from
pyinterpolate.kriging.utils.errors import singular_matrix_error
# Pyinterpolate
from pyinterpolate.kriging.utils.point_kriging_solve import ( get_predictions ,
-
solve_weights )
+
solve_weights ,
+
__experimental_solve_weights_lsa_only )
from pyinterpolate.transform.statistical import sem_to_cov
from pyinterpolate.semivariogram.theoretical.theoretical import TheoreticalVariogram
@@ -828,6 +829,239 @@
Source code for pyinterpolate.kriging.point.ordinary return [ zhat , sigma , unknown_location [ 0 ], unknown_location [ 1 ]]
except np . linalg . LinAlgError as _ :
singular_matrix_error ()
+
+
+def experimental_ordinary_kriging_lsa (
+ theoretical_model : TheoreticalVariogram ,
+ unknown_locations : Union [
+ np . ndarray , Point , List , Tuple , GeoSeries , GeometryArray , ArrayLike ],
+ known_locations : ArrayLike = None ,
+ known_values : ArrayLike = None ,
+ known_geometries : ArrayLike = None ,
+ neighbors_range = None ,
+ no_neighbors = 4 ,
+ max_tick = 5. ,
+ use_all_neighbors_in_range = False ,
+ progress_bar : bool = True
+) -> np . ndarray :
+ """
+ Function predicts value at unknown location using Least Squares
+ Approximation.
+
+ Parameters
+ ----------
+ theoretical_model : TheoreticalVariogram
+ Fitted theoretical variogram model.
+
+ unknown_locations : Union[ArrayLike, Point]
+ Points where you want to estimate value ``(x, y) <-> (lon, lat)``.
+
+ known_locations : numpy array
+ Known locations: ``[x, y, value]``.
+
+ known_values : ArrayLike, optional
+ Observation in the i-th geometry (from ``known_geometries``). Optional
+ parameter, if not given then ``known_locations`` must be provided.
+
+ known_geometries : ArrayLike, optional
+ Array or similar structure with geometries. It must have the same
+ length as ``known_values``. Optional parameter, if not given then
+ ``known_locations`` must be provided. Point type geometry.
+
+ neighbors_range : float, default=None
+ The maximum distance where we search for neighbors. If ``None`` is
+ given then the range is selected from the Theoretical
+ Model's ``rang`` attribute.
+
+ no_neighbors : int, default = 4
+ The number of **n-closest neighbors** used for interpolation.
+
+ max_tick : float, default=5.
+ If searching for neighbors in a specific direction how big should be
+ a tolerance for increasing the search angle (how many degrees more).
+
+ use_all_neighbors_in_range : bool, default = False
+ ``True``: if the real number of neighbors within
+ the ``neighbors_range`` is greater than the ``number_of_neighbors``
+ then take all of them anyway.
+
+ progress_bar : bool, default=True
+ Show a progress bar during the interpolation process.
+
+ Returns
+ -------
+ : numpy array
+ ``[predicted value, variance error, longitude (x), latitude (y)]``
+
+ Raises
+ ------
+ RunetimeError
+ Singular Matrix in the Kriging system.
+
+ Examples
+ --------
+ >>> import geopandas as gpd
+ >>> import numpy as np
+ >>> import pandas as pd
+ >>>
+ >>> from pyinterpolate import (build_experimental_variogram,
+ ... build_theoretical_variogram, ordinary_kriging)
+ >>>
+ >>> dem = gpd.read_file('dem.gpkg')
+ >>> unknown_locations = gpd.read_file('unknown_locations.gpkg')
+ >>> step_size = 500
+ >>> max_range = 10000
+ >>> exp_variogram = build_experimental_variogram(
+ ... values=dem['dem'],
+ ... geometries=dem['geometry'],
+ ... step_size=step_size,
+ ... max_range=max_range
+ ... )
+ >>> theo_variogram = build_theoretical_variogram(exp_variogram)
+ >>> interp = ordinary_kriging(
+ ... theoretical_model=theo_variogram,
+ ... unknown_locations=unknown_locations['geometry'],
+ ... known_values=dem['dem'],
+ ... known_geometries=dem['geometry']
+ ... )
+ >>> print(interp[0])
+ [7.91222896e+01 9.72740449e+01 2.38012302e+05 5.51466805e+05]
+ """
+ # Check if known locations are in the right format
+ if not isinstance ( known_locations , VariogramPoints ):
+ known_locations = VariogramPoints ( points = known_locations ,
+ geometries = known_geometries ,
+ values = known_values )
+ known_locations = known_locations . points
+
+ unknown_locations = InterpolationPoints ( unknown_locations ) . points
+
+ interpolated_results = []
+
+ _disable_progress_bar = not progress_bar
+
+ for upoints in tqdm ( unknown_locations , disable = _disable_progress_bar ):
+ res = __experimental_ok_calc_lsa (
+ theoretical_model = theoretical_model ,
+ known_locations = known_locations ,
+ unknown_location = upoints ,
+ neighbors_range = neighbors_range ,
+ no_neighbors = no_neighbors ,
+ max_tick = max_tick ,
+ use_all_neighbors_in_range = use_all_neighbors_in_range
+ )
+
+ interpolated_results . append (
+ res
+ )
+
+ return np . array ( interpolated_results )
+
+
+def __experimental_ok_calc_lsa (
+ theoretical_model : TheoreticalVariogram ,
+ unknown_location : ArrayLike ,
+ known_locations : ArrayLike = None ,
+ known_values : ArrayLike = None ,
+ known_geometries : ArrayLike = None ,
+ neighbors_range = None ,
+ no_neighbors = 4 ,
+ max_tick = 5. ,
+ use_all_neighbors_in_range = False
+):
+ """
+ Function predicts value at unknown location with Ordinary Kriging
+ technique.
