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    <h1>Fit nonlinear mixed models with SAEM</h1>
    <small class="dont-index">Source: <a href='https://github.com/jranke/mkin/blob/master/R/saem.R'><code>R/saem.R</code></a></small>
    <div class="hidden name"><code>saem.Rd</code></div>
    </div>

    <div class="ref-description">
    <p>This function uses <code><a href='https://rdrr.io/pkg/saemix/man/saemix.html'>saemix::saemix()</a></code> as a backend for fitting nonlinear mixed
effects models created from <a href='mmkin.html'>mmkin</a> row objects using the Stochastic Approximation
Expectation Maximisation algorithm (SAEM).</p>
    </div>

    <pre class="usage"><span class='fu'>saem</span><span class='op'>(</span><span class='va'>object</span>, <span class='va'>control</span>, <span class='va'>...</span><span class='op'>)</span>

<span class='co'># S3 method for mmkin</span>
<span class='fu'>saem</span><span class='op'>(</span>
  <span class='va'>object</span>,
  control <span class='op'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/list.html'>list</a></span><span class='op'>(</span>displayProgress <span class='op'>=</span> <span class='cn'>FALSE</span>, print <span class='op'>=</span> <span class='cn'>FALSE</span>, save <span class='op'>=</span> <span class='cn'>FALSE</span>, save.graphs <span class='op'>=</span>
    <span class='cn'>FALSE</span><span class='op'>)</span>,
  cores <span class='op'>=</span> <span class='fl'>1</span>,
  verbose <span class='op'>=</span> <span class='cn'>FALSE</span>,
  suppressPlot <span class='op'>=</span> <span class='cn'>TRUE</span>,
  quiet <span class='op'>=</span> <span class='cn'>FALSE</span>,
  <span class='va'>...</span>
<span class='op'>)</span>

<span class='co'># S3 method for saem.mmkin</span>
<span class='fu'><a href='https://rdrr.io/r/base/print.html'>print</a></span><span class='op'>(</span><span class='va'>x</span>, digits <span class='op'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/Extremes.html'>max</a></span><span class='op'>(</span><span class='fl'>3</span>, <span class='fu'><a href='https://rdrr.io/r/base/options.html'>getOption</a></span><span class='op'>(</span><span class='st'>"digits"</span><span class='op'>)</span> <span class='op'>-</span> <span class='fl'>3</span><span class='op'>)</span>, <span class='va'>...</span><span class='op'>)</span>

<span class='fu'>saemix_model</span><span class='op'>(</span><span class='va'>object</span>, cores <span class='op'>=</span> <span class='fl'>1</span>, verbose <span class='op'>=</span> <span class='cn'>FALSE</span>, <span class='va'>...</span><span class='op'>)</span>

<span class='fu'>saemix_data</span><span class='op'>(</span><span class='va'>object</span>, verbose <span class='op'>=</span> <span class='cn'>FALSE</span>, <span class='va'>...</span><span class='op'>)</span></pre>

    <h2 class="hasAnchor" id="arguments"><a class="anchor" href="#arguments"></a>Arguments</h2>
    <table class="ref-arguments">
    <colgroup><col class="name" /><col class="desc" /></colgroup>
    <tr>
      <th>object</th>
      <td><p>An <a href='mmkin.html'>mmkin</a> row object containing several fits of the same
<a href='mkinmod.html'>mkinmod</a> model to different datasets</p></td>
    </tr>
    <tr>
      <th>control</th>
      <td><p>Passed to <a href='https://rdrr.io/pkg/saemix/man/saemix.html'>saemix::saemix</a></p></td>
    </tr>
    <tr>
      <th>...</th>
      <td><p>Further parameters passed to <a href='https://rdrr.io/pkg/saemix/man/saemixModel.html'>saemix::saemixModel</a>.</p></td>
    </tr>
    <tr>
      <th>cores</th>
      <td><p>The number of cores to be used for multicore processing using
<code><a href='https://rdrr.io/r/parallel/mclapply.html'>parallel::mclapply()</a></code>. Using more than 1 core is experimental and may
lead to excessive forking, apparently depending on the BLAS version
used.</p></td>
    </tr>
    <tr>
      <th>verbose</th>
      <td><p>Should we print information about created objects of
type <a href='https://rdrr.io/pkg/saemix/man/SaemixModel-class.html'>saemix::SaemixModel</a> and <a href='https://rdrr.io/pkg/saemix/man/SaemixData-class.html'>saemix::SaemixData</a>?</p></td>
    </tr>
    <tr>
      <th>suppressPlot</th>
      <td><p>Should we suppress any plotting that is done
by the saemix function?</p></td>
    </tr>
    <tr>
      <th>quiet</th>
      <td><p>Should we suppress the messages saemix prints at the beginning
and the end of the optimisation process?</p></td>
    </tr>
    <tr>
      <th>x</th>
      <td><p>An saem.mmkin object to print</p></td>
    </tr>
    <tr>
      <th>digits</th>
      <td><p>Number of digits to use for printing</p></td>
    </tr>
    </table>

    <h2 class="hasAnchor" id="value"><a class="anchor" href="#value"></a>Value</h2>

    <p>An S3 object of class 'saem.mmkin', containing the fitted
<a href='https://rdrr.io/pkg/saemix/man/SaemixObject-class.html'>saemix::SaemixObject</a> as a list component named 'so'. The
object also inherits from 'mixed.mmkin'.</p>
<p>An <a href='https://rdrr.io/pkg/saemix/man/SaemixModel-class.html'>saemix::SaemixModel</a> object.</p>
