[0b00607] | 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 alpha 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 type="text/javascript" src="../_static/jquery.js"></script> |
---|
| 25 | <script type="text/javascript" src="../_static/underscore.js"></script> |
---|
| 26 | <script type="text/javascript" src="../_static/doctools.js"></script> |
---|
| 27 | <script type="text/javascript" src="../_static/language_data.js"></script> |
---|
| 28 | <script async="async" type="text/javascript" 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 |
---|
| 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="../installation.html">Installation</a></li> |
---|
| 91 | <li class="toctree-l1"><a class="reference internal" href="../quick_start.html">Quick Start</a></li> |
---|
| 92 | <li class="toctree-l1"><a class="reference internal" href="../ecmwf_data.html">ECMWF Data</a></li> |
---|
| 93 | <li class="toctree-l1"><a class="reference internal" href="../documentation.html">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> |
---|
[30f7911] | 163 | <span></span><span class="ch">#!/usr/bin/env python3</span> |
---|
[0b00607] | 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"># @License:</span> |
---|
| 184 | <span class="c1"># (C) Copyright 2014-2019.</span> |
---|
| 185 | <span class="c1"># Anne Philipp, Leopold Haimberger</span> |
---|
| 186 | <span class="c1">#</span> |
---|
[30f7911] | 187 | <span class="c1"># SPDX-License-Identifier: CC-BY-4.0</span> |
---|
| 188 | <span class="c1">#</span> |
---|
[0b00607] | 189 | <span class="c1"># This work is licensed under the Creative Commons Attribution 4.0</span> |
---|
| 190 | <span class="c1"># International License. To view a copy of this license, visit</span> |
---|
| 191 | <span class="c1"># http://creativecommons.org/licenses/by/4.0/ or send a letter to</span> |
---|
| 192 | <span class="c1"># Creative Commons, PO Box 1866, Mountain View, CA 94042, USA.</span> |
---|
| 193 | <span class="c1">#</span> |
---|
| 194 | <span class="c1"># @Methods:</span> |
---|
| 195 | <span class="c1"># - dapoly</span> |
---|
| 196 | <span class="c1"># - darain</span> |
---|
| 197 | <span class="c1"># - IA3</span> |
---|
| 198 | <span class="c1">#*******************************************************************************</span> |
---|
| 199 | <span class="sd">'''Disaggregation of deaccumulated flux data from an ECMWF model FG field.</span> |
---|
| 200 | |
---|
| 201 | <span class="sd">Initially the flux data to be concerned are:</span> |
---|
| 202 | <span class="sd"> - large-scale precipitation</span> |
---|
| 203 | <span class="sd"> - convective precipitation</span> |
---|
| 204 | <span class="sd"> - surface sensible heat flux</span> |
---|
| 205 | <span class="sd"> - surface solar radiation</span> |
---|
| 206 | <span class="sd"> - u stress</span> |
---|
| 207 | <span class="sd"> - v stress</span> |
---|
| 208 | |
---|
| 209 | <span class="sd">Different versions of disaggregation is provided for rainfall</span> |
---|
| 210 | <span class="sd">data (darain, modified linear) and the surface fluxes and</span> |
---|
| 211 | <span class="sd">stress data (dapoly, cubic polynomial).</span> |
---|
| 212 | <span class="sd">'''</span> |
---|
| 213 | |
---|
| 214 | <span class="c1"># ------------------------------------------------------------------------------</span> |
---|
| 215 | <span class="c1"># MODULES</span> |
---|
| 216 | <span class="c1"># ------------------------------------------------------------------------------</span> |
---|
| 217 | |
---|
| 218 | <span class="c1"># ------------------------------------------------------------------------------</span> |
---|
| 219 | <span class="c1"># FUNCTIONS</span> |
---|
| 220 | <span class="c1"># ------------------------------------------------------------------------------</span> |
---|
| 221 | <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> |
---|
| 222 | <span class="sd">"""Cubic polynomial interpolation of deaccumulated fluxes.</span> |
---|
| 223 | |
---|
| 224 | <span class="sd"> Interpolation of deaccumulated fluxes of an ECMWF model FG field</span> |
---|
| 225 | <span class="sd"> using a cubic polynomial solution which conserves the integrals</span> |
---|
| 226 | <span class="sd"> of the fluxes within each timespan.</span> |
---|
| 227 | <span class="sd"> Disaggregation is done for 4 accumluated timespans which</span> |
---|
| 228 | <span class="sd"> generates a new, disaggregated value which is output at the</span> |
---|