+
+ Parameters
+ ----------
+ theoretical_model : TheoreticalVariogram
+ Fitted theoretical variogram model.
+
+ unknown_location : Union[ArrayLike, Point]
+ Points where you want to estimate value ``(x, y) <-> (lon, lat)``.
+
+ known_locations : numpy array
+ Known locations: ``[x, y, value]``.
+
+ known_values : ArrayLike, optional
+ Observation in the i-th geometry (from ``known_geometries``). Optional
+ parameter, if not given then ``known_locations`` must be provided.
+
+ known_geometries : ArrayLike, optional
+ Array or similar structure with geometries. It must have the same
+ length as ``known_values``. Optional parameter, if not given then
+ ``known_locations`` must be provided. Point type geometry.
+
+ neighbors_range : float, default=None
+ The maximum distance where we search for neighbors. If ``None`` is
+ given then the range is selected from the Theoretical
+ Model's ``rang`` attribute.
+
+ no_neighbors : int, default = 4
+ The number of **n-closest neighbors** used for interpolation.
+
+ max_tick : float, default=5.
+ If searching for neighbors in a specific direction how big should be
+ a tolerance for increasing the search angle (how many degrees more).
+
+ use_all_neighbors_in_range : bool, default = False
+ ``True``: if the real number of neighbors within
+ the ``neighbors_range`` is greater than the ``number_of_neighbors``
+ then take all of them anyway.
+
+ Returns
+ -------
+ : numpy array
+ ``[predicted value, variance error, longitude (x), latitude (y)]``
+
+ Raises
+ ------
+ RunetimeError
+ Singular Matrix in the Kriging system.
+ """
+ # Check if known locations are in the right format
+ # Validate points
+ if not isinstance ( known_locations , VariogramPoints ):
+ known_locations = VariogramPoints ( points = known_locations ,
+ geometries = known_geometries ,
+ values = known_values )
+ known_locations = known_locations . points
+
+ # Check if unknown location is Point
+ if isinstance ( unknown_location , Point ):
+ unknown_location = (
+ unknown_location . x ,
+ unknown_location . y
+ )
+ unknown_location = np . array ( unknown_location )
+
+ k , predicted , dataset = get_predictions ( theoretical_model ,
+ known_locations ,
+ unknown_location ,
+ neighbors_range ,
+ no_neighbors ,
+ use_all_neighbors_in_range ,
+ max_tick )
+
+ k_ones = np . ones ( 1 )[ 0 ]
+ k = np . r_ [ k , k_ones ]
+
+ p_ones = np . ones (( predicted . shape [ 0 ], 1 ))
+ predicted_with_ones_col = np . c_ [ predicted , p_ones ]
+ p_ones_row = np . ones (( 1 , predicted_with_ones_col . shape [ 1 ]))
+ p_ones_row [ 0 ][ - 1 ] = 0.
+ weights = np . r_ [ predicted_with_ones_col , p_ones_row ]
+
+ output_weights = __experimental_solve_weights_lsa_only ( weights , k )
+ zhat = dataset [:, - 2 ] . dot ( output_weights [: - 1 ])
+
+ sigma = np . matmul ( output_weights . T , k )
+
+ if sigma < 0 :
+ return [ zhat , np . nan , unknown_location [ 0 ], unknown_location [ 1 ]]
+
+ return [ zhat , sigma , unknown_location [ 0 ], unknown_location [ 1 ]]
diff --git a/docs/build/html/_modules/pyinterpolate/semivariogram/experimental/experimental_semivariogram.html b/docs/build/html/_modules/pyinterpolate/semivariogram/experimental/experimental_semivariogram.html
index c3435445..c9112828 100644
--- a/docs/build/html/_modules/pyinterpolate/semivariogram/experimental/experimental_semivariogram.html
+++ b/docs/build/html/_modules/pyinterpolate/semivariogram/experimental/experimental_semivariogram.html
@@ -7,7 +7,7 @@
-
pyinterpolate.semivariogram.experimental.experimental_semivariogram — pyinterpolate 1.1.0 documentation
+
pyinterpolate.semivariogram.experimental.experimental_semivariogram — pyinterpolate 1.2.0 documentation
@@ -38,7 +38,7 @@
-
+
@@ -111,7 +111,7 @@
-
pyinterpolate 1.1.0 documentation
+
pyinterpolate 1.2.0 documentation
The weighted distance between blocks is derived from the equation 3 given
+in publication [1] from References.
