1 | |
---|
2 | |
---|
3 | <!DOCTYPE html> |
---|
4 | <!--[if IE 8]><html class="no-js lt-ie9" lang="en" > <![endif]--> |
---|
5 | <!--[if gt IE 8]><!--> <html class="no-js" lang="en" > <!--<![endif]--> |
---|
6 | <head> |
---|
7 | <meta charset="utf-8"> |
---|
8 | |
---|
9 | <meta name="viewport" content="width=device-width, initial-scale=1.0"> |
---|
10 | |
---|
11 | <title>disaggregation — flex_extract 7.1.2 documentation</title> |
---|
12 | |
---|
13 | |
---|
14 | |
---|
15 | |
---|
16 | |
---|
17 | |
---|
18 | |
---|
19 | |
---|
20 | <script type="text/javascript" src="../_static/js/modernizr.min.js"></script> |
---|
21 | |
---|
22 | |
---|
23 | <script type="text/javascript" id="documentation_options" data-url_root="../" src="../_static/documentation_options.js"></script> |
---|
24 | <script src="../_static/jquery.js"></script> |
---|
25 | <script src="../_static/underscore.js"></script> |
---|
26 | <script src="../_static/doctools.js"></script> |
---|
27 | <script src="../_static/language_data.js"></script> |
---|
28 | <script async="async" src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/latest.js?config=TeX-AMS-MML_HTMLorMML"></script> |
---|
29 | |
---|
30 | <script type="text/javascript" src="../_static/js/theme.js"></script> |
---|
31 | |
---|
32 | |
---|
33 | |
---|
34 | |
---|
35 | <link rel="stylesheet" href="../_static/css/theme.css" type="text/css" /> |
---|
36 | <link rel="stylesheet" href="../_static/pygments.css" type="text/css" /> |
---|
37 | <link rel="stylesheet" href="../_static/css/custom.css" type="text/css" /> |
---|
38 | <link rel="stylesheet" href="../_static/css/theme_overrides.css" type="text/css" /> |
---|
39 | <link rel="index" title="Index" href="../genindex.html" /> |
---|
40 | <link rel="search" title="Search" href="../search.html" /> |
---|
41 | </head> |
---|
42 | |
---|
43 | <body class="wy-body-for-nav"> |
---|
44 | |
---|
45 | |
---|
46 | <div class="wy-grid-for-nav"> |
---|
47 | |
---|
48 | <nav data-toggle="wy-nav-shift" class="wy-nav-side"> |
---|
49 | <div class="wy-side-scroll"> |
---|
50 | <div class="wy-side-nav-search" > |
---|
51 | |
---|
52 | |
---|
53 | |
---|
54 | <a href="../index.html" class="icon icon-home"> flex_extract |
---|
55 | |
---|
56 | |
---|
57 | |
---|
58 | </a> |
---|
59 | |
---|
60 | |
---|
61 | |
---|
62 | |
---|
63 | <div class="version"> |
---|
64 | 7.1.2 |
---|
65 | </div> |
---|
66 | |
---|
67 | |
---|
68 | |
---|
69 | |
---|
70 | <div role="search"> |
---|
71 | <form id="rtd-search-form" class="wy-form" action="../search.html" method="get"> |
---|
72 | <input type="text" name="q" placeholder="Search docs" /> |
---|
73 | <input type="hidden" name="check_keywords" value="yes" /> |
---|
74 | <input type="hidden" name="area" value="default" /> |
---|
75 | </form> |
---|
76 | </div> |
---|
77 | |
---|
78 | |
---|
79 | </div> |
---|
80 | |
---|
81 | <div class="wy-menu wy-menu-vertical" data-spy="affix" role="navigation" aria-label="main navigation"> |
---|
82 | |
---|
83 | |
---|
84 | |
---|
85 | |
---|
86 | |
---|
87 | |
---|
88 | <p class="caption"><span class="caption-text">Table of Contents:</span></p> |
---|
89 | <ul> |
---|
90 | <li class="toctree-l1"><a class="reference internal" href="../ecmwf_data.html">ECMWF Data</a></li> |
---|
91 | <li class="toctree-l1"><a class="reference internal" href="../installation.html">Installation</a></li> |
---|
92 | <li class="toctree-l1"><a class="reference internal" href="../quick_start.html">Usage</a></li> |
---|
93 | <li class="toctree-l1"><a class="reference internal" href="../documentation.html">Code-Level Documentation</a></li> |
---|
94 | <li class="toctree-l1"><a class="reference internal" href="../evaluation.html">Evaluation</a></li> |
---|
95 | <li class="toctree-l1"><a class="reference internal" href="../dev_guide.html">Developer Guide</a></li> |
---|
96 | <li class="toctree-l1"><a class="reference internal" href="../changelog.html">Changelog</a></li> |
---|
97 | <li class="toctree-l1"><a class="reference internal" href="../support.html">Support</a></li> |
---|
98 | <li class="toctree-l1"><a class="reference internal" href="../Support/faq.html">FAQ - Frequently asked questions</a></li> |
---|
99 | <li class="toctree-l1"><a class="reference internal" href="../authors.html">Developer Team</a></li> |
---|
100 | </ul> |
---|
101 | |
---|
102 | |
---|
103 | |
---|
104 | </div> |
---|
105 | </div> |
---|
106 | </nav> |
---|
107 | |
---|
108 | <section data-toggle="wy-nav-shift" class="wy-nav-content-wrap"> |
---|
109 | |
---|
110 | |
---|
111 | <nav class="wy-nav-top" aria-label="top navigation"> |
---|
112 | |
---|
113 | <i data-toggle="wy-nav-top" class="fa fa-bars"></i> |
---|
114 | <a href="../index.html">flex_extract</a> |
---|
115 | |
---|
116 | </nav> |
---|
117 | |
---|
118 | |
---|
119 | <div class="wy-nav-content"> |
---|
120 | |
---|
121 | <div class="rst-content"> |
---|
122 | |
---|
123 | |
---|
124 | |
---|
125 | |
---|
126 | |
---|
127 | |
---|
128 | |
---|
129 | |
---|
130 | |
---|
131 | |
---|
132 | |
---|
133 | |
---|
134 | |
---|
135 | |
---|
136 | |
---|
137 | |
---|
138 | |
---|
139 | <div role="navigation" aria-label="breadcrumbs navigation"> |
---|
140 | |
---|
141 | <ul class="wy-breadcrumbs"> |
---|
142 | |
---|
143 | <li><a href="../index.html">Docs</a> »</li> |
---|
144 | |
---|
145 | <li><a href="index.html">Module code</a> »</li> |
---|
146 | |
---|
147 | <li>disaggregation</li> |
---|
148 | |
---|
149 | |
---|
150 | <li class="wy-breadcrumbs-aside"> |
---|
151 | |
---|
152 | </li> |
---|
153 | |
---|
154 | </ul> |
---|
155 | |
---|
156 | |
---|
157 | <hr/> |
---|
158 | </div> |
---|
159 | <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> |
---|
160 | <div itemprop="articleBody"> |
---|
161 | |
---|
162 | <h1>Source code for disaggregation</h1><div class="highlight"><pre> |
---|
163 | <span></span><span class="ch">#!/usr/bin/env python3</span> |
---|
164 | <span class="c1"># -*- coding: utf-8 -*-</span> |
---|
165 | <span class="c1">#*******************************************************************************</span> |
---|
166 | <span class="c1"># @Author: Anne Philipp (University of Vienna)</span> |
---|
167 | <span class="c1">#</span> |
---|
168 | <span class="c1"># @Date: March 2018</span> |
---|
169 | <span class="c1">#</span> |
---|
170 | <span class="c1"># @Change History:</span> |
---|
171 | <span class="c1">#</span> |
---|
172 | <span class="c1"># November 2015 - Leopold Haimberger (University of Vienna):</span> |
---|
173 | <span class="c1"># - migration of the methods dapoly and darain from Fortran</span> |
---|
174 | <span class="c1"># (flex_extract_v6 and earlier) to Python</span> |
---|
175 | <span class="c1">#</span> |
---|
176 | <span class="c1"># April 2018 - Anne Philipp (University of Vienna):</span> |
---|
177 | <span class="c1"># - applied PEP8 style guide</span> |
---|
178 | <span class="c1"># - added structured documentation</span> |
---|
179 | <span class="c1"># - outsourced the disaggregation functions dapoly and darain</span> |
---|
180 | <span class="c1"># to a new module named disaggregation</span> |
---|
181 | <span class="c1"># - added the new disaggregation method for precipitation</span> |
---|
182 | <span class="c1">#</span> |
---|
183 | <span class="c1"># June 2020 - Anne Philipp (University of Vienna):</span> |
---|
184 | <span class="c1"># - reformulated formular for dapoly</span> |
---|
185 | <span class="c1">#</span> |
---|
186 | <span class="c1"># @License:</span> |
---|
187 | <span class="c1"># (C) Copyright 2014-2020.</span> |
---|
188 | <span class="c1"># Anne Philipp, Leopold Haimberger</span> |
---|
189 | <span class="c1">#</span> |
---|
190 | <span class="c1"># SPDX-License-Identifier: CC-BY-4.0</span> |
---|
191 | <span class="c1">#</span> |
---|
192 | <span class="c1"># This work is licensed under the Creative Commons Attribution 4.0</span> |
---|
193 | <span class="c1"># International License. To view a copy of this license, visit</span> |
---|
194 | <span class="c1"># http://creativecommons.org/licenses/by/4.0/ or send a letter to</span> |
---|
195 | <span class="c1"># Creative Commons, PO Box 1866, Mountain View, CA 94042, USA.</span> |
---|
196 | <span class="c1">#</span> |
---|
197 | <span class="c1"># @Methods:</span> |
---|
198 | <span class="c1"># - dapoly</span> |
---|
199 | <span class="c1"># - darain</span> |
---|
200 | <span class="c1"># - IA3</span> |
---|
201 | <span class="c1">#*******************************************************************************</span> |
