coord_transform/s_coord_transform_toroidal_bspline.f90

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    coord_transform/s_coord_transform_toroidal_bspline.f90
    
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        Exec
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        !> @file s_coord_transform_toroidal_bspline.f90
      
        !> @brief Submodule implementing ToroidalBSplineTransform methods
      
        submodule(m_coord_transform_toroidal_bspline) s_coord_transform_toroidal_bspline
      
          implicit none
      
        contains
      
        7
          module function init_ToroidalBSplineTransform(major_radius, minor_radius, bspline) result(this)
      
            use m_bspline_linalg, only: l2_projection
      
            real(wp), intent(in) :: major_radius, minor_radius
      
            type(BSplineSpace), intent(in) :: bspline
      
            type(ToroidalBSplineTransform) :: this
      
        7
            this%major_radius = major_radius
      
        7
            this%minor_radius = minor_radius
      
        7
            this%is_orthogonal = .false.
      
        7
            this%has_polar_xy_singularity = .true.
      
            ! TODO why not allow for clamped B-splines?
      
        7
            if (.not. bspline%is_periodic) then
      
              write (*, '(A)') "ERROR in ToroidalBSplineTransform: B-spline basis must be periodic. " &
      
        ✗
                //"Clamped B-splines are not supported for toroidal B-spline transformations."
      
        ✗
              error stop 1
      
            end if
      
        7
            call l2_projection(this%cos_bspline, bspline, cosine)
      
        7
            call l2_projection(this%sin_bspline, bspline, sine)
      
            ! NOTE: L2 projection should preserve the integral value, but we enforce zero mean anyways (in agreement with the polar
      
            ! NOTE regularity constraint)
      
            this%cos_bspline%data = this%cos_bspline%data - sum(this%cos_bspline%data(0:this%cos_bspline%bspline%nr_bsplines - 1)) / &
      
          4/4✓ Branch 10 → 11 taken 88 times.
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✓ Branch 13 → 14 taken 103 times.
✓ Branch 13 → 15 taken 7 times.

        198
                                    this%cos_bspline%bspline%nr_bsplines
      
            this%sin_bspline%data = this%sin_bspline%data - sum(this%sin_bspline%data(0:this%sin_bspline%bspline%nr_bsplines - 1)) / &
      
          5/6✗ Branch 2 → 3 not taken.
✓ Branch 2 → 7 taken 7 times.
✓ Branch 16 → 17 taken 88 times.
✓ Branch 16 → 18 taken 7 times.
✓ Branch 19 → 20 taken 103 times.
✓ Branch 19 → 21 taken 7 times.

        205
                                    this%sin_bspline%bspline%nr_bsplines
      
          contains
      
        292
            pure real(wp) function cosine(yp) result(ans)
      
              real(wp), intent(in) :: yp
      
        292
              ans = cos(2 * pi * yp)
      
        292
            end function cosine
      
        292
            pure real(wp) function sine(yp) result(ans)
      
              real(wp), intent(in) :: yp
      
        292
              ans = sin(2 * pi * yp)
      
        292
            end function sine
      
          end function init_ToroidalBSplineTransform
      
        1800
          module procedure toroidal_bspline_transform
      
          !$acc routine seq
      
        2400
          select case (i)
      
          case (1)
      
        600
            ans = (this%major_radius + this%minor_radius * xp * evaluate(this%sin_bspline, yp)) * cos(2 * pi * zp)
      
          case (2)
      
        600
            ans = (this%major_radius + this%minor_radius * xp * evaluate(this%sin_bspline, yp)) * sin(2 * pi * zp)
      
          case (3)
      
          3/4✓ Branch 2 → 3 taken 600 times.
✓ Branch 2 → 4 taken 600 times.
✓ Branch 2 → 5 taken 600 times.
✗ Branch 2 → 6 not taken.

