Add docs generated using released version 0.9.52

author: Johannes Ranke <jranke@uni-bremen.de> 2020-05-27 07:12:51 +0200
committer: Johannes Ranke <jranke@uni-bremen.de> 2020-05-27 07:12:51 +0200
commit: b5ee48a86e4b1d4c05aaadb80b44954e2e994ebc (patch)
tree: aeeeaf623e4a6102b9ca2440cf0e32ff7a7a1d25 /docs/articles
parent: a77a10ea6c607346778ba0700b3b66ac393101a2 (diff)
18 files changed, 347 insertions, 462 deletions
diff --git a/docs/articles/FOCUS_D.html b/docs/articles/FOCUS_D.html
index 243ebee1..cdd85f43 100644
--- a/docs/articles/FOCUS_D.html
+++ b/docs/articles/FOCUS_D.html
@@ -68,9 +68,6 @@
     <li>
       <a href="../articles/web_only/NAFTA_examples.html">Example evaluation of NAFTA SOP Attachment examples</a>
     </li>
-    <li>
-      <a href="../articles/web_only/benchmarks.html">Some benchmark timings</a>
-    </li>
   </ul>
 </li>
 <li>
@@ -100,10 +97,10 @@
       <h1 data-toc-skip>Example evaluation of FOCUS Example Dataset D</h1>
                         <h4 class="author">Johannes Ranke</h4>
             
-            <h4 class="date">2020-05-14</h4>
+            <h4 class="date">2020-05-27</h4>
       
-      <small class="dont-index">Source: <a href="http://github.com/jranke/mkin/blob/master/vignettes/FOCUS_D.rmd"><code>vignettes/FOCUS_D.rmd</code></a></small>
-      <div class="hidden name"><code>FOCUS_D.rmd</code></div>
+      <small class="dont-index">Source: <a href="http://github.com/jranke/mkin/blob/master/vignettes/FOCUS_D.Rmd"><code>vignettes/FOCUS_D.Rmd</code></a></small>
+      <div class="hidden name"><code>FOCUS_D.Rmd</code></div>
 
     </div>
 
@@ -180,8 +177,8 @@
 <div class="sourceCode" id="cb11"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/summary.html">summary</a></span>(<span class="no">fit</span>)</pre></body></html></div>
 <pre><code>## mkin version used for fitting:    0.9.50.2 
 ## R version used for fitting:       4.0.0 
-## Date of fit:     Thu May 14 17:07:12 2020 
-## Date of summary: Thu May 14 17:07:12 2020 
+## Date of fit:     Wed May 27 07:05:33 2020 
+## Date of summary: Wed May 27 07:05:34 2020 
 ## 
 ## Equations:
 ## d_parent/dt = - k_parent * parent
@@ -189,7 +186,7 @@
 ## 
 ## Model predictions using solution type analytical 
 ## 
-## Fitted using 421 model solutions performed in 0.167 s
+## Fitted using 421 model solutions performed in 0.166 s
 ## 
 ## Error model: Constant variance 
 ## 
@@ -228,11 +225,11 @@
 ## 
 ## Parameter correlation:
 ##                  parent_0 log_k_parent   log_k_m1 f_parent_ilr_1      sigma
-## parent_0        1.000e+00    5.174e-01 -1.688e-01     -5.471e-01 -3.214e-07
+## parent_0        1.000e+00    5.174e-01 -1.688e-01     -5.471e-01 -3.190e-07
 ## log_k_parent    5.174e-01    1.000e+00 -3.263e-01     -5.426e-01  3.168e-07
-## log_k_m1       -1.688e-01   -3.263e-01  1.000e+00      7.478e-01 -1.410e-07
-## f_parent_ilr_1 -5.471e-01   -5.426e-01  7.478e-01      1.000e+00  5.093e-10
-## sigma          -3.214e-07    3.168e-07 -1.410e-07      5.093e-10  1.000e+00
+## log_k_m1       -1.688e-01   -3.263e-01  1.000e+00      7.478e-01 -1.406e-07
+## f_parent_ilr_1 -5.471e-01   -5.426e-01  7.478e-01      1.000e+00 -1.587e-10
+## sigma          -3.190e-07    3.168e-07 -1.406e-07     -1.587e-10  1.000e+00
 ## 
 ## Backtransformed parameters:
 ## Confidence intervals for internally transformed parameters are asymmetric.
diff --git a/docs/articles/FOCUS_L.html b/docs/articles/FOCUS_L.html
index df5c77c4..2a58b4e5 100644
--- a/docs/articles/FOCUS_L.html
+++ b/docs/articles/FOCUS_L.html
@@ -68,9 +68,6 @@
     <li>
       <a href="../articles/web_only/NAFTA_examples.html">Example evaluation of NAFTA SOP Attachment examples</a>
     </li>
-    <li>
-      <a href="../articles/web_only/benchmarks.html">Some benchmark timings</a>
-    </li>
   </ul>
 </li>
 <li>
@@ -100,10 +97,10 @@
       <h1 data-toc-skip>Example evaluation of FOCUS Laboratory Data L1 to L3</h1>
                         <h4 class="author">Johannes Ranke</h4>
             
-            <h4 class="date">2020-05-14</h4>
+            <h4 class="date">2020-05-27</h4>
       
-      <small class="dont-index">Source: <a href="http://github.com/jranke/mkin/blob/master/vignettes/FOCUS_L.rmd"><code>vignettes/FOCUS_L.rmd</code></a></small>
-      <div class="hidden name"><code>FOCUS_L.rmd</code></div>
+      <small class="dont-index">Source: <a href="http://github.com/jranke/mkin/blob/master/vignettes/FOCUS_L.Rmd"><code>vignettes/FOCUS_L.Rmd</code></a></small>
+      <div class="hidden name"><code>FOCUS_L.Rmd</code></div>
 
