From 1ef7008be2a72a0847064ad9c2ddcfa16b055482 Mon Sep 17 00:00:00 2001 From: Johannes Ranke Date: Fri, 3 May 2019 19:14:15 +0200 Subject: Improve error model fitting Now we have a three stage fitting process for nonconstant error models: - Unweighted least squares - Only optimize the error model - Optimize both Static documentation rebuilt by pkgdown --- docs/articles/web_only/FOCUS_Z.html | 138 ++++++++++---------- .../figure-html/FOCUS_2006_Z_fits_10-1.png | Bin 128677 -> 128674 bytes .../figure-html/FOCUS_2006_Z_fits_11-1.png | Bin 127690 -> 127674 bytes .../figure-html/FOCUS_2006_Z_fits_11a-1.png | Bin 96509 -> 96502 bytes .../figure-html/FOCUS_2006_Z_fits_11b-1.png | Bin 22308 -> 22316 bytes .../figure-html/FOCUS_2006_Z_fits_6-1.png | Bin 128965 -> 128979 bytes .../figure-html/FOCUS_2006_Z_fits_9-1.png | Bin 108421 -> 108437 bytes docs/articles/web_only/NAFTA_examples.html | 145 +++++++++++---------- .../NAFTA_examples_files/figure-html/p14-1.png | Bin 54038 -> 54036 bytes .../NAFTA_examples_files/figure-html/p9b-1.png | Bin 50012 -> 50009 bytes docs/articles/web_only/benchmarks.html | 112 ++++++++-------- docs/articles/web_only/compiled_models.html | 12 +- 12 files changed, 206 insertions(+), 201 deletions(-) (limited to 'docs/articles/web_only') diff --git a/docs/articles/web_only/FOCUS_Z.html b/docs/articles/web_only/FOCUS_Z.html index 950e8eab..9e64ae3a 100644 --- a/docs/articles/web_only/FOCUS_Z.html +++ b/docs/articles/web_only/FOCUS_Z.html @@ -88,7 +88,7 @@

Example evaluation of FOCUS dataset Z

Johannes Ranke

-

2019-05-02

+

2019-05-03

@@ -132,11 +132,11 @@ 

summary(m.Z.2a, data = FALSE)$bpar
##             Estimate se_notrans    t value     Pr(>t)    Lower    Upper
-## Z0_0      9.7015e+01   3.394776 2.8578e+01 6.5093e-21 91.66556 102.3642
-## k_Z0_sink 4.0301e-10   0.225510 1.7871e-09 5.0000e-01  0.00000      Inf
-## k_Z0_Z1   2.2360e+00   0.159161 1.4049e+01 1.1412e-13  1.95303   2.5600
-## k_Z1_sink 4.8212e-01   0.065499 7.3608e+00 5.1791e-08  0.40341   0.5762
-## sigma     4.8041e+00   0.637657 7.5340e+00 3.4468e-08  3.52677   6.0815
+## Z0_0 9.7015e+01 3.393176 2.8591e+01 6.4352e-21 91.66556 102.3642 +## k_Z0_sink 7.2231e-10 0.225254 3.2067e-09 5.0000e-01 0.00000 Inf +## k_Z0_Z1 2.2360e+00 0.159134 1.4051e+01 1.1369e-13 1.95303 2.5600 +## k_Z1_sink 4.8212e-01 0.065454 7.3658e+00 5.1186e-08 0.40341 0.5762 +## sigma 4.8041e+00 0.637618 7.5345e+00 3.4431e-08 3.52677 6.0815

As obvious from the parameter summary (the component of the summary), the kinetic rate constant from parent compound Z to sink is very small and the t-test for this parameter suggests that it is not significantly different from zero. This suggests, in agreement with the analysis in the FOCUS kinetics report, to simplify the model by removing the pathway to sink.

A similar result can be obtained when formation fractions are used in the model formulation:

Z.2a.ff <- mkinmod(Z0 = mkinsub("SFO", "Z1"),
@@ -199,20 +199,18 @@
                      quiet = TRUE)
## Warning in mkinfit(Z.FOCUS, FOCUS_2006_Z_mkin, parms.ini = m.Z.
 ## 5$bparms.ode, : Observations with value of zero were removed from the data
-
## Warning in mkinfit(Z.FOCUS, FOCUS_2006_Z_mkin, parms.ini = m.Z.5$bparms.ode, : Optimisation did not converge:
-## false convergence (8)
-
plot_sep(m.Z.FOCUS)
+
plot_sep(m.Z.FOCUS)

-
summary(m.Z.FOCUS, data = FALSE)$bpar
+
summary(m.Z.FOCUS, data = FALSE)$bpar
##             Estimate se_notrans t value     Pr(>t)     Lower      Upper
-## Z0_0       96.838619   1.994272 48.5584 4.0282e-42 92.826596 100.850642
-## k_Z0        2.215408   0.118459 18.7018 1.0415e-23  1.989468   2.467007
-## k_Z1        0.478300   0.028257 16.9267 6.2407e-22  0.424701   0.538663
-## k_Z2        0.451618   0.042138 10.7177 1.6308e-14  0.374327   0.544869
-## k_Z3        0.058693   0.015246  3.8498 1.7805e-04  0.034804   0.098981
-## f_Z2_to_Z3  0.471508   0.058352  8.0804 9.6647e-11  0.357725   0.588332
+## Z0_0       96.838607   1.994273 48.5584 4.0283e-42 92.826626 100.850589
+## k_Z0        2.215405   0.118459 18.7018 1.0415e-23  1.989465   2.467003
+## k_Z1        0.478300   0.028257 16.9267 6.2408e-22  0.424701   0.538662
+## k_Z2        0.451618   0.042138 10.7177 1.6308e-14  0.374328   0.544867
+## k_Z3        0.058693   0.015246  3.8498 1.7806e-04  0.034805   0.098978
+## f_Z2_to_Z3  0.471508   0.058352  8.0804 9.6648e-11  0.357735   0.588320
 ## sigma       3.984431   0.383402 10.3923 4.5575e-14  3.213126   4.755736
-
endpoints(m.Z.FOCUS)
+
endpoints(m.Z.FOCUS)
## $ff
 ##   Z2_Z3 Z2_sink 
 ## 0.47151 0.52849 
@@ -225,7 +223,7 @@
 ## Z0  0.31288  1.0394
 ## Z1  1.44919  4.8141
 ## Z2  1.53481  5.0985
-## Z3 11.80962 39.2307
+## Z3 11.80965 39.2308

