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| Syntax |
conjgrad(function fval, xin, scale, eps, maxit, level) |
| See Also | conjdir , minline , sqp , nlsq |
f(x) with respect to x.
The real or double-precision column vector xini specifies the
initial estimate for the value that minimizes the objective f.
The column vector scale has the same type and dimension as
x.
The i-th element of scale specifies the maximum
absolute change for the i-th element of x between iterations.
Every element of scale must be greater than 0.
The scalar eps has the same type as xini and
specifies the convergence criteria.
Convergence is accepted when the absolute change in x(i)
is less than eps times scale(i) for all i.
The integer scalar maxit specifies the maximum number of
iterations to attempt before giving up on convergence.
The integer scalar level specifies the amount of tracing.
If level > 1,
the current value of f(x) is printed at each iteration.
If level > 2,
the current argument value x and the gradient g
are printed at each iteration.
If level > 3, the step size and the
function value are printed at each iteration of the line search.
x at the i-th iteration.
(The first column contains the initial value xin.)
The return value has same type and row dimension as xini.
Its column dimension is equal to the number of iterations plus 1.
(x, fout)
fval(x, fout, gout)
Computes the value of the objective and its gradient at the point
specified by x, where x is a column vector with the
same type and dimension as xini.
The input value of fout has no effect.
On output, fout is equal to f(x).
If the gout argument is present,
its input value has no effect and its output value is the gradient of
f(x) evaluated at the point x and has the same
type and dimension as x.
The i-th element of gout is the derivative of
f(x) with respect to the i-th element of x.
2 2
minimize (x - 1) + (x - 2) with respect to x
1 1
x = {1, 2}
clear
#
function fval(x, fout, gout) begin
fout = (x(1) - 1.)^2. + (x(2) - 2.)^2
if arg(0) == 3 then begin
f_x1 = 2. * (x(1) - 1.)
f_x2 = 2. * (x(2) - 2.)
gout = {f_x1, f_x2}
end
return
end
xini = {0., 0.}
scale = {3., 3.}
eps = 1e-4
maxit = 20
level = 0
x = conjgrad(function fval, xini, scale, eps, maxit, level)
xout = x.col(coldim(x))
print xout