| 229 | <span class="sd"> central point of the 4 accumulation timespans.</span> |
---|
| 230 | <span class="sd"> This new point is used for linear interpolation of the complete</span> |
---|
| 231 | <span class="sd"> timeseries afterwards.</span> |
---|
| 232 | |
---|
| 233 | <span class="sd"> Parameters</span> |
---|
| 234 | <span class="sd"> ----------</span> |
---|
| 235 | <span class="sd"> alist : list of array of float</span> |
---|
| 236 | <span class="sd"> List of 4 timespans as 2-dimensional, horizontal fields.</span> |
---|
| 237 | <span class="sd"> E.g. [[array_t1], [array_t2], [array_t3], [array_t4]]</span> |
---|
| 238 | |
---|
| 239 | <span class="sd"> Return</span> |
---|
| 240 | <span class="sd"> ------</span> |
---|
| 241 | <span class="sd"> nfield : array of float</span> |
---|
| 242 | <span class="sd"> Interpolated flux at central point of accumulation timespan.</span> |
---|
| 243 | |
---|
| 244 | <span class="sd"> Note</span> |
---|
| 245 | <span class="sd"> ----</span> |
---|
| 246 | <span class="sd"> March 2000 : P. JAMES</span> |
---|
| 247 | <span class="sd"> Original author</span> |
---|
| 248 | |
---|
| 249 | <span class="sd"> June 2003 : A. BECK</span> |
---|
| 250 | <span class="sd"> Adaptations</span> |
---|
| 251 | |
---|
| 252 | <span class="sd"> November 2015 : Leopold Haimberger (University of Vienna)</span> |
---|
| 253 | <span class="sd"> Migration from Fortran to Python</span> |
---|
| 254 | |
---|
| 255 | <span class="sd"> """</span> |
---|
| 256 | |
---|
| 257 | <span class="n">pya</span> <span class="o">=</span> <span class="p">(</span><span class="n">alist</span><span class="p">[</span><span class="mi">3</span><span class="p">]</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> <span class="mf">3.</span> <span class="o">*</span> <span class="p">(</span><span class="n">alist</span><span class="p">[</span><span class="mi">1</span><span class="p">]</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> <span class="mf">6.</span> |
---|
| 258 | <span class="n">pyb</span> <span class="o">=</span> <span class="p">(</span><span class="n">alist</span><span class="p">[</span><span class="mi">2</span><span class="p">]</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> <span class="mf">2.</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> <span class="mf">9.</span> <span class="o">*</span> <span class="n">pya</span> <span class="o">/</span> <span class="mf">2.</span> |
---|
| 259 | <span class="n">pyc</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> <span class="n">alist</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">-</span> <span class="mf">7.</span> <span class="o">*</span> <span class="n">pya</span> <span class="o">/</span> <span class="mf">2.</span> <span class="o">-</span> <span class="mf">2.</span> <span class="o">*</span> <span class="n">pyb</span> |
---|
| 260 | <span class="n">pyd</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> <span class="n">pya</span> <span class="o">/</span> <span class="mf">4.</span> <span class="o">-</span> <span class="n">pyb</span> <span class="o">/</span> <span class="mf">3.</span> <span class="o">-</span> <span class="n">pyc</span> <span class="o">/</span> <span class="mf">2.</span> |
---|
| 261 | <span class="n">nfield</span> <span class="o">=</span> <span class="mf">8.</span> <span class="o">*</span> <span class="n">pya</span> <span class="o">+</span> <span class="mf">4.</span> <span class="o">*</span> <span class="n">pyb</span> <span class="o">+</span> <span class="mf">2.</span> <span class="o">*</span> <span class="n">pyc</span> <span class="o">+</span> <span class="n">pyd</span> |
---|
| 262 | |
---|
| 263 | <span class="k">return</span> <span class="n">nfield</span></div> |
---|
| 264 | |
---|
| 265 | |
---|
| 266 | <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> |
---|
| 267 | <span class="sd">"""Linear interpolation of deaccumulated fluxes.</span> |
---|
| 268 | |
---|
| 269 | <span class="sd"> Interpolation of deaccumulated fluxes of an ECMWF model FG rainfall</span> |
---|
| 270 | <span class="sd"> field using a modified linear solution which conserves the integrals</span> |
---|
| 271 | <span class="sd"> of the fluxes within each timespan.</span> |
---|
| 272 | <span class="sd"> Disaggregation is done for 4 accumluated timespans which generates</span> |
---|
| 273 | <span class="sd"> a new, disaggregated value which is output at the central point</span> |
---|
| 274 | <span class="sd"> of the 4 accumulation timespans. This new point is used for linear</span> |
