add example with conversion and spmv

Author: jalvesz

doc/specs/stdlib_sparse.md

@@ -225,4 +225,9 @@ This module provides facility functions for converting between storage formats.
 
 `sellc`, `intent(inout)`: Shall be a `SELLC` type of `real` or `complex` type.
 
-`chunk`, `intent(in)`, `optional`: chunk size for the Sliced ELLPACK format.
+`chunk`, `intent(in)`, `optional`: chunk size for the Sliced ELLPACK format.
+
+## Example
+```fortran
+{!example/strings/example_sparse_spmv.f90!}
+```

example/linalg/example_sparse_spmv.f90

@@ -0,0 +1,36 @@
+program example_sparse_spmv
+    use stdlib_linalg_constants, only: dp
+    use stdlib_sparse
+    implicit none
+
+    integer, parameter :: m = 4, n = 2
+    real(dp) :: A(m,n), x(n)
+    real(dp) :: y_dense(m), y_coo(m), y_csr(m)
+    real(dp) :: alpha, beta
+    type(COO_dp) :: COO
+    type(CSR_dp) :: CSR
+
+    call random_number(A)
+    ! Convert from dense to COO and CSR matrices
+    call dense2coo( A , COO )
+    call coo2csr( COO , CSR )
+    
+    ! Initialize vectors
+    x       = 1._dp
+    y_dense = 2._dp
+    y_coo   = y_dense
+    y_csr   = y_dense
+
+    ! Perform matrix-vector product
+    alpha = 3._dp; beta = 2._dp
+    y_dense = alpha * matmul(A,x) + beta * y_dense
+    call spmv( COO , x , y_coo , alpha = alpha, beta = beta )
+    call spmv( CSR , x , y_csr , alpha = alpha, beta = beta )
+    
+    print *, 'dense :', y_dense
+    print *, 'coo   :', y_coo
+    print *, 'csr   :', y_csr
+  
+  end program example_sparse_spmv
+  
+