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.

@@ -233,17 +231,17 @@ Using the SFORB model

As the FOCUS report states, there is a certain tailing of the time course of metabolite Z3. Also, the time course of the parent compound is not fitted very well using the SFO model, as residues at a certain low level remain.

Therefore, an additional model is offered here, using the single first-order reversible binding (SFORB) model for metabolite Z3. As expected, the \(\chi^2\) error level is lower for metabolite Z3 using this model and the graphical fit for Z3 is improved. However, the covariance matrix is not returned.

-
Z.mkin.1 <- mkinmod(Z0 = mkinsub("SFO", "Z1", sink = FALSE),
-                    Z1 = mkinsub("SFO", "Z2", sink = FALSE),
-                    Z2 = mkinsub("SFO", "Z3"),
-                    Z3 = mkinsub("SFORB"))
+
Z.mkin.1 <- mkinmod(Z0 = mkinsub("SFO", "Z1", sink = FALSE),
+                    Z1 = mkinsub("SFO", "Z2", sink = FALSE),
+                    Z2 = mkinsub("SFO", "Z3"),
+                    Z3 = mkinsub("SFORB"))
## Successfully compiled differential equation model from auto-generated C code.
-
m.Z.mkin.1 <- mkinfit(Z.mkin.1, FOCUS_2006_Z_mkin, quiet = TRUE)
+
m.Z.mkin.1 <- mkinfit(Z.mkin.1, FOCUS_2006_Z_mkin, quiet = TRUE)
## Warning in mkinfit(Z.mkin.1, FOCUS_2006_Z_mkin, quiet = TRUE): Observations
 ## with value of zero were removed from the data
-
plot_sep(m.Z.mkin.1)
+
plot_sep(m.Z.mkin.1)

-
summary(m.Z.mkin.1, data = FALSE)$cov.unscaled
+
summary(m.Z.mkin.1, data = FALSE)$cov.unscaled
##                            Z0_0 log_k_Z0_Z1 log_k_Z1_Z2 log_k_Z2_sink
 ## Z0_0                 3.8375e+00  5.4918e-03  3.0584e-02    1.2969e-01
 ## log_k_Z0_Z1          5.4918e-03  2.7613e-03 -1.8820e-04    2.6634e-04
@@ -251,9 +249,9 @@
 ## log_k_Z2_sink        1.2969e-01  2.6634e-04  3.2177e-03    3.4256e-02
 ## log_k_Z2_Z3_free    -2.4223e-02 -2.6169e-04 -1.1845e-03   -8.1134e-03
 ## log_k_Z3_free_sink  -6.5467e-02 -4.0815e-04 -3.2978e-03   -3.6010e-02
-## log_k_Z3_free_bound -6.0658e-02 -4.4768e-04 -3.0588e-03   -3.9074e-02
-## log_k_Z3_bound_free  4.7821e+00  5.5819e-03  1.0267e-01    1.1956e+00
-## sigma               -1.4345e-08  8.6519e-11 -6.1861e-10   -4.7499e-10
+## log_k_Z3_free_bound -6.0659e-02 -4.4768e-04 -3.0588e-03   -3.9074e-02
+## log_k_Z3_bound_free  5.2844e-01  4.5458e-03  7.9800e-03    4.6274e-02
+## sigma                2.0366e-10 -3.4658e-10  8.9910e-11   -2.5946e-10
 ##                     log_k_Z2_Z3_free log_k_Z3_free_sink
 ## Z0_0                     -2.4223e-02        -6.5467e-02
 ## log_k_Z0_Z1              -2.6169e-04        -4.0815e-04
@@ -262,84 +260,84 @@
 ## log_k_Z2_Z3_free          1.5500e-02         2.1583e-02
 ## log_k_Z3_free_sink        2.1583e-02         7.5705e-02
 ## log_k_Z3_free_bound       2.5836e-02         1.1964e-01
-## log_k_Z3_bound_free      -2.1303e-01        -9.0584e-01
-## sigma                     5.8776e-10         1.0773e-09
+## log_k_Z3_bound_free       5.2534e-02         2.9441e-01
+## sigma                     1.3063e-10         3.4170e-10
 ##                     log_k_Z3_free_bound log_k_Z3_bound_free       sigma
-## Z0_0                        -6.0658e-02          4.7821e+00 -1.4345e-08
-## log_k_Z0_Z1                 -4.4768e-04          5.5819e-03  8.6519e-11
-## log_k_Z1_Z2                 -3.0588e-03          1.0267e-01 -6.1861e-10
-## log_k_Z2_sink               -3.9074e-02          1.1956e+00 -4.7499e-10
-## log_k_Z2_Z3_free             2.5836e-02         -2.1303e-01  5.8776e-10
-## log_k_Z3_free_sink           1.1964e-01         -9.0584e-01  1.0773e-09
-## log_k_Z3_free_bound          6.5902e-01          4.2011e+00  2.1743e-09
-## log_k_Z3_bound_free          4.2011e+00          3.6036e+08  7.2404e-02
-## sigma                        2.1743e-09          7.2404e-02  1.4170e-01
+## Z0_0 -6.0659e-02 5.2844e-01 2.0366e-10 +## log_k_Z0_Z1 -4.4768e-04 4.5458e-03 -3.4658e-10 +## log_k_Z1_Z2 -3.0588e-03 7.9800e-03 8.9910e-11 +## log_k_Z2_sink -3.9074e-02 4.6274e-02 -2.5946e-10 +## log_k_Z2_Z3_free 2.5836e-02 5.2534e-02 1.3063e-10 +## log_k_Z3_free_sink 1.1964e-01 2.9441e-01 3.4170e-10 +## log_k_Z3_free_bound 6.5902e-01 5.4737e+00 -6.7704e-10 +## log_k_Z3_bound_free 5.4737e+00 2.8722e+08 7.2421e-02 +## sigma -6.7704e-10 7.2421e-02 1.4170e-01