        1800
            ans = this%minor_radius * xp * evaluate(this%cos_bspline, yp)
      
          end select
      
        1800
          end procedure toroidal_bspline_transform
      
        ✗
          module procedure toroidal_bspline_inverse_transform
      
          !$acc routine seq
      
          ! character(len=256) :: error_msg
      
          ! write (error_msg, '(A)') "ERROR in ToroidalBSplineTransform::inverse_transform: inverse transform is not implemented. " &
      
          !   //"Consider using the analytical ToroidalTransform instead if inverse transformation is required."
      
          ! error stop error_msg
      
          ans = 0._wp
      
        ✗
          end procedure toroidal_bspline_inverse_transform
      
        70326964
          module procedure toroidal_bspline_jacobian
      
          !$acc routine seq
      
          ans = xp * 2 * pi * this%minor_radius**2 * toroidal_twopi(this, yp) * (this%major_radius + this%minor_radius * xp *&
      
        70326964
            & evaluate(this%sin_bspline, yp))
      
        70326964
          end procedure toroidal_bspline_jacobian
      
        96595316
          module procedure toroidal_twopi
      
          !$acc routine seq
      
          ans = evaluate(this%cos_bspline, yp) * evaluate(this%sin_bspline, yp, derivative=.true.) &
      
        96595316
                - evaluate(this%sin_bspline, yp) * evaluate(this%cos_bspline, yp, derivative=.true.)
      
        96595316
          end procedure toroidal_twopi
      
        5100
          module procedure toroidal_bspline_jacobian_matrix
      
          !$acc routine seq
      
        6800
          select case (i)
      
          case (1)
      
        4000
            select case (j)
      
            case (1)
      
        600
              ans = this%minor_radius * evaluate(this%sin_bspline, yp) * cos(2 * pi * zp)
      
            case (2)
      
        600
              ans = this%minor_radius * xp * evaluate(this%sin_bspline, yp, derivative=.true.) * cos(2 * pi * zp)
      
            case (3)
      
          3/4✗ Branch 4 → 3 not taken.
✓ Branch 4 → 5 taken 600 times.
✓ Branch 4 → 6 taken 600 times.
✓ Branch 4 → 7 taken 500 times.

        1700
              ans = -2 * pi * (this%major_radius + this%minor_radius * xp * evaluate(this%sin_bspline, yp)) * sin(2 * pi * zp)
      
            end select
      
          case (2)
      
        4000
            select case (j)
      
            case (1)
      
        600
              ans = this%minor_radius * evaluate(this%sin_bspline, yp) * sin(2 * pi * zp)
      
            case (2)
      
        600
              ans = this%minor_radius * xp * evaluate(this%sin_bspline, yp, derivative=.true.) * sin(2 * pi * zp)
      
            case (3)
      
          3/4✗ Branch 8 → 3 not taken.
✓ Branch 8 → 9 taken 600 times.
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✓ Branch 8 → 11 taken 500 times.

        1700
              ans = 2 * pi * (this%major_radius + this%minor_radius * xp * evaluate(this%sin_bspline, yp)) * cos(2 * pi * zp)
      
            end select
      
          case (3)
      
          3/4✗ Branch 2 → 3 not taken.
✓ Branch 2 → 4 taken 1700 times.
✓ Branch 2 → 8 taken 1700 times.
✓ Branch 2 → 12 taken 1700 times.

        5100
            select case (j)
      
            case (1)
      
        600
              ans = this%minor_radius * evaluate(this%cos_bspline, yp)
      
            case (2)
      
        600
              ans = this%minor_radius * xp * evaluate(this%cos_bspline, yp, derivative=.true.)
      
            case (3)
      
          3/4✗ Branch 12 → 3 not taken.
✓ Branch 12 → 13 taken 600 times.
✓ Branch 12 → 14 taken 600 times.
✓ Branch 12 → 15 taken 500 times.

        1700
              ans = 0._wp
      
            end select
      
          end select
      
        5100
          end procedure toroidal_bspline_jacobian_matrix
      
        900
          module procedure toroidal_bspline_jacobian_matrix_inv
      
          !$acc routine seq
      
          integer :: k
      
          real(wp) :: tmp
      
          ! We use the identity: J^-1 = G^-1 * J^T
      
          ans = 0._wp
      
          2/2✓ Branch 3 → 4 taken 2700 times.
✓ Branch 3 → 7 taken 900 times.

