bspline/m_bspline_matrix.f90 - GCC Code Coverage Report

Directory:	src/
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	Coverage	Exec / Excl / Total
Lines:	91.7%	88 / 0 / 96
Functions:	100.0%	3 / 0 / 3
Branches:	57.4%	139 / 0 / 242

    bspline/m_bspline_matrix.f90
    
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        !> The B-spline matrix module
      
        !>
      
        !> This module provides functions to compute matrices related to B-spline spaces, such as mass and divgrad
      
        module m_bspline_matrix
      
        #include "petsc.fi"
      
          implicit none
      
          private
      
          public :: mass_matrix, divgrad_matrix
      
          !> @brief Compute the mass matrix of two B-spline spaces
      
          interface mass_matrix
      
            module procedure mass_matrix_1d
      
          end interface
      
          !> @brief Compute the divgrad matrix of a B-spline basis (i.e., the discretization of the Laplace operator)
      
          interface divgrad_matrix
      
            module procedure divgrad_matrix_1d
      
          end interface
      
        contains
      
          !> @brief Compute the mass matrix of two B-spline spaces
      
          !>
      
          !> @param[out] M The mass matrix
      
          !> @param[in] bspline1 The first B-spline spaces
      
          !> @param[in] bspline2 The second B-spline spaces
      
          !> @param[in] coordfun _(optional)_ The coordinate function
      
          !> @param[in] n_quad_extra _(optional)_ The additional number of quadrature points on top of those needed for exact integration of
      
          !>            the B-spline spaces
      
        7716
          subroutine mass_matrix_1d(M, bspline1, bspline2, coordfun, n_quad_extra)
      
            use m_common, only: wp, user_function_1d_interface
      
            use m_bspline_basis, only: BSplineSpace, size, get_internal_and_actual_inds
      
            use m_bspline_quadrature, only: BSplineQuadrature, quadrature_product, n_quad_exact, DEFAULT_EXTRA_QUADRATURE_POINTS
      
            implicit none
      
            Mat, intent(out) :: M
      
            type(BSplineSpace), intent(in) :: bspline1, bspline2
      
            procedure(user_function_1d_interface), optional :: coordfun
      
            integer, intent(in), optional :: n_quad_extra
      
        7716
            type(BSplineQuadrature) :: bspline1_quad, bspline2_quad
      
            integer :: ierr, n_quad, n_quad_extra_
      
            integer :: j1, j2, j1_internal, j2_internal, j1_minus_i, j2_minus_i, i, ndx
      
            integer :: local_nz_per_row, nonlocal_nz_per_row, j2_minus_i_max
      
            logical :: bspline_mirrored_1, bspline_mirrored_2, equal_spaces
      
            real(wp), allocatable :: vals(:, :), coordfun_vals(:), bspline1_vals(:)
      
            integer, allocatable :: cols(:), rows(:)
      
            real(wp) :: val, x
      
        7716
            n_quad = n_quad_exact(bspline1, bspline2)
      
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        7716
            if (present(coordfun)) then
      
        ✗
              if (present(n_quad_extra)) then
      
        ✗
                n_quad_extra_ = n_quad_extra
      
              else
      
                n_quad_extra_ = DEFAULT_EXTRA_QUADRATURE_POINTS
      
              end if
      
        ✗
              n_quad = n_quad + n_quad_extra_
      
            end if
      
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        7716
            if (bspline1%nr_intervals /= bspline2%nr_intervals) then
      
        ✗
              error stop "B-spline spaces must have the same number of intervals for the computation of the mass matrix"
      
            end if
      
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        7716
            bspline1_quad = BSplineQuadrature(bspline1, n_quad)
      
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        7716
            bspline2_quad = BSplineQuadrature(bspline2, n_quad)
      
            ! Create a sparse matrix
      
        7716
            local_nz_per_row = 1 + bspline1%degree + bspline2%degree
      
        7716
            nonlocal_nz_per_row = 0 ! NOTE: sequential
      
            call MatCreateAIJ(PETSC_COMM_SELF, size(bspline1),    &
      
           &      size(bspline2), size(bspline1),    &
      
           &      size(bspline2), local_nz_per_row, PETSC_NULL_INTEGER_ARRAY, nonlocal_nz_per_row,              &
      
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        7716
           &      PETSC_NULL_INTEGER_ARRAY, M, ierr); CHKERRQ(ierr)
      
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        30864
            allocate (vals(0:bspline2%degree, 0:bspline1%degree))
      
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            allocate (cols(0:bspline2%degree))
      
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        23148
            allocate (rows(0:bspline1%degree))
      
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        23148
            allocate (coordfun_vals(1:n_quad))
      
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        46832
            coordfun_vals = 1._wp
      
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        15432
            allocate (bspline1_vals(1:n_quad))
      
            equal_spaces = size(bspline1) == size(bspline2) .and. &
      
                           (bspline1%is_scaled .eqv. bspline2%is_scaled) .and. &
      
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        7716
                           (bspline1%is_periodic .eqv. bspline2%is_periodic)
      
