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<h1>Source code for pyinterpolate.distance.distance</h1><div class="highlight"><pre>
<span></span><span class="sd">"""</span>
<span class="sd">Distance calculation functions.</span>
<span class="sd">Authors</span>
<span class="sd">-------</span>
<span class="sd">1. Szymon Moliński | @SimonMolinsky</span>
<span class="sd">"""</span>
<span class="kn">from</span> <span class="nn">typing</span> <span class="kn">import</span> <span class="n">Dict</span><span class="p">,</span> <span class="n">Union</span><span class="p">,</span> <span class="n">Iterable</span>
<span class="kn">import</span> <span class="nn">geopandas</span> <span class="k">as</span> <span class="nn">gpd</span>
<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
<span class="kn">import</span> <span class="nn">pandas</span> <span class="k">as</span> <span class="nn">pd</span>
<span class="kn">from</span> <span class="nn">scipy.spatial.distance</span> <span class="kn">import</span> <span class="n">cdist</span>
<span class="kn">from</span> <span class="nn">pyinterpolate.processing.preprocessing.blocks</span> <span class="kn">import</span> <span class="n">PointSupport</span>
<span class="kn">from</span> <span class="nn">pyinterpolate.processing.transform.transform</span> <span class="kn">import</span> <span class="n">point_support_to_dict</span><span class="p">,</span> <span class="n">block_dataframe_to_dict</span>
<span class="k">def</span> <span class="nf">_calc_b2b_dist_from_array</span><span class="p">(</span><span class="n">blocks</span><span class="p">:</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">)</span> <span class="o">-></span> <span class="n">Dict</span><span class="p">:</span>
<span class="w"> </span><span class="sd">"""Function calculates distances between blocks.</span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> blocks : numpy array</span>
<span class="sd"> [[block id, point x, point y, value]]</span>
<span class="sd"> Returns</span>
<span class="sd"> -------</span>
<span class="sd"> block_distances : Dict</span>
<span class="sd"> {block id : [distances to other blocks]}. Block ids in the order from the list of</span>
<span class="sd"> distances.</span>
<span class="sd"> """</span>
<span class="n">block_keys</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">unique</span><span class="p">(</span><span class="n">blocks</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">])</span>
<span class="n">block_distances</span> <span class="o">=</span> <span class="nb">dict</span><span class="p">()</span>
<span class="k">for</span> <span class="n">k_i</span> <span class="ow">in</span> <span class="n">block_keys</span><span class="p">:</span>
<span class="n">i_block</span> <span class="o">=</span> <span class="n">blocks</span><span class="p">[</span><span class="n">blocks</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">]</span> <span class="o">==</span> <span class="n">k_i</span><span class="p">][:,</span> <span class="mi">1</span><span class="p">:]</span>
<span class="n">distances</span> <span class="o">=</span> <span class="p">[]</span>
<span class="k">for</span> <span class="n">k_j</span> <span class="ow">in</span> <span class="n">block_keys</span><span class="p">:</span>
<span class="n">j_block</span> <span class="o">=</span> <span class="n">blocks</span><span class="p">[</span><span class="n">blocks</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">]</span> <span class="o">==</span> <span class="n">k_j</span><span class="p">][:,</span> <span class="mi">1</span><span class="p">:]</span>
<span class="k">if</span> <span class="n">k_i</span> <span class="o">==</span> <span class="n">k_j</span><span class="p">:</span>
<span class="n">distances</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
<span class="k">else</span><span class="p">:</span>
<span class="n">value</span> <span class="o">=</span> <span class="n">_calculate_block_to_block_distance</span><span class="p">(</span><span class="n">i_block</span><span class="p">,</span> <span class="n">j_block</span><span class="p">)</span>
<span class="n">distances</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">value</span><span class="p">)</span>
<span class="n">block_distances</span><span class="p">[</span><span class="n">k_i</span><span class="p">]</span> <span class="o">=</span> <span class="n">distances</span>
<span class="k">return</span> <span class="n">block_distances</span>
<span class="k">def</span> <span class="nf">_calc_b2b_dist_from_dataframe</span><span class="p">(</span><span class="n">blocks</span><span class="p">:</span> <span class="n">Union</span><span class="p">[</span><span class="n">pd</span><span class="o">.</span><span class="n">DataFrame</span><span class="p">,</span> <span class="n">gpd</span><span class="o">.</span><span class="n">GeoDataFrame</span><span class="p">])</span> <span class="o">-></span> <span class="n">Dict</span><span class="p">:</span>