Therefore, a further stepwise model building is performed starting from the stage of parent and two metabolites, starting from the assumption that the model fit for the parent compound can be improved by using the SFORB model.

-
Z.mkin.3 <- mkinmod(Z0 = mkinsub("SFORB", "Z1", sink = FALSE),
-                    Z1 = mkinsub("SFO", "Z2", sink = FALSE),
-                    Z2 = mkinsub("SFO"))
+
Z.mkin.3 <- mkinmod(Z0 = mkinsub("SFORB", "Z1", sink = FALSE),
+                    Z1 = mkinsub("SFO", "Z2", sink = FALSE),
+                    Z2 = mkinsub("SFO"))
## Successfully compiled differential equation model from auto-generated C code.
-
m.Z.mkin.3 <- mkinfit(Z.mkin.3, FOCUS_2006_Z_mkin, quiet = TRUE)
+
m.Z.mkin.3 <- mkinfit(Z.mkin.3, FOCUS_2006_Z_mkin, quiet = TRUE)
## Warning in mkinfit(Z.mkin.3, FOCUS_2006_Z_mkin, quiet = TRUE): Observations
 ## with value of zero were removed from the data
-
plot_sep(m.Z.mkin.3)
+
plot_sep(m.Z.mkin.3)

This results in a much better representation of the behaviour of the parent compound Z0.

Finally, Z3 is added as well. These models appear overparameterised (no covariance matrix returned) if the sink for Z1 is left in the models.

-
Z.mkin.4 <- mkinmod(Z0 = mkinsub("SFORB", "Z1", sink = FALSE),
-                    Z1 = mkinsub("SFO", "Z2", sink = FALSE),
-                    Z2 = mkinsub("SFO", "Z3"),
-                    Z3 = mkinsub("SFO"))
+
Z.mkin.4 <- mkinmod(Z0 = mkinsub("SFORB", "Z1", sink = FALSE),
+                    Z1 = mkinsub("SFO", "Z2", sink = FALSE),
+                    Z2 = mkinsub("SFO", "Z3"),
+                    Z3 = mkinsub("SFO"))
## Successfully compiled differential equation model from auto-generated C code.
- + 
## Warning in mkinfit(Z.mkin.4, FOCUS_2006_Z_mkin, parms.ini = m.Z.mkin.
 ## 3$bparms.ode, : Observations with value of zero were removed from the data
-
plot_sep(m.Z.mkin.4)
+
plot_sep(m.Z.mkin.4)

The error level of the fit, but especially of metabolite Z3, can be improved if the SFORB model is chosen for this metabolite, as this model is capable of representing the tailing of the metabolite decline phase.

-
Z.mkin.5 <- mkinmod(Z0 = mkinsub("SFORB", "Z1", sink = FALSE),
-                    Z1 = mkinsub("SFO", "Z2", sink = FALSE),
-                    Z2 = mkinsub("SFO", "Z3"),
-                    Z3 = mkinsub("SFORB"))
+
Z.mkin.5 <- mkinmod(Z0 = mkinsub("SFORB", "Z1", sink = FALSE),
+                    Z1 = mkinsub("SFO", "Z2", sink = FALSE),
+                    Z2 = mkinsub("SFO", "Z3"),
+                    Z3 = mkinsub("SFORB"))
## Successfully compiled differential equation model from auto-generated C code.
- + 
## Warning in mkinfit(Z.mkin.5, FOCUS_2006_Z_mkin, parms.ini = m.Z.mkin.
 ## 4$bparms.ode[1:4], : Observations with value of zero were removed from the
 ## data
-
plot_sep(m.Z.mkin.5)
+
plot_sep(m.Z.mkin.5)

The summary view of the backtransformed parameters shows that we get no confidence intervals due to overparameterisation. As the optimized is excessively small, it seems reasonable to fix it to zero.

- + 
## Warning in mkinfit(Z.mkin.5, FOCUS_2006_Z_mkin, parms.ini = c(m.Z.mkin.
 ## 5$bparms.ode[1:7], : Observations with value of zero were removed from the
 ## data
-
plot_sep(m.Z.mkin.5a)
+
plot_sep(m.Z.mkin.5a)

As expected, the residual plots for Z0 and Z3 are more random than in the case of the all SFO model for which they were shown above. In conclusion, the model is proposed as the best-fit model for the dataset from Appendix 7 of the FOCUS report.