---|
| 275 | <span class="sd"> interpolation of the complete timeseries afterwards.</span> |
---|
| 276 | |
---|
| 277 | <span class="sd"> Parameters</span> |
---|
| 278 | <span class="sd"> ----------</span> |
---|
| 279 | <span class="sd"> alist : list of array of float</span> |
---|
| 280 | <span class="sd"> List of 4 timespans as 2-dimensional, horizontal fields.</span> |
---|
| 281 | <span class="sd"> E.g. [[array_t1], [array_t2], [array_t3], [array_t4]]</span> |
---|
| 282 | |
---|
| 283 | <span class="sd"> Return</span> |
---|
| 284 | <span class="sd"> ------</span> |
---|
| 285 | <span class="sd"> nfield : array of float</span> |
---|
| 286 | <span class="sd"> Interpolated flux at central point of accumulation timespan.</span> |
---|
| 287 | |
---|
| 288 | <span class="sd"> Note</span> |
---|
| 289 | <span class="sd"> ----</span> |
---|
| 290 | <span class="sd"> March 2000 : P. JAMES</span> |
---|
| 291 | <span class="sd"> Original author</span> |
---|
| 292 | |
---|
| 293 | <span class="sd"> June 2003 : A. BECK</span> |
---|
| 294 | <span class="sd"> Adaptations</span> |
---|
| 295 | |
---|
| 296 | <span class="sd"> November 2015 : Leopold Haimberger (University of Vienna)</span> |
---|
| 297 | <span class="sd"> Migration from Fortran to Python</span> |
---|
| 298 | <span class="sd"> """</span> |
---|
| 299 | |
---|
| 300 | <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> |
---|
| 301 | <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> |
---|
| 302 | <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> |
---|
| 303 | <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> |
---|
| 304 | <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> |
---|
| 305 | <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> |
---|
| 306 | <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> |
---|
| 307 | <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> |
---|
| 308 | |
---|
| 309 | <span class="n">xac</span> <span class="o">=</span> <span class="mf">0.5</span> <span class="o">*</span> <span class="n">xb</span> |
---|
| 310 | <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> |
---|
| 311 | <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> |
---|
| 312 | <span class="n">xbd</span> <span class="o">=</span> <span class="mf">0.5</span> <span class="o">*</span> <span class="n">xc</span> |
---|
| 313 | <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> |
---|
| 314 | <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> |
---|
| 315 | <span class="n">nfield</span> <span class="o">=</span> <span class="n">xac</span> <span class="o">+</span> <span class="n">xbd</span> |
---|
| 316 | |
---|
| 317 | <span class="k">return</span> <span class="n">nfield</span></div> |
---|
| 318 | |
---|
| 319 | <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> |
---|
| 320 | <span class="sd">""" Interpolation with a non-negative geometric mean based algorithm.</span> |
---|
| 321 | |
---|
| 322 | <span class="sd"> The original grid is reconstructed by adding two sampling points in each</span> |
---|
| 323 | <span class="sd"> data series interval. This subgrid is used to keep all information during</span> |
---|
| 324 | <span class="sd"> the interpolation within the associated interval. Additionally, an advanced</span> |
---|
| 325 | <span class="sd"> monotonicity filter is applied to improve the monotonicity properties of</span> |
---|
| 326 | <span class="sd"> the series.</span> |
---|
| 327 | |
---|
| 328 | <span class="sd"> Note</span> |
---|
| 329 | <span class="sd"> ----</span> |
---|
| 330 | <span class="sd"> (C) Copyright 2017-2019</span> |
---|
| 331 | <span class="sd"> Sabine Hittmeir, Anne Philipp, Petra Seibert</span> |
---|
| 332 | |
---|
| 333 | <span class="sd"> This work is licensed under the Creative Commons Attribution 4.0</span> |
---|
| 334 | <span class="sd"> International License. To view a copy of this license, visit</span> |
---|
| 335 | <span class="sd"> http://creativecommons.org/licenses/by/4.0/ or send a letter to</span> |
---|
| 336 | <span class="sd"> Creative Commons, PO Box 1866, Mountain View, CA 94042, USA.</span> |
---|
| 337 | |
---|
| 338 | <span class="sd"> Parameters</span> |
---|
| 339 | <span class="sd"> ----------</span> |
---|
| 340 | <span class="sd"> g : list of float</span> |
---|
| 341 | <span class="sd"> Complete data series that will be interpolated having</span> |
---|
| 342 | <span class="sd"> the dimension of the original raw series.</span> |