     </div>
 
@@ -126,15 +123,15 @@
 <span class="fu"><a href="https://rdrr.io/r/base/summary.html">summary</a></span>(<span class="no">m.L1.SFO</span>)</pre></body></html></div>
 <pre><code>## mkin version used for fitting:    0.9.50.2 
 ## R version used for fitting:       4.0.0 
-## Date of fit:     Thu May 14 17:07:14 2020 
-## Date of summary: Thu May 14 17:07:14 2020 
+## Date of fit:     Wed May 27 07:05:36 2020 
+## Date of summary: Wed May 27 07:05:36 2020 
 ## 
 ## Equations:
 ## d_parent/dt = - k_parent_sink * parent
 ## 
 ## Model predictions using solution type analytical 
 ## 
-## Fitted using 133 model solutions performed in 0.032 s
+## Fitted using 133 model solutions performed in 0.031 s
 ## 
 ## Error model: Constant variance 
 ## 
@@ -166,9 +163,9 @@
 ## 
 ## Parameter correlation:
 ##                     parent_0 log_k_parent_sink      sigma
-## parent_0           1.000e+00         6.186e-01 -1.516e-09
-## log_k_parent_sink  6.186e-01         1.000e+00 -3.124e-09
-## sigma             -1.516e-09        -3.124e-09  1.000e+00
+## parent_0           1.000e+00         6.186e-01 -1.712e-09
+## log_k_parent_sink  6.186e-01         1.000e+00 -3.237e-09
+## sigma             -1.712e-09        -3.237e-09  1.000e+00
 ## 
 ## Backtransformed parameters:
 ## Confidence intervals for internally transformed parameters are asymmetric.
@@ -221,14 +218,14 @@
 <div class="sourceCode" id="cb8"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/plot.html">plot</a></span>(<span class="no">m.L1.FOMC</span>, <span class="kw">show_errmin</span> <span class="kw">=</span> <span class="fl">TRUE</span>, <span class="kw">main</span> <span class="kw">=</span> <span class="st">"FOCUS L1 - FOMC"</span>)</pre></body></html></div>
 <p><img src="FOCUS_L_files/figure-html/unnamed-chunk-6-1.png" width="576"></p>
 <div class="sourceCode" id="cb9"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/summary.html">summary</a></span>(<span class="no">m.L1.FOMC</span>, <span class="kw">data</span> <span class="kw">=</span> <span class="fl">FALSE</span>)</pre></body></html></div>
-<pre><code>## Warning in sqrt(diag(covar)): NaNs wurden erzeugt</code></pre>
-<pre><code>## Warning in sqrt(1/diag(V)): NaNs wurden erzeugt</code></pre>
+<pre><code>## Warning in sqrt(diag(covar)): NaNs produced</code></pre>
+<pre><code>## Warning in sqrt(1/diag(V)): NaNs produced</code></pre>
 <pre><code>## Warning in cov2cor(ans$covar): diag(.) had 0 or NA entries; non-finite result is
 ## doubtful</code></pre>
 <pre><code>## mkin version used for fitting:    0.9.50.2 
 ## R version used for fitting:       4.0.0 
-## Date of fit:     Thu May 14 17:07:14 2020 
-## Date of summary: Thu May 14 17:07:14 2020 
+## Date of fit:     Wed May 27 07:05:36 2020 
+## Date of summary: Wed May 27 07:05:36 2020 
 ## 
 ## 
 ## Warning: Optimisation did not converge:
@@ -240,7 +237,7 @@
 ## 
 ## Model predictions using solution type analytical 
 ## 
-## Fitted using 380 model solutions performed in 0.081 s
+## Fitted using 899 model solutions performed in 0.204 s
 ## 
 ## Error model: Constant variance 
 ## 
@@ -264,31 +261,31 @@
 ## Results:
 ## 
 ##        AIC      BIC    logLik
-##   95.88778 99.44927 -43.94389
+##   95.88835 99.44984 -43.94418
 ## 
 ## Optimised, transformed parameters with symmetric confidence intervals:
 ##           Estimate Std. Error  Lower  Upper
-## parent_0     92.47     1.2820 89.720 95.220
-## log_alpha    16.92        NaN    NaN    NaN
-## log_beta     19.26        NaN    NaN    NaN
-## sigma         2.78     0.4501  1.814  3.745
+## parent_0     92.47     1.2800 89.730 95.220
+## log_alpha    10.58        NaN    NaN    NaN
+## log_beta     12.93        NaN    NaN    NaN
+## sigma         2.78     0.4507  1.813  3.747
 ## 
 ## Parameter correlation:
-##           parent_0 log_alpha log_beta    sigma
-## parent_0  1.000000       NaN      NaN 0.002218
-## log_alpha      NaN         1      NaN      NaN
-## log_beta       NaN       NaN        1      NaN
-## sigma     0.002218       NaN      NaN 1.000000
+##           parent_0 log_alpha log_beta   sigma
+## parent_0   1.00000       NaN      NaN 0.01452
+## log_alpha      NaN         1      NaN     NaN
+## log_beta       NaN       NaN        1     NaN
+## sigma      0.01452       NaN      NaN 1.00000
 ## 
 ## Backtransformed parameters:
 ## Confidence intervals for internally transformed parameters are asymmetric.
 ## t-test (unrealistically) based on the assumption of normal distribution
 ## for estimators of untransformed parameters.
-##           Estimate t value Pr(&gt;t)  Lower  Upper
-## parent_0 9.247e+01      NA     NA 89.720 95.220
-## alpha    2.223e+07      NA     NA     NA     NA
-## beta     2.325e+08      NA     NA     NA     NA
-## sigma    2.780e+00      NA     NA  1.814  3.745
+##           Estimate  t value    Pr(&gt;t)  Lower  Upper
+## parent_0     92.47 72.13000 1.052e-19 89.730 95.220
+## alpha     39440.00  0.02397 4.906e-01     NA     NA
+## beta     412500.00  0.02397 4.906e-01     NA     NA
+## sigma         2.78  6.00000 1.628e-05  1.813  3.747
 ## 
 ## FOCUS Chi2 error levels in percent:
 ##          err.min n.optim df
@@ -296,8 +293,8 @@
 ## parent     3.619       3  6
 ## 
 ## Estimated disappearance times:
-##        DT50  DT90 DT50back
-## parent 7.25 24.08     7.25</code></pre>
+##         DT50  DT90 DT50back
+## parent 7.249 24.08    7.249</code></pre>
 <p>We get a warning that the default optimisation algorithm <code>Port</code> did not converge, which is an indication that the model is overparameterised, <em>i.e.</em> contains too many parameters that are ill-defined as a consequence.</p>
 <p>And in fact, due to the higher number of parameters, and the lower number of degrees of freedom of the fit, the <span class="math inline">\(\chi^2\)</span> error level is actually higher for the FOMC model (3.6%) than for the SFO model (3.4%). Additionally, the parameters <code>log_alpha</code> and <code>log_beta</code> internally fitted in the model have excessive confidence intervals, that span more than 25 orders of magnitude (!) when backtransformed to the scale of <code>alpha</code> and <code>beta</code>. Also, the t-test for significant difference from zero does not indicate such a significant difference, with p-values greater than 0.1, and finally, the parameter correlation of <code>log_alpha</code> and <code>log_beta</code> is 1.000, clearly indicating that the model is overparameterised.</p>
 <p>The <span class="math inline">\(\chi^2\)</span> error levels reported in Appendix 3 and Appendix 7 to the FOCUS kinetics report are rounded to integer percentages and partly deviate by one percentage point from the results calculated by mkin. The reason for this is not known. However, mkin gives the same <span class="math inline">\(\chi^2\)</span> error levels as the kinfit package and the calculation routines of the kinfit package have been extensively compared to the results obtained by the KinGUI software, as documented in the kinfit package vignette. KinGUI was the first widely used standard package in this field. Also, the calculation of <span class="math inline">\(\chi^2\)</span> error levels was compared with KinGUII, CAKE and DegKin manager in a project sponsored by the German Umweltbundesamt <span class="citation">(Ranke 2014)</span>.</p>
@@ -335,8 +332,8 @@
 <div class="sourceCode" id="cb17"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/summary.html">summary</a></span>(<span class="no">m.L2.FOMC</span>, <span class="kw">data</span> <span class="kw">=</span> <span class="fl">FALSE</span>)</pre></body></html></div>
 <pre><code>## mkin version used for fitting:    0.9.50.2 
 ## R version used for fitting:       4.0.0 
-## Date of fit:     Thu May 14 17:07:15 2020 
-## Date of summary: Thu May 14 17:07:15 2020 
+## Date of fit:     Wed May 27 07:05:37 2020 
+## Date of summary: Wed May 27 07:05:37 2020 
 ## 
 ## Equations:
 ## d_parent/dt = - (alpha/beta) * 1/((time/beta) + 1) * parent
@@ -378,10 +375,10 @@
 ## 
 ## Parameter correlation:
 ##             parent_0  log_alpha   log_beta      sigma
-## parent_0   1.000e+00 -1.151e-01 -2.085e-01 -7.436e-09
+## parent_0   1.000e+00 -1.151e-01 -2.085e-01 -7.637e-09
 ## log_alpha -1.151e-01  1.000e+00  9.741e-01 -1.617e-07
-## log_beta  -2.085e-01  9.741e-01  1.000e+00 -1.386e-07
-## sigma     -7.436e-09 -1.617e-07 -1.386e-07  1.000e+00
+## log_beta  -2.085e-01  9.741e-01  1.000e+00 -1.387e-07
+## sigma     -7.637e-09 -1.617e-07 -1.387e-07  1.000e+00
 ## 
 ## Backtransformed parameters:
 ## Confidence intervals for internally transformed parameters are asymmetric.
@@ -414,8 +411,8 @@
 <div class="sourceCode" id="cb20"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/summary.html">summary</a></span>(<span class="no">m.L2.DFOP</span>, <span class="kw">data</span> <span class="kw">=</span> <span class="fl">FALSE</span>)</pre></body></html></div>
 <pre><code>## mkin version used for fitting:    0.9.50.2 
 ## R version used for fitting:       4.0.0 
-## Date of fit:     Thu May 14 17:07:15 2020 
-## Date of summary: Thu May 14 17:07:15 2020 
+## Date of fit:     Wed May 27 07:05:37 2020 
+## Date of summary: Wed May 27 07:05:37 2020 
 ## 
 ## Equations:
 ## d_parent/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 *
@@ -424,7 +421,7 @@
 ## 
 ## Model predictions using solution type analytical 
 ## 
-## Fitted using 572 model solutions performed in 0.131 s
+## Fitted using 572 model solutions performed in 0.132 s
 ## 
 ## Error model: Constant variance 
 ## 
@@ -455,18 +452,18 @@
 ## Optimised, transformed parameters with symmetric confidence intervals:
 ##          Estimate Std. Error      Lower     Upper
 ## parent_0  93.9500  9.998e-01    91.5900   96.3100
-## log_k1     3.1370  2.376e+03 -5615.0000 5622.0000
+## log_k1     3.1370  2.376e+03 -5616.0000 5622.0000
 ## log_k2    -1.0880  6.285e-02    -1.2370   -0.9394
 ## g_ilr     -0.2821  7.033e-02    -0.4484   -0.1158
 ## sigma      1.4140  2.886e-01     0.7314    2.0960
 ## 
 ## Parameter correlation:
 ##            parent_0     log_k1     log_k2      g_ilr      sigma
-## parent_0  1.000e+00  5.157e-07  2.376e-09  2.665e-01 -6.837e-09
-## log_k1    5.157e-07  1.000e+00  8.434e-05 -1.659e-04 -7.786e-06
-## log_k2    2.376e-09  8.434e-05  1.000e+00 -7.903e-01 -1.263e-08
-## g_ilr     2.665e-01 -1.659e-04 -7.903e-01  1.000e+00  3.248e-08
-## sigma    -6.837e-09 -7.786e-06 -1.263e-08  3.248e-08  1.000e+00
+## parent_0  1.000e+00  5.155e-07  2.371e-09  2.665e-01 -6.849e-09
+## log_k1    5.155e-07  1.000e+00  8.434e-05 -1.659e-04 -7.791e-06
+## log_k2    2.371e-09  8.434e-05  1.000e+00 -7.903e-01 -1.262e-08
+## g_ilr     2.665e-01 -1.659e-04 -7.903e-01  1.000e+00  3.241e-08
+## sigma    -6.849e-09 -7.791e-06 -1.262e-08  3.241e-08  1.000e+00
 ## 
 ## Backtransformed parameters:
 ## Confidence intervals for internally transformed parameters are asymmetric.
@@ -517,8 +514,8 @@
 <div class="sourceCode" id="cb24"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/summary.html">summary</a></span>(<span class="no">mm.L3</span><span class="kw">[[</span><span class="st">"DFOP"</span>, <span class="fl">1</span>]])</pre></body></html></div>
 <pre><code>## mkin version used for fitting:    0.9.50.2 
 ## R version used for fitting:       4.0.0 
-## Date of fit:     Thu May 14 17:07:16 2020 
-## Date of summary: Thu May 14 17:07:16 2020 
+## Date of fit:     Wed May 27 07:05:38 2020 
+## Date of summary: Wed May 27 07:05:38 2020 
 ## 
 ## Equations:
 ## d_parent/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 *
@@ -565,11 +562,11 @@
 ## 
 ## Parameter correlation:
 ##            parent_0     log_k1     log_k2      g_ilr      sigma
-## parent_0  1.000e+00  1.732e-01  2.282e-02  4.009e-01 -6.868e-07
-## log_k1    1.732e-01  1.000e+00  4.945e-01 -5.809e-01  3.175e-07
-## log_k2    2.282e-02  4.945e-01  1.000e+00 -6.812e-01  7.631e-07
-## g_ilr     4.009e-01 -5.809e-01 -6.812e-01  1.000e+00 -8.694e-07
-## sigma    -6.868e-07  3.175e-07  7.631e-07 -8.694e-07  1.000e+00
+## parent_0  1.000e+00  1.732e-01  2.282e-02  4.009e-01 -6.872e-07
+## log_k1    1.732e-01  1.000e+00  4.945e-01 -5.809e-01  3.200e-07
+## log_k2    2.282e-02  4.945e-01  1.000e+00 -6.812e-01  7.673e-07
+## g_ilr     4.009e-01 -5.809e-01 -6.812e-01  1.000e+00 -8.731e-07
+## sigma    -6.872e-07  3.200e-07  7.673e-07 -8.731e-07  1.000e+00
 ## 
 ## Backtransformed parameters:
 ## Confidence intervals for internally transformed parameters are asymmetric.
@@ -626,8 +623,8 @@
 <div class="sourceCode" id="cb29"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/summary.html">summary</a></span>(<span class="no">mm.L4</span><span class="kw">[[</span><span class="st">"SFO"</span>, <span class="fl">1</span>]], <span class="kw">data</span> <span class="kw">=</span> <span class="fl">FALSE</span>)</pre></body></html></div>
 <pre><code>## mkin version used for fitting:    0.9.50.2 
 ## R version used for fitting:       4.0.0 
-## Date of fit:     Thu May 14 17:07:16 2020 
-## Date of summary: Thu May 14 17:07:16 2020 
+## Date of fit:     Wed May 27 07:05:38 2020 
+## Date of summary: Wed May 27 07:05:38 2020 
 ## 
 ## Equations:
 ## d_parent/dt = - k_parent_sink * parent
@@ -666,9 +663,9 @@
 ## 
 ## Parameter correlation:
 ##                    parent_0 log_k_parent_sink     sigma
-## parent_0          1.000e+00         5.938e-01 3.387e-07
-## log_k_parent_sink 5.938e-01         1.000e+00 5.830e-07
-## sigma             3.387e-07         5.830e-07 1.000e+00
+## parent_0          1.000e+00         5.938e-01 3.440e-07
+## log_k_parent_sink 5.938e-01         1.000e+00 5.885e-07
+## sigma             3.440e-07         5.885e-07 1.000e+00
 ## 
 ## Backtransformed parameters:
 ## Confidence intervals for internally transformed parameters are asymmetric.
@@ -690,8 +687,8 @@
 <div class="sourceCode" id="cb31"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/summary.html">summary</a></span>(<span class="no">mm.L4</span><span class="kw">[[</span><span class="st">"FOMC"</span>, <span class="fl">1</span>]], <span class="kw">data</span> <span class="kw">=</span> <span class="fl">FALSE</span>)</pre></body></html></div>
 <pre><code>## mkin version used for fitting:    0.9.50.2 
 ## R version used for fitting:       4.0.0 
-## Date of fit:     Thu May 14 17:07:16 2020 
-## Date of summary: Thu May 14 17:07:16 2020 
+## Date of fit:     Wed May 27 07:05:38 2020 
+## Date of summary: Wed May 27 07:05:38 2020 
 ## 
 ## Equations:
 ## d_parent/dt = - (alpha/beta) * 1/((time/beta) + 1) * parent
@@ -733,10 +730,10 @@
 ## 
 ## Parameter correlation:
 ##             parent_0  log_alpha   log_beta      sigma
-## parent_0   1.000e+00 -4.696e-01 -5.543e-01 -2.456e-07
-## log_alpha -4.696e-01  1.000e+00  9.889e-01  2.169e-08
-## log_beta  -5.543e-01  9.889e-01  1.000e+00  4.910e-08
-## sigma     -2.456e-07  2.169e-08  4.910e-08  1.000e+00
+## parent_0   1.000e+00 -4.696e-01 -5.543e-01 -2.563e-07
+## log_alpha -4.696e-01  1.000e+00  9.889e-01  4.066e-08
+## log_beta  -5.543e-01  9.889e-01  1.000e+00  6.818e-08
+## sigma     -2.563e-07  4.066e-08  6.818e-08  1.000e+00
 ## 
 ## Backtransformed parameters:
 ## Confidence intervals for internally transformed parameters are asymmetric.
diff --git a/docs/articles/FOCUS_L_files/figure-html/unnamed-chunk-15-1.png b/docs/articles/FOCUS_L_files/figure-html/unnamed-chunk-15-1.png
index db54326e..2e5071d9 100644
--- a/docs/articles/FOCUS_L_files/figure-html/unnamed-chunk-15-1.png
+++ b/docs/articles/FOCUS_L_files/figure-html/unnamed-chunk-15-1.png
diff --git a/docs/articles/FOCUS_L_files/figure-html/unnamed-chunk-6-1.png b/docs/articles/FOCUS_L_files/figure-html/unnamed-chunk-6-1.png
index bfa271dd..16235059 100644
--- a/docs/articles/FOCUS_L_files/figure-html/unnamed-chunk-6-1.png
+++ b/docs/articles/FOCUS_L_files/figure-html/unnamed-chunk-6-1.png
diff --git a/docs/articles/index.html b/docs/articles/index.html
index 7b003598..6f97722c 100644
--- a/docs/articles/index.html
+++ b/docs/articles/index.html
@@ -71,7 +71,7 @@
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../index.html">mkin</a>
-        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">0.9.50.3</span>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">0.9.50.2</span>
       </span>
     </div>
 
@@ -108,9 +108,6 @@
     <li>
       <a href="../articles/web_only/NAFTA_examples.html">Example evaluation of NAFTA SOP Attachment examples</a>
     </li>
-    <li>
-      <a href="../articles/web_only/benchmarks.html">Some benchmark timings</a>
-    </li>
   </ul>
 </li>
 <li>
@@ -157,7 +154,7 @@
         <dd></dt>
         <dt><a href="web_only/NAFTA_examples.html">Evaluation of example datasets from Attachment 1 to the US EPA SOP for the NAFTA guidance</a></dt>
         <dd></dt>
-        <dt><a href="web_only/benchmarks.html">Benchmark timings for mkin</a></dt>
+        <dt><a href="web_only/benchmarks.html">Benchmark timings for mkin on various systems</a></dt>
         <dd></dt>
         <dt><a href="web_only/compiled_models.html">Performance benefit by using compiled model definitions in mkin</a></dt>
         <dd></dt>
diff --git a/docs/articles/mkin.html b/docs/articles/mkin.html
index 37b7b1a1..5f858d57 100644
--- a/docs/articles/mkin.html
+++ b/docs/articles/mkin.html
@@ -68,9 +68,6 @@
     <li>
       <a href="../articles/web_only/NAFTA_examples.html">Example evaluation of NAFTA SOP Attachment examples</a>
     </li>
-    <li>
-      <a href="../articles/web_only/benchmarks.html">Some benchmark timings</a>
-    </li>
   </ul>
 </li>
 <li>
@@ -100,10 +97,10 @@
       <h1 data-toc-skip>Introduction to mkin</h1>
                         <h4 class="author">Johannes Ranke</h4>
             
-            <h4 class="date">2020-05-14</h4>
+            <h4 class="date">2020-05-27</h4>
       
-      <small class="dont-index">Source: <a href="http://github.com/jranke/mkin/blob/master/vignettes/mkin.rmd"><code>vignettes/mkin.rmd</code></a></small>
-      <div class="hidden name"><code>mkin.rmd</code></div>
+      <small class="dont-index">Source: <a href="http://github.com/jranke/mkin/blob/master/vignettes/mkin.Rmd"><code>vignettes/mkin.Rmd</code></a></small>
+      <div class="hidden name"><code>mkin.Rmd</code></div>
 
     </div>
 
@@ -142,7 +139,7 @@
 
 <span class="co"># Plot the results separately for parent and metabolites</span>
 <span class="fu"><a href="../reference/plot.mkinfit.html">plot_sep</a></span>(<span class="no">f_SFO_SFO_SFO</span>, <span class="kw">lpos</span> <span class="kw">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span>(<span class="st">"topright"</span>, <span class="st">"bottomright"</span>, <span class="st">"bottomright"</span>))</pre></body></html></div>
-<p><img src="mkin_files/figure-html/unnamed-chunk-2-1.png" width="768"></p>
+<p><img src="../docs/articles/mkin_files/figure-html/unnamed-chunk-2-1.png" width="768"></p>
 </div>
 <div id="background" class="section level1">
 <h1 class="hasAnchor">
diff --git a/docs/articles/mkin_files/figure-html/unnamed-chunk-2-1.png b/docs/articles/mkin_files/figure-html/unnamed-chunk-2-1.png
deleted file mode 100644
index bdc067c1..00000000
--- a/docs/articles/mkin_files/figure-html/unnamed-chunk-2-1.png
+++ /dev/null
diff --git a/docs/articles/twa.html b/docs/articles/twa.html
index c231e17d..e70205f2 100644
--- a/docs/articles/twa.html
+++ b/docs/articles/twa.html
@@ -68,9 +68,6 @@
     <li>
       <a href="../articles/web_only/NAFTA_examples.html">Example evaluation of NAFTA SOP Attachment examples</a>
     </li>
-    <li>
-      <a href="../articles/web_only/benchmarks.html">Some benchmark timings</a>
-    </li>
   </ul>
 </li>
 <li>
@@ -100,10 +97,10 @@
       <h1 data-toc-skip>Calculation of time weighted average concentrations with mkin</h1>
                         <h4 class="author">Johannes Ranke</h4>
             
-            <h4 class="date">2020-05-14</h4>
+            <h4 class="date">2020-05-27</h4>
       
-      <small class="dont-index">Source: <a href="http://github.com/jranke/mkin/blob/master/vignettes/twa.rmd"><code>vignettes/twa.rmd</code></a></small>
-      <div class="hidden name"><code>twa.rmd</code></div>
+      <small class="dont-index">Source: <a href="http://github.com/jranke/mkin/blob/master/vignettes/twa.Rmd"><code>vignettes/twa.Rmd</code></a></small>
+      <div class="hidden name"><code>twa.Rmd</code></div>
 
