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(kill(all), 'done);
'done$
(load("lbfgs"), float_approx_equal_tolerance : 1e-12, 'done);
'done$
block([n, FOM], local(t1, t2),
t1[j] := 1 - u[j],
t2[j] := 10*(u[j + 1] - u[j]^2),
n : 8,
FOM : sum (t1[2*j - 1]^2 + t2[2*j - 1]^2, j, 1, n/2),
lbfgs (FOM, '[u[1],u[2],u[3],u[4],u[5],u[6],u[7],u[8]],
[-1.2, 1, -1.2, 1, -1.2, 1, -1.2, 1], 1e-3, [1, 0]));
[u[1] = 1.000005339816132,u[2] = 1.000009942840108,u[3] = 1.000005339816132,
u[4] = 1.000009942840108,u[5] = 1.000005339816132,u[6] = 1.000009942840108,
u[7] = 1.000005339816132,u[8] = 1.000009942840108]$
block([FOM, X, Y], local(F),
FOM : '((1/length(X))*sum((F(X[i]) - Y[i])^2, i, 1,
length(X))),
X : [1, 2, 3, 4, 5],
Y : [0, 0.5, 1, 1.25, 1.5],
F(x) := A/(1 + exp(-B*(x - C))),
lbfgs (FOM, '[A, B, C], [1, 1, 1], 1e-4, [1, 0]));
[A = 1.461933911464101, B = 1.601593973254801,
C = 2.528933072164855]$
block(local(F_grad, F), F(a, b, c) := (a - 5)^2 + (b - 3)^4 + (c - 2)^6,
define(F_grad(a, b, c),
map (lambda ([x], diff (F(a, b, c), x)), [a, b, c])),
lbfgs ([F, F_grad],
[a, b, c], [0, 0, 0], 1e-4, [1, 0]));
[a = 5.000086823042934, b = 3.052395429705181,
c = 1.927980629919583]$
/* fails
x: 42;
lbfgs ('x^2, ['x], [1], 1e-4, [-1, -1]);
*/
/* should return last approximation if max function evaluations reached */
block ([lbfgs_nfeval_max:10], lbfgs (x^6 + y^6, [x, y], [1, 1], 1e-12, [1, 0]));
[x = 0.1082428019264297, y = 0.1082428019264297];
(reset(float_approx_equal_tolerance),0);
0
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