A graphical representation of the confidence intervals can finally be obtained.

-
mkinparplot(m.Z.mkin.5a)
+
mkinparplot(m.Z.mkin.5a)

The endpoints obtained with this model are

-
endpoints(m.Z.mkin.5a)
+
endpoints(m.Z.mkin.5a)
## $ff
 ##   Z0_free_Z1        Z1_Z2      Z2_sink   Z2_Z3_free Z3_free_sink 
 ##      1.00000      1.00000      0.46344      0.53656      1.00000 
 ## 
 ## $SFORB
 ##     Z0_b1     Z0_b2     Z3_b1     Z3_b2 
-## 2.4471329 0.0075123 0.0800074 0.0000000 
+## 2.4471381 0.0075124 0.0800075 0.0000000 
 ## 
 ## $distimes
 ##      DT50   DT90 DT50_Z0_b1 DT50_Z0_b2 DT50_Z3_b1 DT50_Z3_b2
-## Z0 0.3043 1.1848    0.28325     92.268         NA         NA
+## Z0 0.3043 1.1848    0.28325     92.267         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     8.6635        Inf
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Evaluation of example datasets from Attachment 1 to the US EPA SOP for the NAFTA guidance

Johannes Ranke

-

2019-05-02

+

2019-05-03

@@ -141,7 +141,7 @@ ## Estimate Pr(>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 3.41e-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 ## @@ -150,7 +150,7 @@ ## 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 3.70e+11 2.03e+11 +## DFOP 55.5 4.42e+11 2.42e+11 ## ## Representative half-life: ## [1] 321.51 @@ -189,7 +189,7 @@ ## Estimate Pr(>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 8.28e-12 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 ## @@ -198,7 +198,7 @@ ## 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 1.37e+11 8.37e+10 +## DFOP 83.6 9.80e+10 5.98e+10 ## ## Representative half-life: ## [1] 215.87 @@ -222,7 +222,7 @@ ## Parameters: ## $SFO ## Estimate Pr(>t) Lower Upper -## parent_0 94.7759 7.29e-24 92.3479 97.2039 +## parent_0 94.7759 7.29e-24 92.3478 97.2039 ## k_parent_sink 0.0179 8.02e-16 0.0166 0.0194 ## sigma 3.0696 3.81e-06 2.0456 4.0936 ## @@ -237,7 +237,7 @@ ## Estimate Pr(>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 3.87e-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 ## @@ -246,7 +246,7 @@ ## 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 8.43e+09 1.79e+10 +## DFOP 34.1 6.66e+09 1.41e+10 ## ## Representative half-life: ## [1] 53.17 @@ -285,7 +285,7 @@ ## Estimate Pr(>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 2.46e-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 ## @@ -294,7 +294,7 @@ ## 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 5.58e+09 2.82e+09 +## DFOP 96.4 6.97e+09 3.52e+09 ## ## Representative half-life: ## [1] 454.55 @@ -397,7 +397,7 @@ ## Estimate Pr(>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 5.75e-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 ## @@ -406,7 +406,7 @@ ## 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 2.17e+12 1.21e+12 +## DFOP 10.5 2.07e+12 1.15e+12 ## ## Representative half-life: ## [1] 101.43 @@ -416,12 +416,16 @@

Example on page 9, lower panel

p9b <- nafta(NAFTA_SOP_Attachment[["p9b"]])
+
## Warning in sqrt(diag(covar)): NaNs wurden erzeugt
## Warning in sqrt(diag(covar_notrans)): NaNs wurden erzeugt
+
## Warning in sqrt(1/diag(V)): NaNs wurden erzeugt
+
## Warning in cov2cor(ans$cov.unscaled): diag(.) had 0 or NA entries; non-
+## finite result is doubtful
## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c
## The half-life obtained from the IORE model may be used
-
plot(p9b)
+
plot(p9b)

-
print(p9b)
+
print(p9b)
## Sums of squares:
 ##      SFO     IORE     DFOP 
 ## 35.64867 23.22334 35.64867 
@@ -446,9 +450,9 @@
 ## $DFOP
 ##          Estimate   Pr(>t)   Lower   Upper
 ## parent_0  94.7123 1.61e-16 93.1355 96.2891
-## k1         0.0389      NaN  0.0306  0.0495
-## k2         0.0389 1.10e-06  0.0186  0.0812
-## g          0.7598      NaN  0.0000  1.0000
+## k1         0.0389 1.43e-06  0.0312  0.0485
+## k2         0.0389 6.67e-03  0.0186  0.0812
+## g          0.7742      NaN      NA      NA
 ## sigma      1.5957 2.50e-04  0.9135  2.2779
 ## 
 ## 
@@ -465,12 +469,12 @@
 

 

 Example on page 10

-
p10 <- nafta(NAFTA_SOP_Attachment[["p10"]])

+
p10 <- nafta(NAFTA_SOP_Attachment[["p10"]])

 
## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c

 
## The half-life obtained from the IORE model may be used

-
plot(p10)

+
plot(p10)

 

-
print(p10)

+
print(p10)

 
## Sums of squares:
 ##      SFO     IORE     DFOP 
 ## 899.4089 336.4348 899.4089 
@@ -495,8 +499,8 @@
 ## $DFOP
 ##          Estimate   Pr(>t)   Lower    Upper
 ## parent_0 101.7315 1.41e-09 91.6534 111.8097
-## k1         0.0495 6.41e-04  0.0303   0.0809
-## k2         0.0495 1.66e-02  0.0201   0.1219
+## 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
 ## 
@@ -518,12 +522,12 @@
 