<p>An <a href='https://rdrr.io/pkg/saemix/man/SaemixData-class.html'>saemix::SaemixData</a> object.</p>
    <h2 class="hasAnchor" id="details"><a class="anchor" href="#details"></a>Details</h2>

    <p>An mmkin row object is essentially a list of mkinfit objects that have been
obtained by fitting the same model to a list of datasets using <a href='mkinfit.html'>mkinfit</a>.</p>
<p>Starting values for the fixed effects (population mean parameters, argument
psi0 of <code><a href='https://rdrr.io/pkg/saemix/man/saemixModel.html'>saemix::saemixModel()</a></code> are the mean values of the parameters found
using <a href='mmkin.html'>mmkin</a>.</p>
    <h2 class="hasAnchor" id="see-also"><a class="anchor" href="#see-also"></a>See also</h2>

    <div class='dont-index'><p><a href='summary.saem.mmkin.html'>summary.saem.mmkin</a> <a href='plot.mixed.mmkin.html'>plot.mixed.mmkin</a></p></div>

    <h2 class="hasAnchor" id="examples"><a class="anchor" href="#examples"></a>Examples</h2>
    <pre class="examples"><div class='input'><span class='co'># \dontrun{</span>
<span class='va'>ds</span> <span class='op'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/r/base/lapply.html'>lapply</a></span><span class='op'>(</span><span class='va'>experimental_data_for_UBA_2019</span><span class='op'>[</span><span class='fl'>6</span><span class='op'>:</span><span class='fl'>10</span><span class='op'>]</span>,
 <span class='kw'>function</span><span class='op'>(</span><span class='va'>x</span><span class='op'>)</span> <span class='fu'><a href='https://rdrr.io/r/base/subset.html'>subset</a></span><span class='op'>(</span><span class='va'>x</span><span class='op'>$</span><span class='va'>data</span><span class='op'>[</span><span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span><span class='st'>"name"</span>, <span class='st'>"time"</span>, <span class='st'>"value"</span><span class='op'>)</span><span class='op'>]</span><span class='op'>)</span><span class='op'>)</span>
<span class='fu'><a href='https://rdrr.io/r/base/names.html'>names</a></span><span class='op'>(</span><span class='va'>ds</span><span class='op'>)</span> <span class='op'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/r/base/paste.html'>paste</a></span><span class='op'>(</span><span class='st'>"Dataset"</span>, <span class='fl'>6</span><span class='op'>:</span><span class='fl'>10</span><span class='op'>)</span>
<span class='va'>f_mmkin_parent_p0_fixed</span> <span class='op'>&lt;-</span> <span class='fu'><a href='mmkin.html'>mmkin</a></span><span class='op'>(</span><span class='st'>"FOMC"</span>, <span class='va'>ds</span>, cores <span class='op'>=</span> <span class='fl'>1</span>,
  state.ini <span class='op'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span>parent <span class='op'>=</span> <span class='fl'>100</span><span class='op'>)</span>, fixed_initials <span class='op'>=</span> <span class='st'>"parent"</span>, quiet <span class='op'>=</span> <span class='cn'>TRUE</span><span class='op'>)</span>
<span class='va'>f_saem_p0_fixed</span> <span class='op'>&lt;-</span> <span class='fu'>saem</span><span class='op'>(</span><span class='va'>f_mmkin_parent_p0_fixed</span><span class='op'>)</span>
</div><div class='output co'>#&gt; Running main SAEM algorithm
#&gt; [1] "Mon Nov 30 15:53:02 2020"
#&gt; ....
#&gt;     Minimisation finished
#&gt; [1] "Mon Nov 30 15:53:04 2020"</div><div class='input'>
<span class='va'>f_mmkin_parent</span> <span class='op'>&lt;-</span> <span class='fu'><a href='mmkin.html'>mmkin</a></span><span class='op'>(</span><span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span><span class='st'>"SFO"</span>, <span class='st'>"FOMC"</span>, <span class='st'>"DFOP"</span><span class='op'>)</span>, <span class='va'>ds</span>, quiet <span class='op'>=</span> <span class='cn'>TRUE</span><span class='op'>)</span>
<span class='va'>f_saem_sfo</span> <span class='op'>&lt;-</span> <span class='fu'>saem</span><span class='op'>(</span><span class='va'>f_mmkin_parent</span><span class='op'>[</span><span class='st'>"SFO"</span>, <span class='op'>]</span><span class='op'>)</span>
</div><div class='output co'>#&gt; Running main SAEM algorithm
#&gt; [1] "Mon Nov 30 15:53:05 2020"
#&gt; ....
#&gt;     Minimisation finished
#&gt; [1] "Mon Nov 30 15:53:07 2020"</div><div class='input'><span class='va'>f_saem_fomc</span> <span class='op'>&lt;-</span> <span class='fu'>saem</span><span class='op'>(</span><span class='va'>f_mmkin_parent</span><span class='op'>[</span><span class='st'>"FOMC"</span>, <span class='op'>]</span><span class='op'>)</span>
</div><div class='output co'>#&gt; Running main SAEM algorithm
#&gt; [1] "Mon Nov 30 15:53:07 2020"
#&gt; ....
#&gt;     Minimisation finished
#&gt; [1] "Mon Nov 30 15:53:09 2020"</div><div class='input'><span class='va'>f_saem_dfop</span> <span class='op'>&lt;-</span> <span class='fu'>saem</span><span class='op'>(</span><span class='va'>f_mmkin_parent</span><span class='op'>[</span><span class='st'>"DFOP"</span>, <span class='op'>]</span><span class='op'>)</span>
</div><div class='output co'>#&gt; Running main SAEM algorithm
#&gt; [1] "Mon Nov 30 15:53:10 2020"
#&gt; ....