---|
202 | <span class="sd">'''Disaggregation of deaccumulated flux data from an ECMWF model FG field.</span> |
---|
203 | |
---|
204 | <span class="sd">Initially the flux data to be concerned are:</span> |
---|
205 | <span class="sd"> - large-scale precipitation</span> |
---|
206 | <span class="sd"> - convective precipitation</span> |
---|
207 | <span class="sd"> - surface sensible heat flux</span> |
---|
208 | <span class="sd"> - surface solar radiation</span> |
---|
209 | <span class="sd"> - u stress</span> |
---|
210 | <span class="sd"> - v stress</span> |
---|
211 | |
---|
212 | <span class="sd">Different versions of disaggregation is provided for rainfall</span> |
---|
213 | <span class="sd">data (darain, modified linear) and the surface fluxes and</span> |
---|
214 | <span class="sd">stress data (dapoly, cubic polynomial).</span> |
---|
215 | <span class="sd">'''</span> |
---|
216 | |
---|
217 | <span class="c1"># ------------------------------------------------------------------------------</span> |
---|
218 | <span class="c1"># MODULES</span> |
---|
219 | <span class="c1"># ------------------------------------------------------------------------------</span> |
---|
220 | |
---|
221 | <span class="c1"># ------------------------------------------------------------------------------</span> |
---|
222 | <span class="c1"># FUNCTIONS</span> |
---|
223 | <span class="c1"># ------------------------------------------------------------------------------</span> |
---|
224 | <div class="viewcode-block" id="dapoly"><a class="viewcode-back" href="../Documentation/Api/api_python.html#disaggregation.dapoly">[docs]</a><span class="k">def</span> <span class="nf">dapoly</span><span class="p">(</span><span class="n">alist</span><span class="p">):</span> |
---|
225 | <span class="sd">"""Cubic polynomial interpolation of deaccumulated fluxes.</span> |
---|
226 | |
---|
227 | <span class="sd"> Interpolation of deaccumulated fluxes of an ECMWF model FG field</span> |
---|
228 | <span class="sd"> using a cubic polynomial solution which conserves the integrals</span> |
---|
229 | <span class="sd"> of the fluxes within each timespan.</span> |
---|
230 | <span class="sd"> Disaggregation is done for 4 accumluated timespans which</span> |
---|
231 | <span class="sd"> generates a new, disaggregated value which is output at the</span> |
---|
232 | <span class="sd"> central point of the 4 accumulation timespans.</span> |
---|
233 | <span class="sd"> This new point is used for linear interpolation of the complete</span> |
---|
234 | <span class="sd"> timeseries afterwards.</span> |
---|
235 | |
---|
236 | <span class="sd"> Parameters</span> |
---|
237 | <span class="sd"> ----------</span> |
---|
238 | <span class="sd"> alist : list of array of float</span> |
---|
239 | <span class="sd"> List of 4 timespans as 2-dimensional, horizontal fields.</span> |
---|
240 | <span class="sd"> E.g. [[array_t1], [array_t2], [array_t3], [array_t4]]</span> |
---|
241 | |
---|
242 | <span class="sd"> Return</span> |
---|
243 | <span class="sd"> ------</span> |
---|
244 | <span class="sd"> nfield : array of float</span> |
---|
245 | <span class="sd"> Interpolated flux at central point of accumulation timespan.</span> |
---|
246 | |
---|
247 | <span class="sd"> Note</span> |
---|
248 | <span class="sd"> ----</span> |
---|
249 | <span class="sd"> March 2000 : P. JAMES</span> |
---|
250 | <span class="sd"> Original author</span> |
---|
251 | |
---|
252 | <span class="sd"> June 2003 : A. BECK</span> |
---|
253 | <span class="sd"> Adaptations</span> |
---|
254 | |
---|
255 | <span class="sd"> November 2015 : Leopold Haimberger (University of Vienna)</span> |
---|
256 | <span class="sd"> Migration from Fortran to Python</span> |
---|
257 | |
---|
258 | <span class="sd"> """</span> |
---|
259 | |
---|
260 | <span class="n">nfield</span> <span class="o">=</span> <span class="o">-</span><span class="mf">1.</span><span class="o">/</span><span class="mf">12.</span><span class="o">*</span><span class="n">alist</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">+</span> \ |
---|
261 | <span class="mf">7.</span><span class="o">/</span><span class="mf">12.</span><span class="o">*</span><span class="n">alist</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">+</span> \ |
---|
262 | <span class="mf">7.</span><span class="o">/</span><span class="mf">12.</span><span class="o">*</span><span class="n">alist</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span> <span class="o">-</span> \ |
---|
263 | <span class="mf">1.</span><span class="o">/</span><span class="mf">12.</span><span class="o">*</span><span class="n">alist</span><span class="p">[</span><span class="mi">3</span><span class="p">]</span> |
---|
264 | |
---|
265 | <span class="k">return</span> <span class="n">nfield</span></div> |
---|
266 | |
---|
267 | |
---|
268 | <div class="viewcode-block" id="darain"><a class="viewcode-back" href="../Documentation/Api/api_python.html#disaggregation.darain">[docs]</a><span class="k">def</span> <span class="nf">darain</span><span class="p">(</span><span class="n">alist</span><span class="p">):</span> |
---|
269 | <span class="sd">"""Linear interpolation of deaccumulated fluxes.</span> |
---|
270 | |
---|
271 | <span class="sd"> Interpolation of deaccumulated fluxes of an ECMWF model FG rainfall</span> |
---|
272 | <span class="sd"> field using a modified linear solution which conserves the integrals</span> |
---|
273 | <span class="sd"> of the fluxes within each timespan.</span> |
---|
274 | <span class="sd"> Disaggregation is done for 4 accumluated timespans which generates</span> |
---|
275 | <span class="sd"> a new, disaggregated value which is output at the central point</span> |
---|
276 | <span class="sd"> of the 4 accumulation timespans. This new point is used for linear</span> |
---|
277 | <span class="sd"> interpolation of the complete timeseries afterwards.</span> |
---|
278 | |
---|
279 | <span class="sd"> Parameters</span> |
---|
280 | <span class="sd"> ----------</span> |
---|
281 | <span class="sd"> alist : list of array of float</span> |
---|
282 | <span class="sd"> List of 4 timespans as 2-dimensional, horizontal fields.</span> |
---|
283 | <span class="sd"> E.g. [[array_t1], [array_t2], [array_t3], [array_t4]]</span> |
---|
284 | |
---|
285 | <span class="sd"> Return</span> |
---|
286 | <span class="sd"> ------</span> |
---|
287 | <span class="sd"> nfield : array of float</span> |
---|
288 | <span class="sd"> Interpolated flux at central point of accumulation timespan.</span> |
---|
289 | |
---|
290 | <span class="sd"> Note</span> |
---|
291 | <span class="sd"> ----</span> |
---|
292 | <span class="sd"> March 2000 : P. JAMES</span> |
---|
293 | <span class="sd"> Original author</span> |
---|
294 | |
---|
295 | <span class="sd"> June 2003 : A. BECK</span> |
---|
296 | <span class="sd"> Adaptations</span> |
---|
297 | |
---|
298 | <span class="sd"> November 2015 : Leopold Haimberger (University of Vienna)</span> |
---|
299 | <span class="sd"> Migration from Fortran to Python</span> |
---|
300 | <span class="sd"> """</span> |
---|
301 | |
---|
302 | <span class="n">xa</span> <span class="o">=</span> <span class="n">alist</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> |
---|
303 | <span class="n">xb</span> <span class="o">=</span> <span class="n">alist</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> |
---|
304 | <span class="n">xc</span> <span class="o">=</span> <span class="n">alist</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span> |
---|
305 | <span class="n">xd</span> <span class="o">=</span> <span class="n">alist</span><span class="p">[</span><span class="mi">3</span><span class="p">]</span> |
---|
306 | <span class="n">xa</span><span class="p">[</span><span class="n">xa</span> <span class="o"><</span> <span class="mf">0.</span><span class="p">]</span> <span class="o">=</span> <span class="mf">0.</span> |
---|
307 | <span class="n">xb</span><span class="p">[</span><span class="n">xb</span> <span class="o"><</span> <span class="mf">0.</span><span class="p">]</span> <span class="o">=</span> <span class="mf">0.</span> |
---|
308 | <span class="n">xc</span><span class="p">[</span><span class="n">xc</span> <span class="o"><</span> <span class="mf">0.</span><span class="p">]</span> <span class="o">=</span> <span class="mf">0.</span> |
---|