        3600
          do k = 1, 3
      
        2700
            tmp = toroidal_bspline_G_matrix_inv(this, i, k, xp, yp, zp)
      
          2/2✓ Branch 4 → 5 taken 1500 times.
✓ Branch 4 → 6 taken 1200 times.

        3600
            if (tmp /= 0._wp) then
      
        1500
              ans = ans + tmp * toroidal_bspline_jacobian_matrix(this, j, k, xp, yp, zp)
      
            end if
      
          end do
      
        900
          end procedure toroidal_bspline_jacobian_matrix_inv
      
        50375556
          module procedure toroidal_bspline_G_matrix
      
          !$acc routine seq
      
        69811824
          select case (i)
      
          case (1)
      
        42449884
            select case (j)
      
            case (1)
      
        6221764
              ans = this%minor_radius**2 * (evaluate(this%cos_bspline, yp)**2 + evaluate(this%sin_bspline, yp)**2)
      
            case (2)
      
              ans = this%minor_radius**2 * xp * &
      
                & (evaluate(this%cos_bspline, yp) * evaluate(this%cos_bspline, yp, derivative=.true.) + &
      
        6607252
                & evaluate(this%sin_bspline, yp) * evaluate(this%sin_bspline, yp, derivative=.true.))
      
            case (3)
      
          3/4✓ Branch 3 → 4 taken 6221764 times.
✓ Branch 3 → 5 taken 6607252 times.
✓ Branch 3 → 10 taken 6607252 times.
✗ Branch 3 → 12 not taken.

        19436268
              ans = 0._wp
      
            end select
      
          case (2)
      
        34902124
            select case (j)
      
            case (1)
      
              ans = this%minor_radius**2 * xp * &
      
                & (evaluate(this%cos_bspline, yp) * evaluate(this%cos_bspline, yp, derivative=.true.) + &
      
        3962836
                & evaluate(this%sin_bspline, yp) * evaluate(this%sin_bspline, yp, derivative=.true.))
      
            case (2)
      
              ans = (this%minor_radius * xp)**2 * (evaluate(this%cos_bspline, yp, derivative=.true.)**2 + &
      
        6221764
                & evaluate(this%sin_bspline, yp, derivative=.true.)**2)
      
            case (3)
      
          3/4✓ Branch 6 → 7 taken 3962836 times.
✓ Branch 6 → 8 taken 6221764 times.
✓ Branch 6 → 10 taken 6607252 times.
✗ Branch 6 → 12 not taken.

        16791852
              ans = 0._wp
      
            end select
      
          case (3)
      
          3/4✓ Branch 2 → 3 taken 19436268 times.
✓ Branch 2 → 6 taken 16791852 times.
✓ Branch 2 → 9 taken 14147436 times.
✗ Branch 2 → 12 not taken.

        50375556
            select case (j)
      
            case (1)
      
              ans = 0._wp
      
            case (2)
      
        6221764
              ans = 0._wp
      
            case (3)
      
          2/3✓ Branch 9 → 10 taken 7925672 times.
✓ Branch 9 → 11 taken 6221764 times.
✗ Branch 9 → 12 not taken.

        14147436
              ans = (2 * pi * (this%major_radius + this%minor_radius * xp * evaluate(this%sin_bspline, yp)))**2
      
            end select
      
          end select
      
        50375556
          end procedure toroidal_bspline_G_matrix
      
        57825936
          module procedure toroidal_bspline_G_matrix_inv
      
          !$acc routine seq
      
        79745664
          select case (i)
      
          case (1)
      
        48188080
            select case (j)
      
            case (1)
      
              ans = (evaluate(this%cos_bspline, yp, derivative=.true.)**2 + &
      
                & evaluate(this%sin_bspline, yp, derivative=.true.)**2) / &
      
        6993040
                & (toroidal_twopi(this, yp)**2 * this%minor_radius**2)
      
            case (2)
      
              ans = -(evaluate(this%cos_bspline, yp) * evaluate(this%cos_bspline, yp, derivative=.true.) + evaluate(this%sin_bspline, yp)&
      
        7463344
                     & * evaluate(this%sin_bspline, yp, derivative=.true.)) / (toroidal_twopi(this, yp)**2 * this%minor_radius**2 * xp)
      
            case (3)
      
          3/4✓ Branch 3 → 4 taken 6993040 times.
✓ Branch 3 → 5 taken 7463344 times.
✓ Branch 3 → 10 taken 7463344 times.
✗ Branch 3 → 12 not taken.