#&gt;     Minimisation finished
#&gt; [1] "Mon Nov 30 15:53:13 2020"</div><div class='input'>
<span class='co'># The returned saem.mmkin object contains an SaemixObject, therefore we can use</span>
<span class='co'># functions from saemix</span>
<span class='kw'><a href='https://rdrr.io/r/base/library.html'>library</a></span><span class='op'>(</span><span class='va'>saemix</span><span class='op'>)</span>
</div><div class='output co'>#&gt; <span class='message'>Package saemix, version 3.1.9000</span>
#&gt; <span class='message'>  please direct bugs, questions and feedback to emmanuelle.comets@inserm.fr</span></div><div class='input'><span class='fu'><a href='https://rdrr.io/pkg/saemix/man/compare.saemix.html'>compare.saemix</a></span><span class='op'>(</span><span class='fu'><a href='https://rdrr.io/r/base/list.html'>list</a></span><span class='op'>(</span><span class='va'>f_saem_sfo</span><span class='op'>$</span><span class='va'>so</span>, <span class='va'>f_saem_fomc</span><span class='op'>$</span><span class='va'>so</span>, <span class='va'>f_saem_dfop</span><span class='op'>$</span><span class='va'>so</span><span class='op'>)</span><span class='op'>)</span>
</div><div class='output co'>#&gt; Likelihoods computed by importance sampling </div><div class='output co'>#&gt;        AIC      BIC
#&gt; 1 624.2484 622.2956
#&gt; 2 467.7096 464.9757
#&gt; 3 495.4373 491.9222</div><div class='input'><span class='fu'><a href='https://rdrr.io/pkg/saemix/man/plot-SaemixObject-method.html'>plot</a></span><span class='op'>(</span><span class='va'>f_saem_fomc</span><span class='op'>$</span><span class='va'>so</span>, plot.type <span class='op'>=</span> <span class='st'>"convergence"</span><span class='op'>)</span>
</div><div class='output co'>#&gt; Plotting convergence plots</div><div class='input'><span class='fu'><a href='https://rdrr.io/pkg/saemix/man/plot-SaemixObject-method.html'>plot</a></span><span class='op'>(</span><span class='va'>f_saem_fomc</span><span class='op'>$</span><span class='va'>so</span>, plot.type <span class='op'>=</span> <span class='st'>"individual.fit"</span><span class='op'>)</span>
</div><div class='img'><img src='saem-1.png' alt='' width='700' height='433' /></div><div class='output co'>#&gt; Plotting individual fits</div><div class='input'><span class='fu'><a href='https://rdrr.io/pkg/saemix/man/plot-SaemixObject-method.html'>plot</a></span><span class='op'>(</span><span class='va'>f_saem_fomc</span><span class='op'>$</span><span class='va'>so</span>, plot.type <span class='op'>=</span> <span class='st'>"npde"</span><span class='op'>)</span>
</div><div class='img'><img src='saem-2.png' alt='' width='700' height='433' /></div><div class='output co'>#&gt; Simulating data using nsim = 1000 simulated datasets
#&gt; Computing WRES and npde .
#&gt; Plotting npde</div><div class='img'><img src='saem-3.png' alt='' width='700' height='433' /></div><div class='output co'>#&gt; ---------------------------------------------
#&gt; Distribution of npde:
#&gt;            mean= -0.01528   (SE= 0.098 )
#&gt;        variance= 0.862   (SE= 0.13 )
#&gt;        skewness= 0.5016 
#&gt;        kurtosis= 1.18 
#&gt; ---------------------------------------------
#&gt; 
#&gt; Statistical tests
#&gt;   Wilcoxon signed rank test  : 0.679
#&gt;   Fisher variance test       : 0.36
#&gt;   SW test of normality       : 0.0855 .
#&gt; Global adjusted p-value      : 0.257
#&gt; ---
#&gt; Signif. codes: '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 
#&gt; ---------------------------------------------</div><div class='input'><span class='fu'><a href='https://rdrr.io/pkg/saemix/man/plot-SaemixObject-method.html'>plot</a></span><span class='op'>(</span><span class='va'>f_saem_fomc</span><span class='op'>$</span><span class='va'>so</span>, plot.type <span class='op'>=</span> <span class='st'>"vpc"</span><span class='op'>)</span>
</div><div class='output co'>#&gt; Performing simulations under the model.
#&gt; Plotting VPC
#&gt; Method used for VPC: binning by quantiles on X , dividing into the following intervals
#&gt;   Interval  Centered.On
#&gt; 1 (-1,3]      1.3      
#&gt; 2 (3,8]       7.4      
#&gt; 3 (8,14]     13.2      
#&gt; 4 (14,21]    20.5      
#&gt; 5 (21,37.7]  29.5      
#&gt; 6 (37.7,60]  50.4      
#&gt; 7 (60,90]    76.6      
#&gt; 8 (90,120]  109.0      
#&gt; 9 (120,180] 156.0      </div><div class='img'><img src='saem-4.png' alt='' width='700' height='433' /></div><div class='input'>
<span class='va'>f_mmkin_parent_tc</span> <span class='op'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/r/stats/update.html'>update</a></span><span class='op'>(</span><span class='va'>f_mmkin_parent</span>, error_model <span class='op'>=</span> <span class='st'>"tc"</span><span class='op'>)</span>
<span class='va'>f_saem_fomc_tc</span> <span class='op'>&lt;-</span> <span class='fu'>saem</span><span class='op'>(</span><span class='va'>f_mmkin_parent_tc</span><span class='op'>[</span><span class='st'>"FOMC"</span>, <span class='op'>]</span><span class='op'>)</span>
</div><div class='output co'>#&gt; Running main SAEM algorithm
#&gt; [1] "Mon Nov 30 15:53:15 2020"
#&gt; ....
