module kinds_modTypes:
private type hilbert_table public type hilbert_iterVariables:
integer (kind=i_k), private, parameter :: SFC_MAX_LEV = 12 integer (kind=i_k), private, parameter :: SFC_DIMS = 3 type (hilbert_table), private, parameter, dimension (0:23) :: tab = (/ hilbert_table ((/ 1, 3, -1, 2, 1, -3, -1 /), (/ 1, 2, 2, 20, 20, 4, 4, 5 /), (/ 0, 1, 5, 4, 6, 7, 3, 2 /), (/ 0, 1, 7, 6, 3, 2, 4, 5 /)), hilbert_table ((/ 3, 2, -3, 1, 3, -2, -3 /), (/ 6, 7, 7, 19, 19, 9, 9, 10 /), (/ 0, 4, 6, 2, 3, 7, 5, 1 /), (/ 0, 7, 3, 4, 1, 6, 2, 5 /)), hilbert_table ((/ 1, 2, -1, 3, 1, -2, -1 /), (/ 11, 0, 0, 23, 23, 14, 14, 15 /), (/ 0, 1, 3, 2, 6, 7, 5, 4 /), (/ 0, 1, 3, 2, 7, 6, 4, 5 /)), hilbert_table ((/ -1, -3, 1, 2, -1, 3, 1 /), (/ 16, 17, 17, 7, 7, 13, 13, 8 /), (/ 5, 4, 0, 1, 3, 2, 6, 7 /), (/ 2, 3, 5, 4, 1, 0, 6, 7 /)), hilbert_table ((/ 1, -2, -1, -3, 1, 2, -1 /), (/ 19, 14, 14, 10, 10, 0, 0, 22 /), (/ 6, 7, 5, 4, 0, 1, 3, 2 /), (/ 4, 5, 7, 6, 3, 2, 0, 1 /)), hilbert_table ((/ 3, -2, -3, -1, 3, 2, -3 /), (/ 23, 9, 9, 15, 15, 7, 7, 21 /), (/ 3, 7, 5, 1, 0, 4, 6, 2 /), (/ 4, 3, 7, 0, 5, 2, 6, 1 /)), hilbert_table ((/ 2, 1, -2, 3, 2, -1, -2 /), (/ 0, 11, 11, 13, 13, 15, 15, 14 /), (/ 0, 2, 3, 1, 5, 7, 6, 4 /), (/ 0, 3, 1, 2, 7, 4, 6, 5 /)), hilbert_table ((/ 3, 1, -3, 2, 3, -1, -3 /), (/ 2, 1, 1, 3, 3, 5, 5, 4 /), (/ 0, 4, 5, 1, 3, 7, 6, 2 /), (/ 0, 3, 7, 4, 1, 2, 6, 5 /)), hilbert_table ((/ -3, -2, 3, 1, -3, 2, 3 /), (/ 21, 18, 18, 11, 11, 20, 20, 23 /), (/ 6, 2, 0, 4, 5, 1, 3, 7 /), (/ 2, 5, 1, 6, 3, 4, 0, 7 /)), hilbert_table ((/ 3, -1, -3, -2, 3, 1, -3 /), (/ 13, 5, 5, 14, 14, 1, 1, 17 /), (/ 3, 7, 6, 2, 0, 4, 5, 1 /), (/ 4, 7, 3, 0, 5, 6, 2, 1 /)), hilbert_table ((/ 2, -1, -2, -3, 2, 1, -2 /), (/ 3, 15, 15, 4, 4, 11, 11, 12 /), (/ 5, 7, 6, 4, 0, 2, 3, 1 /), (/ 4, 7, 5, 6, 3, 0, 2, 1 /)), hilbert_table ((/ 2, 3, -2, 1, 2, -3, -2 /), (/ 7, 6, 6, 8, 8, 10, 10, 9 /), (/ 0, 2, 6, 4, 5, 7, 3, 1 /), (/ 0, 7, 1, 6, 3, 4, 2, 5 /)), hilbert_table ((/ -1, 3, 1, -2, -1, -3, 1 /), (/ 5, 13, 13, 18, 18, 17, 17, 1 /), (/ 3, 2, 6, 7, 5, 4, 0, 1 /), (/ 6, 7, 1, 0, 5, 4, 2, 3 /)), hilbert_table ((/ -1, -2, 1, 3, -1, 2, 1 /), (/ 22, 12, 12, 6, 6, 3, 3, 19 /), (/ 3, 2, 0, 1, 5, 4, 6, 7 /), (/ 2, 3, 1, 0, 5, 4, 6, 7 /)), hilbert_table ((/ 1, -3, -1, -2, 1, 3, -1 /), (/ 8, 4, 4, 9, 9, 2, 2, 16 /), (/ 6, 7, 3, 2, 0, 1, 5, 4 /), (/ 4, 5, 3, 2, 7, 6, 0, 1 /)), hilbert_table ((/ 2, -3, -2, -1, 2, 3, -2 /), (/ 20, 10, 10, 5, 5, 6, 6, 18 /), (/ 5, 7, 3, 1, 0, 2, 6, 4 /), (/ 4, 3, 5, 2, 7, 0, 6, 1 /)), hilbert_table ((/ -3, 2, 3, -1, -3, -2, 3 /), (/ 10, 20, 20, 22, 22, 18, 18, 6 /), (/ 5, 1, 3, 7, 6, 2, 0, 4 /), (/ 6, 1, 5, 2, 7, 0, 4, 3 /)), hilbert_table ((/ -1, 2, 1, -3, -1, -2, 1 /), (/ 15, 3, 3, 21, 21, 12, 12, 11 /), (/ 5, 4, 6, 7, 3, 2, 0, 1 /), (/ 6, 7, 5, 4, 1, 0, 2, 3 /)), hilbert_table ((/ -3, 1, 