Logistic kinetics

Here we get a performance benefit of a factor of 9 using the version of the differential equation model compiled from C code!

Add the function ‘logLik.mkinfit’ which makes it possible to calculate an AIC for mkinfit objects
‘mkinfit’: Improve the correctness of the fitted two component error model by fitting the mean absolute deviance at each observation against the observed values, weighting with the current two-component error model
‘tests/testthat/test_irls.R’: Test if the components of the error model used to generate the data can be reproduced with moderate accuracy
Add the function ‘CAKE_export’ to facilitate cross-checking of results
Implement the logistic model (only tested for parent fits)

@@ -675,7 +676,7 @@

0.9.47.6
0.9.48.1
0.9.47.5
0.9.47.3
0.9.47.2

IORE.solution()

Indeterminate order rate equation kinetics

logistic.solution()

Logistic kinetics

Logistic kinetics — logistic.solution • mkin

+ + + +

+ +

+ + +

+ +

Function describing exponential decline from a defined starting value, with + an increasing rate constant, supposedly caused by microbial growth

+ +

logistic.solution(t, parent.0, kmax, k0, r)

+ +

Arguments

+ + + + + + + + + + + + + + + + + + + + + + +

t	Time.
parent.0	Starting value for the response variable at time zero.
kmax	Maximum rate constant.
k0	Minumum rate constant effective at time zero.
r	Growth rate of the increase in the rate constant.

+ +

Note

+ +

The solution of the logistic model reduces to the + SFO.solution if k0 is equal to + kmax.

+ +

Value

+ +

The value of the response variable at time t.

+ +

References

+ +

FOCUS (2014) “Generic guidance for Estimating Persistence and + Degradation Kinetics from Environmental Fate Studies on Pesticides in EU + Registration” Report of the FOCUS Work Group on Degradation Kinetics, + Version 1.1, 18 December 2014 + http://esdac.jrc.ec.europa.eu/projects/degradation-kinetics

+ + +

Examples

  # Reproduce the plot on page 57 of FOCUS (2014)
+  plot(function(x) logistic.solution(x, 100, 0.08, 0.0001, 0.2),
+       from = 0, to = 100, ylim = c(0, 100),
+       xlab = "Time", ylab = "Residue")
  plot(function(x) logistic.solution(x, 100, 0.08, 0.0001, 0.4),
+       from = 0, to = 100, add = TRUE, lty = 2, col = 2)
  plot(function(x) logistic.solution(x, 100, 0.08, 0.0001, 0.8),
+       from = 0, to = 100, add = TRUE, lty = 3, col = 3)
  plot(function(x) logistic.solution(x, 100, 0.08, 0.001, 0.2),
+       from = 0, to = 100, add = TRUE, lty = 4, col = 4)
  plot(function(x) logistic.solution(x, 100, 0.08, 0.08, 0.2),
+       from = 0, to = 100, add = TRUE, lty = 5, col = 5)
  legend("topright", inset = 0.05,
+         legend = paste0("k0 = ", c(0.0001, 0.0001, 0.0001, 0.001, 0.08),
+                         ", r = ", c(0.2, 0.4, 0.8, 0.2, 0.2)),
+         lty = 1:5, col = 1:5)