        21919728
              ans = 0._wp
      
            end select
      
          case (2)
      
        40725136
            select case (j)
      
            case (1)
      
              ans = -(evaluate(this%cos_bspline, yp) * evaluate(this%cos_bspline, yp, derivative=.true.) + &
      
                & evaluate(this%sin_bspline, yp) *&
      
        4818928
                & evaluate(this%sin_bspline, yp, derivative=.true.)) / (toroidal_twopi(this, yp)**2 * this%minor_radius**2 * xp)
      
            case (2)
      
              ans = (evaluate(this%cos_bspline, yp)**2 + evaluate(this%sin_bspline, yp)**2) / &
      
        6993040
                & (toroidal_twopi(this, yp)**2 * this%minor_radius**2 * xp**2)
      
            case (3)
      
          3/4✓ Branch 6 → 7 taken 4818928 times.
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        19275312
              ans = 0._wp
      
            end select
      
          case (3)
      
          3/4✓ Branch 2 → 3 taken 21919728 times.
✓ Branch 2 → 6 taken 19275312 times.
✓ Branch 2 → 9 taken 16630896 times.
✗ Branch 2 → 12 not taken.

        57825936
            select case (j)
      
            case (1)
      
              ans = 0._wp
      
            case (2)
      
        6993040
              ans = 0._wp
      
            case (3)
      
          2/3✓ Branch 9 → 10 taken 9637856 times.
✓ Branch 9 → 11 taken 6993040 times.
✗ Branch 9 → 12 not taken.

        16630896
              ans = 1 / (2 * pi * (this%major_radius + this%minor_radius * xp * evaluate(this%sin_bspline, yp)))**2
      