309 | <span class="n">xd</span><span class="p">[</span><span class="n">xd</span> <span class="o"><</span> <span class="mf">0.</span><span class="p">]</span> <span class="o">=</span> <span class="mf">0.</span> |
---|
310 | |
---|
311 | <span class="n">xac</span> <span class="o">=</span> <span class="mf">0.5</span> <span class="o">*</span> <span class="n">xb</span> |
---|
312 | <span class="n">mask</span> <span class="o">=</span> <span class="n">xa</span> <span class="o">+</span> <span class="n">xc</span> <span class="o">></span> <span class="mf">0.</span> |
---|
313 | <span class="n">xac</span><span class="p">[</span><span class="n">mask</span><span class="p">]</span> <span class="o">=</span> <span class="n">xb</span><span class="p">[</span><span class="n">mask</span><span class="p">]</span> <span class="o">*</span> <span class="n">xc</span><span class="p">[</span><span class="n">mask</span><span class="p">]</span> <span class="o">/</span> <span class="p">(</span><span class="n">xa</span><span class="p">[</span><span class="n">mask</span><span class="p">]</span> <span class="o">+</span> <span class="n">xc</span><span class="p">[</span><span class="n">mask</span><span class="p">])</span> |
---|
314 | <span class="n">xbd</span> <span class="o">=</span> <span class="mf">0.5</span> <span class="o">*</span> <span class="n">xc</span> |
---|
315 | <span class="n">mask</span> <span class="o">=</span> <span class="n">xb</span> <span class="o">+</span> <span class="n">xd</span> <span class="o">></span> <span class="mf">0.</span> |
---|
316 | <span class="n">xbd</span><span class="p">[</span><span class="n">mask</span><span class="p">]</span> <span class="o">=</span> <span class="n">xb</span><span class="p">[</span><span class="n">mask</span><span class="p">]</span> <span class="o">*</span> <span class="n">xc</span><span class="p">[</span><span class="n">mask</span><span class="p">]</span> <span class="o">/</span> <span class="p">(</span><span class="n">xb</span><span class="p">[</span><span class="n">mask</span><span class="p">]</span> <span class="o">+</span> <span class="n">xd</span><span class="p">[</span><span class="n">mask</span><span class="p">])</span> |
---|
317 | <span class="n">nfield</span> <span class="o">=</span> <span class="n">xac</span> <span class="o">+</span> <span class="n">xbd</span> |
---|
318 | |
---|
319 | <span class="k">return</span> <span class="n">nfield</span></div> |
---|
320 | |
---|
321 | <div class="viewcode-block" id="IA3"><a class="viewcode-back" href="../Documentation/Api/api_python.html#disaggregation.IA3">[docs]</a><span class="k">def</span> <span class="nf">IA3</span><span class="p">(</span><span class="n">g</span><span class="p">):</span> |
---|
322 | <span class="sd">""" Interpolation with a non-negative geometric mean based algorithm.</span> |
---|
323 | |
---|
324 | <span class="sd"> The original grid is reconstructed by adding two sampling points in each</span> |
---|
325 | <span class="sd"> data series interval. This subgrid is used to keep all information during</span> |
---|
326 | <span class="sd"> the interpolation within the associated interval. Additionally, an advanced</span> |
---|
327 | <span class="sd"> monotonicity filter is applied to improve the monotonicity properties of</span> |
---|
328 | <span class="sd"> the series.</span> |
---|
329 | |
---|
330 | <span class="sd"> Note</span> |
---|
331 | <span class="sd"> ----</span> |
---|
332 | <span class="sd"> (C) Copyright 2017-2019</span> |
---|
333 | <span class="sd"> Sabine Hittmeir, Anne Philipp, Petra Seibert</span> |
---|
334 | |
---|
335 | <span class="sd"> This work is licensed under the Creative Commons Attribution 4.0</span> |
---|
336 | <span class="sd"> International License. To view a copy of this license, visit</span> |
---|
337 | <span class="sd"> http://creativecommons.org/licenses/by/4.0/ or send a letter to</span> |
---|
338 | <span class="sd"> Creative Commons, PO Box 1866, Mountain View, CA 94042, USA.</span> |
---|
339 | |
---|
340 | <span class="sd"> Parameters</span> |
---|
341 | <span class="sd"> ----------</span> |
---|
342 | <span class="sd"> g : list of float</span> |
---|
343 | <span class="sd"> Complete data series that will be interpolated having</span> |
---|
344 | <span class="sd"> the dimension of the original raw series.</span> |
---|
345 | |
---|
346 | <span class="sd"> Return</span> |
---|
347 | <span class="sd"> ------</span> |
---|
348 | <span class="sd"> f : list of float</span> |
---|
349 | <span class="sd"> The interpolated data series with additional subgrid points.</span> |
---|
350 | <span class="sd"> Its dimension is equal to the length of the input data series</span> |
---|
351 | <span class="sd"> times three.</span> |
---|
352 | |
---|
353 | |
---|
354 | <span class="sd"> References</span> |
---|
355 | <span class="sd"> ----------</span> |
---|
356 | <span class="sd"> For more information see article:</span> |
---|
357 | <span class="sd"> Hittmeir, S.; Philipp, A.; Seibert, P. (2017): A conservative</span> |
---|
358 | <span class="sd"> interpolation scheme for extensive quantities with application to the</span> |
---|
359 | <span class="sd"> Lagrangian particle dispersion model FLEXPART.,</span> |
---|
360 | <span class="sd"> Geoscientific Model Development</span> |
---|
361 | <span class="sd"> """</span> |
---|
362 | |
---|
363 | <span class="c1">####################### variable description #############################</span> |
---|
364 | <span class="c1"># #</span> |
---|
365 | <span class="c1"># i - index variable for looping over the data series #</span> |
---|
366 | <span class="c1"># g - input data series #</span> |
---|
367 | <span class="c1"># f - interpolated and filtered data series with additional #</span> |
---|
368 | <span class="c1"># grid points #</span> |
---|
369 | <span class="c1"># fi - function value at position i, f_i #</span> |
---|
370 | <span class="c1"># fi1 - first sub-grid function value f_i^1 #</span> |
---|
371 | <span class="c1"># fi2 - second sub-grid function value f_i^2 #</span> |
---|
372 | <span class="c1"># fip1 - next function value at position i+1, f_(i+1) #</span> |
---|
373 | <span class="c1"># dt - time step #</span> |
---|
374 | <span class="c1"># fmon - monotonicity filter #</span> |
---|
375 | <span class="c1"># #</span> |
---|
376 | <span class="c1">###########################################################################</span> |
---|
377 | |
---|
378 | |
---|
379 | <span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span> |
---|
380 | |
---|
381 | <span class="c1"># time step</span> |
---|
382 | <span class="n">dt</span> <span class="o">=</span> <span class="mf">1.0</span> |
---|
383 | |
---|
384 | <span class="c1">############### Non-negative Geometric Mean Based Algorithm ###############</span> |
---|
385 | |
---|
386 | <span class="c1"># for the left boundary the following boundary condition is valid:</span> |
---|
387 | <span class="c1"># the value at t=0 of the interpolation algorithm coincides with the</span> |
---|
388 | <span class="c1"># first data value according to the persistence hypothesis</span> |
---|
389 | <span class="n">f</span> <span class="o">=</span> <span class="p">[</span><span class="n">g</span><span class="p">[</span><span class="mi">0</span><span class="p">]]</span> |
---|
390 | |
---|
391 | <span class="c1"># compute two first sub-grid intervals without monotonicity check</span> |
---|
392 | <span class="c1"># go through the data series and extend each interval by two sub-grid</span> |
---|
393 | <span class="c1"># points and interpolate the corresponding data values</span> |
---|
394 | <span class="c1"># except for the last interval due to boundary conditions</span> |
---|
395 | <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">2</span><span class="p">):</span> |
---|
396 | |
---|
397 | <span class="c1"># as a requirement:</span> |
---|
398 | <span class="c1"># if there is a zero data value such that g[i]=0, then the whole</span> |
---|
399 | <span class="c1"># interval in f has to be zero to such that f[i+1]=f[i+2]=f[i+3]=0</span> |
---|
400 | <span class="c1"># according to Eq. (6)</span> |
---|
401 | <span class="k">if</span> <span class="n">g</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">==</span> <span class="mf">0.</span><span class="p">:</span> |
---|
402 | <span class="n">f</span><span class="o">.</span><span class="n">extend</span><span class="p">([</span><span class="mf">0.</span><span class="p">,</span> <span class="mf">0.</span><span class="p">,</span> <span class="mf">0.</span><span class="p">])</span> |