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        7716
            PetscCall(MatSetFromOptions(M, ierr))
      
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        7716
            if (equal_spaces) then
      
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        7716
              PetscCall(MatSetOption(M, MAT_SYMMETRIC, PETSC_TRUE, ierr))
      
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        7716
              PetscCall(MatSetOption(M, MAT_SPD, PETSC_TRUE, ierr))
      
            end if
      
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        7716
            PetscCall(MatSetUp(M, ierr))
      
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        179986
            do i = 0, bspline1%nr_intervals - 1
      
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        172270
              if (present(coordfun)) then
      
        ✗
                do ndx = 1, n_quad
      
        ✗
                  x = (i + .5_wp + bspline1_quad%nodes(ndx) / 2) * bspline1_quad%bspline%h
      
        ✗
                  coordfun_vals(ndx) = coordfun(x)
      
                end do
      
              end if
      
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        1032300
              do j1_minus_i = 0, bspline1%degree
      
        860030
                call get_internal_and_actual_inds(bspline1, i, j1_minus_i, j1, j1_internal, bspline_mirrored_1)
      
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        860030
                if (bspline_mirrored_1) then
      
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        477745
                  bspline1_vals = bspline1_quad%bspline_at_nodes(j1_internal, bspline1%degree - j1_minus_i)%data(n_quad:1:-1)
      
                else
      
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                  bspline1_vals = bspline1_quad%bspline_at_nodes(j1_internal, j1_minus_i)%data(1:n_quad)
      
                end if
      
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                bspline1_vals = bspline1_vals * bspline1_quad%weights
      
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        860030
                if (equal_spaces) then
      
                  j2_minus_i_max = j1_minus_i
      
                else
      
                  j2_minus_i_max = bspline2%degree
      
                end if
      
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        3579264
                do j2_minus_i = 0, j2_minus_i_max
      
        2719234
                  call get_internal_and_actual_inds(bspline2, i, j2_minus_i, j2, j2_internal, bspline_mirrored_2)
      
                  val = 0._wp
      
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        2719234
                  if (bspline_mirrored_2) then
      
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        1193172
                    do ndx = 1, n_quad
      
                      val = val + coordfun_vals(ndx) * bspline1_vals(ndx) *&
      
        1193172
                        & bspline2_quad%bspline_at_nodes(j2_internal, bspline2%degree - j2_minus_i)%data(n_quad + 1 - ndx)
      
                    end do
      
                  else
      
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                    do ndx = 1, n_quad
      
                      val = val + coordfun_vals(ndx) * bspline1_vals(ndx) * &
      
        16854710
                        & bspline2_quad%bspline_at_nodes(j2_internal, j2_minus_i)%data(ndx)
      
                    end do
      
                  end if
      
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                  vals(j2_minus_i, j1_minus_i) = val
      
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                  if (j1_minus_i == bspline1%degree) then
      
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                    cols(j2_minus_i) = j2
      
                  end if
      
                end do
      
        1892330
                rows(j1_minus_i) = j1
      
              end do
      
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              if (equal_spaces) then
      
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                do j1_minus_i = 0, bspline1%degree
      
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                do j2_minus_i = j1_minus_i + 1, bspline2%degree
      
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                  vals(j2_minus_i, j1_minus_i) = vals(j1_minus_i, j2_minus_i)
      
                end do
      
                end do
      
              end if
      
              ! NOTE: vals is transposed for fast acces, this means the role of rows and cols is swapped
      
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        10196892
              PetscCall(MatSetValues(M, size(cols), cols, size(rows), rows, [vals(:, :)], ADD_VALUES, ierr))
      
            end do
      
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            deallocate (vals)
      
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            deallocate (cols)
      
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            deallocate (rows)
      
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            deallocate (coordfun_vals)
      
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        7716
            deallocate (bspline1_vals)
      
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        7716
            PetscCall(MatAssemblyBegin(M, MAT_FINAL_ASSEMBLY, ierr))
      
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        7716
            PetscCall(MatAssemblyEnd(M, MAT_FINAL_ASSEMBLY, ierr))
      
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        7716
          end subroutine mass_matrix_1d
      
          !> @brief Compute the difference matrix (consisting of a '1' and a '-1' for each row) of a 1D B-spline space
      
          !>
      
          !> @param[out] D The difference matrix
      
          !> @param[in] bspline The B-spline space
      
        48
          subroutine difference_matrix(D, bspline)
      
            use m_common, only: wp
      
            use m_bspline_basis, only: BSplineSpace, size
      
            implicit none
      
            Mat, intent(out) :: D
      
            type(BSplineSpace), intent(in) :: bspline
      
            integer :: n_basis, ierr, row, c0, c1, n_rows
      
            integer :: local_nz_per_row, nonlocal_nz_per_row
      
        48
            n_basis = size(bspline)
      
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        48
            if (.not. bspline%is_periodic) then
      