     </div>
 
diff --git a/docs/articles/web_only/FOCUS_Z.html b/docs/articles/web_only/FOCUS_Z.html
index 3427afb6..ccbfcc86 100644
--- a/docs/articles/web_only/FOCUS_Z.html
+++ b/docs/articles/web_only/FOCUS_Z.html
@@ -68,9 +68,6 @@
     <li>
       <a href="../../articles/web_only/NAFTA_examples.html">Example evaluation of NAFTA SOP Attachment examples</a>
     </li>
-    <li>
-      <a href="../../articles/web_only/benchmarks.html">Some benchmark timings</a>
-    </li>
   </ul>
 </li>
 <li>
@@ -100,10 +97,10 @@
       <h1 data-toc-skip>Example evaluation of FOCUS dataset Z</h1>
                         <h4 class="author">Johannes Ranke</h4>
             
-            <h4 class="date">2020-05-14</h4>
+            <h4 class="date">2020-05-27</h4>
       
-      <small class="dont-index">Source: <a href="http://github.com/jranke/mkin/blob/master/vignettes/web_only/FOCUS_Z.rmd"><code>vignettes/web_only/FOCUS_Z.rmd</code></a></small>
-      <div class="hidden name"><code>FOCUS_Z.rmd</code></div>
+      <small class="dont-index">Source: <a href="http://github.com/jranke/mkin/blob/master/vignettes/web_only/FOCUS_Z.Rmd"><code>vignettes/web_only/FOCUS_Z.Rmd</code></a></small>
+      <div class="hidden name"><code>FOCUS_Z.Rmd</code></div>
 
     </div>
 
@@ -216,25 +213,25 @@
 <div class="sourceCode" id="cb33"><html><body><pre class="r"><span class="fu"><a href="../../reference/plot.mkinfit.html">plot_sep</a></span>(<span class="no">m.Z.FOCUS</span>)</pre></body></html></div>
 <p><img src="FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_6-1.png" width="700"></p>
 <div class="sourceCode" id="cb34"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/summary.html">summary</a></span>(<span class="no">m.Z.FOCUS</span>, <span class="kw">data</span> <span class="kw">=</span> <span class="fl">FALSE</span>)$<span class="no">bpar</span></pre></body></html></div>
-<pre><code>##             Estimate se_notrans t value     Pr(&gt;t)     Lower      Upper
-## Z0_0       96.838721   1.994275 48.5584 4.0283e-42 92.826878 100.850563
-## k_Z0        2.215400   0.118459 18.7019 1.0414e-23  1.989462   2.466998
-## k_Z1        0.478301   0.028257 16.9267 6.2411e-22  0.424705   0.538662
-## k_Z2        0.451623   0.042138 10.7176 1.6313e-14  0.374336   0.544867
-## k_Z3        0.058694   0.015246  3.8499 1.7804e-04  0.034809   0.098967
-## f_Z2_to_Z3  0.471510   0.058352  8.0804 9.6640e-11  0.357775   0.588283
-## sigma       3.984431   0.383402 10.3923 4.5575e-14  3.213126   4.755736</code></pre>
+<pre><code>##             Estimate se_notrans t value     Pr(&gt;t)     Lower     Upper
+## Z0_0       96.840695   1.994285 48.5591 4.0254e-42 92.828744 100.85265
+## k_Z0        2.215467   0.118463 18.7018 1.0417e-23  1.989524   2.46707
+## k_Z1        0.478325   0.028259 16.9265 6.2441e-22  0.424725   0.53869
+## k_Z2        0.451638   0.042139 10.7177 1.6309e-14  0.374346   0.54489
+## k_Z3        0.058692   0.015245  3.8498 1.7807e-04  0.034806   0.09897
+## f_Z2_to_Z3  0.471484   0.058348  8.0805 9.6599e-11  0.357736   0.58827
+## sigma       3.984431   0.383402 10.3923 4.5576e-14  3.213126   4.75574</code></pre>
 <div class="sourceCode" id="cb36"><html><body><pre class="r"><span class="fu"><a href="../../reference/endpoints.html">endpoints</a></span>(<span class="no">m.Z.FOCUS</span>)</pre></body></html></div>
 <pre><code>## $ff
 ##   Z2_Z3 Z2_sink 
-## 0.47151 0.52849 
+## 0.47148 0.52852 
 ## 
 ## $distimes
 ##        DT50    DT90
-## Z0  0.31288  1.0394
-## Z1  1.44919  4.8141
-## Z2  1.53479  5.0985
-## Z3 11.80955 39.2305</code></pre>
+## Z0  0.31287  1.0393
+## Z1  1.44911  4.8138
+## Z2  1.53474  5.0983
+## Z3 11.80989 39.2316</code></pre>
 <p>This fit corresponds to the final result chosen in Appendix 7 of the FOCUS report. Confidence intervals returned by mkin are based on internally transformed parameters, however.</p>
 </div>
 <div id="using-the-sforb-model" class="section level1">
@@ -313,11 +310,11 @@
 ## 
 ## $SFORB
 ##     Z0_b1     Z0_b2     Z3_b1     Z3_b2 
-## 2.4471358 0.0075126 0.0800073 0.0000000 
+## 2.4471337 0.0075125 0.0800071 0.0000000 
 ## 
 ## $distimes
 ##      DT50   DT90 DT50_Z0_b1 DT50_Z0_b2 DT50_Z3_b1 DT50_Z3_b2
-## Z0 0.3043 1.1848    0.28325     92.265         NA         NA
+## Z0 0.3043 1.1848    0.28325     92.266         NA         NA
 ## Z1 1.5148 5.0320         NA         NA         NA         NA
 ## Z2 1.6414 5.4526         NA         NA         NA         NA
 ## Z3     NA     NA         NA         NA     8.6636        Inf</code></pre>
diff --git a/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_10-1.png b/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_10-1.png
index d3702fb6..96738dd0 100644
--- a/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_10-1.png
+++ b/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_10-1.png
diff --git a/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_11-1.png b/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_11-1.png
index 4a6fce4f..4f3c2554 100644
--- a/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_11-1.png
+++ b/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_11-1.png
diff --git a/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_11a-1.png b/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_11a-1.png
index dd6537b7..b8c3ed26 100644
--- a/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_11a-1.png
+++ b/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_11a-1.png
diff --git a/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_11b-1.png b/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_11b-1.png
index b986c30b..132a7317 100644
--- a/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_11b-1.png
+++ b/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_11b-1.png
diff --git a/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_6-1.png b/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_6-1.png
index 47d806c0..b25bf26a 100644
--- a/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_6-1.png
+++ b/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_6-1.png
diff --git a/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_9-1.png b/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_9-1.png
index 0c698299..dd5d89cd 100644
--- a/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_9-1.png
+++ b/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_9-1.png
diff --git a/docs/articles/web_only/NAFTA_examples.html b/docs/articles/web_only/NAFTA_examples.html
index 46cb7aa5..b91e7ee7 100644
--- a/docs/articles/web_only/NAFTA_examples.html
+++ b/docs/articles/web_only/NAFTA_examples.html
@@ -68,9 +68,6 @@
     <li>
       <a href="../../articles/web_only/NAFTA_examples.html">Example evaluation of NAFTA SOP Attachment examples</a>
     </li>
-    <li>
-      <a href="../../articles/web_only/benchmarks.html">Some benchmark timings</a>
-    </li>
   </ul>
 </li>
 <li>
@@ -100,10 +97,10 @@
       <h1 data-toc-skip>Evaluation of example datasets from Attachment 1 to the US EPA SOP for the NAFTA guidance</h1>
                         <h4 class="author">Johannes Ranke</h4>
             
-            <h4 class="date">2020-05-14</h4>
+            <h4 class="date">2020-05-27</h4>
       
-      <small class="dont-index">Source: <a href="http://github.com/jranke/mkin/blob/master/vignettes/web_only/NAFTA_examples.rmd"><code>vignettes/web_only/NAFTA_examples.rmd</code></a></small>
-      <div class="hidden name"><code>NAFTA_examples.rmd</code></div>
+      <small class="dont-index">Source: <a href="http://github.com/jranke/mkin/blob/master/vignettes/web_only/NAFTA_examples.Rmd"><code>vignettes/web_only/NAFTA_examples.Rmd</code></a></small>
+      <div class="hidden name"><code>NAFTA_examples.Rmd</code></div>
 
