# file "Rsteep4"  (related to Q4 of HW#2)

x = c(3,4,8,10,11)

y = c(5,10,21,35,40)

f = function(delta, beta) { sum((y - delta * x^beta)^2) }

fdelta = function(delta,beta) { sum(-2*(y-delta*x^beta)*x^beta) }

fbeta = function(delta,beta) { sum(-2*(y-delta*x^beta)*delta*x^beta*log(x)) }

alpha = -0.2

deltalist = betalist = c(1)

for (i in 1:500) {

    deltaprev = deltalist[length(deltalist)]
    betaprev = betalist[length(betalist)]

    deltanew = deltaprev + alpha * fdelta(deltaprev,betaprev)
    betanew = betaprev + alpha * fbeta(deltaprev,betaprev)

    # Do the "retraction" step.
    while ( f(deltanew,betanew) > f(deltaprev,betaprev) ) {
        deltanew = (deltanew+deltaprev)/2
        betanew = (betanew+betaprev)/2
    }

    deltalist = c( deltalist, deltanew )
    betalist = c( betalist, betanew )

}

print(deltalist[length(deltalist)])
print(betalist[length(betalist)])

plot(deltalist, betalist, type='b')