---|
403 | |
---|
404 | <span class="c1"># otherwise the sub-grid values are calculated and added to the list</span> |
---|
405 | <span class="k">else</span><span class="p">:</span> |
---|
406 | <span class="c1"># temporal save of last value in interpolated list</span> |
---|
407 | <span class="c1"># since it is the left boundary and hence the new (fi) value</span> |
---|
408 | <span class="n">fi</span> <span class="o">=</span> <span class="n">f</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span> |
---|
409 | |
---|
410 | <span class="c1"># the value at the end of the interval (fip1) is prescribed by the</span> |
---|
411 | <span class="c1"># geometric mean, restricted such that non-negativity is guaranteed</span> |
---|
412 | <span class="c1"># according to Eq. (25)</span> |
---|
413 | <span class="n">fip1</span> <span class="o">=</span> <span class="nb">min</span><span class="p">(</span><span class="mf">3.</span> <span class="o">*</span> <span class="n">g</span><span class="p">[</span><span class="n">i</span><span class="p">],</span> <span class="mf">3.</span> <span class="o">*</span> <span class="n">g</span><span class="p">[</span><span class="n">i</span> <span class="o">+</span> <span class="mi">1</span><span class="p">],</span> <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="n">g</span><span class="p">[</span><span class="n">i</span> <span class="o">+</span> <span class="mi">1</span><span class="p">]</span> <span class="o">*</span> <span class="n">g</span><span class="p">[</span><span class="n">i</span><span class="p">]))</span> |
---|
414 | |
---|
415 | <span class="c1"># the function value at the first sub-grid point (fi1) is determined</span> |
---|
416 | <span class="c1"># according to the equal area condition with Eq. (19)</span> |
---|
417 | <span class="n">fi1</span> <span class="o">=</span> <span class="mf">3.</span><span class="o">/</span><span class="mf">2.</span><span class="o">*</span><span class="n">g</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="o">-</span><span class="mf">5.</span><span class="o">/</span><span class="mf">12.</span><span class="o">*</span><span class="n">fip1</span><span class="o">-</span><span class="mf">1.</span><span class="o">/</span><span class="mf">12.</span><span class="o">*</span><span class="n">fi</span> |
---|
418 | |
---|
419 | <span class="c1"># the function value at the second sub-grid point (fi2) is determined</span> |
---|
420 | <span class="c1"># according Eq. (18)</span> |
---|
421 | <span class="n">fi2</span> <span class="o">=</span> <span class="n">fi1</span><span class="o">+</span><span class="mf">1.</span><span class="o">/</span><span class="mf">3.</span><span class="o">*</span><span class="p">(</span><span class="n">fip1</span><span class="o">-</span><span class="n">fi</span><span class="p">)</span> |
---|
422 | |
---|
423 | <span class="c1"># add next interval of interpolated (sub-)grid values</span> |
---|
424 | <span class="n">f</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">fi1</span><span class="p">)</span> |
---|
425 | <span class="n">f</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">fi2</span><span class="p">)</span> |
---|
426 | <span class="n">f</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">fip1</span><span class="p">)</span> |
---|
427 | |
---|
428 | <span class="c1"># compute rest of the data series intervals</span> |
---|
429 | <span class="c1"># go through the data series and extend each interval by two sub-grid</span> |
---|
430 | <span class="c1"># points and interpolate the corresponding data values</span> |
---|
431 | <span class="c1"># except for the last interval due to boundary conditions</span> |
---|
432 | <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="nb">len</span><span class="p">(</span><span class="n">g</span><span class="p">)</span><span class="o">-</span><span class="mi">1</span><span class="p">):</span> |
---|
433 | |
---|
434 | <span class="c1"># as a requirement:</span> |
---|
435 | <span class="c1"># if there is a zero data value such that g[i]=0, then the whole</span> |
---|
436 | <span class="c1"># interval in f has to be zero to such that f[i+1]=f[i+2]=f[i+3]=0</span> |
---|
437 | <span class="c1"># according to Eq. (6)</span> |
---|
438 | <span class="k">if</span> <span class="n">g</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">==</span> <span class="mf">0.</span><span class="p">:</span> |
---|
439 | <span class="c1"># apply monotonicity filter for interval before</span> |
---|
440 | <span class="c1"># check if there is "M" or "W" shape</span> |
---|
441 | <span class="k">if</span> <span class="n">np</span><span class="o">.</span><span class="n">sign</span><span class="p">(</span><span class="n">f</span><span class="p">[</span><span class="o">-</span><span class="mi">5</span><span class="p">]</span><span class="o">-</span><span class="n">f</span><span class="p">[</span><span class="o">-</span><span class="mi">6</span><span class="p">])</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">sign</span><span class="p">(</span><span class="n">f</span><span class="p">[</span><span class="o">-</span><span class="mi">4</span><span class="p">]</span><span class="o">-</span><span class="n">f</span><span class="p">[</span><span class="o">-</span><span class="mi">5</span><span class="p">])</span> <span class="o">==</span> <span class="o">-</span><span class="mi">1</span> \ |
---|
442 | <span class="ow">and</span> <span class="n">np</span><span class="o">.</span><span class="n">sign</span><span class="p">(</span><span class="n">f</span><span class="p">[</span><span class="o">-</span><span class="mi">4</span><span class="p">]</span><span class="o">-</span><span class="n">f</span><span class="p">[</span><span class="o">-</span><span class="mi">5</span><span class="p">])</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">sign</span><span class="p">(</span><span class="n">f</span><span class="p">[</span><span class="o">-</span><span class="mi">3</span><span class="p">]</span><span class="o">-</span><span class="n">f</span><span class="p">[</span><span class="o">-</span><span class="mi">4</span><span class="p">])</span> <span class="o">==</span> <span class="o">-</span><span class="mi">1</span> \ |
---|
443 | <span class="ow">and</span> <span class="n">np</span><span class="o">.</span><span class="n">sign</span><span class="p">(</span><span class="n">f</span><span class="p">[</span><span class="o">-</span><span class="mi">3</span><span class="p">]</span><span class="o">-</span><span class="n">f</span><span class="p">[</span><span class="o">-</span><span class="mi">4</span><span class="p">])</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">sign</span><span class="p">(</span><span class="n">f</span><span class="p">[</span><span class="o">-</span><span class="mi">2</span><span class="p">]</span><span class="o">-</span><span class="n">f</span><span class="p">[</span><span class="o">-</span><span class="mi">3</span><span class="p">])</span> <span class="o">==</span> <span class="o">-</span><span class="mi">1</span><span class="p">:</span> |
---|
444 | |
---|
445 | <span class="c1"># the monotonicity filter corrects the value at (fim1) by</span> |
---|
446 | <span class="c1"># substituting (fim1) with (fmon), see Eq. (27), (28) and (29)</span> |
---|
447 | <span class="n">fmon</span> <span class="o">=</span> <span class="nb">min</span><span class="p">(</span><span class="mf">3.</span> <span class="o">*</span> <span class="n">g</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">2</span><span class="p">],</span> |
---|
448 | <span class="mf">3.</span> <span class="o">*</span> <span class="n">g</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">],</span> |
---|
449 | <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="nb">max</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="p">(</span><span class="mf">18.</span> <span class="o">/</span> <span class="mf">13.</span> <span class="o">*</span> <span class="n">g</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">2</span><span class="p">]</span> <span class="o">-</span> <span class="mf">5.</span> <span class="o">/</span> <span class="mf">13.</span> <span class="o">*</span> <span class="n">f</span><span class="p">[</span><span class="o">-</span><span class="mi">7</span><span class="p">])</span> <span class="o">*</span> |
---|