     </div>
 
@@ -153,7 +150,7 @@
 ##          Estimate   Pr(&gt;t)   Lower    Upper
 ## parent_0 9.99e+01 1.41e-26 98.8116 101.0810
 ## k1       2.67e-02 5.05e-06  0.0243   0.0295
-## k2       2.17e-12 5.00e-01  0.0000      Inf
+## k2       2.86e-12 5.00e-01  0.0000      Inf
 ## g        6.47e-01 3.67e-06  0.6248   0.6677
 ## sigma    1.27e+00 8.91e-06  0.8395   1.6929
 ## 
@@ -162,7 +159,7 @@
 ##      DT50     DT90 DT50_rep
 ## SFO  67.7 2.25e+02 6.77e+01
 ## IORE 58.2 1.07e+03 3.22e+02
-## DFOP 55.5 5.83e+11 3.20e+11
+## DFOP 55.5 4.42e+11 2.42e+11
 ## 
 ## Representative half-life:
 ## [1] 321.51</code></pre>
@@ -201,7 +198,7 @@
 ##          Estimate   Pr(&gt;t)   Lower   Upper
 ## parent_0 9.84e+01 1.24e-27 97.8078 98.9187
 ## k1       1.55e-02 4.10e-04  0.0143  0.0167
-## k2       1.04e-11 5.00e-01  0.0000     Inf
+## k2       1.16e-11 5.00e-01  0.0000     Inf
 ## g        6.89e-01 2.92e-03  0.6626  0.7142
 ## sigma    6.48e-01 2.38e-05  0.4147  0.8813
 ## 
@@ -210,7 +207,7 @@
 ##      DT50     DT90 DT50_rep
 ## SFO  86.6 2.88e+02 8.66e+01
 ## IORE 85.5 7.17e+02 2.16e+02
-## DFOP 83.6 1.09e+11 6.67e+10
+## DFOP 83.6 9.80e+10 5.98e+10
 ## 
 ## Representative half-life:
 ## [1] 215.87</code></pre>
@@ -249,7 +246,7 @@
 ##          Estimate   Pr(&gt;t)   Lower   Upper
 ## parent_0 9.66e+01 1.57e-25 95.3476 97.8979
 ## k1       2.55e-02 7.33e-06  0.0233  0.0278
-## k2       3.88e-11 5.00e-01  0.0000     Inf
+## k2       4.90e-11 5.00e-01  0.0000     Inf
 ## g        8.61e-01 7.55e-06  0.8314  0.8867
 ## sigma    1.46e+00 6.93e-06  0.9661  1.9483
 ## 
@@ -258,7 +255,7 @@
 ##      DT50     DT90 DT50_rep
 ## SFO  38.6 1.28e+02 3.86e+01
 ## IORE 34.0 1.77e+02 5.32e+01
-## DFOP 34.1 8.42e+09 1.79e+10
+## DFOP 34.1 6.66e+09 1.41e+10
 ## 
 ## Representative half-life:
 ## [1] 53.17</code></pre>
@@ -297,7 +294,7 @@
 ##          Estimate   Pr(&gt;t)   Lower    Upper
 ## parent_0 9.89e+01 9.44e-49 95.4640 102.2573
 ## k1       1.81e-02 1.75e-01  0.0116   0.0281
-## k2       2.30e-10 5.00e-01  0.0000      Inf
+## k2       1.97e-10 5.00e-01  0.0000      Inf
 ## g        6.06e-01 2.19e-01  0.4826   0.7178
 ## sigma    7.40e+00 2.97e-15  6.0201   8.7754
 ## 
@@ -306,7 +303,7 @@
 ##      DT50     DT90 DT50_rep
 ## SFO  94.3 3.13e+02 9.43e+01
 ## IORE 96.7 1.51e+03 4.55e+02
-## DFOP 96.4 5.95e+09 3.01e+09
+## DFOP 96.4 6.97e+09 3.52e+09
 ## 
 ## Representative half-life:
 ## [1] 454.55</code></pre>
@@ -402,7 +399,7 @@
 ##          Estimate   Pr(&gt;t)  Lower  Upper
 ## parent_0 9.85e+01 2.54e-20 97.390 99.672
 ## k1       1.38e-01 3.52e-05  0.131  0.146
-## k2       6.69e-13 5.00e-01  0.000    Inf
+## k2       6.02e-13 5.00e-01  0.000    Inf
 ## g        6.52e-01 8.13e-06  0.642  0.661
 ## sigma    7.88e-01 6.13e-02  0.481  1.095
 ## 
@@ -411,7 +408,7 @@
 ##      DT50     DT90 DT50_rep
 ## SFO  16.9 5.63e+01 1.69e+01
 ## IORE 11.6 3.37e+02 1.01e+02
-## DFOP 10.5 1.86e+12 1.04e+12
+## DFOP 10.5 2.07e+12 1.15e+12
 ## 
 ## Representative half-life:
 ## [1] 101.43</code></pre>
@@ -421,11 +418,16 @@
 <h2 class="hasAnchor">
 <a href="#example-on-page-9-lower-panel" class="anchor"></a>Example on page 9, lower panel</h2>
 <div class="sourceCode" id="cb37"><html><body><pre class="r"><span class="no">p9b</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span>(<span class="no">NAFTA_SOP_Attachment</span><span class="kw">[[</span><span class="st">"p9b"</span>]])</pre></body></html></div>
+<pre><code>## Warning in sqrt(diag(covar)): NaNs produced</code></pre>
+<pre><code>## Warning in sqrt(diag(covar_notrans)): NaNs produced</code></pre>
+<pre><code>## Warning in sqrt(1/diag(V)): NaNs produced</code></pre>
+<pre><code>## Warning in cov2cor(ans$covar): diag(.) had 0 or NA entries; non-finite result is
+## doubtful</code></pre>
 <pre><code>## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</code></pre>
 <pre><code>## The half-life obtained from the IORE model may be used</code></pre>
-<div class="sourceCode" id="cb40"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/plot.html">plot</a></span>(<span class="no">p9b</span>)</pre></body></html></div>
+<div class="sourceCode" id="cb44"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/plot.html">plot</a></span>(<span class="no">p9b</span>)</pre></body></html></div>
 <p><img src="NAFTA_examples_files/figure-html/p9b-1.png" width="700"></p>
-<div class="sourceCode" id="cb41"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/print.html">print</a></span>(<span class="no">p9b</span>)</pre></body></html></div>
+<div class="sourceCode" id="cb45"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/print.html">print</a></span>(<span class="no">p9b</span>)</pre></body></html></div>
 <pre><code>## Sums of squares:
 ##      SFO     IORE     DFOP 
 ## 35.64867 23.22334 35.64867 
@@ -452,7 +454,7 @@
 ## parent_0  94.7123 1.61e-16 93.1355 96.2891
 ## k1         0.0389 1.43e-06  0.0312  0.0485
 ## k2         0.0389 6.67e-03  0.0186  0.0812
-## g          0.7742 5.00e-01  0.0000  1.0000
+## g          0.7742      NaN      NA      NA
 ## sigma      1.5957 2.50e-04  0.9135  2.2779
 ## 
 ## 
@@ -469,12 +471,12 @@
 <div id="example-on-page-10" class="section level2">
 <h2 class="hasAnchor">
 <a href="#example-on-page-10" class="anchor"></a>Example on page 10</h2>
-<div class="sourceCode" id="cb43"><html><body><pre class="r"><span class="no">p10</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span>(<span class="no">NAFTA_SOP_Attachment</span><span class="kw">[[</span><span class="st">"p10"</span>]])</pre></body></html></div>
+<div class="sourceCode" id="cb47"><html><body><pre class="r"><span class="no">p10</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span>(<span class="no">NAFTA_SOP_Attachment</span><span class="kw">[[</span><span class="st">"p10"</span>]])</pre></body></html></div>
 <pre><code>## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</code></pre>
 <pre><code>## The half-life obtained from the IORE model may be used</code></pre>
-<div class="sourceCode" id="cb46"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/plot.html">plot</a></span>(<span class="no">p10</span>)</pre></body></html></div>
+<div class="sourceCode" id="cb50"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/plot.html">plot</a></span>(<span class="no">p10</span>)</pre></body></html></div>
 <p><img src="NAFTA_examples_files/figure-html/p10-1.png" width="700"></p>
-<div class="sourceCode" id="cb47"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/print.html">print</a></span>(<span class="no">p10</span>)</pre></body></html></div>
+<div class="sourceCode" id="cb51"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/print.html">print</a></span>(<span class="no">p10</span>)</pre></body></html></div>
 <pre><code>## Sums of squares:
 ##      SFO     IORE     DFOP 
 ## 899.4089 336.4348 899.4089 
@@ -497,12 +499,12 @@
 ## sigma                   4.90 1.77e-04  2.837   6.968
 ## 
 ## $DFOP
-##          Estimate   Pr(&gt;t)   Lower   Upper
-## parent_0 101.7315 1.41e-09 91.6534 111.810
-## k1         0.0495 6.48e-04  0.0303   0.081
-## k2         0.0495 1.67e-02  0.0201   0.122
-## g          0.6634 5.00e-01  0.0000   1.000
-## sigma      8.0152 2.50e-04  4.5886  11.442
+##          Estimate   Pr(&gt;t)   Lower    Upper
+## parent_0 101.7315 1.41e-09 91.6534 111.8097
+## k1         0.0495 6.42e-04  0.0301   0.0814
+## k2         0.0495 1.66e-02  0.0200   0.1225
+## g          0.6634 5.00e-01  0.0000   1.0000
+## sigma      8.0152 2.50e-04  4.5886  11.4418
 ## 
 ## 
 ## DTx values:
@@ -522,12 +524,12 @@
 <div id="example-on-page-11" class="section level2">
 <h2 class="hasAnchor">
 <a href="#example-on-page-11" class="anchor"></a>Example on page 11</h2>
-<div class="sourceCode" id="cb49"><html><body><pre class="r"><span class="no">p11</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span>(<span class="no">NAFTA_SOP_Attachment</span><span class="kw">[[</span><span class="st">"p11"</span>]])</pre></body></html></div>
+<div class="sourceCode" id="cb53"><html><body><pre class="r"><span class="no">p11</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span>(<span class="no">NAFTA_SOP_Attachment</span><span class="kw">[[</span><span class="st">"p11"</span>]])</pre></body></html></div>
 <pre><code>## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</code></pre>
 <pre><code>## The half-life obtained from the IORE model may be used</code></pre>
-<div class="sourceCode" id="cb52"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/plot.html">plot</a></span>(<span class="no">p11</span>)</pre></body></html></div>
+<div class="sourceCode" id="cb56"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/plot.html">plot</a></span>(<span class="no">p11</span>)</pre></body></html></div>
 <p><img src="NAFTA_examples_files/figure-html/p11-1.png" width="700"></p>
-<div class="sourceCode" id="cb53"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/print.html">print</a></span>(<span class="no">p11</span>)</pre></body></html></div>
+<div class="sourceCode" id="cb57"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/print.html">print</a></span>(<span class="no">p11</span>)</pre></body></html></div>
 <pre><code>## Sums of squares:
 ##      SFO     IORE     DFOP 
 ## 579.6805 204.7932 144.7783 
@@ -565,7 +567,7 @@
 ## DFOP 4.21e+11 2.64e+12 9.56e+11
 ## 
 ## Representative half-life:
-## [1] 41148171</code></pre>
+## [1] 41148169</code></pre>
 <p>In this case, the DFOP fit reported for PestDF resulted in a negative value for the slower rate constant, which is not possible in mkin. The other results are in agreement.</p>
 </div>
 </div>
@@ -576,14 +578,14 @@
 <div id="example-on-page-12-upper-panel" class="section level2">
 <h2 class="hasAnchor">
 <a href="#example-on-page-12-upper-panel" class="anchor"></a>Example on page 12, upper panel</h2>
-<div class="sourceCode" id="cb55"><html><body><pre class="r"><span class="no">p12a</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span>(<span class="no">NAFTA_SOP_Attachment</span><span class="kw">[[</span><span class="st">"p12a"</span>]])</pre></body></html></div>
+<div class="sourceCode" id="cb59"><html><body><pre class="r"><span class="no">p12a</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span>(<span class="no">NAFTA_SOP_Attachment</span><span class="kw">[[</span><span class="st">"p12a"</span>]])</pre></body></html></div>
 <pre><code>## Warning in summary.mkinfit(x): Could not calculate correlation; no covariance
 ## matrix</code></pre>
 <pre><code>## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</code></pre>
 <pre><code>## The half-life obtained from the IORE model may be used</code></pre>
-<div class="sourceCode" id="cb59"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/plot.html">plot</a></span>(<span class="no">p12a</span>)</pre></body></html></div>
+<div class="sourceCode" id="cb63"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/plot.html">plot</a></span>(<span class="no">p12a</span>)</pre></body></html></div>
 <p><img src="NAFTA_examples_files/figure-html/p12a-1.png" width="700"></p>
-<div class="sourceCode" id="cb60"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/print.html">print</a></span>(<span class="no">p12a</span>)</pre></body></html></div>
+<div class="sourceCode" id="cb64"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/print.html">print</a></span>(<span class="no">p12a</span>)</pre></body></html></div>
 <pre><code>## Sums of squares:
 ##      SFO     IORE     DFOP 
 ## 695.4440 220.0685 695.4440 
@@ -608,8 +610,8 @@
 ## $DFOP
 ##          Estimate   Pr(&gt;t)   Lower   Upper
 ## parent_0  100.521 2.74e-10 92.2366 108.805
-## k1          0.124 5.75e-06  0.0958   0.161
-## k2          0.124 6.72e-02  0.0319   0.484
+## k1          0.124 5.74e-06  0.0958   0.161
+## k2          0.124 6.61e-02  0.0319   0.484
 ## g           0.877 5.00e-01  0.0000   1.000
 ## sigma       7.048 2.50e-04  4.0349  10.061
 ## 
@@ -626,20 +628,20 @@
 <div id="example-on-page-12-lower-panel" class="section level2">
 <h2 class="hasAnchor">
 <a href="#example-on-page-12-lower-panel" class="anchor"></a>Example on page 12, lower panel</h2>
-<div class="sourceCode" id="cb62"><html><body><pre class="r"><span class="no">p12b</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span>(<span class="no">NAFTA_SOP_Attachment</span><span class="kw">[[</span><span class="st">"p12b"</span>]])</pre></body></html></div>
-<pre><code>## Warning in sqrt(diag(covar)): NaNs wurden erzeugt</code></pre>
-<pre><code>## Warning in qt(alpha/2, rdf): NaNs wurden erzeugt</code></pre>
-<pre><code>## Warning in qt(1 - alpha/2, rdf): NaNs wurden erzeugt</code></pre>
-<pre><code>## Warning in sqrt(diag(covar_notrans)): NaNs wurden erzeugt</code></pre>
-<pre><code>## Warning in pt(abs(tval), rdf, lower.tail = FALSE): NaNs wurden erzeugt</code></pre>
-<pre><code>## Warning in sqrt(1/diag(V)): NaNs wurden erzeugt</code></pre>
+<div class="sourceCode" id="cb66"><html><body><pre class="r"><span class="no">p12b</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span>(<span class="no">NAFTA_SOP_Attachment</span><span class="kw">[[</span><span class="st">"p12b"</span>]])</pre></body></html></div>
+<pre><code>## Warning in sqrt(diag(covar)): NaNs produced</code></pre>
+<pre><code>## Warning in qt(alpha/2, rdf): NaNs produced</code></pre>
+<pre><code>## Warning in qt(1 - alpha/2, rdf): NaNs produced</code></pre>
+<pre><code>## Warning in sqrt(diag(covar_notrans)): NaNs produced</code></pre>
+<pre><code>## Warning in pt(abs(tval), rdf, lower.tail = FALSE): NaNs produced</code></pre>
+<pre><code>## Warning in sqrt(1/diag(V)): NaNs produced</code></pre>
 <pre><code>## Warning in cov2cor(ans$covar): diag(.) had 0 or NA entries; non-finite result is
 ## doubtful</code></pre>
 <pre><code>## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</code></pre>
 <pre><code>## The half-life obtained from the IORE model may be used</code></pre>
-<div class="sourceCode" id="cb72"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/plot.html">plot</a></span>(<span class="no">p12b</span>)</pre></body></html></div>
+<div class="sourceCode" id="cb76"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/plot.html">plot</a></span>(<span class="no">p12b</span>)</pre></body></html></div>
 <p><img src="NAFTA_examples_files/figure-html/p12b-1.png" width="700"></p>
-<div class="sourceCode" id="cb73"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/print.html">print</a></span>(<span class="no">p12b</span>)</pre></body></html></div>
+<div class="sourceCode" id="cb77"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/print.html">print</a></span>(<span class="no">p12b</span>)</pre></body></html></div>
 <pre><code>## Sums of squares:
 ##      SFO     IORE     DFOP 
 ## 58.90242 19.06353 58.90242 
@@ -682,12 +684,16 @@
 <div id="example-on-page-13" class="section level2">
 <h2 class="hasAnchor">
 <a href="#example-on-page-13" class="anchor"></a>Example on page 13</h2>
-<div class="sourceCode" id="cb75"><html><body><pre class="r"><span class="no">p13</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span>(<span class="no">NAFTA_SOP_Attachment</span><span class="kw">[[</span><span class="st">"p13"</span>]])</pre></body></html></div>
+<div class="sourceCode" id="cb79"><html><body><pre class="r"><span class="no">p13</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span>(<span class="no">NAFTA_SOP_Attachment</span><span class="kw">[[</span><span class="st">"p13"</span>]])</pre></body></html></div>
+<pre><code>## Warning in sqrt(diag(covar)): NaNs produced</code></pre>
+<pre><code>## Warning in sqrt(1/diag(V)): NaNs produced</code></pre>
+<pre><code>## Warning in cov2cor(ans$covar): diag(.) had 0 or NA entries; non-finite result is
+## doubtful</code></pre>
 <pre><code>## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</code></pre>
 <pre><code>## The half-life obtained from the IORE model may be used</code></pre>
-<div class="sourceCode" id="cb78"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/plot.html">plot</a></span>(<span class="no">p13</span>)</pre></body></html></div>