3, -2, -3, -1, 3 /), (/ 4, 8, 8, 12, 12, 16, 16, 2 /), (/ 6, 2, 3, 7, 5, 1, 0, 4 /), (/ 6, 5, 1, 2, 7, 4, 0, 3 /)), hilbert_table ((/ -2, -3, 2, 1, -2, 3, 2 /), (/ 18, 21, 21, 1, 1, 23, 23, 20 /), (/ 6, 4, 0, 2, 3, 1, 5, 7 /), (/ 2, 5, 3, 4, 1, 6, 0, 7 /)), hilbert_table ((/ -3, -1, 3, 2, -3, 1, 3 /), (/ 17, 16, 16, 0, 0, 8, 8, 13 /), (/ 5, 1, 0, 4, 6, 2, 3, 7 /), (/ 2, 1, 5, 6, 3, 0, 4, 7 /)), hilbert_table ((/ -2, 1, 2, -3, -2, -1, 2 /), (/ 14, 19, 19, 17, 17, 22, 22, 0 /), (/ 6, 4, 5, 7, 3, 1, 0, 2 /), (/ 6, 5, 7, 4, 1, 2, 0, 3 /)), hilbert_table ((/ -2, 3, 2, -1, -2, -3, 2 /), (/ 9, 23, 23, 16, 16, 21, 21, 7 /), (/ 3, 1, 5, 7, 6, 4, 0, 2 /), (/ 6, 1, 7, 0, 5, 2, 4, 3 /)), hilbert_table ((/ -2, -1, 2, 3, -2, 1, 2 /), (/ 12, 22, 22, 2, 2, 19, 19, 3 /), (/ 3, 1, 0, 2, 6, 4, 5, 7 /), (/ 2, 1, 3, 0, 5, 6, 4, 7 /)) /)Subroutines and functions:
public pure subroutine hilbert_c2i (lev, p, idx) public pure subroutine hilbert_i2c (lev, idx, p) public pure subroutine hilbert_c2i_qsz (lev, qsz, p, idx) public pure subroutine hilbert_i2c_qsz (lev, qsz, idx, p, iter) public pure subroutine hilbert_iter_init (iter, lev, opt_qsz) public pure subroutine hilbert_iter_set (iter, idx) public pure subroutine hilbert_iter_next (iter)
Routines accept position and hilbert-index starting at 1 (instead of 0 in hilbert.F90)
Author: Matthias Lieber
private type hilbert_table integer (kind=i_k), dimension (0:6) :: mv integer (kind=i_k), dimension (0:7) :: next integer (kind=i_k), dimension (0:7) :: num2ref integer (kind=i_k), dimension (0:7) :: ref2num end type hilbert_tableComponents:
mv | spatial moves of the curve |
next | next states when refinining (octant is sequence number) |
num2ref | sequence number on curve primitve to reference (spatial) octant |
ref2num | reference (spatial) octant to sequence number on curve primitve |
Values of the mv item are:
public type hilbert_iter integer (kind=i_k) :: idx = -1 integer (kind=i_k), dimension (SFC_DIMS) :: p = -1 integer (kind=i_k) :: lev = -1 integer (kind=i_k), dimension (SFC_DIMS) :: qsz = -1 integer (kind=i_k) :: len = -1 integer (kind=i_k) :: clev = -1 integer (kind=i_k), dimension (SFC_MAX_LEV) :: s = -1 integer (kind=i_k), dimension (SFC_MAX_LEV) :: c = -1 integer (kind=i_K) :: jump_level = SFC_MAX_LEV + 1 end type hilbert_iterIterator to traverse the 3D Hilbert curve
public pure subroutine hilbert_c2i (lev, p, idx) integer (kind=i_k), intent(in) :: lev integer (kind=i_k), intent(in), dimension (3) :: p integer (kind=i_k), intent(out) :: idx end subroutine hilbert_c2iParameters:
lev | level of the hilbert curve (1=2x2x2, 2=4x4x4, 3=8x8x8, etc) |
p | 3D coordinates [1 ... 2^lev] |
idx | index on the 3D hilbert curve [1 ... (2^lev)^3] |
Has logarithmic complexity: number of loop iterations = lev. Due to performance reasons, no checking of arguments is performend!