450 | <span class="p">(</span><span class="mf">18.</span> <span class="o">/</span> <span class="mf">13.</span> <span class="o">*</span> <span class="n">g</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]</span> <span class="o">-</span> <span class="mf">5.</span> <span class="o">/</span> <span class="mf">13.</span> <span class="o">*</span> <span class="n">f</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]))))</span> |
---|
451 | |
---|
452 | <span class="c1"># recomputation of the sub-grid interval values while the</span> |
---|
453 | <span class="c1"># interval boundaries (fi) and (fip2) remains unchanged</span> |
---|
454 | <span class="c1"># see Eq. (18) and (19)</span> |
---|
455 | <span class="n">f</span><span class="p">[</span><span class="o">-</span><span class="mi">4</span><span class="p">]</span> <span class="o">=</span> <span class="n">fmon</span> |
---|
456 | <span class="n">f</span><span class="p">[</span><span class="o">-</span><span class="mi">6</span><span class="p">]</span> <span class="o">=</span> <span class="mf">3.</span><span class="o">/</span><span class="mf">2.</span><span class="o">*</span><span class="n">g</span><span class="p">[</span><span class="n">i</span><span class="o">-</span><span class="mi">2</span><span class="p">]</span><span class="o">-</span><span class="mf">5.</span><span class="o">/</span><span class="mf">12.</span><span class="o">*</span><span class="n">fmon</span><span class="o">-</span><span class="mf">1.</span><span class="o">/</span><span class="mf">12.</span><span class="o">*</span><span class="n">f</span><span class="p">[</span><span class="o">-</span><span class="mi">7</span><span class="p">]</span> |
---|
457 | <span class="n">f</span><span class="p">[</span><span class="o">-</span><span class="mi">5</span><span class="p">]</span> <span class="o">=</span> <span class="n">f</span><span class="p">[</span><span class="o">-</span><span class="mi">6</span><span class="p">]</span><span class="o">+</span><span class="p">(</span><span class="n">fmon</span><span class="o">-</span><span class="n">f</span><span class="p">[</span><span class="o">-</span><span class="mi">7</span><span class="p">])</span><span class="o">/</span><span class="mf">3.</span> |
---|
458 | <span class="n">f</span><span class="p">[</span><span class="o">-</span><span class="mi">3</span><span class="p">]</span> <span class="o">=</span> <span class="mf">3.</span><span class="o">/</span><span class="mf">2.</span><span class="o">*</span><span class="n">g</span><span class="p">[</span><span class="n">i</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span><span class="o">-</span><span class="mf">5.</span><span class="o">/</span><span class="mf">12.</span><span class="o">*</span><span class="n">f</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span><span class="o">-</span><span class="mf">1.</span><span class="o">/</span><span class="mf">12.</span><span class="o">*</span><span class="n">fmon</span> |
---|
459 | <span class="n">f</span><span class="p">[</span><span class="o">-</span><span class="mi">2</span><span class="p">]</span> <span class="o">=</span> <span class="n">f</span><span class="p">[</span><span class="o">-</span><span class="mi">3</span><span class="p">]</span><span class="o">+</span><span class="p">(</span><span class="n">f</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">fmon</span><span class="p">)</span><span class="o">/</span><span class="mf">3.</span> |
---|
460 | |
---|
461 | <span class="n">f</span><span class="o">.</span><span class="n">extend</span><span class="p">([</span><span class="mf">0.</span><span class="p">,</span> <span class="mf">0.</span><span class="p">,</span> <span class="mf">0.</span><span class="p">])</span> |
---|
462 | |
---|
463 | <span class="c1"># otherwise the sub-grid values are calculated and added to the list</span> |
---|
464 | <span class="k">else</span><span class="p">:</span> |
---|
465 | <span class="c1"># temporal save of last value in interpolated list</span> |
---|
466 | <span class="c1"># since it is the left boundary and hence the new (fi) value</span> |
---|
467 | <span class="n">fi</span> <span class="o">=</span> <span class="n">f</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span> |
---|
468 | |
---|
469 | <span class="c1"># the value at the end of the interval (fip1) is prescribed by the</span> |
---|
470 | <span class="c1"># geometric mean, restricted such that non-negativity is guaranteed</span> |
---|
471 | <span class="c1"># according to Eq. (25)</span> |
---|
472 | <span class="n">fip1</span> <span class="o">=</span> <span class="nb">min</span><span class="p">(</span><span class="mf">3.</span> <span class="o">*</span> <span class="n">g</span><span class="p">[</span><span class="n">i</span><span class="p">],</span> <span class="mf">3.</span> <span class="o">*</span> <span class="n">g</span><span class="p">[</span><span class="n">i</span> <span class="o">+</span> <span class="mi">1</span><span class="p">],</span> <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="n">g</span><span class="p">[</span><span class="n">i</span> <span class="o">+</span> <span class="mi">1</span><span class="p">]</span> <span class="o">*</span> <span class="n">g</span><span class="p">[</span><span class="n">i</span><span class="p">]))</span> |
---|
473 | |
---|
474 | <span class="c1"># the function value at the first sub-grid point (fi1) is determined</span> |
---|
475 | <span class="c1"># according to the equal area condition with Eq. (19)</span> |
---|
476 | <span class="n">fi1</span> <span class="o">=</span> <span class="mf">3.</span><span class="o">/</span><span class="mf">2.</span><span class="o">*</span><span class="n">g</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="o">-</span><span class="mf">5.</span><span class="o">/</span><span class="mf">12.</span><span class="o">*</span><span class="n">fip1</span><span class="o">-</span><span class="mf">1.</span><span class="o">/</span><span class="mf">12.</span><span class="o">*</span><span class="n">fi</span> |
---|
477 | |
---|
478 | <span class="c1"># the function value at the second sub-grid point (fi2) is determined</span> |
---|
479 | <span class="c1"># according Eq. (18)</span> |
---|
480 | <span class="n">fi2</span> <span class="o">=</span> <span class="n">fi1</span><span class="o">+</span><span class="mf">1.</span><span class="o">/</span><span class="mf">3.</span><span class="o">*</span><span class="p">(</span><span class="n">fip1</span><span class="o">-</span><span class="n">fi</span><span class="p">)</span> |
---|
481 | |
---|
482 | <span class="c1"># apply monotonicity filter for interval before</span> |
---|
483 | <span class="c1"># check if there is "M" or "W" shape</span> |
---|
484 | <span class="k">if</span> <span class="n">np</span><span class="o">.</span><span class="n">sign</span><span class="p">(</span><span class="n">f</span><span class="p">[</span><span class="o">-</span><span class="mi">5</span><span class="p">]</span><span class="o">-</span><span class="n">f</span><span class="p">[</span><span class="o">-</span><span class="mi">6</span><span class="p">])</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">sign</span><span class="p">(</span><span class="n">f</span><span class="p">[</span><span class="o">-</span><span class="mi">4</span><span class="p">]</span><span class="o">-</span><span class="n">f</span><span class="p">[</span><span class="o">-</span><span class="mi">5</span><span class="p">])</span> <span class="o">==</span> <span class="o">-</span><span class="mi">1</span> \ |
---|
485 | <span class="ow">and</span> <span class="n">np</span><span class="o">.</span><span class="n">sign</span><span class="p">(</span><span class="n">f</span><span class="p">[</span><span class="o">-</span><span class="mi">4</span><span class="p">]</span><span class="o">-</span><span class="n">f</span><span class="p">[</span><span class="o">-</span><span class="mi">5</span><span class="p">])</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">sign</span><span class="p">(</span><span class="n">f</span><span class="p">[</span><span class="o">-</span><span class="mi">3</span><span class="p">]</span><span class="o">-</span><span class="n">f</span><span class="p">[</span><span class="o">-</span><span class="mi">4</span><span class="p">])</span> <span class="o">==</span> <span class="o">-</span><span class="mi">1</span> \ |
---|
