# Source code for pyinterp.rtree

#
"""
RTree spatial index
-------------------
"""
from typing import Optional, Tuple

import numpy as np

from . import core, geodetic

[docs]class RTree: """R*Tree spatial index for geodetic scalar values. Args: system: WGS of the coordinate system used to transform equatorial spherical positions (longitudes, latitudes, altitude) into ECEF coordinates. If not set the geodetic system used is WGS-84. Default to None. dtype: Data type of the instance to create. ndims: The number of dimensions of the tree. This dimension must be at least equal to 3 to store the ECEF coordinates of the points. Default to 3. """ def __init__(self, system: Optional[geodetic.Spheroid] = None, dtype: Optional[np.dtype] = None, ndims: int = 3): """Initialize a new R*Tree.""" dtype = dtype or np.dtype("float64") if ndims < 3: raise ValueError("ndims must be >= 3") if dtype == np.dtype("float64"): self._instance = getattr(core, f"RTree{ndims}DFloat64")(system) elif dtype == np.dtype("float32"): self._instance = getattr(core, f"RTree{ndims}DFloat32")(system) else: raise ValueError(f"dtype {dtype} not handled by the object") self.dtype = dtype
[docs] def bounds( self ) -> Tuple[Tuple[float, float, float], Tuple[float, float, float]]: """Returns the box able to contain all values stored in the container. Returns: A tuple that contains the coordinates of the minimum and maximum corners of the box able to contain all values stored in the container or an empty tuple if there are no values in the container. """ return self._instance.bounds()
[docs] def clear(self) -> None: """Removes all values stored in the container.""" return self._instance.clear()
[docs] def __len__(self): """Returns the number of values stored in the tree.""" return self._instance.__len__()
[docs] def __bool__(self): """Returns true if the tree is not empty.""" return self._instance.__bool__()
[docs] def packing(self, coordinates: np.ndarray, values: np.ndarray) -> None: """The tree is created using packing algorithm (The old data is erased before construction.) Args: coordinates: a matrix (n, ndims) where n is the number of observations and ndims is the number of coordinates in order: longitude and latitude in degrees, altitude in meters and then the other coordinates defined in Euclidean space if dims > 3. If the shape of the matrix is (n, ndims) then the method considers the altitude constant and equal to zero. values: An array of size (n) containing the values associated with the coordinates provided. """ self._instance.packing(coordinates, values)
[docs] def insert(self, coordinates: np.ndarray, values: np.ndarray) -> None: """Insert new data into the search tree. Args: coordinates: a matrix (n, ndims) where n is the number of observations and ndims is the number of coordinates in order: longitude and latitude in degrees, altitude in meters and then the other coordinates defined in Euclidean space if dims > 3. If the shape of the matrix is (n, ndims) then the method considers the altitude constant and equal to zero. values: An array of size (n) containing the values associated with the coordinates provided. """ self._instance.insert(coordinates, values)
[docs] def query(self, coordinates: np.ndarray, k: Optional[int] = 4, within: Optional[bool] = True, num_threads: Optional[int] = 0) -> Tuple[np.ndarray, np.ndarray]: """Search for the nearest K nearest neighbors of a given point. Args: coordinates: a matrix (n, ndims) where n is the number of observations and ndims is the number of coordinates in order: longitude and latitude in degrees, altitude in meters and then the other coordinates defined in Euclidean space if dims > 3. If the shape of the matrix is (n, ndims) then the method considers the altitude constant and equal to zero. k: The number of nearest neighbors to be searched. Defaults to 4. within: If true, the method ensures that the neighbors found are located within the point of interest. Defaults to false. num_threads: The number of threads to use for the computation. If 0 all CPUs are used. If 1 is given, no parallel computing code is used at all, which is useful for debugging. Defaults to 0. Returns: A tuple containing a matrix describing for each provided position, the distance, in meters, between the provided position and the found neighbors and a matrix containing the value of the different neighbors found for all provided positions. If no neighbors are found, the distance and the value are set to -1. """ return self._instance.query(coordinates, k, within, num_threads)
