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ktras merged 5 commits into from
Feb 25, 2026
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Add metadata decorations to check_x functions in tests #9

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ee7b9f4
Add empty metadata decorations to `check_x` functions in tests
ktras Feb 23, 2026
8d6849d
Add metadata comments to test generated by an LLM
ktras Feb 24, 2026
01a1bcc
Update tests metadata based on PR review
ktras Feb 25, 2026
741fefe
Apply suggestions from code review
ktras Feb 25, 2026
54d8366
Update tests metadata based on PR review
ktras Feb 25, 2026
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95 changes: 94 additions & 1 deletion test/divergence_operator_1D_test_m.F90
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Original file line number Diff line number Diff line change
Expand Up @@ -65,6 +65,27 @@ pure function parabola(x) result(y)
y = (x**2)/2
end function

! PURPOSE: Tests that the 2nd-order discrete divergence of the gradient operator correctly computes
! div(grad(f)) for a parabolic function (x^2/2), which should yield a constant value of
! 1.0 everywhere, and reports a passing or failing test diagnosis based on whether the
! computed values approximate the expected result within a tight tolerance.
! KEYWORDS: divergence, gradient, div-grad, laplacian-equivalence, finite-difference,
! defined operation, unit-test, scalar_1D, parabola, 2nd-order, structured-grid, staggered-grid,
! test-diagnosis, differential-operator, verification, compound-operator
! CONTEXT: This function is part of the operator test suite in the formal library, which provides
! defined operations (.grad., .div., .laplacian., etc.) for staggered-grid
! scalar fields. It tests the compound expression .div. (.grad. f), which should be
! mathematically equivalent to the Laplacian but is computed by composing the gradient and
! divergence operators separately rather than using the dedicated .laplacian. operator. The
! scalar field is initialized as a parabola (x^2/2) on a 16-cell 1D domain [0, 5] at
! 2nd-order accuracy, and the expected div(grad) value is the constant 1.0. This
! complements the direct Laplacian tests by verifying that the discrete gradient and
! divergence operators compose correctly. A tight_tolerance is used, reflecting that the
! parabola is within the polynomial exactness range of the 2nd-order stencils. The
! conditional compilation directives handle differences between gfortran and other compilers
! regarding associate-block support for user-defined operator results. The test result is
! accumulated using the .also. and .approximates. defined operations and the
! passing_test()/test_diagnosis_t testing infrastructure.
function check_2nd_order_div_grad_parabola() result(test_diagnosis)
type(test_diagnosis_t) test_diagnosis
procedure(scalar_1D_initializer_i), pointer :: scalar_1D_initializer => parabola
Expand All @@ -84,7 +105,30 @@ function check_2nd_order_div_grad_parabola() result(test_diagnosis)
end associate
#endif
end function
! END CODE CHUNK

! PURPOSE: Tests that the 4th-order discrete divergence of the gradient operator correctly computes
! div(grad(f)) for a parabolic function (x^2/2), which should yield a constant value of
! 1.0 everywhere, and reports a passing or failing test diagnosis based on whether the
! computed values approximate the expected result within a tight tolerance.
! KEYWORDS: divergence, gradient, div-grad, laplacian-equivalence, finite-difference,
! defined operation, unit-test, scalar_1D, parabola, 4th-order, structured-grid, staggered-grid,
! test-diagnosis, differential-operator, verification, compound-operator,
! higher-order-accuracy
! CONTEXT: This function is part of the operator test suite in the formal library, which provides
! defined operations (.grad., .div., .laplacian., etc.) for staggered-grid
! scalar fields. It tests the compound expression .div. (.grad. f), which should be
! mathematically equivalent to the Laplacian but is computed by composing the gradient and
! divergence operators separately rather than using the dedicated .laplacian. operator. The
! scalar field is initialized as a parabola (x^2/2) on a 16-cell 1D domain [0, 9] at
! 4th-order accuracy, and the expected div(grad) value is the constant 1.0. Compared to the
! 2nd-order variant, this test uses a wider domain [0, 9] vs [0, 5], which tests the
! higher-order stencil on a coarser effective resolution. A tight_tolerance is still used,
! as the parabola is well within the polynomial exactness range of the 4th-order stencils.
! The conditional compilation directives handle differences between gfortran and other
! compilers regarding associate-block support for user-defined operator results. The test
! result is accumulated using the .also. and .approximates. defined operations and the
! passing_test()/test_diagnosis_t testing infrastructure.
function check_4th_order_div_grad_parabola() result(test_diagnosis)
type(test_diagnosis_t) test_diagnosis
procedure(scalar_1D_initializer_i), pointer :: scalar_1D_initializer => parabola
Expand All @@ -104,13 +148,36 @@ function check_4th_order_div_grad_parabola() result(test_diagnosis)
end associate
#endif
end function
! END CODE CHUNK

pure function sinusoid(x) result(y)
double precision, intent(in) :: x(:)
double precision, allocatable :: y(:)
y = sin(x) + cos(x)
end function