 

 Example on page 11

-
p11 <- nafta(NAFTA_SOP_Attachment[["p11"]])

+
p11 <- nafta(NAFTA_SOP_Attachment[["p11"]])

 
## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c

 
## The half-life obtained from the IORE model may be used

-
plot(p11)

+
plot(p11)

 

-
print(p11)

+
print(p11)

 
## Sums of squares:
 ##      SFO     IORE     DFOP 
 ## 579.6805 204.7932 144.7783 
@@ -549,7 +553,7 @@
 ##          Estimate   Pr(>t)    Lower    Upper
 ## parent_0 1.05e+02 9.47e-13  99.9990 109.1224
 ## k1       4.41e-02 5.95e-03   0.0296   0.0658
-## k2       9.20e-13 5.00e-01   0.0000      Inf
+## k2       7.25e-13 5.00e-01   0.0000      Inf
 ## g        3.22e-01 1.45e-03   0.2814   0.3650
 ## sigma    3.22e+00 3.52e-04   1.8410   4.5906
 ## 
@@ -558,7 +562,7 @@
 ##          DT50     DT90 DT50_rep
 ## SFO  2.16e+02 7.18e+02 2.16e+02
 ## IORE 9.73e+02 1.37e+08 4.11e+07
-## DFOP 3.31e+11 2.08e+12 7.53e+11
+## DFOP 4.21e+11 2.64e+12 9.56e+11
 ## 
 ## Representative half-life:
 ## [1] 41148169

@@ -572,19 +576,14 @@
 

 

 Example on page 12, upper panel

-
p12a <- nafta(NAFTA_SOP_Attachment[["p12a"]])

+
p12a <- nafta(NAFTA_SOP_Attachment[["p12a"]])

 
## Warning in summary.mkinfit(x): Could not estimate covariance matrix;
 ## singular system.

-
## Warning in sqrt(diag(covar)): NaNs wurden erzeugt

-
## Warning in sqrt(diag(covar_notrans)): NaNs wurden erzeugt

-
## Warning in sqrt(1/diag(V)): NaNs wurden erzeugt

-
## Warning in cov2cor(ans$cov.unscaled): diag(.) had 0 or NA entries; non-
-## finite result is doubtful

 
## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c

 
## The half-life obtained from the IORE model may be used

-
plot(p12a)

+
plot(p12a)

 

-
print(p12a)

+
print(p12a)

 
## Sums of squares:
 ##      SFO     IORE     DFOP 
 ## 695.4440 220.0685 695.4440 
@@ -609,9 +608,9 @@
 ## $DFOP
 ##          Estimate   Pr(>t)   Lower   Upper
 ## parent_0  100.521 2.74e-10 92.2366 108.805
-## k1          0.124 5.43e-06  0.0959   0.161
-## k2          0.124 6.45e-02  0.0315   0.490
-## g           0.880      NaN      NA      NA
+## 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
 ## 
 ## 
@@ -627,7 +626,7 @@
 

 

 Example on page 12, lower panel

-
p12b <- nafta(NAFTA_SOP_Attachment[["p12b"]])

+
p12b <- nafta(NAFTA_SOP_Attachment[["p12b"]])

 
## Warning in sqrt(diag(covar)): NaNs wurden erzeugt

 
## Warning in qt(alpha/2, rdf): NaNs wurden erzeugt

 
## Warning in qt(1 - alpha/2, rdf): NaNs wurden erzeugt

@@ -638,9 +637,9 @@
 ## finite result is doubtful

 
## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c

 
## The half-life obtained from the IORE model may be used

-
plot(p12b)

+
plot(p12b)

 

-
print(p12b)

+
print(p12b)

 
## Sums of squares:
 ##      SFO     IORE     DFOP 
 ## 58.90242 19.06353 58.90242 
@@ -667,7 +666,7 @@
 ## parent_0  97.6840    NaN   NaN   NaN
 ## k1         0.0589    NaN    NA    NA
 ## k2         0.0589    NaN    NA    NA
-## g          0.8275    NaN    NA    NA
+## g          0.6902    NaN    NA    NA
 ## sigma      3.4323    NaN   NaN   NaN
 ## 
 ## 
@@ -683,12 +682,16 @@
 

 

 Example on page 13

-
p13 <- nafta(NAFTA_SOP_Attachment[["p13"]])

+
p13 <- nafta(NAFTA_SOP_Attachment[["p13"]])

+
## Warning in sqrt(diag(covar)): NaNs wurden erzeugt

+
## Warning in sqrt(1/diag(V)): NaNs wurden erzeugt

+
## Warning in cov2cor(ans$cov.unscaled): diag(.) had 0 or NA entries; non-
+## finite result is doubtful

 
## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c

 
## The half-life obtained from the IORE model may be used

-
plot(p13)

+
plot(p13)

 

-
print(p13)

+
print(p13)

 
## Sums of squares:
 ##      SFO     IORE     DFOP 
 ## 174.5971 142.3951 174.5971 
@@ -713,9 +716,9 @@
 ## $DFOP
 ##          Estimate   Pr(>t)    Lower    Upper
 ## parent_0 92.73500 9.25e-15 8.95e+01 9.59e+01
-## k1        0.00258 4.28e-01 1.25e-08 5.31e+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
 ## 
 ## 
@@ -732,16 +735,16 @@
 