#&gt;     Minimisation finished
#&gt; [1] "Mon Nov 30 15:53:20 2020"</div><div class='input'><span class='fu'><a href='https://rdrr.io/pkg/saemix/man/compare.saemix.html'>compare.saemix</a></span><span class='op'>(</span><span class='fu'><a href='https://rdrr.io/r/base/list.html'>list</a></span><span class='op'>(</span><span class='va'>f_saem_fomc</span><span class='op'>$</span><span class='va'>so</span>, <span class='va'>f_saem_fomc_tc</span><span class='op'>$</span><span class='va'>so</span><span class='op'>)</span><span class='op'>)</span>
</div><div class='output co'>#&gt; Likelihoods computed by importance sampling </div><div class='output co'>#&gt;        AIC      BIC
#&gt; 1 467.7096 464.9757
#&gt; 2 469.5208 466.3963</div><div class='input'>
<span class='va'>sfo_sfo</span> <span class='op'>&lt;-</span> <span class='fu'><a href='mkinmod.html'>mkinmod</a></span><span class='op'>(</span>parent <span class='op'>=</span> <span class='fu'><a href='mkinmod.html'>mkinsub</a></span><span class='op'>(</span><span class='st'>"SFO"</span>, <span class='st'>"A1"</span><span class='op'>)</span>,
  A1 <span class='op'>=</span> <span class='fu'><a href='mkinmod.html'>mkinsub</a></span><span class='op'>(</span><span class='st'>"SFO"</span><span class='op'>)</span><span class='op'>)</span>
</div><div class='output co'>#&gt; <span class='message'>Temporary DLL for differentials generated and loaded</span></div><div class='input'><span class='va'>fomc_sfo</span> <span class='op'>&lt;-</span> <span class='fu'><a href='mkinmod.html'>mkinmod</a></span><span class='op'>(</span>parent <span class='op'>=</span> <span class='fu'><a href='mkinmod.html'>mkinsub</a></span><span class='op'>(</span><span class='st'>"FOMC"</span>, <span class='st'>"A1"</span><span class='op'>)</span>,
  A1 <span class='op'>=</span> <span class='fu'><a href='mkinmod.html'>mkinsub</a></span><span class='op'>(</span><span class='st'>"SFO"</span><span class='op'>)</span><span class='op'>)</span>
</div><div class='output co'>#&gt; <span class='message'>Temporary DLL for differentials generated and loaded</span></div><div class='input'><span class='va'>dfop_sfo</span> <span class='op'>&lt;-</span> <span class='fu'><a href='mkinmod.html'>mkinmod</a></span><span class='op'>(</span>parent <span class='op'>=</span> <span class='fu'><a href='mkinmod.html'>mkinsub</a></span><span class='op'>(</span><span class='st'>"DFOP"</span>, <span class='st'>"A1"</span><span class='op'>)</span>,
  A1 <span class='op'>=</span> <span class='fu'><a href='mkinmod.html'>mkinsub</a></span><span class='op'>(</span><span class='st'>"SFO"</span><span class='op'>)</span><span class='op'>)</span>
</div><div class='output co'>#&gt; <span class='message'>Temporary DLL for differentials generated and loaded</span></div><div class='input'><span class='co'># The following fit uses analytical solutions for SFO-SFO and DFOP-SFO,</span>
<span class='co'># and compiled ODEs for FOMC that are much slower</span>
<span class='va'>f_mmkin</span> <span class='op'>&lt;-</span> <span class='fu'><a href='mmkin.html'>mmkin</a></span><span class='op'>(</span><span class='fu'><a href='https://rdrr.io/r/base/list.html'>list</a></span><span class='op'>(</span>
    <span class='st'>"SFO-SFO"</span> <span class='op'>=</span> <span class='va'>sfo_sfo</span>, <span class='st'>"FOMC-SFO"</span> <span class='op'>=</span> <span class='va'>fomc_sfo</span>, <span class='st'>"DFOP-SFO"</span> <span class='op'>=</span> <span class='va'>dfop_sfo</span><span class='op'>)</span>,
  <span class='va'>ds</span>, quiet <span class='op'>=</span> <span class='cn'>TRUE</span><span class='op'>)</span>
<span class='co'># These take about five seconds each on this system, as we use</span>
<span class='co'># analytical solutions written for saemix. When using the analytical</span>
<span class='co'># solutions written for mkin this took around four minutes</span>
<span class='va'>f_saem_sfo_sfo</span> <span class='op'>&lt;-</span> <span class='fu'>saem</span><span class='op'>(</span><span class='va'>f_mmkin</span><span class='op'>[</span><span class='st'>"SFO-SFO"</span>, <span class='op'>]</span><span class='op'>)</span>
</div><div class='output co'>#&gt; Running main SAEM algorithm
#&gt; [1] "Mon Nov 30 15:53:23 2020"
#&gt; ....
#&gt;     Minimisation finished
#&gt; [1] "Mon Nov 30 15:53:28 2020"</div><div class='input'><span class='va'>f_saem_dfop_sfo</span> <span class='op'>&lt;-</span> <span class='fu'>saem</span><span class='op'>(</span><span class='va'>f_mmkin</span><span class='op'>[</span><span class='st'>"DFOP-SFO"</span>, <span class='op'>]</span><span class='op'>)</span>
</div><div class='output co'>#&gt; Running main SAEM algorithm
#&gt; [1] "Mon Nov 30 15:53:29 2020"
#&gt; ....
#&gt;     Minimisation finished
#&gt; [1] "Mon Nov 30 15:53:38 2020"</div><div class='input'><span class='co'># We can use print, plot and summary methods to check the results</span>
<span class='fu'><a href='https://rdrr.io/r/base/print.html'>print</a></span><span class='op'>(</span><span class='va'>f_saem_dfop_sfo</span><span class='op'>)</span>