! PURPOSE: Tests that the 2nd-order discrete divergence operator converges at the expected rate by
! comparing coarse-grid (100 cells) and fine-grid (101 cells) solutions of the divergence
! of the vector field [sin(x) + cos(x)] against the analytical divergence cos(x) - sin(x).
! It verifies that both grids approximate the expected divergence within a rough tolerance
! and that the observed convergence rate matches 2nd-order accuracy.
! KEYWORDS: divergence, finite-difference, convergence-rate, 2nd-order, defined operation,
! unit-test, vector_1D, sinusoid, structured-grid, staggered-grid, test-diagnosis, differential-operator,
! verification, grid-refinement, order-of-accuracy
! CONTEXT: This function is part of the divergence operator test suite in the formal library, which
! provides defined operations (.div., .grad., .laplacian., etc.) for
! staggered-grid scalar and vector fields. It constructs two vector_1D_t objects
! initialized with a sinusoidal function on the domain [0, 2*pi] at 2nd-order accuracy
! with coarse (100) and fine (101) cell counts, applies the .div. operator to both, and
! compares the results against the analytical divergence cos(x) - sin(x). This test mirrors
! the structure of the gradient convergence tests but exercises the divergence operator on
! a vector field rather than the gradient operator on a scalar field. The observed
! convergence rate is computed via log(coarse_error/fine_error)/log(fine_cells/coarse_cells)
! and checked against the desired 2nd order. A rough_tolerance is used for all checks. The
! conditional compilation directives handle differences between gfortran and other compilers
! regarding associate-block support for user-defined operator results. The test result is
! accumulated using the .also. and .approximates. defined operations and the
! passing_test()/test_diagnosis_t testing infrastructure.
function check_2nd_order_div_sinusoid_convergence() result(test_diagnosis)
type(test_diagnosis_t) test_diagnosis
procedure(vector_1D_initializer_i), pointer :: vector_1D_initializer => sinusoid
Expand Down Expand Up @@ -155,7 +222,32 @@ function check_2nd_order_div_sinusoid_convergence() result(test_diagnosis)
end associate
#endif
end function
! END CODE CHUNK

! PURPOSE: Tests that the 4th-order discrete divergence operator converges at the expected rate by
! comparing coarse-grid (500 cells) and fine-grid (501 cells) solutions of the divergence
! of the vector field [sin(x) + cos(x)] against the analytical divergence cos(x) - sin(x).
! It verifies that both grids approximate the expected divergence within a loose tolerance
! and that the observed convergence rate matches 4th-order accuracy.
! KEYWORDS: divergence, finite-difference, convergence-rate, 4th-order, defined operation,
! unit-test, vector_1D, sinusoid, structured-grid, staggered-grid, test-diagnosis, differential-operator,
! verification, grid-refinement, order-of-accuracy, higher-order-accuracy
! CONTEXT: This function is part of the divergence operator test suite in the formal library, which
! provides defined operations (.div., .grad., .laplacian., etc.) for
! staggered-grid scalar and vector fields. It constructs two vector_1D_t objects
! initialized with a sinusoidal function on the domain [0, 2*pi] at 4th-order accuracy
! with coarse (500) and fine (501) cell counts, applies the .div. operator to both, and
! compares the results against the analytical divergence cos(x) - sin(x). Compared to the
! 2nd-order divergence convergence test, this test uses significantly more cells (500/501
! vs 100/101) to ensure stable convergence rate estimation at higher order. The point-wise
! accuracy checks use loose_tolerance rather than rough_tolerance, reflecting the tighter
! errors achievable with the 4th-order stencil on finer grids, while the convergence rate
! check uses crude_tolerance. The observed convergence rate is computed via
! log(coarse_error/fine_error)/log(fine_cells/coarse_cells) and checked against the desired
! 4th order. The conditional compilation directives handle differences between gfortran and
! other compilers regarding associate-block support for user-defined operator results. The
! test result is accumulated using the .also. and .approximates. defined operations and
! the passing_test()/test_diagnosis_t testing infrastructure.
function check_4th_order_div_sinusoid_convergence() result(test_diagnosis)
type(test_diagnosis_t) test_diagnosis
procedure(vector_1D_initializer_i), pointer :: vector_1D_initializer => sinusoid
Expand Down Expand Up @@ -203,5 +295,6 @@ function check_4th_order_div_sinusoid_convergence() result(test_diagnosis)
end associate
#endif
end function
! END CODE CHUNK

end module divergence_operator_1D_test_m
end module divergence_operator_1D_test_m
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