 

 DT50 not observed in the study and DFOP problems in PestDF

-
p14 <- nafta(NAFTA_SOP_Attachment[["p14"]])

+
p14 <- nafta(NAFTA_SOP_Attachment[["p14"]])

 
## Warning in sqrt(diag(covar)): NaNs wurden erzeugt

 
## Warning in sqrt(1/diag(V)): NaNs wurden erzeugt

 
## Warning in cov2cor(ans$cov.unscaled): diag(.) had 0 or NA entries; non-
 ## finite result is doubtful

 
## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c

 
## The half-life obtained from the IORE model may be used

-
plot(p14)

+
plot(p14)

 

-
print(p14)

+
print(p14)

 
## Sums of squares:
 ##      SFO     IORE     DFOP 
 ## 48.43249 28.67746 27.26248 
@@ -767,7 +770,7 @@
 ##          Estimate   Pr(>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       5.42e-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
 ## 
@@ -776,7 +779,7 @@
 ##          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 3.41e+10 3.31e+11 1.28e+11
+## DFOP 2.54e+10 2.46e+11 9.51e+10
 ## 
 ## Representative half-life:
 ## [1] 6697.44

@@ -785,7 +788,7 @@
 

 

 N is less than 1 and DFOP fraction parameter is below zero

-
p15a <- nafta(NAFTA_SOP_Attachment[["p15a"]])

+
p15a <- nafta(NAFTA_SOP_Attachment[["p15a"]])

 
## Warning in sqrt(diag(covar)): NaNs wurden erzeugt

 
## Warning in sqrt(diag(covar_notrans)): NaNs wurden erzeugt

 
## Warning in sqrt(1/diag(V)): NaNs wurden erzeugt

@@ -793,9 +796,9 @@
 ## finite result is doubtful

 
## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c

 
## The half-life obtained from the IORE model may be used

-
plot(p15a)

+
plot(p15a)

 

-
print(p15a)

+
print(p15a)

 
## Sums of squares:
 ##      SFO     IORE     DFOP 
 ## 245.5248 135.0132 245.5248 
@@ -819,10 +822,10 @@
 ## 
 ## $DFOP
 ##          Estimate   Pr(>t)    Lower    Upper
-## parent_0 97.96751 2.85e-13 94.21913 101.7159
-## k1        0.00952 5.68e-02  0.00262   0.0347
-## k2        0.00952 1.52e-04  0.00639   0.0142
-## g         0.22357      NaN       NA       NA
+## 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
 ## 
 ## 
@@ -834,12 +837,16 @@
 ## 
 ## Representative half-life:
 ## [1] 41.33

-
p15b <- nafta(NAFTA_SOP_Attachment[["p15b"]])

+
p15b <- nafta(NAFTA_SOP_Attachment[["p15b"]])

+
## Warning in sqrt(diag(covar)): NaNs wurden erzeugt

+
## Warning in sqrt(1/diag(V)): NaNs wurden erzeugt

+
## Warning in cov2cor(ans$cov.unscaled): diag(.) had 0 or NA entries; non-
+## finite result is doubtful

 
## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c

 
## The half-life obtained from the IORE model may be used

-
plot(p15b)

+
plot(p15b)

 

-
print(p15b)

+
print(p15b)

 
## Sums of squares:
 ##       SFO      IORE      DFOP 
 ## 106.91629  68.55574 106.91629 
@@ -864,9 +871,9 @@
 ## $DFOP
 ##          Estimate Pr(>t)    Lower    Upper
 ## parent_0 1.01e+02     NA 9.82e+01 1.04e+02
-## k1       4.86e-03     NA 6.49e-04 3.64e-02
-## k2       4.86e-03     NA 3.36e-03 7.03e-03
-## g        1.50e-01     NA 0.00e+00 1.00e+00
+## 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 1.58e+00 3.94e+00
 ## 
 ## 
@@ -883,14 +890,14 @@
 

 

 The DFOP fraction parameter is greater than 1

-
p16 <- nafta(NAFTA_SOP_Attachment[["p16"]])

+
p16 <- nafta(NAFTA_SOP_Attachment[["p16"]])

 
## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c

 
## The representative half-life of the IORE model is longer than the one corresponding

 
## to the terminal degradation rate found with the DFOP model.

 
## The representative half-life obtained from the DFOP model may be used

-
plot(p16)

+
plot(p16)

 

-
print(p16)

+
print(p16)

 
## Sums of squares:
 ##      SFO     IORE     DFOP 
 ## 3831.804 2062.008 1550.980 
@@ -915,7 +922,7 @@
 ## $DFOP
 ##          Estimate   Pr(>t)   Lower  Upper
 ## parent_0  88.5333 7.40e-18 79.9836 97.083
-## k1        18.6315 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/NAFTA_examples_files/figure-html/p14-1.png b/docs/articles/web_only/NAFTA_examples_files/figure-html/p14-1.png
index 8ffc5375..396828c3 100644
Binary files a/docs/articles/web_only/NAFTA_examples_files/figure-html/p14-1.png and b/docs/articles/web_only/NAFTA_examples_files/figure-html/p14-1.png differ
diff --git a/docs/articles/web_only/NAFTA_examples_files/figure-html/p9b-1.png b/docs/articles/web_only/NAFTA_examples_files/figure-html/p9b-1.png
index 48d65737..57bf4014 100644
Binary files a/docs/articles/web_only/NAFTA_examples_files/figure-html/p9b-1.png and b/docs/articles/web_only/NAFTA_examples_files/figure-html/p9b-1.png differ
diff --git a/docs/articles/web_only/benchmarks.html b/docs/articles/web_only/benchmarks.html
index 5f6312ce..6df96c14 100644
--- a/docs/articles/web_only/benchmarks.html
+++ b/docs/articles/web_only/benchmarks.html
@@ -88,7 +88,7 @@
       