---|
| 343 | |
---|
| 344 | <span class="sd"> Return</span> |
---|
| 345 | <span class="sd"> ------</span> |
---|
| 346 | <span class="sd"> f : list of float</span> |
---|
| 347 | <span class="sd"> The interpolated data series with additional subgrid points.</span> |
---|
| 348 | <span class="sd"> Its dimension is equal to the length of the input data series</span> |
---|
| 349 | <span class="sd"> times three.</span> |
---|
| 350 | |
---|
| 351 | |
---|
| 352 | <span class="sd"> References</span> |
---|
| 353 | <span class="sd"> ----------</span> |
---|
| 354 | <span class="sd"> For more information see article:</span> |
---|
| 355 | <span class="sd"> Hittmeir, S.; Philipp, A.; Seibert, P. (2017): A conservative</span> |
---|
| 356 | <span class="sd"> interpolation scheme for extensive quantities with application to the</span> |
---|
| 357 | <span class="sd"> Lagrangian particle dispersion model FLEXPART.,</span> |
---|
| 358 | <span class="sd"> Geoscientific Model Development</span> |
---|
| 359 | <span class="sd"> """</span> |
---|
| 360 | |
---|
| 361 | <span class="c1">####################### variable description #############################</span> |
---|
| 362 | <span class="c1"># #</span> |
---|
| 363 | <span class="c1"># i - index variable for looping over the data series #</span> |
---|
| 364 | <span class="c1"># g - input data series #</span> |
---|
| 365 | <span class="c1"># f - interpolated and filtered data series with additional #</span> |
---|
| 366 | <span class="c1"># grid points #</span> |
---|
| 367 | <span class="c1"># fi - function value at position i, f_i #</span> |
---|
| 368 | <span class="c1"># fi1 - first sub-grid function value f_i^1 #</span> |
---|
| 369 | <span class="c1"># fi2 - second sub-grid function value f_i^2 #</span> |
---|
| 370 | <span class="c1"># fip1 - next function value at position i+1, f_(i+1) #</span> |
---|
| 371 | <span class="c1"># dt - time step #</span> |
---|
| 372 | <span class="c1"># fmon - monotonicity filter #</span> |
---|
| 373 | <span class="c1"># #</span> |
---|
| 374 | <span class="c1">###########################################################################</span> |
---|
| 375 | |
---|
| 376 | |
---|
| 377 | <span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span> |
---|
| 378 | |
---|
| 379 | <span class="c1"># time step</span> |
---|
| 380 | <span class="n">dt</span> <span class="o">=</span> <span class="mf">1.0</span> |
---|
| 381 | |
---|
| 382 | <span class="c1">############### Non-negative Geometric Mean Based Algorithm ###############</span> |
---|
| 383 | |
---|
| 384 | <span class="c1"># for the left boundary the following boundary condition is valid:</span> |
---|
| 385 | <span class="c1"># the value at t=0 of the interpolation algorithm coincides with the</span> |
---|
| 386 | <span class="c1"># first data value according to the persistence hypothesis</span> |
---|
| 387 | <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> |
---|
| 388 | |
---|
| 389 | <span class="c1"># compute two first sub-grid intervals without monotonicity check</span> |
---|
| 390 | <span class="c1"># go through the data series and extend each interval by two sub-grid</span> |
---|
| 391 | <span class="c1"># points and interpolate the corresponding data values</span> |
---|
| 392 | <span class="c1"># except for the last interval due to boundary conditions</span> |
---|
| 393 | <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> |
---|
| 394 | |
---|
| 395 | <span class="c1"># as a requirement:</span> |
---|
| 396 | <span class="c1"># if there is a zero data value such that g[i]=0, then the whole</span> |
---|
| 397 | <span class="c1"># interval in f has to be zero to such that f[i+1]=f[i+2]=f[i+3]=0</span> |
---|
| 398 | <span class="c1"># according to Eq. (6)</span> |
---|
| 399 | <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> |
---|
| 400 | <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> |
---|
| 401 | |
---|
| 402 | <span class="c1"># otherwise the sub-grid values are calculated and added to the list</span> |
---|
| 403 | <span class="k">else</span><span class="p">:</span> |
---|
| 404 | <span class="c1"># temporal save of last value in interpolated list</span> |
---|
| 405 | <span class="c1"># since it is the left boundary and hence the new (fi) value</span> |
---|
| 406 | <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> |
---|
| 407 | |
---|
| 408 | <span class="c1"># the value at the end of the interval (fip1) is prescribed by the</span> |
