##  ============================================================
##  Gradient descent using R - on quadratic function (no graph)

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##  ============================================================

## Assume that we have the following quadratic function
##   quadratic function: x^2 - 3*x +1

##  1. Let's create our gradient of our quadratic function
##  as we need it for gradient descent
##  --------------------------------------------------
gradient_quadratic_fn <- function(x){
  2*x - 3
} 


##  2. Create a gradient descent function that can trace every steps
##  ----------------------------------------------------------------
##  Note: This gradient descent is only designed to work on our specified
##  quadratic function.

gradient_descent<- function(x, learn_rate, conv_threshold, max_iter){
  ##  1. Initialise key parameters
  ##  ----------------------------
  y <- quadratic_func(x)
  converged = F
  iterations = 0
  learn_rate0 = learn_rate
  
  ##  2. Create the gradient descent loop
  ##  --------------------------------------
  while(converged == F) {
    
    ##  (a) core gradient descent algorithm
    ##  -----------------------------------
    gradient <- gradient_quadratic_fn(x)
    x_new <- x - learn_rate * gradient
    y <- quadratic_func(x_new)
    
    ##  (b) checking for convergence
    ##  ----------------------------
    if( abs(x_new - x) <= conv_threshold) {
      converged = T
    }

    ##  (c) checking if max iteration is reached
    ##  ------------------------------------
    if(iterations >= max_iter) {
      break
    }
    
    x <- x_new
  }
  return(c(x_new, y))
  
}

##  3.  Using our gradient descent function
##  ---------------------------------------------
gradient_descent(x = 0.2,                  ## initial x_value
                 learn_rate = 0.2,         ## learning rate
                 conv_threshold = 0.00001, ## convergence threshold
                 max_iter = 100            ## maximum iteration
                 )