Draft: adding cpp version of codes

What is the new feature

Creating the C++ version of existing code

The people involved in porting the existing codes to C++ are @b382190, @b382899, @m301159, @k202204, @k202194, @k202174 and @k202170

Mandatory steps before review

• Gitlab CI passes (Hint: use make format for linting)
• New feature is covered by additional unit tests
• Mark the merge request as ready by removing Draft:

Mandatory steps before merge

• Reviewed by a maintainer
• Incorporate review suggestions
• Remember to edit the commit message and select the proper changelog category (feature/bugfix/other)
• Prior to merging, please remove any boilerplate from the MR description, retaining only the Please describe your feature in a couple of words and describe important implementation details of the feature section to maintain

You are not supposed to merge this request by yourself, the maintainers of libiconmath take care of this action!

test/fortran/test_math_utilities.f90

@@ -253,13 +253,15 @@ CONTAINS
 
     DO i = 1, n
       DO j = 1, n
-        a(i, j) = 1.0_wp
-        b(i, j) = 2.0_wp
-        c(i, j) = 1.0_wp
-        d(i, j) = 1.0_wp
+        a(i, j) = 1.0_wp*(i+j)
+        b(i, j) = 2.0_wp*(i+j)
+        c(i, j) = 1.0_wp*(i+j)
+        d(i, j) = 1.0_wp*(i+j)
       END DO
     END DO
 
+    tol = 1d-15
+
     CALL CPU_TIME(start_time)
 #ifndef __USE_CPP_BINDINGS
     CALL tdma_solver_vec(a, b, c, d, 1, n, 1, n, x)
@@ -278,12 +280,27 @@ CONTAINS
     DO i = 1, n
       DO j = 1, n
         sum = sum + x(i, j)
-      ! write(*,"(a,f24.16)") ' x(i, 1): ', x(i, 1)
       END DO
     END DO
     sum_ref = 27.2727272727272769_wp
-    tol = 1d-15
-    CALL TAG_TEST("TEST_tdma_solver_vec")
+    CALL TAG_TEST("TEST_tdma_solver_vec_full")
+    CALL ASSERT_ALMOST_EQUAL(sum, sum_ref, tol)
+
+    x = 0.0_wp
+#ifndef __USE_CPP_BINDINGS
+    CALL tdma_solver_vec(a, b, c, d, 2, n-1, 2, n-1, x)
+#else
+    CALL tdma_solver_vec(a, b, c, d, 1, n-1, 1, n-1, n, n, x, -1)
+#endif
+    sum = 0.0_wp
+    DO i = 2, n-1
+      DO j = 2, n-1
+        sum = sum + x(i, j)
+      END DO
+    END DO
+    sum_ref = 17.7777777777777679_wp
+
+    CALL TAG_TEST("TEST_tdma_solver_vec_partial")
     CALL ASSERT_ALMOST_EQUAL(sum, sum_ref, tol)
 
   END SUBROUTINE TEST_tdma_solver_vec