<span class="w"> </span><span class="sd">"""Function calculates distances between blocks.</span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> blocks : Union[pd.DataFrame, gpd.GeoDataFrame]</span>
<span class="sd"> DataFrame and GeoDataFrame: columns={x, y, ds, index}</span>
<span class="sd"> Returns</span>
<span class="sd"> -------</span>
<span class="sd"> block_distances : Dict</span>
<span class="sd"> {block id : [distances to other blocks]}. Block ids in the order from the list of</span>
<span class="sd"> distances.</span>
<span class="sd"> """</span>
<span class="n">expected_cols</span> <span class="o">=</span> <span class="p">{</span><span class="s1">'x'</span><span class="p">,</span> <span class="s1">'y'</span><span class="p">,</span> <span class="s1">'ds'</span><span class="p">,</span> <span class="s1">'index'</span><span class="p">}</span>
<span class="k">if</span> <span class="ow">not</span> <span class="n">expected_cols</span><span class="o">.</span><span class="n">issubset</span><span class="p">(</span><span class="nb">set</span><span class="p">(</span><span class="n">blocks</span><span class="o">.</span><span class="n">columns</span><span class="p">)):</span>
<span class="k">raise</span> <span class="ne">KeyError</span><span class="p">(</span><span class="sa">f</span><span class="s1">'Given dataframe doesnt have all expected columns </span><span class="si">{</span><span class="n">expected_cols</span><span class="si">}</span><span class="s1">. '</span>
<span class="sa">f</span><span class="s1">'It has </span><span class="si">{</span><span class="n">blocks</span><span class="o">.</span><span class="n">columns</span><span class="si">}</span><span class="s1"> instead.'</span><span class="p">)</span>
<span class="n">dsdict</span> <span class="o">=</span> <span class="n">block_dataframe_to_dict</span><span class="p">(</span><span class="n">blocks</span><span class="p">)</span>
<span class="n">bdists</span> <span class="o">=</span> <span class="n">_calc_b2b_dist_from_dict</span><span class="p">(</span><span class="n">dsdict</span><span class="p">)</span>
<span class="k">return</span> <span class="n">bdists</span>
<span class="k">def</span> <span class="nf">_calc_b2b_dist_from_dict</span><span class="p">(</span><span class="n">blocks</span><span class="p">:</span> <span class="n">Dict</span><span class="p">)</span> <span class="o">-></span> <span class="n">Dict</span><span class="p">:</span>
<span class="w"> </span><span class="sd">"""Function calculates distances between blocks.</span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> blocks : Dict</span>
<span class="sd"> Dict: {block id: [[point x, point y, value]]}</span>
<span class="sd"> Returns</span>
<span class="sd"> -------</span>
<span class="sd"> block_distances : Dict</span>
<span class="sd"> {block id : [distances to other blocks]}. Block ids in the order from the list of</span>
<span class="sd"> distances.</span>
<span class="sd"> """</span>
<span class="n">block_keys</span> <span class="o">=</span> <span class="nb">list</span><span class="p">(</span><span class="n">blocks</span><span class="o">.</span><span class="n">keys</span><span class="p">())</span>
<span class="n">block_distances</span> <span class="o">=</span> <span class="nb">dict</span><span class="p">()</span>
<span class="k">for</span> <span class="n">k_i</span> <span class="ow">in</span> <span class="n">block_keys</span><span class="p">:</span>
<span class="n">i_block</span> <span class="o">=</span> <span class="n">blocks</span><span class="p">[</span><span class="n">k_i</span><span class="p">]</span>
<span class="n">distances</span> <span class="o">=</span> <span class="p">[]</span>
<span class="k">for</span> <span class="n">k_j</span> <span class="ow">in</span> <span class="n">block_keys</span><span class="p">:</span>
<span class="n">j_block</span> <span class="o">=</span> <span class="n">blocks</span><span class="p">[</span><span class="n">k_j</span><span class="p">]</span>
<span class="k">if</span> <span class="n">k_i</span> <span class="o">==</span> <span class="n">k_j</span><span class="p">:</span>
<span class="n">distances</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
<span class="k">else</span><span class="p">:</span>
<span class="n">value</span> <span class="o">=</span> <span class="n">_calculate_block_to_block_distance</span><span class="p">(</span><span class="n">i_block</span><span class="p">,</span> <span class="n">j_block</span><span class="p">)</span>
