then
                 do i = 1, nrows
                     do k = 1, MNZ_P_ROW
@@ -78,10 +95,9 @@ contains
                 end do
             #:endif
             end if
-        end associate
     end subroutine
-    
+
     #:endfor
     #:endfor
 
-end submodule stdlib_sparse_spmv_ell
\ No newline at end of file
+end submodule stdlib_sparse_spmv_ell
diff --git a/test/linalg/test_linalg_sparse.fypp b/test/linalg/test_linalg_sparse.fypp
index b0e907c69..77fadeb6d 100644
--- a/test/linalg/test_linalg_sparse.fypp
+++ b/test/linalg/test_linalg_sparse.fypp
@@ -231,16 +231,31 @@ contains
             
             allocate( vec_x(5) , source = 1._wp )
             allocate( vec_y(4) , source = 0._wp )
+            !High-level API
             call spmv( ELL, vec_x, vec_y )
             
             call check(error, all(vec_y == real([6,11,15,15],kind=wp)) )
             if (allocated(error)) return
 
+            !Low-level API
+            call spmv_ell( ELL%data, ELL%index, ELL%K, &
+                ELL%nnz, ELL%nrows, ELL%ncols, ELL%storage, vec_x, vec_y )
+
+            call check(error, all(vec_y == real([6,11,15,15],kind=wp)) )
+            if (allocated(error)) return
+
             ! Test in-place transpose
             vec_y = 1._wp
+            !High-level API
             call spmv( ELL, vec_y, vec_x, op=sparse_op_transpose )
             call check(error, all(vec_x == real([17,15,4,14,-3],kind=wp)) )
             if (allocated(error)) return
+
+            !Low-level API
+            call spmv_ell( ELL%data, ELL%index, ELL%K, &
+                ELL%nnz, ELL%nrows, ELL%ncols, ELL%storage, vec_y, vec_x, op=sparse_op_transpose )
+            call check(error, all(vec_x == real([17,15,4,14,-3],kind=wp)) )
+            if (allocated(error)) return
         end block
         #:endfor
         

From 7f4309aaca2fff74a3f9d4012084a25d2f699c38 Mon Sep 17 00:00:00 2001
From: Jeremie Vandenplas <jeremie.vandenplas@gmail.com>
Date: Mon, 4 May 2026 21:01:42 +0200
Subject: [PATCH 8/8] SELLC: low-level API

---
 src/sparse/stdlib_sparse_spmv.fypp       | 26 +++++++++++++++++++++
 src/sparse/stdlib_sparse_spmv_sellc.fypp | 29 +++++++++++++++++++-----
 test/linalg/test_linalg_sparse.fypp      | 18 ++++++++++++++-
 3 files changed, 66 insertions(+), 7 deletions(-)

diff --git a/src/sparse/stdlib_sparse_spmv.fypp b/src/sparse/stdlib_sparse_spmv.fypp
index f7a36e9cb..6f408f2b0 100644
--- a/src/sparse/stdlib_sparse_spmv.fypp
+++ b/src/sparse/stdlib_sparse_spmv.fypp
@@ -168,10 +168,36 @@ module stdlib_sparse_spmv
         #:endfor
     end interface
 
+    !! Version experimental
+    !!
+    !! Apply the SELLC sparse matrix-vector product $$y = \alpha * op(M) * x + \beta * y $$
+    !! [Specifications](../page/specs/stdlib_sparse.html#spmv)
+    interface spmv_sellc
+        #:for k1, t1, s1 in (KINDS_TYPES)
+        module subroutine spmv_sellc_sub_${s1}$(data,ia,ja,cs,nnz,nrows,ncols,storage,vec_x,vec_y,alpha,beta,op)
+            !! This algorithm was gracefully provided by Ivan Privec and adapted by Jose Alves
+            ${t1}$, intent(in) :: data(:,:)
+            integer(ilp), intent(in) :: ia(:)
+            integer(ilp), intent(in) :: ja(:,:)
+            integer, intent(in) :: cs
+            integer(ilp), intent(in) :: nnz
+            integer(ilp), intent(in) :: nrows
+            integer(ilp), intent(in) :: ncols
+            integer, intent(in) :: storage
+            ${t1}$, intent(in)    :: vec_x(:)
+            ${t1}$, intent(inout) :: vec_y(:)
+            ${t1}$, intent(in), optional :: alpha
+            ${t1}$, intent(in), optional :: beta
+            character(1), intent(in), optional :: op
+        end subroutine
+        #:endfor
+    end interface
+
     public :: spmv
     public :: spmv_coo
     public :: spmv_csc
     public :: spmv_csr
     public :: spmv_ell
+    public :: spmv_sellc
 
