tensorprod/m_tensorprod_matrix.f90
| Line | Branch | Exec | Source |
|---|---|---|---|
| 1 | !> @brief Module for the mass matrix of a 3D tensor product B-spline space | ||
| 2 | !> | ||
| 3 | !> The mass matrix is stored in a sparse dedicated format, which can easily be converted to a PETSc matrix | ||
| 4 | module m_tensorprod_matrix | ||
| 5 | use m_common, only: wp, user_function_3d_interface, user_function_1d_interface | ||
| 6 | use m_tensorprod_basis, only: TensorProdSpace | ||
| 7 | use m_tensorprod_indices, only: TensorProdIndices | ||
| 8 | #include "petsc.fi" | ||
| 9 | |||
| 10 | implicit none | ||
| 11 | |||
| 12 | private | ||
| 13 | public :: TensorProdMat | ||
| 14 | public :: get_petsc, mass_matrix | ||
| 15 | |||
| 16 | !> @brief Type for the mass matrix of a 3D tensor product B-spline basis | ||
| 17 | type TensorProdMat | ||
| 18 | !> The tensor product B-spline space for the row index | ||
| 19 | type(TensorProdSpace) :: space_row | ||
| 20 | !> The tensor product B-spline space for the column index | ||
| 21 | type(TensorProdSpace) :: space_col | ||
| 22 | |||
| 23 | !> The values of the mass matrix (:, :, :, local_row) | ||
| 24 | real(wp), allocatable :: vals(:, :, :, :, :, :) | ||
| 25 | |||
| 26 | !> The column indices of the mass matrix (:, :, :, local_row) | ||
| 27 | integer, allocatable :: cols(:, :, :, :, :, :) | ||
| 28 | |||
| 29 | !> The row indices of the mass matrix (local_row -> global_row) | ||
| 30 | integer, allocatable :: rows(:, :, :) | ||
| 31 | |||
| 32 | !> | ||
| 33 | type(TensorProdIndices) :: rank_actv_bsplines | ||
| 34 | |||
| 35 | !> The number of non-zero entries per row | ||
| 36 | integer :: total_nz_per_row | ||
| 37 | |||
| 38 | !> The numer of rows | ||
| 39 | integer :: nr_rows | ||
| 40 | !> The number of rows for the current rank | ||
| 41 | integer :: my_nr_rows | ||
| 42 | |||
| 43 | !> The number of columns | ||
| 44 | integer :: nr_cols | ||
| 45 | !> The number of columns for the current rank | ||
| 46 | integer :: my_nr_cols | ||
| 47 | |||
| 48 | !> Whether the matrix is symmetric | ||
| 49 | logical :: symmetric | ||
| 50 | |||
| 51 | !> Whether the matrix is symmetric positive definite | ||
| 52 | logical :: spd | ||
| 53 | contains | ||
| 54 | procedure :: init => init_mat | ||
| 55 | procedure :: destroy => destroy_mat | ||
| 56 | end type TensorProdMat | ||
| 57 | |||
| 58 | !> @brief Construct a mass matrix for two 3D tensor product B-spline spaces | ||
| 59 | interface mass_matrix | ||
| 60 | procedure mass_matrix_3d | ||
| 61 | end interface mass_matrix | ||
| 62 | |||
| 63 | !> @brief Get the PETSc matrix from the (array of) TensorProdMat(s) | ||
| 64 | interface get_petsc | ||
| 65 | module procedure get_petsc_mat_single, get_petsc_mat_blocks, get_petsc_mat_diagonal | ||
| 66 | end interface | ||
| 67 | contains | ||
| 68 | |||
| 69 | !> @brief Initialize the TensorProdMat | ||
| 70 | !> | ||
| 71 | !> @param[inout] this The TensorProdMat object | ||
| 72 | !> @param[in] space1 The first tensor product B-spline basis | ||
| 73 | !> @param[in] space2 The second tensor product B-spline basis | ||
| 74 | !> @param[in] symmetric _(optional)_ Whether the matrix is symmetric | ||
| 75 | !> @param[in] spd _(optional)_ Whether the matrix is symmetric positive definite | ||
| 76 | 1957 | subroutine init_mat(this, space1, space2, symmetric, spd) | |
| 77 | use m_tensorprod_basis, only: size | ||
| 78 | use m_tensorprod_indices, only: size | ||
| 79 | implicit none | ||
| 80 | class(TensorProdMat), intent(inout) :: this | ||
| 81 | type(TensorProdSpace), intent(in) :: space1, space2 | ||
| 82 | logical, intent(in), optional :: symmetric, spd | ||
| 83 | |||
| 84 | integer :: sze1, sze2, sze3 | ||
| 85 | |||
| 86 | 1957 | this%space_row = space1 | |
| 87 | 1957 | this%space_col = space2 | |
| 88 | |||
| 89 | 1957 | sze1 = 1 + space1%spaces(1)%degree + space2%spaces(1)%degree | |
| 90 | 1957 | sze2 = 1 + space1%spaces(2)%degree + space2%spaces(2)%degree | |
| 91 | 1957 | sze3 = 1 + space1%spaces(3)%degree + space2%spaces(3)%degree | |
| 92 | |||
| 93 | ! The number of local rows is equal to the active B-splines on this rank | ||
| 94 | 1957 | this%rank_actv_bsplines = space1%rank_resp_intervals | |
| 95 | 1957 | this%rank_actv_bsplines%i1 = this%rank_actv_bsplines%i1 + space1%spaces(1)%degree | |
| 96 | 1957 | this%rank_actv_bsplines%j1 = this%rank_actv_bsplines%j1 + space1%spaces(2)%degree | |
| 97 | 1957 | this%rank_actv_bsplines%k1 = this%rank_actv_bsplines%k1 + space1%spaces(3)%degree | |
| 98 | |||
| 99 | ✗ | allocate (this%vals(0:sze1 - 1, 0:sze2 - 1, 0:sze3 - 1, & | |
| 100 | this%rank_actv_bsplines%i0:this%rank_actv_bsplines%i1, & | ||
| 101 | this%rank_actv_bsplines%j0:this%rank_actv_bsplines%j1, & | ||
| 102 |
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15656 | this%rank_actv_bsplines%k0:this%rank_actv_bsplines%k1)) |
| 103 | ✗ | allocate (this%cols(0:sze1 - 1, 0:sze2 - 1, 0:sze3 - 1, & | |
| 104 | this%rank_actv_bsplines%i0:this%rank_actv_bsplines%i1, & | ||
| 105 | this%rank_actv_bsplines%j0:this%rank_actv_bsplines%j1, & | ||
| 106 |
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15656 | this%rank_actv_bsplines%k0:this%rank_actv_bsplines%k1)) |
| 107 | ✗ | allocate (this%rows(this%rank_actv_bsplines%i0:this%rank_actv_bsplines%i1, & | |
| 108 | this%rank_actv_bsplines%j0:this%rank_actv_bsplines%j1, & | ||
| 109 |
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9785 | this%rank_actv_bsplines%k0:this%rank_actv_bsplines%k1)) |
| 110 | |||
| 111 |
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716032612 | this%vals(:, :, :, :, :, :) = 0._wp |
| 112 |
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716032612 | this%cols(:, :, :, :, :, :) = -1 |
| 113 |
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2926431 | this%rows(:, :, :) = -1 |
| 114 | |||
| 115 | 1957 | this%total_nz_per_row = sze1 * sze2 * sze3 | |
| 116 | 1957 | this%nr_rows = size(space1) | |
| 117 | 1957 | this%nr_cols = size(space2) | |
| 118 | |||
| 119 | 1957 | this%my_nr_rows = size(space1, my_rank=.true.) | |
| 120 | 1957 | this%my_nr_cols = size(space2, my_rank=.true.) | |
| 121 | |||
| 122 | 1957 | this%symmetric = .false. | |
| 123 | 1957 | this%spd = .false. | |
| 124 | |||
| 125 |
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1957 | if (present(symmetric)) this%symmetric = symmetric |
| 126 |
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1957 | if (present(spd)) this%spd = spd |
| 127 | 1957 | end subroutine init_mat | |
| 128 | |||
| 129 | !> @brief destroy for the TensorProdMat | ||
| 130 | !> | ||
| 131 | !> @param[inout] this The TensorProdMat object | ||
| 132 | 4939 | subroutine destroy_mat(this) | |
| 133 | implicit none | ||
| 134 | class(TensorProdMat), intent(inout) :: this | ||
| 135 | |||
| 136 |
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4939 | if (allocated(this%vals)) deallocate (this%vals) |
| 137 |
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4939 | if (allocated(this%cols)) deallocate (this%cols) |