</div><div class='output co'>#&gt; Kinetic nonlinear mixed-effects model fit by SAEM
#&gt; Structural model:
#&gt; d_parent/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 *
#&gt;            time)) / (g * exp(-k1 * time) + (1 - g) * exp(-k2 * time)))
#&gt;            * parent
#&gt; d_A1/dt = + f_parent_to_A1 * ((k1 * g * exp(-k1 * time) + k2 * (1 - g)
#&gt;            * exp(-k2 * time)) / (g * exp(-k1 * time) + (1 - g) *
#&gt;            exp(-k2 * time))) * parent - k_A1 * A1
#&gt; 
#&gt; Data:
#&gt; 170 observations of 2 variable(s) grouped in 5 datasets
#&gt; 
#&gt; Likelihood computed by importance sampling
#&gt;     AIC   BIC logLik
#&gt;   841.6 836.5 -407.8
#&gt; 
#&gt; Fitted parameters:
#&gt;                     estimate    lower   upper
#&gt; parent_0            93.76647 91.15312 96.3798
#&gt; log_k_A1            -6.13235 -8.45788 -3.8068
#&gt; f_parent_qlogis     -0.97364 -1.36940 -0.5779
#&gt; log_k1              -2.53176 -3.80372 -1.2598
#&gt; log_k2              -3.58667 -5.29524 -1.8781
#&gt; g_qlogis             0.01238 -1.07968  1.1044
#&gt; Var.parent_0         7.61106 -3.34955 18.5717
#&gt; Var.log_k_A1         4.64679 -2.73133 12.0249
#&gt; Var.f_parent_qlogis  0.19693 -0.05498  0.4488
#&gt; Var.log_k1           2.01717 -0.51980  4.5542
#&gt; Var.log_k2           3.63412 -0.92964  8.1979
#&gt; Var.g_qlogis         0.20045 -0.97425  1.3751
#&gt; a.1                  1.88335  1.66636  2.1004
#&gt; SD.parent_0          2.75881  0.77234  4.7453
#&gt; SD.log_k_A1          2.15564  0.44429  3.8670
#&gt; SD.f_parent_qlogis   0.44377  0.15994  0.7276
#&gt; SD.log_k1            1.42027  0.52714  2.3134
#&gt; SD.log_k2            1.90634  0.70934  3.1033
#&gt; SD.g_qlogis          0.44771 -0.86417  1.7596</div><div class='input'><span class='fu'><a href='https://rdrr.io/pkg/saemix/man/plot-SaemixObject-method.html'>plot</a></span><span class='op'>(</span><span class='va'>f_saem_dfop_sfo</span><span class='op'>)</span>
</div><div class='img'><img src='saem-5.png' alt='' width='700' height='433' /></div><div class='input'><span class='fu'><a href='https://rdrr.io/pkg/saemix/man/summary-methods.html'>summary</a></span><span class='op'>(</span><span class='va'>f_saem_dfop_sfo</span>, data <span class='op'>=</span> <span class='cn'>TRUE</span><span class='op'>)</span>
</div><div class='output co'>#&gt; saemix version used for fitting:      3.1.9000 
#&gt; mkin version used for pre-fitting:  0.9.50.4 
#&gt; R version used for fitting:         4.0.3 
#&gt; Date of fit:     Mon Nov 30 15:53:38 2020 
#&gt; Date of summary: Mon Nov 30 15:53:39 2020 
#&gt; 
#&gt; Equations:
#&gt; d_parent/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 *
#&gt;            time)) / (g * exp(-k1 * time) + (1 - g) * exp(-k2 * time)))
#&gt;            * parent
#&gt; d_A1/dt = + f_parent_to_A1 * ((k1 * g * exp(-k1 * time) + k2 * (1 - g)
#&gt;            * exp(-k2 * time)) / (g * exp(-k1 * time) + (1 - g) *
#&gt;            exp(-k2 * time))) * parent - k_A1 * A1
#&gt; 
#&gt; Data:
#&gt; 170 observations of 2 variable(s) grouped in 5 datasets
#&gt; 
#&gt; Model predictions using solution type analytical 
#&gt; 
#&gt; Fitted in 9.963 s using 300, 100 iterations
#&gt; 
#&gt; Variance model: Constant variance 
#&gt; 
#&gt; Mean of starting values for individual parameters:
#&gt;        parent_0        log_k_A1 f_parent_qlogis          log_k1          log_k2 
#&gt;      93.8101519      -9.7647455      -0.9711148      -1.8799371      -4.2708142 
#&gt;        g_qlogis 
#&gt;       0.1356441 
#&gt; 
#&gt; Fixed degradation parameter values:
#&gt; None
#&gt; 
#&gt; Results:
#&gt; 
#&gt; Likelihood computed by importance sampling
#&gt;     AIC   BIC logLik
#&gt;   841.6 836.5 -407.8
#&gt; 
#&gt; Optimised, transformed parameters with symmetric confidence intervals:
#&gt;                     est.  lower   upper
#&gt; parent_0        93.76647 91.153 96.3798
#&gt; log_k_A1        -6.13235 -8.458 -3.8068
#&gt; f_parent_qlogis -0.97364 -1.369 -0.5779
#&gt; log_k1          -2.53176 -3.804 -1.2598
#&gt; log_k2          -3.58667 -5.295 -1.8781
#&gt; g_qlogis         0.01238 -1.080  1.1044
#&gt; 
#&gt; Correlation: 
#&gt;                 prnt_0 lg__A1 f_prn_ log_k1 log_k2
#&gt; log_k_A1        -0.013                            
#&gt; f_parent_qlogis -0.025  0.050                     
#&gt; log_k1           0.030  0.000 -0.005              
#&gt; log_k2           0.010  0.005 -0.003  0.032       
#&gt; g_qlogis        -0.063 -0.015  0.010 -0.167 -0.177
#&gt; 
#&gt; Random effects:
#&gt;                      est.   lower  upper
#&gt; SD.parent_0        2.7588  0.7723 4.7453
#&gt; SD.log_k_A1        2.1556  0.4443 3.8670
#&gt; SD.f_parent_qlogis 0.4438  0.1599 0.7276
#&gt; SD.log_k1          1.4203  0.5271 2.3134
#&gt; SD.log_k2          1.9063  0.7093 3.1033
#&gt; SD.g_qlogis        0.4477 -0.8642 1.7596
#&gt; 
#&gt; Variance model:
#&gt;      est. lower upper
#&gt; a.1 1.883 1.666   2.1
#&gt; 
#&gt; Backtransformed parameters with asymmetric confidence intervals:
#&gt;                     est.     lower    upper
#&gt; parent_0       93.766473 9.115e+01 96.37983
#&gt; k_A1            0.002171 2.122e-04  0.02222
