This function provids a visual illustration for the process of minimizing a realvalued function through Gradient Descent Algorithm.
1 2 3 
FUN 
a bivariate objective function to be minimized (variable names do
not have to be 
rg 
ranges for independent variables to plot contours; in a 
init 
starting values 
gamma 
size of a step 
tol 
tolerance to stop the iterations, i.e. the minimum difference between F(x[i]) and F(x[i+1]) 
gr 
the gradient of 
len 
desired length of the independent sequences (to compute z values for contours) 
interact 
logical; whether choose the starting values by clicking on the contour plot directly? 
col.contour, col.arrow 
colors for the contour lines and arrows respectively (default to be red and blue) 
main 
the title of the plot; if missing, it will be derived from

Gradient descent is an optimization algorithm. To find a local minimum of a function using gradient descent, one takes steps proportional to the negative of the gradient (or the approximate gradient) of the function at the current point. If instead one takes steps proportional to the gradient, one approaches a local maximum of that function; the procedure is then known as gradient ascent.
The arrows are indicating the result of iterations and the process of
minimization; they will go to a local minimum in the end if the maximum
number of iterations ani.options('nmax')
has not been reached.
A list containing
par 
the solution for the local minimum 
value 
the value of the objective function corresponding to

iter 
the number of iterations; if it is equal to

gradient 
the gradient function of the objective function 
persp 
a function to make the perspective plot of the objective
function; can accept further arguments from 
Please make sure the function FUN
provided is differentiable at
init
, what's more, it should also be 'differentiable' using
deriv
if you do not provide the gradient function gr
.
If the arrows cannot reach the local minimum, the maximum number of
iterations nmax
in ani.options
may need to be
increased.
Yihui Xie
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