+\[d(v_{a}, v_{b})=\frac{1}{\sum_{s=1}^{P_{a}} \sum_{s'=1}^{P_{b}} n(u_{s}) n(u_{s'})} * \sum_{s=1}^{P_{a}} \sum_{s'=1}^{P_{b}} n(u_{s})n(u_{s'})||u_{s}-u_{s'}||\]
>>> import os
>>> import geopandas as gpd
diff --git a/docs/build/html/api/kriging/block_kriging.html b/docs/build/html/api/kriging/block_kriging.html
index 58d64fb2..d2aeed52 100644
--- a/docs/build/html/api/kriging/block_kriging.html
+++ b/docs/build/html/api/kriging/block_kriging.html
@@ -455,7 +455,7 @@ Block and Poisson Kriging
-pyinterpolate. centroid_poisson_kriging ( semivariogram_model : TheoreticalVariogram point_support : PointSupport unknown_block_index : str | Hashable number_of_neighbors : int neighbors_range : float = None is_weighted_by_point_support = True raise_when_negative_prediction = True raise_when_negative_error = True allow_lsa = False ) → Dict [source]
+pyinterpolate. centroid_poisson_kriging ( semivariogram_model : TheoreticalVariogram point_support : PointSupport unknown_block_index : str | Hashable number_of_neighbors : int neighbors_range : float = None is_weighted_by_point_support = True raise_when_negative_prediction = True raise_when_negative_error = True allow_lsa = False negative_prediction_to_zero = False ) → Dict [source] Function performs centroid-based Poisson Kriging of blocks (areal) data.
Parameters:
@@ -484,6 +484,8 @@ Centroid-based Poisson Kriging
Returns:
@@ -571,7 +573,7 @@ Centroid-based Poisson Kriging
-pyinterpolate. area_to_area_pk ( semivariogram_model : TheoreticalVariogram point_support : PointSupport unknown_block_index : str | Hashable number_of_neighbors : int neighbors_range : float = None raise_when_negative_prediction = True raise_when_negative_error = True ) → dict [source]
+pyinterpolate. area_to_area_pk ( semivariogram_model : TheoreticalVariogram point_support : PointSupport unknown_block_index : str | Hashable number_of_neighbors : int neighbors_range : float = None raise_when_negative_prediction = True raise_when_negative_error = True negative_prediction_to_zero = False ) → dict [source] Function predicts areal value in an unknown location based on
the area-to-area Poisson Kriging
@@ -593,6 +595,8 @@ Area-to-area Poisson Kriging
Returns:
@@ -680,7 +684,7 @@ Area-to-area Poisson Kriging
-pyinterpolate. area_to_point_pk ( semivariogram_model : TheoreticalVariogram point_support : PointSupport unknown_block_index : str | Hashable number_of_neighbors : int neighbors_range : float = None raise_when_negative_prediction = True raise_when_negative_error = True err_to_nan = True ) [source]
+pyinterpolate. area_to_point_pk ( semivariogram_model : TheoreticalVariogram point_support : PointSupport unknown_block_index : str | Hashable number_of_neighbors : int neighbors_range : float = None raise_when_negative_prediction = True raise_when_negative_error = True err_to_nan = True negative_prediction_to_zero = False ) [source] Function predicts point-support value in the unknown location based on
the area-to-point Poisson Kriging
@@ -705,6 +709,8 @@ Area-to-point Poisson Kriging
Returns:
diff --git a/docs/build/html/api/semivariogram/experimental.html b/docs/build/html/api/semivariogram/experimental.html
index 363c8383..a145d88d 100644
--- a/docs/build/html/api/semivariogram/experimental.html
+++ b/docs/build/html/api/semivariogram/experimental.html
@@ -775,10 +775,11 @@ Experimental Variogram where:
\(h\) : lag,
\(n(h)\) : number of point pairs within the lag \(h\) ,
\(g(h)\) : empirical semivariance for lag \(h\) ,
\(n(h)\) : number of point pairs within a specific lag,
\(z(x_i)\) : point a (value of observation at point a),