#&gt; f_parent_to_A1  0.274156 2.027e-01  0.35942
#&gt; k1              0.079519 2.229e-02  0.28371
#&gt; k2              0.027691 5.015e-03  0.15288
#&gt; g               0.503095 2.536e-01  0.75109
#&gt; 
#&gt; Resulting formation fractions:
#&gt;                 ff
#&gt; parent_A1   0.2742
#&gt; parent_sink 0.7258
#&gt; 
#&gt; Estimated disappearance times:
#&gt;          DT50    DT90 DT50back DT50_k1 DT50_k2
#&gt; parent  14.11   59.53    17.92   8.717   25.03
#&gt; A1     319.21 1060.38       NA      NA      NA
#&gt; 
#&gt; Data:
#&gt;          ds   name time observed predicted residual   std standardized
#&gt;   Dataset 6 parent    0     97.2  95.79523 -1.40477 1.883    -0.745888
#&gt;   Dataset 6 parent    0     96.4  95.79523 -0.60477 1.883    -0.321114
#&gt;   Dataset 6 parent    3     71.1  71.32042  0.22042 1.883     0.117035
#&gt;   Dataset 6 parent    3     69.2  71.32042  2.12042 1.883     1.125873
#&gt;   Dataset 6 parent    6     58.1  56.45256 -1.64744 1.883    -0.874739
#&gt;   Dataset 6 parent    6     56.6  56.45256 -0.14744 1.883    -0.078288
#&gt;   Dataset 6 parent   10     44.4  44.48523  0.08523 1.883     0.045256
#&gt;   Dataset 6 parent   10     43.4  44.48523  1.08523 1.883     0.576224
#&gt;   Dataset 6 parent   20     33.3  29.75774 -3.54226 1.883    -1.880826
#&gt;   Dataset 6 parent   20     29.2  29.75774  0.55774 1.883     0.296141
#&gt;   Dataset 6 parent   34     17.6  19.35710  1.75710 1.883     0.932966
#&gt;   Dataset 6 parent   34     18.0  19.35710  1.35710 1.883     0.720578
#&gt;   Dataset 6 parent   55     10.5  10.48443 -0.01557 1.883    -0.008266
#&gt;   Dataset 6 parent   55      9.3  10.48443  1.18443 1.883     0.628895
#&gt;   Dataset 6 parent   90      4.5   3.78622 -0.71378 1.883    -0.378995
#&gt;   Dataset 6 parent   90      4.7   3.78622 -0.91378 1.883    -0.485188
#&gt;   Dataset 6 parent  112      3.0   1.99608 -1.00392 1.883    -0.533048
#&gt;   Dataset 6 parent  112      3.4   1.99608 -1.40392 1.883    -0.745435
#&gt;   Dataset 6 parent  132      2.3   1.11539 -1.18461 1.883    -0.628990
#&gt;   Dataset 6 parent  132      2.7   1.11539 -1.58461 1.883    -0.841377
#&gt;   Dataset 6     A1    3      4.3   4.66132  0.36132 1.883     0.191849
#&gt;   Dataset 6     A1    3      4.6   4.66132  0.06132 1.883     0.032559
#&gt;   Dataset 6     A1    6      7.0   7.41087  0.41087 1.883     0.218157
#&gt;   Dataset 6     A1    6      7.2   7.41087  0.21087 1.883     0.111964
#&gt;   Dataset 6     A1   10      8.2   9.50878  1.30878 1.883     0.694921
#&gt;   Dataset 6     A1   10      8.0   9.50878  1.50878 1.883     0.801114
#&gt;   Dataset 6     A1   20     11.0  11.69902  0.69902 1.883     0.371157
#&gt;   Dataset 6     A1   20     13.7  11.69902 -2.00098 1.883    -1.062455
#&gt;   Dataset 6     A1   34     11.5  12.67784  1.17784 1.883     0.625396
#&gt;   Dataset 6     A1   34     12.7  12.67784 -0.02216 1.883    -0.011765
#&gt;   Dataset 6     A1   55     14.9  12.78556 -2.11444 1.883    -1.122701
#&gt;   Dataset 6     A1   55     14.5  12.78556 -1.71444 1.883    -0.910314
#&gt;   Dataset 6     A1   90     12.1  11.52954 -0.57046 1.883    -0.302898
#&gt;   Dataset 6     A1   90     12.3  11.52954 -0.77046 1.883    -0.409092
#&gt;   Dataset 6     A1  112      9.9  10.43825  0.53825 1.883     0.285793
#&gt;   Dataset 6     A1  112     10.2  10.43825  0.23825 1.883     0.126503
#&gt;   Dataset 6     A1  132      8.8   9.42830  0.62830 1.883     0.333609
#&gt;   Dataset 6     A1  132      7.8   9.42830  1.62830 1.883     0.864577
#&gt;   Dataset 7 parent    0     93.6  90.91477 -2.68523 1.883    -1.425772
#&gt;   Dataset 7 parent    0     92.3  90.91477 -1.38523 1.883    -0.735514
#&gt;   Dataset 7 parent    3     87.0  84.76874 -2.23126 1.883    -1.184726
#&gt;   Dataset 7 parent    3     82.2  84.76874  2.56874 1.883     1.363919
#&gt;   Dataset 7 parent    7     74.0  77.62735  3.62735 1.883     1.926003
#&gt;   Dataset 7 parent    7     73.9  77.62735  3.72735 1.883     1.979100
#&gt;   Dataset 7 parent   14     64.2  67.52266  3.32266 1.883     1.764224
#&gt;   Dataset 7 parent   14     69.5  67.52266 -1.97734 1.883    -1.049904
#&gt;   Dataset 7 parent   30     54.0  52.41949 -1.58051 1.883    -0.839202
#&gt;   Dataset 7 parent   30     54.6  52.41949 -2.18051 1.883    -1.157783
#&gt;   Dataset 7 parent   60     41.1  39.36582 -1.73418 1.883    -0.920794
#&gt;   Dataset 7 parent   60     38.4  39.36582  0.96582 1.883     0.512818
#&gt;   Dataset 7 parent   90     32.5  33.75388  1.25388 1.883     0.665771
#&gt;   Dataset 7 parent   90     35.5  33.75388 -1.74612 1.883    -0.927132
#&gt;   Dataset 7 parent  120     28.1  30.41716  2.31716 1.883     1.230335
#&gt;   Dataset 7 parent  120     29.0  30.41716  1.41716 1.883     0.752464
#&gt;   Dataset 7 parent  180     26.5  25.66046 -0.83954 1.883    -0.445767
#&gt;   Dataset 7 parent  180     27.6  25.66046 -1.93954 1.883    -1.029832
#&gt;   Dataset 7     A1    3      3.9   2.69355 -1.20645 1.883    -0.640585
#&gt;   Dataset 7     A1    3      3.1   2.69355 -0.40645 1.883    -0.215811
#&gt;   Dataset 7     A1    7      6.9   5.81807 -1.08193 1.883    -0.574470