| 138 | 4939 | end subroutine destroy_mat | |
| 139 | |||
| 140 | !> @brief Get the PETSc matrix from the TensorProdMat | ||
| 141 | !> | ||
| 142 | !> @param[out] M The PETSc matrix | ||
| 143 | !> @param[in] this The TensorProdMat object | ||
| 144 | 232 | subroutine get_petsc_mat_single(M, this) | |
| 145 | implicit none | ||
| 146 | Mat, intent(out) :: M | ||
| 147 | type(TensorProdMat), intent(in) :: this | ||
| 148 | |||
| 149 | integer :: ierr, nonlocal_nz_per_row | ||
| 150 | integer :: i, j, k | ||
| 151 | |||
| 152 | 232 | nonlocal_nz_per_row = this%total_nz_per_row ! TODO a better upper bound of the local/non-local nz per row | |
| 153 | call MatCreateAIJ(this%space_row%domain%comm, this%my_nr_rows, this%my_nr_cols, this%nr_rows, & | ||
| 154 | & this%nr_cols, this%total_nz_per_row, PETSC_NULL_INTEGER_ARRAY, nonlocal_nz_per_row, & | ||
| 155 |
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232 | & PETSC_NULL_INTEGER_ARRAY, M, ierr); CHKERRQ(ierr) |
| 156 | |||
| 157 |
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232 | PetscCall(MatSetFromOptions(M, ierr)) |
| 158 |
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232 | PetscCall(MatSetOption(M, MAT_SYMMETRIC, merge(PETSC_TRUE, PETSC_FALSE, this%symmetric), ierr)) |
| 159 |
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232 | PetscCall(MatSetOption(M, MAT_SPD, merge(PETSC_TRUE, PETSC_FALSE, this%spd), ierr)) |
| 160 |
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232 | PetscCall(MatSetUp(M, ierr)) |
| 161 | |||
| 162 | ! Copy the values to the PETSC matrix object | ||
| 163 |
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1809 | do k = this%rank_actv_bsplines%k0, this%rank_actv_bsplines%k1 |
| 164 |
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18616 | do j = this%rank_actv_bsplines%j0, this%rank_actv_bsplines%j1 |
| 165 |
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308453 | do i = this%rank_actv_bsplines%i0, this%rank_actv_bsplines%i1 |
| 166 | call petsc_insert_single_row(M, this%rows(i, j, k), this%total_nz_per_row, this%cols(:, :, :, i, j, k), & | ||
| 167 | 306876 | this%vals(:, :, :, i, j, k)) | |
| 168 | end do | ||
| 169 | end do | ||
| 170 | end do | ||
| 171 | |||
| 172 |
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232 | PetscCall(MatAssemblyBegin(M, MAT_FINAL_ASSEMBLY, ierr)) |
| 173 |
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232 | PetscCall(MatAssemblyEnd(M, MAT_FINAL_ASSEMBLY, ierr)) |
| 174 | |||
| 175 | end subroutine get_petsc_mat_single | ||
| 176 | |||
| 177 | !> @brief Insert a single row into the PETSc matrix | ||
| 178 | !> | ||
| 179 | !> @param[inout] M The PETSc matrix | ||
| 180 | !> @param[in] row The row index to insert | ||
| 181 | !> @param[in] nr_elements The number of elements to insert | ||
| 182 | !> @param[in] cols The column indices of the elements to insert | ||
| 183 | !> @param[in] vals The values of the elements to insert | ||
| 184 | 2740871 | subroutine petsc_insert_single_row(M, row, nr_elements, cols, vals) | |
| 185 | implicit none | ||
| 186 | |||
| 187 | Mat, intent(inout) :: M | ||
| 188 | integer, intent(in) :: row | ||
| 189 | integer, intent(in) :: nr_elements | ||
| 190 | integer, contiguous, target, intent(in) :: cols(:, :, :) | ||
| 191 | real(wp), contiguous, target, intent(in) :: vals(:, :, :) | ||
| 192 | |||
| 193 | 2740871 | integer, pointer :: col_pointer(:) | |
| 194 | real(wp), pointer :: val_pointer(:) | ||
| 195 | integer :: ierr | ||
| 196 | |||
| 197 | ! Avoid allocating for reshape | ||
| 198 | |||
| 199 | 2740871 | col_pointer(1:nr_elements) => cols(:, :, :) | |
| 200 | 2740871 | val_pointer(1:nr_elements) => vals(:, :, :) | |
| 201 |
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5481742 | PetscCall(MatSetValues(M, 1, [row], nr_elements, col_pointer, val_pointer, ADD_VALUES, ierr)) |
| 202 | ! NOTE: use ADD_VALUES because a cols might not be unique | ||
| 203 | end subroutine | ||
| 204 | |||
| 205 | !> @brief Get the PETSc matrix from the block-diagonal TensorProdMat blocks | ||
| 206 | !> | ||
| 207 | !> @param[out] M The PETSc matrix | ||
| 208 | !> @param[in] this The block-diagonal TensorProdMat objects | ||
| 209 | !> | ||
| 210 | !> @note It is assumed thaat the column indices of the blocks of 'this' are global indices | ||
| 211 |
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497 | subroutine get_petsc_mat_diagonal(M, this) |
| 212 | implicit none | ||
| 213 | Mat, intent(out) :: M | ||
| 214 | type(TensorProdMat), intent(in) :: this(:) | ||
| 215 | |||
| 216 | integer :: ierr, nonlocal_nz_per_row, local_nz_per_row | ||
| 217 | |||
| 218 | integer :: blk, i, j, k | ||
| 219 | integer :: nr_rows, nr_cols, my_nr_rows, my_nr_cols | ||
| 220 | |||
| 221 |
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1988 | nr_rows = sum(this%nr_rows) |
| 222 |
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1988 | nr_cols = sum(this%nr_cols) |
| 223 |
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1988 | my_nr_rows = sum(this%my_nr_rows) |
| 224 |
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1988 | my_nr_cols = sum(this%my_nr_cols) |
| 225 | |||
| 226 | ! TODO a better upper bound of the local/non-local nz per row | ||
| 227 |
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1988 | local_nz_per_row = maxval(this%total_nz_per_row) |
| 228 | 497 | nonlocal_nz_per_row = local_nz_per_row | |
| 229 | |||
| 230 | call MatCreateAIJ(this(1)%space_row%domain%comm, & | ||
| 231 | & my_nr_rows, & | ||
| 232 | & my_nr_cols, & | ||
| 233 | & nr_rows, & | ||
| 234 | & nr_cols, & | ||
| 235 | & local_nz_per_row, & | ||
| 236 |
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497 | & PETSC_NULL_INTEGER_ARRAY, nonlocal_nz_per_row, PETSC_NULL_INTEGER_ARRAY, M, ierr); CHKERRQ(ierr) |
| 237 | |||
| 238 |
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497 | PetscCall(MatSetFromOptions(M, ierr)) |
| 239 |
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497 | PetscCall(MatSetOption(M, MAT_SYMMETRIC, PETSC_TRUE, ierr)) |
| 240 |
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497 | PetscCall(MatSetOption(M, MAT_SPD, PETSC_TRUE, ierr)) |
| 241 |
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497 | PetscCall(MatSetUp(M, ierr)) |
| 242 | |||
| 243 | ! Copy the values to the PETSC matrix object | ||
| 244 |
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1988 | do blk = 1, size(this) |
| 245 | ! The indices are already global | ||
| 246 |
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8493 | do k = this(blk)%rank_actv_bsplines%k0, this(blk)%rank_actv_bsplines%k1 |
| 247 |
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85548 | do j = this(blk)%rank_actv_bsplines%j0, this(blk)%rank_actv_bsplines%j1 |
| 248 |
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1548543 | do i = this(blk)%rank_actv_bsplines%i0, this(blk)%rank_actv_bsplines%i1 |
