Mimic minimize function from Python in R

I have the following data points:

xdata looks like the following.

ydata looks like the following.

I am running the following commands in python:

results = minimize(fit.dataFit,cParams,args=(xdata,np.array(ydata)))
curve = np.array(ydata)+results.residual
Std = [list(i) for i in zip(xdata,ydata, curve)]

My main problem is being unable to track the stream of changes to the data. dataFit does the following operation:

y_model = (ymax*xdata / (ec50 + xdata)) + Ns* xdata + ymin return y_model - ydata

where

ymax = 1624.75
ymin = 91.85
ec50 = 3
Ns = 0.2045514

Lastly, minimize is being called from the following library:

from lmfit import minimize,Minimizer,Parameters,Parameter,report_errors,report_fit

The results I get for Std in python are:

I am trying to replicate the same results in R or in Excel. Either one will be sufficient. The problem I am having is that I unable to accurately mimic the same behavior as the minimize (which is minimizing least-squares) and residual. I have tried searching for corresponding libraries in R with the minimize and residual function; however, I was not able to find any(nor use it correctly) that gave me the same results as in Python.

When I graph xdata, ydata, and the results of minimize (which I have provided above), I get the following graph in Python. Ultimately, I would just like to reproduce this same graph in R or Excel.

How to proceed? I am not an expert in Python, hence, I am not able to correctly port the code from Python to R or Excel.

Solution

You can replicate this in R using the function nls(). First, I set up your data so it can be read into R.

## Replicate results from Python `minimize` with R `nls()`
# First I load your data in
df <- data.frame(xdata = c(1000.00,300.00,100.00,30.00,10.00,3.00,1.00,0.30,
                           0.10,0.03,0.01,0.00),
                 ydata = c(91.8,95.3,100,123,203,620,1210,1520,1510,1520,1590,
                           1620))

# Now we estimate the model via nonlinear least squares
nls.fit <- nls(ydata ~ (ymax*xdata / (ec50 + xdata)) + Ns*xdata + ymin, data=df,
    start=list(ymax=1624.75, ymin = 91.85, ec50 = 3, Ns = 0.2045514))

I use your starting values for the parameters, although these are not the values that the model settles on. To see the parameters type nls.fit into the console and R will display information about the fitted model.

df$nls.pred <- fitted(nls.fit) # We extract the predicted values of the model
head(df) # We can examine the values of `xdata`, `ydata` and our predictions

  xdata ydata  nls.pred
1  1000  91.8 109.48985
2   300  95.3  49.02029
3   100 100.0  52.29715
4    30 123.0 120.61060
5    10 203.0 298.55367
6     3 620.0 687.63743

# We can see that the values we have obtained are very close to 
# what you obtained in the variable you named Std in python.

# I now load the ggplot2 library to recreate your plot
library(ggplot2)
ggplot(df, aes(xdata, ydata))+geom_point(color='red')+
  geom_line(data=df, aes(xdata, nls.pred))+
  theme_classic()+ # This makes the background black and white as in your plot 
  scale_x_log10() # The axis in your post is logged