486 | <span class="ow">and</span> <span class="n">np</span><span class="o">.</span><span class="n">sign</span><span class="p">(</span><span class="n">f</span><span class="p">[</span><span class="o">-</span><span class="mi">3</span><span class="p">]</span><span class="o">-</span><span class="n">f</span><span class="p">[</span><span class="o">-</span><span class="mi">4</span><span class="p">])</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">sign</span><span class="p">(</span><span class="n">f</span><span class="p">[</span><span class="o">-</span><span class="mi">2</span><span class="p">]</span><span class="o">-</span><span class="n">f</span><span class="p">[</span><span class="o">-</span><span class="mi">3</span><span class="p">])</span> <span class="o">==</span> <span class="o">-</span><span class="mi">1</span><span class="p">:</span> |
---|
487 | |
---|
488 | <span class="c1"># the monotonicity filter corrects the value at (fim1) by</span> |
---|
489 | <span class="c1"># substituting (fim1) with fmon, see Eq. (27), (28) and (29)</span> |
---|
490 | <span class="n">fmon</span> <span class="o">=</span> <span class="nb">min</span><span class="p">(</span><span class="mf">3.</span> <span class="o">*</span> <span class="n">g</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">2</span><span class="p">],</span> |
---|
491 | <span class="mf">3.</span> <span class="o">*</span> <span class="n">g</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">],</span> |
---|
492 | <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="nb">max</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="p">(</span><span class="mf">18.</span> <span class="o">/</span> <span class="mf">13.</span> <span class="o">*</span> <span class="n">g</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">2</span><span class="p">]</span> <span class="o">-</span> <span class="mf">5.</span> <span class="o">/</span> <span class="mf">13.</span> <span class="o">*</span> <span class="n">f</span><span class="p">[</span><span class="o">-</span><span class="mi">7</span><span class="p">])</span> <span class="o">*</span> |
---|
493 | <span class="p">(</span><span class="mf">18.</span> <span class="o">/</span> <span class="mf">13.</span> <span class="o">*</span> <span class="n">g</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]</span> <span class="o">-</span> <span class="mf">5.</span> <span class="o">/</span> <span class="mf">13.</span> <span class="o">*</span> <span class="n">f</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]))))</span> |
---|
494 | |
---|
495 | <span class="c1"># recomputation of the sub-grid interval values while the</span> |
---|
496 | <span class="c1"># interval boundaries (fi) and (fip2) remains unchanged</span> |
---|
497 | <span class="c1"># see Eq. (18) and (19)</span> |
---|
498 | <span class="n">f</span><span class="p">[</span><span class="o">-</span><span class="mi">4</span><span class="p">]</span> <span class="o">=</span> <span class="n">fmon</span> |
---|
499 | <span class="n">f</span><span class="p">[</span><span class="o">-</span><span class="mi">6</span><span class="p">]</span> <span class="o">=</span> <span class="mf">3.</span><span class="o">/</span><span class="mf">2.</span><span class="o">*</span><span class="n">g</span><span class="p">[</span><span class="n">i</span><span class="o">-</span><span class="mi">2</span><span class="p">]</span><span class="o">-</span><span class="mf">5.</span><span class="o">/</span><span class="mf">12.</span><span class="o">*</span><span class="n">fmon</span><span class="o">-</span><span class="mf">1.</span><span class="o">/</span><span class="mf">12.</span><span class="o">*</span><span class="n">f</span><span class="p">[</span><span class="o">-</span><span class="mi">7</span><span class="p">]</span> |
---|
500 | <span class="n">f</span><span class="p">[</span><span class="o">-</span><span class="mi">5</span><span class="p">]</span> <span class="o">=</span> <span class="n">f</span><span class="p">[</span><span class="o">-</span><span class="mi">6</span><span class="p">]</span><span class="o">+</span><span class="p">(</span><span class="n">fmon</span><span class="o">-</span><span class="n">f</span><span class="p">[</span><span class="o">-</span><span class="mi">7</span><span class="p">])</span><span class="o">/</span><span class="mf">3.</span> |
---|
501 | <span class="n">f</span><span class="p">[</span><span class="o">-</span><span class="mi">3</span><span class="p">]</span> <span class="o">=</span> <span class="mf">3.</span><span class="o">/</span><span class="mf">2.</span><span class="o">*</span><span class="n">g</span><span class="p">[</span><span class="n">i</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span><span class="o">-</span><span class="mf">5.</span><span class="o">/</span><span class="mf">12.</span><span class="o">*</span><span class="n">f</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span><span class="o">-</span><span class="mf">1.</span><span class="o">/</span><span class="mf">12.</span><span class="o">*</span><span class="n">fmon</span> |
---|
502 | <span class="n">f</span><span class="p">[</span><span class="o">-</span><span class="mi">2</span><span class="p">]</span> <span class="o">=</span> <span class="n">f</span><span class="p">[</span><span class="o">-</span><span class="mi">3</span><span class="p">]</span><span class="o">+</span><span class="p">(</span><span class="n">f</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">fmon</span><span class="p">)</span><span class="o">/</span><span class="mf">3.</span> |
---|
503 | |
---|
504 | <span class="c1"># add next interval of interpolated (sub-)grid values</span> |
---|
505 | <span class="n">f</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">fi1</span><span class="p">)</span> |
---|
506 | <span class="n">f</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">fi2</span><span class="p">)</span> |
---|
507 | <span class="n">f</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">fip1</span><span class="p">)</span> |
---|
508 | |
---|
509 | <span class="c1"># separate treatment of the final interval</span> |
---|
510 | |
---|
511 | <span class="c1"># as a requirement:</span> |
---|
512 | <span class="c1"># if there is a zero data value such that g[i]=0, then the whole</span> |
---|
513 | <span class="c1"># interval in f has to be zero to such that f[i+1]=f[i+2]=f[i+3]=0</span> |
---|
514 | <span class="c1"># according to Eq. (6)</span> |
---|
515 | <span class="k">if</span> <span class="n">g</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="o">==</span> <span class="mf">0.</span><span class="p">:</span> |
---|
516 | <span class="c1"># apply monotonicity filter for interval before</span> |
---|
517 | <span class="c1"># check if there is "M" or "W" shape</span> |
---|
518 | <span class="k">if</span> <span class="n">np</span><span class="o">.</span><span class="n">sign</span><span class="p">(</span><span class="n">f</span><span class="p">[</span><span class="o">-</span><span class="mi">5</span><span class="p">]</span><span class="o">-</span><span class="n">f</span><span class="p">[</span><span class="o">-</span><span class="mi">6</span><span class="p">])</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">sign</span><span class="p">(</span><span class="n">f</span><span class="p">[</span><span class="o">-</span><span class="mi">4</span><span class="p">]</span><span class="o">-</span><span class="n">f</span><span class="p">[</span><span class="o">-</span><span class="mi">5</span><span class="p">])</span> <span class="o">==</span> <span class="o">-</span><span class="mi">1</span> \ |
---|
519 | <span class="ow">and</span> <span class="n">np</span><span class="o">.</span><span class="n">sign</span><span class="p">(</span><span class="n">f</span><span class="p">[</span><span class="o">-</span><span class="mi">4</span><span class="p">]</span><span class="o">-</span><span class="n">f</span><span class="p">[</span><span class="o">-</span><span class="mi">5</span><span class="p">])</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">sign</span><span class="p">(</span><span class="n">f</span><span class="p">[</span><span class="o">-</span><span class="mi">3</span><span class="p">]</span><span class="o">-</span><span class="n">f</span><span class="p">[</span><span class="o">-</span><span class="mi">4</span><span class="p">])</span> <span class="o">==</span> <span class="o">-</span><span class="mi">1</span> \ |
---|