| 249 | call petsc_insert_single_row(M, this(blk)%rows(i, j, k), this(blk)%total_nz_per_row, this(blk)%cols(:, :, :, i, j, k), & | ||
| 250 | 1542038 | this(blk)%vals(:, :, :, i, j, k)) | |
| 251 | end do | ||
| 252 | end do | ||
| 253 | end do | ||
| 254 | end do | ||
| 255 | |||
| 256 |
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497 | PetscCall(MatAssemblyBegin(M, MAT_FINAL_ASSEMBLY, ierr)) |
| 257 |
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497 | PetscCall(MatAssemblyEnd(M, MAT_FINAL_ASSEMBLY, ierr)) |
| 258 | |||
| 259 | end subroutine get_petsc_mat_diagonal | ||
| 260 | |||
| 261 | !> @brief Get the PETSc matrix from the TensorProdMat blocks | ||
| 262 | !> | ||
| 263 | !> @param[out] M The PETSc matrix | ||
| 264 | !> @param[in] this The TensorProdMat objects | ||
| 265 | !> | ||
| 266 | !> @note It is assumed thaat the column indices of the blocks of 'this' are global indices | ||
| 267 |
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26 | subroutine get_petsc_mat_blocks(M, this) |
| 268 | implicit none | ||
| 269 | Mat, intent(out) :: M | ||
| 270 | type(TensorProdMat), intent(in) :: this(:, :) | ||
| 271 | |||
| 272 | integer :: ierr, nonlocal_nz_per_row, local_nz_per_row | ||
| 273 | integer :: blk_row, blk_col, i, j, k | ||
| 274 | |||
| 275 | integer :: nr_rows, nr_cols, my_nr_rows, my_nr_cols | ||
| 276 | |||
| 277 |
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104 | nr_rows = sum(this(:, 1)%nr_rows) |
| 278 |
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104 | nr_cols = sum(this(1, :)%nr_cols) |
| 279 |
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104 | my_nr_rows = sum(this(:, 1)%my_nr_rows) |
| 280 |
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104 | my_nr_cols = sum(this(1, :)%my_nr_cols) |
| 281 | |||
| 282 |
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338 | local_nz_per_row = maxval(sum(this%total_nz_per_row, dim=2)) |
| 283 | 26 | nonlocal_nz_per_row = local_nz_per_row ! TODO a better upper bound of the local/non-local nz per row | |
| 284 | call MatCreateAIJ(this(1, 1)%space_row%domain%comm, & | ||
| 285 | & my_nr_rows, & | ||
| 286 | & my_nr_cols, & | ||
| 287 | & nr_rows, & | ||
| 288 | & nr_cols, & | ||
| 289 | & local_nz_per_row, & | ||
| 290 |
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26 | & PETSC_NULL_INTEGER_ARRAY, nonlocal_nz_per_row, PETSC_NULL_INTEGER_ARRAY, M, ierr); CHKERRQ(ierr) |
| 291 | |||
| 292 |
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26 | PetscCall(MatSetFromOptions(M, ierr)) |
| 293 |
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26 | PetscCall(MatSetOption(M, MAT_SYMMETRIC, PETSC_TRUE, ierr)) |
| 294 |
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26 | PetscCall(MatSetOption(M, MAT_SPD, PETSC_TRUE, ierr)) |
| 295 |
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26 | PetscCall(MatSetUp(M, ierr)) |
| 296 | |||
| 297 | ! Copy the values to the PETSC matrix object | ||
| 298 |
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104 | do blk_row = 1, size(this, dim=1) |
| 299 |
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338 | do blk_col = 1, size(this, dim=2) |
| 300 |
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4068 | do k = this(blk_row, blk_col)%rank_actv_bsplines%k0, this(blk_row, blk_col)%rank_actv_bsplines%k1 |
| 301 |
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81396 | do j = this(blk_row, blk_col)%rank_actv_bsplines%j0, this(blk_row, blk_col)%rank_actv_bsplines%j1 |
| 302 |
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1067478 | do i = this(blk_row, blk_col)%rank_actv_bsplines%i0, this(blk_row, blk_col)%rank_actv_bsplines%i1 |
| 303 | call petsc_insert_single_row(M, this(blk_row, blk_col)%rows(i, j, k), this(blk_row, blk_col)%total_nz_per_row, & | ||
| 304 | 1063722 | & this(blk_row, blk_col)%cols(:, :, :, i, j, k), this(blk_row, blk_col)%vals(:, :, :, i, j, k)) | |
| 305 | end do | ||
| 306 | end do | ||
| 307 | end do | ||
| 308 | end do | ||
| 309 | end do | ||
| 310 | |||
| 311 |
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26 | PetscCall(MatAssemblyBegin(M, MAT_FINAL_ASSEMBLY, ierr)) |
| 312 |
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26 | PetscCall(MatAssemblyEnd(M, MAT_FINAL_ASSEMBLY, ierr)) |
| 313 | |||
| 314 | end subroutine get_petsc_mat_blocks | ||
| 315 | |||
| 316 | !> @brief Compute the mass matrix for a 3D tensor product B-spline basis | ||
| 317 | !> | ||
| 318 | !> The resulting matrix is such that the (row, col) element correspnds to the L2 inner product of the 'row' B-spline basis | ||
| 319 | !> function from the first basis and the 'col' B-spline basis function from the second basis, optionally weighted with coordfun | ||
| 320 | !> | ||
| 321 | !> @param M The mass matrix of type TensorProdMat | ||
| 322 | !> @param tp_space1 The first tensor product B-spline basis | ||
| 323 | !> @param tp_space2 The second tensor product B-spline basis | ||
| 324 | !> @param coordfun _(optional)_ The coordinate function | ||
| 325 | !> @param n_quad_extra _(optional)_ The extra number of quadrature points on top of those needed to exactly integrate the B-spline | ||
| 326 | !> spaces | ||
| 327 |
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|
1957 | subroutine mass_matrix_3d(M, tp_space1, tp_space2, coordfun, n_quad_extra) |
| 328 | use m_bspline_basis, only: MAX_BSPLINE_DEGREE, get_internal_and_actual_inds | ||
| 329 | use m_bspline_quadrature, only: BSplineQuadrature, n_quad_exact | ||
| 330 | use m_common, only: set_union | ||
| 331 | use m_tensorprod_basis, only: TensorProdSpace, cartesian_to_linear, size, actv_interval_inds | ||
| 332 | use m_tensorprod_quadrature, only: TensorProdQuadrature, evaluate_at_nodes, DEFAULT_EXTRA_QUADRATURE_POINTS | ||
| 333 | |||
| 334 | implicit none | ||
| 335 | |||
| 336 | type(TensorProdMat), intent(out) :: M | ||
| 337 | type(TensorProdSpace), intent(in) :: tp_space1, tp_space2 | ||
| 338 | procedure(user_function_3d_interface), optional :: coordfun | ||
| 339 | integer, intent(in), optional :: n_quad_extra | ||
| 340 | |||
| 341 | integer :: row, col ! Linearly indexed B-spline indices: row = first basis, col = second basis | ||
| 342 | integer :: degree_x1, degree_y1, degree_z1 ! B-spline degree per direction of the first B-spline basis | ||
| 343 | integer :: degree_x2, degree_y2, degree_z2 ! B-spline degree per direction of the second B-spline basis | ||
| 344 | integer :: n_quad1, n_quad2, n_quad3 ! Number of quadrature points in each direction | ||
| 345 | integer :: nr_intervals_x, nr_intervals_y, nr_intervals_z ! Number of intervals per direction (must be equal for both B-spline | ||
| 346 | ! spaces) | ||
| 347 | logical :: equal_spaces_x, equal_spaces_y, equal_spaces_z ! Whether the B-spline spaces are equal in the respective direction | ||
| 348 | logical :: equal_spaces_all ! Whether the B-spline spaces are equal in each direction | ||
| 349 | integer :: i1, j1, k1, i2, j2, k2 ! The B-spline indices (for the first and second B-spline basis) | ||