public pure subroutine hilbert_i2c (lev, idx, p) integer (kind=i_k), intent(in) :: lev integer (kind=i_k), intent(in) :: idx integer (kind=i_k), intent(out), dimension (3) :: p end subroutine hilbert_i2cParameters:
lev | level of the hilbert curve (1=2x2x2, 2=4x4x4, 3=8x8x8, etc) |
idx | index on the 3D hilbert curve [1 ... (2^lev)^3 ] |
p | 3D coordinates [1 ... 2^lev] |
Has logarithmic complexity: number of loop iterations = lev. Due to performance reasons, no checking of arguments is performend!
public pure subroutine hilbert_c2i_qsz (lev, qsz, p, idx) integer (kind=i_k), intent(in) :: lev integer (kind=i_k), intent(in), dimension (3) :: qsz integer (kind=i_k), intent(in), dimension (3) :: p integer (kind=i_k), intent(out) :: idx end subroutine hilbert_c2i_qszParameters:
lev | level of the hilbert curve (1=2x2x2, 2=4x4x4, 3=8x8x8, etc) |
qsz | query region size |
p | 3D coordinates [1 ... 2^lev] |
idx | index on the 3D hilbert curve [1 ... (2^lev)^3] |
The size of the query region is restricted by qsz for each dimension. qsz must be <= lev**2 and pos must be <= qsz.
Has logarithmic complexity: number of loop iterations = lev. Due to performance reasons, no checking of arguments is performend!
public pure subroutine hilbert_i2c_qsz (lev, qsz, idx, p, iter) integer (kind=i_k), intent(in) :: lev integer (kind=i_k), intent(in), dimension (3) :: qsz integer (kind=i_k), intent(in) :: idx integer (kind=i_k), intent(out), dimension (3) :: p type (hilbert_iter), optional, intent(inout) :: iter end subroutine hilbert_i2c_qszParameters:
lev | level of the hilbert curve (1=2x2x2, 2=4x4x4, 3=8x8x8, etc) |
qsz | query region size |
idx | index on the 3D hilbert curve [1 ... (2^lev)^3 ] |
p | 3D coordinates [1 ... 2^lev] |
iter | for internal use only |
The size of the query region is restricted by qsz for each dimension. qsz must be <= lev**2 and pos must be <= qsz.
Has logarithmic complexity: number of loop iterations = lev. Due to performance reasons, no checking of arguments is performend!
public pure subroutine hilbert_iter_init (iter, lev, opt_qsz) type (hilbert_iter), intent(inout) :: iter integer (kind=i_k), intent(in) :: lev integer (kind=i_k), optional, intent(in), dimension (SFC_DIMS) :: opt_qsz end subroutine hilbert_iter_initInitialize the iterator.
The current index is iter%idx and the current 3D position iter%p.
call hilbert_iter_init(iter, lev, qsz) do while(iter%idx > 0) array(iter%p(1),iter%p(2),iter%p(3)) = iter%idx call hilbert_iter_next(iter) end do
public pure subroutine hilbert_iter_set (iter, idx) type (hilbert_iter), intent(inout) :: iter integer (kind=i_k), intent(in) :: idx end subroutine hilbert_iter_setSet the iterator to given index
public pure subroutine hilbert_iter_next (iter) type (hilbert_iter), intent(inout) :: iter end subroutine hilbert_iter_nextIterate to next point on the hilbert curve
After reaching the end of the curve, iter%idx is set to 0.