#&gt;   Dataset 7     A1    7      6.6   5.81807 -0.78193 1.883    -0.415180
#&gt;   Dataset 7     A1   14     10.4  10.22529 -0.17471 1.883    -0.092767
#&gt;   Dataset 7     A1   14      8.3  10.22529  1.92529 1.883     1.022265
#&gt;   Dataset 7     A1   30     14.4  16.75484  2.35484 1.883     1.250345
#&gt;   Dataset 7     A1   30     13.7  16.75484  3.05484 1.883     1.622022
#&gt;   Dataset 7     A1   60     22.1  22.22540  0.12540 1.883     0.066583
#&gt;   Dataset 7     A1   60     22.3  22.22540 -0.07460 1.883    -0.039610
#&gt;   Dataset 7     A1   90     27.5  24.38799 -3.11201 1.883    -1.652376
#&gt;   Dataset 7     A1   90     25.4  24.38799 -1.01201 1.883    -0.537344
#&gt;   Dataset 7     A1  120     28.0  25.53294 -2.46706 1.883    -1.309927
#&gt;   Dataset 7     A1  120     26.6  25.53294 -1.06706 1.883    -0.566572
#&gt;   Dataset 7     A1  180     25.8  26.94943  1.14943 1.883     0.610309
#&gt;   Dataset 7     A1  180     25.3  26.94943  1.64943 1.883     0.875793
#&gt;   Dataset 8 parent    0     91.9  91.53246 -0.36754 1.883    -0.195151
#&gt;   Dataset 8 parent    0     90.8  91.53246  0.73246 1.883     0.388914
#&gt;   Dataset 8 parent    1     64.9  67.73197  2.83197 1.883     1.503686
#&gt;   Dataset 8 parent    1     66.2  67.73197  1.53197 1.883     0.813428
#&gt;   Dataset 8 parent    3     43.5  41.58448 -1.91552 1.883    -1.017081
#&gt;   Dataset 8 parent    3     44.1  41.58448 -2.51552 1.883    -1.335661
#&gt;   Dataset 8 parent    8     18.3  19.62286  1.32286 1.883     0.702395
#&gt;   Dataset 8 parent    8     18.1  19.62286  1.52286 1.883     0.808589
#&gt;   Dataset 8 parent   14     10.2  10.77819  0.57819 1.883     0.306999
#&gt;   Dataset 8 parent   14     10.8  10.77819 -0.02181 1.883    -0.011582
#&gt;   Dataset 8 parent   27      4.9   3.26977 -1.63023 1.883    -0.865599
#&gt;   Dataset 8 parent   27      3.3   3.26977 -0.03023 1.883    -0.016051
#&gt;   Dataset 8 parent   48      1.6   0.48024 -1.11976 1.883    -0.594557
#&gt;   Dataset 8 parent   48      1.5   0.48024 -1.01976 1.883    -0.541460
#&gt;   Dataset 8 parent   70      1.1   0.06438 -1.03562 1.883    -0.549881
#&gt;   Dataset 8 parent   70      0.9   0.06438 -0.83562 1.883    -0.443688
#&gt;   Dataset 8     A1    1      9.6   7.61539 -1.98461 1.883    -1.053761
#&gt;   Dataset 8     A1    1      7.7   7.61539 -0.08461 1.883    -0.044923
#&gt;   Dataset 8     A1    3     15.0  15.47954  0.47954 1.883     0.254622
#&gt;   Dataset 8     A1    3     15.1  15.47954  0.37954 1.883     0.201525
#&gt;   Dataset 8     A1    8     21.2  20.22616 -0.97384 1.883    -0.517076
#&gt;   Dataset 8     A1    8     21.1  20.22616 -0.87384 1.883    -0.463979
#&gt;   Dataset 8     A1   14     19.7  20.00067  0.30067 1.883     0.159645
#&gt;   Dataset 8     A1   14     18.9  20.00067  1.10067 1.883     0.584419
#&gt;   Dataset 8     A1   27     17.5  16.38142 -1.11858 1.883    -0.593929
#&gt;   Dataset 8     A1   27     15.9  16.38142  0.48142 1.883     0.255619
#&gt;   Dataset 8     A1   48      9.5  10.25357  0.75357 1.883     0.400123
#&gt;   Dataset 8     A1   48      9.8  10.25357  0.45357 1.883     0.240833
#&gt;   Dataset 8     A1   70      6.2   5.95728 -0.24272 1.883    -0.128878
#&gt;   Dataset 8     A1   70      6.1   5.95728 -0.14272 1.883    -0.075781
#&gt;   Dataset 9 parent    0     99.8  97.47274 -2.32726 1.883    -1.235697
#&gt;   Dataset 9 parent    0     98.3  97.47274 -0.82726 1.883    -0.439246
#&gt;   Dataset 9 parent    1     77.1  79.72257  2.62257 1.883     1.392500
#&gt;   Dataset 9 parent    1     77.2  79.72257  2.52257 1.883     1.339404
#&gt;   Dataset 9 parent    3     59.0  56.26497 -2.73503 1.883    -1.452212
#&gt;   Dataset 9 parent    3     58.1  56.26497 -1.83503 1.883    -0.974342
#&gt;   Dataset 9 parent    8     27.4  31.66985  4.26985 1.883     2.267151
#&gt;   Dataset 9 parent    8     29.2  31.66985  2.46985 1.883     1.311410
#&gt;   Dataset 9 parent   14     19.1  22.39789  3.29789 1.883     1.751071
#&gt;   Dataset 9 parent   14     29.6  22.39789 -7.20211 1.883    -3.824090
#&gt;   Dataset 9 parent   27     10.1  14.21758  4.11758 1.883     2.186301
#&gt;   Dataset 9 parent   27     18.2  14.21758 -3.98242 1.883    -2.114537
#&gt;   Dataset 9 parent   48      4.5   7.27921  2.77921 1.883     1.475671
#&gt;   Dataset 9 parent   48      9.1   7.27921 -1.82079 1.883    -0.966780
#&gt;   Dataset 9 parent   70      2.3   3.61470  1.31470 1.883     0.698065
#&gt;   Dataset 9 parent   70      2.9   3.61470  0.71470 1.883     0.379485
#&gt;   Dataset 9 parent   91      2.0   1.85303 -0.14697 1.883    -0.078038
#&gt;   Dataset 9 parent   91      1.8   1.85303  0.05303 1.883     0.028155
#&gt;   Dataset 9 parent  120      2.0   0.73645 -1.26355 1.883    -0.670906
#&gt;   Dataset 9 parent  120      2.2   0.73645 -1.46355 1.883    -0.777099
#&gt;   Dataset 9     A1    1      4.2   3.87843 -0.32157 1.883    -0.170743
#&gt;   Dataset 9     A1    1      3.9   3.87843 -0.02157 1.883    -0.011453
#&gt;   Dataset 9     A1    3      7.4   8.90535  1.50535 1.883     0.799291
#&gt;   Dataset 9     A1    3      7.9   8.90535  1.00535 1.883     0.533807