| 350 | integer :: ii, jj, kk ! The interval indices | ||
| 351 | integer :: qdx, qdy, qdz ! The quadrature point indices | ||
| 352 | integer :: i1_minus_ii, j1_minus_jj, k1_minus_kk ! Equal to i1 - ii, j1 - jj, k1 - kk | ||
| 353 | integer :: i2_minus_ii, j2_minus_jj, k2_minus_kk ! Equal to i2 - ii, j2 - jj, k2 - kk | ||
| 354 | integer, dimension(0:MAX_BSPLINE_DEGREE) :: i1_internals, j1_internals, k1_internals | ||
| 355 | integer, dimension(0:MAX_BSPLINE_DEGREE) :: i2_internals, j2_internals, k2_internals | ||
| 356 | integer :: i1_internal, j1_internal, k1_internal ! The internal B-spline indices (there are at most degree + 1 different | ||
| 357 | ! B-splines per direction) | ||
| 358 | integer :: i2_internal, j2_internal, k2_internal ! Same for the second B-spline basis | ||
| 359 | integer :: n_quad_extra_ ! The number of extra quadrature points | ||
| 360 | |||
| 361 | integer :: local_cdx_i, local_cdx_j, local_cdx_k | ||
| 362 | logical, dimension(0:MAX_BSPLINE_DEGREE) :: bspline_mirrored_x1s, bspline_mirrored_y1s, bspline_mirrored_z1s | ||
| 363 | logical, dimension(0:MAX_BSPLINE_DEGREE) :: bspline_mirrored_x2s, bspline_mirrored_y2s, bspline_mirrored_z2s | ||
| 364 | logical :: bspline_mirrored_x1, bspline_mirrored_y1, bspline_mirrored_z1 | ||
| 365 | logical :: bspline_mirrored_x2, bspline_mirrored_y2, bspline_mirrored_z2 | ||
| 366 | logical :: is_periodic_x, is_periodic_y, is_periodic_z | ||
| 367 | integer :: i2_minus_ii_max, j2_minus_jj_max, k2_minus_kk_max | ||
| 368 | |||
| 369 | 1957 | real(wp), allocatable :: coordfun_vals(:, :, :) !> Values of coordfun at the quadrature points of the current interval | |
| 370 | real(wp) :: val !> Value of the mass matrix | ||
| 371 | real(wp), allocatable :: vals(:, :, :, :, :, :) !> Values of the mass matrix per interval (i2-ii, i1-ii, j2-jj, j1-jj, k2-kk, | ||
| 372 | !> k1-kk) | ||
| 373 | integer, allocatable :: cols(:, :, :) !> Column indices corresponding to vals (i1-ii, j1-jj, k1-kk) | ||
| 374 | integer, allocatable :: rows(:, :, :) !> Row indices corresponding to vals (i2-ii, j2-jj, k2-kk) | ||
| 375 | |||
| 376 | real(wp), allocatable :: bspline1_vals_x(:), bspline1_vals_y(:), bspline1_vals_z(:) | ||
| 377 | real(wp), allocatable :: bspline_vals_x(:), bspline_vals_y(:), bspline_vals_z(:) | ||
| 378 | |||
| 379 | real(wp), allocatable :: partial_sum_z(:, :), partial_sum_yz(:) | ||
| 380 | |||
| 381 |
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13699 | type(TensorProdQuadrature) :: tp_space1_quad, tp_space2_quad |
| 382 | |||
| 383 | ! The number of quadrature points in each diriection is determined such that | ||
| 384 | ! the quadrature is exact for the given B-spline spaces | ||
| 385 | 1957 | n_quad1 = n_quad_exact(tp_space1%spaces(1), tp_space2%spaces(1)) | |
| 386 | 1957 | n_quad2 = n_quad_exact(tp_space1%spaces(2), tp_space2%spaces(2)) | |
| 387 | 1957 | n_quad3 = n_quad_exact(tp_space1%spaces(3), tp_space2%spaces(3)) | |
| 388 |
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1957 | if (present(coordfun)) then |
| 389 |
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1110 | if (present(n_quad_extra)) then |
| 390 | 289 | n_quad_extra_ = n_quad_extra | |
| 391 | else | ||
| 392 | n_quad_extra_ = DEFAULT_EXTRA_QUADRATURE_POINTS | ||
| 393 | end if | ||
| 394 | |||
| 395 | ! The number of quadrature points in each direction is increased | ||
| 396 | 1110 | n_quad1 = n_quad1 + n_quad_extra_ | |
| 397 | 1110 | n_quad2 = n_quad2 + n_quad_extra_ | |
| 398 | 1110 | n_quad3 = n_quad3 + n_quad_extra_ | |
| 399 | end if | ||
| 400 | |||
| 401 |
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|
7828 | do i1 = 1, size(tp_space1%spaces) |
| 402 |
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9030 | if (.not. (tp_space1%spaces(i1)%is_periodic .eqv. tp_space2%spaces(i1)%is_periodic .and. & |
| 403 | 1957 | & tp_space1%spaces(i1)%nr_intervals == tp_space2%spaces(i1)%nr_intervals)) then | |
| 404 | ✗ | error stop "B-spline spaces must have the same periodicity and number of intervals for the computation of the mass matrix" | |
| 405 | end if | ||
| 406 | end do | ||
| 407 | |||
| 408 | ! We precompute the value of the B-spline basis functions at the quadrature points | ||
| 409 | tp_space1_quad = TensorProdQuadrature(BSplineQuadrature(tp_space1%spaces(1), n_quad1), & | ||
| 410 | BSplineQuadrature(tp_space1%spaces(2), n_quad2), & | ||
| 411 |
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|
27398 | BSplineQuadrature(tp_space1%spaces(3), n_quad3)) |
| 412 | tp_space2_quad = TensorProdQuadrature(BSplineQuadrature(tp_space2%spaces(1), n_quad1), & | ||
| 413 | BSplineQuadrature(tp_space2%spaces(2), n_quad2), & | ||
| 414 |
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|
27398 | BSplineQuadrature(tp_space2%spaces(3), n_quad3)) |
| 415 | |||
| 416 | 1957 | degree_x1 = tp_space1%spaces(1)%degree | |
| 417 | 1957 | degree_y1 = tp_space1%spaces(2)%degree | |
| 418 | 1957 | degree_z1 = tp_space1%spaces(3)%degree | |
| 419 | 1957 | degree_x2 = tp_space2%spaces(1)%degree | |
| 420 | 1957 | degree_y2 = tp_space2%spaces(2)%degree | |
| 421 | 1957 | degree_z2 = tp_space2%spaces(3)%degree | |
| 422 | |||
| 423 | 1957 | is_periodic_x = tp_space1%spaces(1)%is_periodic | |
| 424 | 1957 | is_periodic_y = tp_space1%spaces(2)%is_periodic | |
| 425 | 1957 | is_periodic_z = tp_space1%spaces(3)%is_periodic | |
| 426 | |||
| 427 | ! Per interval the symmetry can be exploited and computations can be re-used | ||
| 428 | ! TODO even if the spaces are not equal, we can still exploit symmetry: the only difference is scaling, which is a constant | ||
| 429 | ! TODO factor per B-spline | ||
| 430 | equal_spaces_x = size(tp_space1%spaces(1)) == size(tp_space2%spaces(1)) .and. & | ||
| 431 | (tp_space1%spaces(1)%is_scaled .eqv. tp_space2%spaces(1)%is_scaled) .and. & | ||
| 432 | (tp_space1%spaces(1)%is_periodic .eqv. tp_space2%spaces(1)%is_periodic) .and. & | ||
| 433 |
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1957 | degree_x1 == degree_x2 |
| 434 | |||
| 435 | equal_spaces_y = size(tp_space1%spaces(2)) == size(tp_space2%spaces(2)) .and. & | ||
| 436 | (tp_space1%spaces(2)%is_scaled .eqv. tp_space2%spaces(2)%is_scaled) .and. & | ||
| 437 | (tp_space1%spaces(2)%is_periodic .eqv. tp_space2%spaces(2)%is_periodic) .and. & | ||
| 438 |
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1957 | degree_y1 == degree_y2 |
| 439 | |||
| 440 | equal_spaces_z = size(tp_space1%spaces(3)) == size(tp_space2%spaces(3)) .and. & | ||
| 441 | (tp_space1%spaces(3)%is_scaled .eqv. tp_space2%spaces(3)%is_scaled) .and. & | ||
| 442 | (tp_space1%spaces(3)%is_periodic .eqv. tp_space2%spaces(3)%is_periodic) .and. & | ||
| 443 |
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1957 | degree_z1 == degree_z2 |
| 444 | |||
| 445 |
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1957 | equal_spaces_all = equal_spaces_x .and. equal_spaces_y .and. equal_spaces_z |
| 446 | |||
| 447 | i2_minus_ii_max = degree_x2 | ||