+  # Fit with synthetic data
+  logistic <- mkinmod(parent = mkinsub("logistic"))
+
+  sampling_times = c(0, 1, 3, 7, 14, 28, 60, 90, 120)
+  parms_logistic <- c(kmax = 0.08, k0 = 0.0001, r = 0.2)
+  parms_logistic_optim <- c(parent_0 = 100, parms_logistic)
+  d_logistic <- mkinpredict(logistic,
+    parms_logistic, c(parent = 100),
+    sampling_times)
+  d_2_1 <- add_err(d_logistic,
+    sdfunc = function(x) sigma_twocomp(x, 0.5, 0.07),
+    n = 1, reps = 2, digits = 5, LOD = 0.1, seed = 123456)[[1]]
+
+  m <- mkinfit("logistic", d_2_1)
#> Model cost at call  1 :  789.6044 
+#> Model cost at call  2 :  789.6043 
+#> Model cost at call  7 :  716.9934 
+#> Model cost at call  12 :  697.1186 
+#> Model cost at call  15 :  697.1185 
+#> Model cost at call  16 :  697.1184 
+#> Model cost at call  17 :  661.1574 
+#> Model cost at call  20 :  661.1573 
+#> Model cost at call  22 :  620.0542 
+#> Model cost at call  25 :  620.0541 
+#> Model cost at call  29 :  616.6874 
+#> Model cost at call  32 :  616.6874 
+#> Model cost at call  33 :  616.6874 
+#> Model cost at call  34 :  615.1671 
+#> Model cost at call  37 :  615.1671 
+#> Model cost at call  39 :  612.0795 
+#> Model cost at call  42 :  612.0795 
+#> Model cost at call  43 :  612.0795 
+#> Model cost at call  44 :  605.9119 
+#> Model cost at call  45 :  593.0433 
+#> Model cost at call  46 :  548.0815 
+#> Model cost at call  47 :  504.9062 
+#> Model cost at call  50 :  504.9061 
+#> Model cost at call  51 :  504.9061 
+#> Model cost at call  53 :  485.929 
+#> Model cost at call  55 :  485.929 
+#> Model cost at call  56 :  485.929 
+#> Model cost at call  58 :  485.241 
+#> Model cost at call  60 :  485.241 
+#> Model cost at call  61 :  485.2409 
+#> Model cost at call  62 :  485.2409 
+#> Model cost at call  63 :  484.0717 
+#> Model cost at call  69 :  483.9062 
+#> Model cost at call  74 :  483.5646 
+#> Model cost at call  79 :  483.4908 
+#> Model cost at call  84 :  483.4859 
+#> Model cost at call  85 :  483.4859 
+#> Model cost at call  89 :  483.4848 
+#> Model cost at call  90 :  483.4836 
+#> Model cost at call  92 :  483.4836 
+#> Model cost at call  94 :  483.4836 
+#> Model cost at call  97 :  483.4833 
+#> Model cost at call  100 :  483.4833 
+#> Model cost at call  105 :  483.4832 
+#> Model cost at call  108 :  483.4832 
+#> Model cost at call  114 :  483.4832 
+#> Model cost at call  128 :  483.4832 
+#> Optimisation by method Port successfully terminated.
  plot_sep(m)
  summary(m)$bpar
#>              Estimate   se_notrans    t value       Pr(>t)        Lower
+#> parent_0 1.057896e+02 2.3743105248 44.5559374 6.656664e-16 1.006602e+02
+#> kmax     6.398190e-02 0.0193490291  3.3067243 2.836921e-03 3.329058e-02
+#> k0       1.612775e-04 0.0009640761  0.1672871 4.348592e-01 3.972250e-10
+#> r        2.263946e-01 0.2822811886  0.8020181 2.184792e-01 1.531165e-02
+#>                Upper
+#> parent_0 110.9190170
+#> kmax       0.1229682
+#> k0        65.4803698
+#> r          3.3474197

+ +

+ + +

anisole

list

type

"SFO"

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

fit.1 <- mkinfit(SFO_SFO_SFO, subset(mccall81_245T, soil == "Commerce"), quiet = TRUE) summary(fit.1, data = FALSE)

#> mkin version used for fitting: 0.9.47.6 #> R version used for fitting: 3.5.2 -#> Date of fit: Thu Jan 31 16:51:05 2019 -#> Date of summary: Thu Jan 31 16:51:05 2019 +#> Date of fit: Thu Feb 21 14:30:31 2019 +#> Date of summary: Thu Feb 21 14:30:31 2019 #> #> Equations: #> d_T245/dt = - k_T245_sink * T245 - k_T245_phenol * T245 @@ -171,7 +171,7 @@ #> #> Model predictions using solution type deSolve #> -#> Fitted with method Port using 574 model solutions performed in 3.87 s +#> Fitted with method Port using 574 model solutions performed in 3.822 s #> #> Weighting: none #> @@ -249,8 +249,8 @@ fixed_parms = "k_phenol_sink", quiet = TRUE) summary(fit.2, data = FALSE)

#> mkin version used for fitting: 0.9.47.6 #> R version used for fitting: 3.5.2 -#> Date of fit: Thu Jan 31 16:51:07 2019 -#> Date of summary: Thu Jan 31 16:51:07 2019 +#> Date of fit: Thu Feb 21 14:30:32 2019 +#> Date of summary: Thu Feb 21 14:30:32 2019 #> #> Equations: #> d_T245/dt = - k_T245_sink * T245 - k_T245_phenol * T245 @@ -260,7 +260,7 @@ #> #> Model predictions using solution type deSolve #> -#> Fitted with method Port using 246 model solutions performed in 1.618 s +#> Fitted with method Port using 246 model solutions performed in 1.601 s #> #> Weighting: none #> diff --git a/docs/reference/mkinfit.html b/docs/reference/mkinfit.html index 42845d68..d09b9232 100644 --- a/docs/reference/mkinfit.html +++ b/docs/reference/mkinfit.html @@ -438,15 +438,15 @@ fit <- mkinfit("FOMC", FOCUS_2006_C, quiet = TRUE) summary(fit)