+<div class="sourceCode" id="cb85"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/plot.html">plot</a></span>(<span class="no">p13</span>)</pre></body></html></div>
 <p><img src="NAFTA_examples_files/figure-html/p13-1.png" width="700"></p>
-<div class="sourceCode" id="cb79"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/print.html">print</a></span>(<span class="no">p13</span>)</pre></body></html></div>
+<div class="sourceCode" id="cb86"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/print.html">print</a></span>(<span class="no">p13</span>)</pre></body></html></div>
 <pre><code>## Sums of squares:
 ##      SFO     IORE     DFOP 
 ## 174.5971 142.3951 174.5971 
@@ -712,9 +718,9 @@
 ## $DFOP
 ##          Estimate   Pr(&gt;t)    Lower    Upper
 ## parent_0 92.73500 9.25e-15 8.95e+01 9.59e+01
-## k1        0.00258 4.28e-01 1.45e-08 4.61e+02
+## k1        0.00258 4.28e-01 1.70e-08 3.92e+02
 ## k2        0.00258 3.69e-08 2.20e-03 3.03e-03
-## g         0.00442 5.00e-01 0.00e+00 1.00e+00
+## g         0.00442 5.00e-01       NA       NA
 ## sigma     3.41172 1.35e-04 2.02e+00 4.80e+00
 ## 
 ## 
@@ -731,16 +737,16 @@
 <div id="dt50-not-observed-in-the-study-and-dfop-problems-in-pestdf" class="section level1">
 <h1 class="hasAnchor">
 <a href="#dt50-not-observed-in-the-study-and-dfop-problems-in-pestdf" class="anchor"></a>DT50 not observed in the study and DFOP problems in PestDF</h1>
-<div class="sourceCode" id="cb81"><html><body><pre class="r"><span class="no">p14</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span>(<span class="no">NAFTA_SOP_Attachment</span><span class="kw">[[</span><span class="st">"p14"</span>]])</pre></body></html></div>
-<pre><code>## Warning in sqrt(diag(covar)): NaNs wurden erzeugt</code></pre>
-<pre><code>## Warning in sqrt(1/diag(V)): NaNs wurden erzeugt</code></pre>
+<div class="sourceCode" id="cb88"><html><body><pre class="r"><span class="no">p14</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span>(<span class="no">NAFTA_SOP_Attachment</span><span class="kw">[[</span><span class="st">"p14"</span>]])</pre></body></html></div>
+<pre><code>## Warning in sqrt(diag(covar)): NaNs produced</code></pre>
+<pre><code>## Warning in sqrt(1/diag(V)): NaNs produced</code></pre>
 <pre><code>## Warning in cov2cor(ans$covar): diag(.) had 0 or NA entries; non-finite result is
 ## doubtful</code></pre>
 <pre><code>## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</code></pre>
 <pre><code>## The half-life obtained from the IORE model may be used</code></pre>
-<div class="sourceCode" id="cb87"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/plot.html">plot</a></span>(<span class="no">p14</span>)</pre></body></html></div>
+<div class="sourceCode" id="cb94"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/plot.html">plot</a></span>(<span class="no">p14</span>)</pre></body></html></div>
 <p><img src="NAFTA_examples_files/figure-html/p14-1.png" width="700"></p>
-<div class="sourceCode" id="cb88"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/print.html">print</a></span>(<span class="no">p14</span>)</pre></body></html></div>
+<div class="sourceCode" id="cb95"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/print.html">print</a></span>(<span class="no">p14</span>)</pre></body></html></div>
 <pre><code>## Sums of squares:
 ##      SFO     IORE     DFOP 
 ## 48.43249 28.67746 27.26248 
@@ -766,7 +772,7 @@
 ##          Estimate   Pr(&gt;t)    Lower    Upper
 ## parent_0 1.00e+02 2.96e-28 99.40280 101.2768
 ## k1       9.53e-03 1.20e-01  0.00638   0.0143
-## k2       7.70e-12 5.00e-01  0.00000      Inf
+## k2       7.29e-12 5.00e-01  0.00000      Inf
 ## g        3.98e-01 2.19e-01  0.30481   0.4998
 ## sigma    1.17e+00 7.68e-06  0.77406   1.5610
 ## 
@@ -775,7 +781,7 @@
 ##          DT50     DT90 DT50_rep
 ## SFO  2.48e+02 8.25e+02 2.48e+02
 ## IORE 4.34e+02 2.22e+04 6.70e+03
-## DFOP 2.41e+10 2.33e+11 9.00e+10
+## DFOP 2.54e+10 2.46e+11 9.51e+10
 ## 
 ## Representative half-life:
 ## [1] 6697.44</code></pre>
@@ -784,16 +790,17 @@
 <div id="n-is-less-than-1-and-dfop-fraction-parameter-is-below-zero" class="section level1">
 <h1 class="hasAnchor">
 <a href="#n-is-less-than-1-and-dfop-fraction-parameter-is-below-zero" class="anchor"></a>N is less than 1 and DFOP fraction parameter is below zero</h1>
-<div class="sourceCode" id="cb90"><html><body><pre class="r"><span class="no">p15a</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span>(<span class="no">NAFTA_SOP_Attachment</span><span class="kw">[[</span><span class="st">"p15a"</span>]])</pre></body></html></div>
-<pre><code>## Warning in sqrt(diag(covar)): NaNs wurden erzeugt</code></pre>
-<pre><code>## Warning in sqrt(1/diag(V)): NaNs wurden erzeugt</code></pre>
+<div class="sourceCode" id="cb97"><html><body><pre class="r"><span class="no">p15a</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span>(<span class="no">NAFTA_SOP_Attachment</span><span class="kw">[[</span><span class="st">"p15a"</span>]])</pre></body></html></div>
+<pre><code>## Warning in sqrt(diag(covar)): NaNs produced</code></pre>
+<pre><code>## Warning in sqrt(diag(covar_notrans)): NaNs produced</code></pre>
+<pre><code>## Warning in sqrt(1/diag(V)): NaNs produced</code></pre>
 <pre><code>## Warning in cov2cor(ans$covar): diag(.) had 0 or NA entries; non-finite result is
 ## doubtful</code></pre>
 <pre><code>## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</code></pre>
 <pre><code>## The half-life obtained from the IORE model may be used</code></pre>
-<div class="sourceCode" id="cb96"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/plot.html">plot</a></span>(<span class="no">p15a</span>)</pre></body></html></div>
+<div class="sourceCode" id="cb104"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/plot.html">plot</a></span>(<span class="no">p15a</span>)</pre></body></html></div>
 <p><img src="NAFTA_examples_files/figure-html/p15a-1.png" width="700"></p>
-<div class="sourceCode" id="cb97"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/print.html">print</a></span>(<span class="no">p15a</span>)</pre></body></html></div>
+<div class="sourceCode" id="cb105"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/print.html">print</a></span>(<span class="no">p15a</span>)</pre></body></html></div>
 <pre><code>## Sums of squares:
 ##      SFO     IORE     DFOP 
 ## 245.5248 135.0132 245.5248 
@@ -816,12 +823,12 @@
 ## sigma                  3.105 1.78e-04  1.795  4.416
 ## 
 ## $DFOP
-##          Estimate Pr(&gt;t)    Lower    Upper
-## parent_0 97.96752     NA 94.21914 101.7159
-## k1        0.00952     NA  0.00241   0.0377
-## k2        0.00952     NA  0.00747   0.0121
-## g         0.17247     NA       NA       NA
-## sigma     4.18778     NA  2.39747   5.9781
+##          Estimate   Pr(&gt;t)    Lower    Upper
+## parent_0 97.96752 2.85e-13 94.21914 101.7159
+## k1        0.00952 6.80e-02  0.00277   0.0327
+## k2        0.00952 3.82e-06  0.00902   0.0100
+## g         0.17247      NaN       NA       NA
+## sigma     4.18778 2.50e-04  2.39747   5.9781
 ## 
 ## 
 ## DTx values:
@@ -832,16 +839,16 @@
 ## 
 ## Representative half-life:
 ## [1] 41.33</code></pre>
-<div class="sourceCode" id="cb99"><html><body><pre class="r"><span class="no">p15b</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span>(<span class="no">NAFTA_SOP_Attachment</span><span class="kw">[[</span><span class="st">"p15b"</span>]])</pre></body></html></div>
-<pre><code>## Warning in sqrt(diag(covar)): NaNs wurden erzeugt</code></pre>
-<pre><code>## Warning in sqrt(1/diag(V)): NaNs wurden erzeugt</code></pre>
+<div class="sourceCode" id="cb107"><html><body><pre class="r"><span class="no">p15b</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span>(<span class="no">NAFTA_SOP_Attachment</span><span class="kw">[[</span><span class="st">"p15b"</span>]])</pre></body></html></div>
+<pre><code>## Warning in sqrt(diag(covar)): NaNs produced</code></pre>
+<pre><code>## Warning in sqrt(1/diag(V)): NaNs produced</code></pre>
 <pre><code>## Warning in cov2cor(ans$covar): diag(.) had 0 or NA entries; non-finite result is
 ## doubtful</code></pre>
 <pre><code>## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</code></pre>
 <pre><code>## The half-life obtained from the IORE model may be used</code></pre>
-<div class="sourceCode" id="cb105"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/plot.html">plot</a></span>(<span class="no">p15b</span>)</pre></body></html></div>
+<div class="sourceCode" id="cb113"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/plot.html">plot</a></span>(<span class="no">p15b</span>)</pre></body></html></div>
 <p><img src="NAFTA_examples_files/figure-html/p15b-1.png" width="700"></p>
-<div class="sourceCode" id="cb106"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/print.html">print</a></span>(<span class="no">p15b</span>)</pre></body></html></div>
+<div class="sourceCode" id="cb114"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/print.html">print</a></span>(<span class="no">p15b</span>)</pre></body></html></div>
 <pre><code>## Sums of squares:
 ##       SFO      IORE      DFOP 
 ## 106.91629  68.55574 106.91629 
@@ -858,18 +865,18 @@
 ## 
 ## $IORE
 ##                     Estimate   Pr(&gt;t)    Lower  Upper
-## parent_0               99.83 1.81e-16 97.51348 102.14
+## parent_0               99.83 1.81e-16 97.51349 102.14
 ## k__iore_parent_sink     0.38 3.22e-01  0.00352  41.05
-## N_parent                0.00 5.00e-01 -1.07696   1.08
+## N_parent                0.00 5.00e-01 -1.07695   1.08
 ## sigma                   2.21 2.57e-04  1.23245   3.19
 ## 
 ## $DFOP
 ##          Estimate Pr(&gt;t)    Lower    Upper
-## parent_0 1.01e+02     NA 98.24464 1.04e+02
-## k1       4.86e-03     NA  0.00068 3.47e-02
-## k2       4.86e-03     NA  0.00338 6.99e-03
+## parent_0 1.01e+02     NA 9.82e+01 1.04e+02
+## k1       4.86e-03     NA 6.75e-04 3.49e-02
+## k2       4.86e-03     NA 3.37e-03 6.99e-03
 ## g        1.50e-01     NA       NA       NA
-## sigma    2.76e+00     NA  1.58208 3.94e+00
+## sigma    2.76e+00     NA 1.58e+00 3.94e+00
 ## 
 ## 
 ## DTx values:
@@ -885,14 +892,14 @@
 <div id="the-dfop-fraction-parameter-is-greater-than-1" class="section level1">
 <h1 class="hasAnchor">
 <a href="#the-dfop-fraction-parameter-is-greater-than-1" class="anchor"></a>The DFOP fraction parameter is greater than 1</h1>
-<div class="sourceCode" id="cb108"><html><body><pre class="r"><span class="no">p16</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span>(<span class="no">NAFTA_SOP_Attachment</span><span class="kw">[[</span><span class="st">"p16"</span>]])</pre></body></html></div>
+<div class="sourceCode" id="cb116"><html><body><pre class="r"><span class="no">p16</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span>(<span class="no">NAFTA_SOP_Attachment</span><span class="kw">[[</span><span class="st">"p16"</span>]])</pre></body></html></div>
 <pre><code>## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</code></pre>
 <pre><code>## The representative half-life of the IORE model is longer than the one corresponding</code></pre>
 <pre><code>## to the terminal degradation rate found with the DFOP model.</code></pre>
 <pre><code>## The representative half-life obtained from the DFOP model may be used</code></pre>
-<div class="sourceCode" id="cb113"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/plot.html">plot</a></span>(<span class="no">p16</span>)</pre></body></html></div>
+<div class="sourceCode" id="cb121"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/plot.html">plot</a></span>(<span class="no">p16</span>)</pre></body></html></div>
 <p><img src="NAFTA_examples_files/figure-html/p16-1.png" width="700"></p>
-<div class="sourceCode" id="cb114"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/print.html">print</a></span>(<span class="no">p16</span>)</pre></body></html></div>
+<div class="sourceCode" id="cb122"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/print.html">print</a></span>(<span class="no">p16</span>)</pre></body></html></div>
 <pre><code>## Sums of squares:
 ##      SFO     IORE     DFOP 
 ## 3831.804 2062.008 1550.980 
@@ -917,7 +924,7 @@
 ## $DFOP
 ##          Estimate   Pr(&gt;t)   Lower  Upper
 ## parent_0  88.5333 7.40e-18 79.9836 97.083
-## k1        18.5560 5.00e-01  0.0000    Inf
+## k1        18.5561 5.00e-01  0.0000    Inf
 ## k2         0.0776 1.41e-05  0.0518  0.116
 ## g          0.4733 1.41e-09  0.3674  0.582
 ## sigma      7.1902 2.11e-08  5.2785  9.102
diff --git a/docs/articles/web_only/benchmarks.html b/docs/articles/web_only/benchmarks.html
index 97e22303..0698baf6 100644
--- a/docs/articles/web_only/benchmarks.html
+++ b/docs/articles/web_only/benchmarks.html
@@ -5,13 +5,13 @@
 <meta charset="utf-8">
 <meta http-equiv="X-UA-Compatible" content="IE=edge">
 <meta name="viewport" content="width=device-width, initial-scale=1.0">
-<title>Benchmark timings for mkin • mkin</title>
+<title>Benchmark timings for mkin on various systems • mkin</title>
 <!-- jquery --><script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/3.4.1/jquery.min.js" integrity="sha256-CSXorXvZcTkaix6Yvo6HppcZGetbYMGWSFlBw8HfCJo=" crossorigin="anonymous"></script><!-- Bootstrap --><link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/twitter-bootstrap/3.4.1/css/bootstrap.min.css" integrity="sha256-bZLfwXAP04zRMK2BjiO8iu9pf4FbLqX6zitd+tIvLhE=" crossorigin="anonymous">
 <script src="https://cdnjs.cloudflare.com/ajax/libs/twitter-bootstrap/3.4.1/js/bootstrap.min.js" integrity="sha256-nuL8/2cJ5NDSSwnKD8VqreErSWHtnEP9E7AySL+1ev4=" crossorigin="anonymous"></script><!-- bootstrap-toc --><link rel="stylesheet" href="../../bootstrap-toc.css">
 <script src="../../bootstrap-toc.js"></script><!-- Font Awesome icons --><link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.12.1/css/all.min.css" integrity="sha256-mmgLkCYLUQbXn0B1SRqzHar6dCnv9oZFPEC1g1cwlkk=" crossorigin="anonymous">
 <link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.12.1/css/v4-shims.min.css" integrity="sha256-wZjR52fzng1pJHwx4aV2AO3yyTOXrcDW7jBpJtTwVxw=" crossorigin="anonymous">
 <!-- clipboard.js --><script src="https://cdnjs.cloudflare.com/ajax/libs/clipboard.js/2.0.6/clipboard.min.js" integrity="sha256-inc5kl9MA1hkeYUt+EC3BhlIgyp/2jDIyBLS6k3UxPI=" crossorigin="anonymous"></script><!-- headroom.js --><script src="https://cdnjs.cloudflare.com/ajax/libs/headroom/0.11.0/headroom.min.js" integrity="sha256-AsUX4SJE1+yuDu5+mAVzJbuYNPHj/WroHuZ8Ir/CkE0=" crossorigin="anonymous"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/headroom/0.11.0/jQuery.headroom.min.js" integrity="sha256-ZX/yNShbjqsohH1k95liqY9Gd8uOiE1S4vZc+9KQ1K4=" crossorigin="anonymous"></script><!-- pkgdown --><link href="../../pkgdown.css" rel="stylesheet">
-<script src="../../pkgdown.js"></script><meta property="og:title" content="Benchmark timings for mkin">
+<script src="../../pkgdown.js"></script><meta property="og:title" content="Benchmark timings for mkin on various systems">
 <meta property="og:description" content="mkin">
 <!-- mathjax --><script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/MathJax.js" integrity="sha256-nvJJv9wWKEm88qvoQl9ekL2J+k/RWIsaSScxxlsrv8k=" crossorigin="anonymous"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/config/TeX-AMS-MML_HTMLorMML.js" integrity="sha256-84DKXVJXs0/F8OTMzX4UR909+jtl4G7SPypPavF+GfA=" crossorigin="anonymous"></script><!--[if lt IE 9]>
 <script src="https://oss.maxcdn.com/html5shiv/3.7.3/html5shiv.min.js"></script>
@@ -68,9 +68,6 @@
     <li>
       <a href="../../articles/web_only/NAFTA_examples.html">Example evaluation of NAFTA SOP Attachment examples</a>
     </li>
-    <li>
-      <a href="../../articles/web_only/benchmarks.html">Some benchmark timings</a>
-    </li>
   </ul>
 </li>
 <li>
@@ -97,47 +94,60 @@
       </header><div class="row">
   <div class="col-md-9 contents">
     <div class="page-header toc-ignore">
-      <h1 data-toc-skip>Benchmark timings for mkin</h1>
+      <h1 data-toc-skip>Benchmark timings for mkin on various systems</h1>
                         <h4 class="author">Johannes Ranke</h4>
             
