# [Rcpp-devel] Cxx Function Signature for gradient descent algorithm

ANKIT CHAKRABORTY ankitchak396 at gmail.com
Wed Jul 22 14:16:05 CEST 2020

```Hello Team,
Greetings. I am implementing the gradient descent
function on the cxx function and have not been able to find the correct
function argument without errors. Could you please suggest the *correct
function argument* for implementing it. The complete R code for the
gradient descent algorithm and my code is provided below :

--------------------------------------------------------------

DESCENT ALGORITHM#OBJECTIVE: MINIMIZE THE FUNCTION *

*#FIRST, DEFINE THE FUNCTION f(theta)objfun <- function(theta){  return(1 +
3*(theta + 3)^2 )}#DEFINE A FUNCTION THAT CALCULATES THE DERIVATIVE
f'(theta) # AT INPUT VALUE thetaderiv <- function(theta){  return( 6*(theta
+ 3 ) )}#PLOT THE FUNCTION WE ARE SEEKING TO MINIMIZE OVER THE RANGE [-15,
15]theta_seq <- seq(-20,15, len = 1000)plot(theta_seq, objfun(theta_seq),
type = "l",      ylab = "f(theta)", xlab = "theta")points(10, objfun(10),
col = "red")tol <- 0.0000001 #CONVERGENCE THRESHOLDalpha <- 0.01  #LEARNING
RATEtheta0 <- 10  #SELECT INITIAL GUESS FOR THETAnewval <- objfun( theta0 )
#inital value of f(theta)points(theta0, newval, col = "red") #add current
theta to plotrel_ch <- 1 #(arbitrary) init. val for relative change in
objective functionj <- 1 #iteration countertheta <- c() #vector to store
theta at each iterationtheta[j] <- theta0 #theta[j] stores current value of
theta#update theta while relative change in f(theta) is greater than
tolwhile( rel_ch > tol ) {  j <- j+1; #increment j  #update theta  #set
theta_new =  theta_previous - ( learning rate )* f'(theta_previous)
theta[j] <- theta[j-1] - alpha * deriv(theta[ j-1 ])    #test relative
absolute change in target function  oldval <- newval #store
f(theta_previous)   newval <- objfun(theta[j]) #calculate f(theta_new)
points(theta[j], newval, col = "red") #add new theta to plot
Sys.sleep(0.1) #pause algorithm to give you time to see dot appear on plot
#calculate relative change f(theta) from previous iteration to current
iteration  rel_ch <- abs(  ( newval - oldval ) / oldval ) #use to test
convergence}#R version EXECUTED WITHOUT A PLOT (NON SLOW MOTION
VERSION)gdes <- function( theta0  , tol = 0.00000001, alpha = 0.01 ){
newval <- objfun( theta0 ) #inital value of target function  rel_ch <- 1
#to store relative change in objective function  j <- 1 #iteration counter
theta <- c(theta0) #vector to store parameter    while( rel_ch > tol )  {
j <- j+1; #increment counter    theta[j] <- theta[j-1] - alpha *
deriv(theta[ j-1 ])        #test relative absolute change in target
function    oldval <- newval    newval <- objfun(theta[j])    rel_ch <-
abs(  ( newval - oldval ) / oldval )  } #end of while    return( list(
theta = theta[j], thetavec = theta, min_f = newval, niter = j ) )} #end of
gdes function opt <- gdes(10) opt\$thetaopt\$min_f*

--------------------------------------------------------------------------

MY  TRY :

*library(Rcpp)library(inline)# and define our version in C++src <- 'int
theta0 = as<int>(ns);int j = as<int>(ns1);int rel_ch = as<int>(ns2);int
min_f = as<int>(ns22);int oldval = as<int>(rup);int dif = as<int>(ank);int
newval = as<int>(saha);int niter = as<int>(nit);NumericVector theta =
as<NumericVector>(theta1);NumericVector thetavec =
as<NumericVector>(thetavector);double tol = as<double>(xs);double alpha =
as<double>(rt);while(rel_ch>tol) j=j+1; theta[j] = theta[j-1] - alpha *
6*(theta[j-1] + 3 ); oldval = (1 + 3*pow(theta0 + 3),2); newval = (1 +
3*pow(theta[j] + 3),2); dif = (newval - oldval);rel_ch = abs(dif) / oldval
);              theta = theta[j];thetavec = theta;min_f = newval;niter = j;
return wrap(theta);return wrap(thetavec);return wrap(min_f);return
wrap(niter);'al <- cxxfunction(signature(ns="integer", nit="integer",ns22 =
"integer",ns1 = "integer", ns2 = "integer", ank = "integer", rup =
"integer", saha =
"integer",theta1="NumericVector",thetavector="NumericVector",
xs="numeric",rt="numeric"),                  body=src,
plugin="Rcpp")*
----------------------------------------------------------------------------------

Sincerely,
Ankit Chakraborty
Machine Learning Engineer, EEGRAB
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