Ignore:
Timestamp:
Jan 15, 2019, 1:03:37 AM (5 years ago)
Author:
Anne Philipp <anne.philipp@…>
Branches:
master, ctbto, dev
Children:
6f951ca
Parents:
0629ba8
Message:

new build of sphinx for updated api

File:
1 edited

Legend:

Unmodified
Added
Removed

  • documentation/Sphinx/build/html/_modules/disaggregation.html

    r708c667 r2625ca8  
    170170<span class="c1">#        - outsourced the disaggregation functions dapoly and darain</span>
    171171<span class="c1">#          to a new module named disaggregation</span>
     172<span class="c1">#        - added the new disaggregation method for precipitation</span>
    172173<span class="c1">#</span>
    173174<span class="c1"># @License:</span>
    174 <span class="c1">#    (C) Copyright 2015-2018.</span>
     175<span class="c1">#    (C) Copyright 2014-2019.</span>
     176<span class="c1">#    Anne Philipp, Leopold Haimberger</span>
    175177<span class="c1">#</span>
    176 <span class="c1">#    This software is licensed under the terms of the Apache Licence Version 2.0</span>
    177 <span class="c1">#    which can be obtained at http://www.apache.org/licenses/LICENSE-2.0.</span>
     178<span class="c1">#    This work is licensed under the Creative Commons Attribution 4.0</span>
     179<span class="c1">#    International License. To view a copy of this license, visit</span>
     180<span class="c1">#    http://creativecommons.org/licenses/by/4.0/ or send a letter to</span>
     181<span class="c1">#    Creative Commons, PO Box 1866, Mountain View, CA 94042, USA.</span>
    178182<span class="c1">#</span>
    179 <span class="c1"># @Module Description:</span>
    180 <span class="c1">#    disaggregation of deaccumulated flux data from an ECMWF model FG field.</span>
    181 <span class="c1">#    Initially the flux data to be concerned are:</span>
    182 <span class="c1">#    - large-scale precipitation</span>
    183 <span class="c1">#    - convective precipitation</span>
    184 <span class="c1">#    - surface sensible heat flux</span>
    185 <span class="c1">#    - surface solar radiation</span>
    186 <span class="c1">#    - u stress</span>
    187 <span class="c1">#    - v stress</span>
    188 <span class="c1">#    Different versions of disaggregation is provided for rainfall</span>
    189 <span class="c1">#    data (darain, modified linear) and the surface fluxes and</span>
    190 <span class="c1">#    stress data (dapoly, cubic polynomial).</span>
    191 <span class="c1">#</span>
    192 <span class="c1"># @Module Content:</span>
     183<span class="c1"># @Methods:</span>
    193184<span class="c1">#    - dapoly</span>
    194185<span class="c1">#    - darain</span>
    195186<span class="c1">#    - IA3</span>
    196 <span class="c1">#</span>
    197187<span class="c1">#*******************************************************************************</span>
     188<span class="sd">&#39;&#39;&#39;Disaggregation of deaccumulated flux data from an ECMWF model FG field.</span>
     189
     190<span class="sd">Initially the flux data to be concerned are:</span>
     191<span class="sd">    - large-scale precipitation</span>
     192<span class="sd">    - convective precipitation</span>
     193<span class="sd">    - surface sensible heat flux</span>
     194<span class="sd">    - surface solar radiation</span>
     195<span class="sd">    - u stress</span>
     196<span class="sd">    - v stress</span>
     197
     198<span class="sd">Different versions of disaggregation is provided for rainfall</span>
     199<span class="sd">data (darain, modified linear) and the surface fluxes and</span>
     200<span class="sd">stress data (dapoly, cubic polynomial).</span>
     201<span class="sd">&#39;&#39;&#39;</span>
    198202
    199203<span class="c1"># ------------------------------------------------------------------------------</span>
    … …  
    218222<span class="sd">    Parameters</span>
    219223<span class="sd">    ----------</span>
    220 <span class="sd">    alist : :obj:`list` of :obj:`array` of :obj:`float`</span>
     224<span class="sd">    alist : list of array of float</span>
    221225<span class="sd">        List of 4 timespans as 2-dimensional, horizontal fields.</span>
    222226<span class="sd">        E.g. [[array_t1], [array_t2], [array_t3], [array_t4]]</span>
    … …  
    224228<span class="sd">    Return</span>
    225229<span class="sd">    ------</span>
    226 <span class="sd">    nfield : :obj:`array` of :obj:`float`</span>
     230<span class="sd">    nfield : array of float</span>
    227231<span class="sd">        Interpolated flux at central point of accumulation timespan.</span>
    228232
    … …  
    262266<span class="sd">    Parameters</span>
    263267<span class="sd">    ----------</span>
    264 <span class="sd">    alist : :obj:`list` of :obj:`array` of :obj:`float`</span>
     268<span class="sd">    alist : list of array of float</span>
    265269<span class="sd">        List of 4 timespans as 2-dimensional, horizontal fields.</span>
    266270<span class="sd">        E.g. [[array_t1], [array_t2], [array_t3], [array_t4]]</span>
    … …  
    268272<span class="sd">    Return</span>
    269273<span class="sd">    ------</span>
    270 <span class="sd">    nfield : :obj:`array` of :obj:`float`</span>
     274<span class="sd">    nfield : array of float</span>
    271275<span class="sd">        Interpolated flux at central point of accumulation timespan.</span>
    272276
    … …  
    313317<span class="sd">    Note</span>
    314318<span class="sd">    ----</span>
    315 <span class="sd">    Copyright 2017</span>
     319<span class="sd">    (C) Copyright 2017-2019</span>
    316320<span class="sd">    Sabine Hittmeir, Anne Philipp, Petra Seibert</span>
    317321
    … …  
    323327<span class="sd">    Parameters</span>
    324328<span class="sd">    ----------</span>
    325 <span class="sd">    g : :obj:`list` of :obj:`float`</span>
     329<span class="sd">    g : list of float</span>
    326330<span class="sd">        Complete data series that will be interpolated having</span>
    327331<span class="sd">        the dimension of the original raw series.</span>
    … …  
    329333<span class="sd">    Return</span>
    330334<span class="sd">    ------</span>
    331 <span class="sd">    f : :obj:`list` of :obj:`float`</span>
     335<span class="sd">    f : list of float</span>
    332336<span class="sd">        The interpolated data series with additional subgrid points.</span>
    333337<span class="sd">        Its dimension is equal to the length of the input data series</span>
    … …  
    363367
    364368    <span class="c1"># time step</span>
    365     <span class="n">dt</span><span class="o">=</span><span class="mf">1.0</span>
     369    <span class="n">dt</span> <span class="o">=</span> <span class="mf">1.0</span>