<span class="n">distances</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">value</span><span class="p">)</span>
<span class="n">block_distances</span><span class="p">[</span><span class="n">k_i</span><span class="p">]</span> <span class="o">=</span> <span class="n">distances</span>
<span class="k">return</span> <span class="n">block_distances</span>
<span class="k">def</span> <span class="nf">_calc_b2b_dist_from_ps</span><span class="p">(</span><span class="n">blocks</span><span class="p">:</span> <span class="n">PointSupport</span><span class="p">)</span> <span class="o">-></span> <span class="n">Dict</span><span class="p">:</span>
<span class="w"> </span><span class="sd">"""Function calculates distances between blocks.</span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> blocks : PointSupport</span>
<span class="sd"> Returns</span>
<span class="sd"> -------</span>
<span class="sd"> block_distances : Dict</span>
<span class="sd"> {block id : [distances to other blocks]}. Block ids in the order from the list of</span>
<span class="sd"> distances.</span>
<span class="sd"> """</span>
<span class="n">dsdict</span> <span class="o">=</span> <span class="n">point_support_to_dict</span><span class="p">(</span><span class="n">point_support</span><span class="o">=</span><span class="n">blocks</span><span class="p">)</span>
<span class="n">block_distances</span> <span class="o">=</span> <span class="n">_calc_b2b_dist_from_dict</span><span class="p">(</span><span class="n">dsdict</span><span class="p">)</span>
<span class="k">return</span> <span class="n">block_distances</span>
<div class="viewcode-block" id="calc_block_to_block_distance"><a class="viewcode-back" href="../../../api/distance/distance.html#pyinterpolate.calc_block_to_block_distance">[docs]</a><span class="k">def</span> <span class="nf">calc_block_to_block_distance</span><span class="p">(</span><span class="n">blocks</span><span class="p">:</span> <span class="n">Union</span><span class="p">[</span><span class="n">Dict</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">,</span> <span class="n">gpd</span><span class="o">.</span><span class="n">GeoDataFrame</span><span class="p">,</span> <span class="n">pd</span><span class="o">.</span><span class="n">DataFrame</span><span class="p">,</span> <span class="n">PointSupport</span><span class="p">])</span> <span class="o">-></span> <span class="n">Dict</span><span class="p">:</span>
<span class="w"> </span><span class="sd">"""Function calculates distances between blocks.</span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> blocks : Union[Dict, np.ndarray, gpd.GeoDataFrame, pd.DataFrame, PointSupport]</span>
<span class="sd"> The point support of polygons.</span>
<span class="sd"> * ``Dict``: ``{block id: [[point x, point y, value]]}``,</span>
<span class="sd"> * ``numpy array``: ``[[block id, x, y, value]]``,</span>
<span class="sd"> * ``DataFrame`` and ``GeoDataFrame``: ``columns={x, y, ds, index}``,</span>
<span class="sd"> * ``PointSupport``.</span>
<span class="sd"> Returns</span>
<span class="sd"> -------</span>
<span class="sd"> block_distances : Dict</span>
<span class="sd"> Ordered block ids (the order from the list of distances): {block id : [distances to other]}.</span>
<span class="sd"> Raises</span>
<span class="sd"> ------</span>
<span class="sd"> TypeError</span>
<span class="sd"> Wrong input's data type.</span>
<span class="sd"> """</span>
<span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">blocks</span><span class="p">,</span> <span class="n">Dict</span><span class="p">):</span>
<span class="n">block_distances</span> <span class="o">=</span> <span class="n">_calc_b2b_dist_from_dict</span><span class="p">(</span><span class="n">blocks</span><span class="p">)</span>
<span class="k">elif</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">blocks</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">):</span>
<span class="n">block_distances</span> <span class="o">=</span> <span class="n">_calc_b2b_dist_from_array</span><span class="p">(</span><span class="n">blocks</span><span class="p">)</span>
<span class="k">elif</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">blocks</span><span class="p">,</span> <span class="n">pd</span><span class="o">.</span><span class="n">DataFrame</span><span class="p">)</span> <span class="ow">or</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">blocks</span><span class="p">,</span> <span class="n">gpd</span><span class="o">.</span><span class="n">GeoDataFrame</span><span class="p">):</span>
<span class="n">block_distances</span> <span class="o">=</span> <span class="n">_calc_b2b_dist_from_dataframe</span><span class="p">(</span><span class="n">blocks</span><span class="p">)</span>