#> mkin version used for fitting: 0.9.47.6 #> R version used for fitting: 3.5.2 -#> Date of fit: Thu Jan 31 16:51:10 2019 -#> Date of summary: Thu Jan 31 16:51:10 2019 +#> Date of fit: Thu Feb 21 14:30:35 2019 +#> Date of summary: Thu Feb 21 14:30:35 2019 #> #> Equations: #> d_parent/dt = - (alpha/beta) * 1/((time/beta) + 1) * parent #> #> Model predictions using solution type analytical #> -#> Fitted with method Port using 64 model solutions performed in 0.162 s +#> Fitted with method Port using 64 model solutions performed in 0.16 s #> #> Weighting: none #> @@ -515,7 +515,7 @@ m1 = mkinsub("SFO"))

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

# Fit the model to the FOCUS example dataset D using defaults print(system.time(fit <- mkinfit(SFO_SFO, FOCUS_2006_D, solution_type = "eigen", quiet = TRUE)))

#> User System verstrichen -#> 1.022 0.000 1.025

coef(fit)

#> parent_0 log_k_parent_sink log_k_parent_m1 log_k_m1_sink +#> 1.017 0.004 1.022

coef(fit)

#> parent_0 log_k_parent_sink log_k_parent_m1 log_k_m1_sink #> 99.59848 -3.03822 -2.98030 -5.24750

endpoints(fit)

#> $ff #> parent_sink parent_m1 m1_sink #> 0.485524 0.514476 1.000000 @@ -590,7 +590,7 @@ #> Model cost at call 146 : 371.2134 #> Optimisation by method Port successfully terminated. #> User System verstrichen -#> 0.823 0.000 0.823

coef(fit.deSolve)

#> parent_0 log_k_parent_sink log_k_parent_m1 log_k_m1_sink +#> 0.845 0.000 0.846

coef(fit.deSolve)

#> parent_0 log_k_parent_sink log_k_parent_m1 log_k_m1_sink #> 99.59848 -3.03822 -2.98030 -5.24750

endpoints(fit.deSolve)

#> $ff #> parent_sink parent_m1 m1_sink #> 0.485524 0.514476 1.000000 @@ -628,8 +628,8 @@ m1 = mkinsub("SFO"), use_of_ff = "max")

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

f.noweight <- mkinfit(SFO_SFO.ff, FOCUS_2006_D, quiet = TRUE) summary(f.noweight)

#> mkin version used for fitting: 0.9.47.6 #> R version used for fitting: 3.5.2 -#> Date of fit: Thu Jan 31 16:51:22 2019 -#> Date of summary: Thu Jan 31 16:51:22 2019 +#> Date of fit: Thu Feb 21 14:30:47 2019 +#> Date of summary: Thu Feb 21 14:30:47 2019 #> #> Equations: #> d_parent/dt = - k_parent * parent @@ -637,7 +637,7 @@ #> #> Model predictions using solution type deSolve #> -#> Fitted with method Port using 186 model solutions performed in 0.872 s +#> Fitted with method Port using 186 model solutions performed in 0.86 s #> #> Weighting: none #> @@ -745,8 +745,8 @@ #> 120 m1 33.31 28.78984 4.520e+00

f.irls <- mkinfit(SFO_SFO.ff, FOCUS_2006_D, reweight.method = "obs", quiet = TRUE) summary(f.irls)

#> mkin version used for fitting: 0.9.47.6 #> R version used for fitting: 3.5.2 -#> Date of fit: Thu Jan 31 16:51:24 2019 -#> Date of summary: Thu Jan 31 16:51:24 2019 +#> Date of fit: Thu Feb 21 14:30:50 2019 +#> Date of summary: Thu Feb 21 14:30:50 2019 #> #> Equations: #> d_parent/dt = - k_parent * parent @@ -754,7 +754,7 @@ #> #> Model predictions using solution type deSolve #> -#> Fitted with method Port using 551 model solutions performed in 2.558 s +#> Fitted with method Port using 551 model solutions performed in 2.529 s #> #> Weighting: none #> @@ -867,8 +867,8 @@ #> 120 m1 33.31 28.80898 4.501e+00 2.722

f.w.mean <- mkinfit(SFO_SFO.ff, FOCUS_2006_D, weight = "mean", quiet = TRUE) summary(f.w.mean)