-            <h4 class="date">2020-05-14</h4>
+            <h4 class="date">2020-05-27</h4>
       
-      <small class="dont-index">Source: <a href="http://github.com/jranke/mkin/blob/master/vignettes/web_only/benchmarks.rmd"><code>vignettes/web_only/benchmarks.rmd</code></a></small>
-      <div class="hidden name"><code>benchmarks.rmd</code></div>
+      <small class="dont-index">Source: <a href="http://github.com/jranke/mkin/blob/master/vignettes/web_only/benchmarks.Rmd"><code>vignettes/web_only/benchmarks.Rmd</code></a></small>
+      <div class="hidden name"><code>benchmarks.Rmd</code></div>
 
     </div>
 
     
     
-<p>Each system is characterized by its CPU type, the operating system type and the mkin version. Currently only values for one system are available. A compiler was available, so if no analytical solution was available, compiled ODE models are used.</p>
-<div id="test-cases" class="section level2">
+<div id="systems" class="section level2">
 <h2 class="hasAnchor">
-<a href="#test-cases" class="anchor"></a>Test cases</h2>
-<p>Parent only:</p>
-<div class="sourceCode" id="cb1"><html><body><pre class="r"><span class="no">FOCUS_C</span> <span class="kw">&lt;-</span> <span class="no">FOCUS_2006_C</span>
-<span class="no">FOCUS_D</span> <span class="kw">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/subset.html">subset</a></span>(<span class="no">FOCUS_2006_D</span>, <span class="no">value</span> <span class="kw">!=</span> <span class="fl">0</span>)
-<span class="no">parent_datasets</span> <span class="kw">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span>(<span class="no">FOCUS_C</span>, <span class="no">FOCUS_D</span>)
+<a href="#systems" class="anchor"></a>Systems</h2>
+<p>Each system is characterized by its CPU type, the operating system type and the mkin version.</p>
+<div class="sourceCode" id="cb1"><html><body><pre class="r"><span class="no">cpu_model</span> <span class="kw">&lt;-</span> <span class="kw pkg">benchmarkme</span><span class="kw ns">::</span><span class="fu"><a href="https://rdrr.io/pkg/benchmarkme/man/get_cpu.html">get_cpu</a></span>()$<span class="no">model_name</span>
+<span class="no">operating_system</span> <span class="kw">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/Sys.info.html">Sys.info</a></span>()<span class="kw">[[</span><span class="st">"sysname"</span>]]
+<span class="no">mkin_version</span> <span class="kw">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/character.html">as.character</a></span>(<span class="fu"><a href="https://rdrr.io/r/utils/packageDescription.html">packageVersion</a></span>(<span class="st">"mkin"</span>))
+<span class="no">system_string</span> <span class="kw">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/paste.html">paste0</a></span>(<span class="no">operating_system</span>, <span class="st">", "</span>, <span class="no">cpu_model</span>, <span class="st">", mkin version "</span>, <span class="no">mkin_version</span>)
+<span class="fu"><a href="https://rdrr.io/r/base/load.html">load</a></span>(<span class="st">"~/git/mkin/vignettes/web_only/mkin_benchmarks.rda"</span>)
+<span class="no">mkin_benchmarks</span>[<span class="no">system_string</span>, <span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span>(<span class="st">"CPU"</span>, <span class="st">"OS"</span>, <span class="st">"mkin"</span>)] <span class="kw">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span>(<span class="no">cpu_model</span>, <span class="no">operating_system</span>, <span class="no">mkin_version</span>)
 
-<span class="no">t1</span> <span class="kw">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/system.time.html">system.time</a></span>(<span class="fu">mmkin_bench</span>(<span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span>(<span class="st">"SFO"</span>, <span class="st">"FOMC"</span>, <span class="st">"DFOP"</span>, <span class="st">"HS"</span>), <span class="no">parent_datasets</span>))<span class="kw">[[</span><span class="st">"elapsed"</span>]]
-<span class="no">t2</span> <span class="kw">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/system.time.html">system.time</a></span>(<span class="fu">mmkin_bench</span>(<span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span>(<span class="st">"SFO"</span>, <span class="st">"FOMC"</span>, <span class="st">"DFOP"</span>, <span class="st">"HS"</span>), <span class="no">parent_datasets</span>,
-    <span class="kw">error_model</span> <span class="kw">=</span> <span class="st">"tc"</span>))<span class="kw">[[</span><span class="st">"elapsed"</span>]]</pre></body></html></div>
-<p>One metabolite:</p>
-<div class="sourceCode" id="cb2"><html><body><pre class="r"><span class="no">SFO_SFO</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span>(
+<span class="kw">if</span> (<span class="no">mkin_version</span> <span class="kw">&gt;</span> <span class="st">"0.9.48.1"</span>) {
+  <span class="no">mmkin_bench</span> <span class="kw">&lt;-</span> <span class="kw">function</span>(<span class="no">models</span>, <span class="no">datasets</span>, <span class="no">error_model</span> <span class="kw">=</span> <span class="st">"const"</span>) <span class="fu"><a href="../../reference/mmkin.html">mmkin</a></span>(<span class="no">models</span>, <span class="no">datasets</span>, <span class="kw">error_model</span> <span class="kw">=</span> <span class="no">error_model</span>, <span class="kw">cores</span> <span class="kw">=</span> <span class="fl">1</span>, <span class="kw">quiet</span> <span class="kw">=</span> <span class="fl">TRUE</span>)
+} <span class="kw">else</span> {
+  <span class="no">mmkin_bench</span> <span class="kw">&lt;-</span> <span class="kw">function</span>(<span class="no">models</span>, <span class="no">datasets</span>, <span class="no">error_model</span> <span class="kw">=</span> <span class="kw">NULL</span>) <span class="fu"><a href="../../reference/mmkin.html">mmkin</a></span>(<span class="no">models</span>, <span class="no">datasets</span>, <span class="kw">reweight.method</span> <span class="kw">=</span> <span class="no">error_model</span>, <span class="kw">cores</span> <span class="kw">=</span> <span class="fl">1</span>, <span class="kw">quiet</span> <span class="kw">=</span> <span class="fl">TRUE</span>)
+}</pre></body></html></div>
+<div class="sourceCode" id="cb2"><html><body><pre class="r"><span class="no">FOCUS_C</span> <span class="kw">&lt;-</span> <span class="no">FOCUS_2006_C</span>
+<span class="no">FOCUS_D</span> <span class="kw">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/subset.html">subset</a></span>(<span class="no">FOCUS_2006_D</span>, <span class="no">value</span> <span class="kw">!=</span> <span class="fl">0</span>)
+<span class="co"># Parent only</span>
+<span class="no">t1</span> <span class="kw">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/system.time.html">system.time</a></span>(<span class="fu">mmkin_bench</span>(<span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span>(<span class="st">"SFO"</span>, <span class="st">"FOMC"</span>, <span class="st">"DFOP"</span>, <span class="st">"HS"</span>), <span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span>(<span class="no">FOCUS_C</span>, <span class="no">FOCUS_D</span>)))<span class="kw">[[</span><span class="st">"elapsed"</span>]]
+<span class="no">t2</span> <span class="kw">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/system.time.html">system.time</a></span>(<span class="fu">mmkin_bench</span>(<span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span>(<span class="st">"SFO"</span>, <span class="st">"FOMC"</span>, <span class="st">"DFOP"</span>, <span class="st">"HS"</span>), <span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span>(<span class="no">FOCUS_C</span>, <span class="no">FOCUS_D</span>), <span class="kw">error_model</span> <span class="kw">=</span> <span class="st">"tc"</span>))<span class="kw">[[</span><span class="st">"elapsed"</span>]]</pre></body></html></div>
+<pre><code>## Warning in mkinfit(models[[model_index]], datasets[[dataset_index]], ...): Optimisation did not converge:
+## iteration limit reached without convergence (10)</code></pre>
+<div class="sourceCode" id="cb4"><html><body><pre class="r"><span class="co"># One metabolite</span>
+<span class="no">SFO_SFO</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span>(
   <span class="kw">parent</span> <span class="kw">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>, <span class="st">"m1"</span>),
-  <span class="kw">m1</span> <span class="kw">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>))
-<span class="no">FOMC_SFO</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span>(
+  <span class="kw">m1</span> <span class="kw">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>))</pre></body></html></div>
+<pre><code>## Successfully compiled differential equation model from auto-generated C code.</code></pre>
+<div class="sourceCode" id="cb6"><html><body><pre class="r"><span class="no">FOMC_SFO</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span>(
   <span class="kw">parent</span> <span class="kw">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"FOMC"</span>, <span class="st">"m1"</span>),
-  <span class="kw">m1</span> <span class="kw">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>))
-<span class="no">DFOP_SFO</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span>(
+  <span class="kw">m1</span> <span class="kw">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>))</pre></body></html></div>
+<pre><code>## Successfully compiled differential equation model from auto-generated C code.</code></pre>
+<div class="sourceCode" id="cb8"><html><body><pre class="r"><span class="no">DFOP_SFO</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span>(
   <span class="kw">parent</span> <span class="kw">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"FOMC"</span>, <span class="st">"m1"</span>),
-  <span class="kw">m1</span> <span class="kw">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>))
-<span class="no">t3</span> <span class="kw">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/system.time.html">system.time</a></span>(<span class="fu">mmkin_bench</span>(<span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span>(<span class="no">SFO_SFO</span>, <span class="no">FOMC_SFO</span>, <span class="no">DFOP_SFO</span>), <span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span>(<span class="no">FOCUS_D</span>)))<span class="kw">[[</span><span class="st">"elapsed"</span>]]
-<span class="no">t4</span> <span class="kw">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/system.time.html">system.time</a></span>(<span class="fu">mmkin_bench</span>(<span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span>(<span class="no">SFO_SFO</span>, <span class="no">FOMC_SFO</span>, <span class="no">DFOP_SFO</span>), <span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span>(<span class="no">FOCUS_D</span>),
-    <span class="kw">error_model</span> <span class="kw">=</span> <span class="st">"tc"</span>))<span class="kw">[[</span><span class="st">"elapsed"</span>]]
-<span class="no">t5</span> <span class="kw">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/system.time.html">system.time</a></span>(<span class="fu">mmkin_bench</span>(<span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span>(<span class="no">SFO_SFO</span>, <span class="no">FOMC_SFO</span>, <span class="no">DFOP_SFO</span>), <span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span>(<span class="no">FOCUS_D</span>),
-    <span class="kw">error_model</span> <span class="kw">=</span> <span class="st">"obs"</span>))<span class="kw">[[</span><span class="st">"elapsed"</span>]]</pre></body></html></div>
-<p>Two metabolites, synthetic data:</p>
-<div class="sourceCode" id="cb3"><html><body><pre class="r"><span class="no">m_synth_SFO_lin</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span>(<span class="kw">parent</span> <span class="kw">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>, <span class="st">"M1"</span>),
+  <span class="kw">m1</span> <span class="kw">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>))</pre></body></html></div>
+<pre><code>## Successfully compiled differential equation model from auto-generated C code.</code></pre>
+<div class="sourceCode" id="cb10"><html><body><pre class="r"><span class="no">t3</span> <span class="kw">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/system.time.html">system.time</a></span>(<span class="fu">mmkin_bench</span>(<span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span>(<span class="no">SFO_SFO</span>, <span class="no">FOMC_SFO</span>, <span class="no">DFOP_SFO</span>), <span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span>(<span class="no">FOCUS_D</span>)))<span class="kw">[[</span><span class="st">"elapsed"</span>]]
+<span class="no">t4</span> <span class="kw">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/system.time.html">system.time</a></span>(<span class="fu">mmkin_bench</span>(<span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span>(<span class="no">SFO_SFO</span>, <span class="no">FOMC_SFO</span>, <span class="no">DFOP_SFO</span>), <span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span>(<span class="no">FOCUS_D</span>), <span class="kw">error_model</span> <span class="kw">=</span> <span class="st">"tc"</span>))<span class="kw">[[</span><span class="st">"elapsed"</span>]]
+<span class="no">t5</span> <span class="kw">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/system.time.html">system.time</a></span>(<span class="fu">mmkin_bench</span>(<span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span>(<span class="no">SFO_SFO</span>, <span class="no">FOMC_SFO</span>, <span class="no">DFOP_SFO</span>), <span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span>(<span class="no">FOCUS_D</span>), <span class="kw">error_model</span> <span class="kw">=</span> <span class="st">"obs"</span>))<span class="kw">[[</span><span class="st">"elapsed"</span>]]
+
+<span class="co"># Two metabolites, synthetic data</span>
+<span class="no">m_synth_SFO_lin</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span>(<span class="kw">parent</span> <span class="kw">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>, <span class="st">"M1"</span>),
                            <span class="kw">M1</span> <span class="kw">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>, <span class="st">"M2"</span>),
                            <span class="kw">M2</span> <span class="kw">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>),
                            <span class="kw">use_of_ff</span> <span class="kw">=</span> <span class="st">"max"</span>, <span class="kw">quiet</span> <span class="kw">=</span> <span class="fl">TRUE</span>)
@@ -151,194 +161,81 @@
 
 <span class="no">DFOP_par_c</span> <span class="kw">&lt;-</span> <span class="no">synthetic_data_for_UBA_2014</span><span class="kw">[[</span><span class="fl">12</span>]]$<span class="no">data</span>
 
-<span class="no">t6</span> <span class="kw">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/system.time.html">system.time</a></span>(<span class="fu">mmkin_bench</span>(<span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span>(<span class="no">m_synth_SFO_lin</span>), <span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span>(<span class="no">SFO_lin_a</span>)))<span class="kw">[[</span><span class="st">"elapsed"</span>]]
-<span class="no">t7</span> <span class="kw">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/system.time.html">system.time</a></span>(<span class="fu">mmkin_bench</span>(<span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span>(<span class="no">m_synth_DFOP_par</span>), <span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span>(<span class="no">DFOP_par_c</span>)))<span class="kw">[[</span><span class="st">"elapsed"</span>]]
+<span class="no">t6</span> <span class="kw">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/system.time.html">system.time</a></span>(<span class="fu">mmkin_bench</span>(<span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span>(<span class="no">m_synth_SFO_lin</span>), <span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span>(<span class="no">SFO_lin_a</span>)))[<span class="st">"elapsed"</span>]
+<span class="no">t7</span> <span class="kw">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/system.time.html">system.time</a></span>(<span class="fu">mmkin_bench</span>(<span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span>(<span class="no">m_synth_DFOP_par</span>), <span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span>(<span class="no">DFOP_par_c</span>)))[<span class="st">"elapsed"</span>]
 