        48
              n_rows = n_basis - 1
      
            else
      
        ✗
              n_rows = n_basis
      
            end if
      
        48
            local_nz_per_row = 2
      
        48
            nonlocal_nz_per_row = 0 ! NOTE: currently sequential
      
            ! Create a sparse matrix
      
            call MatCreateAIJ(PETSC_COMM_SELF, n_rows, n_basis, n_rows, &
      
           &      n_basis, local_nz_per_row, PETSC_NULL_INTEGER_ARRAY, nonlocal_nz_per_row,&
      
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        48
           &      PETSC_NULL_INTEGER_ARRAY, D, ierr); CHKERRQ(ierr)
      
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        48
            PetscCall(MatSetFromOptions(D, ierr))
      
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        48
            PetscCall(MatSetUp(D, ierr))
      
            ! Set the values of the matrix
      
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        1728
            do row = 0, n_rows - 1
      
              c0 = row
      
        1680
              c1 = mod(row + 1, n_basis)
      
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        6768
              PetscCall(MatSetValues(D, 1, [row], 2, [c0, c1], [-1._wp, +1._wp], INSERT_VALUES, ierr))
      
            end do
      
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        48
            PetscCall(MatAssemblyBegin(D, MAT_FINAL_ASSEMBLY, ierr))
      
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        48
            PetscCall(MatAssemblyEnd(D, MAT_FINAL_ASSEMBLY, ierr))
      
          end subroutine
      
          !> @brief Compute the divgrad (Laplace) matrix of a 1D B-spline space
      
          !>
      
          !> @param[out] The resulting Laplace matrix
      
          !> @param[in] bspline The B-spline space
      
          !> @param[in] dbspline The derivative B-spline space
      
        96
          subroutine divgrad_matrix_1d(L, bspline, dbspline)
      
            use m_common, only: wp
      
            use m_bspline_basis, only: BSplineSpace, size
      
            implicit none
      
            Mat, intent(out) :: L
      
            type(BSplineSpace), intent(in) :: bspline, dbspline
      
            Mat :: D, M
      
            Vec :: nullspace_vec
      
            MatNullSpace :: nullspace
      
            integer :: ierr
      
            integer :: n_basis, dn_basis, i
      
            real(wp) :: tmp
      
            real(wp) :: EXPECTED_FILL_RATIO = 1.0_wp
      
        48
            n_basis = size(bspline)
      
            dn_basis = size(dbspline)
      
        48
            call mass_matrix(M, dbspline, dbspline)
      
        48
            call difference_matrix(D, bspline)
      
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        48
            PetscCall(MatPtAP(M, D, MAT_INITIAL_MATRIX, EXPECTED_FILL_RATIO, L, ierr))
      
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        48
            PetscCall(MatDestroy(M, ierr))
      
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        48
            PetscCall(MatDestroy(D, ierr))
      
            ! The Laplace matrix still has a nullspace (no boundary conditions are imposed)
      
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        48
            PetscCall(VecCreate(PETSC_COMM_SELF, nullspace_vec, ierr))
      
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        48
            PetscCall(VecSetSizes(nullspace_vec, n_basis, n_basis, ierr))
      
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        48
            PetscCall(VecSetFromOptions(nullspace_vec, ierr))
      
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            do i = 0, n_basis - 1
      
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              PetscCall(VecSetValue(nullspace_vec, i, 1._wp, INSERT_VALUES, ierr))
      
            end do
      
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        48
            PetscCall(VecNormalize(nullspace_vec, tmp, ierr))
      
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        48
            PetscCall(VecAssemblyBegin(nullspace_vec, ierr))
      
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        48
            PetscCall(VecAssemblyEnd(nullspace_vec, ierr))
      
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        96
            PetscCall(MatNullSpaceCreate(PETSC_COMM_SELF, PETSC_FALSE, 1, [nullspace_vec], nullspace, ierr))
      
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        48
            PetscCall(MatSetNullSpace(L, nullspace, ierr))
      
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        48
            PetscCall(MatNullSpaceDestroy(nullspace, ierr))
      