[docs] def inverse_distance_weighting( self, coordinates: np.ndarray, radius: Optional[float] = None, k: Optional[int] = 9, p: Optional[int] = 2, within: Optional[bool] = True, num_threads: Optional[int] = 0) -> Tuple[np.ndarray, np.ndarray]: """Interpolation of the value at the requested position by inverse distance weighting method. Args: coordinates: a matrix (n, ndims) where n is the number of observations and ndims is the number of coordinates in order: longitude and latitude in degrees, altitude in meters and then the other coordinates defined in Euclidean space if dims > 3. If the shape of the matrix is (n, ndims) then the method considers the altitude constant and equal to zero. radius: The maximum radius of the search (m). Defaults The maximum distance between two points. k: The number of nearest neighbors to be used for calculating the interpolated value. Defaults to 9. p: The power parameters. Defaults to 2. within: If true, the method ensures that the neighbors found are located around the point of interest. In other words, this parameter ensures that the calculated values will not be extrapolated. Defaults to true. num_threads: The number of threads to use for the computation. If 0 all CPUs are used. If 1 is given, no parallel computing code is used at all, which is useful for debugging. Defaults to 0. Returns: The interpolated value and the number of neighbors used in the calculation. """ return self._instance.inverse_distance_weighting( coordinates, radius, k, p, within, num_threads)
[docs] def radial_basis_function( self, coordinates: np.ndarray, radius: Optional[float] = None, k: Optional[int] = 9, rbf: Optional[str] = None, epsilon: Optional[float] = None, smooth: Optional[float] = 0, within: Optional[bool] = True, num_threads: Optional[int] = 0) -> Tuple[np.ndarray, np.ndarray]: """Interpolation of the value at the requested position by radial basis function interpolation. Args: coordinates: a matrix (n, ndims) where n is the number of observations and ndims is the number of coordinates in order: longitude and latitude in degrees, altitude in meters and then the other coordinates defined in Euclidean space if dims > 3. If the shape of the matrix is (n, ndims) then the method considers the altitude constant and equal to zero. radius: The maximum radius of the search (m). Defaults The maximum distance between two points. k: The number of nearest neighbors to be used for calculating the interpolated value. Defaults to 9. rbf: The radial basis function, based on the radius, :math:r given by the distance between points. This parameter can take one of the following values: * cubic: :math:\\varphi(r) = r^3 * gaussian: :math:\\varphi(r) = e^{-(\\dfrac{r} {\\varepsilon})^2} * inverse_multiquadric: :math:\\varphi(r) = \\dfrac{1} {\\sqrt{1+(\\dfrac{r}{\\varepsilon})^2}} * linear: :math:\\varphi(r) = r * multiquadric: :math:\\varphi(r) = \\sqrt{1+( \\dfrac{r}{\\varepsilon})^2} * thin_plate: :math:\\varphi(r) = r^2 \\ln(r) Default to multiquadric epsilon: adjustable constant for gaussian or multiquadrics functions. Default to the average distance between nodes. smooth: values greater than zero increase the smoothness of the approximation. Default to 0 (interpolation). within: If true, the method ensures that the neighbors found are located around the point of interest. In other words, this parameter ensures that the calculated values will not be extrapolated. Defaults to true. num_threads: The number of threads to use for the computation. If 0 all CPUs are used. If 1 is given, no parallel computing code is used at all, which is useful for debugging. Defaults to 0. Returns: The interpolated value and the number of neighbors used in the calculation. """ adjustable = ['gaussian', 'inverse_multiquadric', 'multiquadric'] non_adjustable = ['cubic', 'linear', 'thin_plate'] rbf = rbf or adjustable[-1] if epsilon is not None and rbf in non_adjustable: raise ValueError( f"epsilon must be None for {', '.join(non_adjustable)} RBF") if rbf not in adjustable + non_adjustable: raise ValueError(f"Radial basis function {rbf!r} is not defined") rbf = "".join(item.capitalize() for item in rbf.split("_")) return self._instance.radial_basis_function( coordinates, radius, k, getattr(core.RadialBasisFunction, rbf), epsilon, smooth, within, num_threads)
