Source code for verde.mask

# Copyright (c) 2017 The Verde Developers.
# Distributed under the terms of the BSD 3-Clause License.
# SPDX-License-Identifier: BSD-3-Clause
#
# This code is part of the Fatiando a Terra project (https://www.fatiando.org)
#
"""
Mask grid points based on different criteria.
"""
import numpy as np
from scipy.spatial import Delaunay

from .base.utils import check_coordinates, n_1d_arrays
from .utils import kdtree


[docs]def distance_mask( data_coordinates, maxdist, coordinates=None, grid=None, projection=None ): """ Mask grid points that are too far from the given data points. Distances are Euclidean norms. If using geographic data, provide a projection function to convert coordinates to Cartesian before distance calculations. Either *coordinates* or *grid* must be given: * If *coordinates* is not None, produces an array that is False when a point is more than *maxdist* from the closest data point and True otherwise. * If *grid* is not None, produces a mask and applies it to *grid* (an :class:`xarray.Dataset`). .. note:: If installed, package ``pykdtree`` will be used instead of :class:`scipy.spatial.cKDTree` for better performance. Parameters ---------- data_coordinates : tuple of arrays Same as *coordinates* but for the data points. maxdist : float The maximum distance that a point can be from the closest data point. coordinates : None or tuple of arrays Arrays with the coordinates of each point that will be masked. Should be in the following order: (easting, northing, ...). Only easting and northing will be used, all subsequent coordinates will be ignored. grid : None or :class:`xarray.Dataset` 2D grid with values to be masked. Will use the first two dimensions of the grid as northing and easting coordinates, respectively. For this to work, the grid dimensions **must be ordered as northing then easting**. The mask will be applied to *grid* using the :meth:`xarray.Dataset.where` method. projection : callable or None If not None, then should be a callable object ``projection(easting, northing) -> (proj_easting, proj_northing)`` that takes in easting and northing coordinate arrays and returns projected easting and northing coordinate arrays. This function will be used to project the given coordinates (or the ones extracted from the grid) before calculating distances. Returns ------- mask : array or :class:`xarray.Dataset` If *coordinates* was given, then a boolean array with the same shape as the elements of *coordinates*. If *grid* was given, then an :class:`xarray.Dataset` with the mask applied to it. Examples -------- >>> from verde import grid_coordinates >>> region = (0, 5, -10, -4) >>> spacing = 1 >>> coords = grid_coordinates(region, spacing=spacing) >>> mask = distance_mask((2.5, -7.5), maxdist=2, coordinates=coords) >>> print(mask) [[False False False False False False] [False False True True False False] [False True True True True False] [False True True True True False] [False False True True False False] [False False False False False False] [False False False False False False]] >>> # Mask an xarray.Dataset directly >>> import xarray as xr >>> coords_dict = {"easting": coords[0][0, :], "northing": coords[1][:, 0]} >>> data_vars = {"scalars": (["northing", "easting"], np.ones(mask.shape))} >>> grid = xr.Dataset(data_vars, coords=coords_dict) >>> masked = distance_mask((3.5, -7.5), maxdist=2, grid=grid) >>> print(masked.scalars.values) [[nan nan nan nan nan nan] [nan nan nan 1. 1. nan] [nan nan 1. 1. 1. 1.] [nan nan 1. 1. 1. 1.] [nan nan nan 1. 1. nan] [nan nan nan nan nan nan] [nan nan nan nan nan nan]] """ coordinates, shape = _get_grid_coordinates(coordinates, grid) if projection is not None: data_coordinates = projection(*n_1d_arrays(data_coordinates, 2)) coordinates = projection(*n_1d_arrays(coordinates, 2)) tree = kdtree(data_coordinates[:2]) distance = tree.query(np.transpose(n_1d_arrays(coordinates, 2)))[0].reshape(shape) mask = distance <= maxdist if grid is not None: return grid.where(mask) return mask
