module kinds_modTypes:
private type hilbert_table public type hilbert2d_iterVariables:
integer (kind=i_k), private, parameter :: SFC_MAX_LEV = 12 integer (kind=i_k), private, parameter :: SFC_DIMS = 2 type (hilbert_table), private, parameter, dimension (0:3) :: tab = (/ hilbert_table ((/ 2, 1, -2 /), (/ 1, 0, 0, 2 /), (/ 0, 2, 3, 1 /), (/ 0, 3, 1, 2 /)), hilbert_table ((/ 1, 2, -1 /), (/ 0, 1, 1, 3 /), (/ 0, 1, 3, 2 /), (/ 0, 1, 3, 2 /)), hilbert_table ((/ -1, -2, 1 /), (/ 3, 2, 2, 0 /), (/ 3, 2, 0, 1 /), (/ 2, 3, 1, 0 /)), hilbert_table ((/ -2, -1, 2 /), (/ 2, 3, 3, 1 /), (/ 3, 1, 0, 2 /), (/ 2, 1, 3, 0 /)) /)Subroutines and functions:
public pure subroutine hilbert2d_c2i (lev, p, idx) public pure subroutine hilbert2d_i2c (lev, idx, p) public pure subroutine hilbert2d_c2i_qsz (lev, qsz, p, idx) public pure subroutine hilbert2d_i2c_qsz (lev, qsz, idx, p, iter) public pure subroutine hilbert2d_iter_init (iter, lev, opt_qsz) public pure subroutine hilbert2d_iter_set (iter, idx) public pure subroutine hilbert2d_iter_next (iter)
Routines accept position and hilbert-index starting at 1.
Author: Matthias Lieber
private type hilbert_table integer (kind=i_k), dimension (0:2) :: mv integer (kind=i_k), dimension (0:3) :: next integer (kind=i_k), dimension (0:3) :: num2ref integer (kind=i_k), dimension (0:3) :: ref2num end type hilbert_tableComponents:
mv | spatial moves of the curve |
next | next states when refinining (quadrant is sequence number) |
num2ref | sequence number on curve primitve to reference (spatial) quadrant |
ref2num | reference (spatial) quadrant to sequence number on curve primitve |
Values of the mv item are:
public type hilbert2d_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 hilbert2d_iterIterator to traverse the 2D Hilbert curve
public pure subroutine hilbert2d_c2i (lev, p, idx) integer (kind=i_k), intent(in) :: lev integer (kind=i_k), intent(in), dimension (2) :: p integer (kind=i_k), intent(out) :: idx end subroutine hilbert2d_c2iParameters:
lev | level of the hilbert curve (1=2x2, 2=4x4, 3=8x8, etc) |
p | 2D coordinates [1 ... 2^lev] |
idx | index on the 2D hilbert curve [1 ... (2^lev)^2] |
Has logarithmic complexity: number of loop iterations = lev. Due to performance reasons, no checking of arguments is performend!
public pure subroutine hilbert2d_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 (2) :: p end subroutine hilbert2d_i2cParameters:
lev | level of the hilbert curve (1=2x2, 2=4x4, 3=8x8, etc) |
idx | index on the 2D hilbert curve [1 ... (2^lev)^2 ] |
p | 2D 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 hilbert2d_c2i_qsz (lev, qsz, p, idx) integer (kind=i_k), intent(in) :: lev integer (kind=i_k), intent(in), dimension (2) :: qsz integer (kind=i_k), intent(in), dimension (2) :: p integer (kind=i_k), intent(out) :: idx end subroutine hilbert2d_c2i_qszParameters:
lev | level of the hilbert curve (1=2x2, 2=4x4, 3=8x8, etc) |
qsz | query region size |
p | 2D coordinates [1 ... 2^lev] |
idx | index on the 2D hilbert curve [1 ... (2^lev)^2] |
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 hilbert2d_i2c_qsz (lev, qsz, idx, p, iter) integer (kind=i_k), intent(in) :: lev integer (kind=i_k), intent(in), dimension (2) :: qsz integer (kind=i_k), intent(in) :: idx integer (kind=i_k), intent(out), dimension (2) :: p type (hilbert2d_iter), optional, intent(inout) :: iter end subroutine hilbert2d_i2c_qszParameters:
lev | level of the hilbert curve (1=2x2, 2=4x4, 3=8x8, etc) |
qsz | query region size |
idx | index on the 2D hilbert curve [1 ... (2^lev)^2 ] |
p | 2D 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 hilbert2d_iter_init (iter, lev, opt_qsz) type (hilbert2d_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 hilbert2d_iter_initInitialize the iterator.
The current index is iter%idx and the current 2D position iter%p.
call hilbert2d_iter_init(iter, lev, qsz) do while(iter%idx > 0) array(iter%p(1),iter%p(2)) = iter%idx call hilbert2d_iter_next(iter) end do
public pure subroutine hilbert2d_iter_set (iter, idx) type (hilbert2d_iter), intent(inout) :: iter integer (kind=i_k), intent(in) :: idx end subroutine hilbert2d_iter_setSet the iterator to given index
public pure subroutine hilbert2d_iter_next (iter) type (hilbert2d_iter), intent(inout) :: iter end subroutine hilbert2d_iter_nextIterate to next point on the hilbert curve
After reaching the end of the curve, iter%idx is set to 0.