| 448 | j2_minus_jj_max = degree_y2 | ||
| 449 | k2_minus_kk_max = degree_z2 | ||
| 450 | |||
| 451 |
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|
9785 | allocate (coordfun_vals(n_quad3, n_quad2, n_quad1)) |
| 452 |
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|
15656 | allocate (vals(0:degree_x2, 0:degree_x1, 0:degree_y2, 0:degree_y1, 0:degree_z2, 0:degree_z1)) |
| 453 |
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|
9785 | allocate (cols(0:degree_x2, 0:degree_y2, 0:degree_z2)) |
| 454 |
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|
9785 | allocate (rows(0:degree_x1, 0:degree_y1, 0:degree_z1)) |
| 455 | |||
| 456 |
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|
5871 | allocate (bspline1_vals_x(n_quad1)) |
| 457 |
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|
5871 | allocate (bspline1_vals_y(n_quad2)) |
| 458 |
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|
5871 | allocate (bspline1_vals_z(n_quad3)) |
| 459 | |||
| 460 |
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|
3914 | allocate (bspline_vals_x(n_quad1)) |
| 461 |
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3914 | allocate (bspline_vals_y(n_quad2)) |
| 462 |
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|
3914 | allocate (bspline_vals_z(n_quad3)) |
| 463 | |||
| 464 |
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|
7828 | allocate (partial_sum_z(n_quad2, n_quad1)) |
| 465 |
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|
3914 | allocate (partial_sum_yz(n_quad1)) |
| 466 | |||
| 467 | 1957 | call M%init(tp_space1, tp_space2, symmetric=equal_spaces_all, spd=equal_spaces_all) | |
| 468 | |||
| 469 | ! Loop over all intervals first such that the coordfun is evaluated only once per quadrature point | ||
| 470 |
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|
12800 | do kk = tp_space1%rank_resp_intervals%k0, tp_space1%rank_resp_intervals%k1 |
| 471 |
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150908 | do jj = tp_space1%rank_resp_intervals%j0, tp_space1%rank_resp_intervals%j1 |
| 472 |
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2029770 | do ii = tp_space1%rank_resp_intervals%i0, tp_space1%rank_resp_intervals%i1 |
| 473 |
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|
1880819 | if (present(coordfun)) then |
| 474 | 1492907 | call evaluate_at_nodes(tp_space1_quad, coordfun, ii, jj, kk, coordfun_vals) | |
| 475 | end if | ||
| 476 | |||
| 477 |
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|
6702501 | do k1_minus_kk = 0, degree_z1 |
| 478 | call get_internal_and_actual_inds(tp_space1%spaces(3), kk, k1_minus_kk, k1, k1_internals(k1_minus_kk), & | ||
| 479 | 6702501 | & bspline_mirrored_z1s(k1_minus_kk)) | |
| 480 | ! TODO simplify get_internal_and_actual_inds: don't need k1 from there | ||
| 481 | end do | ||
| 482 |
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|
6702501 | do k2_minus_kk = 0, degree_z2 |
| 483 | call get_internal_and_actual_inds(tp_space2%spaces(3), kk, k2_minus_kk, k2, k2_internals(k2_minus_kk), & | ||
| 484 | 6702501 | & bspline_mirrored_z2s(k2_minus_kk)) | |
| 485 | end do | ||
| 486 |
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|
8630888 | do j1_minus_jj = 0, degree_y1 |
| 487 | call get_internal_and_actual_inds(tp_space1%spaces(2), jj, j1_minus_jj, j1, j1_internals(j1_minus_jj), & | ||
| 488 | 8630888 | & bspline_mirrored_y1s(j1_minus_jj)) | |
| 489 | end do | ||
| 490 |
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|
8630888 | do j2_minus_jj = 0, degree_y2 |
| 491 | call get_internal_and_actual_inds(tp_space2%spaces(2), jj, j2_minus_jj, j2, j2_internals(j2_minus_jj), & | ||
| 492 | 8630888 | & bspline_mirrored_y2s(j2_minus_jj)) | |
| 493 | end do | ||
| 494 |
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|
8836144 | do i1_minus_ii = 0, degree_x1 |
| 495 | call get_internal_and_actual_inds(tp_space1%spaces(1), ii, i1_minus_ii, i1, i1_internals(i1_minus_ii), & | ||
| 496 | 8836144 | & bspline_mirrored_x1s(i1_minus_ii)) | |
| 497 | end do | ||
| 498 |
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|
8836144 | do i2_minus_ii = 0, degree_x2 |
| 499 | call get_internal_and_actual_inds(tp_space2%spaces(1), ii, i2_minus_ii, i2, i2_internals(i2_minus_ii), & | ||
| 500 | 8836144 | & bspline_mirrored_x2s(i2_minus_ii)) | |
| 501 | end do | ||
| 502 | |||
| 503 | ! Loop over the third index (k or z-direction) of the B-spline basis function of the first basis | ||
| 504 | ! The B-splines have compact support: they contribute only if k1 is in the interval [kk, kk+degree_z1] | ||
| 505 |
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|
6702501 | do k1_minus_kk = 0, degree_z1 |
| 506 | 4821682 | k1_internal = k1_internals(k1_minus_kk) | |
| 507 | 4821682 | bspline_mirrored_z1 = bspline_mirrored_z1s(k1_minus_kk) | |
| 508 | |||
| 509 |
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|
4821682 | if (bspline_mirrored_z1) then |
| 510 |
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|
236468 | bspline1_vals_z = tp_space1_quad%bspline_quad(3)%bspline_at_nodes(k1_internal, degree_z1 - k1_minus_kk)%data(n_quad3:1:-1) |
| 511 | else | ||
| 512 |
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33635470 | bspline1_vals_z = tp_space1_quad%bspline_quad(3)%bspline_at_nodes(k1_internal, k1_minus_kk)%data(1:n_quad3) |
| 513 | end if | ||
| 514 |
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33871938 | bspline1_vals_z = bspline1_vals_z * tp_space1_quad%bspline_quad(3)%weights |
| 515 | |||
| 516 |
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|
4821682 | if (equal_spaces_z) then |
| 517 | ! If the spaces are equal in the z direction, we can exploit symmetry | ||
| 518 | ! by computing "the lower triangular part" of the contribution to the | ||
| 519 | ! mass matrix. This yields a factor 1/2 of computation per equal direction | ||
| 520 | k2_minus_kk_max = k1_minus_kk | ||
| 521 | end if | ||
| 522 | |||
| 523 | ! Loop over the third index (k or z-direction) of the B-spline basis function of the second basis | ||
| 524 |
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|
18014255 | do k2_minus_kk = 0, k2_minus_kk_max |
| 525 | 11311754 | k2_internal = k2_internals(k2_minus_kk) | |
| 526 | 11311754 | bspline_mirrored_z2 = bspline_mirrored_z2s(k2_minus_kk) | |
| 527 | ! Given kk (interval in the z-direction) and k2_minus_kk (B-spline index in the z-direction of the second basis relative | ||
| 528 | ! to kk), determine the actual B-spline index k2 (in the z-direction), the internally used B-spline index k2_internal, | ||
| 529 | ! and determine if the B-spline is mirrored | ||
| 530 |
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|
11311754 | if (bspline_mirrored_z2) then |
| 531 | ! This means that the clamped B-spline is at the right-hand side boundary, and is | ||
| 532 | ! therefore defined as the mirror image of a B-spline at the left-hand side boundary | ||
| 533 | bspline_vals_z = bspline1_vals_z * & | ||
| 534 |