        48
          end subroutine divgrad_matrix_1d
      
        end module m_bspline_matrix

Line	Branch	Exec	Source
1			!> The B-spline matrix module
2			!>
3			!> This module provides functions to compute matrices related to B-spline spaces, such as mass and divgrad
4			module m_bspline_matrix
5			#include "petsc.fi"
6			implicit none
7
8			private
9			public :: mass_matrix, divgrad_matrix
10
11			!> @brief Compute the mass matrix of two B-spline spaces
12			interface mass_matrix
13			module procedure mass_matrix_1d
14			end interface
15
16			!> @brief Compute the divgrad matrix of a B-spline basis (i.e., the discretization of the Laplace operator)
17			interface divgrad_matrix
18			module procedure divgrad_matrix_1d
19			end interface
20			contains
21
22			!> @brief Compute the mass matrix of two B-spline spaces
23			!>
24			!> @param[out] M The mass matrix
25			!> @param[in] bspline1 The first B-spline spaces
26			!> @param[in] bspline2 The second B-spline spaces
27			!> @param[in] coordfun _(optional)_ The coordinate function
28			!> @param[in] n_quad_extra _(optional)_ The additional number of quadrature points on top of those needed for exact integration of
29			!> the B-spline spaces
30		7716	subroutine mass_matrix_1d(M, bspline1, bspline2, coordfun, n_quad_extra)
31			use m_common, only: wp, user_function_1d_interface
32			use m_bspline_basis, only: BSplineSpace, size, get_internal_and_actual_inds
33			use m_bspline_quadrature, only: BSplineQuadrature, quadrature_product, n_quad_exact, DEFAULT_EXTRA_QUADRATURE_POINTS
34
35			implicit none
36
37			Mat, intent(out) :: M
38			type(BSplineSpace), intent(in) :: bspline1, bspline2
39			procedure(user_function_1d_interface), optional :: coordfun
40			integer, intent(in), optional :: n_quad_extra
41
42		7716	type(BSplineQuadrature) :: bspline1_quad, bspline2_quad
43			integer :: ierr, n_quad, n_quad_extra_
44			integer :: j1, j2, j1_internal, j2_internal, j1_minus_i, j2_minus_i, i, ndx
45			integer :: local_nz_per_row, nonlocal_nz_per_row, j2_minus_i_max
46			logical :: bspline_mirrored_1, bspline_mirrored_2, equal_spaces
47			real(wp), allocatable :: vals(:, :), coordfun_vals(:), bspline1_vals(:)
48			integer, allocatable :: cols(:), rows(:)
49			real(wp) :: val, x
50
51		7716	n_quad = n_quad_exact(bspline1, bspline2)
52	1/2 ✗ Branch 2 → 3 not taken. ✓ Branch 2 → 6 taken 7716 times.	7716	if (present(coordfun)) then
53		✗	if (present(n_quad_extra)) then
54		✗	n_quad_extra_ = n_quad_extra
55			else
56			n_quad_extra_ = DEFAULT_EXTRA_QUADRATURE_POINTS
57			end if
58		✗	n_quad = n_quad + n_quad_extra_
59			end if
60
61	1/2 ✗ Branch 6 → 7 not taken. ✓ Branch 6 → 8 taken 7716 times.	7716	if (bspline1%nr_intervals /= bspline2%nr_intervals) then
62		✗	error stop "B-spline spaces must have the same number of intervals for the computation of the mass matrix"
63			end if
64
65	3/6 ✓ Branch 10 → 11 taken 7716 times. ✗ Branch 10 → 12 not taken. ✓ Branch 12 → 13 taken 7716 times. ✗ Branch 12 → 14 not taken. ✓ Branch 14 → 15 taken 7716 times. ✗ Branch 14 → 16 not taken.	7716	bspline1_quad = BSplineQuadrature(bspline1, n_quad)
66	3/6 ✓ Branch 18 → 19 taken 7716 times. ✗ Branch 18 → 20 not taken. ✓ Branch 20 → 21 taken 7716 times. ✗ Branch 20 → 22 not taken. ✓ Branch 22 → 23 taken 7716 times. ✗ Branch 22 → 24 not taken.	7716	bspline2_quad = BSplineQuadrature(bspline2, n_quad)
67
68			! Create a sparse matrix
69		7716	local_nz_per_row = 1 + bspline1%degree + bspline2%degree
70		7716	nonlocal_nz_per_row = 0 ! NOTE: sequential
71			call MatCreateAIJ(PETSC_COMM_SELF, size(bspline1), &
72			& size(bspline2), size(bspline1), &