520 | <span class="ow">and</span> <span class="n">np</span><span class="o">.</span><span class="n">sign</span><span class="p">(</span><span class="n">f</span><span class="p">[</span><span class="o">-</span><span class="mi">3</span><span class="p">]</span><span class="o">-</span><span class="n">f</span><span class="p">[</span><span class="o">-</span><span class="mi">4</span><span class="p">])</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">sign</span><span class="p">(</span><span class="n">f</span><span class="p">[</span><span class="o">-</span><span class="mi">2</span><span class="p">]</span><span class="o">-</span><span class="n">f</span><span class="p">[</span><span class="o">-</span><span class="mi">3</span><span class="p">])</span> <span class="o">==</span> <span class="o">-</span><span class="mi">1</span><span class="p">:</span> |
---|
521 | |
---|
522 | <span class="c1"># the monotonicity filter corrects the value at (fim1) by</span> |
---|
523 | <span class="c1"># substituting (fim1) with (fmon), see Eq. (27), (28) and (29)</span> |
---|
524 | <span class="n">fmon</span> <span class="o">=</span> <span class="nb">min</span><span class="p">(</span><span class="mf">3.</span> <span class="o">*</span> <span class="n">g</span><span class="p">[</span><span class="o">-</span><span class="mi">3</span><span class="p">],</span> |
---|
525 | <span class="mf">3.</span> <span class="o">*</span> <span class="n">g</span><span class="p">[</span><span class="o">-</span><span class="mi">2</span><span class="p">],</span> |
---|
526 | <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="nb">max</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="p">(</span><span class="mf">18.</span> <span class="o">/</span> <span class="mf">13.</span> <span class="o">*</span> <span class="n">g</span><span class="p">[</span><span class="o">-</span><span class="mi">3</span><span class="p">]</span> <span class="o">-</span> <span class="mf">5.</span> <span class="o">/</span> <span class="mf">13.</span> <span class="o">*</span> <span class="n">f</span><span class="p">[</span><span class="o">-</span><span class="mi">7</span><span class="p">])</span> <span class="o">*</span> |
---|
527 | <span class="p">(</span><span class="mf">18.</span> <span class="o">/</span> <span class="mf">13.</span> <span class="o">*</span> <span class="n">g</span><span class="p">[</span><span class="o">-</span><span class="mi">2</span><span class="p">]</span> <span class="o">-</span> <span class="mf">5.</span> <span class="o">/</span> <span class="mf">13.</span> <span class="o">*</span> <span class="n">f</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]))))</span> |
---|
528 | |
---|
529 | <span class="c1"># recomputation of the sub-grid interval values while the</span> |
---|
530 | <span class="c1"># interval boundaries (fi) and (fip2) remains unchanged</span> |
---|
531 | <span class="c1"># see Eq. (18) and (19)</span> |
---|
532 | <span class="n">f</span><span class="p">[</span><span class="o">-</span><span class="mi">4</span><span class="p">]</span> <span class="o">=</span> <span class="n">fmon</span> |
---|
533 | <span class="n">f</span><span class="p">[</span><span class="o">-</span><span class="mi">6</span><span class="p">]</span> <span class="o">=</span> <span class="mf">3.</span><span class="o">/</span><span class="mf">2.</span><span class="o">*</span><span class="n">g</span><span class="p">[</span><span class="o">-</span><span class="mi">3</span><span class="p">]</span><span class="o">-</span><span class="mf">5.</span><span class="o">/</span><span class="mf">12.</span><span class="o">*</span><span class="n">fmon</span><span class="o">-</span><span class="mf">1.</span><span class="o">/</span><span class="mf">12.</span><span class="o">*</span><span class="n">f</span><span class="p">[</span><span class="o">-</span><span class="mi">7</span><span class="p">]</span> |
---|
534 | <span class="n">f</span><span class="p">[</span><span class="o">-</span><span class="mi">5</span><span class="p">]</span> <span class="o">=</span> <span class="n">f</span><span class="p">[</span><span class="o">-</span><span class="mi">6</span><span class="p">]</span><span class="o">+</span><span class="p">(</span><span class="n">fmon</span><span class="o">-</span><span class="n">f</span><span class="p">[</span><span class="o">-</span><span class="mi">7</span><span class="p">])</span><span class="o">/</span><span class="mf">3.</span> |
---|
535 | <span class="n">f</span><span class="p">[</span><span class="o">-</span><span class="mi">3</span><span class="p">]</span> <span class="o">=</span> <span class="mf">3.</span><span class="o">/</span><span class="mf">2.</span><span class="o">*</span><span class="n">g</span><span class="p">[</span><span class="o">-</span><span class="mi">2</span><span class="p">]</span><span class="o">-</span><span class="mf">5.</span><span class="o">/</span><span class="mf">12.</span><span class="o">*</span><span class="n">f</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span><span class="o">-</span><span class="mf">1.</span><span class="o">/</span><span class="mf">12.</span><span class="o">*</span><span class="n">fmon</span> |
---|
536 | <span class="n">f</span><span class="p">[</span><span class="o">-</span><span class="mi">2</span><span class="p">]</span> <span class="o">=</span> <span class="n">f</span><span class="p">[</span><span class="o">-</span><span class="mi">3</span><span class="p">]</span><span class="o">+</span><span class="p">(</span><span class="n">f</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">fmon</span><span class="p">)</span><span class="o">/</span><span class="mf">3.</span> |
---|
537 | |
---|
538 | <span class="n">f</span><span class="o">.</span><span class="n">extend</span><span class="p">([</span><span class="mf">0.</span><span class="p">,</span> <span class="mf">0.</span><span class="p">,</span> <span class="mf">0.</span><span class="p">])</span> |
---|
539 | |
---|
540 | <span class="c1"># otherwise the sub-grid values are calculated and added to the list</span> |
---|
541 | <span class="c1"># using the persistence hypothesis as boundary condition</span> |
---|
542 | <span class="k">else</span><span class="p">:</span> |
---|
543 | <span class="c1"># temporal save of last value in interpolated list</span> |
---|
544 | <span class="c1"># since it is the left boundary and hence the new (fi) value</span> |
---|
545 | <span class="n">fi</span> <span class="o">=</span> <span class="n">f</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span> |
---|
546 | <span class="c1"># since last interval in series, last value is also fip1</span> |
---|
547 | <span class="n">fip1</span> <span class="o">=</span> <span class="n">g</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span> |
---|
548 | <span class="c1"># the function value at the first sub-grid point (fi1) is determined</span> |
---|
549 | <span class="c1"># according to the equal area condition with Eq. (19)</span> |
---|
550 | <span class="n">fi1</span> <span class="o">=</span> <span class="mf">3.</span><span class="o">/</span><span class="mf">2.</span><span class="o">*</span><span class="n">g</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span><span class="o">-</span><span class="mf">5.</span><span class="o">/</span><span class="mf">12.</span><span class="o">*</span><span class="n">fip1</span><span class="o">-</span><span class="mf">1.</span><span class="o">/</span><span class="mf">12.</span><span class="o">*</span><span class="n">fi</span> |
---|
551 | <span class="c1"># the function value at the second sub-grid point (fi2) is determined</span> |
---|
552 | <span class="c1"># according Eq. (18)</span> |
---|
553 | <span class="n">fi2</span> <span class="o">=</span> <span class="n">fi1</span><span class="o">+</span><span class="n">dt</span><span class="o">/</span><span class="mf">3.</span><span class="o">*</span><span class="p">(</span><span class="n">fip1</span><span class="o">-</span><span class="n">fi</span><span class="p">)</span> |
---|
554 | |
---|
555 | <span class="c1"># apply monotonicity filter for interval before</span> |
---|
556 | <span class="c1"># check if there is "M" or "W" shape</span> |
---|
557 | <span class="k">if</span> <span class="n">np</span><span class="o">.</span><span class="n">sign</span><span class="p">(</span><span class="n">f</span><span class="p">[</span><span class="o">-</span><span class="mi">5</span><span class="p">]</span><span class="o">-</span><span class="n">f</span><span class="p">[</span><span class="o">-</span><span class="mi">6</span><span class="p">])</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">sign</span><span class="p">(</span><span class="n">f</span><span class="p">[</span><span class="o">-</span><span class="mi">4</span><span class="p">]</span><span class="o">-</span><span class="n">f</span><span class="p">[</span><span class="o">-</span><span class="mi">5</span><span class="p">])</span> <span class="o">==</span> <span class="o">-</span><span class="mi">1</span> \ |