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|
450560 | & tp_space2_quad%bspline_quad(3)%bspline_at_nodes(k2_internal, degree_z2 - k2_minus_kk)%data(n_quad3:1:-1) |
| 535 | else | ||
| 536 | bspline_vals_z = bspline1_vals_z * & | ||
| 537 |
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|
82322134 | & tp_space2_quad%bspline_quad(3)%bspline_at_nodes(k2_internal, k2_minus_kk)%data(1:n_quad3) |
| 538 | end if | ||
| 539 | |||
| 540 |
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|
11311754 | if (present(coordfun)) then |
| 541 | ! We precompute the partial sum over the z-direction: this reduces the | ||
| 542 | ! complexity from (assuming n_quad = degree for simplicity) | ||
| 543 | ! nr_intervals^3 * degree^9 | ||
| 544 | ! to | ||
| 545 | ! nr_intervals^3 * degree^7 | ||
| 546 |
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53207072 | do qdx = 1, n_quad1 |
| 547 |
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321667485 | do qdy = 1, n_quad2 |
| 548 | val = 0._wp | ||
| 549 |
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1820500772 | do qdz = 1, n_quad3 |
| 550 | 1820500772 | val = val + bspline_vals_z(qdz) * coordfun_vals(qdz, qdy, qdx) | |
| 551 | end do | ||
| 552 | 313859393 | partial_sum_z(qdy, qdx) = val | |
| 553 | end do | ||
| 554 | end do | ||
| 555 | else | ||
| 556 | ! partial_sum_z(qdx, qdy) = sum(bspline_vals_z) | ||
| 557 | end if | ||
| 558 | |||
| 559 | ! Loop over the second index (j or y-direction) of the B-spline basis function of the first basis | ||
| 560 |
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|
52429390 | do j1_minus_jj = 0, degree_y1 |
| 561 | 41117636 | j1_internal = j1_internals(j1_minus_jj) | |
| 562 | 41117636 | bspline_mirrored_y1 = bspline_mirrored_y1s(j1_minus_jj) | |
| 563 |
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41117636 | if (bspline_mirrored_y1) then |
| 564 | bspline1_vals_y = & | ||
| 565 |
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26027832 | & tp_space1_quad%bspline_quad(2)%bspline_at_nodes(j1_internal, degree_y1 - j1_minus_jj)%data(n_quad2:1:-1) |
| 566 | else | ||
| 567 |
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|
276092088 | bspline1_vals_y = tp_space1_quad%bspline_quad(2)%bspline_at_nodes(j1_internal, j1_minus_jj)%data(1:n_quad2) |
| 568 | end if | ||
| 569 |
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302119920 | bspline1_vals_y = bspline1_vals_y * tp_space1_quad%bspline_quad(2)%weights |
| 570 | |||
| 571 |
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|
41117636 | if (equal_spaces_y) then |
| 572 | j2_minus_jj_max = j1_minus_jj | ||
| 573 | end if | ||
| 574 | |||
| 575 | ! Loop over the second index (j or y-direction) of the B-spline basis function of the second basis | ||
| 576 |
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158290838 | do j2_minus_jj = 0, j2_minus_jj_max |
| 577 | 105861448 | j2_internal = j2_internals(j2_minus_jj) | |
| 578 | 105861448 | bspline_mirrored_y2 = bspline_mirrored_y2s(j2_minus_jj) | |
| 579 |
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105861448 | if (bspline_mirrored_y2) then |
| 580 | bspline_vals_y = bspline1_vals_y * & | ||
| 581 |
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45029666 | & tp_space2_quad%bspline_quad(2)%bspline_at_nodes(j2_internal, degree_y2 - j2_minus_jj)%data(n_quad2:1:-1) |
| 582 | else | ||
| 583 | bspline_vals_y = bspline1_vals_y * & | ||
| 584 |
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756410968 | & tp_space2_quad%bspline_quad(2)%bspline_at_nodes(j2_internal, j2_minus_jj)%data(1:n_quad2) |
| 585 | end if | ||
| 586 | |||
| 587 |
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105861448 | if (present(coordfun)) then |
| 588 | ! We precompute the partial sum over the yz-directions | ||
| 589 |
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545098168 | do qdx = 1, n_quad1 |
| 590 | val = 0._wp | ||
| 591 |
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3422531672 | do qdy = 1, n_quad2 |
| 592 | 3422531672 | val = val + bspline_vals_y(qdy) * partial_sum_z(qdy, qdx) | |
| 593 | end do | ||
| 594 | 545098168 | partial_sum_yz(qdx) = val | |
| 595 | end do | ||
| 596 | else | ||
| 597 |
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|
391441770 | partial_sum_yz = sum(bspline_vals_y) * sum(bspline_vals_z) |
| 598 | end if | ||
| 599 | |||
| 600 | ! Loop over the first index (i or x-direction) of the B-spline basis function of the first basis | ||
| 601 |
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528489796 | do i1_minus_ii = 0, degree_x1 |
| 602 | 422628348 | i1_internal = i1_internals(i1_minus_ii) | |
| 603 | 422628348 | bspline_mirrored_x1 = bspline_mirrored_x1s(i1_minus_ii) | |
| 604 |
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422628348 | if (bspline_mirrored_x1) then |
| 605 | bspline1_vals_x = & | ||
| 606 |
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374379638 | & tp_space1_quad%bspline_quad(1)%bspline_at_nodes(i1_internal, degree_x1 - i1_minus_ii)%data(n_quad1:1:-1) |
| 607 | else | ||
| 608 | bspline1_vals_x = & | ||
| 609 |
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2885431182 | & tp_space1_quad%bspline_quad(1)%bspline_at_nodes(i1_internal, i1_minus_ii)%data(1:n_quad1) |
| 610 | end if | ||
| 611 |
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3259810820 | bspline1_vals_x = bspline1_vals_x * tp_space1_quad%bspline_quad(1)%weights |
| 612 | |||
| 613 |
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422628348 | if (equal_spaces_x) then |
| 614 | i2_minus_ii_max = i1_minus_ii | ||
| 615 | end if | ||
| 616 | |||
| 617 | ! Loop over the first index (i or x-direction) of the B-spline basis function of the second basis | ||
| 618 |
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1688438676 | do i2_minus_ii = 0, i2_minus_ii_max |
| 619 | 1159948880 | i2_internal = i2_internals(i2_minus_ii) | |
| 620 | 1159948880 | bspline_mirrored_x2 = bspline_mirrored_x2s(i2_minus_ii) | |
| 621 | |||
| 622 | val = 0._wp | ||
| 623 |
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1159948880 | if (bspline_mirrored_x2) then |
| 624 |
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|
710654088 | do qdx = 1, n_quad1 |
| 625 | val = val + bspline1_vals_x(qdx) * partial_sum_yz(qdx) * & | ||
| 626 | 710654088 | & tp_space2_quad%bspline_quad(1)%bspline_at_nodes(i2_internal, degree_x2 - i2_minus_ii)%data(n_quad1 + 1 - qdx) | |
| 627 | end do | ||
| 628 | else | ||
| 629 | ✗ | do qdx = 1, n_quad1 | |
| 630 | val = val + bspline1_vals_x(qdx) * partial_sum_yz(qdx) * & | ||
| 631 | ✗ | & tp_space2_quad%bspline_quad(1)%bspline_at_nodes(i2_internal, i2_minus_ii)%data(qdx) | |
| 632 | end do | ||
| 633 | end if | ||
| 634 | |||
| 635 | 1582577228 | vals(i2_minus_ii, i1_minus_ii, j2_minus_jj, j1_minus_jj, k2_minus_kk, k1_minus_kk) = val | |
| 636 | |||
| 637 | end do ! i2_minus_ii | ||
| 638 | end do ! i1_minus_ii | ||
| 639 | |||
| 640 |
2/2✓ Branch 515 → 516 taken 91220488 times.