73			& size(bspline2), local_nz_per_row, PETSC_NULL_INTEGER_ARRAY, nonlocal_nz_per_row, &
74	1/2 ✗ Branch 25 → 26 not taken. ✓ Branch 25 → 27 taken 7716 times.	7716	& PETSC_NULL_INTEGER_ARRAY, M, ierr); CHKERRQ(ierr)
75
76	8/16 ✗ Branch 27 → 28 not taken. ✓ Branch 27 → 29 taken 7716 times. ✓ Branch 29 → 28 taken 7716 times. ✗ Branch 29 → 30 not taken. ✗ Branch 30 → 31 not taken. ✓ Branch 30 → 32 taken 7716 times. ✓ Branch 32 → 31 taken 7716 times. ✗ Branch 32 → 33 not taken. ✓ Branch 33 → 34 taken 7716 times. ✗ Branch 33 → 35 not taken. ✓ Branch 35 → 36 taken 7716 times. ✗ Branch 35 → 37 not taken. ✗ Branch 37 → 38 not taken. ✓ Branch 37 → 39 taken 7716 times. ✗ Branch 39 → 40 not taken. ✓ Branch 39 → 41 taken 7716 times.	30864	allocate (vals(0:bspline2%degree, 0:bspline1%degree))
77	6/12 ✗ Branch 41 → 42 not taken. ✓ Branch 41 → 43 taken 7716 times. ✓ Branch 43 → 42 taken 7716 times. ✗ Branch 43 → 44 not taken. ✓ Branch 44 → 45 taken 7716 times. ✗ Branch 44 → 46 not taken. ✓ Branch 46 → 47 taken 7716 times. ✗ Branch 46 → 48 not taken. ✗ Branch 48 → 49 not taken. ✓ Branch 48 → 50 taken 7716 times. ✗ Branch 50 → 51 not taken. ✓ Branch 50 → 52 taken 7716 times.	23148	allocate (cols(0:bspline2%degree))
78	6/12 ✗ Branch 52 → 53 not taken. ✓ Branch 52 → 54 taken 7716 times. ✓ Branch 54 → 53 taken 7716 times. ✗ Branch 54 → 55 not taken. ✓ Branch 55 → 56 taken 7716 times. ✗ Branch 55 → 57 not taken. ✓ Branch 57 → 58 taken 7716 times. ✗ Branch 57 → 59 not taken. ✗ Branch 59 → 60 not taken. ✓ Branch 59 → 61 taken 7716 times. ✗ Branch 61 → 62 not taken. ✓ Branch 61 → 63 taken 7716 times.	23148	allocate (rows(0:bspline1%degree))
79
80	6/12 ✗ Branch 63 → 64 not taken. ✓ Branch 63 → 65 taken 7716 times. ✓ Branch 65 → 64 taken 7716 times. ✗ Branch 65 → 66 not taken. ✓ Branch 66 → 67 taken 7716 times. ✗ Branch 66 → 68 not taken. ✓ Branch 68 → 69 taken 7716 times. ✗ Branch 68 → 70 not taken. ✗ Branch 70 → 71 not taken. ✓ Branch 70 → 72 taken 7716 times. ✗ Branch 72 → 73 not taken. ✓ Branch 72 → 74 taken 7716 times.	23148	allocate (coordfun_vals(1:n_quad))
81	2/2 ✓ Branch 74 → 75 taken 39116 times. ✓ Branch 74 → 76 taken 7716 times.	46832	coordfun_vals = 1._wp
82
83	4/8 ✗ Branch 76 → 77 not taken. ✓ Branch 76 → 78 taken 7716 times. ✓ Branch 78 → 77 taken 7716 times. ✗ Branch 78 → 79 not taken. ✗ Branch 79 → 80 not taken. ✓ Branch 79 → 81 taken 7716 times. ✗ Branch 81 → 82 not taken. ✓ Branch 81 → 83 taken 7716 times.	15432	allocate (bspline1_vals(1:n_quad))
84
85			equal_spaces = size(bspline1) == size(bspline2) .and. &
86			(bspline1%is_scaled .eqv. bspline2%is_scaled) .and. &
87	2/4 ✓ Branch 83 → 84 taken 7716 times. ✗ Branch 83 → 85 not taken. ✗ Branch 84 → 85 not taken. ✓ Branch 84 → 86 taken 7716 times.	7716	(bspline1%is_periodic .eqv. bspline2%is_periodic)
88
89	1/2 ✗ Branch 87 → 88 not taken. ✓ Branch 87 → 90 taken 7716 times.	7716	PetscCall(MatSetFromOptions(M, ierr))
90	1/2 ✓ Branch 90 → 91 taken 7716 times. ✗ Branch 90 → 97 not taken.	7716	if (equal_spaces) then
91	1/2 ✗ Branch 92 → 93 not taken. ✓ Branch 92 → 94 taken 7716 times.	7716	PetscCall(MatSetOption(M, MAT_SYMMETRIC, PETSC_TRUE, ierr))
92	1/2 ✗ Branch 95 → 96 not taken. ✓ Branch 95 → 97 taken 7716 times.	7716	PetscCall(MatSetOption(M, MAT_SPD, PETSC_TRUE, ierr))
93			end if
94	1/2 ✗ Branch 98 → 99 not taken. ✓ Branch 98 → 100 taken 7716 times.	7716	PetscCall(MatSetUp(M, ierr))
95
96	2/2 ✓ Branch 101 → 102 taken 172270 times. ✓ Branch 101 → 175 taken 7716 times.	179986	do i = 0, bspline1%nr_intervals - 1
97	1/2 ✗ Branch 102 → 103 not taken. ✓ Branch 102 → 107 taken 172270 times.	172270	if (present(coordfun)) then
