def gradient(y, slope, guess, e, iter, prev_val, prev_gk):
iter = iter + 1
# slope_val holds values of slope at guess value
slope_gk = slope.subs(x1, guess[0]).subs(x2, guess[1])
if iter > 1:
# iteration 2 onwards consists of new direction search
# find new direction dependent on previous direction
slope_val = (-1 * slope_gk) + (
(slope_gk.transpose() * slope_gk)[0] / (prev_gk.transpose() * prev_gk)[0]
) * prev_val
else:
slope_val = -1 * slope_gk
# xiter and yiter hold x and y coordinates of guess for plotting
xiter.append(guess[0])
yiter.append(guess[1])
# prev holds guess for comparison
prev = guess
# gold holds guess with alpha parameter ready for golden search
gold = [guess[0] + (h * slope_val[0, 0]), guess[1] + (h * slope_val[1, 0])]
# alpha is the function in alpha parameter ready to be minimized
alpha = function(gold)
# minima holds minimum value of alpha after golden section search
# minimizer(function, start, end, interval spacing)
minima = golden_search.minimizer(alpha, -10, 10, 1)
# get new guess value
guess = [guess[0] + (minima * slope_val[0, 0]), guess[1] + (minima * slope_val[1, 0])]
print guess
# check condition and proceed
if math.fabs(prev[0] - guess[0]) > e or math.fabs(prev[1] - guess[1]) > e:
# store current slope value (slope_val) in prev_val
gradient(y, slope, guess, e, iter, slope_val, slope_gk)
return xiter, yiter
def gradient(y, slope, guess, e):
#slope_val holds values of slope at guess value
slope_val = slope.subs(x1, guess[0]).subs(x2, guess[1])
#xiter and yiter hold x and y coordinates of guess for plotting
xiter.append(guess[0])
yiter.append(guess[1])
funcval.append(function([guess[0], guess[1]]))
#prev holds guess for comparison
prev = guess
#gold holds guess with alpha parameter ready for golden search
gold = [guess[0] - (h * slope_val[0, 0]), guess[1] - (h * slope_val[1, 0])]
#alpha is the function in alpha parameter ready to be minimized
alpha = function(gold)
#minima holds minimum value of alpha after golden section search
#minimizer(function, start, end, interval spacing)
minima = golden_search.minimizer(alpha, -10, 10, 1)
#get new guess value
guess = [guess[0] - (minima * slope_val[0, 0]), guess[1] - (minima * slope_val[1, 0])]
print guess
#check condition and proceed
if math.fabs(prev[0] - guess[0]) > e or math.fabs(prev[1] - guess[1]) > e:
gradient(y, slope, guess, e)
return xiter, yiter