-<span class="no">t8</span> <span class="kw">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/system.time.html">system.time</a></span>(<span class="fu">mmkin_bench</span>(<span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span>(<span class="no">m_synth_SFO_lin</span>), <span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span>(<span class="no">SFO_lin_a</span>),
-    <span class="kw">error_model</span> <span class="kw">=</span> <span class="st">"tc"</span>))<span class="kw">[[</span><span class="st">"elapsed"</span>]]
-<span class="no">t9</span> <span class="kw">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/system.time.html">system.time</a></span>(<span class="fu">mmkin_bench</span>(<span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span>(<span class="no">m_synth_DFOP_par</span>), <span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span>(<span class="no">DFOP_par_c</span>),
-    <span class="kw">error_model</span> <span class="kw">=</span> <span class="st">"tc"</span>))<span class="kw">[[</span><span class="st">"elapsed"</span>]]
+<span class="no">t8</span> <span class="kw">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/system.time.html">system.time</a></span>(<span class="fu">mmkin_bench</span>(<span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span>(<span class="no">m_synth_SFO_lin</span>), <span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span>(<span class="no">SFO_lin_a</span>), <span class="kw">error_model</span> <span class="kw">=</span> <span class="st">"tc"</span>))[<span class="st">"elapsed"</span>]
+<span class="no">t9</span> <span class="kw">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/system.time.html">system.time</a></span>(<span class="fu">mmkin_bench</span>(<span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span>(<span class="no">m_synth_DFOP_par</span>), <span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span>(<span class="no">DFOP_par_c</span>), <span class="kw">error_model</span> <span class="kw">=</span> <span class="st">"tc"</span>))[<span class="st">"elapsed"</span>]
 
-<span class="no">t10</span> <span class="kw">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/system.time.html">system.time</a></span>(<span class="fu">mmkin_bench</span>(<span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span>(<span class="no">m_synth_SFO_lin</span>), <span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span>(<span class="no">SFO_lin_a</span>),
-    <span class="kw">error_model</span> <span class="kw">=</span> <span class="st">"obs"</span>))<span class="kw">[[</span><span class="st">"elapsed"</span>]]
-<span class="no">t11</span> <span class="kw">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/system.time.html">system.time</a></span>(<span class="fu">mmkin_bench</span>(<span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span>(<span class="no">m_synth_DFOP_par</span>), <span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span>(<span class="no">DFOP_par_c</span>),
-    <span class="kw">error_model</span> <span class="kw">=</span> <span class="st">"obs"</span>))<span class="kw">[[</span><span class="st">"elapsed"</span>]]</pre></body></html></div>
-<div class="sourceCode" id="cb4"><html><body><pre class="r"><span class="no">mkin_benchmarks</span>[<span class="no">system_string</span>, <span class="fu"><a href="https://rdrr.io/r/base/paste.html">paste0</a></span>(<span class="st">"t"</span>, <span class="fl">1</span>:<span class="fl">11</span>)] <span class="kw">&lt;-</span>
-  <span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span>(<span class="no">t1</span>, <span class="no">t2</span>, <span class="no">t3</span>, <span class="no">t4</span>, <span class="no">t5</span>, <span class="no">t6</span>, <span class="no">t7</span>, <span class="no">t8</span>, <span class="no">t9</span>, <span class="no">t10</span>, <span class="no">t11</span>)
-<span class="fu"><a href="https://rdrr.io/r/base/save.html">save</a></span>(<span class="no">mkin_benchmarks</span>, <span class="kw">file</span> <span class="kw">=</span> <span class="st">"~/git/mkin/vignettes/web_only/mkin_benchmarks.rda"</span>)</pre></body></html></div>
-</div>
-<div id="results" class="section level2">
-<h2 class="hasAnchor">
-<a href="#results" class="anchor"></a>Results</h2>
-<p>Currently, we only have benchmark information on one system, therefore only the mkin version is shown with the results below. Timings are in seconds, shorter is better. All results were obtained by serial, i.e. not using multiple computing cores.</p>
-<p>Benchmarks for all available error models are shown.</p>
-<div id="parent-only" class="section level3">
-<h3 class="hasAnchor">
-<a href="#parent-only" class="anchor"></a>Parent only</h3>
-<p>Constant variance (t1) and two-component error model (t2) for four models fitted to two datasets, i.e. eight fits for each test.</p>
-<table class="table">
-<thead><tr class="header">
-<th align="left">mkin version</th>
-<th align="right">t1 [s]</th>
-<th align="right">t2 [s]</th>
-</tr></thead>
-<tbody>
-<tr class="odd">
-<td align="left">0.9.48.1</td>
-<td align="right">3.610</td>
-<td align="right">11.019</td>
-</tr>
-<tr class="even">
-<td align="left">0.9.49.1</td>
-<td align="right">8.184</td>
-<td align="right">22.889</td>
-</tr>
-<tr class="odd">
-<td align="left">0.9.49.2</td>
-<td align="right">7.064</td>
-<td align="right">12.558</td>
-</tr>
-<tr class="even">
-<td align="left">0.9.49.3</td>
-<td align="right">7.296</td>
-<td align="right">21.239</td>
-</tr>
-<tr class="odd">
-<td align="left">0.9.49.4</td>
-<td align="right">5.936</td>
-<td align="right">20.545</td>
-</tr>
-<tr class="even">
-<td align="left">0.9.50.2</td>
-<td align="right">1.714</td>
-<td align="right">3.971</td>
-</tr>
-</tbody>
-</table>
-</div>
-<div id="one-metabolite" class="section level3">
-<h3 class="hasAnchor">
-<a href="#one-metabolite" class="anchor"></a>One metabolite</h3>
-<p>Constant variance (t3), two-component error model (t4), and variance by variable (t5) for three models fitted to one dataset, i.e. three fits for each test.</p>
-<table class="table">
-<thead><tr class="header">
-<th align="left">mkin version</th>
-<th align="right">t3 [s]</th>
-<th align="right">t4 [s]</th>
-<th align="right">t5 [s]</th>
-</tr></thead>
-<tbody>
-<tr class="odd">
-<td align="left">0.9.48.1</td>
-<td align="right">3.764</td>
-<td align="right">14.347</td>
-<td align="right">9.495</td>
-</tr>
-<tr class="even">
-<td align="left">0.9.49.1</td>
-<td align="right">4.649</td>
-<td align="right">13.789</td>
-<td align="right">6.395</td>
-</tr>
-<tr class="odd">
-<td align="left">0.9.49.2</td>
-<td align="right">4.786</td>
-<td align="right">8.461</td>
-<td align="right">5.675</td>
-</tr>
-<tr class="even">
-<td align="left">0.9.49.3</td>
-<td align="right">4.510</td>
-<td align="right">13.805</td>
-<td align="right">7.386</td>
-</tr>
-<tr class="odd">
-<td align="left">0.9.49.4</td>
-<td align="right">4.446</td>
-<td align="right">15.335</td>
-<td align="right">6.002</td>
-</tr>
-<tr class="even">
-<td align="left">0.9.50.2</td>
-<td align="right">1.402</td>
-<td align="right">6.174</td>
-<td align="right">2.764</td>
-</tr>
-</tbody>
-</table>
-</div>
-<div id="two-metabolites" class="section level3">
-<h3 class="hasAnchor">
-<a href="#two-metabolites" class="anchor"></a>Two metabolites</h3>
-<p>Constant variance (t6 and t7), two-component error model (t8 and t9), and variance by variable (t10 and t11) for one model fitted to one dataset, i.e. one fit for each test.</p>
-<table class="table">
-<thead><tr class="header">
-<th align="left">mkin version</th>
-<th align="right">t6 [s]</th>
-<th align="right">t7 [s]</th>
-<th align="right">t8 [s]</th>
-<th align="right">t9 [s]</th>
-<th align="right">t10 [s]</th>
-<th align="right">t11 [s]</th>
-</tr></thead>
-<tbody>
-<tr class="odd">
-<td align="left">0.9.48.1</td>
-<td align="right">2.623</td>
-<td align="right">4.587</td>
-<td align="right">7.525</td>
-<td align="right">16.621</td>
-<td align="right">8.576</td>
-<td align="right">31.267</td>
-</tr>
-<tr class="even">
-<td align="left">0.9.49.1</td>
-<td align="right">2.542</td>
-<td align="right">4.128</td>
-<td align="right">4.632</td>
-<td align="right">8.171</td>
-<td align="right">3.676</td>
-<td align="right">5.636</td>
-</tr>
-<tr class="odd">
-<td align="left">0.9.49.2</td>
-<td align="right">2.723</td>
-<td align="right">4.478</td>
-<td align="right">4.862</td>
-<td align="right">7.618</td>
-<td align="right">3.579</td>
-<td align="right">5.574</td>
-</tr>
-<tr class="even">
-<td align="left">0.9.49.3</td>
-<td align="right">2.643</td>
-<td align="right">4.374</td>
-<td align="right">7.020</td>
-<td align="right">11.124</td>
-<td align="right">5.388</td>
-<td align="right">7.365</td>
-</tr>
-<tr class="odd">
-<td align="left">0.9.49.4</td>
-<td align="right">2.635</td>
-<td align="right">4.259</td>
-<td align="right">4.737</td>
-<td align="right">7.763</td>
-<td align="right">3.427</td>
-<td align="right">5.626</td>
-</tr>
-<tr class="even">
-<td align="left">0.9.50.2</td>
-<td align="right">0.777</td>
-<td align="right">1.236</td>
-<td align="right">1.332</td>
-<td align="right">2.872</td>
-<td align="right">2.069</td>
-<td align="right">2.987</td>
-</tr>
-</tbody>
-</table>
-</div>
+<span class="no">t10</span> <span class="kw">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/system.time.html">system.time</a></span>(<span class="fu">mmkin_bench</span>(<span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span>(<span class="no">m_synth_SFO_lin</span>), <span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span>(<span class="no">SFO_lin_a</span>), <span class="kw">error_model</span> <span class="kw">=</span> <span class="st">"obs"</span>))[<span class="st">"elapsed"</span>]
+<span class="no">t11</span> <span class="kw">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/system.time.html">system.time</a></span>(<span class="fu">mmkin_bench</span>(<span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span>(<span class="no">m_synth_DFOP_par</span>), <span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span>(<span class="no">DFOP_par_c</span>), <span class="kw">error_model</span> <span class="kw">=</span> <span class="st">"obs"</span>))[<span class="st">"elapsed"</span>]
+
+<span class="no">mkin_benchmarks</span>[<span class="no">system_string</span>, <span class="fu"><a href="https://rdrr.io/r/base/paste.html">paste0</a></span>(<span class="st">"t"</span>, <span class="fl">1</span>:<span class="fl">11</span>)] <span class="kw">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span>(<span class="no">t1</span>, <span class="no">t2</span>, <span class="no">t3</span>, <span class="no">t4</span>, <span class="no">t5</span>, <span class="no">t6</span>, <span class="no">t7</span>, <span class="no">t8</span>, <span class="no">t9</span>, <span class="no">t10</span>, <span class="no">t11</span>)
+<span class="no">mkin_benchmarks</span>[, -<span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span>(<span class="fl">1</span>:<span class="fl">3</span>)]</pre></body></html></div>
+<pre><code>##                                                                        t1
+## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.48.1 3.610
+## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.1 8.184
+## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.2 7.064
+## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.3 7.296
+## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.4 5.936
+## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.50.2 1.679
+##                                                                         t2
+## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.48.1 11.019
+## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.1 22.889
+## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.2 12.558
+## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.3 21.239
+## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.4 20.545
+## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.50.2  3.613
+##                                                                        t3
+## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.48.1 3.764
+## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.1 4.649
+## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.2 4.786
+## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.3 4.510
+## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.4 4.446
+## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.50.2 1.366
+##                                                                         t4
+## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.48.1 14.347
+## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.1 13.789
+## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.2  8.461
+## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.3 13.805
+## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.4 15.335
+## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.50.2  6.545
+##                                                                        t5    t6
+## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.48.1 9.495 2.623
+## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.1 6.395 2.542
+## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.2 5.675 2.723
+## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.3 7.386 2.643
+## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.4 6.002 2.635
+## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.50.2 2.709 0.752
+##                                                                        t7    t8
+## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.48.1 4.587 7.525
+## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.1 4.128 4.632
+## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.2 4.478 4.862
+## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.3 4.374  7.02
+## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.4 4.259 4.737
+## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.50.2 1.214 1.455
+##                                                                         t9
+## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.48.1 16.621
+## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.1  8.171
+## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.2  7.618
+## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.3 11.124
+## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.4  7.763
+## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.50.2  4.196
+##                                                                       t10
+## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.48.1 8.576
+## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.1 3.676
+## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.2 3.579
+## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.3 5.388
+## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.4 3.427
+## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.50.2 1.996
+##                                                                        t11
+## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.48.1 31.267
+## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.1  5.636
+## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.2  5.574
+## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.3  7.365
+## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.4  5.626
+## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.50.2    3.1</code></pre>
+<div class="sourceCode" id="cb12"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/save.html">save</a></span>(<span class="no">mkin_benchmarks</span>, <span class="kw">file</span> <span class="kw">=</span> <span class="st">"~/git/mkin/vignettes/mkin_benchmarks.rda"</span>)</pre></body></html></div>
 </div>
   </div>
 
diff --git a/docs/articles/web_only/compiled_models.html b/docs/articles/web_only/compiled_models.html
index 837b288b..5aaa09bc 100644
--- a/docs/articles/web_only/compiled_models.html
+++ b/docs/articles/web_only/compiled_models.html
@@ -68,9 +68,6 @@
     <li>
       <a href="../../articles/web_only/NAFTA_examples.html">Example evaluation of NAFTA SOP Attachment examples</a>
     </li>
-    <li>
-      <a href="../../articles/web_only/benchmarks.html">Some benchmark timings</a>
-    </li>
   </ul>
 </li>
 <li>
@@ -100,10 +97,10 @@
       <h1 data-toc-skip>Performance benefit by using compiled model definitions in mkin</h1>
                         <h4 class="author">Johannes Ranke</h4>
             
-            <h4 class="date">2020-05-14</h4>
+            <h4 class="date">2020-05-27</h4>
       