---|
| 409 | <span class="c1"># geometric mean, restricted such that non-negativity is guaranteed</span> |
---|
| 410 | <span class="c1"># according to Eq. (25)</span> |
---|
| 411 | <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="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="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> <span class="p">)</span> |
---|
| 412 | |
---|
| 413 | <span class="c1"># the function value at the first sub-grid point (fi1) is determined</span> |
---|
| 414 | <span class="c1"># according to the equal area condition with Eq. (19)</span> |
---|
| 415 | <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> |
---|
| 416 | |
---|
| 417 | <span class="c1"># the function value at the second sub-grid point (fi2) is determined</span> |
---|
| 418 | <span class="c1"># according Eq. (18)</span> |
---|
| 419 | <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> |
---|
| 420 | |
---|
| 421 | <span class="c1"># add next interval of interpolated (sub-)grid values</span> |
---|
| 422 | <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> |
---|
| 423 | <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> |
---|
| 424 | <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> |
---|
| 425 | |
---|
| 426 | <span class="c1"># compute rest of the data series intervals</span> |
---|
| 427 | <span class="c1"># go through the data series and extend each interval by two sub-grid</span> |
---|
| 428 | <span class="c1"># points and interpolate the corresponding data values</span> |
---|
| 429 | <span class="c1"># except for the last interval due to boundary conditions</span> |
---|
| 430 | <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> |
---|
| 431 | |
---|
| 432 | <span class="c1"># as a requirement:</span> |
---|
| 433 | <span class="c1"># if there is a zero data value such that g[i]=0, then the whole</span> |
---|
| 434 | <span class="c1"># interval in f has to be zero to such that f[i+1]=f[i+2]=f[i+3]=0</span> |
---|
| 435 | <span class="c1"># according to Eq. (6)</span> |
---|
| 436 | <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> |
---|
| 437 | <span class="c1"># apply monotonicity filter for interval before</span> |
---|
| 438 | <span class="c1"># check if there is "M" or "W" shape</span> |
---|
| 439 | <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> \ |
---|
| 440 | <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> \ |
---|
| 441 | <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> |
---|
| 442 | |
---|
| 443 | <span class="c1"># the monotonicity filter corrects the value at (fim1) by</span> |
---|
| 444 | <span class="c1"># substituting (fim1) with (fmon), see Eq. (27), (28) and (29)</span> |
---|
| 445 | <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> \ |
---|
| 446 | <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> \ |
---|
| 447 | <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="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> |
---|
| 448 | <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> |
---|
| 449 | |
---|
| 450 | <span class="c1"># recomputation of the sub-grid interval values while the</span> |
---|
| 451 | <span class="c1"># interval boundaries (fi) and (fip2) remains unchanged</span> |
---|
| 452 | <span class="c1"># see Eq. (18) and (19)</span> |
---|
| 453 | <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> |
---|
| 454 | <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> |
---|
| 455 | <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> |
---|
| 456 | <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> |
---|
| 457 | <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> |
---|
| 458 | |
---|
| 459 | <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> |
---|
| 460 | |
---|
| 461 | <span class="c1"># otherwise the sub-grid values are calculated and added to the list</span> |
---|
| 462 | <span class="k">else</span><span class="p">:</span> |
---|
| 463 | <span class="c1"># temporal save of last value in interpolated list</span> |
---|
| 464 | <span class="c1"># since it is the left boundary and hence the new (fi) value</span> |
---|
| 465 | <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> |
---|
| 466 | |
---|
| 467 | <span class="c1"># the value at the end of the interval (fip1) is prescribed by the</span> |
---|
| 468 | <span class="c1"># geometric mean, restricted such that non-negativity is guaranteed</span> |
---|
| 469 | <span class="c1"># according to Eq. (25)</span> |