#> mkin version used for fitting: 0.9.47.6 #> R version used for fitting: 3.5.2 -#> Date of fit: Thu Jan 31 16:51:25 2019 -#> Date of summary: Thu Jan 31 16:51:25 2019 +#> Date of fit: Thu Feb 21 14:30:51 2019 +#> Date of summary: Thu Feb 21 14:30:51 2019 #> #> Equations: #> d_parent/dt = - k_parent * parent @@ -876,7 +876,7 @@ #> #> Model predictions using solution type deSolve #> -#> Fitted with method Port using 155 model solutions performed in 0.711 s +#> Fitted with method Port using 155 model solutions performed in 0.707 s #> #> Weighting: mean #> @@ -985,8 +985,8 @@ quiet = TRUE) summary(f.w.value)

#> mkin version used for fitting: 0.9.47.6 #> R version used for fitting: 3.5.2 -#> Date of fit: Thu Jan 31 16:51:26 2019 -#> Date of summary: Thu Jan 31 16:51:26 2019 +#> Date of fit: Thu Feb 21 14:30:52 2019 +#> Date of summary: Thu Feb 21 14:30:52 2019 #> #> Equations: #> d_parent/dt = - k_parent * parent @@ -994,7 +994,7 @@ #> #> Model predictions using solution type deSolve #> -#> Fitted with method Port using 174 model solutions performed in 0.807 s +#> Fitted with method Port using 174 model solutions performed in 0.792 s #> #> Weighting: manual #> @@ -1105,8 +1105,8 @@ f.w.man <- mkinfit(SFO_SFO.ff, dw, err = "err.man", quiet = TRUE) summary(f.w.man)

#> mkin version used for fitting: 0.9.47.6 #> R version used for fitting: 3.5.2 -#> Date of fit: Thu Jan 31 16:51:28 2019 -#> Date of summary: Thu Jan 31 16:51:28 2019 +#> Date of fit: Thu Feb 21 14:30:53 2019 +#> Date of summary: Thu Feb 21 14:30:53 2019 #> #> Equations: #> d_parent/dt = - k_parent * parent @@ -1114,7 +1114,7 @@ #> #> Model predictions using solution type deSolve #> -#> Fitted with method Port using 270 model solutions performed in 1.257 s +#> Fitted with method Port using 270 model solutions performed in 1.243 s #> #> Weighting: manual #> @@ -1223,8 +1223,8 @@ reweight.method = "obs") summary(f.w.man.irls)

#> mkin version used for fitting: 0.9.47.6 #> R version used for fitting: 3.5.2 -#> Date of fit: Thu Jan 31 16:51:31 2019 -#> Date of summary: Thu Jan 31 16:51:31 2019 +#> Date of fit: Thu Feb 21 14:30:57 2019 +#> Date of summary: Thu Feb 21 14:30:57 2019 #> #> Equations: #> d_parent/dt = - k_parent * parent @@ -1232,7 +1232,7 @@ #> #> Model predictions using solution type deSolve #> -#> Fitted with method Port using 692 model solutions performed in 3.3 s +#> Fitted with method Port using 692 model solutions performed in 3.27 s #> #> Weighting: manual #> diff --git a/docs/reference/mkinmod.html b/docs/reference/mkinmod.html index 84b335f7..0710e6de 100644 --- a/docs/reference/mkinmod.html +++ b/docs/reference/mkinmod.html @@ -231,7 +231,7 @@ For the definition of model types and their parameters, the equations given SFO_SFO <- mkinmod( parent = mkinsub("SFO", "m1"), m1 = mkinsub("SFO"), verbose = TRUE)