98		✗	do ndx = 1, n_quad
99		✗	x = (i + .5_wp + bspline1_quad%nodes(ndx) / 2) * bspline1_quad%bspline%h
100		✗	coordfun_vals(ndx) = coordfun(x)
101			end do
102			end if
103	2/2 ✓ Branch 108 → 109 taken 860030 times. ✓ Branch 108 → 149 taken 172270 times.	1032300	do j1_minus_i = 0, bspline1%degree
104		860030	call get_internal_and_actual_inds(bspline1, i, j1_minus_i, j1, j1_internal, bspline_mirrored_1)
105	2/2 ✓ Branch 110 → 111 taken 52765 times. ✓ Branch 110 → 119 taken 807265 times.	860030	if (bspline_mirrored_1) then
106	4/8 ✓ Branch 111 → 112 taken 52765 times. ✗ Branch 111 → 113 not taken. ✗ Branch 112 → 113 not taken. ✓ Branch 112 → 116 taken 52765 times. ✗ Branch 113 → 114 not taken. ✗ Branch 113 → 115 not taken. ✓ Branch 117 → 118 taken 372215 times. ✓ Branch 117 → 127 taken 52765 times.	477745	bspline1_vals = bspline1_quad%bspline_at_nodes(j1_internal, bspline1%degree - j1_minus_i)%data(n_quad:1:-1)
107			else
108	4/8 ✓ Branch 119 → 120 taken 807265 times. ✗ Branch 119 → 121 not taken. ✗ Branch 120 → 121 not taken. ✓ Branch 120 → 124 taken 807265 times. ✗ Branch 121 → 122 not taken. ✗ Branch 121 → 123 not taken. ✓ Branch 125 → 126 taken 4206223 times. ✓ Branch 125 → 127 taken 807265 times.	5820753	bspline1_vals = bspline1_quad%bspline_at_nodes(j1_internal, j1_minus_i)%data(1:n_quad)
109			end if
110	3/4 ✗ Branch 127 → 128 not taken. ✓ Branch 127 → 129 taken 860030 times. ✓ Branch 130 → 131 taken 4578438 times. ✓ Branch 130 → 132 taken 860030 times.	6298498	bspline1_vals = bspline1_vals * bspline1_quad%weights
111
112	1/2 ✗ Branch 132 → 133 not taken. ✓ Branch 132 → 134 taken 860030 times.	860030	if (equal_spaces) then
113			j2_minus_i_max = j1_minus_i
114			else
115			j2_minus_i_max = bspline2%degree
116			end if
117	2/2 ✓ Branch 135 → 136 taken 2719234 times. ✓ Branch 135 → 147 taken 860030 times.	3579264	do j2_minus_i = 0, j2_minus_i_max
118		2719234	call get_internal_and_actual_inds(bspline2, i, j2_minus_i, j2, j2_internal, bspline_mirrored_2)
119
120			val = 0._wp
121	2/2 ✓ Branch 137 → 138 taken 141660 times. ✓ Branch 137 → 140 taken 2577574 times.	2719234	if (bspline_mirrored_2) then
122	2/2 ✓ Branch 138 → 139 taken 1051512 times. ✓ Branch 138 → 143 taken 141660 times.	1193172	do ndx = 1, n_quad
123			val = val + coordfun_vals(ndx) * bspline1_vals(ndx) *&
124		1193172	& bspline2_quad%bspline_at_nodes(j2_internal, bspline2%degree - j2_minus_i)%data(n_quad + 1 - ndx)
125			end do
126			else
127	2/2 ✓ Branch 140 → 141 taken 2577574 times. ✓ Branch 140 → 142 taken 14277136 times.	16854710	do ndx = 1, n_quad
128			val = val + coordfun_vals(ndx) * bspline1_vals(ndx) * &
129		16854710	& bspline2_quad%bspline_at_nodes(j2_internal, j2_minus_i)%data(ndx)
130			end do
131			end if
132
133		2719234	vals(j2_minus_i, j1_minus_i) = val
134	2/2 ✓ Branch 144 → 145 taken 860030 times. ✓ Branch 144 → 146 taken 1859204 times.	6298498	if (j1_minus_i == bspline1%degree) then
135		860030	cols(j2_minus_i) = j2
136			end if
137			end do
138
139		1892330	rows(j1_minus_i) = j1
140			end do
141
142	1/2 ✓ Branch 150 → 151 taken 172270 times. ✗ Branch 150 → 159 not taken.	172270	if (equal_spaces) then
143	2/2 ✓ Branch 152 → 153 taken 860030 times. ✓ Branch 152 → 158 taken 172270 times.	1032300	do j1_minus_i = 0, bspline1%degree
144	2/2 ✓ Branch 154 → 155 taken 1859204 times. ✓ Branch 154 → 156 taken 860030 times.	2891504	do j2_minus_i = j1_minus_i + 1, bspline2%degree
145		2719234	vals(j2_minus_i, j1_minus_i) = vals(j1_minus_i, j2_minus_i)
146			end do
147			end do
148			end if
149
150			! NOTE: vals is transposed for fast acces, this means the role of rows and cols is swapped