<span class="k">elif</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">blocks</span><span class="p">,</span> <span class="n">PointSupport</span><span class="p">):</span>
<span class="n">block_distances</span> <span class="o">=</span> <span class="n">_calc_b2b_dist_from_ps</span><span class="p">(</span><span class="n">blocks</span><span class="p">)</span>
<span class="k">else</span><span class="p">:</span>
<span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="sa">f</span><span class="s1">'Blocks data type </span><span class="si">{</span><span class="nb">type</span><span class="p">(</span><span class="n">blocks</span><span class="p">)</span><span class="si">}</span><span class="s1"> not recognized. You may use PointSupport,'</span>
<span class="sa">f</span><span class="s1">' Geopandas GeoDataFrame, Pandas DataFrame or numpy array. See docs.'</span><span class="p">)</span>
<span class="k">return</span> <span class="n">block_distances</span></div>
<span class="k">def</span> <span class="nf">_calculate_block_to_block_distance</span><span class="p">(</span><span class="n">block_1</span><span class="p">:</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">,</span> <span class="n">block_2</span><span class="p">:</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">)</span> <span class="o">-></span> <span class="nb">float</span><span class="p">:</span>
<span class="w"> </span><span class="sd">"""Function calculates distance between two blocks based on how they are divided (into the point support grid).</span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> block_1 : numpy array</span>
<span class="sd"> block_2 : numpy array</span>
<span class="sd"> Returns</span>
<span class="sd"> -------</span>
<span class="sd"> weighted_distances : float</span>
<span class="sd"> Weighted distance between blocks.</span>
<span class="sd"> Notes</span>
<span class="sd"> -----</span>
<span class="sd"> The weighted distance between blocks is derived from the equation:</span>
<span class="sd"> $$d(v_{a}, v_{b})=\frac{1}{\sum_{s=1}^{P_{a}} \sum_{s'=1}^{P_{b}} n(u_{s}) n(u_{s'})} *</span>
<span class="sd"> \sum_{s=1}^{P_{a}} \sum_{s'=1}^{P_{b}} n(u_{s})n(u_{s'})||u_{s}-u_{s'}||$$</span>
<span class="sd"> where:</span>
<span class="sd"> $P_{a}$ and $P_{b}$: number of points $u_{s}$ and $u_{s'}$ used to discretize the two units $v_{a}$ and $v_{b}$,</span>
<span class="sd"> $n(u_{s})$ and $n(u_{s'})$ - population size in the cells $u_{s}$ and $u_{s'}$.</span>
<span class="sd"> References</span>
<span class="sd"> ----------</span>
<span class="sd"> .. [1] Goovaerts, P. Kriging and Semivariogram Deconvolution in the Presence of Irregular Geographical Units.</span>
<span class="sd"> Math Geosci 40, 101–128 (2008). https://doi.org/10.1007/s11004-007-9129-1</span>
<span class="sd"> """</span>
<span class="n">a_shape</span> <span class="o">=</span> <span class="n">block_1</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
<span class="n">b_shape</span> <span class="o">=</span> <span class="n">block_2</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
<span class="n">ax</span> <span class="o">=</span> <span class="n">block_1</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">a_shape</span><span class="p">)</span>
<span class="n">bx</span> <span class="o">=</span> <span class="n">block_2</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">b_shape</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
<span class="n">dx</span> <span class="o">=</span> <span class="n">ax</span> <span class="o">-</span> <span class="n">bx</span>
<span class="n">ay</span> <span class="o">=</span> <span class="n">block_1</span><span class="p">[:,</span> <span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">a_shape</span><span class="p">)</span>
<span class="n">by</span> <span class="o">=</span> <span class="n">block_2</span><span class="p">[:,</span> <span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">b_shape</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
<span class="n">dy</span> <span class="o">=</span> <span class="n">ay</span> <span class="o">-</span> <span class="n">by</span>
<span class="n">aval</span> <span class="o">=</span> <span class="n">block_1</span><span class="p">[:,</span> <span class="o">-</span><span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">a_shape</span><span class="p">)</span>
<span class="n">bval</span> <span class="o">=</span> <span class="n">block_2</span><span class="p">[:,</span> <span class="o">-</span><span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">b_shape</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
<span class="n">w</span> <span class="o">=</span> <span class="n">aval</span> <span class="o">*</span> <span class="n">bval</span>