---|
558 | <span class="ow">and</span> <span class="n">np</span><span class="o">.</span><span class="n">sign</span><span class="p">(</span><span class="n">f</span><span class="p">[</span><span class="o">-</span><span class="mi">4</span><span class="p">]</span><span class="o">-</span><span class="n">f</span><span class="p">[</span><span class="o">-</span><span class="mi">5</span><span class="p">])</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">sign</span><span class="p">(</span><span class="n">f</span><span class="p">[</span><span class="o">-</span><span class="mi">3</span><span class="p">]</span><span class="o">-</span><span class="n">f</span><span class="p">[</span><span class="o">-</span><span class="mi">4</span><span class="p">])</span> <span class="o">==</span> <span class="o">-</span><span class="mi">1</span> \ |
---|
559 | <span class="ow">and</span> <span class="n">np</span><span class="o">.</span><span class="n">sign</span><span class="p">(</span><span class="n">f</span><span class="p">[</span><span class="o">-</span><span class="mi">3</span><span class="p">]</span><span class="o">-</span><span class="n">f</span><span class="p">[</span><span class="o">-</span><span class="mi">4</span><span class="p">])</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">sign</span><span class="p">(</span><span class="n">f</span><span class="p">[</span><span class="o">-</span><span class="mi">2</span><span class="p">]</span><span class="o">-</span><span class="n">f</span><span class="p">[</span><span class="o">-</span><span class="mi">3</span><span class="p">])</span> <span class="o">==</span> <span class="o">-</span><span class="mi">1</span><span class="p">:</span> |
---|
560 | |
---|
561 | <span class="c1"># the monotonicity filter corrects the value at (fim1) by</span> |
---|
562 | <span class="c1"># substituting (fim1) with (fmon), see Eq. (27), (28) and (29)</span> |
---|
563 | <span class="n">fmon</span> <span class="o">=</span> <span class="nb">min</span><span class="p">(</span><span class="mf">3.</span> <span class="o">*</span> <span class="n">g</span><span class="p">[</span><span class="o">-</span><span class="mi">3</span><span class="p">],</span> |
---|
564 | <span class="mf">3.</span> <span class="o">*</span> <span class="n">g</span><span class="p">[</span><span class="o">-</span><span class="mi">2</span><span class="p">],</span> |
---|
565 | <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="nb">max</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="p">(</span><span class="mf">18.</span> <span class="o">/</span> <span class="mf">13.</span> <span class="o">*</span> <span class="n">g</span><span class="p">[</span><span class="o">-</span><span class="mi">3</span><span class="p">]</span> <span class="o">-</span> <span class="mf">5.</span> <span class="o">/</span> <span class="mf">13.</span> <span class="o">*</span> <span class="n">f</span><span class="p">[</span><span class="o">-</span><span class="mi">7</span><span class="p">])</span> <span class="o">*</span> |
---|
566 | <span class="p">(</span><span class="mf">18.</span> <span class="o">/</span> <span class="mf">13.</span> <span class="o">*</span> <span class="n">g</span><span class="p">[</span><span class="o">-</span><span class="mi">2</span><span class="p">]</span> <span class="o">-</span> <span class="mf">5.</span> <span class="o">/</span> <span class="mf">13.</span> <span class="o">*</span> <span class="n">f</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]))))</span> |
---|
567 | |
---|
568 | <span class="c1"># recomputation of the sub-grid interval values while the</span> |
---|
569 | <span class="c1"># interval boundaries (fi) and (fip2) remains unchanged</span> |
---|
570 | <span class="c1"># see Eq. (18) and (19)</span> |
---|
571 | <span class="n">f</span><span class="p">[</span><span class="o">-</span><span class="mi">4</span><span class="p">]</span> <span class="o">=</span> <span class="n">fmon</span> |
---|
572 | <span class="n">f</span><span class="p">[</span><span class="o">-</span><span class="mi">6</span><span class="p">]</span> <span class="o">=</span> <span class="mf">3.</span><span class="o">/</span><span class="mf">2.</span><span class="o">*</span><span class="n">g</span><span class="p">[</span><span class="o">-</span><span class="mi">3</span><span class="p">]</span><span class="o">-</span><span class="mf">5.</span><span class="o">/</span><span class="mf">12.</span><span class="o">*</span><span class="n">fmon</span><span class="o">-</span><span class="mf">1.</span><span class="o">/</span><span class="mf">12.</span><span class="o">*</span><span class="n">f</span><span class="p">[</span><span class="o">-</span><span class="mi">7</span><span class="p">]</span> |
---|
573 | <span class="n">f</span><span class="p">[</span><span class="o">-</span><span class="mi">5</span><span class="p">]</span> <span class="o">=</span> <span class="n">f</span><span class="p">[</span><span class="o">-</span><span class="mi">6</span><span class="p">]</span><span class="o">+</span><span class="p">(</span><span class="n">fmon</span><span class="o">-</span><span class="n">f</span><span class="p">[</span><span class="o">-</span><span class="mi">7</span><span class="p">])</span><span class="o">/</span><span class="mf">3.</span> |
---|
574 | <span class="n">f</span><span class="p">[</span><span class="o">-</span><span class="mi">3</span><span class="p">]</span> <span class="o">=</span> <span class="mf">3.</span><span class="o">/</span><span class="mf">2.</span><span class="o">*</span><span class="n">g</span><span class="p">[</span><span class="o">-</span><span class="mi">2</span><span class="p">]</span><span class="o">-</span><span class="mf">5.</span><span class="o">/</span><span class="mf">12.</span><span class="o">*</span><span class="n">f</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span><span class="o">-</span><span class="mf">1.</span><span class="o">/</span><span class="mf">12.</span><span class="o">*</span><span class="n">fmon</span> |
---|
575 | <span class="n">f</span><span class="p">[</span><span class="o">-</span><span class="mi">2</span><span class="p">]</span> <span class="o">=</span> <span class="n">f</span><span class="p">[</span><span class="o">-</span><span class="mi">3</span><span class="p">]</span><span class="o">+</span><span class="p">(</span><span class="n">f</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">fmon</span><span class="p">)</span><span class="o">/</span><span class="mf">3.</span> |
---|
576 | |
---|
577 | <span class="c1"># add next interval of interpolated (sub-)grid values</span> |
---|
578 | <span class="n">f</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">fi1</span><span class="p">)</span> |
---|
579 | <span class="n">f</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">fi2</span><span class="p">)</span> |
---|
580 | <span class="n">f</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">fip1</span><span class="p">)</span> |
---|
581 | |
---|
582 | <span class="k">return</span> <span class="n">f</span></div> |
---|
583 | </pre></div> |
---|
584 | |
---|
585 | </div> |
---|
586 | |
---|
587 | </div> |
---|
588 | <footer> |
---|
589 | |
---|
590 | |
---|
591 | <hr/> |
---|
592 | |
---|
593 | <div role="contentinfo"> |
---|
594 | <p> |
---|
595 | © Copyright 2020, Anne Philipp, Leopold Haimberger and Petra Seibert |
---|
596 | |
---|
597 | </p> |
---|
598 | </div> |
---|
599 | Built with <a href="http://sphinx-doc.org/">Sphinx</a> using a <a href="https://github.com/rtfd/sphinx_rtd_theme">theme</a> provided by <a href="https://readthedocs.org">Read the Docs</a>. |
---|
600 | |
---|
601 | </footer> |
---|
602 | |
---|
603 | </div> |
---|
604 | </div> |
---|
605 | |
---|
606 | </section> |
---|
607 | |
---|
608 | </div> |
---|
609 | |
---|
610 | |
---|
611 | |
---|
612 | <script type="text/javascript"> |
---|
613 | jQuery(function () { |
---|
614 | SphinxRtdTheme.Navigation.enable(true); |
---|
615 | }); |
---|
616 | </script> |
---|
617 | |
---|
618 | |
---|
619 | |
---|
620 | |
---|
621 | |
---|
622 | |
---|
623 | </body> |
---|
624 | </html> |
---|