    366370
    367371    <span class="c1">############### Non-negative Geometric Mean Based Algorithm ###############</span>
    … …  
    370374    <span class="c1"># the value at t=0 of the interpolation algorithm coincides with the</span>
    371375    <span class="c1"># first data value according to the persistence hypothesis</span>
    372     <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>
     376    <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>
    373377
    374378    <span class="c1"># compute two first sub-grid intervals without monotonicity check</span>
    … …  
    376380    <span class="c1"># points and interpolate the corresponding data values</span>
    377381    <span class="c1"># except for the last interval due to boundary conditions</span>
    378     <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>
     382    <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>
    379383
    380384        <span class="c1"># as a requirement:</span>
    … …  
    382386        <span class="c1"># interval in f has to be zero to such that f[i+1]=f[i+2]=f[i+3]=0</span>
    383387        <span class="c1"># according to Eq. (6)</span>
    384         <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>
    385             <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>
     388        <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>
     389            <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>
    386390
    387391        <span class="c1"># otherwise the sub-grid values are calculated and added to the list</span>
    … …  
    398402            <span class="c1"># the function value at the first sub-grid point (fi1) is determined</span>
    399403            <span class="c1"># according to the equal area condition with Eq. (19)</span>
    400             <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>
     404            <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>
    401405
    402406            <span class="c1"># the function value at the second sub-grid point (fi2) is determined</span>
    403407            <span class="c1"># according Eq. (18)</span>
    404             <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>
     408            <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>
    405409
    406410            <span class="c1"># add next interval of interpolated (sub-)grid values</span>
    … …  
    413417    <span class="c1"># points and interpolate the corresponding data values</span>
    414418    <span class="c1"># except for the last interval due to boundary conditions</span>
    415     <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>
     419    <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>
    416420
    417421        <span class="c1"># as a requirement:</span>
    … …  
    419423        <span class="c1"># interval in f has to be zero to such that f[i+1]=f[i+2]=f[i+3]=0</span>
    420424        <span class="c1"># according to Eq. (6)</span>
    421         <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>
     425        <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>
    422426            <span class="c1"># apply monotonicity filter for interval before</span>
    423427            <span class="c1"># check if there is &quot;M&quot; or &quot;W&quot; shape</span>
    424             <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="mi">1</span> \
    425                <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="mi">1</span> \
    426                <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="mi">1</span><span class="p">:</span>
     428            <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> \
     429               <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> \
     430               <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>
    427431
    428432                <span class="c1"># the monotonicity filter corrects the value at (fim1) by</span>
    … …  
    436440                <span class="c1"># interval boundaries (fi) and (fip2) remains unchanged</span>
    437441                <span class="c1"># see Eq. (18) and (19)</span>
    438                 <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>
    439                 <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>
    440                 <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>
    441                 <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>
    442                 <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>
     442                <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>
     443                <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>
     444                <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>
     445                <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>
     446                <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>
    443447
    444448            <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>
    … …  
    453457            <span class="c1"># geometric mean, restricted such that non-negativity is guaranteed</span>
    454458            <span class="c1"># according to Eq. (25)</span>
    455             <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>
     459            <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>
    456460
    457461            <span class="c1"># the function value at the first sub-grid point (fi1) is determined</span>
    458462            <span class="c1"># according to the equal area condition with Eq. (19)</span>
    459             <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>
     463            <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>
    460464
    461465            <span class="c1"># the function value at the second sub-grid point (fi2) is determined</span>
    462466            <span class="c1"># according Eq. (18)</span>
    463             <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>
     467            <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>
    464468
    465469            <span class="c1"># apply monotonicity filter for interval before</span>
    466470            <span class="c1"># check if there is &quot;M&quot; or &quot;W&quot; shape</span>
    467             <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="mi">1</span> \
    468                <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="mi">1</span> \
    469                <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="mi">1</span><span class="p">:</span>
     471            <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> \
     472               <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> \
     473               <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>