<span class="n">dist</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="n">dx</span> <span class="o">**</span> <span class="mi">2</span> <span class="o">+</span> <span class="n">dy</span> <span class="o">**</span> <span class="mi">2</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="nb">float</span><span class="p">,</span> <span class="n">casting</span><span class="o">=</span><span class="s1">'unsafe'</span><span class="p">)</span>
<span class="n">wdist</span> <span class="o">=</span> <span class="n">dist</span> <span class="o">*</span> <span class="n">w</span>
<span class="n">distances_sum</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">wdist</span><span class="p">)</span> <span class="o">/</span> <span class="n">np</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">w</span><span class="p">)</span>
<span class="k">return</span> <span class="n">distances_sum</span>
<span class="k">def</span> <span class="nf">_calc_angle_between_points</span><span class="p">(</span><span class="n">v1</span><span class="p">,</span> <span class="n">v2</span><span class="p">,</span> <span class="n">origin</span><span class="p">):</span>
<span class="n">ang1</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arctan2</span><span class="p">(</span><span class="n">v1</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">-</span> <span class="n">origin</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">v1</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">-</span> <span class="n">origin</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span>
<span class="n">ang2</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arctan2</span><span class="p">(</span><span class="n">v2</span><span class="p">[:,</span> <span class="mi">1</span><span class="p">]</span> <span class="o">-</span> <span class="n">origin</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">v2</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">]</span> <span class="o">-</span> <span class="n">origin</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span>
<span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">rad2deg</span><span class="p">((</span><span class="n">ang1</span> <span class="o">-</span> <span class="n">ang2</span><span class="p">)</span> <span class="o">%</span> <span class="p">(</span><span class="mi">2</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span><span class="p">))</span>
<span class="k">def</span> <span class="nf">_calc_angle_from_origin</span><span class="p">(</span><span class="n">vec</span><span class="p">,</span> <span class="n">origin</span><span class="p">):</span>
<span class="n">ys</span> <span class="o">=</span> <span class="n">vec</span><span class="p">[:,</span> <span class="mi">1</span><span class="p">]</span> <span class="o">-</span> <span class="n">origin</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span>
<span class="n">xs</span> <span class="o">=</span> <span class="n">vec</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">]</span> <span class="o">-</span> <span class="n">origin</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
<span class="n">ang</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arctan2</span><span class="p">(</span><span class="n">ys</span><span class="p">,</span> <span class="n">xs</span><span class="p">)</span>
<span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">rad2deg</span><span class="p">(</span><span class="n">ang</span> <span class="o">%</span> <span class="p">(</span><span class="mi">2</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span><span class="p">))</span>
<span class="k">def</span> <span class="nf">calc_angles_between_points</span><span class="p">(</span><span class="n">vec1</span><span class="p">,</span> <span class="n">vec2</span><span class="p">,</span> <span class="n">origin</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
<span class="w"> </span><span class="sd">"""</span>
<span class="sd"> Function calculates distances between two groups of points as their cross product.</span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> vec1 : numpy array</span>
<span class="sd"> The first set of coordinates.</span>
<span class="sd"> vec2 : numpy array</span>
<span class="sd"> The second set of coordinates.</span>
<span class="sd"> origin : Iterable, optional</span>
<span class="sd"> The coordinates (x, y) of origin.</span>
<span class="sd"> Returns</span>
<span class="sd"> -------</span>
<span class="sd"> angles : numpy array</span>
<span class="sd"> An array with angles between all points from ``vec1`` to all points from ``vec2``, where rows are angles between</span>
<span class="sd"> points from ``vec1`` to points from ``vec2`` (columns).</span>
<span class="sd"> """</span>