[docs] def window_function( self, coordinates: np.ndarray, radius: float, k: Optional[int] = 9, wf: Optional[str] = None, arg: Optional[float] = None, within: Optional[bool] = True, num_threads: Optional[int] = 0) -> Tuple[np.ndarray, np.ndarray]: """Interpolation of the value at the requested position by window function. The interpolated value will be equal to the expression: .. math:: \\frac{\\sum_{i=1}^{k} \\omega(d_i,r)x_i} {\\sum_{i=1}^{k} \\omega(d_i,r)} where :math:d_i is the distance between the point of interest and the :math:i-th neighbor, :math:r is the radius of the search, :math:x_i is the value of the :math:i-th neighbor, and :math:\\omega(d_i,r) is weight calculated by the window function describe above. Args: coordinates: a matrix (n, ndims) where n is the number of observations and ndims is the number of coordinates in order: longitude and latitude in degrees, altitude in meters and then the other coordinates defined in Euclidean space if dims > 3. If the shape of the matrix is (n, ndims) then the method considers the altitude constant and equal to zero. radius: The maximum radius of the search (m). k: The number of nearest neighbors to be used for calculating the interpolated value. Defaults to 9. wf: The window function, based on the distance the distance between points (:math:d) and the radius (:math:r). This parameter can take one of the following values: * blackman: :math:w(d) = 0.42659 - 0.49656 \\cos( \\frac{\\pi (d + r)}{r}) + 0.076849 \\cos( \\frac{2 \\pi (d + r)}{r}) * blackman_harris: :math:w(d) = 0.35875 - 0.48829 \\cos(\\frac{\\pi (d + r)}{r}) + 0.14128 \\cos(\\frac{2 \\pi (d + r)}{r}) - 0.01168 \\cos(\\frac{3 \\pi (d + r)}{r}) * boxcar: :math:w(d) = 1 * flat_top: :math:w(d) = 0.21557895 - 0.41663158 \\cos(\\frac{\\pi (d + r)}{r}) + 0.277263158 \\cos(\\frac{2 \\pi (d + r)}{r}) - 0.083578947 \\cos(\\frac{3 \\pi (d + r)}{r}) + 0.006947368 \\cos(\\frac{4 \\pi (d + r)}{r}) * lanczos: :math:w(d) = \\left\\{\\begin{array}{ll} sinc(\\frac{d}{r}) \\times sinc(\\frac{d}{arg \\times r}), & d \\le arg \\times r \\\\ 0, & d \\gt arg \\times r \\end{array} \\right\\} * gaussian: :math:w(d) = e^{ -\\frac{1}{2}\\left( \\frac{d}{\\sigma}\\right)^2 } * hamming: :math:w(d) = 0.53836 - 0.46164 \\cos(\\frac{\\pi (d + r)}{r}) * nuttall: :math:w(d) = 0.3635819 - 0.4891775 \\cos(\\frac{\\pi (d + r)}{r}) + 0.1365995 \\cos(\\frac{2 \\pi (d + r)}{r}) * parzen: :math:w(d) = \\left\\{ \\begin{array}{ll} 1 - 6 \\left(\\frac{2*d}{2*r}\\right)^2 \\left(1 - \\frac{2*d}{2*r}\\right), & d \\le \\frac{2r + arg}{4} \\\\ 2\\left(1 - \\frac{2*d}{2*r}\\right)^3 & \\frac{2r + arg}{2} \\le d \\lt \\frac{2r +arg}{4} \\end{array} \\right\\} * parzen_swot: :math:w(d) = \\left\\{\\begin{array}{ll} 1 - 6\\left(\\frac{2 * d}{2 * r}\\right)^2 + 6\\left(1 - \\frac{2 * d}{2 * r}\\right), & d \\le \\frac{2r}{4} \\\\ 2\\left(1 - \\frac{2 * d}{2 * r}\\right)^3 & \\frac{2r}{2} \\ge d \\gt \\frac{2r}{4} \\end{array} \\right\\} arg: The optional argument of the window function. Defaults to 1 for lanczos, to 0 for parzen and for all other functions is None. within: If true, the method ensures that the neighbors found are located around the point of interest. In other words, this parameter ensures that the calculated values will not be extrapolated. Defaults to true. num_threads: The number of threads to use for the computation. If 0 all CPUs are used. If 1 is given, no parallel computing code is used at all, which is useful for debugging. Defaults to 0. Returns: The interpolated value and the number of neighbors used in the calculation. """ wf = wf or "blackman" if wf not in [ "blackman", "blackman_harris", "boxcar", "flattop", "gaussian", "hamming", "lanczos", "nuttall", "parzen", "parzen_swot", ]: raise ValueError(f"Window function {wf!r} is not defined") if wf in ["gaussian", "lanczos", "parzen"]: if arg is None: defaults = dict(gaussian=None, lanczos=1, parzen=0) arg = defaults[wf] if wf == "lanczos" and arg < 1: # type: ignore raise ValueError( f"The argument of the function {wf!r} must be " "greater than 1") if wf == "parzen" and arg < 0: # type: ignore raise ValueError( f"The argument of the function {wf!r} must be " "greater than 0") if wf == "gaussian" and arg is None: raise ValueError( f"The argument of the function {wf!r} must be " "specified") else: if arg is not None: raise ValueError(f"The function {wf!r} does not support the " "optional argument") wf = "".join(item.capitalize() for item in wf.split("_")) return self._instance.window_function(coordinates, radius, k, getattr(core.WindowFunction, wf), arg, within, num_threads)
[docs] def __getstate__(self) -> Tuple: """Return the state of the object for pickling purposes. Returns: The state of the object for pickling purposes. """ return (self.dtype, self._instance.__getstate__())
[docs] def __setstate__(self, state: Tuple): """Set the state of the object from pickling. Args: state: The state of the object for pickling purposes. """ if len(state) != 2: raise ValueError("invalid state") _class = RTree(None, state[0]) self.dtype = _class.dtype _class._instance.__setstate__(state[1]) self._instance = _class._instance