151	9/12 ✗ Branch 159 → 160 not taken. ✓ Branch 159 → 161 taken 172270 times. ✓ Branch 161 → 162 taken 860030 times. ✓ Branch 161 → 166 taken 172270 times. ✓ Branch 163 → 164 taken 4578438 times. ✓ Branch 163 → 165 taken 860030 times. ✓ Branch 166 → 167 taken 172270 times. ✗ Branch 166 → 168 not taken. ✓ Branch 169 → 170 taken 4578438 times. ✓ Branch 169 → 171 taken 172270 times. ✗ Branch 172 → 173 not taken. ✓ Branch 172 → 174 taken 172270 times.	10196892	PetscCall(MatSetValues(M, size(cols), cols, size(rows), rows, [vals(:, :)], ADD_VALUES, ierr))
152			end do
153
154	1/2 ✗ Branch 176 → 177 not taken. ✓ Branch 176 → 178 taken 7716 times.	7716	deallocate (vals)
155	1/2 ✗ Branch 178 → 179 not taken. ✓ Branch 178 → 180 taken 7716 times.	7716	deallocate (cols)
156	1/2 ✗ Branch 180 → 181 not taken. ✓ Branch 180 → 182 taken 7716 times.	7716	deallocate (rows)
157
158	1/2 ✗ Branch 182 → 183 not taken. ✓ Branch 182 → 184 taken 7716 times.	7716	deallocate (coordfun_vals)
159
160	1/2 ✗ Branch 184 → 185 not taken. ✓ Branch 184 → 186 taken 7716 times.	7716	deallocate (bspline1_vals)
161
162	1/2 ✗ Branch 187 → 188 not taken. ✓ Branch 187 → 190 taken 7716 times.	7716	PetscCall(MatAssemblyBegin(M, MAT_FINAL_ASSEMBLY, ierr))
163	1/2 ✗ Branch 191 → 192 not taken. ✓ Branch 191 → 193 taken 7716 times.	7716	PetscCall(MatAssemblyEnd(M, MAT_FINAL_ASSEMBLY, ierr))
164
165	11/22 ✗ Branch 193 → 194 not taken. ✓ Branch 193 → 195 taken 7716 times. ✗ Branch 195 → 196 not taken. ✓ Branch 195 → 197 taken 7716 times. ✗ Branch 197 → 198 not taken. ✓ Branch 197 → 199 taken 7716 times. ✗ Branch 199 → 200 not taken. ✓ Branch 199 → 201 taken 7716 times. ✓ Branch 201 → 202 taken 7716 times. ✗ Branch 201 → 203 not taken. ✓ Branch 203 → 204 taken 7716 times. ✗ Branch 203 → 205 not taken. ✓ Branch 205 → 206 taken 7716 times. ✗ Branch 205 → 207 not taken. ✗ Branch 207 → 208 not taken. ✓ Branch 207 → 209 taken 7716 times. ✓ Branch 209 → 210 taken 7716 times. ✗ Branch 209 → 211 not taken. ✓ Branch 211 → 212 taken 7716 times. ✗ Branch 211 → 213 not taken. ✓ Branch 213 → 214 taken 7716 times. ✗ Branch 213 → 215 not taken.	7716	end subroutine mass_matrix_1d
166
167			!> @brief Compute the difference matrix (consisting of a '1' and a '-1' for each row) of a 1D B-spline space
168			!>
169			!> @param[out] D The difference matrix
170			!> @param[in] bspline The B-spline space
171		48	subroutine difference_matrix(D, bspline)
172			use m_common, only: wp
173			use m_bspline_basis, only: BSplineSpace, size
174			implicit none
175
176			Mat, intent(out) :: D
177			type(BSplineSpace), intent(in) :: bspline
178
179			integer :: n_basis, ierr, row, c0, c1, n_rows
180			integer :: local_nz_per_row, nonlocal_nz_per_row
181
182		48	n_basis = size(bspline)
183
184	1/2 ✓ Branch 2 → 3 taken 48 times. ✗ Branch 2 → 4 not taken.	48	if (.not. bspline%is_periodic) then
185		48	n_rows = n_basis - 1
186			else
187		✗	n_rows = n_basis
188			end if
189
190		48	local_nz_per_row = 2
191		48	nonlocal_nz_per_row = 0 ! NOTE: currently sequential
192
193			! Create a sparse matrix
194			call MatCreateAIJ(PETSC_COMM_SELF, n_rows, n_basis, n_rows, &
195			& n_basis, local_nz_per_row, PETSC_NULL_INTEGER_ARRAY, nonlocal_nz_per_row,&
196	1/2 ✗ Branch 6 → 7 not taken. ✓ Branch 6 → 8 taken 48 times.	48	& PETSC_NULL_INTEGER_ARRAY, D, ierr); CHKERRQ(ierr)
197
198	1/2 ✗ Branch 9 → 10 not taken. ✓ Branch 9 → 11 taken 48 times.	48	PetscCall(MatSetFromOptions(D, ierr))
199	1/2 ✗ Branch 12 → 13 not taken. ✓ Branch 12 → 14 taken 48 times.	48	PetscCall(MatSetUp(D, ierr))
200
201			! Set the values of the matrix