Benchmark timings for mkin on various systems

                         
Johannes Ranke

             
-            
2019-05-02

+            
2019-05-03

       
       
       
@@ -115,32 +115,32 @@
 }

 
# Parent only
 t1 <- system.time(mmkin_bench(c("SFO", "FOMC", "DFOP", "HS"), list(FOCUS_2006_C, FOCUS_2006_D)))[["elapsed"]]
-t2 <- system.time(mmkin_bench(c("SFO", "FOMC", "DFOP", "HS"), list(FOCUS_2006_C, FOCUS_2006_D), error_model = "tc"))[["elapsed"]]

-
## Warning in mkinfit(models[[model_index]], datasets[[dataset_index]], ...): Optimisation did not converge:
-## false convergence (8)

-
+t2 <- system.time(mmkin_bench(c("SFO", "FOMC", "DFOP", "HS"), list(FOCUS_2006_C, FOCUS_2006_D), error_model = "tc"))[["elapsed"]]
+
+# One metabolite
+SFO_SFO <- mkinmod(
+  parent = mkinsub("SFO", "m1"),
+  m1 = mkinsub("SFO"))

 
## Successfully compiled differential equation model from auto-generated C code.

-
FOMC_SFO <- mkinmod(
+
+
## Successfully compiled differential equation model from auto-generated C code.

+
 
## Successfully compiled differential equation model from auto-generated C code.

-
-
## Successfully compiled differential equation model from auto-generated C code.

-
t3 <- system.time(mmkin_bench(list(SFO_SFO, FOMC_SFO, DFOP_SFO), list(FOCUS_2006_D)))[["elapsed"]]

-
## Warning in mkinfit(models[[model_index]], datasets[[dataset_index]], ...):
-## Observations with value of zero were removed from the data

+
t3 <- system.time(mmkin_bench(list(SFO_SFO, FOMC_SFO, DFOP_SFO), list(FOCUS_2006_D)))[["elapsed"]]

 
## Warning in mkinfit(models[[model_index]], datasets[[dataset_index]], ...):
 ## Observations with value of zero were removed from the data
 
+## Warning in mkinfit(models[[model_index]], datasets[[dataset_index]], ...):
+## Observations with value of zero were removed from the data
+
 ## Warning in mkinfit(models[[model_index]], datasets[[dataset_index]], ...):
 ## Observations with value of zero were removed from the data

-
t4 <- system.time(mmkin_bench(list(SFO_SFO, FOMC_SFO, DFOP_SFO), list(subset(FOCUS_2006_D, value != 0)), error_model = "tc"))[["elapsed"]]
-t5 <- system.time(mmkin_bench(list(SFO_SFO, FOMC_SFO, DFOP_SFO), list(FOCUS_2006_D), error_model = "obs"))[["elapsed"]]

+
t4 <- system.time(mmkin_bench(list(SFO_SFO, FOMC_SFO, DFOP_SFO), list(subset(FOCUS_2006_D, value != 0)), error_model = "tc"))[["elapsed"]]
+t5 <- system.time(mmkin_bench(list(SFO_SFO, FOMC_SFO, DFOP_SFO), list(FOCUS_2006_D), error_model = "obs"))[["elapsed"]]

 
## Warning in mkinfit(models[[model_index]], datasets[[dataset_index]], ...):
 ## Observations with value of zero were removed from the data
 
@@ -149,32 +149,32 @@
 
 ## Warning in mkinfit(models[[model_index]], datasets[[dataset_index]], ...):
 ## Observations with value of zero were removed from the data

-
# Two metabolites, synthetic data
-m_synth_SFO_lin <- mkinmod(parent = mkinsub("SFO", "M1"),
-                           M1 = mkinsub("SFO", "M2"),
-                           M2 = mkinsub("SFO"),
-                           use_of_ff = "max", quiet = TRUE)
-
-m_synth_DFOP_par <- mkinmod(parent = mkinsub("DFOP", c("M1", "M2")),
-                           M1 = mkinsub("SFO"),
-                           M2 = mkinsub("SFO"),
-                           use_of_ff = "max", quiet = TRUE)
-
-SFO_lin_a <- synthetic_data_for_UBA_2014[[1]]$data
-
-DFOP_par_c <- synthetic_data_for_UBA_2014[[12]]$data
-
-t6 <- system.time(mmkin_bench(list(m_synth_SFO_lin), list(SFO_lin_a)))["elapsed"]
-t7 <- system.time(mmkin_bench(list(m_synth_DFOP_par), list(DFOP_par_c)))["elapsed"]
-
-t8 <- system.time(mmkin_bench(list(m_synth_SFO_lin), list(SFO_lin_a), error_model = "tc"))["elapsed"]
-t9 <- system.time(mmkin_bench(list(m_synth_DFOP_par), list(DFOP_par_c), error_model = "tc"))["elapsed"]
-
-t10 <- system.time(mmkin_bench(list(m_synth_SFO_lin), list(SFO_lin_a), error_model = "obs"))["elapsed"]
-t11 <- system.time(mmkin_bench(list(m_synth_DFOP_par), list(DFOP_par_c), error_model = "obs"))["elapsed"]
-
-mkin_benchmarks[system_string, paste0("t", 1:11)] <- c(t1, t2, t3, t4, t5, t6, t7, t8, t9, t10, t11)
-mkin_benchmarks