<span class="n">angles</span> <span class="o">=</span> <span class="p">[]</span>
<span class="k">for</span> <span class="n">point</span> <span class="ow">in</span> <span class="n">vec1</span><span class="p">:</span>
<span class="n">row</span> <span class="o">=</span> <span class="n">calc_angles</span><span class="p">(</span><span class="n">vec2</span><span class="p">,</span> <span class="n">origin</span><span class="o">=</span><span class="n">point</span><span class="p">)</span>
<span class="n">angles</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">row</span><span class="o">.</span><span class="n">flatten</span><span class="p">())</span>
<span class="n">angles</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">angles</span><span class="p">)</span><span class="o">.</span><span class="n">flatten</span><span class="p">()</span>
<span class="k">return</span> <span class="n">angles</span>
<span class="k">def</span> <span class="nf">calc_angles</span><span class="p">(</span><span class="n">points_b</span><span class="p">:</span> <span class="n">Iterable</span><span class="p">,</span> <span class="n">point_a</span><span class="p">:</span> <span class="n">Iterable</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span> <span class="n">origin</span><span class="p">:</span> <span class="n">Iterable</span> <span class="o">=</span> <span class="kc">None</span><span class="p">):</span>
<span class="w"> </span><span class="sd">"""</span>
<span class="sd"> Function calculates angles between points and origin or between vectors from origin to points and a vector from</span>
<span class="sd"> a specific point to origin.</span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> points_b : numpy array</span>
<span class="sd"> Other point coordinates.</span>
<span class="sd"> point_a : Iterable</span>
<span class="sd"> The point coordinates, default is equal to (0, 0).</span>
<span class="sd"> origin : Iterable</span>
<span class="sd"> The origin coordinates, default is (0, 0).</span>
<span class="sd"> Returns</span>
<span class="sd"> -------</span>
<span class="sd"> angles : numpy array</span>
<span class="sd"> Angles from the ``points_b`` to origin, or angles between vectors ``points_b`` to origin and ``point_a``</span>
<span class="sd"> to origin.</span>
<span class="sd"> """</span>
<span class="k">if</span> <span class="n">origin</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
<span class="n">origin</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">((</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">))</span>
<span class="k">else</span><span class="p">:</span>
<span class="k">if</span> <span class="ow">not</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">origin</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">):</span>
<span class="n">origin</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">origin</span><span class="p">)</span>
<span class="k">if</span> <span class="ow">not</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">points_b</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">):</span>
<span class="n">points_b</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">points_b</span><span class="p">)</span>
<span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">points_b</span><span class="o">.</span><span class="n">shape</span><span class="p">)</span> <span class="o">==</span> <span class="mi">1</span><span class="p">:</span>
<span class="n">points_b</span> <span class="o">=</span> <span class="n">points_b</span><span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">newaxis</span><span class="p">,</span> <span class="o">...</span><span class="p">]</span>
<span class="k">if</span> <span class="n">point_a</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
<span class="n">angles</span> <span class="o">=</span> <span class="n">_calc_angle_from_origin</span><span class="p">(</span><span class="n">points_b</span><span class="p">,</span> <span class="n">origin</span><span class="p">)</span>
<span class="k">else</span><span class="p">:</span>
<span class="n">angles</span> <span class="o">=</span> <span class="n">_calc_angle_between_points</span><span class="p">(</span><span class="n">point_a</span><span class="p">,</span> <span class="n">points_b</span><span class="p">,</span> <span class="n">origin</span><span class="p">)</span>
<span class="k">return</span> <span class="n">angles</span>
<div class="viewcode-block" id="calc_point_to_point_distance"><a class="viewcode-back" href="../../../api/distance/distance.html#pyinterpolate.calc_point_to_point_distance">[docs]</a><span class="k">def</span> <span class="nf">calc_point_to_point_distance</span><span class="p">(</span><span class="n">points_a</span><span class="p">,</span> <span class="n">points_b</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