✓ Branch 515 → 524 taken 14640960 times.
|
146979084 | if (equal_spaces_x) then |
| 641 | ! Impose symmetry of the local values (set remainder of i2_minus_ii > i1_minus_ii) | ||
| 642 |
2/2✓ Branch 517 → 518 taken 370869468 times.
✓ Branch 517 → 523 taken 91220488 times.
|
462089956 | do i1_minus_ii = 0, degree_x1 |
| 643 |
2/2✓ Branch 519 → 520 taken 604909172 times.
✓ Branch 519 → 521 taken 370869468 times.
|
1066999128 | do i2_minus_ii = i1_minus_ii + 1, degree_x2 |
| 644 | ! SWAPPED SWAPPED | ||
| 645 | vals(i2_minus_ii, i1_minus_ii, j2_minus_jj, j1_minus_jj, k2_minus_kk, k1_minus_kk) = & | ||
| 646 | 975778640 | vals(i1_minus_ii, i2_minus_ii, j2_minus_jj, j1_minus_jj, k2_minus_kk, k1_minus_kk) | |
| 647 | end do | ||
| 648 | end do | ||
| 649 | end if | ||
| 650 | end do ! j2_minus_jj | ||
| 651 | end do ! j1_minus_jj | ||
| 652 | |||
| 653 |
2/2✓ Branch 528 → 529 taken 9728490 times.
✓ Branch 528 → 545 taken 1583264 times.
|
16133436 | if (equal_spaces_y) then |
| 654 | ! Impose symmetry of the local values (set remainder of j2_minus_jj > j1_minus_jj) | ||
| 655 |
2/2✓ Branch 530 → 531 taken 35976308 times.
✓ Branch 530 → 544 taken 9728490 times.
|
45704798 | do j1_minus_jj = 0, degree_y1 |
| 656 |
2/2✓ Branch 532 → 533 taken 52813780 times.
✓ Branch 532 → 542 taken 35976308 times.
|
98518578 | do j2_minus_jj = j1_minus_jj + 1, degree_y2 |
| 657 |
2/2✓ Branch 534 → 535 taken 217284475 times.
✓ Branch 534 → 540 taken 52813780 times.
|
306074563 | do i1_minus_ii = 0, degree_x1 |
| 658 |
2/2✓ Branch 536 → 537 taken 933658933 times.
✓ Branch 536 → 538 taken 217284475 times.
|
1203757188 | do i2_minus_ii = 0, degree_x2 |
| 659 | ! SWAPPED SWAPPED | ||
| 660 | vals(i2_minus_ii, i1_minus_ii, j2_minus_jj, j1_minus_jj, k2_minus_kk, k1_minus_kk) = & | ||
| 661 | 1150943408 | vals(i2_minus_ii, i1_minus_ii, j1_minus_jj, j2_minus_jj, k2_minus_kk, k1_minus_kk) | |
| 662 | end do | ||
| 663 | end do | ||
| 664 | end do | ||
| 665 | end do | ||
| 666 | end if | ||
| 667 | end do ! k2_minus_kk | ||
| 668 | end do ! k1_minus_kk | ||
| 669 | |||
| 670 |
2/2✓ Branch 549 → 550 taken 1589427 times.
✓ Branch 549 → 574 taken 291392 times.
|
1880819 | if (equal_spaces_z) then |
| 671 | ! Impose symmetry of the local values (set remainder of k2_minus_kk > k1_minus_kk) | ||
| 672 |
2/2✓ Branch 551 → 552 taken 4148434 times.
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|
5737861 | do k1_minus_kk = 0, degree_z1 |
| 673 |
2/2✓ Branch 553 → 554 taken 5455032 times.
✓ Branch 553 → 571 taken 4148434 times.
|
11192893 | do k2_minus_kk = k1_minus_kk + 1, degree_z2 |
| 674 |
2/2✓ Branch 555 → 556 taken 20387740 times.
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|
29991206 | do j1_minus_jj = 0, degree_y1 |
| 675 |
2/2✓ Branch 557 → 558 taken 80521628 times.
✓ Branch 557 → 567 taken 20387740 times.
|
106364400 | do j2_minus_jj = 0, degree_y2 |
| 676 |
2/2✓ Branch 559 → 560 taken 333047232 times.
✓ Branch 559 → 565 taken 80521628 times.
|
433956600 | do i1_minus_ii = 0, degree_x1 |
| 677 |
2/2✓ Branch 561 → 562 taken 1433793152 times.
✓ Branch 561 → 563 taken 333047232 times.
|
1847362012 | do i2_minus_ii = 0, degree_x2 |
| 678 | ! SWAPPED SWAPPED | ||
| 679 | vals(i2_minus_ii, i1_minus_ii, j2_minus_jj, j1_minus_jj, k2_minus_kk, k1_minus_kk) = & | ||
| 680 | 1766840384 | vals(i2_minus_ii, i1_minus_ii, j2_minus_jj, j1_minus_jj, k1_minus_kk, k2_minus_kk) | |
| 681 | end do | ||
| 682 | end do | ||
| 683 | end do | ||
| 684 | end do | ||
| 685 | end do | ||
| 686 | end do | ||
| 687 | end if | ||
| 688 | |||
| 689 | ! Determine row indices | ||
| 690 |
2/2✓ Branch 575 → 576 taken 4821682 times.
✓ Branch 575 → 592 taken 1880819 times.
|
6702501 | do k1_minus_kk = 0, degree_z1 |
| 691 | 4821682 | k1 = k1_minus_kk + kk | |
| 692 |
2/2✓ Branch 576 → 577 taken 4419168 times.
✓ Branch 576 → 578 taken 402514 times.
|
4821682 | if (is_periodic_z) k1 = modulo(k1, tp_space1%spaces(3)%nr_bsplines) |
| 693 |
2/2✓ Branch 579 → 580 taken 17215112 times.
✓ Branch 579 → 590 taken 4821682 times.
|
23917613 | do j1_minus_jj = 0, degree_y1 |
| 694 | 17215112 | j1 = j1_minus_jj + jj | |
| 695 |
2/2✓ Branch 580 → 581 taken 12405552 times.