            end select
      
          end select
      
        57825936
          end procedure toroidal_bspline_G_matrix_inv
      
        end submodule s_coord_transform_toroidal_bspline

Line	Branch	Exec	Source
1			!> @file s_coord_transform_toroidal_bspline.f90
2			!> @brief Submodule implementing ToroidalBSplineTransform methods
3			submodule(m_coord_transform_toroidal_bspline) s_coord_transform_toroidal_bspline
4			implicit none
5
6			contains
7
8		7	module function init_ToroidalBSplineTransform(major_radius, minor_radius, bspline) result(this)
9			use m_bspline_linalg, only: l2_projection
10
11			real(wp), intent(in) :: major_radius, minor_radius
12			type(BSplineSpace), intent(in) :: bspline
13			type(ToroidalBSplineTransform) :: this
14
15		7	this%major_radius = major_radius
16		7	this%minor_radius = minor_radius
17		7	this%is_orthogonal = .false.
18		7	this%has_polar_xy_singularity = .true.
19
20			! TODO why not allow for clamped B-splines?
21		7	if (.not. bspline%is_periodic) then
22			write (*, '(A)') "ERROR in ToroidalBSplineTransform: B-spline basis must be periodic. " &
23		✗	//"Clamped B-splines are not supported for toroidal B-spline transformations."
24		✗	error stop 1
25			end if
26
27		7	call l2_projection(this%cos_bspline, bspline, cosine)
28		7	call l2_projection(this%sin_bspline, bspline, sine)
29
30			! NOTE: L2 projection should preserve the integral value, but we enforce zero mean anyways (in agreement with the polar
31			! NOTE regularity constraint)
32			this%cos_bspline%data = this%cos_bspline%data - sum(this%cos_bspline%data(0:this%cos_bspline%bspline%nr_bsplines - 1)) / &
33	4/4 ✓ Branch 10 → 11 taken 88 times. ✓ Branch 10 → 12 taken 7 times. ✓ Branch 13 → 14 taken 103 times. ✓ Branch 13 → 15 taken 7 times.	198	this%cos_bspline%bspline%nr_bsplines
34			this%sin_bspline%data = this%sin_bspline%data - sum(this%sin_bspline%data(0:this%sin_bspline%bspline%nr_bsplines - 1)) / &
35	5/6 ✗ Branch 2 → 3 not taken. ✓ Branch 2 → 7 taken 7 times. ✓ Branch 16 → 17 taken 88 times. ✓ Branch 16 → 18 taken 7 times. ✓ Branch 19 → 20 taken 103 times. ✓ Branch 19 → 21 taken 7 times.	205	this%sin_bspline%bspline%nr_bsplines
36			contains
37		292	pure real(wp) function cosine(yp) result(ans)
38			real(wp), intent(in) :: yp
39		292	ans = cos(2 * pi * yp)
40		292	end function cosine
41
42		292	pure real(wp) function sine(yp) result(ans)
43			real(wp), intent(in) :: yp
44		292	ans = sin(2 * pi * yp)
45		292	end function sine
46			end function init_ToroidalBSplineTransform
47
48		1800	module procedure toroidal_bspline_transform
49			!$acc routine seq
50		2400	select case (i)
51			case (1)
52		600	ans = (this%major_radius + this%minor_radius * xp * evaluate(this%sin_bspline, yp)) * cos(2 * pi * zp)
53			case (2)
54		600	ans = (this%major_radius + this%minor_radius * xp * evaluate(this%sin_bspline, yp)) * sin(2 * pi * zp)
55			case (3)
56	3/4 ✓ Branch 2 → 3 taken 600 times. ✓ Branch 2 → 4 taken 600 times. ✓ Branch 2 → 5 taken 600 times. ✗ Branch 2 → 6 not taken.	1800	ans = this%minor_radius * xp * evaluate(this%cos_bspline, yp)
57			end select
58		1800	end procedure toroidal_bspline_transform
59
60		✗	module procedure toroidal_bspline_inverse_transform
61			!$acc routine seq
62			! character(len=256) :: error_msg
63
64			! write (error_msg, '(A)') "ERROR in ToroidalBSplineTransform::inverse_transform: inverse transform is not implemented. " &
65			! //"Consider using the analytical ToroidalTransform instead if inverse transformation is required."
66			! error stop error_msg
67			ans = 0._wp
68		✗	end procedure toroidal_bspline_inverse_transform