 end module
diff --git a/src/sparse/stdlib_sparse_spmv_sellc.fypp b/src/sparse/stdlib_sparse_spmv_sellc.fypp
index 52205debd..c4982e3fd 100644
--- a/src/sparse/stdlib_sparse_spmv_sellc.fypp
+++ b/src/sparse/stdlib_sparse_spmv_sellc.fypp
@@ -16,6 +16,28 @@ contains
         ${t1}$, intent(in), optional :: alpha
         ${t1}$, intent(in), optional :: beta
         character(1), intent(in), optional :: op
+
+        call spmv_sellc_sub_${s1}$(matrix%data, matrix%rowptr, matrix%col, matrix%chunk_size, &
+            matrix%nnz, matrix%nrows, matrix%ncols, matrix%storage, &
+            vec_x,vec_y,alpha,beta,op)
+
+    end subroutine
+
+    module subroutine spmv_sellc_sub_${s1}$(data,ia,ja,cs,nnz,nrows,ncols,storage,vec_x,vec_y,alpha,beta,op)
+        !! This algorithm was gracefully provided by Ivan Privec and adapted by Jose Alves
+        ${t1}$, intent(in) :: data(:,:)
+        integer(ilp), intent(in) :: ia(:)
+        integer(ilp), intent(in) :: ja(:,:)
+        integer, intent(in) :: cs
+        integer(ilp), intent(in) :: nnz
+        integer(ilp), intent(in) :: nrows
+        integer(ilp), intent(in) :: ncols
+        integer, intent(in) :: storage
+        ${t1}$, intent(in)    :: vec_x(:)
+        ${t1}$, intent(inout) :: vec_y(:)
+        ${t1}$, intent(in), optional :: alpha
+        ${t1}$, intent(in), optional :: beta
+        character(1), intent(in), optional :: op
         ${t1}$ :: alpha_
         character(1) :: op_
         integer(ilp) :: i, nz, rowidx, num_chunks, rm
@@ -29,9 +51,6 @@ contains
             vec_y = zero_${s1}$
         endif
 
-        associate( data => matrix%data, ia => matrix%rowptr , ja => matrix%col, cs => matrix%chunk_size, &
-        &   nnz => matrix%nnz, nrows => matrix%nrows, ncols => matrix%ncols, storage => matrix%storage  )
-
         if( .not.any( ${CHUNKS}$ == cs ) ) then
             print *, "error: sellc chunk size not supported."
             return
@@ -107,7 +126,6 @@ contains
             print *, "error: sellc format for spmv operation not yet supported."
             return
         end if
-        end associate
 
     contains
         #:for chunk in CHUNKS
@@ -187,7 +205,6 @@ contains
         #:endif
 
     end subroutine
-    
     #:endfor
 
-end submodule stdlib_sparse_spmv_sellc
\ No newline at end of file
+end submodule stdlib_sparse_spmv_sellc
diff --git a/test/linalg/test_linalg_sparse.fypp b/test/linalg/test_linalg_sparse.fypp
index 77fadeb6d..396bae95e 100644
--- a/test/linalg/test_linalg_sparse.fypp
+++ b/test/linalg/test_linalg_sparse.fypp
@@ -289,17 +289,33 @@ contains
             allocate( vec_x(6) , source = 1._wp )
             allocate( vec_y(6) , source = 0._wp )
             
+            !High-level API
             call spmv( SELLC, vec_x, vec_y )
             
             call check(error, all(vec_y == real([6,22,27,23,27,48],kind=wp)) )
             if (allocated(error)) return
 
+            !Low-level API
+            call spmv_sellc( SELLC%data, SELLC%rowptr, SELLC%col, SELLC%chunk_size, &
+                SELLC%nnz, SELLC%nrows, SELLC%ncols, SELLC%storage, vec_x, vec_y )
+
+            call check(error, all(vec_y == real([6,22,27,23,27,48],kind=wp)) )
+            if (allocated(error)) return
+
             ! Test in-place transpose
             vec_x = real( [1,2,3,4,5,6] , kind=wp )
             call spmv( CSR, vec_x, vec_y , op = sparse_op_transpose )
             allocate( vec_y2(6) , source = 0._wp )
+            !High-level API
             call spmv( SELLC, vec_x, vec_y2 , op = sparse_op_transpose )
-            
+
+            call check(error, all(vec_y == vec_y2))
+            if (allocated(error)) return
+
+            !Low-level API
+            call spmv_sellc( SELLC%data, SELLC%rowptr, SELLC%col, SELLC%chunk_size, &
+                SELLC%nnz, SELLC%nrows, SELLC%ncols, SELLC%storage, vec_x, vec_y2 , op = sparse_op_transpose )
+
             call check(error, all(vec_y == vec_y2))
             if (allocated(error)) return