✓ Branch 580 → 582 taken 4809560 times.
|
17215112 | if (is_periodic_y) j1 = modulo(j1, tp_space1%spaces(2)%nr_bsplines) |
| 696 |
2/2✓ Branch 583 → 584 taken 66455345 times.
✓ Branch 583 → 588 taken 17215112 times.
|
88492139 | do i1_minus_ii = 0, degree_x1 |
| 697 | 66455345 | i1 = i1_minus_ii + ii | |
| 698 |
2/2✓ Branch 584 → 585 taken 16615880 times.
✓ Branch 584 → 586 taken 49839465 times.
|
66455345 | if (is_periodic_x) i1 = modulo(i1, tp_space1%spaces(1)%nr_bsplines) |
| 699 | |||
| 700 | 66455345 | call cartesian_to_linear(tp_space1, row, i1, j1, k1) | |
| 701 | 66455345 | rows(i1_minus_ii, j1_minus_jj, k1_minus_kk) = row | |
| 702 | 83670457 | M%rows(i1_minus_ii + ii, j1_minus_jj + jj, k1_minus_kk + kk) = row | |
| 703 | end do | ||
| 704 | end do | ||
| 705 | end do | ||
| 706 | |||
| 707 | ! Determine column indices | ||
| 708 |
2/2✓ Branch 593 → 594 taken 1443731 times.
✓ Branch 593 → 616 taken 437088 times.
|
1880819 | if (equal_spaces_all) then |
| 709 |
10/22✓ Branch 594 → 595 taken 1443731 times.
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✓ Branch 612 → 613 taken 54656561 times.
✓ Branch 612 → 614 taken 13810152 times.
|
75124241 | cols = rows |
| 710 | else | ||
| 711 |
2/2✓ Branch 617 → 618 taken 1051616 times.
✓ Branch 617 → 634 taken 437088 times.
|
1488704 | do k2_minus_kk = 0, degree_z2 |
| 712 | 1051616 | k2 = k2_minus_kk + kk | |
| 713 |
1/2✓ Branch 618 → 619 taken 1051616 times.
✗ Branch 618 → 620 not taken.
|
1051616 | if (is_periodic_z) k2 = modulo(k2, tp_space2%spaces(3)%nr_bsplines) |
| 714 |
2/2✓ Branch 621 → 622 taken 3404960 times.
✓ Branch 621 → 632 taken 1051616 times.
|
4893664 | do j2_minus_jj = 0, degree_y2 |
| 715 | 3404960 | j2 = j2_minus_jj + jj | |
| 716 |
1/2✓ Branch 622 → 623 taken 3404960 times.
✗ Branch 622 → 624 not taken.
|
3404960 | if (is_periodic_y) j2 = modulo(j2, tp_space2%spaces(2)%nr_bsplines) |
| 717 |
2/2✓ Branch 625 → 626 taken 11798784 times.
✓ Branch 625 → 630 taken 3404960 times.
|
16255360 | do i2_minus_ii = 0, degree_x2 |
| 718 | 11798784 | i2 = i2_minus_ii + ii | |
| 719 |
1/2✗ Branch 626 → 627 not taken.
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|
11798784 | if (is_periodic_x) i2 = modulo(i2, tp_space2%spaces(1)%nr_bsplines) |
| 720 | |||
| 721 | 11798784 | call cartesian_to_linear(tp_space2, col, i2, j2, k2) | |
| 722 | 15203744 | cols(i2_minus_ii, j2_minus_jj, k2_minus_kk) = col | |
| 723 | end do | ||
| 724 | end do | ||
| 725 | end do | ||
| 726 | end if | ||
| 727 | |||
| 728 | ! Accumulate entries of the mass matrix | ||
| 729 |
2/2✓ Branch 636 → 637 taken 4821682 times.
✓ Branch 636 → 660 taken 1880819 times.
|
6840609 | do k1_minus_kk = 0, degree_z1 |
| 730 |
2/2✓ Branch 638 → 639 taken 16766786 times.
✓ Branch 638 → 658 taken 4821682 times.
|
23469287 | do k2_minus_kk = 0, degree_z2 |
| 731 | 16766786 | local_cdx_k = degree_z1 + k2_minus_kk - k1_minus_kk | |
| 732 | 16766786 | k1 = k1_minus_kk + kk | |
| 733 |
2/2✓ Branch 640 → 641 taken 61505376 times.
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|
83093844 | do j1_minus_jj = 0, degree_y1 |
| 734 |
2/2✓ Branch 642 → 643 taken 239196856 times.
✓ Branch 642 → 654 taken 61505376 times.
|
317469018 | do j2_minus_jj = 0, degree_y2 |
| 735 | 239196856 | local_cdx_j = degree_y1 + j2_minus_jj - j1_minus_jj | |
| 736 | 239196856 | j1 = j1_minus_jj + jj | |
| 737 |
2/2✓ Branch 644 → 645 taken 972960055 times.
✓ Branch 644 → 652 taken 239196856 times.
|
1273662287 | do i1_minus_ii = 0, degree_x1 |
| 738 | ✗ | do i2_minus_ii = 0, degree_x2 | |
| 739 | 4132310137 | i1 = i1_minus_ii + ii | |
| 740 | 4132310137 | local_cdx_i = degree_x1 + i2_minus_ii - i1_minus_ii | |
| 741 | |||
| 742 |
2/2✓ Branch 647 → 648 taken 437809477 times.
✓ Branch 647 → 649 taken 3694500660 times.
|
4132310137 | if (M%cols(local_cdx_i, local_cdx_j, local_cdx_k, i1, j1, k1) == -1) then |
| 743 | 437809477 | M%cols(local_cdx_i, local_cdx_j, local_cdx_k, i1, j1, k1) = cols(i2_minus_ii, j2_minus_jj, k2_minus_kk) | |
| 744 | end if | ||
| 745 | |||
| 746 | M%vals(local_cdx_i, local_cdx_j, local_cdx_k, i1, j1, k1) = M%vals(local_cdx_i, local_cdx_j, local_cdx_k, i1, j1, k1) + & | ||
| 747 | ✗ | & vals(i2_minus_ii, i1_minus_ii, j2_minus_jj, j1_minus_jj, k2_minus_kk, k1_minus_kk) | |
| 748 | end do | ||
| 749 | end do | ||
| 750 | end do | ||
| 751 | end do | ||
| 752 | end do | ||
| 753 | end do | ||
| 754 | end do ! ii | ||
| 755 | end do ! jj | ||
| 756 | end do ! kk | ||
| 757 | |||
| 758 |
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|
1957 | deallocate (coordfun_vals) |
| 759 |
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|
1957 | deallocate (vals) |
| 760 |
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|
1957 | deallocate (cols) |
| 761 |
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|
1957 | deallocate (rows) |
| 762 | |||
| 763 |
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|
1957 | deallocate (bspline1_vals_x) |
| 764 |
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|
1957 | deallocate (bspline1_vals_y) |
| 765 |
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|
1957 | deallocate (bspline1_vals_z) |
| 766 | |||
| 767 |
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|
1957 | deallocate (bspline_vals_x) |
| 768 |
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|
1957 | deallocate (bspline_vals_y) |
| 769 |
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|
1957 | deallocate (bspline_vals_z) |
| 770 | |||
| 771 |
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|
1957 | deallocate (partial_sum_z) |
| 772 |
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|
1957 | deallocate (partial_sum_yz) |
| 773 | |||
| 774 | 1957 | call tp_space1_quad%destroy() | |
| 775 | 1957 | call tp_space2_quad%destroy() | |
| 776 | |||
| 777 |
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|
13699 | end subroutine mass_matrix_3d |
| 778 | |||
| 779 |
4/30None:
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__m_tensorprod_matrix_MOD___copy_m_tensorprod_matrix_Tensorprodmat:
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__m_tensorprod_matrix_MOD___final_m_tensorprod_matrix_Tensorprodmat:
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|
15656 | end module m_tensorprod_matrix |
| 780 |