69
70		70326964	module procedure toroidal_bspline_jacobian
71			!$acc routine seq
72			ans = xp * 2 * pi * this%minor_radius*2 toroidal_twopi(this, yp) * (this%major_radius + this%minor_radius * xp *&
73		70326964	& evaluate(this%sin_bspline, yp))
74		70326964	end procedure toroidal_bspline_jacobian
75
76		96595316	module procedure toroidal_twopi
77			!$acc routine seq
78			ans = evaluate(this%cos_bspline, yp) * evaluate(this%sin_bspline, yp, derivative=.true.) &
79		96595316	- evaluate(this%sin_bspline, yp) * evaluate(this%cos_bspline, yp, derivative=.true.)
80		96595316	end procedure toroidal_twopi
81
82		5100	module procedure toroidal_bspline_jacobian_matrix
83			!$acc routine seq
84		6800	select case (i)
85			case (1)
86		4000	select case (j)
87			case (1)
88		600	ans = this%minor_radius * evaluate(this%sin_bspline, yp) * cos(2 * pi * zp)
89			case (2)
90		600	ans = this%minor_radius * xp * evaluate(this%sin_bspline, yp, derivative=.true.) * cos(2 * pi * zp)
91			case (3)
92	3/4 ✗ Branch 4 → 3 not taken. ✓ Branch 4 → 5 taken 600 times. ✓ Branch 4 → 6 taken 600 times. ✓ Branch 4 → 7 taken 500 times.	1700	ans = -2 * pi * (this%major_radius + this%minor_radius * xp * evaluate(this%sin_bspline, yp)) * sin(2 * pi * zp)
93			end select
94			case (2)
95		4000	select case (j)
96			case (1)
97		600	ans = this%minor_radius * evaluate(this%sin_bspline, yp) * sin(2 * pi * zp)
98			case (2)
99		600	ans = this%minor_radius * xp * evaluate(this%sin_bspline, yp, derivative=.true.) * sin(2 * pi * zp)
100			case (3)
101	3/4 ✗ Branch 8 → 3 not taken. ✓ Branch 8 → 9 taken 600 times. ✓ Branch 8 → 10 taken 600 times. ✓ Branch 8 → 11 taken 500 times.	1700	ans = 2 * pi * (this%major_radius + this%minor_radius * xp * evaluate(this%sin_bspline, yp)) * cos(2 * pi * zp)
102			end select
103			case (3)
104	3/4 ✗ Branch 2 → 3 not taken. ✓ Branch 2 → 4 taken 1700 times. ✓ Branch 2 → 8 taken 1700 times. ✓ Branch 2 → 12 taken 1700 times.	5100	select case (j)
105			case (1)
106		600	ans = this%minor_radius * evaluate(this%cos_bspline, yp)
107			case (2)
108		600	ans = this%minor_radius * xp * evaluate(this%cos_bspline, yp, derivative=.true.)
109			case (3)
110	3/4 ✗ Branch 12 → 3 not taken. ✓ Branch 12 → 13 taken 600 times. ✓ Branch 12 → 14 taken 600 times. ✓ Branch 12 → 15 taken 500 times.	1700	ans = 0._wp
111			end select
112			end select
113		5100	end procedure toroidal_bspline_jacobian_matrix
114
115		900	module procedure toroidal_bspline_jacobian_matrix_inv
116			!$acc routine seq
117			integer :: k
118			real(wp) :: tmp
119
120			! We use the identity: J^-1 = G^-1 * J^T
121			ans = 0._wp
122	2/2 ✓ Branch 3 → 4 taken 2700 times. ✓ Branch 3 → 7 taken 900 times.	3600	do k = 1, 3
123		2700	tmp = toroidal_bspline_G_matrix_inv(this, i, k, xp, yp, zp)
124	2/2 ✓ Branch 4 → 5 taken 1500 times. ✓ Branch 4 → 6 taken 1200 times.	3600	if (tmp /= 0._wp) then
125		1500	ans = ans + tmp * toroidal_bspline_jacobian_matrix(this, j, k, xp, yp, zp)
126			end if
127			end do
128		900	end procedure toroidal_bspline_jacobian_matrix_inv
129
130		50375556	module procedure toroidal_bspline_G_matrix
131			!$acc routine seq
132		69811824	select case (i)
133			case (1)
134		42449884	select case (j)
135			case (1)
136		6221764	ans = this%minor_radius*2 (evaluate(this%cos_bspline, yp)2 + evaluate(this%sin_bspline, yp)2)
137			case (2)
138			ans = this%minor_radius*2 xp * &
139			& (evaluate(this%cos_bspline, yp) * evaluate(this%cos_bspline, yp, derivative=.true.) + &
140		6607252	& evaluate(this%sin_bspline, yp) * evaluate(this%sin_bspline, yp, derivative=.true.))
141			case (3)