#&gt;   Dataset 9     A1    8     14.5  13.75172 -0.74828 1.883    -0.397312
#&gt;   Dataset 9     A1    8     13.7  13.75172  0.05172 1.883     0.027462
#&gt;   Dataset 9     A1   14     14.2  14.97541  0.77541 1.883     0.411715
#&gt;   Dataset 9     A1   14     12.2  14.97541  2.77541 1.883     1.473650
#&gt;   Dataset 9     A1   27     13.7  14.94728  1.24728 1.883     0.662266
#&gt;   Dataset 9     A1   27     13.2  14.94728  1.74728 1.883     0.927750
#&gt;   Dataset 9     A1   48     13.6  13.66078  0.06078 1.883     0.032272
#&gt;   Dataset 9     A1   48     15.4  13.66078 -1.73922 1.883    -0.923470
#&gt;   Dataset 9     A1   70     10.4  11.84899  1.44899 1.883     0.769365
#&gt;   Dataset 9     A1   70     11.6  11.84899  0.24899 1.883     0.132204
#&gt;   Dataset 9     A1   91     10.0  10.09177  0.09177 1.883     0.048727
#&gt;   Dataset 9     A1   91      9.5  10.09177  0.59177 1.883     0.314211
#&gt;   Dataset 9     A1  120      9.1   7.91379 -1.18621 1.883    -0.629841
#&gt;   Dataset 9     A1  120      9.0   7.91379 -1.08621 1.883    -0.576745
#&gt;  Dataset 10 parent    0     96.1  93.65257 -2.44743 1.883    -1.299505
#&gt;  Dataset 10 parent    0     94.3  93.65257 -0.64743 1.883    -0.343763
#&gt;  Dataset 10 parent    8     73.9  77.85906  3.95906 1.883     2.102132
#&gt;  Dataset 10 parent    8     73.9  77.85906  3.95906 1.883     2.102132
#&gt;  Dataset 10 parent   14     69.4  70.17143  0.77143 1.883     0.409606
#&gt;  Dataset 10 parent   14     73.1  70.17143 -2.92857 1.883    -1.554974
#&gt;  Dataset 10 parent   21     65.6  63.99188 -1.60812 1.883    -0.853862
#&gt;  Dataset 10 parent   21     65.3  63.99188 -1.30812 1.883    -0.694572
#&gt;  Dataset 10 parent   41     55.9  54.64292 -1.25708 1.883    -0.667467
#&gt;  Dataset 10 parent   41     54.4  54.64292  0.24292 1.883     0.128985
#&gt;  Dataset 10 parent   63     47.0  49.61303  2.61303 1.883     1.387433
#&gt;  Dataset 10 parent   63     49.3  49.61303  0.31303 1.883     0.166207
#&gt;  Dataset 10 parent   91     44.7  45.17807  0.47807 1.883     0.253839
#&gt;  Dataset 10 parent   91     46.7  45.17807 -1.52193 1.883    -0.808096
#&gt;  Dataset 10 parent  120     42.1  41.27970 -0.82030 1.883    -0.435552
#&gt;  Dataset 10 parent  120     41.3  41.27970 -0.02030 1.883    -0.010778
#&gt;  Dataset 10     A1    8      3.3   3.99294  0.69294 1.883     0.367929
#&gt;  Dataset 10     A1    8      3.4   3.99294  0.59294 1.883     0.314832
#&gt;  Dataset 10     A1   14      3.9   5.92756  2.02756 1.883     1.076570
#&gt;  Dataset 10     A1   14      2.9   5.92756  3.02756 1.883     1.607538
#&gt;  Dataset 10     A1   21      6.4   7.47313  1.07313 1.883     0.569799
#&gt;  Dataset 10     A1   21      7.2   7.47313  0.27313 1.883     0.145025
#&gt;  Dataset 10     A1   41      9.1   9.76819  0.66819 1.883     0.354786
#&gt;  Dataset 10     A1   41      8.5   9.76819  1.26819 1.883     0.673367
#&gt;  Dataset 10     A1   63     11.7  10.94733 -0.75267 1.883    -0.399643
#&gt;  Dataset 10     A1   63     12.0  10.94733 -1.05267 1.883    -0.558933
#&gt;  Dataset 10     A1   91     13.3  11.93773 -1.36227 1.883    -0.723321
#&gt;  Dataset 10     A1   91     13.2  11.93773 -1.26227 1.883    -0.670224
#&gt;  Dataset 10     A1  120     14.3  12.77666 -1.52334 1.883    -0.808847
#&gt;  Dataset 10     A1  120     12.1  12.77666  0.67666 1.883     0.359282</div><div class='input'>
<span class='co'># Using a single core, the following takes about 6 minutes as we do not have an</span>
<span class='co'># analytical solution. Using 10 cores it is slower instead of faster</span>
<span class='va'>f_saem_fomc</span> <span class='op'>&lt;-</span> <span class='fu'>saem</span><span class='op'>(</span><span class='va'>f_mmkin</span><span class='op'>[</span><span class='st'>"FOMC-SFO"</span>, <span class='op'>]</span>, cores <span class='op'>=</span> <span class='fl'>1</span><span class='op'>)</span>
</div><div class='output co'>#&gt; Running main SAEM algorithm
#&gt; [1] "Mon Nov 30 15:53:39 2020"
#&gt; DLSODA-  At current T (=R1), MXSTEP (=I1) steps   
#&gt;       taken on this call before reaching TOUT     
#&gt; In above message, I1 = 5000
#&gt;  
#&gt; In above message, R1 = 0.00156238
#&gt;  
#&gt; DLSODA-  At T (=R1) and step size H (=R2), the    
#&gt;       corrector convergence failed repeatedly     
#&gt;       or with ABS(H) = HMIN   
#&gt; In above message, R1 = 0, R2 = 1.1373e-10
#&gt;  
#&gt; DLSODA-  At current T (=R1), MXSTEP (=I1) steps   
#&gt;       taken on this call before reaching TOUT     
#&gt; In above message, I1 = 5000
#&gt;  
#&gt; In above message, R1 = 2.24752e-06
#&gt;  
#&gt; ....
#&gt;     Minimisation finished
#&gt; [1] "Mon Nov 30 16:00:45 2020"</div><div class='input'><span class='fu'><a href='https://rdrr.io/pkg/saemix/man/plot-SaemixObject-method.html'>plot</a></span><span class='op'>(</span><span class='va'>f_saem_fomc</span><span class='op'>)</span>
</div><div class='img'><img src='saem-6.png' alt='' width='700' height='433' /></div><div class='input'><span class='co'># }</span>
</div></pre>
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