-      <small class="dont-index">Source: <a href="http://github.com/jranke/mkin/blob/master/vignettes/web_only/compiled_models.rmd"><code>vignettes/web_only/compiled_models.rmd</code></a></small>
-      <div class="hidden name"><code>compiled_models.rmd</code></div>
+      <small class="dont-index">Source: <a href="http://github.com/jranke/mkin/blob/master/vignettes/web_only/compiled_models.Rmd"><code>vignettes/web_only/compiled_models.Rmd</code></a></small>
+      <div class="hidden name"><code>compiled_models.Rmd</code></div>
 
     </div>
 
@@ -122,57 +119,56 @@
 <p>into your .Rprofile startup file. This is just a text file with some R code that is executed when your R session starts. It has to be named .Rprofile and has to be located in your home directory, which will generally be your Documents folder. You can check the location of the home directory used by R by issuing</p>
 <div class="sourceCode" id="cb3"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/Sys.getenv.html">Sys.getenv</a></span>(<span class="st">"HOME"</span>)</pre></body></html></div>
 </div>
-<div id="comparison-with-other-solution-methods" class="section level2">
+<div id="comparison-with-eigenvalue-based-solutions" class="section level2">
 <h2 class="hasAnchor">
-<a href="#comparison-with-other-solution-methods" class="anchor"></a>Comparison with other solution methods</h2>
-<p>First, we build a simple degradation model for a parent compound with one metabolite, and we remove zero values from the dataset.</p>
+<a href="#comparison-with-eigenvalue-based-solutions" class="anchor"></a>Comparison with Eigenvalue based solutions</h2>
+<p>First, we build a simple degradation model for a parent compound with one metabolite.</p>
 <div class="sourceCode" id="cb4"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/library.html">library</a></span>(<span class="st">"mkin"</span>, <span class="kw">quietly</span> <span class="kw">=</span> <span class="fl">TRUE</span>)
 <span class="no">SFO_SFO</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span>(
   <span class="kw">parent</span> <span class="kw">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>, <span class="st">"m1"</span>),
   <span class="kw">m1</span> <span class="kw">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>))</pre></body></html></div>
 <pre><code>## Successfully compiled differential equation model from auto-generated C code.</code></pre>
-<div class="sourceCode" id="cb6"><html><body><pre class="r"><span class="no">FOCUS_D</span> <span class="kw">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/subset.html">subset</a></span>(<span class="no">FOCUS_2006_D</span>, <span class="no">value</span> <span class="kw">!=</span> <span class="fl">0</span>)</pre></body></html></div>
-<p>We can compare the performance of the Eigenvalue based solution against the compiled version and the R implementation of the differential equations using the benchmark package. In the output of below code, the warnings about zero being removed from the FOCUS D dataset are suppressed. Since mkin version 0.9.49.11, an analytical solution is also implemented, which is included in the tests below.</p>
-<div class="sourceCode" id="cb7"><html><body><pre class="r"><span class="kw">if</span> (<span class="fu"><a href="https://rdrr.io/r/base/library.html">require</a></span>(<span class="no">rbenchmark</span>)) {
+<p>We can compare the performance of the Eigenvalue based solution against the compiled version and the R implementation of the differential equations using the benchmark package. In the output of below code, the warnings about zero being removed from the FOCUS D dataset are suppressed.</p>
+<div class="sourceCode" id="cb6"><html><body><pre class="r"><span class="kw">if</span> (<span class="fu"><a href="https://rdrr.io/r/base/library.html">require</a></span>(<span class="no">rbenchmark</span>)) {
   <span class="no">b.1</span> <span class="kw">&lt;-</span> <span class="fu"><a href="https://rdrr.io/pkg/rbenchmark/man/benchmark.html">benchmark</a></span>(
-    <span class="st">"deSolve, not compiled"</span> <span class="kw">=</span> <span class="fu"><a href="../../reference/mkinfit.html">mkinfit</a></span>(<span class="no">SFO_SFO</span>, <span class="no">FOCUS_D</span>,
-       <span class="kw">solution_type</span> <span class="kw">=</span> <span class="st">"deSolve"</span>,
-       <span class="kw">use_compiled</span> <span class="kw">=</span> <span class="fl">FALSE</span>, <span class="kw">quiet</span> <span class="kw">=</span> <span class="fl">TRUE</span>),
-    <span class="st">"Eigenvalue based"</span> <span class="kw">=</span> <span class="fu"><a href="../../reference/mkinfit.html">mkinfit</a></span>(<span class="no">SFO_SFO</span>, <span class="no">FOCUS_D</span>,
-       <span class="kw">solution_type</span> <span class="kw">=</span> <span class="st">"eigen"</span>, <span class="kw">quiet</span> <span class="kw">=</span> <span class="fl">TRUE</span>),
-    <span class="st">"deSolve, compiled"</span> <span class="kw">=</span> <span class="fu"><a href="../../reference/mkinfit.html">mkinfit</a></span>(<span class="no">SFO_SFO</span>, <span class="no">FOCUS_D</span>,
-       <span class="kw">solution_type</span> <span class="kw">=</span> <span class="st">"deSolve"</span>, <span class="kw">quiet</span> <span class="kw">=</span> <span class="fl">TRUE</span>),
-    <span class="st">"analytical"</span> <span class="kw">=</span> <span class="fu"><a href="../../reference/mkinfit.html">mkinfit</a></span>(<span class="no">SFO_SFO</span>, <span class="no">FOCUS_D</span>,
-       <span class="kw">solution_type</span> <span class="kw">=</span> <span class="st">"analytical"</span>,
-       <span class="kw">use_compiled</span> <span class="kw">=</span> <span class="fl">FALSE</span>, <span class="kw">quiet</span> <span class="kw">=</span> <span class="fl">TRUE</span>),
-    <span class="kw">replications</span> <span class="kw">=</span> <span class="fl">1</span>, <span class="kw">order</span> <span class="kw">=</span> <span class="st">"relative"</span>,
-    <span class="kw">columns</span> <span class="kw">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span>(<span class="st">"test"</span>, <span class="st">"replications"</span>, <span class="st">"relative"</span>, <span class="st">"elapsed"</span>))
+    <span class="st">"deSolve, not compiled"</span> <span class="kw">=</span> <span class="fu"><a href="../../reference/mkinfit.html">mkinfit</a></span>(<span class="no">SFO_SFO</span>, <span class="no">FOCUS_2006_D</span>,
+                                      <span class="kw">solution_type</span> <span class="kw">=</span> <span class="st">"deSolve"</span>,
+                                      <span class="kw">use_compiled</span> <span class="kw">=</span> <span class="fl">FALSE</span>, <span class="kw">quiet</span> <span class="kw">=</span> <span class="fl">TRUE</span>),
+    <span class="st">"Eigenvalue based"</span> <span class="kw">=</span> <span class="fu"><a href="../../reference/mkinfit.html">mkinfit</a></span>(<span class="no">SFO_SFO</span>, <span class="no">FOCUS_2006_D</span>,
+                                 <span class="kw">solution_type</span> <span class="kw">=</span> <span class="st">"eigen"</span>, <span class="kw">quiet</span> <span class="kw">=</span> <span class="fl">TRUE</span>),
+    <span class="st">"deSolve, compiled"</span> <span class="kw">=</span> <span class="fu"><a href="../../reference/mkinfit.html">mkinfit</a></span>(<span class="no">SFO_SFO</span>, <span class="no">FOCUS_2006_D</span>,
+                                  <span class="kw">solution_type</span> <span class="kw">=</span> <span class="st">"deSolve"</span>, <span class="kw">quiet</span> <span class="kw">=</span> <span class="fl">TRUE</span>),
+    <span class="kw">replications</span> <span class="kw">=</span> <span class="fl">3</span>)
   <span class="fu"><a href="https://rdrr.io/r/base/print.html">print</a></span>(<span class="no">b.1</span>)
+  <span class="no">factor_SFO_SFO</span> <span class="kw">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/Round.html">round</a></span>(<span class="no">b.1</span>[<span class="st">"1"</span>, <span class="st">"relative"</span>])
 } <span class="kw">else</span> {
+  <span class="no">factor_SFO_SFO</span> <span class="kw">&lt;-</span> <span class="fl">NA</span>
   <span class="fu"><a href="https://rdrr.io/r/base/print.html">print</a></span>(<span class="st">"R package rbenchmark is not available"</span>)
 }</pre></body></html></div>
-<pre><code>##                    test replications relative elapsed
-## 4            analytical            1    1.000   0.191
-## 3     deSolve, compiled            1    1.801   0.344
-## 2      Eigenvalue based            1    2.105   0.402
-## 1 deSolve, not compiled            1   42.864   8.187</code></pre>
-<p>We see that using the compiled model is by more than a factor of 10 faster than using deSolve without compiled code.</p>
+<pre><code>##                    test replications elapsed relative user.self sys.self
+## 3     deSolve, compiled            3   0.997    1.000     0.997    0.000
+## 1 deSolve, not compiled            3  24.417   24.490    24.405    0.001
+## 2      Eigenvalue based            3   1.159    1.162     1.159    0.000
+##   user.child sys.child
+## 3          0         0
+## 1          0         0
+## 2          0         0</code></pre>
+<p>We see that using the compiled model is by a factor of around 24 faster than using the R version with the default ode solver, and it is even faster than the Eigenvalue based solution implemented in R which does not need iterative solution of the ODEs.</p>
 </div>
-<div id="model-without-analytical-solution" class="section level2">
+<div id="model-that-can-not-be-solved-with-eigenvalues" class="section level2">
 <h2 class="hasAnchor">
-<a href="#model-without-analytical-solution" class="anchor"></a>Model without analytical solution</h2>
-<p>This evaluation is also taken from the example section of mkinfit. No analytical solution is available for this system, and now Eigenvalue based solution is possible, so only deSolve using with or without compiled code is available.</p>
-<div class="sourceCode" id="cb9"><html><body><pre class="r"><span class="kw">if</span> (<span class="fu"><a href="https://rdrr.io/r/base/library.html">require</a></span>(<span class="no">rbenchmark</span>)) {
+<a href="#model-that-can-not-be-solved-with-eigenvalues" class="anchor"></a>Model that can not be solved with Eigenvalues</h2>
+<p>This evaluation is also taken from the example section of mkinfit.</p>
+<div class="sourceCode" id="cb8"><html><body><pre class="r"><span class="kw">if</span> (<span class="fu"><a href="https://rdrr.io/r/base/library.html">require</a></span>(<span class="no">rbenchmark</span>)) {
   <span class="no">FOMC_SFO</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span>(
     <span class="kw">parent</span> <span class="kw">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"FOMC"</span>, <span class="st">"m1"</span>),
     <span class="kw">m1</span> <span class="kw">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span>( <span class="st">"SFO"</span>))
 
   <span class="no">b.2</span> <span class="kw">&lt;-</span> <span class="fu"><a href="https://rdrr.io/pkg/rbenchmark/man/benchmark.html">benchmark</a></span>(
-    <span class="st">"deSolve, not compiled"</span> <span class="kw">=</span> <span class="fu"><a href="../../reference/mkinfit.html">mkinfit</a></span>(<span class="no">FOMC_SFO</span>, <span class="no">FOCUS_D</span>,
+    <span class="st">"deSolve, not compiled"</span> <span class="kw">=</span> <span class="fu"><a href="../../reference/mkinfit.html">mkinfit</a></span>(<span class="no">FOMC_SFO</span>, <span class="no">FOCUS_2006_D</span>,
                                       <span class="kw">use_compiled</span> <span class="kw">=</span> <span class="fl">FALSE</span>, <span class="kw">quiet</span> <span class="kw">=</span> <span class="fl">TRUE</span>),
-    <span class="st">"deSolve, compiled"</span> <span class="kw">=</span> <span class="fu"><a href="../../reference/mkinfit.html">mkinfit</a></span>(<span class="no">FOMC_SFO</span>, <span class="no">FOCUS_D</span>, <span class="kw">quiet</span> <span class="kw">=</span> <span class="fl">TRUE</span>),
-    <span class="kw">replications</span> <span class="kw">=</span> <span class="fl">1</span>, <span class="kw">order</span> <span class="kw">=</span> <span class="st">"relative"</span>,
-    <span class="kw">columns</span> <span class="kw">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span>(<span class="st">"test"</span>, <span class="st">"replications"</span>, <span class="st">"relative"</span>, <span class="st">"elapsed"</span>))
+    <span class="st">"deSolve, compiled"</span> <span class="kw">=</span> <span class="fu"><a href="../../reference/mkinfit.html">mkinfit</a></span>(<span class="no">FOMC_SFO</span>, <span class="no">FOCUS_2006_D</span>, <span class="kw">quiet</span> <span class="kw">=</span> <span class="fl">TRUE</span>),
+    <span class="kw">replications</span> <span class="kw">=</span> <span class="fl">3</span>)
   <span class="fu"><a href="https://rdrr.io/r/base/print.html">print</a></span>(<span class="no">b.2</span>)
   <span class="no">factor_FOMC_SFO</span> <span class="kw">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/Round.html">round</a></span>(<span class="no">b.2</span>[<span class="st">"1"</span>, <span class="st">"relative"</span>])
 } <span class="kw">else</span> {
@@ -180,9 +176,12 @@
   <span class="fu"><a href="https://rdrr.io/r/base/print.html">print</a></span>(<span class="st">"R package benchmark is not available"</span>)
 }</pre></body></html></div>
 <pre><code>## Successfully compiled differential equation model from auto-generated C code.</code></pre>
-<pre><code>##                    test replications relative elapsed
-## 2     deSolve, compiled            1    1.000   0.466
-## 1 deSolve, not compiled            1   30.942  14.419</code></pre>
+<pre><code>##                    test replications elapsed relative user.self sys.self
+## 2     deSolve, compiled            3   1.392    1.000     1.391        0
+## 1 deSolve, not compiled            3  43.021   30.906    43.002        0
+##   user.child sys.child
+## 2          0         0
+## 1          0         0</code></pre>
 <p>Here we get a performance benefit of a factor of 31 using the version of the differential equation model compiled from C code!</p>
 <p>This vignette was built with mkin 0.9.50.2 on</p>
 <pre><code>## R version 4.0.0 (2020-04-24)
author	Johannes Ranke <jranke@uni-bremen.de>	2020-05-27 07:12:51 +0200
committer	Johannes Ranke <jranke@uni-bremen.de>	2020-05-27 07:12:51 +0200
commit	b5ee48a86e4b1d4c05aaadb80b44954e2e994ebc (patch)
tree	aeeeaf623e4a6102b9ca2440cf0e32ff7a7a1d25 /docs/articles
parent	a77a10ea6c607346778ba0700b3b66ac393101a2 (diff)