The latest articles on DEV Community by eyakem-a11 (@eyakema11). https://dev.to/eyakema11 https://media2.dev.to/dynamic/image/width=90,height=90,fit=cover,gravity=auto,format=auto/https:%2F%2Fdev-to-uploads.s3.amazonaws.com%2Fuploads%2Fuser%2Fprofile_image%2F2268276%2F9492427c-69c6-41cf-b638-8c396715fd1e.jpg https://dev.to/eyakema11 en eyakem-a11 Thu, 24 Oct 2024 21:25:34 +0000 https://dev.to/eyakema11/varying-the-unknown-parameter-with-optimization-criteria-5d0m https://dev.to/eyakema11/varying-the-unknown-parameter-with-optimization-criteria-5d0m <p>In the case of M=4 <br> set.seed(1)<br> t= Obr_56_n_T2_250713$V1<br> y= Obr_56_n_T2_250713$V2</p> <h1> definition of the 8D exponential sum square functions </h1> <p>f=function(param) {<br> sum((param[1] + (param[2]<em>exp(-(t)/param[3])+param[4]*exp(-(t)/param[5])+param[6]*exp(-(t)/param[7])+param[8]*exp(-(t)/param[9]) - y)^2))<br> }<br> derivative=function(param) {<br> return(c(2*sum(param[1] +<br> (param[2]*exp(-(t)/param[3])+param[4]*exp(-(t)/param[5])+param[6]*exp(-(t)/param[7])+param[8]*exp(-(t)/param[9])) - y),<br> 2*sum(exp(-(t)/param[3])</em>(param[1] +<br> (param[2]<em>exp(-(t)/param[3])+param[4]*exp(-(t)/param[5])+param[6]*exp(-(t)/param[7])+param[8]*exp(-(t)/param[9])) - y)),<br> 2*sum((param[2]</em>((t)/(param[3])^2)<em>exp(-(t)/param[3]))</em>(param[1] +<br> (param[2]<em>exp(-(t)/param[3])+param[4]*exp(-(t)/param[5])+param[6]*exp(-(t)/param[7])+param[8]*exp(-(t)/param[9])) - y)),<br> 2*sum((exp(-(t)/param[5]))</em>(param[1] +<br> (param[2]<em>exp(-(t)/param[3])+param[4]*exp(-(t)/param[5])+param[6]*exp(-(t)/param[7])+param[8]*exp(-(t)/param[9])) - y)),<br> 2*sum((param[4]</em>((t)/(param[5])^2)<em>exp(-(t)/param[5]))</em>(param[1] +<br> (param[2]<em>exp(-(t)/param[3])+param[4]*exp(-(t)/param[5])+param[6]*exp(-(t)/param[7])+param[8]*exp(-(t)/param[9])) - y)),<br> 2*sum((exp(-(t)/param[7]))</em>(param[1] +<br> (param[2]<em>exp(-(t)/param[3])+param[4]*exp(-(t)/param[5])+param[6]*exp(-(t)/param[7])+param[8]*exp(-(t)/param[9])) - y)),<br> 2*sum((param[6]</em>((t)/(param[7])^2)<em>exp(-(t)/param[7]))</em>(param[1] +<br> (param[2]<em>exp(-(t)/param[3])+param[4]*exp(-(t)/param[5])+param[6]*exp(-(t)/param[7])+param[8]*exp(-(t)/param[9])) - y)),<br> 2*sum((exp(-(t)/param[9]))</em>(param[1] +<br> (param[2]<em>exp(-(t)/param[3])+param[4]*exp(-(t)/param[5])+param[6]*exp(-(t)/param[7])+param[8]*exp(-(t)/param[9])) - y)),<br> 2*sum((param[8]</em>((t)/(param[9])^2)<em>exp(-(t)/param[9]))</em>(param[1] +<br> (param[2]*exp(-(t)/param[3])+param[4]*exp(-(t)/param[5])+param[6]*exp(-(t)/param[7])+param[8]*exp(-(t)/param[9])) - y))))<br> }</p> <h1> locate the minimum of the function using the Nelder-Mead method </h1> <p>result=optim(<br> c(runif(1,0,20000),runif(1,0,20000),runif(1,0,20000),runif(1,0,20000),runif(1,0,20000),runif(1,0,20000),runif(1,0,20000),runif(1,0,20000),runif(1,0,20000)), # start at a random position<br> f, # the function to minimize<br> derivative, # no function gradient<br> method="L-BFGS-B", # use the L-BFGS-B method<br> control=c( # configure Nelder-Mead<br> maxit=100, # maximum iterations of 100<br> factr=1e-8, # response tolerance over-one step<br> alpha=1.0, # reflection factor<br> beta=0.5, # contraction factor<br> gamma=2.0),<br> lower=0.1,<br> upper = Inf<br> )<br> result</p>