verde.expanding_window

verde.expanding_window(coordinates, center, sizes)

Select points on windows of changing size around a center point.

Returns the indices of points falling inside each window.

Parameters

• coordinates (tuple of arrays) – Arrays with the coordinates of each data point. Should be in the following order: (easting, northing, vertical, …). Only easting and northing will be used, all subsequent coordinates will be ignored.

• center (tuple) – The coordinates of the center of the window. Should be in the following order: (easting, northing, vertical, …).

• sizes (array) – The sizes of the windows. Does not have to be in any particular order. The order of indices returned will match the order of window sizes given. Units should match the units of coordinates and center.

Returns

indices (list) – Each element of the list corresponds to the indices of points falling inside a window. Use them to index the coordinates for each window. The indices will depend on the number of dimensions in the input coordinates. For example, if the coordinates are 2D arrays, each window will contain indices for 2 dimensions (row, column).

See also

block_split

Split a region into blocks and label points accordingly.

rolling_window

Select points on a rolling (moving) window.

Examples

Generate a set of sample coordinates on a grid and determine the indices of points for each expanding window:

>>> from verde import grid_coordinates
>>> coords = grid_coordinates((-5, -1, 6, 10), spacing=1)
>>> print(coords[0])
[[-5. -4. -3. -2. -1.]
 [-5. -4. -3. -2. -1.]
 [-5. -4. -3. -2. -1.]
 [-5. -4. -3. -2. -1.]
 [-5. -4. -3. -2. -1.]]
>>> print(coords[1])
[[ 6.  6.  6.  6.  6.]
 [ 7.  7.  7.  7.  7.]
 [ 8.  8.  8.  8.  8.]
 [ 9.  9.  9.  9.  9.]
 [10. 10. 10. 10. 10.]]
>>> # Get the expanding window indices
>>> indices = expanding_window(coords, center=(-3, 8), sizes=[1, 2, 4])
>>> # There is one index per window
>>> print(len(indices))
3
>>> # The points in the first window. Indices are 2D positions because the
>>> # coordinate arrays are 2D.
>>> print(len(indices[0]))
2
>>> for dimension in indices[0]:
...     print(dimension)
[2]
[2]
>>> for dimension in indices[1]:
...     print(dimension)
[1 1 1 2 2 2 3 3 3]
[1 2 3 1 2 3 1 2 3]
>>> for dimension in indices[2]:
...     print(dimension)
[0 0 0 0 0 1 1 1 1 1 2 2 2 2 2 3 3 3 3 3 4 4 4 4 4]
[0 1 2 3 4 0 1 2 3 4 0 1 2 3 4 0 1 2 3 4 0 1 2 3 4]
>>> # To get the coordinates for each window, use indexing
>>> print(coords[0][indices[0]])
[-3.]
>>> print(coords[1][indices[0]])
[8.]
>>> print(coords[0][indices[1]])
[-4. -3. -2. -4. -3. -2. -4. -3. -2.]
>>> print(coords[1][indices[1]])
[7. 7. 7. 8. 8. 8. 9. 9. 9.]

If the coordinates are 1D, the indices will also be 1D:

>>> coords1d = [coord.ravel() for coord in coords]
>>> indices = expanding_window(coords1d, center=(-3, 8), sizes=[1, 2, 4])
>>> print(len(indices))
3
>>> # Since coordinates are 1D, there is only one index
>>> print(len(indices[0]))
1
>>> print(indices[0][0])
[12]
>>> print(indices[1][0])
[ 6  7  8 11 12 13 16 17 18]
>>> # The returned indices can be used in the same way as before
>>> print(coords1d[0][indices[0]])
[-3.]
>>> print(coords1d[1][indices[0]])
[8.]

Only the first 2 coordinates are considered (assumed to be the horizontal ones). All others will be ignored by the function.

>>> coords = grid_coordinates((-5, -1, 6, 10), spacing=1, extra_coords=15)
>>> print(coords[2])
[[15. 15. 15. 15. 15.]
 [15. 15. 15. 15. 15.]
 [15. 15. 15. 15. 15.]
 [15. 15. 15. 15. 15.]
 [15. 15. 15. 15. 15.]]
>>> indices = expanding_window(coords, center=(-3, 8), sizes=[1, 2, 4])
>>> # The returned indices should be the same as before, ignoring coords[2]
>>> print(len(indices[0]))
2
>>> for dimension in indices[0]:
...     print(dimension)
[2]
[2]
>>> for dimension in indices[1]:
...     print(dimension)
[1 1 1 2 2 2 3 3 3]
[1 2 3 1 2 3 1 2 3]
>>> for dimension in indices[2]:
...     print(dimension)
[0 0 0 0 0 1 1 1 1 1 2 2 2 2 2 3 3 3 3 3 4 4 4 4 4]
[0 1 2 3 4 0 1 2 3 4 0 1 2 3 4 0 1 2 3 4 0 1 2 3 4]
>>> # The indices can be used to index all 3 coordinates
>>> print(coords[0][indices[0]])
[-3.]
>>> print(coords[1][indices[0]])
[8.]
>>> print(coords[2][indices[0]])
[15.]