142	3/4 ✓ Branch 3 → 4 taken 6221764 times. ✓ Branch 3 → 5 taken 6607252 times. ✓ Branch 3 → 10 taken 6607252 times. ✗ Branch 3 → 12 not taken.	19436268	ans = 0._wp
143			end select
144			case (2)
145		34902124	select case (j)
146			case (1)
147			ans = this%minor_radius*2 xp * &
148			& (evaluate(this%cos_bspline, yp) * evaluate(this%cos_bspline, yp, derivative=.true.) + &
149		3962836	& evaluate(this%sin_bspline, yp) * evaluate(this%sin_bspline, yp, derivative=.true.))
150			case (2)
151			ans = (this%minor_radius * xp)*2 (evaluate(this%cos_bspline, yp, derivative=.true.)**2 + &
152		6221764	& evaluate(this%sin_bspline, yp, derivative=.true.)**2)
153			case (3)
154	3/4 ✓ Branch 6 → 7 taken 3962836 times. ✓ Branch 6 → 8 taken 6221764 times. ✓ Branch 6 → 10 taken 6607252 times. ✗ Branch 6 → 12 not taken.	16791852	ans = 0._wp
155			end select
156			case (3)
157	3/4 ✓ Branch 2 → 3 taken 19436268 times. ✓ Branch 2 → 6 taken 16791852 times. ✓ Branch 2 → 9 taken 14147436 times. ✗ Branch 2 → 12 not taken.	50375556	select case (j)
158			case (1)
159			ans = 0._wp
160			case (2)
161		6221764	ans = 0._wp
162			case (3)
163	2/3 ✓ Branch 9 → 10 taken 7925672 times. ✓ Branch 9 → 11 taken 6221764 times. ✗ Branch 9 → 12 not taken.	14147436	ans = (2 * pi * (this%major_radius + this%minor_radius * xp * evaluate(this%sin_bspline, yp)))**2
164			end select
165			end select
166		50375556	end procedure toroidal_bspline_G_matrix
167
168		57825936	module procedure toroidal_bspline_G_matrix_inv
169			!$acc routine seq
170		79745664	select case (i)
171			case (1)
172		48188080	select case (j)
173			case (1)
174			ans = (evaluate(this%cos_bspline, yp, derivative=.true.)**2 + &
175			& evaluate(this%sin_bspline, yp, derivative=.true.)**2) / &
176		6993040	& (toroidal_twopi(this, yp)*2 this%minor_radius**2)
177			case (2)
178			ans = -(evaluate(this%cos_bspline, yp) * evaluate(this%cos_bspline, yp, derivative=.true.) + evaluate(this%sin_bspline, yp)&
179		7463344	& * evaluate(this%sin_bspline, yp, derivative=.true.)) / (toroidal_twopi(this, yp)*2 this%minor_radius*2 xp)
180			case (3)
181	3/4 ✓ Branch 3 → 4 taken 6993040 times. ✓ Branch 3 → 5 taken 7463344 times. ✓ Branch 3 → 10 taken 7463344 times. ✗ Branch 3 → 12 not taken.	21919728	ans = 0._wp
182			end select
183			case (2)
184		40725136	select case (j)
185			case (1)
186			ans = -(evaluate(this%cos_bspline, yp) * evaluate(this%cos_bspline, yp, derivative=.true.) + &
187			& evaluate(this%sin_bspline, yp) *&
188		4818928	& evaluate(this%sin_bspline, yp, derivative=.true.)) / (toroidal_twopi(this, yp)*2 this%minor_radius*2 xp)
189			case (2)
190			ans = (evaluate(this%cos_bspline, yp)2 + evaluate(this%sin_bspline, yp)2) / &
191		6993040	& (toroidal_twopi(this, yp)*2 this%minor_radius*2 xp**2)
192			case (3)
193	3/4 ✓ Branch 6 → 7 taken 4818928 times. ✓ Branch 6 → 8 taken 6993040 times. ✓ Branch 6 → 10 taken 7463344 times. ✗ Branch 6 → 12 not taken.	19275312	ans = 0._wp
194			end select
195			case (3)
196	3/4 ✓ Branch 2 → 3 taken 21919728 times. ✓ Branch 2 → 6 taken 19275312 times. ✓ Branch 2 → 9 taken 16630896 times. ✗ Branch 2 → 12 not taken.	57825936	select case (j)
197			case (1)
198			ans = 0._wp
199			case (2)
200		6993040	ans = 0._wp
201			case (3)
202	2/3 ✓ Branch 9 → 10 taken 9637856 times. ✓ Branch 9 → 11 taken 6993040 times. ✗ Branch 9 → 12 not taken.	16630896	ans = 1 / (2 * pi * (this%major_radius + this%minor_radius * xp * evaluate(this%sin_bspline, yp)))**2
203			end select
204			end select
205		57825936	end procedure toroidal_bspline_G_matrix_inv
206
207			end submodule s_coord_transform_toroidal_bspline
208

GCC Code Coverage Report