#> Compilation argument: -#> /usr/lib/R/bin/R CMD SHLIB file165a4bc987b7.c 2> file165a4bc987b7.c.err.txt +#> /usr/lib/R/bin/R CMD SHLIB file33652d0fd552.c 2> file33652d0fd552.c.err.txt #> Program source: #> 1: #include <R.h> #> 2: diff --git a/docs/reference/mkinpredict.html b/docs/reference/mkinpredict.html index c34da511..8c5bf22b 100644 --- a/docs/reference/mkinpredict.html +++ b/docs/reference/mkinpredict.html @@ -325,7 +325,7 @@ c(parent = 100, m1 = 0), seq(0, 20, by = 0.1), solution_type = "eigen")[201,]))

#> time parent m1 #> 201 20 4.978707 27.46227

#> User System verstrichen -#> 0.003 0.000 0.003

system.time( +#> 0.004 0.000 0.004

system.time( print(mkinpredict(SFO_SFO, c(k_parent_m1 = 0.05, k_parent_sink = 0.1, k_m1_sink = 0.01), c(parent = 100, m1 = 0), seq(0, 20, by = 0.1), solution_type = "deSolve")[201,]))

#> time parent m1 @@ -335,7 +335,7 @@ c(parent = 100, m1 = 0), seq(0, 20, by = 0.1), solution_type = "deSolve", use_compiled = FALSE)[201,]))

#> time parent m1 #> 201 20 4.978707 27.46227

#> User System verstrichen -#> 0.042 0.000 0.042

+#> 0.047 0.000 0.047

# Predict from a fitted model f <- mkinfit(SFO_SFO, FOCUS_2006_C)

#> Model cost at call 1 : 552.5739 #> Model cost at call 3 : 552.5739 diff --git a/docs/reference/mmkin.html b/docs/reference/mmkin.html index 3fa5c9a5..75da28c7 100644 --- a/docs/reference/mmkin.html +++ b/docs/reference/mmkin.html @@ -191,8 +191,8 @@ time_1 <- system.time(fits.4 <- mmkin(models, datasets, cores = 1, quiet = TRUE)) time_default

#> User System verstrichen -#> 0.045 0.036 7.264

time_1

#> User System verstrichen -#> 22.905 0.000 22.919

+#> 0.039 0.040 7.082

time_1

#> User System verstrichen +#> 22.650 0.004 22.666

endpoints(fits.0[["SFO_lin", 2]])

#> $ff #> parent_M1 parent_sink M1_M2 M1_sink #> 0.7340480 0.2659520 0.7505686 0.2494314 diff --git a/docs/reference/summary.mkinfit.html b/docs/reference/summary.mkinfit.html index 2815eccb..242d9f63 100644 --- a/docs/reference/summary.mkinfit.html +++ b/docs/reference/summary.mkinfit.html @@ -208,8 +208,8 @@

Examples

  summary(mkinfit(mkinmod(parent = mkinsub("SFO")), FOCUS_2006_A, quiet = TRUE))
#> mkin version used for fitting:    0.9.47.6 
 #> R version used for fitting:       3.5.2 
-#> Date of fit:     Thu Jan 31 16:52:23 2019 
-#> Date of summary: Thu Jan 31 16:52:23 2019 
+#> Date of fit:     Thu Feb 21 14:31:48 2019 
+#> Date of summary: Thu Feb 21 14:31:48 2019 
 #> 
 #> Equations:
 #> d_parent/dt = - k_parent_sink * parent
diff --git a/docs/reference/transform_odeparms.html b/docs/reference/transform_odeparms.html
index d3c20ed8..939fa7b4 100644
--- a/docs/reference/transform_odeparms.html
+++ b/docs/reference/transform_odeparms.html
@@ -202,8 +202,8 @@ The transformation of sets of formation fractions is fragile, as it supposes
 fit <- mkinfit(SFO_SFO, FOCUS_2006_D, quiet = TRUE)
 summary(fit, data=FALSE) # See transformed and backtransformed parameters
#> mkin version used for fitting:    0.9.47.6 
 #> R version used for fitting:       3.5.2 
-#> Date of fit:     Thu Jan 31 16:52:31 2019 
-#> Date of summary: Thu Jan 31 16:52:31 2019 
+#> Date of fit:     Thu Feb 21 14:31:57 2019 
+#> Date of summary: Thu Feb 21 14:31:57 2019 
 #> 
 #> Equations:
 #> d_parent/dt = - k_parent_sink * parent - k_parent_m1 * parent
@@ -211,7 +211,7 @@ The transformation of sets of formation fractions is fragile, as it supposes
 #> 
 #> Model predictions using solution type deSolve 
 #> 
-#> Fitted with method Port using 153 model solutions performed in 0.703 s
+#> Fitted with method Port using 153 model solutions performed in 0.849 s
 #> 
 #> Weighting: none
 #> 
@@ -278,8 +278,8 @@ The transformation of sets of formation fractions is fragile, as it supposes
 