---|
| 470 | <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="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="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> <span class="p">)</span> |
---|
| 471 | |
---|
| 472 | <span class="c1"># the function value at the first sub-grid point (fi1) is determined</span> |
---|
| 473 | <span class="c1"># according to the equal area condition with Eq. (19)</span> |
---|
| 474 | <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> |
---|
| 475 | |
---|
| 476 | <span class="c1"># the function value at the second sub-grid point (fi2) is determined</span> |
---|
| 477 | <span class="c1"># according Eq. (18)</span> |
---|
| 478 | <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> |
---|
| 479 | |
---|
| 480 | <span class="c1"># apply monotonicity filter for interval before</span> |
---|
| 481 | <span class="c1"># check if there is "M" or "W" shape</span> |
---|
| 482 | <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> \ |
---|
| 483 | <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> \ |
---|
| 484 | <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> |
---|
| 485 | |
---|
| 486 | <span class="c1"># the monotonicity filter corrects the value at (fim1) by</span> |
---|
| 487 | <span class="c1"># substituting (fim1) with fmon, see Eq. (27), (28) and (29)</span> |
---|
| 488 | <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> \ |
---|
| 489 | <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> \ |
---|
| 490 | <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="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> |
---|
| 491 | <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> |
---|
| 492 | |
---|
| 493 | <span class="c1"># recomputation of the sub-grid interval values while the</span> |
---|
| 494 | <span class="c1"># interval boundaries (fi) and (fip2) remains unchanged</span> |
---|
| 495 | <span class="c1"># see Eq. (18) and (19)</span> |
---|
| 496 | <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> |
---|
| 497 | <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> |
---|
| 498 | <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> |
---|
| 499 | <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> |
---|
| 500 | <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> |
---|
| 501 | |
---|
| 502 | <span class="c1"># add next interval of interpolated (sub-)grid values</span> |
---|
| 503 | <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> |
---|
| 504 | <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> |
---|
| 505 | <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> |
---|
| 506 | |
---|
| 507 | <span class="c1"># separate treatment of the final interval</span> |
---|
| 508 | |
---|
| 509 | <span class="c1"># as a requirement:</span> |
---|
| 510 | <span class="c1"># if there is a zero data value such that g[i]=0, then the whole</span> |
---|
| 511 | <span class="c1"># interval in f has to be zero to such that f[i+1]=f[i+2]=f[i+3]=0</span> |
---|
| 512 | <span class="c1"># according to Eq. (6)</span> |
---|
| 513 | <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> |
---|
| 514 | <span class="c1"># apply monotonicity filter for interval before</span> |
---|
| 515 | <span class="c1"># check if there is "M" or "W" shape</span> |
---|
| 516 | <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> \ |
---|
| 517 | <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> \ |
---|
| 518 | <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> |
---|
| 519 | |
---|
| 520 | <span class="c1"># the monotonicity filter corrects the value at (fim1) by</span> |
---|
| 521 | <span class="c1"># substituting (fim1) with (fmon), see Eq. (27), (28) and (29)</span> |
---|
| 522 | <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> \ |
---|
| 523 | <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> \ |
---|
| 524 | <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="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> |
---|
| 525 | <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> |
---|
| 526 | |
---|
| 527 | <span class="c1"># recomputation of the sub-grid interval values while the</span> |
---|
| 528 | <span class="c1"># interval boundaries (fi) and (fip2) remains unchanged</span> |
---|
| 529 | <span class="c1"># see Eq. (18) and (19)</span> |
---|
| 530 | <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> |
---|
| 531 | <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> |