[docs]def convexhull_mask( data_coordinates, coordinates=None, grid=None, projection=None, ): """ Mask grid points that are outside the convex hull of the given data points. Either *coordinates* or *grid* must be given: * If *coordinates* is not None, produces an array that is False when a point is outside the convex hull and True otherwise. * If *grid* is not None, produces a mask and applies it to *grid* (an :class:`xarray.Dataset`). Parameters ---------- data_coordinates : tuple of arrays Same as *coordinates* but for the data points. coordinates : None or tuple of arrays Arrays with the coordinates of each point that will be masked. Should be in the following order: (easting, northing, ...). Only easting and northing will be used, all subsequent coordinates will be ignored. grid : None or :class:`xarray.Dataset` 2D grid with values to be masked. Will use the first two dimensions of the grid as northing and easting coordinates, respectively. For this to work, the grid dimensions **must be ordered as northing then easting**. The mask will be applied to *grid* using the :meth:`xarray.Dataset.where` method. projection : callable or None If not None, then should be a callable object ``projection(easting, northing) -> (proj_easting, proj_northing)`` that takes in easting and northing coordinate arrays and returns projected easting and northing coordinate arrays. This function will be used to project the given coordinates (or the ones extracted from the grid) before calculating distances. Returns ------- mask : array or :class:`xarray.Dataset` If *coordinates* was given, then a boolean array with the same shape as the elements of *coordinates*. If *grid* was given, then an :class:`xarray.Dataset` with the mask applied to it. Examples -------- >>> from verde import grid_coordinates >>> region = (0, 5, -10, -4) >>> spacing = 1 >>> coords = grid_coordinates(region, spacing=spacing) >>> data_coords = ((2, 3, 2, 3), (-9, -9, -6, -6)) >>> mask = convexhull_mask(data_coords, coordinates=coords) >>> print(mask) [[False False False False False False] [False False True True False False] [False False True True False False] [False False True True False False] [False False True True False False] [False False False False False False] [False False False False False False]] >>> # Mask an xarray.Dataset directly >>> import xarray as xr >>> coords_dict = {"easting": coords[0][0, :], "northing": coords[1][:, 0]} >>> data_vars = {"scalars": (["northing", "easting"], np.ones(mask.shape))} >>> grid = xr.Dataset(data_vars, coords=coords_dict) >>> masked = convexhull_mask(data_coords, grid=grid) >>> print(masked.scalars.values) [[nan nan nan nan nan nan] [nan nan 1. 1. nan nan] [nan nan 1. 1. nan nan] [nan nan 1. 1. nan nan] [nan nan 1. 1. nan nan] [nan nan nan nan nan nan] [nan nan nan nan nan nan]] """ coordinates, shape = _get_grid_coordinates(coordinates, grid) n_coordinates = 2 # Make sure they are arrays so we can normalize data_coordinates = n_1d_arrays(data_coordinates, n_coordinates) coordinates = n_1d_arrays(coordinates, n_coordinates) if projection is not None: data_coordinates = projection(*data_coordinates) coordinates = projection(*coordinates) # Normalize the coordinates to avoid errors from qhull when values are very # large (as occurs when projections are used). means = [coord.mean() for coord in data_coordinates] stds = [coord.std() for coord in data_coordinates] data_coordinates = tuple( (coord - mean) / std for coord, mean, std in zip(data_coordinates, means, stds) ) coordinates = tuple( (coord - mean) / std for coord, mean, std in zip(coordinates, means, stds) ) triangles = Delaunay(np.transpose(data_coordinates)) # Find the triangle that contains each grid point. # -1 indicates that it's not in any triangle. in_triangle = triangles.find_simplex(np.transpose(coordinates)) mask = (in_triangle != -1).reshape(shape) if grid is not None: return grid.where(mask) return mask
def _get_grid_coordinates(coordinates, grid): """ If coordinates is given, return it and their shape. Otherwise, get coordinate arrays from the grid. """ if coordinates is None and grid is None: raise ValueError("Either coordinates or grid must be given.") if coordinates is None: dims = [grid[var].dims for var in grid.data_vars][0] coordinates = np.meshgrid(grid.coords[dims[1]], grid.coords[dims[0]]) check_coordinates(coordinates) shape = coordinates[0].shape return coordinates, shape