<span class="w"> </span><span class="sd">"""Function calculates distances between two group of points of a single group to itself.</span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> points_a : numpy array</span>
<span class="sd"> The point coordinates.</span>
<span class="sd"> points_b : numpy array, default=None</span>
<span class="sd"> Other point coordinates. If provided then algorithm calculates distances between ``points_a`` against</span>
<span class="sd"> ``points_b``.</span>
<span class="sd"> Returns</span>
<span class="sd"> -------</span>
<span class="sd"> distances : numpy array</span>
<span class="sd"> The distances from each point from the ``points_a`` to other point (from the same ``points_a`` or from the</span>
<span class="sd"> other set of points ``points_b``).</span>
<span class="sd"> """</span>
<span class="k">if</span> <span class="n">points_b</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
<span class="n">distances</span> <span class="o">=</span> <span class="n">cdist</span><span class="p">(</span><span class="n">points_a</span><span class="p">,</span> <span class="n">points_a</span><span class="p">,</span> <span class="s1">'euclidean'</span><span class="p">)</span>
<span class="k">else</span><span class="p">:</span>
<span class="n">distances</span> <span class="o">=</span> <span class="n">cdist</span><span class="p">(</span><span class="n">points_a</span><span class="p">,</span> <span class="n">points_b</span><span class="p">,</span> <span class="s1">'euclidean'</span><span class="p">)</span>
<span class="k">return</span> <span class="n">distances</span></div>
<span class="k">def</span> <span class="nf">calculate_angular_distance</span><span class="p">(</span><span class="n">angles</span><span class="p">:</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">,</span> <span class="n">expected_direction</span><span class="p">:</span> <span class="nb">float</span><span class="p">)</span> <span class="o">-></span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">:</span>
<span class="w"> </span><span class="sd">"""</span>
<span class="sd"> Function calculates minimal direction between one vector and other vectors.</span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> angles : numpy array</span>
<span class="sd"> The array with the direction to the origin of each point.</span>
<span class="sd"> expected_direction : float</span>
<span class="sd"> The variogram direction in degrees.</span>
<span class="sd"> Returns</span>
<span class="sd"> -------</span>
<span class="sd"> angular_distances : numpy array</span>
<span class="sd"> Minimal direction from ``expected_direction`` to other angles.</span>
<span class="sd"> """</span>
<span class="c1"># We should select angles equal to the expected direction</span>
<span class="c1"># and 180 degrees from it</span>
<span class="n">expected_direction_rad</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">deg2rad</span><span class="p">(</span><span class="n">expected_direction</span><span class="p">)</span>
<span class="n">r_angles</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">deg2rad</span><span class="p">(</span><span class="n">angles</span><span class="p">)</span>
<span class="n">norm_a</span> <span class="o">=</span> <span class="n">r_angles</span> <span class="o">-</span> <span class="n">expected_direction_rad</span>
<span class="n">deg_norm_a</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">abs</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">rad2deg</span><span class="p">(</span><span class="n">norm_a</span> <span class="o">%</span> <span class="p">(</span><span class="mi">2</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span><span class="p">)))</span>
<span class="n">norm_b</span> <span class="o">=</span> <span class="n">expected_direction_rad</span> <span class="o">-</span> <span class="n">r_angles</span>
<span class="n">deg_norm_b</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">abs</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">rad2deg</span><span class="p">(</span><span class="n">norm_b</span> <span class="o">%</span> <span class="p">(</span><span class="mi">2</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span><span class="p">)))</span>
<span class="n">normalized_angular_dists</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">minimum</span><span class="p">(</span><span class="n">deg_norm_a</span><span class="p">,</span> <span class="n">deg_norm_b</span><span class="p">)</span>
<span class="k">return</span> <span class="n">normalized_angular_dists</span>
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