    470474
    471475                <span class="c1"># the monotonicity filter corrects the value at (fim1) by</span>
    … …  
    479483                <span class="c1"># interval boundaries (fi) and (fip2) remains unchanged</span>
    480484                <span class="c1"># see Eq. (18) and (19)</span>
    481                 <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>
    482                 <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>
    483                 <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>
    484                 <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>
    485                 <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>
     485                <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>
     486                <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>
     487                <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>
     488                <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>
     489                <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>
    486490
    487491            <span class="c1"># add next interval of interpolated (sub-)grid values</span>
    … …  
    496500    <span class="c1"># interval in f has to be zero to such that f[i+1]=f[i+2]=f[i+3]=0</span>
    497501    <span class="c1"># according to Eq. (6)</span>
    498     <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>
     502    <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>
    499503        <span class="c1"># apply monotonicity filter for interval before</span>
    500504        <span class="c1"># check if there is &quot;M&quot; or &quot;W&quot; shape</span>
    501         <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="mi">1</span> \
    502            <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="mi">1</span> \
    503            <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="mi">1</span><span class="p">:</span>
     505        <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> \
     506           <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> \
     507           <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>
    504508
    505509            <span class="c1"># the monotonicity filter corrects the value at (fim1) by</span>
    … …  
    513517            <span class="c1"># interval boundaries (fi) and (fip2) remains unchanged</span>
    514518            <span class="c1"># see Eq. (18) and (19)</span>
    515             <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>
    516             <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>
    517             <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>
    518             <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>
    519             <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>
     519            <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>
     520            <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>
     521            <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>
     522            <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>
     523            <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>
    520524
    521525        <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>
    … …  
    538542        <span class="c1"># apply monotonicity filter for interval before</span>
    539543        <span class="c1"># check if there is &quot;M&quot; or &quot;W&quot; shape</span>
    540         <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="mi">1</span> \
    541            <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="mi">1</span> \
    542            <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="mi">1</span><span class="p">:</span>
     544        <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> \
     545           <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> \
     546           <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>
    543547
    544548            <span class="c1"># the monotonicity filter corrects the value at (fim1) by</span>
    … …  
    552556            <span class="c1"># interval boundaries (fi) and (fip2) remains unchanged</span>
    553557            <span class="c1"># see Eq. (18) and (19)</span>
    554             <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>
    555             <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>
    556             <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>
    557             <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>
    558             <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>
     558            <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>
     559            <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>
     560            <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>
     561            <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>
     562            <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>
    559563
    560564        <span class="c1"># add next interval of interpolated (sub-)grid values</span>
    … …  
    576580  <div role="contentinfo">
    577581    <p>
    578         &copy; Copyright 2018, Anne Philipp and Leopold Haimberger.
     582        &copy; Copyright 2018, Anne Philipp and Leopold Haimberger
    579583
    580584    </p>
    … …  
    595599 
    596600
    597     <script type="text/javascript">
    598         var DOCUMENTATION_OPTIONS = {
    599             URL_ROOT:'../',
    600             VERSION:'7.1 alpha',
    601             LANGUAGE:'None',
    602             COLLAPSE_INDEX:false,
    603             FILE_SUFFIX:'.html',
    604             HAS_SOURCE:  true,
    605             SOURCELINK_SUFFIX: '.txt'
    606         };
    607     </script>
    608       <script type="text/javascript" src="../_static/jquery.js"></script>
    609       <script type="text/javascript" src="../_static/underscore.js"></script>
    610       <script type="text/javascript" src="../_static/doctools.js"></script>
    611       <script type="text/javascript" src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script>
     601   
     602   
     603      <script type="text/javascript" id="documentation_options" data-url_root="../" src="../_static/documentation_options.js"></script>
     604        <script type="text/javascript" src="../_static/jquery.js"></script>
     605        <script type="text/javascript" src="../_static/underscore.js"></script>
     606        <script type="text/javascript" src="../_static/doctools.js"></script>
     607   
    612608
    613609 
Note: See TracChangeset for help on using the changeset viewer.
hosted by ZAMG