+
# Two metabolites, synthetic data
+m_synth_SFO_lin <- mkinmod(parent = mkinsub("SFO", "M1"),
+                           M1 = mkinsub("SFO", "M2"),
+                           M2 = mkinsub("SFO"),
+                           use_of_ff = "max", quiet = TRUE)
+
+m_synth_DFOP_par <- mkinmod(parent = mkinsub("DFOP", c("M1", "M2")),
+                           M1 = mkinsub("SFO"),
+                           M2 = mkinsub("SFO"),
+                           use_of_ff = "max", quiet = TRUE)
+
+SFO_lin_a <- synthetic_data_for_UBA_2014[[1]]$data
+
+DFOP_par_c <- synthetic_data_for_UBA_2014[[12]]$data
+
+t6 <- system.time(mmkin_bench(list(m_synth_SFO_lin), list(SFO_lin_a)))["elapsed"]
+t7 <- system.time(mmkin_bench(list(m_synth_DFOP_par), list(DFOP_par_c)))["elapsed"]
+
+t8 <- system.time(mmkin_bench(list(m_synth_SFO_lin), list(SFO_lin_a), error_model = "tc"))["elapsed"]
+t9 <- system.time(mmkin_bench(list(m_synth_DFOP_par), list(DFOP_par_c), error_model = "tc"))["elapsed"]
+
+t10 <- system.time(mmkin_bench(list(m_synth_SFO_lin), list(SFO_lin_a), error_model = "obs"))["elapsed"]
+t11 <- system.time(mmkin_bench(list(m_synth_DFOP_par), list(DFOP_par_c), error_model = "obs"))["elapsed"]
+
+mkin_benchmarks[system_string, paste0("t", 1:11)] <- c(t1, t2, t3, t4, t5, t6, t7, t8, t9, t10, t11)
+mkin_benchmarks

 
##                                                                                                       CPU
 ## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.48.1 AMD Ryzen 7 1700 Eight-Core Processor
 ## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.1 AMD Ryzen 7 1700 Eight-Core Processor
@@ -198,68 +198,68 @@
 ## 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 5.850
+## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.4 5.864
 ##                                                                         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 20.019
+## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.4 23.254
 ##                                                                        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 4.293
+## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.4 4.544
 ##                                                                         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 14.570
+## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.4 15.757
 ##                                                                        t5
 ## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.48.1 9.495
 ## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.1 6.395
 ## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.2 5.675
 ## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.3 7.386
-## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.4 5.772
+## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.4 7.870
 ##                                                                        t6
 ## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.48.1 2.623
 ## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.1 2.542
 ## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.2 2.723
 ## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.3 2.643
-## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.4 2.647
+## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.4 2.554
 ##                                                                        t7
 ## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.48.1 4.587
 ## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.1 4.128
 ## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.2 4.478
 ## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.3 4.374
-## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.4 4.257
+## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.4  4.22
 ##                                                                        t8
 ## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.48.1 7.525
 ## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.1 4.632
 ## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.2 4.862
 ## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.3  7.02
-## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.4 4.703
+## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.4 6.479
 ##                                                                         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  7.742
+## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.4 11.236
 ##                                                                       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 3.421
+## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.4 4.803
 ##                                                                        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  5.614

-
save(mkin_benchmarks, file = "~/git/mkin/vignettes/mkin_benchmarks.rda")

+## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.4  7.688

+
save(mkin_benchmarks, file = "~/git/mkin/vignettes/mkin_benchmarks.rda")

 

   

 
diff --git a/docs/articles/web_only/compiled_models.html b/docs/articles/web_only/compiled_models.html
index 362bc72c..feba6e23 100644
--- a/docs/articles/web_only/compiled_models.html
+++ b/docs/articles/web_only/compiled_models.html
@@ -88,7 +88,7 @@
       
Performance benefit by using compiled model definitions in mkin

                         
Johannes Ranke

             
-            
2019-05-02

+            
2019-05-03

       
       
       
@@ -163,9 +163,9 @@
 ## Warning in mkinfit(SFO_SFO, FOCUS_2006_D, solution_type = "deSolve", quiet
 ## = TRUE): Observations with value of zero were removed from the data

 
##                    test replications elapsed relative user.self sys.self
-## 3     deSolve, compiled            3   3.174    1.000     3.172        0
-## 1 deSolve, not compiled            3  28.777    9.066    28.764        0
-## 2      Eigenvalue based            3   4.386    1.382     4.383        0
+## 3     deSolve, compiled            3   3.075    1.000     3.072    0.000
+## 1 deSolve, not compiled            3  28.192    9.168    28.168    0.008
+## 2      Eigenvalue based            3   4.351    1.415     4.349    0.000
 ##   user.child sys.child
 ## 3          0         0
 ## 1          0         0
@@ -214,8 +214,8 @@
 ## Warning in mkinfit(FOMC_SFO, FOCUS_2006_D, quiet = TRUE): Observations with
 ## value of zero were removed from the data

 
##                    test replications elapsed relative user.self sys.self
-## 2     deSolve, compiled            3   4.561    1.000     4.559        0
-## 1 deSolve, not compiled            3  49.847   10.929    49.823        0
+## 2     deSolve, compiled            3   4.933    1.000     4.930        0
+## 1 deSolve, not compiled            3  52.879   10.719    52.853        0
 ##   user.child sys.child
 ## 2          0         0
 ## 1          0         0

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