---|
| 532 | <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> |
---|
| 533 | <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> |
---|
| 534 | <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> |
---|
| 535 | |
---|
| 536 | <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> |
---|
| 537 | |
---|
| 538 | <span class="c1"># otherwise the sub-grid values are calculated and added to the list</span> |
---|
| 539 | <span class="c1"># using the persistence hypothesis as boundary condition</span> |
---|
| 540 | <span class="k">else</span><span class="p">:</span> |
---|
| 541 | <span class="c1"># temporal save of last value in interpolated list</span> |
---|
| 542 | <span class="c1"># since it is the left boundary and hence the new (fi) value</span> |
---|
| 543 | <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> |
---|
| 544 | <span class="c1"># since last interval in series, last value is also fip1</span> |
---|
| 545 | <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> |
---|
| 546 | <span class="c1"># the function value at the first sub-grid point (fi1) is determined</span> |
---|
| 547 | <span class="c1"># according to the equal area condition with Eq. (19)</span> |
---|
| 548 | <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> |
---|
| 549 | <span class="c1"># the function value at the second sub-grid point (fi2) is determined</span> |
---|
| 550 | <span class="c1"># according Eq. (18)</span> |
---|
| 551 | <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> |
---|
| 552 | |
---|
| 553 | <span class="c1"># apply monotonicity filter for interval before</span> |
---|
| 554 | <span class="c1"># check if there is "M" or "W" shape</span> |
---|
| 555 | <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> \ |
---|
| 556 | <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> \ |
---|
| 557 | <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> |
---|
| 558 | |
---|
| 559 | <span class="c1"># the monotonicity filter corrects the value at (fim1) by</span> |
---|
| 560 | <span class="c1"># substituting (fim1) with (fmon), see Eq. (27), (28) and (29)</span> |
---|
| 561 | <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> \ |
---|
| 562 | <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> \ |
---|
| 563 | <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="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> |
---|
| 564 | <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> |
---|
| 565 | |
---|
| 566 | <span class="c1"># recomputation of the sub-grid interval values while the</span> |
---|
| 567 | <span class="c1"># interval boundaries (fi) and (fip2) remains unchanged</span> |
---|
| 568 | <span class="c1"># see Eq. (18) and (19)</span> |
---|
| 569 | <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> |
---|
| 570 | <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> |
---|
| 571 | <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> |
---|
| 572 | <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> |
---|
| 573 | <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> |
---|
| 574 | |
---|
| 575 | <span class="c1"># add next interval of interpolated (sub-)grid values</span> |
---|
| 576 | <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> |
---|
| 577 | <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> |
---|
| 578 | <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> |
---|
| 579 | |
---|
| 580 | <span class="k">return</span> <span class="n">f</span></div> |
---|
| 581 | </pre></div> |
---|
| 582 | |
---|
| 583 | </div> |
---|
| 584 | |
---|
| 585 | </div> |
---|
| 586 | <footer> |
---|
| 587 | |
---|
| 588 | |
---|
| 589 | <hr/> |
---|
| 590 | |
---|
| 591 | <div role="contentinfo"> |
---|
| 592 | <p> |
---|
| 593 | © Copyright 2019, Anne Philipp and Leopold Haimberger |
---|
| 594 | |
---|
| 595 | </p> |
---|
| 596 | </div> |
---|
| 597 | 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>. |
---|
| 598 | |
---|
| 599 | </footer> |
---|
| 600 | |
---|
| 601 | </div> |
---|
| 602 | </div> |
---|
| 603 | |
---|
| 604 | </section> |
---|
| 605 | |
---|
| 606 | </div> |
---|
| 607 | |
---|
| 608 | |
---|
| 609 | |
---|
| 610 | <script type="text/javascript"> |
---|
| 611 | jQuery(function () { |
---|
| 612 | SphinxRtdTheme.Navigation.enable(true); |
---|
| 613 | }); |
---|
| 614 | </script> |
---|
| 615 | |
---|
| 616 | |
---|
| 617 | |
---|
| 618 | |
---|
| 619 | |
---|
| 620 | |
---|
| 621 | </body> |
---|
| 622 | </html> |
---|