fit.2 <- mkinfit(SFO_SFO, FOCUS_2006_D, transform_rates = FALSE, quiet = TRUE)
 summary(fit.2, data=FALSE)
#> mkin version used for fitting:    0.9.47.6 
 #> R version used for fitting:       3.5.2 
-#> Date of fit:     Thu Jan 31 16:52:33 2019 
-#> Date of summary: Thu Jan 31 16:52:33 2019 
+#> Date of fit:     Thu Feb 21 14:31:59 2019 
+#> Date of summary: Thu Feb 21 14:31:59 2019 
 #> 
 #> Equations:
 #> d_parent/dt = - k_parent_sink * parent - k_parent_m1 * parent
@@ -287,7 +287,7 @@ The transformation of sets of formation fractions is fragile, as it supposes
 #> 
 #> Model predictions using solution type deSolve 
 #> 
-#> Fitted with method Port using 350 model solutions performed in 1.597 s
+#> Fitted with method Port using 350 model solutions performed in 1.649 s
 #> 
 #> Weighting: none
 #> 
@@ -366,8 +366,8 @@ The transformation of sets of formation fractions is fragile, as it supposes
 fit.ff <- mkinfit(SFO_SFO.ff, FOCUS_2006_D, quiet = TRUE)
 summary(fit.ff, data = FALSE)
#> mkin version used for fitting:    0.9.47.6 
 #> R version used for fitting:       3.5.2 
-#> Date of fit:     Thu Jan 31 16:52:34 2019 
-#> Date of summary: Thu Jan 31 16:52:34 2019 
+#> Date of fit:     Thu Feb 21 14:32:00 2019 
+#> Date of summary: Thu Feb 21 14:32:00 2019 
 #> 
 #> Equations:
 #> d_parent/dt = - k_parent * parent
@@ -375,7 +375,7 @@ The transformation of sets of formation fractions is fragile, as it supposes
 #> 
 #> Model predictions using solution type deSolve 
 #> 
-#> Fitted with method Port using 186 model solutions performed in 0.898 s
+#> Fitted with method Port using 186 model solutions performed in 0.976 s
 #> 
 #> Weighting: none
 #> 
@@ -450,8 +450,8 @@ The transformation of sets of formation fractions is fragile, as it supposes
 fit.ff.2 <- mkinfit(SFO_SFO.ff.2, FOCUS_2006_D, quiet = TRUE)
 summary(fit.ff.2, data = FALSE)
#> mkin version used for fitting:    0.9.47.6 
 #> R version used for fitting:       3.5.2 
-#> Date of fit:     Thu Jan 31 16:52:35 2019 
-#> Date of summary: Thu Jan 31 16:52:35 2019 
+#> Date of fit:     Thu Feb 21 14:32:01 2019 
+#> Date of summary: Thu Feb 21 14:32:01 2019 
 #> 
 #> Equations:
 #> d_parent/dt = - k_parent * parent
@@ -459,7 +459,7 @@ The transformation of sets of formation fractions is fragile, as it supposes
 #> 
 #> Model predictions using solution type deSolve 
 #> 
-#> Fitted with method Port using 104 model solutions performed in 0.482 s
+#> Fitted with method Port using 104 model solutions performed in 0.512 s
 #> 
 #> Weighting: none
 #> 
-- 
cgit v1.2.1

Example evaluation of FOCUS Example Dataset D

Johannes Ranke

2019-01-31

2019-02-21

Example evaluation of FOCUS Laboratory Data L1 to L3

Johannes Ranke

2019-01-31

2019-02-21

Introduction to mkin

Johannes Ranke

2019-01-31

2019-02-21

Calculation of time weighted average concentrations with mkin

Johannes Ranke

2019-01-31

2019-02-21

Example evaluation of FOCUS dataset Z

Johannes Ranke

2019-01-31

2019-02-21

Performance benefit by using compiled model definitions in mkin

Johannes Ranke

2019-01-31

2019-02-21

-mkin 0.9.47.6 (2019-01-31) Unreleased +mkin 0.9.48.1 (2019-02-21) Unreleased

Contents

Arguments

Note

Value

References

Examples

Contents

Examples