202	2/2 ✓ Branch 15 → 16 taken 1680 times. ✓ Branch 15 → 25 taken 48 times.	1728	do row = 0, n_rows - 1
203			c0 = row
204		1680	c1 = mod(row + 1, n_basis)
205
206	5/6 ✓ Branch 17 → 18 taken 1680 times. ✓ Branch 17 → 19 taken 1680 times. ✓ Branch 20 → 21 taken 3360 times. ✓ Branch 20 → 22 taken 1680 times. ✓ Branch 23 → 15 taken 1680 times. ✗ Branch 23 → 24 not taken.	6768	PetscCall(MatSetValues(D, 1, [row], 2, [c0, c1], [-1._wp, +1._wp], INSERT_VALUES, ierr))
207			end do
208
209	1/2 ✗ Branch 27 → 28 not taken. ✓ Branch 27 → 29 taken 48 times.	48	PetscCall(MatAssemblyBegin(D, MAT_FINAL_ASSEMBLY, ierr))
210	1/2 ✗ Branch 30 → 31 not taken. ✓ Branch 30 → 32 taken 48 times.	48	PetscCall(MatAssemblyEnd(D, MAT_FINAL_ASSEMBLY, ierr))
211			end subroutine
212
213			!> @brief Compute the divgrad (Laplace) matrix of a 1D B-spline space
214			!>
215			!> @param[out] The resulting Laplace matrix
216			!> @param[in] bspline The B-spline space
217			!> @param[in] dbspline The derivative B-spline space
218		96	subroutine divgrad_matrix_1d(L, bspline, dbspline)
219			use m_common, only: wp
220			use m_bspline_basis, only: BSplineSpace, size
221
222			implicit none
223
224			Mat, intent(out) :: L
225			type(BSplineSpace), intent(in) :: bspline, dbspline
226
227			Mat :: D, M
228			Vec :: nullspace_vec
229			MatNullSpace :: nullspace
230			integer :: ierr
231			integer :: n_basis, dn_basis, i
232			real(wp) :: tmp
233			real(wp) :: EXPECTED_FILL_RATIO = 1.0_wp
234
235		48	n_basis = size(bspline)
236			dn_basis = size(dbspline)
237
238		48	call mass_matrix(M, dbspline, dbspline)
239		48	call difference_matrix(D, bspline)
240
241	1/2 ✗ Branch 5 → 6 not taken. ✓ Branch 5 → 7 taken 48 times.	48	PetscCall(MatPtAP(M, D, MAT_INITIAL_MATRIX, EXPECTED_FILL_RATIO, L, ierr))
242
243	1/2 ✗ Branch 8 → 9 not taken. ✓ Branch 8 → 10 taken 48 times.	48	PetscCall(MatDestroy(M, ierr))
244	1/2 ✗ Branch 11 → 12 not taken. ✓ Branch 11 → 13 taken 48 times.	48	PetscCall(MatDestroy(D, ierr))
245
246			! The Laplace matrix still has a nullspace (no boundary conditions are imposed)
247	1/2 ✗ Branch 14 → 15 not taken. ✓ Branch 14 → 16 taken 48 times.	48	PetscCall(VecCreate(PETSC_COMM_SELF, nullspace_vec, ierr))
248	1/2 ✗ Branch 17 → 18 not taken. ✓ Branch 17 → 19 taken 48 times.	48	PetscCall(VecSetSizes(nullspace_vec, n_basis, n_basis, ierr))
249	1/2 ✗ Branch 20 → 21 not taken. ✓ Branch 20 → 22 taken 48 times.	48	PetscCall(VecSetFromOptions(nullspace_vec, ierr))
250	2/2 ✓ Branch 23 → 24 taken 1728 times. ✓ Branch 23 → 28 taken 48 times.	1776	do i = 0, n_basis - 1
251	1/2 ✗ Branch 25 → 26 not taken. ✓ Branch 25 → 27 taken 1728 times.	1776	PetscCall(VecSetValue(nullspace_vec, i, 1._wp, INSERT_VALUES, ierr))
252			end do
253	1/2 ✗ Branch 30 → 31 not taken. ✓ Branch 30 → 32 taken 48 times.	48	PetscCall(VecNormalize(nullspace_vec, tmp, ierr))
254
255	1/2 ✗ Branch 33 → 34 not taken. ✓ Branch 33 → 35 taken 48 times.	48	PetscCall(VecAssemblyBegin(nullspace_vec, ierr))
256	1/2 ✗ Branch 36 → 37 not taken. ✓ Branch 36 → 38 taken 48 times.	48	PetscCall(VecAssemblyEnd(nullspace_vec, ierr))
257
258	3/4 ✓ Branch 39 → 40 taken 48 times. ✓ Branch 39 → 41 taken 48 times. ✗ Branch 42 → 43 not taken. ✓ Branch 42 → 44 taken 48 times.	96	PetscCall(MatNullSpaceCreate(PETSC_COMM_SELF, PETSC_FALSE, 1, [nullspace_vec], nullspace, ierr))
259
260	1/2 ✗ Branch 45 → 46 not taken. ✓ Branch 45 → 47 taken 48 times.	48	PetscCall(MatSetNullSpace(L, nullspace, ierr))
261	1/2 ✗ Branch 48 → 49 not taken. ✓ Branch 48 → 50 taken 48 times.	48	PetscCall(MatNullSpaceDestroy(nullspace, ierr))
262
263		48	end subroutine divgrad_matrix_1d
264			end module m_bspline_matrix
265